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No Stripped Hydrogen in the Nebular Spectra of Nearby Type Ia Supernova 2011fe

A generic prediction of the single-degenerate model for Type Ia supernovae (SNe Ia) is that a significant amount of material will be stripped from the donor star (~0.5 Msun for a giant donor and ~0.15 Msun for a main sequence donor) by the supernova ejecta. This material, excited by gamma-rays from radioactive decay, would then produce relatively narrow (1000 km s-1) emission features observable once the supernova enters the nebular phase. Such emission has never been detected, which already provides strong constraints on Type Ia progenitor models. In this Letter we report the deepest limit yet on the presence of H-alpha emission originating from the stripped hydrogen in the nebular spectrum of a Type Ia supernova obtained using a high signal-to-noise spectrum of the nearby normal SN Ia 2011fe 274 days after B-band maximum light with the Large Binocular Telescope's Multi-Object Double Spectrograph. We put a conservative upper limit on the H-alpha flux of 3.14 x 10^-17 erg s-1 cm-2, which corresponds to a luminosity of 1.57 x 10^35 erg s-1. By scaling models from the literature, our flux limit translates into an upper limit of 0.001 Msun of stripped material. This is an order of magnitude stronger than previous limits. SN 2011fe was a typical Type Ia supernova, special only in its proximity, and we argue that lack of hydrogen emission in its nebular spectrum adds yet another strong constraint on the single degenerate class of models for SNe Ia.

elusive (for a review see . It is commonly accepted that SNe Ia result from the thermonuclear explosion of a carbon-oxygen white dwarf (WD) in a close binary system, but the nature of the binary companion and the sequence of events leading to the SN explosion are still uncertain. There are two dominant models: the double degenerate (DD) scenario, in which the companion is also a WD (Tutukov & Yungelson 1979;Iben & Tutukov 1984;Webbink 1984), and the single degenerate (SD) scenario, in which the companion is a non-degenerate object such as a main sequence (MS) star, a red giant (RG), a sub-giant or a He star (Whelan & Iben 1973;Nomoto 1982). There are additional minor variations on these basic models of the progenitor system for both the SD channel (e.g. Justham 2011;Wheeler 2012) and the DD channel (e.g. Thompson 2011;Shappee & Thompson 2012). These uncertainties about the progenitor systems for SNe Ia remain a substantial problem for understanding the systematic errors in using SNe Ia to study cosmology (e.g. Wood-Vasey et al. 2007).
One of the observational signatures of the SD model is that the material from the companion should be stripped when struck by the SN ejecta (Wheeler et al. 1975), leading to both immediate signatures from the impact of the SN ejecta on the companion (e.g. Marietta et al. 2000;Meng et al. 2007;Pakmor et al. 2008;Pan et al. 2012b;Liu et al. 2012) and major changes in the companion's future evolution (Podsiadlowski 2003;Pan et al. 2012a). Recently, the hydrodynamic simulations of Pan et al. (2012b) and Liu et al. (2012) have shown that ∼ 0.1 − 0.2 M ⊙ of solar-metallicity material is expected to be removed from MS companions by the impact of the SN ejecta. These hydrodynamic simulations show that this material will be embedded in low-velocity supernova debris with a characteristic velocity of 1000 km s −1 . However, the line profiles from the stripped material are somewhat uncertain because this material will be asymmetrically stripped (Liu et al. 2012), and the orientation of the binary relative to our line of sight, at the time of explosion, is unknown. This material will be hidden in early-time spectra by higher velocity, optically thick, iron-rich ejecta, but will then appear in late-time, nebular phase spectra ( 250 days; Mattila et al. 2005) as the higher velocity ejecta become optically thin.
Only a handful of nebular phase, high signal-to-noise (S/N) SNe Ia spectra have been published in the literature, with the strongest limits on late-time hydrogen flux coming from Mattila et al. (2005) and Leonard (2007). Mattila et al. (2005) obtained late-time low-resolution spectra of SN 2001el, modeled the emission from solar-metallicity material stripped from a non-degenerate companion, and used both to place an upper limit of 0.03 M ⊙ on the presence of this material. Leonard (2007) obtained deep, medium-resolution, nebular-phase, multi-epoch spectra of SN 2005am and SN 2005cf at distances ∼37 Mpc and ∼32 Mpc, respectively. Using the approach of Mattila et al. (2005), he placed a 0.01 M ⊙ upper limit on the presence of any low velocity solar-abundance material in both SN. These observations seem to firmly rule out main sequence companions for these three SNe.
However, a more exotic scenario which might evade these constraints has since been proposed by Justham (2011). In this model a WD is spun up by the mass it accretes from its non-degenerate companion, allowing the WD to remain stable above the Chandrasekhar mass and giving the companion time to evolve and contract before the SN explosion. This leaves a smaller and more tightly bound companion at the time of explosion, reducing the amount of stripped material. It therefore is of significant interest to put even stronger constraints on the amount of stripped material for other SNe Ia.
At a mere 6.4 Mpc (Shappee & Stanek 2011) the "plain vanilla" Type Ia SN (as described by Wheeler 2012) is an ideal target for obtaining improved constraints. SN 2011fe was discovered less than one day after explosion by the Palomar Transient Factory (Law et al. 2009) in the Pinwheel Galaxy (M101), a wellstudied, nearby face-on spiral. This SN is the nearest Ia in the last 25 years and the early detection and announcement allowed extensive multi-wavelength follow-up observations (Nugent et al. 2011). Additionally, SN 2011fe is only slightly reddened and is surrounded by a relatively "clean" environment (Patat et al. 2011). Brown et al. (2012) and Bloom et al. (2012) used the very early-time UV and optical observations to constrain the shock heating that would occur as the SN ejecta collide with the companion, ruling out giants and main sequence secondaries more massive than the Sun. These constraints appear to rule out SD models; however, these studies both rely on Kasen (2010), which assumes a Roche-lobe overflowing secondary with a typical stellar structure and depends on the orientation of the binary relative to our line of sight. However, Meng et al. (2007) pointed out that the secondary will be left smaller and more compact than a typical main sequence star after binary evolution, which would produce a more subtle photometric signal at even earlier times which could have been missed by early-time observations.
In this study we place the strongest limits yet on the presence of Hα emission in the nebular spectrum of a Type Ia supernova (SN Ia). We obtained a very high S/N spectrum of SN Ia 2011fe 274 days after maximum B-band light using the Multi-Object Double Spectrograph on the 8.4-meter Large Binocular Telescope. We generally followed the analysis procedures used by Leonard (2007), so our constraints should be directly comparable to earlier results. In Section 2 we describe our observations, in Section 3 we derive our Hα limits, and we summarize our findings in Section 4.

