SN 2008ha: AN EXTREMELY LOW LUMINOSITY AND EXCEPTIONALLY LOW ENERGY SUPERNOVA

Accurate flux measurements of SN 2008ha require galaxy subtraction to isolate the SN flux contribution. A template for the KAIT unfiltered data was constructed using previous observations of the field during the Lick Observatory Supernova Search (LOSS; Filippenko et al. 2001). BVRI KAIT and Nickel templates were not available at the time of publication. To facilitate galaxy subtraction, templates were manually constructed by taking a high-quality image and subtracting the point-spread function (PSF) of the SN to produce a smooth galaxy background. Galaxy subtraction was not attempted with the Nickel data which were taken under inferior conditions. We performed differential photometry on the SN and several local standard stars in the field using the DAOPHOT package in IRAF⁵ (see Table 1 for a list of stars). A single calibration was obtained under photometric conditions using the Nickel telescope to determine the zeropoint. We adopted the statistical errors output by IRAF as our final uncertainty. Our KAIT and Nickel photometry can be found in Table 2.

We obtained NIR (JH) photometry with the refurbished and fully automated 1.3 m Peters Automated Infrared Telescope (PAIRITEL)⁶ located at the Fred L. Whipple Observatory (FLWO). J-band and H-band (1.2 and 1.6 μm; Cohen et al. 2003) images were acquired simultaneously with the three NICMOS3 arrays with individual exposure times of 7.8 s. The PAIRITEL reduction pipeline software (Bloom et al. 2006) estimates the sky background from a star-masked median stack of the SN raw images. After sky subtraction, it then cross correlates, stacks, and subsamples the processed images in order to produce the final image with an effective scale of 1'' pixel⁻¹ and an effective FOV of 10' × 10'.

For the NIR photometry, we adopted the image-analysis pipeline of the ESSENCE and SuperMACHO projects and performed difference photometry (following Wood-Vasey et al. 2008) using the image-subtraction algorithm of Alard (2000). We present our PAIRITEL JH light curves in Table 3.

Observations in JHK were obtained using Magellan PANIC in classically scheduled mode and Gemini NIRI as part of the director's discretionary time (program ID: GN-2008B-DD-6).

The NIRI data were reduced using the noao:gemini:niri IRAF package and its bad-pixel masks. Sky flats were generated using the 7–15 different dither positions that comprised each sequence. After the standard NIRI reduction, we used IRAF imcoadd to combine the dithers in a mosaic stack. Simple aperture photometry (06 radius) then gave the fluxes for SN 2008ha and the 1–2 Two Micron All Sky Survey (2MASS) stars (∼15 mag) in the resulting mosaics. We estimate a systematic uncertainty of 0.03 mag from using two stars and 0.05 mag from using just one 2MASS star.

The PANIC data were reduced using the standard IRAF PANIC reduction software available at the Las Campanas Observatory website. We constructed a bad-pixel mask from on/off pairs of dark and lamp frames, and then used the sky dithers for our flat field. The same 2MASS stars were used as calibration sources as for the NIRI data.

Both the NIRI and PANIC photometry was performed with local sky subtraction in a circular annulus. With the good resolution of the Magellan and Gemini images (∼07) the SN stood out clearly from the galaxy background, and we estimate that the residual uncertainty in the subtraction of the local sky and galaxy background is 0.01 mag. Our light curves are presented in Figure 2 and Table 4.

The Swift team initiated target-of-opportunity observations of SN 2008ha with the UVOT (Roming et al. 2005) and the X-ray Telescope (XRT; Burrows et al. 2005) on board the Swift gamma-ray burst satellite (Gehrels et al. 2004) beginning on 2008 November 11. A second, deeper epoch was obtained two days later near the optical peak, and a final set of reference images was obtained (at our request) on 2009 February 3. We performed digital image subtraction on all of the UVOT data using the final epoch as a template to remove host-galaxy contamination with the ISIS software package (Alard 2000). The U-, B-, and V-band data were then reduced using the photometric-calibration technique described by Li et al. (2006), while photometry from the UV images was obtained using the zeropoints from Poole et al. (2008). The results of our UVOT analysis are displayed in Table 5.

The XRT data were reduced using standard Swift software analysis tools. No X-ray source is detected at the location of SN 2008ha in any of our three epochs of observations. Assuming a power-law spectrum with photon index Γ = 2.0, we place the following limits on the 0.3–10 keV X-ray flux from SN 2008ha: 2008 November 11.32, F_X < 9 × 10⁻¹⁴ erg cm⁻² s⁻¹; 2008 November 13.19, F_X < 5 × 10⁻¹⁴ erg cm⁻² s⁻¹; 2009 February 3.04, F_X < 7 × 10⁻¹⁴ erg cm⁻² s⁻¹. Using our adopted distance modulus, these fluxes correspond to isotropic luminosities of L_X < 5 × 10³⁹ erg s⁻¹, L_X < 3 × 10³⁹ erg s⁻¹, and L_X < 4 × 10³⁹ erg s⁻¹, respectively. Several SNe Ia have been measured to have no X-ray emission at early times with limits an order of magnitude deeper (Hughes et al. 2007), while SNe Ic typically have X-ray luminosities of 10³⁷–10³⁹ erg s⁻¹ (Chevalier & Fransson 2006); therefore, our X-ray limits are not particularly constraining.

