HIGH-DENSITY CIRCUMSTELLAR INTERACTION IN THE LUMINOUS TYPE IIn SN 2010jl: THE FIRST 1100 DAYS

Most of the optical imaging was obtained with the 1.2 m telescope at the F. L. Whipple Observatory (FLWO) using the KeplerCam instrument. KeplerCam data were reduced using the IRAF and IDL procedures described in Hicken et al. (2007). A few additional late-time epochs were obtained with the 6.5 m Baade telescope at the Magellan Observatory using the IMACS instrument and the 2.5 m Nordic Optical Telescope (NOT) using the ALFOSC instrument. These were reduced with IRAF using standard methods. High-quality NOT imaging was used to construct B-, V-, r-, and i-band templates by point-spread function (PSF) subtraction of the SN using the IRAF DAOPHOT package. These templates were then subtracted from the FLWO, Magellan Observatory, and NOT imaging using the HOTPANTS package. Template subtraction is necessary to obtain accurate photometry after ∼100 days because the SN is located close to the center of the galaxy.

The optical photometry was calibrated to the Johnson–Cousins (JC) and Sloan Digital Sky Survey (SDSS) standard systems using local reference stars in the SN field, in turn calibrated using standard field observations on five photometric nights. Because the SN spectral energy distribution (SED), in particular at late phases, is line dominated, we have applied the technique of S corrections (Stritzinger et al. 2002) to transform from the natural system of each instrument to the standard systems. This was done for all bands except the u band. Color terms and filter response functions were adopted from Hicken et al. (2012) for the FLWO and from Ergon et al. (2014) for the NOT. Filter response functions for the JC and SDSS standard systems were adopted from Bessell & Murphy (2012) and Doi et al. (2010).

Most of the near-infrared (NIR) imaging was obtained with the 1.3 m Peters Automated Infrared Imaging Telescope (PAIRITEL) at the FLWO. The data were processed into mosaics using the PAIRITEL Mosaic Pipeline version 3.6 implemented in Python. Details of PAIRITEL observations and reduction of SN data can be found in Friedman et al. (2014). Two additional late-time epochs were obtained with NOT using the NOTCAM instrument. This high-quality imaging was used to construct J-, H-, and K-band templates by PSF subtraction of the SN using the IRAF DAOPHOT package. These templates were then subtracted from the PAIRITEL imaging using the HOTPANTS package. As in the optical, template subtraction is necessary to obtain accurate photometry after ∼100 days and is particularly important for the late J-band photometry.

The NIR photometry was calibrated to the Two Micron All Sky Survey (2MASS) standard system using reference stars from the 2MASS Point Source catalog (Skrutskie et al. 2006) within the SN field. Because the PAIRITEL was one of the two telescopes used for the 2MASS survey, the natural system photometry is already on the 2MASS standard system, and no transformation is needed. The NOT photometry was transformed to the 2MASS standard system using linear color terms from Ergon et al. (2014). The absence of strong lines in the X-shooter NIR spectrum indicates that this is sufficient and that S corrections are not needed.

As a check we can compare with the J, H, and K_s magnitudes from Andrews et al. (2011) at 104 days. Our J and H magnitudes agree within ∼0.1 mag with those of Andrews et al. However, our K_s magnitude close to this epoch is ∼12.7, while that of Andrews et al. is ∼13.75. Judging from the SED plot in Andrews et al., it, however, seems that there is a typographical error and that the magnitude should be 12.75 ± 0.1. In this case there is excellent agreement.

In Tables 1 and 2 we give the photometry for all epochs, including errors.

2.2.1. HST-COS and STIS Observations and Data Reduction

2.2.2. Optical Spectroscopy

From Schlegel et al. (1998), Smith et al. (2011a) estimate a Milky Way reddening corresponding to E_(B-V) = 0.027 mag. Based on the weak Na i lines, Smith et al. (2011a) assume negligible reddening from the host galaxy. From the damping wings of the Lyα absorption in our COS spectra, we can make an independent estimate of this for both the host and for the Milky Way.

We discuss the COS spectrum in detail later. Here we use the damping wings of the Lyα absorption to derive a value for the column density, N_H (e.g., Draine 2011, Chapter 9.4). The Milky Way absorption is affected by the Si iii λ1206.5 absorption on the red side, so we use the blue side for the fit. For the host galaxy we instead use the red side to avoid the slight overlap with the Milky Way absorption. From fits of these, shown in Figure 1, we derive a value of N_H = (1.05 ± 0.3) × 10²⁰ cm⁻² for b = 10 km s⁻¹ for the host galaxy, and the corresponding value is N(H i)_MW = 1.75(± 0.25) × 10²⁰ cm⁻² from the Milky Way. There is some uncertainty on the Milky Way column density because the Si iii 1206.5 Å absorption line from the host galaxy falls on the red edge of the Milky Way Lyα profile.

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Using the N_HI versus E_(B-V) relation in Bohlin et al. (1978), and assuming the same $N({\rm H_2})/N({\rm H\,\scriptsize{I}})$ ratio for the host galaxy of 2010jl as in the Milky Way, we find E_(B-V) = 0.036 mag for the Milky Way and E_(B-V) = 0.022 mag for the host galaxy. The value for the Milky Way agrees well with that derived from the far-IR (FIR) emission, but we also note that there is a nonnegligible absorption from the host galaxy. For the remainder of the paper, where needed, we will adopt a value of E_(B-V) = 0.058 mag for the total reddening.

Figure 2 shows the light curve from our photometry, complemented with early measurements from Stoll et al. (2011). The B, V, and i' bands all show nearly the same slow decline by ∼0.8 mag/100 days during the first ∼175 days. After this the light curves become almost constant up to ∼240 days. However, the r' band already shows signs of flattening at age 100 days. We discuss this band, dominated by Hα, in more detail in Section 3.4. Being most sensitive to the decreasing temperature, the u' band shows the steepest decline.

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After the first gap produced by conjunction with the Sun, all optical bands show a considerably faster decline at ≳ 300 days. In the period 400–850 days, the decline in the optical bands is roughly linear. The decline rate is 8.0 × 10⁻³ mag day⁻¹ in i', 4.9 × 10⁻³ mag day⁻¹ in r', 8.0 × 10⁻³ mag day⁻¹ in V, and 7.1 × 10⁻³ mag day⁻¹ in B. We attribute the slow r-band decline to emission in Hα: as seen in the spectra, Hα is stronger with respect to the continuum as time goes by (Section 3.3).

Compared to the R-band photometry of Ofek et al. (2014), we agree within less than 0.1 mag over the whole period. Up to day 200 our optical photometry also agrees within ∼0.1–0.2 mag in the r', B, and V bands with the light curves by Zhang et al. (2012), in spite of the difference in filter profiles between our r' band and their R band. This is probably because the r' and R bands are both dominated by Hα. Our i' magnitudes are ∼0.5 mag fainter than the I magnitudes by Zhang et al. and ∼0.3 mag fainter in u' compared to their U band. Most likely this difference can be explained by the different filter responses between the SDSS i' and u' bands and the standard I and U bands.

At epochs later than 350 days, our magnitudes are 0.5–1.5 mag fainter in all bands, a difference that increases with time. The origin of this is not clear, but we note that Zhang et al. do not give any errors in their table of the photometry for these epochs. Also, our photometry showed a similar flattening of the light curve until we subtracted the background from the host galaxy.

The NIR light curves show a similar decline to the optical up to ∼200 days. After this, the light curves flatten considerably in J and H, and the K band shows an increase compared to the flux at earlier times. The difference between the NIR and the optical behavior is real and has important consequences for our physical picture for SN 2010jl. As we discuss in Section 4.2, we interpret this emission as coming from dust in the CSM of the progenitor.

The pseudobolometric light curve for the flux in the wavelength range 3500–25,000 Å was calculated using the method described in Ergon et al. (2014). In the optical region where we have a well-sampled spectral sequence, we made use of both photometry and spectroscopy to accurately calculate the bolometric luminosity, whereas in the NIR region we used photometry to interpolate the shape of the SED. The SED has then been dereddened using E_(B-V) = 0.036 mag for the Milky Way and E_(B-V) = 0.022 mag for the host galaxy, as derived in Section 3.1. For the Milky Way reddening, we use the extinction law by Cardelli et al. (1989), and being a star-forming galaxy with Wolf–Rayet (WR) features (Shirazi & Brinchmann 2012), we use the starburst extinction from Calzetti et al. (1994) for the host galaxy.

As is clear from Figure 2, the contribution from the NIR bands becomes increasingly important. The luminosity in the NIR region (9000–24,000 Å) is shown in Figure 3 as red points, whereas the total (3500–25,000 Å) luminosity is shown as black points. While the optical bolometric contribution starts to drop at ∼350 days, the NIR part has a long plateau from 200 to ∼450 days. At age 100 days, the IR represents 33% of the flux, equaling the optical output at day 400; by age 500 days, it is 73%, and by day 770, 85%. This era is dominated by a dust contribution (Section 4.2) and reflects both the instantaneous energy output and a contribution from a light echo. In Section 4.2, we show that the SN itself dominates the NIR at early epochs, but later the NIR comes from an echo.

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The pseudobolometric light curve in Figure 3 only includes the optical and NIR bands and ignores both the UV and mid-IR. Especially at the early phases, the comparatively hot spectrum has a large UV contribution. We will discuss the spectra in more detail later; here we only estimate this contribution from an integration of the flux from COS and STIS for days 44, 107, and 573. We do not include the COS spectrum for day 621 because this is severely contaminated by the host galaxy.

On day 44 we find a luminosity in the 1100–3600 Å range equal to 7.2 × 10⁴² erg s⁻¹, and for day 107 it is 3.4 × 10⁴² erg s⁻¹. For day 573 we find a luminosity of 4.5 × 10⁴¹ erg s⁻¹ in the STIS 1700–3600 Å range. We estimate the uncertainty in these fluxes as ∼25%. There is therefore a substantial UV contribution to the bolometric luminosity, especially at late epochs, up to ∼50% of the optical luminosity at the last epoch. There may also be a substantial EUV and X-ray luminosity that is not included in our observations.

Up to day ∼200, our total bolometric luminosity agrees with that of Zhang et al. (2012). Zhang et al. have, however, no NIR (or UV) observations. These account for an increasing fraction of the luminosity as the event ages, so their luminosities are increasingly incomplete. In addition, the background contribution from the host is very important after day ∼350, as was discussed above. At early epochs there is some discrepancy between our bolometric luminosities and those of Zhang et al. It is not clear what produces this difference: it may be due to Zhang et al. using photometry alone, while we use a combination of photometry and spectroscopy to combine the bands.

Assuming that the luminosity is the same as at our first determinations at day 27 (see below), we find a total integrated energy from day 0 to day 920 in the 3600–9000 Å range of 3.3 × 10⁵⁰ erg and in the 9000–24, 000 Å range of 2.6 × 10⁵⁰ erg. The total in the 3600–24, 000 Å range is therefore 5.8 × 10⁵⁰ erg. The correct way to use the IR measurements depends on the interpretation (Section 4.2) and on the relative contributions between the photosphere emission and dust: NIR light from an echo reflects the optical–UV output, while NIR light from shock-heated dust should be added to the energy budget.

To disentangle the dust and direct photospheric luminosity from the SN, we have made fits to the SED from the photometry for most epochs. We have here included the Spitzer 3.6 and 4.5 μm fluxes from Andrews et al. (2011) at day 87 (JD 2,455,565) and from Fox et al. (2013) for day 254 (JD 2,455,733), as well as unpublished Spitzer observations from the Spitzer archive from days 465, 621, and 844. For these epochs we find fluxes of 8.55, 8.63, and 7.73 mJy at 3.6 μm and 8.30, 8.66, and 8.24 mJy at 4.5 μm.

In Figure 4 we show the SEDs for these dates, as well as for one epoch (750 days) where we only have optical and NIR data. These SEDs are modeled with two blackbodies with different temperatures, and we minimize the chi square with the photospheric effective temperature and radius T_eff and R_phot and the corresponding parameters for the dust shell, T_dust and R_dust, as free parameters. We further discuss the motivation for this choice of spectrum in Section 4.2. In these fits we exclude the r band because it is dominated by the Hα line. For the Spitzer photometry at days 254, 621, and 844, where no other photometry exists, we interpolate the Spitzer fluxes and the NIR and optical photometry to days 238, 586, and 865, respectively. Given the slow evolution of the Spitzer fluxes at these epochs, this should only introduce a minor error.

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From these models we find that up to day ∼400 the photospheric contribution also dominates the NIR, and at later stages the dust component takes over. The best-fit parameters for these models are given in Table 5 for the different dates, and in Figure 5 we show the blackbody temperature, radius, and total luminosity of the dust and photospheric components from these fits, together with the standard deviations. The large errors in T_dust and R_dust at the first two epochs are a result of the dominance of the photospheric component also for the NIR, and the errors in T_eff are mainly a result of the relatively few bands (mainly B, V, and I) where there is a large contribution from this component.

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At epochs earlier than ∼400 days, the dust temperature is constant within errors at ∼1850 ± 200 K and then slowly decays to ∼1400 K at 850 days. The blackbody radius is ∼(1–2) × 10¹⁶ cm for the first ∼300 days and then slowly increases to ∼3 × 10¹⁶ cm at the last observation. The dust luminosities we obtain for the first epochs are lower than the NIR luminosities in Figure 3. The reason for this, as can be seen in Figure 4, is that the photospheric contribution dominates the J, H, and K bands for these epochs. At epochs later than the day 465 observation, the opposite is true, which is a result of including the total dust emission from the blackbody fit and not only the NIR bands.

Already at ∼90 days, Andrews et al. (2011) found from NIR and Spitzer observations an IR excess due to warm dust, but with a lower temperature of ∼750 K than we find. Andrews et al., however, only include the Spitzer fluxes to the dust component, while we also include the J, H, and K bands in this component, which explains our higher dust temperatures. We note that Andrews et al. (2011) underestimate the K-band flux in their SED fit.

Using the SED fitting, we can improve on the bolometric light curve by separating the SN and dust contributions of the IR flux to the bolometric luminosity and add this to the BVri contribution in Figure 3. Based on the UV flux at the epochs with HST observations, we multiply this by a factor of 1.25 (Section 3.2). In this way we arrive at the bolometric light curve from the SN ejecta alone in Figure 6, now shown in a log–log plot. From this we see that the bolometric light curve from the ejecta can be accurately characterized by a power-law decay from ∼20 to 320 days, given by L(t) ∼ 1.75 × 10⁴³(t/100 days)^−0.536 erg s⁻¹ and a final steep decay L(t) = 8.71 × 10⁴²(t/320 days)^−3.39 erg s⁻¹ after day 320.

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Ofek et al. (2014) estimate the bolometric light curve by assuming a constant bolometric correction of −0.27 mag to the R-band photometry. With this assumption, they find a flatter light curve with L(t)∝t^−0.36 for the same explosion date as we use here. The reason for this difference is that the R-band decays slower than most of the other bands, as can be seen from Figure 2. The bolometric light curve will therefore be steeper than the R-band light curve.

The slope depends on the assumed shock breakout date. Ofek et al. (2014) discuss this based on the light curve and find a likely range of 15–25 days before I-band maximum, corresponding to JD 2,455,4692,455,479. Using 2,455,469 instead of our 2,455,479 would change the best-fit luminosity decline to L(t) ∼ 1.9 × 10⁴³(t/100 days)^−0.61 erg s⁻¹.

To estimate the total energy output from the SN, we assume that the bolometric luminosity before our first epoch at 26 days was constant at the level at 26 days, which is supported by the early observations by Stoll et al. (2011), shown in Figure 2. The total energy from the SN (excluding the echo) is then 6.5 × 10⁵⁰ erg. In addition, there is a contribution from the EUV as well as X-rays and mid-IR (Section 4.7). Even ignoring these, we note that the total radiated energy is a large fraction of the energy of a "normal" core-collapse SN (see Section 4.7).

Figures 7 and 8 show the SN 2010jl spectral sequence for days 29–847 obtained with FAST at FLWO and with grism 16 at NOT, respectively. The former have the advantage of showing the full spectral interval between 3500 and 7200 Å, and the NOT spectra below 5100 Å have a higher dispersion, showing the narrow line profiles better.

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From our first optical spectra at 29 days to the last at 848 days, we see surprisingly little change in the lines present (Figure 7). The main difference is that the continuum is getting substantially redder with time. This is also apparent from the steep light curve of the u' band in Figure 2. At the same time, the Balmer discontinuity at 3640 Å becomes weaker.

The most conspicuous features of the spectra are the strong, symmetric Balmer emission lines, from Hα up to Hδ. To the blue of Hδ, the broad emission lines blend into a continuum. In addition to these blended broad emissions in Figure 8, each Balmer line up to at least H16 shows a narrow blueshifted P-Cygni absorption. In addition to the Balmer lines and several He i lines, some of which show prominent P-Cygni profiles (Section 3.4.2), we also see narrow emission lines from [Ne iii] λ3868, [O iii] λλ4363, 4959, 5007, several [Fe iii] lines, as well as He ii λ4686 (for more details see Section 3.4.2). Our high-resolution X-shooter spectrum reveals an additional large number of weaker narrow lines (Section 3.4.3).

Figure 9 shows the far-UV spectrum with COS from days 44, 107, and 621, and Figure 10 shows the STIS spectra from days 34, 44, 107, and 573. Again, we see a number of prominent, broad lines with strong, narrow emission components but also in many cases P-Cygni absorptions. The main difference from the optical is that in the UV we find mainly lines of highly ionized elements, like C iii–iv, N iii–v, O iii–iv, and Si iii–iv, although there are also neutral and low-ionization lines of C ii, O i, and Mg ii. A comparison of the STIS spectra reveals little evolution of the spectrum between the first two epochs. The COS spectra show a similar slow evolution. At the time of the third epoch, the continuum has faded by a factor of ∼2, while the narrow lines have decreased by a modest amount.

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In addition to the lines from the SN, the spectrum also shows a number of interstellar absorption lines from the Milky Way and the host galaxy, shown in the lower part of Figure 9. In wavelength order we identify these as Si ii λλ1190.4, 1193.3, 1194.5, 1197.4, N i λλ1199.6, 1200.2, Si iii λ1206.5, N v λλ1238.8, 1242.8, Si ii λλ1260.4, 1264.7, O i λλ1302.2, 1304.9, 1306.0, C ii λλ1334.5, 1335.7, Si iv λλ1393.8, 1402.8, Si ii λλ1526.7, 1533.4, C iv λλ 1548.2, 1550.8, Fe ii λ1608.5, and Al ii λ1670.8. The lower signal-to-noise (S/N) and spectral resolution of the STIS spectra make interstellar medium (ISM) line identifications more difficult. We do, however, detect a number of strong lines: Fe ii λλ2344.2, 2374.5, 2382.8, 2586.6, 2600.2, 2607.9, Mg ii λλ2796.4, and 2803.5. All of these lines are commonly seen in different directions of the Milky Way as well as in different galaxies.

