THE PECULIAR EXTINCTION LAW OF SN 2014J MEASURED WITH THE HUBBLE SPACE TELESCOPE

The study of the cosmological expansion history using Type Ia supernovae (SNe Ia), of which SN 2014J is the closest in several decades (Goobar et al. 2014, hereafter G14), has revolutionized our picture of the universe. The discovery of the accelerating universe (Riess et al. 1998; Perlmutter et al. 1999) has led to one of the biggest scientific challenges of our time: probing the nature of dark energy through more accurate measurements of cosmological distances and the growth of structure in the universe. SNe Ia remain among the best tools to measure distances and as the sample grows both in number and redshift range, special attention is required to address systematic effects. One important source of uncertainty is the effect of dimming by dust. Despite considerable effort, it remains unclear why the color–brightness relation for SNe Ia from cosmological fits is significantly different from, e.g., dimming by interstellar dust with an average R_V = A_V/E(B − V) = 3.1. In the most recent compilation by Betoule et al. (2014), 740 low- and high-z SNe Ia were used to build a Hubble diagram using the SALT2 lightcurve fitter (Guy et al. 2007). Their analysis yields β = 3.101 ± 0.075, which corresponds to R_V ∼ 2, although the assumed color law in SALT2 differs from the standard Milky-Way-type extinction law (Cardelli et al. 1989).

Several cases of R_V ≲ 2 have been found in studies of color excesses of local, well-measured, SNe Ia (e.g., Krisciunas et al. 2006; Elias-Rosa et al. 2006, 2008; Nobili & Goobar 2008; Folatelli et al. 2010). A low value of R_V corresponds to a steeper wavelength dependence of the extinction, especially for shorter wavelengths. In general terms, this reflects the distribution of dust grain sizes where a low R_V implies that the light encounters mainly small dust grains. Wang (2005) and Goobar (2008) suggest an alternative explanation that non-standard reddening of SNe Ia could originate from multiple scattering of light, e.g., due to a dusty circumstellar medium, a scenario that has been inferred for a few SNe Ia (Patat et al. 2007; Blondin et al. 2009; Dilday et al. 2012).

A tell-tale signature of reddening through multiple scattering is a power-law dependence for reddening (Goobar 2008), possibly also accompanied by a perturbation of the lightcurve shapes (Amanullah & Goobar 2011) and IR emission from heated dust regions (Johansson et al. 2013).

SN 2014J in the nearby galaxy M82 offers a unique opportunity to study the reddening of a spectroscopically normal (G14; Marion et al. 2014) SN Ia, over an unusually wide wavelength range. Hubble Space Telescope (HST) observations allow us to perform a unique study of color excess in the optical and near-UV, where the difference between the extinction models is the largest. Our data set is complemented by UBVRi observations from the Nordic Optical Telescope (NOT) and JHKs from the Mount Abu Observatory.

2.1. HST/WFC3

2.2. Optical and Near-IR Data

The UBVRi data were obtained with the NOT (Program 48-004; PI: Amanullah). The data were reduced with standard IRAF routines, using the QUBA pipeline (see Valenti et al. 2011, for details). The magnitudes are measured with a point-spread function-fitting technique (using daophot) and calibrated to the Landolt system.

Near-IR (NIR) observations in the Mauna Kea Observatory JHKs filters were carried out with the Mount Abu 1.2 m Infrared Telescope. Aperture photometry of the sky-subtracted frames was done using IRAF. The nearby star Two Micron All Sky Survey (2MASS) J09553494+6938552, which registers simultaneously with SN 2014J in the same field, was used for calibration. Results were cross-checked with other 2MASS stars in the field and found to agree within 5%. We adopt this as a systematic uncertainty on the NIR photometry.

All light curves¹⁰ are presented in Table 1 and Figure 1 where we also show a fitted model to the V band using SNooPy (Burns et al. 2011).

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3.1. Intrinsic SN Ia Colors

3.2. Color Excesses of SN 2014J

In this work we studied the color excesses, E(V − X), of all photometric bands with respect to the V band. For each photometric observation in Table 1 we also list the corresponding V magnitude. If the SN was observed in both bands within 12 hr we use the observed V for the corresponding epoch, but when this was not the case we use the fitted V-band SNooPy model shown in Figure 1 to calculate the color.

For each epoch we also present the calculated Galactic reddening correction. Unlike G14, we use the Galactic extinction toward M82 from Dalcanton et al. (2009). They argue that the estimates from the dust maps of Schlegel et al. (1998) are contaminated by M82 itself, and derived E(B − V)_MW = 0.06 from the study of neighboring patches.