By fitting a polynomial to the light-curve peaks, we are able to measure the time of maximum brightness and peak brightness in BVRIJHK for SN 2008ha. We find that SN 2008ha peaked in the B band on JD 2, 454, 783.23 ± 0.16 at 18.23 ± 0.01 mag. SN 2008ha also peaked at V = 17.68 ± 0.01 mag. From our medium-resolution magE spectra (see Section 3), we can place a limit of <0.02 Å for the equivalent with of Na D absorption from the host galaxy, indicating minimal host-galaxy extinction. Using the distance modulus for UGC 12682, and correcting for Milky Way extinction of A_V = 0.25 mag (Schlegel et al. 1998, consistent with our measured equivalent width of the Na D lines corresponding to Milky Way absorption), we find that SN 2008ha peaked at M_V = −14.21 ± 0.15 mag, about 5 mag below the peak absolute magnitude of normal SNe Ia and 2.9 mag fainter than the least luminous known SN Ia (SN 2007ax peaked at M_V = −17.1 mag; Kasliwal et al. 2008). The maximum-light characteristics of SN 2008ha for BVRIJHK can be found in Table 6.

V09 presented R-band and unfiltered photometry of SN 2008ha. Their light curves are broadly consistent with ours. Their first filtered data point occurred on JD 2,454,798.46 with R = 18.36 ± 0.12 mag. This is consistent (within the uncertainties) with our measurement 0.19 days later at R = 18.308 ± 0.022 mag. Their derived peak magnitude is 0.3 mag brighter than our measurement, but with the same time of maximum. Considering that their first filtered observations occur 12 days after our measured date of maximum, the disagreement between our measurement and their extrapolation is not surprising. They adopted a distance modulus of μ = 31.55 mag, 0.09 mag smaller than our adopted value. As a result of these two differences, they measured a peak absolute magnitude that is 0.2 mag brighter than what we have measured. Their late-time R-band points are systematically fainter than our late-time points, probably from undersubtraction (for our photometry) or oversubtraction (for their photometry) of the host-galaxy light. This discrepancy should be reduced after late-time templates are obtained to perform template subtractions.

Comparing our light curves to those of SN 2002cx (Li et al. 2003), SN 2005hk (another object similar to SN 2002cx; Phillips et al. 2007), and SN 2005hg (a normal SN Ib; M. Modjaz, 2009, private communication), we find that our BVRIJHK light curves decline quickly, but are very similar to those of all three SNe if we compress the light curves in time ("stretching" the light curves by ∼0.7 for all three; see Figure 2). The date of B maximum found from matching SN 2008ha to SNe 2002cx and 2005hk is JD 2, 454, 783.6 ± 0.1, very similar to what we found from polynomial fitting.

Our strongest limit on the rise time of SN 2008ha comes from a nondetection in a KAIT search image on 2008 October 25 (m_unf>19.5 mag), 18.4 days before B-band maximum. However, if we assume that SNe 2005hk and 2008ha have similar compositions, opacities, and temperatures (which are reasonable considering their spectral similarities; see Section 3), we can estimate the rise time of SN 2008ha by scaling the light curve of SN 2005hk (which has a well constrained rise time) to match that of SN 2008ha. SN 2005hk has a rise time of 15 days (Phillips et al. 2007), and with a scaling factor of 0.7, we determine that the rise time of SN 2008ha is ∼0.7t_r(SN 2005hk) ≈ 10 days.

Finally, if we assume that SN 2008ha is a homologously expanding object, then we can use an analytic equation to solve for the rise time (Riess et al. 1999). This assumption only holds true at very early times. Using our unfiltered measurements, which are the earliest data, and the discovery measurement from Puckett et al. (2008) with no correction to match their unfiltered measurements to ours, we determine that the rise time in the unfiltered band is 11 days (if we only use the earliest two data points) to 18 days (if we use the earliest three data points). From our polynomial fits, we see that there is a 4 day lag between B maximum and unfiltered maximum; applying this lag to the rise time, we find that SN 2008ha has a B-band rise time of 7–14 days, consistent with the value found above by matching light curves. Our first value (7 days) is measured with only two data points, leaving zero degrees of freedom in our fit. Our second value (14 days) is measured from a fit that includes a light-curve point very close to maximum brightness, so the derived rise time should be considered a relatively strong upper limit.