To show the relative contributions from the UV and optical ranges, we show in Figure 11 the complete UVoptical spectrum at two epochs, one early and one very late. For the first epoch, this is a combination of the COS and STIS spectra from day 44 and an interpolation of the FAST spectra from day 32 and day 58 to this date. For the late spectrum, we exclude the COS spectrum because of the strong contamination of the continuum by the host galaxy by the large COS aperture. The emission lines in this spectrum are well defined and, with a few exceptions, free from contamination.

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From Figure 11 we note the increasing importance of the UV at late phases, as was also concluded from Figure 3. This is similar to other Type IIn SNe, like SN 1995N (Fransson et al. 2002) and SN 1998S (Fransson et al. 2005), but is in contrast to Type IIP and Ibc SNe, which rapidly become faint in the UV. We also see a clear change in the character of the spectrum, from one dominated by a continuum at early epochs to one dominated by line emission at the last epochs.

The medium-resolution optical spectra in Figure 8, as well as the high S/N COS spectrum in Figure 9, clearly show that there are two distinct velocity components in the strongest emission lines. This is apparent for the H i and Mg ii lines but also for high-ionization UV lines like C iv, N iii–v, O iii–iv, Si iv, and N v. The broad components extend to ∼2400–10, 000 km s⁻¹, and the narrow components have an order of magnitude lower velocities. The maximum velocity to where the broad component can be traced depends mainly on the flux of the line and the S/N of the spectra. For both of these reasons, the Hα line displays the most extended wings. We now discuss the properties of these components in more detail.

3.4.1. The Broad Component

In Figure 12 we show the SN 2010jl spectral sequence of the Hα line from day 31 to day 1128. The broad lines display a smooth, peaked profile, characteristic of electron scattering (Münch 1948; Auer & van Blerkom 1972; Hillier 1991; Chugai 2001). At early times the lines are symmetric between the red and blue wings, and after ∼50 days they display a pronounced bump to the blue. As we discuss in detail in Section 4.3, we interpret this as a result of a macroscopic velocity. We discuss (and reject) the alternative, in which dust absorption determines the line shape, in Section 4.3.

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To calculate the flux of Hα, Hβ, and Hγ, we determine the continuum level on either side of the line between −15, 000 and −12, 000 km s⁻¹ and between 12, 000 and 15, 000 km s⁻¹. A continuum level is then determined as a linear interpolation between these velocities and subtracted from the total flux. Figure 12 shows that this should be an accurate estimate.

In Figure 13, we show the Hα luminosity together with the Hα/Hβ and Hβ/Hγ ratios. The dashed lines give polynomial least-squares fits to the data. In addition, we show the continuum flux in the same velocity interval, ±10, 000 km s⁻¹, as the lines. From the figure we see that Hα increases by a factor of ∼2.5 from day 29 to day 175. After the first observational gap between ∼200 days and ∼400 days, the flux has dropped somewhat, and it then drops by another factor of ∼10 from 400 to 850 days. From the polynomial fit it is likely that the maximum Hα luminosity occurred at ∼260 days when the SN was close to the Sun. The bell-shaped light curve of the Hα luminosity is in contrast to the continuum light curve in the same velocity region, shown as black dots, which decreases monotonically, and by a factor of ∼100 from the first observations up to 800 days. The total luminosity (continuum plus Hα) remains nearly constant up to ∼400 days, after which it too drops. The increasing flux in Hα during the first ∼300 days explains the flatter light curve of the r' band shown in Figure 2.

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For the first ∼500 days our Hα luminosity agrees well with the total luminosity from the "narrow" and "intermediate"components of Zhang et al. (2012). Their terminology is different from that used in this paper. Their "narrow" and "intermediate"components are both part of our "broad," and their data do not resolve what we refer to as the "narrow"component. Our light curve, however, covers approximately one more year, showing a continued decay of Hα.

The Hα/Hβ flux ratio increases steadily from ∼3.6 initially to 10–15 at ∼800 days. The Hβ/Hγ ratio similarly increases from ∼3.4 initially to ∼5.0 at ∼400 days, after which it decreases to ∼2.8 at 800 days (Figure 13). For Balmer lines higher than Hδ, the broad components blend together into a quasi-continuum, and the Balmer decrement for these is therefore difficult to determine.

The Lyα line, shown in Figure 14, is severely distorted by interstellar absorption lines both from the host galaxy and from the Milky Way. The broad Lyα absorption from the host galaxy makes it impossible to determine if any narrow emission is present. The red side of the broad component is relatively unaffected by absorptions and extends to ∼2460 km s⁻¹. The blue side reaches into the damping profile of the host-galaxy absorption. However, a lower limit of ∼2300 km s⁻¹ to the blue extent of the line can be determined. As is shown by the comparison with the Hβ line from the same-epoch STIS spectrum, the two lines have similar profiles in the velocity ranges where Lyα is unaffected by absorptions. The lower flux of the Lyα line between −2000 km s⁻¹ and −1000 km s⁻¹ compared to the Hα and Hβ lines is caused by the overlapping ISM absorptions, as is the Si iii λ1206.5 line (Section 3.1). A similar reasoning applies to the other epochs, although we also observe a change in the ratio of the blue and red segments of the line from the first two epochs to the last. This is caused by the blueshift of the line, so more of the red side is absorbed by the host galaxy, and the blue region is increasing for the same reason.

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In Section 3.1 we found that the damping wings of the Lyα absorption imply a value of N_H ∼ (1.05 ± 0.3) × 10²⁰ cm⁻² for b = 10 km s⁻¹ from the host galaxy. This means that the large column density derived from the Chandra observations, ∼10²⁴ cm⁻² (Chandra et al. 2012b), must be intrinsic to the SN itself or its CSM.

The ratios between the Lyα, Hβ, and Hα lines are useful as indicators of the conditions in the broad-line region of active galactic nuclei (AGNs; e.g., Krolik & McKee 1978; Fraser et al. 2013). Because of the broad absorptions, the total flux of the Lyα line cannot be directly determined. Instead we estimate the line ratio of this line to Hα and Hβ by first subtracting the continuum and then scaling the line profiles so that these fit each other as well as possible for the parts of the lines unaffected by interstellar absorptions (see Figure 14). The scaling factor then gives the line ratio.

Including reddening with E_B-V = 0.058 (Section 3.1), we find for the first COS observation at day 44 F(Lyα)/F(Hβ) = 1.1 and F(Hα)/F(Hβ) = 2.8, for day 107 F(Lyα)/F(Hβ) = 0.53 and F(Hα)/F(Hβ) = 4.1, and for day 620 F(Lyα)/F(Hβ) = 2.5 and F(Hα)/F(Hβ) = 9.0. Because of the difficulty in the calibration of the COS spectra relative to the optical spectra, the uncertainty in the Lyα/Hβ ratio is large. We have plotted the Lyα/Hβ ratio in Figure 13 as black dots.

Although the uncertainties in the Lyα flux are large, we see from these ratios that the broad-line region has a Balmer decrement and a Lyα/Hα ratio very different from the recombination values. This is similar to what is found in the dense broad-line regions in AGNs, and it indicates a combination of high optical depths in the lines and high densities. Models show that column densities of ≳ 10²⁴ cm⁻² in combination with high densities, ≳ 5 × 10⁸ cm⁻³, are needed to get these ratios (Krolik & McKee 1978; Kwan 1984; Fraser et al. 2013). A flat X-ray spectrum also lowers the Lyα/Hα ratio and increases the Hα/Hβ ratio (Kwan 1986). There is, however, a substantial degeneracy between the density, column density, and X-ray flux. In Section 4.7 we discuss this further based on real models.

Besides the H i lines, N v λλ1238.8, 1242.8, O i λλ1302.2–1306.0, O iv] λλ1397.2–1407.3 + Si iv λλ1393.8, 1402.8, N iv] λ1486.5, and C iv λλ1548.2–1550.8 also have broad components. This is probably also the case for He ii λ1640.5, O iii] λλ1660.8–1666.2, N iii] λλ1746.8–1754.0, and Si iii] λ1892.0/C iii] λ1908.7, although the flux of the broad component is comparable to the S/N for these lines.

In Figure 15, we compare the broad components from the strong C iv and N iv] lines with the profile of Hβ. Although the S/N in the COS observation is lower, we see that the profiles are basically identical, as expected for electron scattering from lines originating at similar depths.

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Figure 16 shows the evolution of the most important broad UV lines from the COS and STIS observations. The scattering wings of both the N iv] and C iv lines get fainter between the first two observations at 44 and 107 days, opposite to the evolution of the Hα line. At 621 days the wings of the high-ionization lines have completely disappeared, in contrast to the Lyα, O i λλ1302.2–1306.0, and Mg ii lines, which all still have strong wings in the last HST observations. The evolution of the latter lines agrees more with Hα.

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3.4.2. The Narrow Component

As noted by Smith et al. (2011a), many of the optical lines display a narrow component, in most cases with a P-Cygni profile, as shown in Figure 8. In Figure 17 we show the narrow Hα line on a larger velocity scale from NOT/Grism17, TRES, X-shooter, and MDM spectra. The peak of the line is close to zero velocity, and the red wing reaches ∼150 km s⁻¹, as marked by the vertical lines. The blue wing is more complex, consisting of both an absorption reaching ∼−105 km s⁻¹ and a high-velocity emission reaching ∼−250 km s⁻¹. These velocities do not change appreciably with time, although the emission components get weaker.

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The emission wing on the blue side of the P-Cygni absorption is likely to be caused by electron scattering in the CSM of the SN. Examples of this are known for WR stars, where Hillier (1991, see his Figure 8) calculated the P-Cygni profile, including electron scattering in the line-forming zone, and obtained a line profile similar to that seen for Hα. The expansion velocity of the CSM should therefore be ∼−105 km s⁻¹, rather than the higher velocity characteristic of the blue wing. This also shows that the electron scattering optical depth is not negligible in the CSM of the SN.

In Figure 18 we show the net flux of the narrow Hα line from our highest dispersion spectra. For the narrow component we have interpolated the broad line flux on each side of the line (−250 km s⁻¹ and 200 km s⁻¹, respectively) and then calculated the net emission above this level. In the day 461 spectrum, the P-Cygni absorption is stronger than the emission, and the luminosity of the line is consequently negative.

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The main change with time of the narrow component is a decrease of the flux (and equivalent width) of the line, from a net emission line to a line with zero or even negative equivalent width. When we compare the broad and narrow emission we see that they evolve independently from each other. The narrow component is in fact more correlated to the continuum luminosity than to the broad Hα.

Of the He i lines the following lines are detected: λ3889 (blended with H 8-2), λ3965 (P-Cygni), λ4471 (P-Cygni), λ4713 (only emission), λ4922 (probable), λ5016 (P-Cygni), λ5876 (P-Cygni), λ6678 (P-Cygni), and λ7065 (pure emission). Although some of these are seen in H ii regions, the fact that P-Cygni profiles are observed for most of them shows that they originate in the SN environment. Additional He i lines are present in the NIR (Section 3.4.3).

Figure 19 shows a sample of the most important other narrow emission lines in the UV and optical ranges on a velocity scale for the day 44 and day 621 spectra. When comparing the line profiles of these lines, one has to take into account the absorption of the UV resonance lines from the host galaxy at redshift 3207  km s⁻¹ and the Milky Way. An important case is the C iv λλ1548.2, 1550.8 doublet. The velocity separation of the λ1550.8 component relative to the λ1548.2 component corresponds to 500  km s⁻¹. The absorption from the Milky Way does not interfere with the λ1548.2 line below 2700  km s⁻¹. Absorption from the host may, however, be important. Typical rotational velocities are 100–200 km s⁻¹, and this may well interfere with both the absorption and emission components, making a determination of the expansion velocity difficult for these lines.

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When we compare the different lines in Figure 19, we see that the absorptions of the O i λ1302.2, Si iv λ1393.8, and the C iv λ1548.2 lines all are considerably wider than the intercombination lines. The strong N iv] λ1486.5 line has a FWHM of ∼50 km s⁻¹ and extends to ∼100 km s⁻¹ to the red side and ∼80 km s⁻¹ to the blue. These velocities are similar to the red emission component of the C iv lines but are considerably less than the C iv absorption. Similar widths are found for the O iii] λ1666.2 and He ii λ1640.4 lines, although the S/N is lower for these lines. In contrast, the velocity of the blue edge of the C iv λ1548.2 absorption corresponds to ∼−280 km s⁻¹. The extent of the strong emission component to the red is, however, only ∼100 km s⁻¹, although it is difficult to determine this accurately.

The higher velocity of the absorption of the C iv λλ1548.2, 1550.8 lines probably originates in the host-galaxy ISM or possibly in higher velocity CSM gas of low density whose emission is too faint to be seen. This is also consistent with the other resonance lines. For the O i λ1302.2 line one can even distinguish a separation between the P-Cygni absorption at ∼100 km s⁻¹ and the higher absorption component.

When we compare the line profiles of the day 44 and day 621 spectra, we do not see any clear evolution in velocity widths. The velocities of the high-ionization narrow UV lines are similar to the optical lines, i.e., ∼100 km s⁻¹.

The fact that the Balmer and the He i lines have P-Cygni absorptions shows that the population of these excited levels is high even at ∼600 days. This in turn argues for a high density, ≳ 10⁸ cm⁻³, in the line-forming region (Section 4.7). In Section 3.5 we discuss other independent density determinations that indicate high-density circumstellar gas.

Tables 6 and 7 give fluxes of the identified narrow UV lines from the STIS and COS spectra. To measure the fluxes of the different lines, we first determine the continuum level on both sides of the line and fit this to a polynomial, which is subtracted from the total flux in the line. This introduces uncertainties in both the continuum level and the extent of the line, which is most serious for the lower resolution STIS spectrum, which also has a lower S/N. In addition, the low spectral resolution of STIS also has the consequence that multiplets, like N iii] λλ1746.8–1754.0, are not resolved. To complicate things further, several lines, like the N iii], Si iii], and C iii] lines, sit on top of broad electron-scattering profiles (see below). The higher spectral resolution COS spectra are less sensitive to these effects. Unfortunately, this setting of COS does not cover the C iii] lines.

Table 6. STIS Line Catalog

		Line Flux
Species	λvac	(10−14 erg cm−2 s−1)				Notes
	(Å)	day 34	day 44	day 107	day 573
O iii]	1660.81–1666.15	2.8:	2.4:	...		At wavelength limit
N iii]	1746.82–1754.00	18.4 ± 2.0	13.5 ± 2.0	5.88 ± 0.8	0.60 ± 0.10
Si iii]	1882.71–1896.64	8.80 ± 0.6	9.12 ± 1.5	7.64 ± 0.5	0.51 ± 0.15
C iii]	1906.68–1909.60	8.50 ± 1.2	8.40 ± 1.2	5.20 ± 1.0	0.56 ± 0.15
N ii]	2139.68–2143.45	4.37 ± 0.1	5.01 ± 0.2	3.36 ± 0.2	0.45 ± 0.10
C ii]	2324.21–2328.83	2.46 ± 0.3	2.75 ± 0.2	2.12 ± 0.2	0.37 ± 0.10
Mg ii	2796.34–2803.52	14.5 ± 0.5	25.6 ± 1.0	38.4 ± 2.0	12.8 ± 2.00	Broad component
[Ne iii]	3869.85	1.44 ± 0.1	1.37 ± 0.2	0.77 ± 0.3	...
H i	4102.89	7.73 ± 0.3	6.72 ± 3.0	5.43 ± 1.8	0.57 ± 0.20	Broad component
H i	4341.68	18.6 ± 0.9	16.2 ± 2.5	19.1 ± 1.5	2.39 ± 0.30	Broad component
[O iii]	4364.45	0.85 ± 0.2	0.56 ± 0.3	0.50 ± 0.15	0.12 ± 0.03
He ii	4687.02	1.45 ± 0.2	0.57 ± 0.3	−	...	Marginal detection
H i	4862.68	46.9 ± 8.0	46.5 ± 7.0	58.7 ± 3.0	9.03 ± 0.50	Broad component
[O iii]	5008.24	0.79 ± 0.2	0.70 ± 0.3	0.30 ± 0.15	0.23 ± 0.10

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Table 7. SN2010jl COS Line Catalog

		Line Flux
Species	λvac	(10−15 erg cm−2 s−1)			Notes
	(Å)	day 44	day 107	day 620
N v	1238.82	−0.76 ± 0.3	−0.44 ± 0.2	0.08 ± 0.05	P-Cygni abs
N v	1238.82	7.38 ± 0.5	6.64 ± 0.5	4.24 ± 0.10
N v	1242.80	−0.68 ± 0.2	−0.35 ± 0.2	−0.64 ± 0.20	P-Cygni abs
N v	1242.80	3.25 ± 0.5	2.96 ± 0.4	1.68 ± 0.08
O i	1302.17	−2.40 ± 1.0	−2.05 ± 0.9	−2.01 ±	P-Cygni abs
O i	1302.17	1.71 ± 0.6	1.33 ± 0.6	...
O i	1304.86	...	...	−1.42 ±	complex P-Cygni abs
O i	1304.86	2.64 ± 0.3	2.05 ± 0.3	...
O i	1306.03	1.55 ± 0.7	1.84 ± 0.3	...
Si ii	1309.28	−0.61 ± 0.3	−0.57 ± 0.2		P-Cygni abs
Si ii	1309.28	0.37 ± 0.5	0.07 ± 0.4
Si iv	1393.76	−2.21 ± 0.9	−1.66 ± 0.5	−1.23 ± 0.15	P-Cygni abs
Si iv	1393.76	3.36 ± 1.6	1.04 ± 0.4	...
O iv]	1397.20	0.53 ± 0.2	0.39 ± 0.2	...
O iv]	1399.78	0.92 ± 0.2	0.77 ± 0.2	0.22 ± 0.10
O iv	1401.16	4.04 ± 0.2	3.59 ± 0.3	0.59 ± 0.20
Si iv	1402.77	−1.53 ± 0.5	−0.99 ± 0.3	−1.03 ±	P-Cygni abs
Si iv	1402.77	2.16 ± 0.9	0.48 ± 0.3	...
O iv]	1404.81	2.20 ± 0.5	2.52 ± 0.3	0.56 ± 0.15
S iv]	1406.00	1.06 ± 0.2	0.72 ± 0.2	...
O iv]	1407.38	0.40 ± 0.2	0.57 ± 0.2	...
N iv]	1483.32	...	⋅⋅⋅	0.25 ± 0.05
N iv]	1486.50	54.7 ± 1.8	51.7 ± 1.5	9.61 ± 0.10
C iv	1548.19	−4.25 ± 1.7	−2.85 ± 0.5	...	P-Cygni abs
C iv	1548.19	15.9 ± 1.0	8.98 ± 0.8	0.58 ± 0.07
C iv	1550.77	−4.36 ± 0.4	−2.54 ± 0.5	...	P-Cygni abs
C iv	1550.77	8.90 ± 2.0	4.90 ± 0.7	0.31 ± 0.05
Ne iv]	1601.5?	...	...	0.65 ± 0.07
He ii	1640.40	8.55 ± 0.3	8.64 ± 0.3	1.81 ± 0.10
O iii]	1660.81	4.96 ± 0.2	2.88 ± 0.2	0.53 ± 0.10
O iii]	1666.15	12.6 ± 0.3	9.64 ± 0.3	1.48 ± 0.10
N iii]	1746.82	1.53 ± 0.5	0.73 ± 0.3	...
N iii]	1748.65	5.51 ± 0.7	3.89 ± 0.3	...
N iii]	1749.67	42.9 ± 0.8	27.1 ± 0.7	1.62 ± 0.07
N iii]	1752.16	20.8 ± 0.7	15.1 ± 0.4	0.86 ± 0.05
N iii]	1754.00	7.44 ± 0.7	6.47 ± 0.3	0.23 ± 0.05

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A further complication, when using these lines for diagnostic purposes, is that all of the resonance lines in the UV have P-Cygni components. The photons, which give rise to the absorption component, scattered out of the line of sight (LOS) of the observer are partly compensated for by those scattered into the LOS from the area of the wind outside of the projected photosphere. The net emission in a line from the CSM comes from the emission component plus the scattered photons. The fraction of the photons from the back of the SN and that are in the LOS of the optically thick ejecta do not contribute to the emission. An upper limit to this contribution is the absorbed flux relative to the continuum in the absorption component. The exact fraction depends on the emissivity as function of the radius from the photosphere. For this reason we list in Table 7 both the flux in the emission component and the flux deficit in the absorption component for the COS spectra.