We also calculate the corresponding color of SN 2011fe, shown in the last column of Table 1, from the light curves described above. The color excess, E(V_n − X_n), between the V band and some other band X, at an epoch n, can then be obtained under the assumption that the two SNe had nearly identical color evolution. Since the differences in K corrections are negligible for the two very nearby SNe, the color excess is calculated as the difference between the V_n − X_n color, corrected for Galactic extinction, and the corresponding color of SN 2011fe, i.e.,

$$\begin{equation} E({V} _n - {X} _n) = [(V_n -A_{V_n}) - (X_n - A_{X_n})] - \left(V_{n}^{\rm 11fe} - X_{n}^{\rm 11fe}\right). \end{equation} \tag{ 1 }$$

The first term on the right-hand side, the extinction-corrected color of SN 2014J, is plotted in Figure 2 together with the best fit colors derived from the reddened SED, as described in the next section. In Figure 3, E(V_n − X_n) is plotted using data around maximum light.

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An extinction law, $\xi (\lambda ;\bar{p})$, where $\bar{p}$ are free parameters, can be fitted by minimizing

$$\begin{equation} \chi ^2 = \sum _{X}\sum _{n} \frac{[ (E({V} _n-{X} _n) - (A_{V_n} - A_{X_n})]^2}{\sigma _{V_nX_n}^2} . \end{equation} \tag{ 2 }$$

Here E(V_n − X_n) is the measured color excess as described above and $A_{V_n} - A_{X_n}$, the corresponding model color excess,

$$\begin{equation} A_{X_n} = -2.5\log _{10}\left(\frac{\int \xi (\lambda ;\bar{p})T_X(\lambda)S_{\mathrm{11fe}}(\lambda ;n)\lambda \,d\lambda }{ \int T_X(\lambda)S_{\mathrm{11fe}}(\lambda ;n)\lambda \,d\lambda }\right), \end{equation} \tag{ 3 }$$

can be calculated from the filter transmission, T_X(λ), and the SED of SN 2011fe, S_11fe(λ; n), of the given epoch n.

The uncertainties, $\sigma _{V_nX_n}^2$, include the measurement errors shown in Table 1 but is dominated by the adopted intrinsic SN Ia color uncertainties. If a V-band measurement is included in constructing two different colors for a given epoch, then the contribution from the V uncertainty is treated as fully correlated.

In this work we ignore both calibration uncertainties (except for NIR) and systematic errors due to, e.g., Galactic extinction correction. The reason is that these will be correlated between epochs and are negligible in comparison to the intrinsic color uncertainty, which we also assume to be fully correlated. This will put equal weights to all colors, independent of the number of data points obtained in each band.

We further assume that the different colors are uncorrelated in our final analysis. We have tried inducing different correlations between the colors, but this had a minor impact on the conclusions from the fits.

We fitted three different extinction laws: an MW-like extinction law as parameterized by Fitzpatrick (1999, FTZ), the SALT2 law in the version used in Betoule et al. (2014), and a power-law parameterization, A_λ/A_v = (λ/λ_V)^p, shown to be a good approximation for multiple scattering scenarios (Goobar 2008). Each law was fitted using three different epoch ranges: [ − 5, +5] days, i.e., around peak brightness, the tail: [ + 25, +35], and the full epoch range of the HST observations, [ − 5, +35] days since B-band maximum. The FTZ and power law were fitted using all filters, while the SALT2 law is only defined in the wavelength range 2000–7990 Å.

The SN colors are compared at the effective phases, computed for both SN 2011fe and SN 2014J by subtracting the date of the B-max, 55814.5 and 56689.2, respectively, and dividing by the i lightcurve stretches (from SNooPy), 0.96 and 1.14, respectively. For each law we carry out the fit iteratively to all bands except F555W and F631N. The former completely includes our reference band and the latter is too narrow for our assumption of SN 2014J and SN 2011fe being comparable to hold.