In Figure 2, we see that the light curves of both SN 2002cx-like objects (represented by SNe 2002cx and 2005hk) and SNe Ib are similar near maximum light. The offsets in absolute magnitude and stretch factors necessary for each comparison SN to match SN 2008ha are listed in Table 7. SN 2002ha does not have the second maximum in the NIR bands that is common to SNe Ia; however, there appears to be a shoulder in HK around 20–40 days after B-band maximum. SN 2005hk did not have a similar shoulder in its H-band light curve (the K-band coverage for SN 2005hk is only two points, and does not allow a good comparison to SN 2008ha). The extinction-corrected colors at maximum of SNe 2002cx and 2005hk are more similar to SN 2008ha than those of SN 2005hg (σ = 0.20, 0.30, and 0.16 mag for SNe 2002cx, 2005hg, and 2005hk, respectively).

On 2008 November 13 (JD 2,454,783.7), 0.5 days after B maximum, we have concurrent measurements in the UV (from Swift using the zeropoints of Brown et al. 2009) and optical (from KAIT). We also have NIR measurements (from Magellan) 3.3 days later. From Figure 2, we see that the JHK bands are relatively constant between these epochs. A spectral energy distribution (SED) for SN 2008ha covering λ < 0.2 μm to λ>2.2 μm is shown in Figure 3. We see that the SED has a flat f_λ spectrum in the optical and a remarkable drop in flux in the UV.

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We can compare the SED of SN 2008ha to that of other SNe that have UV-optical-IR (UVOIR) coverage near maximum light. In Figure 3, we plot the near-maximum light SEDs of SN 2005cs (Pastorello et al. 2009) and SN 2005hk (Phillips et al. 2007; Brown et al. 2009). All of these SNe have relatively similar optical and NIR colors, but their UV fluxes differ significantly. SN 2005cs has substantial UV flux, while SNe 2005hk and 2008ha have line blanketing in their photosphere causing a depression of UV flux.

In Figure 4, we present several spectra of SN 2008ha, from the classification spectrum (Foley 2008) to a spectrum obtained in 2009 January (corresponding to phases of t = +6.5 to 62.5 days after maximum brightness in the B band). A journal of our observations can be found in Table 8. Our earliest spectra show the distinct characteristics of the SN 2002cx-like class of objects. The spectra exhibit low-velocity lines of intermediate-mass and Fe-group elements (see Figure 8 for line identifications). Examining relatively unblended lines such as O i and Na D, we measure typical ejecta velocities of ∼2000 km s⁻¹. V09 found a higher ejecta velocity of 2300 km s⁻¹. Considering the relatively large systematic uncertainties, we believe that our measurements are consistent with those found by V09.

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At late times, the spectra evolve in a manner similar to that of SN 2002cx, except that SN 2008ha has exceptionally strong [Ca ii] λλ7291, 7323 and Ca ii NIR triplet (λλ8498, 8542, 8662) emission lines. The lack of H lines at any epoch indicates that the progenitor of SN 2008ha did not have a massive H envelope. Since it is difficult to excite the optical lines of He, the absence of He lines in our spectra does not necessarily mean that there was no He in the ejecta.

Tracking the minima of the absorption for several P-Cygni lines, we can measure the distribution of elements within the ejecta. In Figure 5, we show the velocity evolution for four lines (Ca H&K, Fe ii λ4555, Na D, and O i λ7774). We see a modest decrease in the velocities of Na D and O i λ7774 of only ∼500 and ∼800 km s⁻¹ over a 60-day period, respectively. Fe ii λ4555, on the other hand, decreased by ∼1300 km s⁻¹ over the same period, with all three lines having the same velocity in our last spectrum. Meanwhile, Ca H&K has a much higher velocity than the other lines. For our +8 day spectrum we find that the Ca ii NIR triplet has a velocity similar to that of Ca H&K, so we do not believe that the higher velocity is the result of blending of the feature with other lines. Ca ii has a very large optical depth, so we may be seeing the outermost layers of the ejecta moving at larger velocities for Ca H&K. All lines measured are multiplets and at the small line widths, the individual components can create systematic errors in measuring the minima of the features. The Ca H&K, Fe ii λ4555, Na D, and O i λ7774 lines have a velocity difference from their smallest to largest wavelength component relative to the gf-weighted wavelength for the feature of 2640, 8500, 300, and 130 km s⁻¹, respectively. The Na D and O i λ7774 lines should have the least systematic errors in their measurements. The velocity structure of SN 2008ha indicates that the Fe is well distributed throughout the ejecta and is not isolated in clumps. In our +62 day spectrum, the [Ca ii] lines are blueshifted by ∼400 km s⁻¹ relative to the rest frame and have FWHM intensity of ∼1200 km s⁻¹.

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We find no evidence for He i in any of our spectra; see Section 3.3 for more details.

To better understand the nature of SN 2008ha, we have compared our spectra of SN 2008ha with those of other SNe that show some similarities to SN 2008ha. We focus on SNe 1989B (a normal SN Ia; Barbon et al. 1990; Wells et al. 1994), 1991T (the prototype of its subclass of SNe Ia, and similar to SN 2002cx-like objects at early times; Filippenko et al. 1992b; Phillips et al. 1992), 2002cx (the prototype of its subclass of SNe; Li et al. 2003), 2004aw (a peculiar SN Ic that was originally classified as an SN Ia; Taubenberger et al. 2006), 2005E (a "Ca-rich" SN Ib similar to prototypes SNe 2001co and 2003H that was both underluminous and discovered in the halo of an S0/a galaxy; Filippenko et al. 2003a; Foley & Filippenko 2005; Perets et al. 2009), 2005cs (a peculiar and low-luminosity SN II; Pastorello et al. 2006), and 2007J (an SN which is very similar to SN 2002cx at early times, but developed He i lines at later times).