An inspection of Table 6, as well as Figure 10, shows that between the first two epochs there is relatively little evolution of the flux of the narrow lines in the STIS range, although the continuum has decreased somewhat. At 107 days the fluxes of both continuum and lines have, however, decreased by a factor of ∼2. The same trends can be seen in the COS spectra (Table 7 and Figure 9). The decrease in the narrow line fluxes correlates with the broad component of the high-ionization UV lines (Figure 16). In the last STIS spectrum at 573 days, both lines and continuum have dropped by a factor of ∼10, although the Mg ii λλ2796, 2804 only drops by a factor of ∼3.

3.4.3. The X-shooter Spectrum at 461 Days

We also obtained one medium/high-resolution X-shooter spectrum from the VLT for 2012 January 14 (day 461), shown in Figure 20. Because of the higher spectral resolution and NIR coverage, we discuss this spectrum separately.

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Starting with the continuum, we note the excess in the NIR with a maximum at ∼1.5 μm. This NIR excess agrees well with the rise in the J, H, and K_s bands we see in the photometry in Figure 2 later than ∼400 days and is most likely caused by hot dust emission; its origin will be discussed in Section 4.2. We fit this well with a blackbody spectrum at a temperature of ∼1870 K. The corresponding continuum in the optical is fitted with a temperature of ∼9000 K. The value for the dust temperature differs by ∼8% from that obtained from the photometry in Table 5, 2045 K. This gives an estimate of the errors in this parameter from the errors in the photometry, spectral calibration, and fitting errors. Because of the many lines in the optical region, the error in the photospheric temperature is at least as large as this, although here they happen to be very close.

In the NIR the most interesting lines are the strong broad and narrow components of He i λ10, 830, as well as Paα, Paβ, and Paγ. The He i λ10, 830 confirms the identification of the He i λ5876 line in the optical. The λ2.0581 μm line is, however, only seen as a narrow absorption.

We identify the broad, asymmetric feature with a peak at ∼8435 Å with O i λ8446. The extended red wing is a blend of the Ca ii triplet λλ8498.0, 8542.1, 8662.1 and higher members of the Paschen series (n = 12–15). The identification with the O i λ8446 line is supported by the presence of the O i 1.129 μm line. These lines are likely to be a result of Lyβ fluorescence with O i, where the upper level of the 1.129 μm line is pumped by Lyβ and then decays into the 1.129 μm and λ8446 lines (Grandi 1980). The relative flux of these lines agrees well with what is expected, although blending of the O i λ8446 line prevents a detailed comparison.

O i λ8446 was also seen in the Type IIn SN 1995G (Pastorello et al. 2002), although in this case no NIR spectrum exists. There is also a line consistent with O i λ8446 in the SN 1995N spectrum in Fransson et al. (2002), although this was identified as mainly Fe ii λ8451. In the case of SN 2010jl there are, however, no lines corresponding to Fe ii λλ9071, 9128, 9177, which would be expected to accompany the Fe ii λ8451 line.

The high resolution in combination with high S/N allows us to identify a large number of weak, narrow emission lines not seen in the other lower S/N spectra that cast additional light on the CSM. In Figure 21 we show a close-up of the optical range with some of the most important lines marked.

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The most interesting parts of these lines are the large range of ionization stages of forbidden lines from [Fe v–xiv]. The [Fe vii] lines serve as diagnostics of the density and the excitation conditions in the CSM and are discussed in Section 3.5.

Of the coronal lines, [Fe x] λ6374.5 is strong, as is [Fe xi] λ7891.8, but [Fe xiv] λ5302.9 is only barely seen as a weak line. [Fe xiii] λ10, 746 is not seen, but it sits on the strong wing of He i λ10,830. Other high-ionization lines include [Ne v] λλ3345.8, 3425.9, [Ca v] λ6086.8, [Ar x] λ5533.2, and a weak [Ar xiv] λ4412.6. The presence of these lines confirms the high state of ionization in the CSM of this SN.

In these high S/N spectra, the Balmer series can be traced up to n = 33 (λ3659.4) with strong absorption components but only weak P-Cygni emission. The Paschen series is seen from Paα to n = 17 (λ8467.3). In contrast to the Balmer lines, these lines are all in pure emission. Brγ is also seen in emission.

Using fluxes from the previous section, we use the forbidden and intercombination lines in the UV and optical as diagnostics of the density.

The ratios of the N iii] λλ1746.8, 1748.7, 1749.7,1752.2, 1754.0 lines are sensitive to the electron density (Keenan et al. 1994). In particular, the λλ1752.2/1749.7 ratio is 0.55–0.58 in the range 10⁵–10⁸ cm⁻³. Above this density the ratio decreases to become 0.20 at 10¹⁰ cm⁻³. The λλ1754.0/1749.7 ratio has a similar behavior. Unfortunately, the λ1754.0 line is at the very boundary of the wavelength range of the G160M grating, and its flux is uncertain. The λ 1748.7 and λ 1754.0 lines have the same upper level with transition rates within a few percent of each other, so we use the λλ 1748.7/1749.7 ratio instead of the λλ1754.0/1749.7 ratio for the diagnostics.

Figure 22 shows a fit of these lines for different electron densities in the range 10⁷–10¹⁰ cm⁻³ for the day 44 COS spectrum. The fits show that (with the exception of the λ1754.0 line) all lines agree with an electron density in the range 10⁵–10⁸ cm⁻³. Higher values give too low a value for the λλ1752.2/1749.7 ratio. We have also examined the day 107 and day 621 COS spectra and find essentially the same density constraint, although the S/N is somewhat lower.

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Figure 23 shows a similar analysis of the O iv] λλ1393.1, 1397.2, 1399.8, 1401.2, 1404.8, 1407.4 and S IV] λλ1398.0, 1404.8, 1406.0, 1416.9, 1423.8 multiplets. As the red curve shows, the lines are fit with the same density interval, 10⁵–10⁸ cm⁻³, as the N iii] lines. This is not surprising because these ions are expected to arise in the same region.

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The ratio of the N iv] lines at 1482.9 Å and 1486.1 Å is sensitive to density in the range 10⁴–10⁸ cm⁻³ (Keenan et al. 1995), with a ratio of ∼1.6 below 10⁴ cm⁻³ and decreasing above this density. From the 2012 June 20 spectrum we estimate a λλ1482.9/1486.1 flux ratio of 0.029 ± 0.05. From Keenan et al. (1995, their Figure 1) we find that this corresponds to an electron density (3–6) × 10⁶ cm⁻³ for temperatures in the range 10⁴–2 × 10⁴ K.

The O iii] λλ1660.8, 1666.2, and [O iii] λλ4363.2, 4958.9, 5007.0 lines are especially useful as density and temperature diagnostics Crawford et al. (2000). Figure 10 shows the [O iii] λλ4363.2, 4958.9, 5007.0 region for the two first STIS spectra, and all three [O iii] lines are easily identified. This is even clearer in the ground-based spectra in Figure 24. The first thing to note is the very strong λ4363 line, which is usually faint compared to the λλ4949, 5007 lines. Typical [O iii] λλ5007/4363 ratios for H ii regions are ≳ 50 (Osterbrock & Ferland 2006). Pilyugin & Thuan (2007) determine [O iii] λλ4959, 5007/4363 ratios of 166 and 140 for UGC 5189 at different radii, which is much larger than the ratio observed for SN 2010jl and strongly argues for a circumstellar origin of these lines.

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In Figure 25 we give the [O iii] λλ5007/4363 ratio and the [O iii] λ4363 flux for the different dates for selected medium-resolution spectra with NOT and MMT (2010 November 15), as well as the STIS observations. The limited spectral resolution, as well as the S/N, makes the fluxes of the STIS spectra uncertain. They do, however, have the advantage of minimizing the background contamination of especially the λ5007 line.

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We note that the flux of the λ4363 line shows a smooth decay by a factor of ∼2 during the period. However, the λλ5007/4363 ratio varies by a large factor from observation to observation. The reason for this is that the λ5007 line is severely affected by nearby H ii regions in some of the ground-based observations. Observations with poor seeing (≳ 1'') therefore have a much larger λ5007 flux than the ones with good seeing. This is also consistent with the STIS observations, which, in spite of a low S/N, show a low λ5007 flux and a low λλ5007/4363 ratio. Because of the high λλ5007/4363 ratio in the nearby H ii regions (see above), the λ4363 line is only marginally affected by this. For the nebular analysis below we only use the lowest λλ5007/4363 ratios, which are in the range 0.5–0.8.

The region of O iii] λλ1660.8, 1666.2 is noisy in the STIS spectra, but it does show a clear line above the noise (Figure 10). The flux of the line is consequently uncertain. However, the fluxes in the COS and STIS spectra are consistent with each other for the dates of the two COS observations. The observation from day 44 gives a total O iii] λλ1661 + 1666 flux of 1.8 × 10⁻¹⁴ erg s⁻¹, close to that of the STIS observation for the same date. We conclude that the O iii] λλ1661 + 1664 flux is accurate to at least ∼50%. The expected line ratio of O iii] λ1666.2/λ1660.8 is 2.5, consistent with the measured ratio of 2.3 from COS. As a very conservative estimate we take O iii] λλ(1661 + 1666)/5007 = 1.2–8.

Figure 26 shows the [O iii] λλ4363/5007 and λλ1666/5007 ratios as a function of density and temperature. We have also plotted the observed ranges of these ratios as horizontal lines in the figure. The atomic data are taken from Crawford et al. (2000) and Palay et al. (2012). From this figure we see that for reasonable temperatures, i.e., ≲ 50, 000 K, a λλ5007/4363 ratio in the range 0.5–0.8 requires an electron density ≳ 3 × 10⁶ cm⁻³. Further, the λλ1664/5007 ratio results in a range 3 × 10⁶–10⁹ cm⁻³ for T_e = (1–3) × 10⁴ K. A higher reddening than we have assumed would only increase this range marginally.

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We identify faint but clear narrow lines of [Fe iii] at 4657 ± 1 Å and 4701 ± 1 Å in the high S/N NOT spectra (Figure 24). These lines can be seen at all epochs with approximately the same fluxes. In addition, there may also be a weak line at ∼5010 Å, but this is disturbed by the [O iii] λ5007 line, as well as noise. These lines are interesting in that they can provide some independent diagnostics of the narrow line gas. Keenan et al. (1993) find that the [Fe iii] λλ4702/4658 ratio varies from ∼0.30 for n_e ≲ 10³ cm⁻³ to 0.46–0.52 for n_e ≳ 10⁵ cm⁻³. The observed ratio is ∼0.5, in agreement with the high-density limit. The λλ4881/4658 ratio increases from ∼0.2 for n_e ≈ 10² cm⁻³ to ∼0.5 for n_e ≈ 10⁵ cm⁻³; at higher densities it rapidly decreases to ≲ 0.1. There is no sign of the λ4881 line in the spectra, consistent with a density n_e ≳ 10⁵ cm⁻³. The λ5011.3 line is, on the other hand, probably present. Together, these lines are consistent with n_e ≳ 10⁶ cm⁻³.

The final diagnostics come from the [Fe vii] lines in the X-shooter spectrum from day 461 (Figure 21). The [Fe vii] λλ4988.6/5720.7 ratio is 0.16. Using the diagnostic diagram from Keenan et al. (2001), we find that this corresponds to an electron density of ∼5 × 10⁵ cm⁻³. We note, however, that the derived density is sensitive to the uncertain collision strengths, as is discussed in Keenan et al. (2001).

Summarizing these different density diagnostics, i.e., the N iii], N iv], [O iii], O iv], [Fe iii] and [Fe vii] ratios, as well as the presence of P-Cygni absorptions in the Balmer lines, we find that these lines indicate a density 3 × 10⁶–10⁸ cm⁻³ for the region emitting the narrow lines in SN 2010jl.

The strong [N ii], N iii], N iv], and N v lines in the STIS and COS spectra (Figures 9 and 10) indicate a nitrogen enrichment in the narrow-line region of the CSM of the SN.

To estimate the relative CNO abundances, we note that for a photoionized plasma the ionization zones of N iii and C iii coincide closely with each other, and similarly for the C iv, N iv, and O iii zones (Kallman & McCray 1982, their Figure 6(a)). The N v and O iv zones overlap, but not to the same extent as the lower ionization ions. In addition, the temperature in these zones is nearly constant. Using the line fluxes for these ions allows us to derive the relative ionic abundances and, with some assumptions, elemental abundances. Because the excitation energies are similar, the line ratios are insensitive to the temperature for reasonable ranges, (1–3) × 10⁴ K. Here we use T_e = 2 × 10⁴ K. They do depend on the electron density, but this is mainly important above ∼10⁹ cm⁻³, where the lines are suppressed, and densities this high were excluded through the analysis in the previous section. The narrow range of wavelengths also makes the results insensitive to the reddening.

The most interesting lines for the CNO analysis are N iv] λ1486.5, C iv λλ1548.2, 1550.8, O iii] λλ1660.8, 1666.2, N iii] λλ1746.8–1754.0, and C iii] λ1908.7. With the exception of the C iii] lines, all are within the range of our COS spectra, and accurate relative fluxes can be derived (within a few percent). The C iii] line, however, poses a special problem because of the lower S/N and low spectral resolution of the STIS spectra (Figure 10). An additional complication is that the line sits on top of a broad electron-scattering feature centered on the Si iii] λ1892.0 line. This is also the case for the N iii] λλ1746.8–1754.0 lines, but in this case it is easy to determine the background flux from the high-resolution COS spectra. An estimate of the systematic error in the N iii] flux from STIS can consequently be obtained if one compares the COS and STIS fluxes for the same epoch. For the day 44 observation we get for the total N iii] flux (11.5 ± 2.0) × 10⁻¹⁴ erg cm⁻² s⁻¹ in the STIS observation, depending on where the "continuum" level is set, compared to 7.9 × 10⁻¹⁴ erg cm⁻² s⁻¹ for the COS spectrum. For the day 107 spectrum, the corresponding numbers are (5.57 ± 0.8) × 10⁻¹⁴ erg cm⁻² s⁻¹ and (5.33 ± 0.1) × 10⁻¹⁴ erg cm⁻² s⁻¹, respectively. There is a tendency to overestimate the flux from the STIS observations, mainly from the difficulty in determining the continuum level. The same is likely to be the case for the C iii] line.

As a consequence of this discussion, to minimize the systematic error we use the N iii]/C iii] ratio from the STIS observations, in spite of the lower S/N in the STIS observations for N iii] compared to the COS flux. To estimate the systematic error in the C iii] flux, we have calculated the line flux for a range of assumptions about the background "continuum."The error may still be up to ∼50% and dominates the error budget in the relative N iii/C iii ratio. For the other line ratios, N iv]/C iv and N iv]/O iii], we use fluxes from the COS spectra. For the C iv resonance doublet, we assume two limiting cases. In the first case we subtract the full absorption component from the emission component to correct for the scattering, as discussed in Section 3.4.2. This may underestimate the net emission by up to ∼60%. In the other case, we neglect this correction and use the observed flux in the emission component. This is likely to overestimate the net emission. These limits should bracket the thermal excitation emission and is the best we can do without knowledge about the radius of the emission region. The adopted line ratios with errors are given in Table 8. There is a fairly large scatter in both the N iii]/C iii] ratio and the N iv]/C iv ratio, reflecting the difficulties discussed above.

Table 8. Observed and Derived Ionic Abundances

Date	N iii/C iii	N iv/C iv	N iv/O iii
Line fluxes used
34 days	13.5 ± 2.0/2.99 ± 1.2	...	...
44 days	11.5 ± 2.0/2.96 ± 1.2	5.47 ± 0.18/1.62 ± 0.28a	5.47 ± 0.18/1.76 ± 0.05
		5.47 ± 0.18/2.48 ± 0.22b
107 days	5.57 ± 0.8/2.24 ± 1.0	5.17 ± 0.15/0.85 ± 0.13a	5.17 ± 0.15/1.25 ± 0.05
		5.17 ± 0.15/1.39 ± 0.11b
Observed line ratios
34 days	4.51 ± 1.93	...	...
44 days	3.89 ± 1.71	3.37 ± 0.59a	3.11 ± 0.14
		2.21 ± 0.21b
107 days	2.49 ± 1.16	6.08 ± 0.95a	4.14 ± 0.20
		3.71 ± 0.31b
573 days	2.49 ± 1.16	6.08 ± 0.95a	4.14 ± 0.20
		3.71 ± 0.31b
621 days	...	6.08 ± 0.95a	4.14 ± 0.20
		3.71 ± 0.31b
Derived ionic ratiosc
Nov 11	37.9 ± 16.2–30.3 ± 13.0	...	...
Nov 22	32.7 ± 14.4–26.1 ± 11.5	22.2 ± 3.9–22.9 ± 4.0a	0.74 ± 0.04–0.70 ± 0.04
		14.6 ± 1.4–15.0 ± 1.4b
Jan 23	20.9 ± $9.8\hbox{--}16.7$ ± $7.8$	40.1 ± 6.3–41.3 ± 6.5a	0.99 ± 0.05–0.93 ± 0.05
		24.5 ± 1.0–25.9 ± 1.2b

Notes. ^aCorrected for scattering. ^bNo correction for scattering. ^cAssuming n_e in the range 10⁶–10⁹ cm⁻³ and T_e = 2 × 10⁴ K and E_{B − V} = 0.027 mag.