We first calculate the Galactic extinction in each band assuming the pristine SED of SN 2011fe. Then, we carry out the fit by minimizing Equation (2). The fitted extinction law is then applied to the SED of SN 2011fe and the Galactic extinction is recalculated before refitting the law. The procedure is repeated until the value of the fitted parameters changes by less than 1% between iterations. The results of the fits are shown in Table 2, and the best fits to the full range are also shown in Figure 2 while the best fit around maximum is shown in Figure 3. In this figure we also present the best fitted FTZ model with R_V fixed to R_V = 3.1, which is clearly excluded by the data. Our best fit FTZ values are E(B − V) = 1.37 ± 0.03, R_V = 1.4 ± 0.1. We find that our data are also compatible with the power-law model with A_V = 1.85  ±  0.11 and p = −2.1  ±  0.1. Finally, we conclude that the SALT2 model provides a somewhat poorer fit description with c = 1.06 ± 0.04. These findings can be compared with the measured global extinction in M82 by Hutton et al. (2014). Unlike our result for the line of sight of SN 2014J, they conclude that FTZ with R_V = 3.1 provides a good description of the colors of the galaxy based on stellar modeling. However, for the dust in the superwind, they too conclude that a power-law relation provides the best fit, albeit with p = −1.53 ± 0.17.

As a consistency check, we recalculate the synthetic light curves of SN 2011fe using the best fitted FTZ law to redden the spectra. The result is plotted in Figure 1 as dotted lines for each band. For the redder bands, these reddened light curves are similar to the original, but for the blue bands, and in particular in the UV, the light curves are significantly broader, and show a similar decline as the observed data of SN 2014J. We take this as yet another confirmation that SN 2011fe indeed is very similar to SN 2014J and therefore suitable to use as reference for the extinction study presented here. We further conclude (Nugent et al. 2002, and references therein) that the difference in the lightcurve width between the original light curves in the bluer bands mainly stems from the fact that we are probing redder effective wavelengths for SN 2014J than for SN 2011fe when comparing the same passbands.

This also has implications for Figure 3. Here we calculated the weighted average for each color, taking the full covariance into account. However, the color excess is calculated by comparing the magnitudes of a reddened and an unreddened source. The two magnitudes will correspond to different effective wavelengths, and the broader the filter, and the steeper the spectrum, the larger the difference of the two effective wavelengths will become. For Figure 3 we allowed the wavelength to shift, with respect to the average effective wavelength using the FTZ law, until the residuals of the color excess match the weighted average residual from the fit. For the bluest F218W and F225W, the shift becomes 330 Å and 240 Å  respectively. Both of these filters suffer from minor red leaks, e.g., for F218W 0.3% of the light comes from wavelengths redder than 4000 Å. On the other hand, an SN Ia at maximum with the reddening of SN 2014J will typically be ∼6 orders of magnitude brighter at 4000 Å compared to the central wavelength of the F218W filter. The significant shift toward redder wavelengths for these filters is in other words not surprising.

We present the results from fitting three extinction laws to observations of SN 2014J in 16 photometric bands spanning the wavelength range 0.2–2 μm between phases −5 and +35 days with respect to the B maximum. We find a remarkably consistent picture with the reddening law fits only involving two free parameters. Once reddening is accounted for, the similarity between the multi-color light curves of SN 2014J and SN 2011fe is striking.

We measure an overall steep extinction law with a total-to-selective extinction value R_V at the maximum of R_V = 1.4 ± 0.1 for an MW-like extinction law. We also note that the fitted extinction laws are consistent when fitted separately around maximum and using the full phase range.

Although the fits slightly disfavor the empirically derived SALT2 color law for SN Ia, in comparison to an MW-like extinction law as parameterized by FTZ with a low R_V, conclusions should be drawn cautiously. SALT2 has not been specifically trained for the near-UV region considered here. Also, there is no prediction for the NIR. Intriguingly, the power-law extinction proposed by Goobar (2008) as a model for multiple scattering of light provides a good description of the reddening of SN 2014J.

Increasing this sample is crucial to understand the possible diversity in the reddening of SNe Ia used to measure the expansion history of the universe.

We thank Denise Taylor, Claus Leitherer, and John Mackenty at the Space Telescope Science Institute for advising and assisting us in carrying out this program. R.A. and A.G. acknowledge support from the Swedish Research Council and the Swedish Space Board. M.M.K. acknowledges support from the Hubble Fellowship and Carnegie-Princeton Fellowship. Observations were made with the Hubble Space Telescope; the Nordic Optical Telescope, operated by the Nordic Optical Telescope Scientific Association at the Observatorio del Roque de los Muchachos, La Palma, Spain; and the Mount Abu 1.2 m Infrared Telescope, India. STSDAS is a product of the Space Telescope Science Institute, which is operated by AURA for NASA. V.S. acknowledges support from Fundação para a Ciência e a Tecnologia (Ciência 2008) and grant PTDC/CTE-AST/112582/2009.