In Figure 6, we present our +7 day Lick spectrum of SN 2008ha compared to the spectra of SNe 1991T and 2002cx. We have applied an inverse-variance weighted Gaussian smoothing function with characteristic velocities of 800 km s⁻¹ and 2000 km s⁻¹ (Blondin et al. 2006) to our SN 2008ha spectrum. To match the spectral features of SN 2008ha, in addition to removing the recession velocities of the SNe we remove an extra 7500 and 3000 km s⁻¹ for SNe 1991T and 2002cx, respectively. These differences in characteristic velocity correspond to different kinetic energies per unit mass; SN 2008ha has a lower kinetic energy per unit mass than SN 2002cx, which has a lower kinetic energy per unit mass than SN 1991T.

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We see that the SN 2008ha spectrum smoothed with a 800 km s⁻¹ Gaussian is very similar to the spectrum of SN 2002cx, indicating that SN 2008ha is spectroscopically a member of the SN 2002cx subclass of SNe. The SN 2008ha spectrum convolved with a 2000 km s⁻¹ Gaussian is also relatively similar to the SN 1991T spectrum, but with SN 2008ha having a redder continuum than SN 1991T. The overall similarities between these objects is the result of their optical spectra being dominated by Fe ii lines at this phase.

In Figure 7, we present our +62 day spectrum of SN 2008ha with comparison spectra of SNe 1989B, 2004aw, 2005E, 2005cs, and 2007J at similar phases (with the exception of SN 2005cs). Our spectrum of SN 2005cs was obtained 304 days after explosion (Pastorello et al. 2009). We have redshifted the spectra of SNe 1989B and 2004aw (after removing their recession velocity) by a velocity of 3000 km s⁻¹. After this correction, we see that all six objects are broadly consistent, having many similar spectral features. In particular, all objects have strong Na D and Fe ii lines. The main differences are that SN 2008ha has narrower lines than those of the other objects, SNe 2005E, 2005cs, and 2008ha have strong [Ca ii] and Ca ii emission lines, SNe 2004aw, 2005E and 2005cs have [O i] emission, SN 2005cs has a strong Hα line, and SN 2007J has prominent He i emission lines.

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The strong [Ca ii] and Ca ii lines in the latest SN 2008ha spectrum present an interesting clue to the composition of the SN ejecta. The late-time ejecta of SNe II cool through line emission from H transitions. Similarly, SNe Ia and Ib/c cool through [Fe ii] and [O i] lines, respectively. In all cases, these lines dominate the late-time spectra of the objects. Late-time spectra of SNe 2002cx and 2005hk show no strong forbidden emission lines (although there are weak [Ca ii] lines and lines from other intermediate-mass elements), indicating that the SN ejecta were still quite dense at least a year after maximum light (Jha et al. 2006; Sahu et al. 2008). From our measured ejecta velocity and ejecta mass measurement in Section 4, our +62 day spectrum should have an electron density of ∼10⁹ cm⁻³. Integrating the flux in the Ca lines, [Ca ii]/Ca ii ≈0.5. An electron temperature of ∼7000 K is appropriate for this density and line ratio (Ferland & Persson 1989). At ∼200 days after maximum, the electron density should be ∼10⁸ cm⁻³, at which point we should be able to measure the relative abundance of O/Ca (Fransson & Chevalier 1989). However, if the ejecta are in dense clumps, the density may stay high for a longer time.

To investigate the details of our SN spectra, we use the SN spectrum-synthesis code SYNOW (Fisher et al. 1997). Although SYNOW has a simple, parametric approach to creating synthetic spectra, it is a powerful tool to aid line identifications which in turn provide insights into the spectral formation of the objects. To generate a synthetic spectrum, one inputs a blackbody temperature (T_BB), a photospheric velocity (v_ph), and for each involved ion, an optical depth at a reference line, an excitation temperature (T_exc), the maximum velocity of the opacity distribution (v_max), and a velocity scale (v_e). This last variable assumes that the optical depth declines exponentially for velocities above v_ph with an e-folding scale of v_e. The strengths of the lines for each ion are determined by oscillator strengths and the approximation of a Boltzmann distribution of the lower-level populations with a temperature of T_exc.

In Figure 8, we present our +14 day spectrum of SN 2008ha with a synthetic spectrum generated from SYNOW. This fit has T_BB = 5500 K and v_ph = 600 km s⁻¹, and 11 ions are used. Several ions, which we consider to be "secure" identifications, are important for the spectral formation of SN 2008ha; they account for either the most prominent or multiple line features, and include Fe ii, Ca ii, Na i, O i, Ti ii, and Cr ii. An additional 5 ions (Mg ii, Si ii, Mg i, C i, and Sc ii) are considered to be "possible" identifications, as each of them fit one line or multiple weak lines. Because SN 2008ha has exceptionally low expansion velocities and narrow line widths, many otherwise blended lines are resolved. The fact that our SYNOW fit provides an excellent fit to over 70 line features suggests that we have identified the most important ions that contribute to the spectral formation of SN 2008ha.