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Using these line ratios, we can now derive relative ionic abundances. For the collision strengths and radiative transition rates, we use data from the Chianti database (Landi et al. 2012). In Table 8 we show the derived ionic abundances for the different dates and T_e = 2 × 10⁴ K, typical of an X-ray-heated plasma. As discussed above, the results are not very sensitive to the temperature. To show the dependence on the assumed density we give the abundance ratios for both n_e = 10⁶ cm⁻³ and n_e = 10⁹ cm⁻³.

There are several things to note here. The scatter and large errors in the STIS fluxes are reflected in the N iii/C iii ratio. Taking an average of the three epochs, we get $n({\rm N\,\scriptsize{III}})/n({\rm C\,\scriptsize{III}})=30.5 \pm 13.7$ for 10⁶ cm⁻³ and $n({\rm N\,\scriptsize{III}})/n({\rm C\,\scriptsize{III}})= 24.3 \pm 11.0$ for 10⁹ cm⁻³. Also, the N iv/C iv ratio varies greatly with both epoch and the assumption about the scattering contribution. The scattering introduces an uncertainty of ∼60%, and the variation between the different epochs amounts to 70%–80%. These variations are probably related to each other. A decrease in the continuum flux means that the scattering contribution will decrease. There may therefore be an evolution from a line dominated by scattering to a line where scattering is less important. The N iv/O iii ratio does not have any of these complications because this ratio involves two intercombination lines. Consequently, it is relatively constant between the two epochs and also has small individual errors.

In addition to the observational errors and the uncertainty of the scattering correction, there is some uncertainty in the correspondence of the ionization zones. Although both the C iii and N iii zones, as well as the C iv, N iv, and O iii zones, nearly coincide in the X-ray photoionized models by Kallman & McCray (1982), this is not obviously so for our case with a different ionizing spectrum and density, although it is likely that the narrow lines are indeed excited by X-rays (Section 4.1).

In spite of these caveats, the need for a very high N/C ratio is clear. From the N iii/C iii and N iv/C iv ratios we find a "best value" of n(N)/n(C) = 25 ± 15. The N/O ratio is better constrained to be n(N)/n(O) = 0.85 ± 0.15. For comparison, the corresponding solar ratios are n(N)/n(C) = 0.25 and n(N)/n(O) = 0.14 (Asplund et al. 2009).

Our analysis in Section 3 provides several pieces of important information about the SN and its CSM that provide clues to the nature of the progenitor and its evolutionary status. In particular, we have evidence for a CSM of the progenitor with a velocity of ∼100 km s⁻¹ and a density of 3 × 10⁶–10⁸ cm⁻³. Further, the derived CNO abundances indicate a large nitrogen enrichment, n(N)/n(C) = 25 ± 15 and n(N)/n(O) = 0.85 ± 0.15, typical of CNO processed gas.

A large CNO enrichment has been observed for a number of SNe, either in the ejecta itself or in the CSM. This includes SN 1979C (IIL), SN 1995N (IIn), SN 1998S (IIn), SN 1993J (IIb), and SN 1987A (IIpec) (see Fransson et al. 2005 for a summary of these with references). As for potential progenitors, CNO enrichment is observed for several types of evolved massive stars. In particular, this is consistent with an LBV scenario for the progenitor. The best-studied cases are for Eta Carinae and AG Carinae, which we discuss below.

Hillier et al. (2001) make a detailed analysis of STIS observations of the central source in Eta Carinae. The mass-loss rate is determined to be ∼10⁻³  M_☉ yr⁻¹ for a wind velocity of ∼500 km s⁻¹. From the weakness of the electron scattering wings, they conclude that the wind has to be clumpy, with a filling factor of ∼10%. Hillier et al. also find that the N abundance in the primary star is at least a factor of 10 higher than solar, while C and O are severely depleted. In the nebula of Eta Carinae, the CNO abundances can be determined more reliably. In particular, Dufour et al. (1997) and Verner et al. (2005) find that N is enhanced by a factor of 10–20, and C and O are depleted by a factor of 50–100. Smith & Morse (2004) also find a strong radial gradient in the N/O ratio in Eta Carinae, with a high N/O ratio close to the star, decreasing outward.

Most of the mass in the CSM of Eta Carinae is in a molecular shell surrounding the central star. Smith (2006) estimates a total mass of ∼11 M_☉. The distance from the star to this hourglass-shaped shell is between 3 × 10¹⁶ cm and 3 × 10¹⁷ cm. Especially interesting is that Smith (2006) derives a density of ≳ 3 × 10⁶ cm⁻³ for the molecular shell around Eta Carinae. This density bound is similar to what we find for the CSM of SN 2010jl. In addition, gas with similar densities are seen even closer, at distances ∼10¹⁵ cm from the star, as [Fe ii] emission.

Besides Eta Carinae, AG Carinae is one of the most extensively studied LBV stars, showing a variation of the S Doradus type. Over the two periods studied, the mass-loss rate varied in the range (1.5–3.7) × 10⁻⁵  M_☉ yr⁻¹, and the wind velocity varied in the range 300–105 km s⁻¹, in antiphase with the mass loss (Groh et al. 2009). It has clearly undergone a more intense mass loss period earlier, as is apparent from the fact that it has a circumstellar nebula with an ionized mass of ∼4.2 M_☉ and a dynamical age of ∼8.5 × 10³ yr (Nota et al. 1995). An even higher mass of ∼25 M_☉ in the neutral medium has been estimated based on IR imaging, assuming a standard dust-to-gas ratio of 1:100 (Voors et al. 2000). From a spectral analysis of the central star, Groh et al. (2009) find a N mass fraction of 11.5 ± 3.4 times solar, while C is only 0.11 ± 0.03 times solar, and O is 0.04 ± 0.2 times solar, clearly indicating CNO processed material. The abundances in the nebula are more uncertain, with an N/O ratio of 6 ± 2, compared to $39^{+28}_{-18}$ for the star. It is likely that the surface of the star has undergone more CNO processing than the nebula.

The wind velocity we find for SN 2010jl, ∼100 km s⁻¹, is not that of a red supergiant, whose velocities are in the range 10–40 km s⁻¹ (Jura & Kleinmann 1990), so we rule these out as progenitors. Here we differ from Zhang et al. (2012), who find a wind velocity of 28 km s⁻¹, but this is a result of their use of the velocity of maximum absorption in the P-Cygni profile and not the maximum blue velocity. The maximum absorption velocity we observe is also considerably higher than theirs (Figure 17). Their conclusion that the progenitor was a red supergiant is based on a wind velocity that is too low. We find a velocity that is more typical of LBV stars, which have velocities in the range 100–1000 km s⁻¹ (Smith et al. 2011b). The velocity we find, ∼100 km s⁻¹, is on the low end of this range, which may be a potential problem with the LBV interpretation. However, the expansion velocity of the molecular shell in Eta Carinae is highly anisotropic, ranging from ∼60 km s⁻¹ at the equator to ∼650 km s⁻¹ at the poles (Smith 2006), and is likely to vary substantially with time. As we noted above, the velocity in the high mass loss phase of AG Carinae is very similar to the one we derive for SN 2010jl.

Although it is clear that the narrow lines originate in fairly dense circumstellar gas, it is not obvious what excites them. The recombination time is ∼1/αn_e ∼ 5.8(n_e/10⁷ cm⁻³)⁻¹ days for H and T_e ∼ 10⁴ K. The gas is therefore in near equilibrium with the ionizing radiation. An early, undetected UV burst is therefore not likely to be important for the excitation. The widths of the lines, ≲ 100 km s⁻¹, also make it unlikely that the gas is shock ionized.

Instead, we believe that the lines are excited by the same X-rays as are observed with the Chandra satellite (Chandra et al. 2012b). As we discuss in Section 4.3, these are likely to come from fast shocks connected to an anisotropic, high-velocity ejection. We can estimate the state of ionization from the models in Kallman & McCray (1982). With an X-ray luminosity of ∼3 × 10⁴¹ erg s⁻¹, corresponding to the absorbed flux of ∼10⁻¹² erg cm⁻² s⁻¹ (Chandra et al. 2012b), the ionization parameter, ζ = L/n_er², becomes $\zeta \sim 300 (n_{\rm e} / {10^7 \ \rm cm^{-3}})^{-1} (r / 10^{16} \rm \ cm)^{-2}$. From the optically thin Model 1 in Kallman & McCray (1982), we find that the presence of N iii–N v requires log ζ ∼ 0–1. Optically thick models with a density of 10¹¹ cm⁻³ have the same ions at a somewhat higher ionization parameter, log ζ ∼ 1.5. The presence of [Fe xiv] (Section 3.4.3) is also consistent with this ionization parameter. The observed X-ray luminosity indicates a distance of ∼(2–20) × 10¹⁶(n_e/10⁷ cm⁻³)^−1/2 cm. The radius of the shock at 500 days after outburst is ∼1.3 × 10¹⁶(V_s/3000 km s⁻¹)(t/500 days) cm, where V_s is the shock velocity. There is therefore a rough consistency between the estimated distance of the narrow line emitting region and the location of the SN shock wave.

This estimate of the ionization parameter is approximate for several reasons. First, the density has a considerable uncertainty. Further, as we discuss below, the shock velocity, and therefore the shock radius, is also uncertain and may be in the range 500–3000 km s⁻¹. Finally, the X-ray models in Kallman & McCray (1982) are not completely appropriate because these assume a 10 keV bremsstrahlung spectrum, and the X-ray spectrum of SN 2010jl is heavily absorbed, having a deficit of photons below ∼1 keV. The Kallman & McCray (1982) models were also calculated for a density of 10¹¹ cm⁻³, while the narrow lines in SN 2010jl indicate a considerably lower density. Nevertheless, this estimate shows that it is likely that the narrow lines originate in X-ray ionized gas at a distance and density comparable to the molecular shell of Eta Carinae discussed above. In Section 4.7 we discuss more detailed photoionization calculations that confirm these estimates.

The fact that we observe fairly "normal" P-Cygni profiles with both a deep absorption and a red emission wing implies that the CSM at the distance where the narrow lines arise must be fairly symmetrically distributed, unlike the distribution for the broad component as described below. This is discussed further in Section 4.7.

The NIR excess seen in the photometry in Figures 2 and 4, as well as the X-shooter spectrum in Figure 20, is most likely a result of hot dust. From the photometric light curve in Figure 3 we see that by day 400 the flux in the NIR is higher than that in the optical. This NIR/optical ratio increases with time, and at the last epochs the NIR luminosity dominates completely.

In Section 3.2 we used simple blackbody fits of the optical and NIR photometry. We have investigated this in more detail following Kotak et al. (2009). Here we have used the grain emissivities from Draine & Lee (1984) and Laor & Draine (1993) and the escape probability formalism from Osterbrock & Ferland (2006). For the grain sizes we use the MRN distribution with dn/da∝a^−3.5 (Mathis et al. 1977) with a minimum grain size 0.005 μm and a maximum size 0.05 μm. We then fit the sum of the dust spectrum with a given optical depth in the V band, τ_V, and a photospheric blackbody spectrum, minimizing the chi-square with respect to the photospheric effective temperature and radius T_eff and R_phot and the corresponding parameters for the dust shell, T_dust, R_dust. A more detailed modeling, calculating the temperature of the dust as a function of radius, as in Andrews et al. (2011), requires assumptions about the geometry and is outside the scope of this paper.

In Figure 27 we show an example of this kind of fit for day 465 for which we have observations at 3.6 μm and 4.5 μm.

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From this figure it is clear that without any observations longward of 4.5 μm it is impossible to discriminate between the different compositions and only marginally between different optical depths for the dust. This is in agreement with the modeling by Andrews et al. (2011).

The main difference between the optically thin and thick models is the larger radius of the former in order to produce the required luminosity. The dust temperature is lower in the optically thin models. At 465 days the best-fit silicate model in Figure 27 with an optical depth in the V band of τ_V = 0.04 had T_dust = 1680 K and R_dust = 3.3 × 10¹⁷ cm. The photospheric values were less affected with T_eff = 8900 K and R_phot = 6.0 × 10¹⁴ cm. The corresponding graphite model had T_dust = 1360 K, R_dust = 7.8 × 10¹⁷ cm, T_eff = 8600 K, and R_phot = 6.6 × 10¹⁴ cm. These values should be compared to T_dust = 2040 K, R_dust = 2.2 × 10¹⁶ cm, T_eff = 9200 K, and R_phot = 5.6 × 10¹⁴ cm for the optically thick model (Table 5). We find similar results for the other epochs. As Figure 27 shows, the separation between the dust and photospheric components are only marginally affected. The light curves of the photospheric and dust components based on the blackbody fits in Section 3.2 should therefore be accurate.

As an independent check we find from a fit to the NIR continuum of the X-shooter spectrum at 461 days in Figure 20 a dust temperature ∼1870 K and radius R_dust ∼ 2.5 × 10¹⁶ cm for the optically thick model, in good agreement with that derived from the broadband photometry. For the dates with only broadband photometry, we give R_dust in Figure 5.

It should be noted that the blackbody radius only represents a lower limit to the NIR-emitting region. A covering factor, f, less than unity will increase the radius by R_dust∝f^−1/2. As discussed above, an optically thin model would increase this further.

The blackbody radius can be compared to the shock radius, given by R_s ∼ V_st ∼ 1.0 × 10¹⁶ (V_s/3000 km s⁻¹)(t/400 days) cm, where we have scaled the velocity to what we believe is the maximum velocity of the shock (Section 4.3). With this velocity, or higher, the blackbody radius is comparable to the shock radius. In addition, a lower shock velocity is likely in the directions where the column density is larger than that inferred from the X-rays, which would give a smaller shock radius (Section 4.7).

The blackbody and shock radii can also be compared to the evaporation radius, given by $R_{\rm evap} = [L_{\rm max} Q_{\rm abs} / (16\pi \sigma T^{4}_{\rm evap} Q_{\rm emiss}(T_{\rm evap})) ]^{1/2}$ (Draine & Salpeter 1979). Here L_max is the maximum bolometric luminosity of the SN, Q_abs is the wavelength-averaged dust absorption efficiency over the SN spectrum, Q_emiss is the Planck-averaged dust emission efficiency, σ is the Stefan–Boltzmann constant, and T_evap is the evaporation temperature; Q_abs∝a, where a is the size of the dust grain. The parameter Q_abs/Q_emiss depends upon the evaporation temperature of the dust, the grain size of the dust, and the effective temperature of the SN, T_eff. For our calculations of R_evap we adopted values of T_evap = 1900 K for graphite and T_evap = 1500 K for silicates and assumed T_SN = 6000 K and 10,000 K. For both graphite and for silicates we use grain emissivities from Draine & Lee (1984) and Laor & Draine (1993). Because $R_{\rm evap} \propto L_{\rm max} ^{1/2}$, we give values for L_max = 10⁴³ erg s⁻¹ in Table 9, which can then be scaled to different luminosities.

We note that R_evap is not very sensitive to T_eff, except for very small dust grains. As a typical value at shock breakout we use T_eff = 10⁴ K for our estimates below. The peak luminosity of the SN was L_max ∼ 3 × 10⁴³ erg s⁻¹ (Figure 3). Using a grain size of ∼0.001 μm, we get R_evap ∼ 2.5 × 10¹⁷ cm for graphite and R_evap ∼ 4.5 × 10¹⁷ cm for silicates. For a grain size of ∼1 μm, the corresponding values are R_evap ∼ 6.0 × 10¹⁶ cm and R_evap ∼ 2.3 × 10¹⁷ cm, respectively.

The dust temperatures we find at ≲ 500 days, 1600–2000 K, are close to the evaporation (or formation) temperature for dust. It may therefore either be newly formed dust, close to the shock, or dust heated too close to the evaporation temperature by either the radiation from the SN or the shock wave. We now discuss different scenarios for the origin of the dust emission.

The cool, dense shell formed behind a radiative shock has often been mentioned as a favorable place for dust formation. The formation and survival of dust in this environment is, however, difficult to explain at epochs earlier than ∼320 days. Dust formation in the dense postshock gas requires temperatures of ≲ 1900 K. At these epochs, the shock is most likely in the optically thick region of the SN. The photospheric temperature at these epochs is ≳ 7000 K (Table 5). Even if the shock is radiative, it is therefore unlikely to cool to less than this temperature and may be higher. A related argument comes from noticing that the shock radius is well within the evaporation radius, even at ∼200 days. As Table 9 shows, R_evap ≳ 3 × 10¹⁶ cm for a luminosity of ∼10⁴³ erg s⁻¹ at 200 days, independent of dust size or composition for T_eff ≳ 6000 K. It is therefore difficult to see how any dust could form close to the shock region for a realistic shock velocity.

It is also difficult to see how the large IR luminosity at late epochs can be produced by such dust. The photospheric luminosity is then low, and the X-ray luminosity is likely to be less than that at the last observation by Chandra et al. (2012b) on day 373, ∼7 × 10⁴¹ erg s⁻¹, which is a factor of ∼5 lower than the NIR luminosity at 500 days. This agrees with the conclusions by Andrews et al. (2011), although with somewhat different arguments.

Reprocessing of radiation from the SN, possibly resulting in evaporation of preexisting dust or heating and evaporation of the dust by the shock, is more likely. As Andrews et al. conclude, there is evidence for preexisting dust around the progenitor star. The dust heating mechanism is, however, not clear. Previous treatments of dust in Type IIn SNe have discussed both heating by the radiation from the SN in combination with an echo and collisional heating by the hot gas behind the shock (e.g., Gerardy et al. 2002; Fox et al. 2010).

We first discuss the case where the dust emission comes from dust that is collisionally evaporated by the shock of the SN. As discussed in the next section, there is also direct evidence for such a velocity component in other Type IIn SNe. Massive dust shells into which the shock is propagating are also natural if the progenitor is an LBV. However, if we compare the shock radius with the evaporation radius at early epochs, we find that even the lowest values of the latter, R_evap ∼ 7 × 10¹⁶ cm, are considerably larger than the shock radius at the first epochs, R_s ∼ 2.6 × 10¹⁵(V_s/3000 km s⁻¹)(t/100 days) cm, where we have scaled to the velocity derived from the temperature of the X-rays. This radius should be seen as an upper limit to the shock radius. We therefore exclude this possibility.