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V09 presented a SYNOW fit to a spectrum taken a day after our +14 day spectrum. Their fit used the parameters T_BB = 6200 K and v_ph = 1300 km s⁻¹. Both of these values are higher than indicated by our fit. V09 also include He i while excluding Mg i and C i. We find that inclusion of Mg i and C i improves the fit more than Sc ii; thus, Mg i and C i are more secure. We have attempted a fit that includes He i, and while it improves the fit in some wavelength regions, it makes it worse in others. Overall, we believe that adding He i to our particular model spectrum made it appear less like the spectrum of SN 2008ha.

If we simply take the ions used in our SN 2008ha model and increase the photospheric velocity to equal that of SN 2002cx, the SYNOW fit is not a good match to SN 2002cx. However, if we take the SN 2008ha model, remove C i, reduce the strength of Ca ii, and increase the strength of Fe ii, Co i, and Co ii, we can achieve a good match to SN 2002cx. This indicates that SN 2008ha has lower expansion velocities at the photosphere, stronger intermediate-mass element lines, and weaker Fe-peak element lines. These differences can all be explained by a lower energy explosion with less ⁵⁶Ni production in SN 2008ha.

Because of the highly parameterized nature of the SYNOW fits, the derived quantities of the input parameters are often not unique and the associated uncertainties are difficult to estimate. Nonetheless, the distribution of the opacities in velocity space can provide useful information on the spectral formation of the SNe. In Figure 9, we plot the opacity distribution of two representative ions, Ca ii for the intermediate-mass elements and Fe ii for the Fe-peak elements. The opacities are normalized to be unity at the photosphere (to facilitate the making of the plot) and the high-velocity end of the curves marks v_max. While the Ca ii opacity shows a considerably flatter distribution than Fe ii in SN 2002cx, the two distributions are nearly identical in SN 2008ha. The Ca ii opacity distribution shows some overlap in velocity space among the SNe (SN 2008ha has significant opacity in the range 4000–6000 km s⁻¹ because it has an enormous opacity at the photosphere). The Fe ii opacity distribution, on the other hand, is nearly "stratified;" the opacity is only present between 600 and 3000 km s⁻¹ for SN 2008ha and 5000 to 8000 km s⁻¹ for SN 2002cx. The differences in the opacity distributions may offer clues to the nature of the explosions.

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In the literature, there are currently 10 SNe identified as SN 2002cx-like objects. In Figure 11, we present optical spectra of SNe 1991bj, 2004gw, and 2006hn, all of which we propose are new members of this class.

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The spectra of SNe 1991bj and 2006hn were obtained with the UV Schmidt and Kast spectrographs, respectively, mounted on the Lick 3 m Shane telescope. The spectra of SN 2004gw were obtained with LRIS mounted on the Keck I telescope. Classifications based on these spectra were originally reported by Pollas et al. (1992), Foley & Filippenko (2005) and Filippenko & Foley (2005), and Foley et al. (2006) for SNe 1991bj, 2004gw, and 2005hn, respectively. SN 1991bj was recently identified as a potential member of this class (Stanishev et al. 2007). SN 2004gw was originally classified as a probable SN Ia with "a number of spectral peculiarities" (Foley & Filippenko 2005), but Gal-Yam (2005) suggested that it may be an SN Ic. Finally, Filippenko & Foley (2005) reclassified the object as an SN Ia. Additional observing details can be found in those references as well as in R. J. Foley et al. (2009, in preparation). In Figure 11, we compare the spectra of these objects to spectra of SN 2002cx. The spectra shown here demonstrate clearly that each of these SNe belongs to the SN 2002cx class. (Incidentally, a striking number of peculiar SN classes had their first members discovered in 1991.) In addition to these 14 objects, there is one potential member: SN 2007J.

SN 2007J, which had many similarities to SN 2002cx at early times (Filippenko et al. 2007a), eventually developed He emission lines (Filippenko et al. 2007b), unlike any other SN in this class. Although this object has many similarities to SN 2002cx, the presence of He i lines in its spectra casts doubt on its inclusion in this class. SN 2008ha also has some significant differences from SN 2002cx. However, we believe that these differences are caused mainly by the low-energy explosion in SN 2008ha rather than by differences in progenitors.

Using the extended sample of SN 2002cx-like objects, we investigate the host galaxies of this class. In Table 9, the detailed host information for 14 members and 1 potential member is presented. We exclude SN 2007J from the host-galaxy analysis, but its inclusion does not significantly change the results.

None of the SN 2002cx-like objects have elliptical hosts; however, in our extended sample, 1/14 (3/14) objects are hosted in S0 (S0 through Sa) galaxies. A comparison sample was generated using the SNe found in galaxies monitored by KAIT (which includes the host of SN 2008ha). Comparing the host-galaxy morphology of various (sub)classes of SNe may indicate similarities in progenitors. For consistency, we use the host-galaxy classification scheme presented by J. Leaman et al. (2009, in preparation), derived mainly from the NASA/IPAC Extragalactic Database (NED), and we divide the galaxies into eight morphology bins. In Figure 12, the fraction of host galaxies in these eight morphological bins for several SN classes is presented.

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The well known results that SN 1991bg-like objects (Filippenko et al. 1992a; Leibundgut et al. 1993) tend to be found in early-type galaxies (relative to normal SNe Ia; Howell 2001), while SNe Ib, Ic, II, and 1991T-like SNe have distributions skewed to later-type host galaxies relative to the distribution of normal SNe Ia, are immediately apparent in Figure 12. SN 2002cx-like events have, on average, later-type host galaxies than normal SNe Ia.

Examining Figure 12, all distributions other than that of SN 1991bg-like SN host galaxies are somewhat similar. Performing a Kolmogorov–Smirnov (K–S) test on the data, we find that SN 1991bg-like objects, SNe II, and SNe Ic have significantly different distributions from normal SNe Ia. SNe Ib and SN 1991T-like objects have marginally different distributions from normal SNe Ia. In a similar study, Kelly et al. (2008) found that the locations of SNe Ia, Ib, and II all followed the galaxy light, while SNe Ic were more likely to be found in the brightest regions of a galaxy, indicating more massive progenitors for SNe Ic than SNe Ib or II. Except for SN 1991bg-like objects, no SN class has a significantly different host-galaxy morphology distribution from SN 2002cx-like objects. Although these results may change with a slightly different sample (KAIT is biased to luminous galaxies) or with increased numbers, we cannot say that SN 2002cx-like objects have a different host-galaxy morphology distribution from any SN class other than SN 1991bg-like events.

We find that 12% of the normal SN Ia hosts in the KAIT sample are elliptical galaxies. If SN 2002cx-like events have the same host-morphology distribution as normal SNe Ia, we would expect to have found 1.7 ± 1.3 SNe (1.8 ± 1.3 if we include SN 2007J) of the SN 2002cx class in elliptical galaxies, consistent with our finding zero members in elliptical galaxies. We find that 31% of SNe Ia come from E through S0/a galaxies. If we assume that SN 2002cx-like objects and normal SNe Ia have the same host-galaxy morphology distribution, then we would expect 4.4 ± 2.1 SNe (4.7 ± 2.2 if we include SN 2007J) of the SN 2002cx class in early-type galaxies. This prediction is consistent with our measurement of two members in early-type galaxies.

In addition to the morphology measurements for all SN 2002cx-like host galaxies, we have made additional measurements of UGC 12682, the host of SN 2008ha.

Takamiya et al. (1995) measured UGC 12682 to have V = 13.84 mag and B − V = 0.28 mag within an aperture of 845 radius. With our adopted distance modulus and correcting for Milky Way extinction (Schlegel et al. 1998), we find M_V = −18.0 mag, comparable to the absolute magnitude of the Large Magellanic Cloud (LMC; M_V = −18.4 mag).

For our LRIS observation, we positioned the slit to go through a bright knot in UGC 12682. The emission from the host galaxy in a 16'' aperture around this bright knot displays intensity ratios of [N ii] λ6584/Hα = 0.057 and [O iii] λ5007/Hβ = 4.0. The N2 and O3N2 metallicity indicators of Pettini & Pagel (2004) give consistent estimates for the host-galaxy oxygen abundance of 12 + log(O/H) = 8.16 ± 0.15, well below the solar value of 8.9 or 8.7 (Delahaye & Pinsonneault 2006; Asplund et al. 2005).

We can use the far-infrared luminosity of UGC 12682 to estimate its star formation rate (SFR). Assuming a distance of 21.3 Mpc and the IRAS measurements of the 60 and 100 μm flux (Melisse & Israel 1994), the calibration of Kennicutt (1998) yields an estimate for the SFR of 0.07 M_☉ yr⁻¹. Although this seems low for a "star-forming galaxy," it is consistent with its luminosity. Using the same calibration for the far-IR luminosity, Whitney et al. (2008) find an SFR for the LMC of 0.17 M_☉ yr⁻¹, about 2.5 times larger than that of UGC 12682 (while the LMC is about 1.5 times more luminous).

It has been suggested that during the gravitational collapse of a massive star, the entire star may collapse directly to a black hole instead of creating a shock wave that disrupts the outer layers of the star. Alternatively, a massive star could produce a proto-neutron star near the limiting mass during collapse, which would then quickly create a black hole by accreting some material which falls back onto the proto-neutron star. These processes would not produce any or much electromagnetic radiation, resulting in a faint (or potentially no) SN.