A more attractive alternative is based on an echo from radiatively heated dust, as has been discussed for other Type IIns. The plateau in the IR light curve between ∼200 and ∼450 days and a slow decline thereafter (Figures 2 and 3) would then be expected. Also, the energetics may be consistent with this. The integrated optical luminosity from the SN during the first ∼400 days was ∼3.2 × 10⁵⁰ erg. In addition, there is a considerable luminosity in the UV, as well as at shorter wavelengths. This can be compared to the integrated luminosity in the dust component, which we estimate from the blackbody fits in Figure 5; we find a total energy of ∼2.7 × 10⁵⁰ erg. There is therefore reasonable consistency between the energy emitted from the central source and that emitted by the dust. It does, however, require a large covering factor of the dust, as well as a high optical depth in these directions, which is consistent with the blackbody shape of the spectrum. As Andrews et al. discuss, this may indicate an anisotropic geometry; they discuss torus models with different inclinations.

To explain the plateau as an echo, the inner radius would have to be ≳ 450/2 light days or ∼6 × 10¹⁷ cm, depending on the inclination of a disk or torus. At the same time the high temperature indicates that the inner radius is close to the evaporation radius. A radius of ∼6 × 10¹⁷ cm is, however, considerably larger than the earlier estimates for R_evap, even if the luminosity used for this estimate may be an underestimate, considering the fact that only the observed wavelengths were included and also that the peak luminosity may have been before the first observations. A solution to this discrepancy may be that most of the emission comes from very small grains. Some support for the presence of small grains in winds comes from observations and modeling of the emission from some O-rich asymptotic giant branch stars in the LMC, where a grain distribution with a minimum size of 0.01 μm to 0.1 μm gave the best fit (Sargent et al. 2010). Although the most appealing model, this scenario has some difficulties in simultaneously explaining both the light curve and the high dust temperature, unless one stretches the parameters.

We have calculated light curves from an echo from a spherically symmetric dust shell of inner radius 6 × 10¹⁷ cm. We, however, find that the rise of the light curve occurs too rapidly compared to the observed NIR light curve in Figure 3 and the total dust luminosity in Figure 5. Emmering & Chevalier (1988) have studied echoes from asymmetric dust distributions. As shown in their Figures 2 and 3, more disk-like distributions give a considerably slower rise for low values of the inclination of the disk or torus. A low value of the inclination also agrees with the low reddening in the spectrum of the SN, while a high optical depth in the disk is needed for the high dust to SN luminosity, discussed above. Even more asymmetric distributions with most of the dust behind the SN relative to our LOS may also be consistent with the light curve, although we have not studied this quantitatively. The increase of the dust-emitting area and simultaneous decrease of the dust temperature (Figure 5) are, however, qualitatively consistent with an echo, as the light echo paraboloid expands to larger radii into dust with decreasing temperature.

In the discussion about different dust emission mechanisms for Type IIn SNe Fox et al. (2011; see also Gerardy et al. 2002) proposed a scenario where preexisting dust was radiatively heated by the radiation from ongoing circumstellar interaction. Although the heating of the dust is radiative, echo effects are less important, and the shell can be at a smaller evaporation radius, without invoking small grains. If the late luminosity, including all wavelengths, is of the same order as the maximum bolometric luminosity, this may account for the high temperature observed. The main problem is that the luminosity of the late IR emission is high, ≳ 5 × 10⁴² erg s⁻¹ at 500 days, while the optical flux from the SN is decreasing rapidly. This scenario would therefore require a very large EUV–X-ray luminosity. There may be some indication of this from the Hα luminosity, as discussed in Section 4.7.

The profiles of the broad lines give important information about the structure of the envelope and the dynamics of the shock wave. As we discuss in the previous and next sections, dust formation has severe problems in both the ejecta and in connection to the shock at early epochs due to the high luminosity and temperature of the radiation. Instead, the blueshift of the lines is more easily explained as a result of the line formation and dynamics in the outer parts of the extensive envelope/CSM of the progenitor star, as was also suggested as a possible alternative by Smith et al. (2012b). As discussed in detail by, e.g., Chevalier & Irwin (2011), for a radiation-dominated shock in an extended envelope, the radiation starts to escape when τ_e ≲ c/V_s. The region outside the shock is therefore optically thick, and line radiation emitted here will be Compton scattered and can give rise to the broad wings observed, even if the emission is coming from regions that have not yet been accelerated by the shock radiation. Only when the region with τ_e ≲ 1 becomes accelerated will the macroscopic velocity become dominant.

An emission line undergoing electron scattering in a hot medium at rest will give rise to a symmetric line profile because the velocity broadening is provided by the microscopic, thermal velocities of the electrons (Münch 1948). However, if the medium is moving with a bulk velocity toward us, this can introduce a blueshift of the line profile. For a spherically symmetric expansion one expects a redshift of the line peak (Auer & van Blerkom 1972; Fransson & Chevalier 1989). This is clearly not the case here. However, if the scattering medium is primarily moving coherently toward us, one may instead get a blueshift of the peak, although it is still symmetric around the expansion velocity. We believe that this is the case here.

We can test this interpretation quantitatively by first shifting each line in Figure 12 by a macroscopic velocity, V_bulk, to the red. We adjust this so that a reflection about zero velocity gives a best χ² fit for Doppler shifts in the range ∼1000–5000 km s⁻¹, χ² = ∑_i[F_λ(V − V_bulk) − F_λ(− (V − V_bulk))]²]/σ², where V is the velocity rest wavelength and σ is the rms of the flux. The lower velocity limit is chosen to avoid influence on the line profile by the narrow P-Cygni absorption and emission and the scattering wings of this emission. We treat V_bulk as a free parameter representing the macroscopic velocity of the emitting gas. The result of this procedure for a selection of days is shown in Figure 28.

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From this figure we see that this simple, linear transformation results in nearly perfectly symmetric line profiles between the red and blue wings for essentially all epochs. This therefore argues that the blueshift in Figure 12 is due to a macroscopic velocity. In addition, the symmetric line profiles are a natural result of electron scattering. Other processes, like dust or other absorption processes, would result in asymmetric lines about the peak in flux, with a time-dependent line shape (e.g., Lucy et al. 1989). Electron scattering in an expanding medium that is optically thick, however, naturally results in symmetric profiles, as demonstrated explicitly below.

In the upper panel of Figure 29 we show with blue markers the V_bulk as a function of time. In this panel we also show the velocity of the peak of the broad component as red markers. For the early epochs this agrees well with V_bulk, but it is somewhat higher for the later epochs. The broad agreement of these two determinations is another way of showing the symmetry of the line around the velocity-shifted peak of the broad component. Because the peak velocity is more difficult to determine in the late spectra and is somewhat influenced by the narrow component, we prefer to use V_bulk as the macroscopic velocity for the rest of the paper. To quantify the width of the line profiles we use the FWHM as measured from the continuum-subtracted line profiles. This is shown in the lower panel of Figure 29.

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During the first 300–400 days there is an increase in V_bulk to ∼700 km s⁻¹. After this epoch the velocity decreases slightly and then becomes nearly constant at ∼400–500 km s⁻¹. Considering the errors in the last observations, the significance of this decrease is marginal. The FWHM increases from ∼2000 km s⁻¹ to ∼3000 km s⁻¹ during the first ∼200 days and then decreases slowly to ∼1500 km s⁻¹ on day 1128.

Before discussing this result in more detail, we first test the electron scattering interpretation further by fitting the line profiles for a few different dates. This is done by a Monte Carlo code developed for this purpose, which is similar to that developed by Auer & van Blerkom (1972) and Chugai (2001). The details of this are discussed at length in, e.g., Pozdniakov et al. (1977) and Gorecki & Wilczewski (1984). Except for the Compton recoil, which is negligible at these wavelengths, this calculates the line profile for an arbitrary temperature and spatial distribution of electrons. In this calculation, relativistic effects are unimportant and are ignored. Because the macroscopic bulk velocity can be transformed away in the way described above, we only consider scattering in a static medium.

For photons injected at a specific optical depth, τ_e, the parameters determining the line shape are only τ_e and temperature T_e. The optical depth determines the average number of scatterings, $N_{\rm sc} \approx \tau _{\rm e}^2$. The thermal velocity of the electrons is v_rms = 674(T_e/10⁴ K)^1/2  km s⁻¹. The FWHM of the line is ${\sim } N_{\rm sc}^{1/2} v_{\rm rms} \approx 674 \ \tau _{\rm e} (T_{\rm e}/10^4 \ {\rm K})^{1/2} \ \ \rm km\ s^{-1}$. For a constant electron temperature medium with no internal emission, our Monte Carlo calculations show that the FWHM can be fitted more accurately with Δv_FWHM = 900(T_e/10⁴ K)^1/2τ_e  km s⁻¹. A similar scaling also applies if the photons are internally generated. This means that there is some degeneracy in temperature and optical depth for a given Δv_HWHM. There is, however, a constraint on τ_e: the luminosity of the unscattered fraction of photons relative to those scattered is approximately exp (− τ_e).

In Figure 30 we show fits of the Hα profile for two different dates, day 31 and day 222, covering both the very early and late phases. In this model we used an n_e∝r⁻² density and assumed that the photons are injected in the scattering region with an emissivity $\propto n_{\rm e} ^2$, as applies if recombination dominates the Hα emission. Note that the narrow component of the Hα line is at the rest velocity of the galaxy and does not shift in velocity as the broad line becomes blueshifted, showing that these photons are not the dominant source for the scattering. The injected photons span a velocity range of 0–700 km s⁻¹, as expected for radiative acceleration (see Section 4.4.3), which decreases the unscattered narrow peak, in agreement with the observations. The temperature is taken to decrease from 2 × 10⁴ K to 1 × 10⁴ K, similar to what is found in detailed simulations of shocks (e.g., Figure 6 in Moriya et al. 2011), as well as from our photoionization calculations in Section 4.7. However, the profile is not sensitive to these assumptions.

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As can be seen from the figure, we get excellent fits for both dates, except at zero velocity, where the P-Cygni profile from the CSM affects the profile. This confirms that electron scattering dominates the line formation. There is no need for two different velocity components in the broad lines as advocated by Zhang et al. (2012). The same conclusion is reached by Borish et al. (2014) for the day 36 Paβ line.

The fact that the line profile can be explained by electron scattering plus a linear velocity transformation is surprising. As was pointed out above, one expects a redshifted rather than blueshifted line profile if the expansion of the ejecta/CSM is spherically symmetric (see Fransson & Chevalier 1989, Figure 6). Instead we propose that the Hα emission comes from a highly asymmetric, almost planar region expanding toward us (although possibly at some inclination relative to the LOS), as discussed in Section 4.7.

4.4.1. Dust Absorption from the Ejecta

In Figure 29 we see a gradual shift of the Hα peak. We have already in Sections 4.2 and 4.3 argued against dust in the ejecta or at the reverse shock as a reason for this. Nevertheless, this has been discussed by several authors, so we consider additional arguments on this topic.

Smith et al. (2012b) analyze the line profiles during the first 236 days and discuss two different scenarios for the observed blueshift. From a comparison of the optical and near-IR hydrogen line profiles at ∼100 days, they claim to see a wavelength-dependent asymmetry, which they interpret as a sign of wavelength-dependent extinction, indicative of dust formation in the postshock gas. However, Smith et al. also discuss electron scattering as an explanation for the line profile.

Maeda et al. (2013) argue for a dust origin based on the line shift, drop in luminosity, and IR excess. However, their analysis has several limitations, which we discuss based on our observations. The line shifts discussed by Maeda et al. are based on a single spectrum on day 513 with a limited S/N for lines other than Hα (see their Figures 4 and 5). The line shifts derived from these observations are therefore highly uncertain and do not include the red wings of the lines. As we show in Figures 28 and 30, we can get a satisfactory fit of both wings with an electron scattering profile.

Maeda et al. also claim to observe a systematic shift of the velocity with wavelength that is characteristic of dust extinction. In Figure 31 we compare the line profiles of our high S/N X-shooter spectrum for Hα, Hβ, Hγ, and Paβ at 461 days, an epoch not very different from that of Maeda et al. For these lines we have applied a smoothing of ∼50 km s⁻¹ to the spectra and normalized the fluxes to the same peak flux for the broad component and the same "continuum" level in the range ±(6000–7000) km s⁻¹. This is somewhat lower than for the determination of the continuum level of the Hα line in Figure 12, but it is necessary to avoid line contamination for Hβ and Paβ. As seen in Figure 31, this is even more serious for Hγ, and we have therefore scaled this line to the level of the other lines at the peak and at the maximum velocity where the line dominates, ∼2000 km s⁻¹. The high spectral resolution makes it possible to isolate the narrow P-Cygni component of the lines, which contaminates the low-resolution line profiles of Maeda et al. Both the spectral resolution and the S/N are crucial for a reliable determination of the peak velocity as well as the general line profile. Although the day 461 spectrum is the best one in terms of S/N and coverage to the NIR, we do not see any significant difference in the wavelength shifts for any other epochs. This includes the UV lines (Figures 14 and 15), which should be most sensitive to extinction.

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As can be seen from the figure, there is no notable difference in the velocity of the broad lines. The peak of Hα is shifted by ∼720 km s⁻¹ for this date. The Hδ, Hβ, Paβ, and He i λ10, 830 lines have their peaks at 640 km s⁻¹, 670 km s⁻¹, 700 km s⁻¹, and 690 km s⁻¹, respectively. From variations of the smoothing we estimate an error of ±50 km s⁻¹. For Hα, with a very high S/N, the error is ≲ 30 km s⁻¹. We therefore do not find any significant trend of the peak velocity or line shape with wavelength.

Although they are distorted by the interstellar absorptions, one can also compare the Lyα line profile to the Hα and Hβ lines in Figure 14 for days 44, 107, and 621. It is clear that there is no significant difference in these in spite of the large wavelength difference and large time span. This is in contrast to the changing line profiles of the Lyα, Mg II, and Hα in SN 1998S (e.g., Figure 8 in Fransson et al. 2005), where such a difference was indeed seen, indicative of dust formed behind the reverse shock. The line profiles in SN 1998S were also very asymmetric. Thus we find that the main argument for ejecta dust in Maeda et al. is doubtful.

Another indicator of ejecta dust discussed by Maeda et al., the NIR excess, has already been discussed as the probable result of an echo. The third, the drop in the light curve, has a natural explanation in terms of the shock either exiting the circumstellar shell or transiting to a momentum-driven phase, as proposed by Ofek et al. (2014) and discussed in Section 4.5.

After this paper was first submitted Gall et al. (2014, in the following G14) published an analysis of the line shift based on dust absorption. In contrast to Andrews et al. (2011) and this paper, G14 interpret the NIR dust emission as well as the blueshifts as being caused by dust formed behind the reverse shock at an initial radius of ∼2 × 10¹⁶ cm. There are, however, a number of problems with this interpretation. First, it requires the shock to have reached this radius at their first observation, 26 days after peak or 66 days after first detection. This requires a shock velocity of ∼35, 000 km s⁻¹. To support this, G14 claim to see velocities up to ∼20, 000 km s⁻¹ from an assumed P-Cygni absorption in Hβ extending to this velocity. If this would be real, there would in that case also be an emission component up to a similar velocity, because the photosphere, assumed to be at ∼7500 km s⁻¹, will only occult a small fraction of the ejecta. Such a broad emission component is not seen. The only way around this is to assume that the ejecta is extremely asymmetric. The P-Cygni absorptionis instead likely to be the result of contributions by weaker emission lines blueward of Hβ. Further, there are no indications of similar high velocities from any other lines. In particular, the Lyα line, being a resonance line, should show such absorption and emission if real. As seen in Figure 14, this is not the case. Nor do any of the other UV resonance lines show such a component (Figure 15). There are also other observations disfavoring similar high velocities. The analysis of the X-rays imply a velocity of ≲ 6000 km s⁻¹ (Ofek et al. 2014). The only direct evidence for high expansion velocities comes from the NIR spectra, where the He i λ10, 830 line shows evidence for expansion velocities of ∼5500 between 100 and 200 days toward us (Borish et al. 2014).

There are additional problems with the scenario in G14. If the emission lines would be coming from the cool dense shell and absorbed by the dust formed in this, the lines would be expected to have a boxy profile, not a symmetric profile peaked at low velocities. Boxy profiles are indeed seen in objects like SN 1993J (Matheson et al. 2000) and SN 1995N (Fransson et al. 2002), where the cool dense shell is believed to dominate the emission. Also, in objects where there are indeed strong indications for dust formation, like SN 1998S and SN 2006jc, the line profiles are less centrally peaked and more irregular (Leonard et al. 2000; Pozzo et al. 2004; Fransson et al. 2005; Smith et al. 2008b). As we have shown, the line profiles are instead well characterized as resulting from electron scattering. The mechanism behind the blueshift is not discussed in the G14 paper. It would, however, be surprising if this gave an intrinsically symmetric profile a simple shift in velocity, as we find, rather than a more irregular shape, given the expected clumping in a cold dense shell (Chevalier & Blondin 1995).

Taking these results together, we therefore conclude that a cold dense shell at ∼35, 000 km s⁻¹ is unlikely and that the dust emission is instead coming from preexisting dust, as concluded by Andrews et al. (2011). If the shock velocity is much lower than ∼35, 000 km s⁻¹, the shock will be well inside the evaporation radius, even for the large grains G14 propose, as Table 9 and also the estimates in G14 show. Formation of the dust is then very difficult, as discussed before.

We are also surprised that G14 exclude the Hα line in their analysis, given that this is by far the highest S/N line and therefore best suited for this kind of analysis. In addition, it should be noted that the asymmetry of Hα and other lines is sensitive to the assumed continuum level. A continuum subtraction has apparently not been done, as can be seen in Figure 5 of G14. The claims for a strong asymmetry in Hα are therefore doubtful. Instead, it can be seen from our Figure 10 that Hβ is considerably more complicated to analyze, with a number of interfering lines.

G14 further argue against preexisting dust based on the high dust temperature observed. It is not clear what this is based on, and on the contrary this is a natural consequence of dust evaporation by the strong flux from the SN. The same conclusion is reached by Borish et al. (2014).

Taken together, we therefore think the results regarding dust formation and the derived properties of this in G14 are highly questionable.

Based on this and our earlier discussion, we exclude the dust alternative, and instead we believe that the line shifts are due to a bulk velocity of the scattering material. There are at least two possibilities for this.

4.4.2. Gradual Contribution from Postshock Gas

4.4.3. Radiative Acceleration

A different alternative is that the line shift is the result of acceleration of the preshock gas by the extremely energetic radiation field from the shock and thermalized optical radiation from the ejecta and cool shell. This has been discussed earlier in different contexts (e.g., Chevalier 1976; Fransson 1982), but no conclusive observational evidence has been found. As a simple model, we consider an optically thin shell at a radius r(t) illuminated from below by the radiation field of the SN, having a luminosity L(t). Assuming that we can consider the radiation as radially free streaming, which should be a reasonable approximation at small optical depths close to the surface, the velocity is given by

$$\begin{equation} V(t) = {\kappa \over 4 \pi c} \int _0^{t} {L(t^{\prime }) \over r(t^{\prime })^2 } dt^{\prime } . \end{equation} \tag{ 1 }$$

For κ we use the electron scattering opacity, ∼0.35, applicable for an ionized medium with a He/H ratio of 0.1.