The progenitors of these systems must be very massive stars to produce a black hole. Although other factors such as metallicity, binarity, or rotation may determine whether a particular star will directly collapse to a black hole, most estimates suggest that an initial mass of ≳40 M_☉ is necessary (Heger et al. 2003). Similarly, an initial mass of ≳30 M_☉ is necessary to create a black hole through fallback (Fryer 1999).

Massive SN Ic progenitor stars lose their outer hydrogen and helium layers through either stellar winds and outbursts or binary transfer. For a single-star system, the amount of mass loss through winds is directly dependent on the metallicity of the star. Modjaz et al. (2008) found that the sites of broad-lined SNe Ic (a subclass of SNe Ic with expansion velocities up to ∼0.1c) that are not associated with GRBs have metallicities similar to solar metallicity. The progenitors of weak SNe Ic (where a black hole is formed through fallback) should have lower metallicities than that of the progenitors of normal SNe Ic (Heger et al. 2003).

Since the progenitors of black holes must be very massive stars, we expect the distribution of their associated SNe to be heavily biased to star-forming galaxies. The host of SN 2008ha is an irregular galaxy. In Section 5, we found for UGC 12682, the host of SN 2008ha, a subsolar oxygen abundance of 12 + log(O/H) = 8.16 and an SFR of 0.07 M_☉ yr⁻¹, which we determined was large considering its luminosity is comparable to that of the LMC. A 40 M_☉ star with subsolar metallicity has a lifetime of ∼5 × 10⁶ yr (Schaller et al. 1992). With our measured SFR and an LMC initial-mass function (Massey et al. 1995), we calculate that there are 120 stars with M ≳ 40 M_☉ in UGC 12682 at any given time. Using the lifetime of these stars, we estimate an SN rate of 2 × 10⁻⁵ yr⁻¹ for these stars.

All observations of SN 2008ha can be explained through this model if we assume that it had the precise initial conditions necessary to barely produce an explosion, rather than directly collapse to a black hole. V09 make no specific claims regarding this scenario. For the class of SN 2002cx-like objects, this model would explain the diversity of the class. While most objects in this class are hosted by a range of star-forming galaxies, one of these objects have S0 hosts. We do not expect there to be a large population of massive stars in these galaxies (although a more thorough search for current star formation in this particular host is necessary). Furthermore, the amount of ⁵⁶Ni produced in SN 2005hk (∼0.2 M_☉; Phillips et al. 2007) is similar to that of typical-luminosity stripped-envelope core-collapse SNe (e.g., Sauer et al. 2006) and much larger than that expected for fallback events. It is therefore unlikely that this model is the mechanism for all members of the SN 2002cx-like class.

Stars with an initial mass of ∼9 M_☉ will evolve to a super-AGB stage with a massive, degenerate, O–Ne–Mg core. These stars may evolve further to become O–Ne WDs. Either in the AGB or WD phases, electron capture can then induce a core-collapse event, triggering an SN (e.g., Miyaji et al. 1980; Nomoto 1984; Kitaura et al. 2006; Dessart et al. 2006; Metzger et al. 2009). These models predict a small ⁵⁶Ni mass (10⁻² to 10⁻¹ M_☉) and explosion energy (∼10⁵⁰ erg; Kitaura et al. 2006).

Since there is no hydrogen present in the spectra of SN 2008ha, its progenitor could not have been an AGB star. Similarly, the progenitors of SN 2002cx-like objects could not be AGB stars. However, this intermediate-mass range for progenitor stars is consistent with the host-galaxy morphology distribution of SN 2002cx-like events (see Section 5.2). V09 suggest that electron capture of a star with a O–Ne–Mg core is a possible model for SN 2008ha. However, we conclude that if electron capture is the correct model for SN 2008ha, the progenitor must have been a WD.

Metzger et al. (2009) presents a model for a single WD collapsing to a neutron star through electron capture. In this model, they predict the creation of 10⁻² M_☉ of ⁵⁶Ni ejected at relativistic velocities, but essentially no intermediate-mass elements. However, if two WDs merge and subsequently collapse to a neutron star, there will be material at the radius of the recently formed WD and at the radius of the newly formed neutron star. The material around the neutron star would produce the same ejecta with the same energy as the single-star model, but the explosion would occur within the WD accretion disk, mass-loading the explosion, reducing the kinetic energy per unit mass, increasing the opacity (and thus the time scale of the event), and heating the WD accretion disk to temperatures where intermediate-mass elements may form (but not hot enough to produce additional ⁵⁶Ni). Dessart et al. (2006) has modeled electron capture for recently merged WD systems, finding ejecta masses of ∼10⁻³ M_☉ (with ∼25% being ⁵⁶Ni) and explosion energies of up to ∼10⁵⁰ erg.

The conventional electron-capture scenario of an AGB star does not fit the observations of any of the SN 2002cx-like objects. If the progenitor is a single WD, the model fails to produce the intermediate-mass elements or low velocities seen for these objects. However, if there is a WD merger followed by the accretion-induced collapse of the newly formed WD, we may reproduce the observations of SN 2008ha. Since it would be difficult to generate the ⁵⁶Ni necessary for most SN 2002cx-like objects with this model, we believe it is unlikely to produce all SN 2002cx-like objects. However, it is worth noting that if one of the objects was a He WD, this model may explain the He i lines seen in the spectra of SN 2007J.

It has been suggested that SN 2002cx-like objects are the result of a pure deflagration of a possibly sub-Chandrasekhar-mass WD (e.g., Branch et al. 2004; Phillips et al. 2007). This scenario explains the low velocities and luminosities of these events. Such an event would retain a significant amount of unburned material in its core, leading to strong [O i] emission at late times (Kozma et al. 2005); however, this has not been seen in the late-time spectra of SNe 2002cx or 2005hk (Jha et al. 2006; Sahu et al. 2008, although this might simply be the result of the high density at late times).

In the context of SN 2008ha, the energetics constrain the model further. If the progenitor star was a Chandrasekhar-mass WD, the energy released, E_released, during the explosion must be larger than the binding energy, E_binding ≈ 10⁵¹ erg, to unbind the star. With an expansion velocity of 2000 km s⁻¹ and 1.4 M_☉ of ejecta, SN 2008ha would have E_released ≈ E_kin = 5 × 10⁴⁹ erg or E_released ≈ 5 × 10⁻²E_binding. This scenario requires that the energy created in the explosion be just above the binding energy of the star. Since the kinetic energy scales with the ejecta mass (which scales with the progenitor mass in this case), a sub-Chandrasekhar explosion does not improve the energy problem. This balancing problem means that it is unlikely that SN 2008ha was a deflagration of a WD that disrupted its progenitor star. Furthermore, in Section 4, we found M_ej ≈ 0.15 M_☉, significantly below what is expected from a full disruption of a WD.

Numerical models of WD explosions have found some events which produce a deflagration burning front that rises from within the star to the surface, reaching a velocity of ∼5000 km s⁻¹ at the surface with some material up to ∼10,000 km s⁻¹, but does not unbind the star (e.g., Calder et al. 2004; Livne et al. 2005). In this scenario, we expect relatively small ⁵⁶Ni (∼3 × 10⁻²M_☉) and ejecta masses.

Except for the lack of late-time [O i] emission, the higher-luminosity members of the SN 2002cx-like class are consistent with a full deflagration of a WD; however, SN 2008ha is inconsistent. On the other hand, the light curves, line velocities, composition, energetics, and host-galaxy properties of SN 2008ha are all consistent with a failed deflagration. If this model is correct for SN 2007J, the He lines must be the result of interaction with circumstellar material.

For the ".Ia supernova" model, first proposed by Bildsten et al. (2007), a binary WD system similar to AM CVn with a low accretion rate will eventually undergo a particularly luminous outburst caused by nuclear burning of a helium shell with M ≈ 0.05 M_☉. This flash will generate Fe-peak radioactive nuclei similar to an SN Ia, but the smaller mass of radioactive elements and ejected material produce a less luminous, rapid light curve, with high-velocity ejecta.

This model makes several predictions. The ⁵⁶Ni mass should be ∼10⁻² M_☉ and the absolute magnitude should be in the range of −15 to −18 mag. Since the ejecta mass should be small (similar to the mass of the helium shell, 0.05 M_☉), the rise time should be short (2–10 days). Because there is a large $M_{^{56}{\rm Ni}}/M_{\rm ej}$ ratio, the ejecta velocity should be large (∼15,000 km s⁻¹). Given that the progenitors are AM CVn systems, the host-galaxy population should be dominated by early-type galaxies. The rise time and luminosity of SN 2008ha are on the extreme edges of the ranges found by Bildsten et al. (2007). However, the ejecta velocity of SN 2008ha is much lower than that predicted, and its host galaxy is an irregular galaxy, an unlikely host for such an event (but since there are old stellar systems in all galaxies, this alone should not eliminate the model).

If we take the model of Bildsten et al. (2007) and modify it so that the nuclear burning is less efficient, the explosion would produce less ⁵⁶Ni but have a similar amount of ejecta, producing a fainter event with a lower ejecta velocity, while the rise time would be approximately the same. If the kinetic energy is proportional to the ⁵⁶Ni mass, then to match the observed ejecta velocity, we would expect the ⁵⁶Ni to be a factor of ∼50 smaller than that presented by Bildsten et al. (2007). This implies $M_{^{56}{\rm Ni}} = 2 \times 10^{-3}$ M_☉, similar to what we found from an examination of the light curve in Section 4.

The inefficient version of the.Ia model appears to reproduce the properties of SN 2008ha. Since this model involves a He WD, some of the ejecta (or alternatively, circumstellar material from the mass transfer) may be unburned He. This model may explain the He emission lines present in SN 2007J, but lack of strong [O i] in the late-time spectra of SN 2002cx. However, the ejecta mass and rise times predicted by this model do not match those observed for most SN 2002cx-like objects. Additionally, the progenitor systems of this model are members of an old stellar population, so we are unlikely to have discovered these objects exclusively in spiral galaxies. Thus, this model probably does not apply to all SN 2002cx-like events.