For the bolometric luminosity from the SN, we use the result from Figure 6, shown on a linear scale in the upper panel of Figure 32. The total radiated energy from the SN (excluding the echo) was ∼6.5 × 10⁵⁰ erg. Using this energy and assuming a radius constant with time, we can estimate the final velocity as $V \approx 670 (r/3\times 10^{15}\ \rm cm)^{-2} \ \rm km\ s^{-1}$. This estimate is, however, only approximate. The reason is that the hydrodynamic timescale of this gas is comparable to the length over which most of the energy is emitted, t_hydro = 580(r/3 × 10¹⁵ cm)/(V/700 km s⁻¹) days. The increase of the radius of the shell must therefore be taken into account when calculating the velocity. This is really a hydrodynamic problem, which includes the interaction of the shell with the surrounding gas. We ignore the latter effects and treat the expansion as ballistic, calculating the radius as $r = \int _{t_0}^t v(t^{\prime }) dt^{\prime } + r_0$. The only free parameter is the initial radius, r₀, of the emitting shell, which gives the normalization of the velocity.

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For the best fit we find r₀ = 2.6 × 10¹⁵ cm, resulting in a velocity as a function of time shown by the blue dots in the lower panel of Figure 32. Given that there are uncertainties in the estimate of the bolometric luminosity, we find a good agreement with the observed velocity shift from Figure 29 and shown as black dots in Figure 32. At epochs later than ∼500 days, there is considerable scatter in the observed line shift, and it is difficult to judge if there is a slight decrease in the velocity, as may happen if there is a braking effect by the swept-up CSM. Apart from the general agreement with the evolution of the velocity, it is also interesting that the initial radius that gives the best fit, r₀ = 2.6 × 10¹⁵ cm, is close to that which gives the best fit to the photospheric radius from the blackbody fitting of the SED at the early epochs, R_phot ≈ 3.2 × 10¹⁵ cm (Table 5). The final radius after ∼900 days is 7 × 10¹⁵ cm, and the velocity is 650 km s⁻¹.

As we discussed in Section 4.3, an important constraint on the source of the Hα emission is the relation of the narrow unscattered line and the scattered wings, with the fraction of the former approximately given by ∝exp (− τ_e) for a planar geometry. Because the typical optical depth required for the wings is 2–5, depending on the temperature, this would in general give a strong narrow line. This is indeed observed at early time, but it disappears at later epochs at the same time as the blueshift starts (Figure 12). In this scenario, this may be explained by the fact that the source of the Hα photons become increasingly spread out in velocity, reflecting the local, accelerated velocity, but now spanning an increasing velocity range. The peak flux will decrease with the increasing velocity of this material, as observed. One therefore obtains a consistency check between the flux of the unscattered emission and the velocity shift. Note that the narrow CSM line most likely comes from a different, more distant component than the broad lines, based on its constant velocity and different flux evolution (Figure 18).

The velocity of this radiatively accelerated material is considerably lower than the ∼3000 km s⁻¹ one infers from the X-rays. After a time of t ≈ r₀/(V_s − V_acc) ≈ 1.0(r₀/2.6 × 10¹⁵cm)/(V_s/650 km s⁻¹ − 1) yr, the shock will sweep up the accelerated shell. For this not to happen too early, the shock velocity interior to the Hα-emitting shell has to be below ∼1500 km s⁻¹, depending on the velocity of the accelerated shell, corrected for the LOS angle. As discussed earlier, a reason for a lower shock velocity may be that the shell is anisotropic with the highest column density where the broad lines arise. The shock velocity will then be lower than that inferred from the X-rays, which are likely to come from directions of lower column density (see the next section).

The mass of the accelerated gas does not need to be large and is likely to be small. The scattering layer only has to have a τ_e ≳ 1, corresponding to ∼0.14(r/3 × 10¹⁵ cm)²(Ω/4π)  M_☉, where r is the radius of the shell and Ω the solid angle of the shell. To accelerate it to ∼1000 km s⁻¹ only takes ∼1.5 × 10⁴⁸(Ω/4π) erg, which is small compared to the total radiated energy. Most of the mass in the CSM is instead in the optically very thick region inside the accelerated layer.

The high luminosity, ∼3 × 10⁴³ erg s⁻¹ at maximum, and the large total radiated energy, ≳ 6.5 × 10⁵⁰ erg (Section 3.2), require an efficient conversion of kinetic to radiative energy. In Section 4.2 we argued that the flux from the optical and NIR up to ∼350 days is dominated by the direct flux from the SN, and most of the NIR flux is from the echo after this epoch. We now discuss the energetics in terms of the shock propagation through a dense envelope.

The shock breakout for extended SNe has been discussed by several authors (Falk & Arnett 1977; Grasberg & Nadyozhin 1987; Moriya et al. 2011, 2013; Chevalier & Irwin 2011; Ginzburg & Balberg 2012). For large optical depths the shock will be radiation dominated with a width τ_e ∼ c/v (Weaver 1976). Chevalier & Irwin (2011) estimate the diffusion timescale of the CSM, assumed to have ρ∝r⁻², as

$$\begin{eqnarray} t_{\rm diff} &\approx & 6.6 \left({\dot{M} \over 0.1 \ \ M_\odot \ \rm yr^{-1}}\right) \left({u_{\rm w} \over 100 \ \rm km\ s^{-1}}\right)^{-1} \nonumber \\ &&\times\,\left({\kappa \over 0.34 \ \rm cm^2 \ g^{-1}}\right) \rm days. \end{eqnarray} \tag{ 2 }$$

Here $\dot{M}$ is the mass-loss rate, u_w is the wind velocity, and κ is the opacity. For the mass-loss rates we derive below, this is likely to be short for the epochs of interest here. As the shock approaches the surface at τ_e ≲ c/v, a viscous shock will form (for a discussion, see Chevalier & Irwin 2011). If the circumstellar density is high, the viscous shock will be radiative, implying an efficient conversion of kinetic to radiative energy.

The cooling time for the forward shock is given by t_cool = 3kT/n_eΛ, where the cooling rate can be approximated by $\Lambda = 2.4\times 10^{-23} T_8^{0.5}\,\rm erg\,s^{-1}\ cm^3$ for temperatures above ∼2 × 10⁷ K. For close to solar abundances, the shock temperature is given by T_e = 1.2 × 10⁸(V_s/3000 km s⁻¹)² K. For an ejecta profile given by ρ_ejecta∝r⁻ⁿ, the shock radius is

$$\begin{eqnarray} R_{\rm s} &=& 9.47\times 10^{15} {(n-2)\over (n-3)} \left({V_{\rm s,320} \over 3000 \ \rm km\ s^{-1}}\right) \left({t \over {\rm years}}\right)^{(n-3)/(n-2)} \end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray} &=& 1.23\times 10^{16} \left({V_{\rm s,320}\over 3000 \ \rm km\ s^{-1}}\right) \left({t \over {\rm years}}\right)^{0.82} \ \rm cm, \end{eqnarray} \tag{ 4 }$$

for n = 7.6 as we find below. Based on the shock velocity derived by Ofek et al. (2014), we scale this and the following estimates to a shock velocity at 320 days, V_{s, 320}, of 3000 km s⁻¹. Note that this velocity may vary with the direction if the mass-loss rate is anisotropic (see below), as we argue. This gives a density immediately behind the forward shock of

$$\begin{eqnarray} n_{\rm s, e} &=& 8.1\times 10^{8} \left({\dot{M} \over 0.1 \ \ M_\odot \ \rm yr^{-1}}\right) \left({u_{\rm w} \over 100 \ \rm km\ s^{-1}}\right)^{-1} \nonumber \\ &&\times\,\left({V_{\rm s,320} \over 3000 \ \rm km\ s^{-1}}\right) \left({t \over {\rm years}}\right)^{-1.64} \ \rm cm^{-3}, \end{eqnarray} \tag{ 5 }$$

which leads to

$$\begin{eqnarray} t_{\rm cool}& =& 26.6 \left({\dot{M} \over 0.1 \ \ M_\odot \ \rm yr^{-1}}\right)^{-1} \left({u_{\rm w} \over 100 \ \rm km\ s^{-1}}\right) \nonumber \\ &&\times\, \left({V_{\rm s,320} \over 3000 \ \rm km\ s^{-1}}\right)^{3} \left({t \over {\rm years}}\right)^{1.46} \rm days. \end{eqnarray} \tag{ 6 }$$

Therefore, the forward shock should be radiative for several years as long as the shock is in the high-density shell. Further, assuming that the ingoing X-ray flux from the shock is thermalized in the ejecta and cool shell behind the shock, the blackbody luminosity is given by $(1/4) \dot{M} V_{\rm s}^3/u_{\rm w}$. An equal amount will partly be absorbed and ionize the preshock gas and partly escape as the observed X-ray flux. Using this luminosity for the radiation density, the ratio of Compton to free–free cooling is then

$$\begin{eqnarray} &&{P_{\rm Compton}\over P_{\rm free-free}} = 7.4\tau _e \left({V_{\rm s} \over 10^4 \ \rm km\ s^{-1}}\right)^4 \end{eqnarray} \tag{ 7 }$$

(Chevalier & Irwin 2012). Therefore, for shocks with velocity below ∼5000 km s⁻¹, free–free cooling dominates, unless the optical depth is very high.

For a general circumstellar density given by $\rho = \dot{M} /(4 \pi u_{\rm w} r_0^2) (r_0/r)^s$, the ejecta velocity at the shock depends on the mass-loss rate and time as

$$\begin{equation} V_{\rm s} \propto \left({ \dot{M} \over v_{\rm w}} \right)^{-1/(n-s)} t^{-(3-s)/(n-s)}, \end{equation} \tag{ 8 }$$

(e.g., Fransson et al. 1996), assuming the interaction can be described by a similarity solution. If the mass-loss rate is a function of polar angle, V_s will therefore depend on angle as well. For a radiative shock we find for the luminosity

$$\begin{eqnarray} L &=& 2 \pi \rho V_{\rm s}^3 r^2 = {1 \over 2} {\dot{M} \over u_{\rm w}} \left(r_0 \over r\right)^{s-2} V_{\rm s}^3 \nonumber \\ &&\quad\propto \left(\dot{M} \over u_{\rm w}\right)^{(n-5)/(n-s)} t^{-[15+s(n-6)-2n]/(n-s)} . \end{eqnarray} \tag{ 9 }$$

For s = 2 we obtain L∝t^{−3/(n − 2)}.

The fit of Equation (9) to the data in Figure 6 implies a value of n = 7.6 for s = 2, as shown by the dashed line in this figure. The break at ∼320 days in the light curve can either be caused by the breakout of the shock through the dense shell, or as a result of a transition to a momentum-conserving phase, occurring when the swept-up mass is comparable to the ejecta mass (Ofek et al. 2014). The latter explanation has, however, been contested by Moriya (2014), who find that the transition to the momentum-driven phase gives too smooth and slow a decrease of the luminosity. As we discuss in Section 4.7, the breakout in a bipolar shell may be compatible with this.

For s = 2 (consistent with the X-ray light curve, see below) we get

$$\begin{eqnarray} L &=& 8.51 \times 10^{42} \left({\dot{M} \over 0.1 \ \ M_\odot \ \rm yr^{-1}}\right) \left({u_{\rm w} \over 100 \ \rm km\ s^{-1}}\right)^{-1} \nonumber \\ &&\times\,\left({V_{\rm s,320} \over 3000 \ \rm km\ s^{-1}}\right)^3 \left({t \over 320 \ \rm days}\right)^{-0.537}\ \rm erg\ s^{-1}. \quad \end{eqnarray} \tag{ 10 }$$

For a luminosity at the break at ∼320 days of 9.33 × 10⁴² erg s⁻¹ we then find

$$\begin{equation} \dot{M} = 0.11 \left({u_{\rm w} \over 100 \ \rm km\ s^{-1}}\right) \left({V_{\rm s,320} \over 3000 \ \rm km\ s^{-1}}\right)^{-3} \ \ \ M_\odot \ \rm yr^{-1}. \end{equation} \tag{ 11 }$$

The total mass swept up is then

$$\begin{equation} \Delta M = \dot{M} {V_{\rm s} \over u_{\rm w}} t = 2.89 \left({V_{\rm s,320} \over 3000 \ \rm km\ s^{-1}}\right)^{-2} \ \ M_\odot . \end{equation} \tag{ 12 }$$

Both the mass loss and total mass are sensitive to the expansion velocity of the ejecta. In this estimate we assume that the ejecta with a velocity of ∼3000 km s⁻¹ dominates the energy input to the optical light curve. In reality, there should be a range in velocities, and there is therefore a considerable uncertainty in this estimate. The fact that we observe both hard X-rays with a temperature corresponding to a shock velocity of ∼3000 km s⁻¹ and with a column density corresponding to an electron scattering depth of τ_e ≲ 1, as well as high column density gas with τ_e ≳ 3, argues for a highly anisotropic CSM. This is further strengthened by the blue shoulder seen by Borish et al. (2014) in the He i λ10, 830 line in the span ∼100–200 days after explosion. The velocity of this decreases during this interval from ∼6000 km s⁻¹ to ∼5000 km s⁻¹, indicating deceleration of this material. The shock velocity in the X-ray obscured regions may, however, be considerably lower (Equation (8)). The mass-loss rate above, as well as the total mass lost, should therefore be considered as lower limits. Note, however, that while the mass-loss rate scales with the velocity of the CSM, the total mass lost is independent of this parameter.

Ofek et al. (2014) find a considerably higher mass-loss rate of ∼0.8  M_☉ yr⁻¹. The main reason for this is that they are scaling to a higher wind velocity of u_w = 300 km s⁻¹, while we find u_w ≈ 100 km s⁻¹. They also assume an efficiency of ∼0.25 in converting the shock energy into the observed luminosity. The reason for this is not clear. Another important difference is that they assume an ejecta profile n = 10, close to that found by Matzner & McKee (1999) for the ejecta of a radiative envelope, while we derive n ≈ 7.6 from our bolometric light curve. Their larger value of n is a result of the flatter light curve they derive from the R band only, L∝t^−0.38 compared to our L∝t^−0.54 and using L∝t^{−3/(n − 2)} (Equation (9)).

Even considering the above uncertainties, the mass-loss rate and the total mass lost are very large, but as discussed in Section 4.1, these are of the same magnitude as that inferred from the CSM of local LBVs, like Eta and AG Carinae. We discuss the implications of this further in Section 4.7, but we first place it in relation to other Type IIn SNe.

Although interesting as a case by itself, it is at least as interesting to put SN 2010jl into the context of other Type IIn SNe. There have been several Type IIn SNe that show similarities to SN 2010jl to various degrees, although in most cases these events are less extreme in terms of luminosity or total radiated energy. As we show in this section, most of these, SNe 1995N, 1998S, 2005ip, and 2006jd, although observationally quite different, are related to SN 2010jl, and two others recently discussed, SN 2009ip and SN 2010mc, while having some properties in common, show major differences from SN 2010jl.

SN 1998S is one of the best-observed Type IIn SNe and is interesting as a less extreme case of a Type IIn SN. Initially it showed typical Type IIn signatures with narrow symmetric lines (Leonard et al. 2000; Fassia et al. 2001) dominated by electron scattering of H and He i lines (Chugai 2001). The symmetric lines disappeared after about a week, and instead broad P-Cygni profiles with an expansion velocity of ∼7000 km s⁻¹ appeared. Later optical spectra at ≳ 70 days showed increasingly box-like profiles typical of circumstellar interaction, with Hα by far the strongest and a steep Balmer decrement. Spectra later than a year showed a strong suppression of the red wing of Hα, as well as Lyα, indicating dust formation in the ejecta or reverse shock (Leonard et al. 2000; Pozzo et al. 2004; Fransson et al. 2005). As was remarked earlier, these line profiles were very different from those in SN 2010jl.

High-velocity ejecta profiles of Hα were also seen for SN 1995N (Fransson et al. 2002), SN 2005ip, and 2006jd (Smith et al. 2009; Stritzinger et al. 2012). For the latter two, maximum ejecta velocities of 16, 000–18, 000 km s⁻¹ were seen at early times (Smith et al. 2009; Stritzinger et al. 2012). For SN 2006jd a high-velocity wing at ∼7000 km s⁻¹ could be seen even at 1540 days. In addition, an intermediate-velocity component with an FWHM of ∼1800 km s⁻¹ was seen in both SNe. There were no strong indications of electron scattering wings in these SNe, although this may have contributed to the intermediate component or faded away before their discovery, as for SN 1998S.

In the last HST spectra of SN 1998S, broad features from O i λλ1302, 1356 were seen, indicating processed material (Fransson et al. 2005). Recently, Mauerhan & Smith (2012) found that at 14 yr the spectrum of SN 1998S was dominated by strong lines of [O i–iii]. This shows that the reverse shock has now propagated close to the core of the SN and that newly processed gas is dominating the spectrum. There is therefore no doubt that a core collapse has taken place. For SN 2010jl this phase has not yet occurred.

Hard X-rays with kT ∼ 10 keV and a luminosity of ∼(5–8) × 10³⁹ erg s⁻¹ were observed for SN 1998S two to three years after explosion (Pooley et al. 2002). The X-ray light curve of SN 2006jd stayed nearly flat with an unabsorbed luminosity of (3–4) × 10⁴¹ erg s⁻¹ in the span 400–1600 days (Chandra et al. 2012a), lower than for SN 2010jl. Also, the column densities of these SNe, ≲ 1.5 × 10²¹ cm⁻², were considerably lower than for SN 2010jl and did not show any strong time evolution as for SN 2010jl.

High-resolution spectra of SN 1998S by Fassia et al. (2001) exhibited a low-velocity P-Cygni line with a velocity of 40–50 km s⁻¹ and a higher velocity extension with velocity 350 km s⁻¹. The low-velocity component argues for a red supergiant progenitor. The origin of the higher velocity component is not clear. Variations of the wind velocity are also seen in LBVs and S Doradus stars, and such a progenitor is probably not excluded. In the case of SN 2005ip, the narrow component was only marginally resolved with FWHM ∼120 km s⁻¹ (Smith et al. 2009).

The very different optical spectra of SN 1998S and the other mentioned SNe compared to SN 2010jl can naturally be explained as a result of the different CSM densities and shock velocities. The mass-loss rate of SN 1998S was from late observations estimated to be quite modest by Type IIn standards, ∼2 × 10⁻⁵  M_☉ yr⁻¹ (Fassia et al. 2001). The time of optical depth unity to electron scattering is for a steady wind (for simplicity assumed to extend to infinity) given by

$$\begin{eqnarray} t(\tau _{\rm e}=1)&=&{\kappa _{\rm T}\dot{M} \over 4 \pi u_{\rm w} V_{\rm s}} \nonumber \\ &=&\,680 \left({\dot{M} \over 0.1 \ \ M_\odot \ \rm yr^{-1}}\right) \left({u_{\rm w} \over 100 \ \rm km\ s^{-1}}\right)^{-1} \nonumber \\ &&\times\, \left({V_{\rm s}\over 3000 \ \rm km\ s^{-1}}\right)^{-1} \ \rm days, \end{eqnarray} \tag{ 13 }$$

where we have scaled the parameters to SN 2010jl. Note, however, that in Section 4.5 we argue that V_s is considerably lower in the directions we observe. For SN 1998S with $\dot{M} \approx 2\times 10^{-5} \ \ M_\odot \ \rm yr^{-1}$, u_w ≈ 50 km s⁻¹, and V_s ≈ 7000 km s⁻¹, we find that t(τ_e = 1) ≈ 0.1 days. The fact that electron scattering wings were observed for several days argues for a denser shell at ∼10¹⁵ cm from the progenitor with $\dot{M} \approx 3\times 10^{-3} (u_{\rm w} /10 \, {\rm km\ s^{-1}}) M_\odot \, {\rm yr^{-1}}$ (Chugai 2001).

Although there are uncertainties in these quantities, one can therefore conclude that the fast disappearance of the electron scattering wings and the transparency to the processed core in SN 1998S (and the other discussed medium-luminosity Type IIns) compared to SN 2010jl is consistent with the much lower mass-loss rate of the former. Because the X-ray column density is proportional to the electron-scattering optical depth, this also explains the much lower X-ray column densities for these SNe. This argument also applies to the even higher luminosity "superluminous" Type II SNe (e.g., Gal-Yam 2012).

The UVOIR luminosity of SN 1998S was at the peak ∼2 × 10⁴³ erg s⁻¹, but a blackbody fit gave a considerably higher luminosity of ∼6 × 10⁴³ erg s⁻¹ (Fassia et al. 2000). This is similar to the peak luminosity of SN 2010jl. The initially much higher effective temperature, ∼18, 000 K, compared to ∼7300 K for SN 2010jl (Zhang et al. 2012), however, had the consequence that the R-band magnitude at maximum was only ∼−19.1, compared to ∼−20.0 for SN 2010jl. A main difference compared to SN 2010jl was that the decay was nearly exponential up to ∼100 days with a fast decay rate of ∼25 days. Including only the UVOIR luminosity, we estimate an uncertain total energy of ∼1.1 × 10⁵⁰ erg. Using instead the bolometric luminosity from the blackbody fits by Fassia et al., one gets a factor of two to three higher radiated energy.

As Pozzo et al. (2004) argue, the early light curve is likely to be dominated by the released shock energy, and the main reason for the high initial luminosity was the large extent of the progenitor, as indicated by the dense CSM during the first days, discussed above. The fast decay and the lower radiated total energy, however, indicate a lower total mass of the CSM compared to SN 2010jl. Chugai (2001) estimate a total mass of ∼0.1 M_☉ in the CSM of SN 1998S, ∼2 orders of magnitude smaller than for SN 2010jl.

SN 2005ip had a moderate peak luminosity for a Type IIn SN, ∼4 × 10⁴² erg s⁻¹ (Smith et al. 2009; Stritzinger et al. 2012). It then decayed on roughly the ⁵⁶Co timescale to a nearly constant level at ∼200 days, dominated by the NIR. The optical luminosity during this plateau phase was ∼2.5 × 10⁴¹ erg s⁻¹, decaying slowly as t^−0.3 from ∼200 to ≳ 1600 days. From blackbody fits, Stritzinger et al. find a luminosity of ∼8 × 10⁴¹ erg s⁻¹ for the NIR warm component. Stritzinger et al. also discuss optical and IR observations of another interesting Type IIn, SN 2006jd. This SN had a similar early luminosity but considerably higher optical luminosity in the plateau phase, ∼8 × 10⁴¹ erg s⁻¹, and nearly constant from ∼200 to ≳ 1600 days.

From Stritzinger et al. (2012) we estimate the total radiated energy of SN 2005ip to be ∼4 × 10⁴⁹ erg from the photospheric emission and ∼7 × 10⁴⁹ erg in the dust component, and for SN 2006jd to be ∼10⁵⁰ erg from the photospheric emission and ∼2 × 10⁵⁰ erg in the dust component. Although the luminosity and energy are high, both of these SNe are therefore considerably less extreme in terms of mass loss and degree of interaction compared to SN 2010jl.

An independent indicator of strong mass loss is the large observed N/C ratio, characteristic of CNO processed material in the CSM. This is consistent with the fact that high N/C ratios have been observed for all Type IIn, IIb, and IIL SNe observed with HST: SN 1979C, 1993J, 1995N, 1998S, and SN 2010jl (Section 4.1).

A common feature of all these SNe is also the presence of high-ionization lines from the CSM. Ultraviolet spectra of SN 1998S from day 28 to day 485 showed increasingly strong lines from C iii–iv and N iii–v originating in the CSM. Also, SN 2005ip and 2006jd revealed a number of narrow high-ionization lines from the CSM. For SN 2006jd, this included lines from [Fe x–xi] and [Ar x], and SN 2005ip showed even higher ionization lines, including [Fe xiv] λ5302.9 and [Ar xiv] λ4412.3 (Smith et al. 2009). High-ionization lines were also seen in SN 1995N, which showed a spectrum very similar to SN 2006jd (Fransson et al. 2002). We note that Hoffman et al. (2008) observed similar high-ionization coronal lines in the Type IIn SN 1997eg. Nearly all of these SNe had a strong X-ray flux. The connection between this and the presence of circumstellar lines therefore indicates that the latter are excited by the X-rays in most of these cases. Conversely, the presence of circumstellar lines may be used as a diagnostic of a strong X-ray flux.

Near-IR spectra and photometry of SN 1998S by Fassia et al. (2000) revealed a dust excess already at 136 days. Later observations by Pozzo et al. (2004) showed a comparatively hot dust spectrum in the first observations, with a dust temperature ∼1000–1250 K at ∼1 yr, decreasing to ∼750–850 K at 1198 days. Pozzo et al. argue for a dust echo for the first epochs, while the later emission may have an origin in the condensed dust in the cool dense shell. In contrast to SN 2010jl, there is no problem with dust evaporation at the shock radius for epochs later than ∼1 yr because the bolometric luminosity from the SN was then ≲ 10⁴¹ erg s⁻¹ (Pozzo et al. 2004). The dust evaporation radius is then (1–2) × 10¹⁶ cm (Table 9), and the shock radius is ∼3 × 10¹⁶ cm for a shock velocity of 10⁴ km s⁻¹.

Also, the Type Ibn SN 2006jc showed evidence for dust formation behind the reverse shock (Smith et al. 2008b; Mattila et al. 2008). Even at maximum, the luminosity of this SN was ≲ 10⁴² erg s⁻¹, declining to ≲ 2 × 10⁴¹ erg s⁻¹ later than 100 days (Mattila et al. 2008). The expansion velocity was estimated to be ≳ 8000 km s⁻¹, indicating a shock radius of ≳ 7 × 10¹⁵ cm at 100 days. The high dust temperature, ∼1800 K at maximum, argues for carbon dust. From Table 9 we then find a dust evaporation radius of ∼5.6 × 10¹⁵ cm at 100 days for carbon dust with a size of 1 μm. Because of the much lower luminosity compared to SN 2010jl, dust formation behind the reverse shock is therefore possible.

Gerardy et al. (2002) discuss NIR photometry and spectra for several Type IIn SNe. The best observed of these is SN 1995N with NIR observations from 730 to 2435 days after explosion. During the first observations, the NIR luminosity was ∼(7–10) × 10⁴¹ erg s⁻¹, depending on the assumed dust emissivity. It then slowly decayed by a factor of ∼10 at the time of the last observations. The dust temperature was 700–900 K during most of the evolution. The other SNe observed also showed similar high temperatures. From the fading of the red wing of the Hα line in SN 1995N, late dust formation at an age of ∼1000 days was indicated (Fransson et al. 2002).

Evidence for dust formation for SN 2005ip was first presented for this SN based on NIR photometry by Fox et al. (2009). Further observations in the NIR and with Spitzer showed evidence for two dust components with different temperatures (Fox et al. 2010). Fox et al. argue that the hot component comes from newly formed dust in the ejecta or reverse shock, and the cool emission comes from preexisting dust heated by the late circumstellar interaction. Independent evidence for dust came from line profile asymmetries (Smith et al. 2010a).

Both SN 2005ip and 2006jd showed strong IR excesses already shortly after the explosion. The fit to the warm components reveals for both SNe a maximum dust temperature of ∼1600 K at 100–200 days, decreasing to ∼1000 K at 1000 days. The luminosity of the dust component of SN 2006jd increased to ∼3 × 10⁴² erg s⁻¹ at ∼500 days and then decayed slowly to ∼5 × 10⁴¹ erg s⁻¹ at ∼1700 days. The fraction of the bolometric luminosity in this warm component increased already at ∼100 days to ∼80% and to even higher values at later times. SN 2005ip showed a similar behavior, although the luminosity of the warm component was only ∼5 × 10⁴¹ erg s⁻¹ and at a more constant level.

While we believe that an echo from preexisting dust may dominate the NIR emission in SN 2010jl, the other discussed mechanisms may well be important for other Type IIn SNe. All of these are physically plausible, and their relative importance depends on the specific case in terms of progenitor mass-loss rate, dust shell geometries, SN luminosity, including the X-rays, and viewing direction.

Besides the discussed SNe, two recent Type IIn SNe, SN 2009ip (Smith et al. 2010b; Foley et al. 2011; Pastorello et al. 2013; Mauerhan et al. 2013) and SN 2010mc (Ofek et al. 2013), have received considerable attention. Both SNe showed minor outbursts with M_R ∼ −14–15 before the last major eruption. The main outburst had an absolute magnitude of M_R ∼ −18, corresponding to a luminosity of ∼(5–8) × 10⁴² erg s⁻¹, a factor of ∼4–6 lower than SN 2010jl. Another difference is that the flux decayed considerably faster during the first ∼60 days, with an e-folding decay timescale of ∼20 days. From the bolometric light curve we estimate a total radiated energy of ∼2 × 10⁴⁹ erg for SN 2009ip and a similar energy for SN 2010mc. This is more than an order of magnitude lower than what we estimate for SN 2010jl.

Both narrow lines with broad electron scattering wings and broad ejecta lines were seen. Pastorello et al. (2013) stress the important observation that for SN 2009ip, already in the minor outbursts a year before the most recent large outburst, expanding material at a velocity of ∼12, 500 km s⁻¹ was seen. It is therefore clear that high velocities are not a unique signature of a core collapse, but they can also occur in stages before this. In connection to the 2012 September eruption, both an electron scattering profile with FWHM ∼550–800 km s⁻¹ and a broad absorption extending to 14, 000–15, 000 km s⁻¹ were seen.

Based on the large velocities and other arguments, Mauerhan et al. (2013) propose a core collapse scenario, which is, however, challenged by Pastorello et al. (2013). From the fact, mentioned above, that the previous outbreaks also showed similar high velocities, high luminosity, and long term variability, they propose that SN 2009ip is instead a pulsational pair-instability event and that the star may have survived the 2012 September outburst.

From these comparisons we conclude that there are similarities between SN 2010jl and these two objects. All three objects could be classified as Type IIn SNe, based on the narrow lines with profiles typical of electron scattering. It is clear that they all have very dense CSM into which the shock waves are propagating. At least for SN 2009ip there is evidence for preexisting dust that may have been formed a few years before the last eruption (Foley et al. 2011; Smith et al. 2013), like SN 2010jl.

The main differences between these objects and SN 2010jl is that the latter showed a considerably higher peak luminosity, slower decay, and an order of magnitude higher total radiated energy than did SNe 2009ip and 2010mc. We therefore believe that the basic mechanism for these objects is different from that in SN 2010jl. The fact that no very broad lines with velocities typical of core collapse SNe were seen for SN 2010jl is less important. As we have already argued, this is mainly an effect of different mass-loss rates and total mass lost.

In this section we summarize the main points of the previous discussion and discuss how this information can be put together into a coherent scenario for SN 2010jl.

Most of the bolometric luminosity is produced by the radiation from the radiative shock with a velocity of up to ∼3000 km s⁻¹, which propagates through the dense CSM resulting from a mass-loss rate of ≳ 0.1 M_☉ yr⁻¹ and a velocity of ∼100 km s⁻¹, which may be the result of a previous LBV-like eruption. The total mass lost is ≳ 3 M_☉. The ingoing X-rays from the shock will be thermalized at early epochs in the dense shell behind the shock and later in the ejecta. This will there be converted into UV and optical continuum radiation with a spectrum close to a blackbody. Most of the outgoing X-rays will be absorbed by the preshock wind and will there give rise to UV and optical emission lines.

An important issue is the relative location of the source of the UV and optical line emission and the electron scattering region. The fact that the strong high-ionization UV lines, like the N iv], C iv, and N iii] lines, at early epochs had strong electron scattering wings besides the narrow component shows that at least a large fraction of these arise in or interior to the electron scattering region. The same is true for the Balmer lines. As we have already discussed in Section 4.1, the narrow lines most likely arise in a more extended region outside the denser part of the CSM. Because the velocity to which the gas is accelerated is ∝r⁻² (Equation (1)), the absence of line shifts of the narrow component is consistent with a distance ≳ 2 × 10¹⁶ cm of this (Section 4.1).

To explain the broad wings of the lines, the electron scattering optical depth of this CSM has to be ≳ 3. The mass-loss rates we find correspond to a total optical depth to electron scattering of a wind with outer radius R_shell

$$\begin{eqnarray} \tau _{\rm tot} &=& 1.56 \left({\dot{M} \over 0.1 \ \ M_\odot \ \rm yr^{-1}}\right) \left({u_{\rm w} \over 100 \ \rm km\ s^{-1}}\right)^{-1} \nonumber \\ &&\times\,\left({V_{\rm s,320} \over 3000 \ \rm km\ s^{-1}}\right)^{-1} \left({t \over {\rm years}}\right)^{-0.82} \left(1 - {R_s \over R_{\rm shell} } \right)\quad\;\; \end{eqnarray} \tag{ 14 }$$

if completely ionized. From this it is clear that to get large enough τ_tot either the shock velocity has to be lower than that corresponding to the X-ray temperature, ∼3000 km s⁻¹, or the mass-loss rate in these directions is higher than the average, or most likely both, as we discuss in the end of this section.

One can estimate the extent of the ionized region, assuming that most of the X-ray and EUV emission from the cooling shock is absorbed by the CSM in front of the shock and will there give rise to a Strömgren zone (see, e.g., Fransson 1984 for a similar situation). We also assume that the X-rays emitted inward are thermalized by the cool shell and ejecta, resulting in optical and UV emission but only contributing marginally to the ionization. Balancing the number of ionizing photons, _iL/hν_ion, with the number of H ii recombinations, 4πα_B∫n_e(r)²r²dr, where _i is the fraction of the energy going into ionizations, and with τ_e = σ_T∫n_edr, one obtains

$$\begin{equation} \tau _e = { \sigma _T \over \alpha _B } {m_p u_{\rm w} \over \dot{M}} {\epsilon _i L\over h\nu _{\rm ion}}. \end{equation} \tag{ 15 }$$

With $\alpha _B = 2\times 10^{-13}\, T_4^{-0.7}\ {\rm cm^{3} \ s^{-1}}$ one finds

$$\begin{eqnarray} \tau _e &=& 4.05 \epsilon _i \left({L\over 10^{43}\,\rm erg\,s^{-1}}\right) T_4^{0.7} \left({\dot{M} \over 0.1 \ \ M_\odot \ \rm yr^{-1}} \right)^{-1} \nonumber \\ &&\times\,\left({u_{\rm w}\over 100 \ \rm km\ s^{-1}} \right). \end{eqnarray} \tag{ 16 }$$

Assuming that the X-ray/EUV luminosity is produced by the shock and given by Equation (10) (for n = 7.6), we get

$$\begin{equation} \tau _e = 1.9 \epsilon _i T_4^{0.7} \left({V_{\rm s,320} \over 3000 \ \rm km\ s^{-1}}\right)^3 \left({t \over 320 \ {\rm days}}\right)^{-0.54} . \end{equation} \tag{ 17 }$$

Therefore, one obtains naturally a width of the ionized zone in front of the shock of the order of unity independent of the mass-loss rate, wind velocity, or radius. This assumes that the total optical depth of the wind exceeds this value.

To estimate the conversion efficiency from X-rays to Hα, as well as to determine the general UV and optical spectrum expected, we have made some exploratory calculations using CLOUDY (Ferland et al. 2013). For this we have taken a simple free–free X-ray spectrum and a density profile given by a ρ∝r⁻² wind. The X-ray temperature was 10 keV, and we studied a range of shock luminosities and mass-loss rates. A problem here is that for the most interesting parameters the electron scattering optical depth is larger than unity (Equation (17)), which cannot be handled properly by CLOUDY. As pointed out by Chevalier & Irwin (2012), one effect of this is that the state of ionization is underestimated because the relevant quantity for this is the ratio of the radiation to matter density. This is given by ζ = τ_eL/nr², increasing the usual ionization parameter by a factor of τ_e. Nevertheless, the qualitative results are interesting.

With regard to the efficiency of X-ray to Hα conversion, we find that it is very difficult to obtain an efficiency larger than ∼5%–7%, and then only for large column densities and for densities less than ∼10¹⁰ cm⁻³. Above this density the efficiency decreases rapidly due to thermalization of the Hα line. The electron density we infer from the bolometric luminosity in Section 4.5 is for n(He)/n(H) = 0.1

$$\begin{eqnarray} n_{e} &=& 2.86\times 10^{9} \left({\dot{M} \over 0.1 \ \ M_\odot \ \rm yr^{-1}} \right) \left({u_{\rm w}\over 100 \ \rm km\ s^{-1}} \right)^{-1} \nonumber \\ &&\times\,\left({r \over 3\times 10^{15} \ \rm cm} \right)^{-2} \ \rm cm^{-3}, \end{eqnarray} \tag{ 18 }$$

which is in the range where we expect a high Hα efficiency. Further, the observed maximum Hα luminosity was ∼1 × 10⁴² erg s⁻¹ (Figure 13). Although we find that there is some contribution from the photospheric emission from ionizations in the Balmer continuum, the observed Hα luminosity implies a total X-ray luminosity of ≳ 10⁴³ erg s⁻¹. There is therefore a rough agreement between the bolometric luminosity, the Hα luminosity, and a high Hα efficiency.

Compared to this, the observed level of X-rays is ∼10⁴² erg s⁻¹ (Chandra et al. 2012b). This is by itself no problem because most of the X-rays may be absorbed by the preshock gas, and this is in fact needed to explain the UV emission lines. A major problem is, however, that, as discussed in the Introduction, the X-rays at 59 days indicated a column density of ∼10²⁴ cm⁻², decreasing to 3 × 10²³ cm⁻² at 373 days.¹³ This column density corresponds to an electron scattering depth of τ_e ≲ 1, which is too low to explain the line profiles in the optical.

There are several possible explanations for this discrepancy. Ofek et al. (2014) argue that the column density could be decreased by a higher ionization due to a large electron-scattering optical depth. As we argue above, the optical depth of the ionized gas is limited, and the effect will not be dramatic. Instead, we believe that the different column densities are due to large-scale asymmetries in the outflow, giving rise to different column densities in different directions. Alternatively, it could be due to small-scale inhomogeneities resulting in a leakage of X-rays in the low-density regions. This is also supported by the low column density that Ofek et al. (2014) found from their NuSTAR + XMM observations at 728–754 days. We discuss further evidence for these possibilities below.

For a wind, most of Hα originates close to the shock, as can be seen from $dL/dr = 4 \pi \alpha _B r^2 n_e^2 \propto 1/r^2$. This is also the region of largest optical depth to electron scattering. Emission and scattering therefore take place in the same region, although some of the Hα emission also occurs at low optical depths, resulting in a narrow line core as long as the bulk velocity of the emitting material is low (Section 4.4.3). From our CLOUDY calculations we find that high-ionization lines, like N iii] λ1750, N iv] λ1486, and C iv λλ1548, 1551, arise interior to the Hα-emitting region and therefore experience the same electron scattering as Hα. We also find that the luminosities of these lines are comparable to Hα, as is observed. For constant X-ray luminosity, the Hα/Hβ ratio increases as the density decreases, which may explain the trend seen in Figure 13. The temperature in the Hα-emitting zone is ∼(1.5–2) × 10⁴ K.

A related model is discussed by Dessart et al. (2009), who calculate the line formation in Type IIn SNe with application to SN 1994W. Although the authors point out that this is only a preliminary attempt and related to a specific scenario, this is the only self-consistent modeling of the line formation we are aware of. The density of the envelope in the model by Dessart et al. (2009) is 3 × 10⁹ cm⁻³, which is similar to what we find for the density in front of the shock. Dessart et al. also point out a number of useful signatures, depending on the relative location of the region where the Balmer emission originates and the electron scattering region. In particular, they find that if the photons are internally generated, Hα, Hβ, and Hγ form at increasing optical depth. The electron scattering depth also increases for these lines, leading to increasingly strong wings for Hβ and Hγ compared to Hα. If the lines, on the other hand, are created outside the scattering region, they are expected to have similar line profiles.

In principle, these possibilities can be tested with our observations. The limited S/N and relatively steep Balmer decrement makes it difficult to see any differences between these line profiles. The best set of line profiles are from our spectrum from X-shooter in Figure 31. This does show some minor differences in the width of the lines, but these are sensitive to the exact way the continuum is subtracted as well as to blending by other lines. The latter is especially important for the He i λ10, 830 line, which is blended with Paγ; the red wing of Hβ also shows indications of blending. It is therefore premature to draw any firm conclusions.

As argued in Section 4.4.3, we believe that the bulk velocity of ∼600–700 km s⁻¹ of the Balmer emitting region is a result of the preacceleration of the circumstellar material in front of the main shock by the intense radiation from the thermalized radiation from the shock. This is supported by the agreement between the observed velocity evolution and that predicted from the evolution of the bolometric luminosity. A surprising result is that, to produce the line shift of the Hα line, we required that most of the emitting material was moving with similar velocity relative to us. This in turn requires the flow to subtend a fairly small solid angle. The expansion does, however, not necessarily have to be in our LOS, which would increase the true expansion velocity by 1/cos θ, where θ is the angle between these directions.

Both the line shifts and the X-ray observations therefore give evidence for a highly asymmetric ejecta interaction in SN 2010jl. On a larger scale we find evidence for an asymmetric dust distribution (Section 4.2). In addition, the early polarization measurements by Patat et al. (2011) at 14.7 days after discovery showed a large, constant continuum polarization of 1.2%–2%, indicating an asphericity with axial ratio ∼0.7. Close to the center of Hα the polarization decreased to a low level. The wings of the line have, however, a polarization close to the continuum level. As suggested by the authors, this is probably an indication of another component dominated by recombination. Our high-resolution observations do show that, especially at early phases, the narrow component from the CSM is strong and will therefore dominate in the line center. Most likely this is produced mainly by recombination and is probably also coming from a more symmetric CSM, as indicated by the strong absorption component of the P-Cygni lines (Section 4.1).

Asymmetries have been discussed from time to time for Type IIn SNe. This includes the Type IIn SN 1988Z (Chugai & Danziger 1994), SN 1995N (Fransson et al. 2002), SN 1998S (Leonard et al. 2000; Fransson et al. 2005), and SN 2006jd (Stritzinger et al. 2012). In these cases it has been mainly disk-like or clumpy distributions that have been considered. A clumpy model does, however, not have the large-scale asymmetry needed to match the observed bulk velocity of hydrogen lines. A disk-like geometry also has problems because one would then expect the expansion into a disk to be cylindrically symmetric, which would not give the coherent velocity in the LOS indicated by the broad line profiles above.

Instead, we believe that a bipolar outflow may be more compatible with the observations. As was noted in Section 4.1, the expansion velocity of the molecular shell in Eta Carinae is highly anisotropic with a velocity of up to ∼650 km s⁻¹ at the poles (Smith 2006). Even more interesting is that most of the mass is ejected between 45° and the pole. Higher velocities up to ∼6000 km s⁻¹ are also seen, although little mass is involved (Smith 2008).

The initially small shift of the lines in SN 2010jl, however, requires this high-density shell to have a low velocity, ≲ 100 km s⁻¹, before the explosion, similar to what we see from the narrow lines. The increasing velocity shift in Hα may then be a direct representation of the gradual acceleration of this shell. The column density of the shell in Eta Carinae is ∼10²⁴ cm⁻² located at a radius between 3 × 10¹⁶ cm and 3 × 10¹⁷ cm (Smith 2006). This scales as N_H∝r⁻², so if one would observe it at an earlier stage with a radius of a few × 10¹⁵ cm, as in SN 2010jl, the column density would be two to three orders of magnitude higher, more than sufficient for explaining the large electron-scattering optical depths we have evidence for in the broad lines.

The planar geometry of the Hα-emitting gas may resemble that seen in Eta Carinae at high latitudes. Smith (2006) find above ∼60° latitude an almost perfectly planar shape of the molecular shell, containing most of the gas (see, e.g., Figure 4 in Smith 2006). If one would observe an explosion in this direction (or higher latitude), the expansion would clearly be planar. The large column density of the shell would also prevent the observation of the rear parts of the CSM.

The scenario we infer from the observations has many qualitative similarities to the one calculated by van Marle et al. (2010). Using two-dimensional hydrodynamical simulations, they have calculated the interaction of a core collapse SN with a dense circumstellar shell ejected two years before explosion. The total shell mass was in most cases 10 M_☉, while the ejecta mass for this shell mass was varied between 10–60 M_☉. Models with both spherical geometry and a density and mass distribution similar to the bipolar structure observed for Eta Carinae were calculated. Optically thin cooling, but no radiative transfer, was included. At the time the shock collides with the shell, the shock velocity is ∼5500 km s⁻¹ for the chosen parameters, but it decreases to 1000–2000  km s⁻¹ in the shell, depending on mass of ejecta, shell mass, and SN energy. Because of the large density and low velocity, implying a shock temperature of ≲ 10⁷ K, the shock becomes radiative. After the shock has penetrated the shell, the velocity again increases, and the shock then in most cases becomes adiabatic. This evolution illustrates what happens when an SN with "normal" energy interacts with a dense CSM. The low shock velocity resulting from this is in line with what is observed for SN 2010jl.

In their bipolar simulations (models D01–D03), the ejecta first interact with the equatorial region and then later with the polar region. Because of the smaller column density in the equatorial direction, the shock penetrates this region first, at which time the shock temperature increases rapidly. In the polar direction it takes a considerably longer time for the shock to reach the outer boundary of the shell, and the shock velocity is also lower. This may illustrate the range of velocities that may be present in an anisotropic CSM, and it may explain the different column densities inferred from the X-rays and the electron scattering wings, discussed above. These anisotropic models demonstrate nicely how one can have both high shock velocities (in the equatorial directions), giving rise to hard X-rays, and slow shocks still in the optically thick circumstellar shell (in the polar directions) at the same time. The drop in luminosity during the breakout phase in the bipolar models is L∝t^−α, where α = 3.6–4.4 (Figure 16 in van Marle et al. 2010). This depends on the parameters of the models, but it is at least in qualitative agreement with the observations, which show that L(t)∝t^−3.4 after the break (Section 3.2).

For the spherical models in van Marle et al. (2010), the light curves in general consist of a rapid rise when the shock encounters the shell and a slowly decreasing plateau. As the shock passes the outer shell, there is a rapid drop as the shock becomes adiabatic. Because of the gradual emergence of the shock with latitude, the bipolar case results in a smoother evolution of the light curve without the same sharp break as the spherical shell. This result depends on the angular dependence of the column density. A stronger concentration to the poles would give a sharper drop of the light curve, in line with what we see in SN 2010jl. The efficiency in converting kinetic energy into radiation was found to be in the range 10–40%, decreasing with increasing ejecta mass and expansion velocity of the shell (determining the distance of the shell from the SN). With an efficiency in this range, the radiated energy of ∼6.5 × 10⁵⁰ erg would correspond to an explosion energy of ∼(4 ± 3) × 10⁵¹ erg.

The fact that we do not see evidence for expansion in the opposite direction is a natural result of the obscuration of this region by the optically thick material in the core of the SN and from the ionized material exterior to this moving toward us. The decline in the flux at late epochs is a result of the decrease in the photospheric radius (see Table 5), which in principle might indicate that the extent of the photosphere is not large enough to obscure the receding side of the SN. However, the photospheric radius is the thermalization radius, which must be deep inside the τ_e = 1 radius. In our last spectra, at ∼1100 days the optical depth to electron scattering is likely to be ≳ 1. The obscuration of the back side of the SN by the scattering region even at late epochs is therefore not a problem. As we have already discussed, at late epochs the shock should have penetrated the dense circumstellar shell in the low column density regions close to the equator, while it is still inside the optically thick region in our LOS, although outside the photosphere.

With regard to the narrow lines, we note that a steady wind with a mass-loss rate of 10⁻³ M_☉ yr⁻¹, as in the quiescent state in Eta Carinae, and wind velocity of 100 km s⁻¹ corresponds to a density of ${\sim } 3 \times 10^{6} (\dot{M}/10^{-3} \ \ M_\odot \ \rm yr^{-1}) (u_w/100 \ \rm km\ s^{-1})^{-1} (r/10^{16}$ $\rm cm)^{-2} \ \rm cm^{-3}$, which is similar to what we find from the nebular diagnostics of the narrow lines for SN 2010jl, but below that of the Balmer lines. A larger radial extent of the narrow line region,as indicated from the ionization parameter (Section 4.1), is natural in this context.

The deep absorption component in the P-Cygni profile of the narrow Hα line (Figure 12) means that this material must have an appreciable covering factor of the underlying emission from the SN. The emission component of this, as well as the depth of the absorption, tends to decrease with time. This may be a result of the expansion of the SN relative to the slow CSM. An example of this kind of evolution can be seen in the analytical models in Figure 5 of Fransson (1984), where the relative size of the scattering layer to the "photospheric" emission is varied.

The dust shell, giving rise to the echo, is at a considerable larger distance, ≳ 10¹⁷ cm. The high temperature and large distance argues for small dust grains. To reproduce the NIR light curve, the dust should have an anisotropic distribution. The dust is likely to have been formed in previous mass loss phases of the progenitor, as seen in Eta Carinae.

Finally, we remark that even in our last full spectrum at ∼850 days there is no clear transition to a nebular stage, although the spectrum is dominated by emission lines, with Hα by far the strongest line, rather than continuum emission (Figure 7). Electron scattering is apparently still important in the line-emitting region, and there are no signs of any processed material in even the last spectrum. This may in principle speak in favor of the pure LBV scenario without core collapse. Because of the extreme mass-loss rate, the hydrogen envelope is, however, likely to still be opaque to the emission from the core (Section 4.6). We will therefore have to wait until the optical depth is low enough for any firm conclusions.

As discussed by Miller et al. (2010; see also Smith et al. 2008a, 2010a), the extremely luminous Type IIn SNe, with absolute magnitude brighter than M_V = −20, may arise from ejections where the ejected shell has not expanded to more than a few × 10¹⁵ cm, resulting in a dense, optically thick shell. This would correspond to SN 2010jl. Ejected shells that have expanded to larger radii, and therefore have lower density and optical depth, would give rise to more "normal" Type IIns, like SNe 1988Z and 2008iy, with absolute magnitudes fainter than −20. These are also expected to be strong X-ray and radio sources, in contrast to the more luminous Type IIns. As we discuss in Section 4.6, the mass-loss rate and its duration may be the most important parameters distinguishing these properties.

Although we have in this paper mainly discussed our results in terms of conditions around LBVs, the standard LBV scenario has a number of problems in explaining the Type IIn SNe. In particular, the high frequency of Type IIns may be incompatible with very massive progenitors, and the evolutionary state of the LBVs may also be a problem. Recently there have been different suggestions, discussed below, addressing these problems. One should note that the LBV interpretation is mainly phenomenological, based on observational characteristics like the very dense CSM, the CNO processing, and the typical velocities for the CSM. It has also been suggested that a large fraction of Type IIn SNe may arise as a result of explosions in red supergiants with enhanced mass loss (Fransson et al. 2002; Smith et al. 2009), which would alleviate these problems.

A single-star version has recently been put forward by Groh et al. (2013) based on a moderately fast rotating star with a mass 20–25 M_☉. The average rotational velocity on the main sequence was ∼200 km s⁻¹ for these models. The rotation, in combination with mixing, results in a more massive He core than for a nonrotating star. This has the consequence that the star ends up as a hot supergiant, with effective temperature ∼2 × 10⁴ K and with a thin hydrogen envelope. The heavy mass loss in the red supergiant and final hot phase results in a dense CSM.

The most interesting result in the paper by Groh et al. is that a full NLTE atmospheric calculation of the hydrostatic and wind regions in the final phase gives a spectrum similar to that of an LBV, with a large number of emission lines. Because of heavy mass loss and mixing, CNO products are transported to the surface, with essentially complete CNO burning. Their 20 M_☉ model has N/C = 128 and N/O = 16 at the end of C burning. These are considerably higher than our determination for SN 2010jl, including the uncertainty in these. As discussed by Groh et al., this could perhaps be explained by He-burning products mixed to the surface. It may, however, also indicate less complete CNO burning, as is, e.g., seen in the 15 M_☉ models by Ekström et al. (2012). These lower mass stars, however, end their life as red supergiants, not LBV-like objects. A dense CSM may nevertheless be present, but the wind velocity would probably be lower than we observe.

The mass-loss rate Groh et al. find for the 20–25 M_☉ models in the pre-SN phase is (1–4) × 10⁻⁴  M_☉ yr⁻¹ and wind velocity 270–320 km s⁻¹. The wind velocity is considerably higher than what we find for SN 2010jl. Scaling to a lower wind velocity, this mass-loss rate corresponds to an electron density of $\sim 2.3 \times 10^5 (\dot{M} / 10^{-4} \ \ M_\odot \ \rm yr^{-1}) (u_{\rm w}/300 \ \rm km\ s^{-1})^{-1} (r/10^{16}\ \rm cm)^{-2} \ \rm cm^{-3}$, where r is the radius of the line-emitting material. We have assumed a He/H ratio of 0.8 by mass (Groh et al. 2013). Depending on the mass-loss rate and radius of the line-emitting gas, this may be compatible with what we observe for the narrow lines from the CSM in SN 2010jl. However, there are large uncertainties in this estimate. First, as discussed in Sections 3.5 and 4.3, there is considerable uncertainty in the radius of the line-emitting gas. Also, the mass-loss rate of the models is highly uncertain because, as Groh et al. (2013) remark, these stars are close to the Eddington luminosity. An increased mass loss is therefore not unexpected, as discussed by Gräfener et al. (2012, and references therein). The mass-loss rate could also have been higher in the previous red supergiant phase, further boosting the density of the CSM at large radii. Rotational effects could also make the mass loss highly anisotropic. Overall, we find that given these uncertainties there is at least some rough agreement between the models and our observations. This scenario may therefore solve the evolutionary and rate problems and at the same time at least qualitatively explain the observational LBV characteristics. A major issue is to explain the mechanism behind the outbursts needed to explain the dense inner shell.

As a second alternative, based now on a binary model, Chevalier (2012) has proposed a merger scenario, where a compact companion in the form of either a neutron star or a black hole may merge with a normal companion star. The energy released by the in-spiraling will release a large energy into the envelope of the companion star, resulting in heavy mass loss. A dense CSM will therefore result, mainly concentrated to the orbital plane of the binary. This may have implications for the line profiles, but a more definite comparison is outside the scope of this paper. We also remark that an LBV-like eruption may also be the result of a merger or possibly only a tight binary encounter in a lower mass system. This would then be in better agreement with the relatively high frequency of Type IIn SNe. The high luminosity would, however, be difficult to understand.

A third scenario is discussed by Quataert & Shiode (2012) based on convective motions connected to the carbon burning and later stages when the core luminosity is super Eddington. This turbulence in turn excites internal gravity waves that may convert a fraction of their energy into sound waves. These finally dissipate their energy and cause mass loss from the stellar envelope. The advantage with this model is that it directly connects the stellar explosion and strong mass loss of the progenitor. Shiode & Quataert (2014) have developed this further and made predictions for the duration of the wave-driven mass loss, as well as the total mass lost. Most of the mass loss occurs in the Ne- and O-burning stages, which limits the duration to ≲ 10 yr before explosion. Only for stars with He-core masses below ∼10 M_☉, or zero-age main sequence masses below ∼20 M_☉, do they find substantial mass loss, with a total mass lost of 0.1–1 M_☉. Although the wind velocity we find, ∼100 km s⁻¹, is close to the escape velocities of their models, the total mass lost in the wave-driven phase is substantially lower than what we find for SN 2010jl. With a duration of ≲ 10 yr, the extent of the dense shell, ≲ 3 × 10¹⁵ cm, is also on the low side. Although interesting in that this scenario directly connects the heavy mass loss phase with the explosion, many details connected to, e.g., the conversion efficiency, effects of binary interaction and are uncertain and require numerical work along the lines of Meakin & Arnett (2006) to test this scenario. Smith & Arnett (2014) have recently discussed the consequences of instabilities from turbulent convection in the latest burning phase, which may trigger strong mass loss just before explosion.