Observations
We obtained five high-S/N spectra of SN 2011fe from 73 to 274 days after maximum B-band light using the first of the Multi-Object Double Spectrographs (MODS; Pogge et al. 2010) on the Large Binocular Telescope (LBT). The two channels of MODS allowed us to obtain wide spectral coverage (3200 − 10000Å) in a single exposure, which will make these observations useful for many future studies. Details of the observations and the flux standards used are listed in Table 1. All observations were taken through a 1 ′′ wide slit. To perform basic CCD reductions on our spectra we followed the "MODS Basic CCD Reduction with modsCCDRed" manual 6 . We then performed cosmic ray rejection using L.A.Cosmic (van Dokkum 2001) and combined each channel's 2D spectra for each epoch. Next, we extracted the 1D sky-subtracted spectra using the apall task in IRAF. 7 Each spectrum was then wavelength and flux calibrated. We did not attempt to correct small-scale telluric absorption bands as performed by Leonard (2007). This will not adversely affect our results because the telluric absorptions occurs on wavelength scales smaller than the Hα emission expected from the SN. This also avoids adding any noise from telluric spectra to our SN spectra.
Because our spectra were taken under non-photometric conditions with a relatively narrow (1 ′′ ) slit, it is necessary to scale the fluxes of our spectra to place them on an absolute flux scale. To do this we performed aperture photometry on our Sloan r ′ (Fukugita et al. 1996) acquisition images using the IRAF package apphot. Because the SN was saturated in the acquisition image of the first epoch we must treat that spectrum separately. For the remaining epochs we used the four brightest stars in the image to put our photometry on the Sloan Digital Sky Survey (SDSS; York et al. 2000) Data Release 7 (Abazajian et al. 2009) magnitude system. Our r ′ -band magnitudes are reported in Table 1. We then scale the spectrum so that its synthetic r ′ -band photometry matches the computed r ′ -band aperture photometry. For the first epoch we scaled the spectrum such that a synthetic R-band magnitude (Bessell & Murphy 2012) matches the R-band magnitude for its epoch found by interpolating the combined R-band light curves of Richmond & Smith (2012) and Munari et al. (2013). To convert from the AB magnitude system (Oke 1974) of our synthetic photometry to the Vega magnitude system reported in Richmond & Smith (2012) and Munari et al. (2013), we use the conversion presented in Blanton & Roweis (2007). The factor by which each spectrum was multiplied is reported in Table 1. From the last four epochs' spectra, which are calibrated from the acquisition image but are also covered by the combined R-band light curves of Richmond & Smith (2012) and Munari et al. (2013), we estimate that our absolute flux calibration in the R-band (where Hα is located) is accurate to 10% or better. In Figure 1 we show the BVRI light curves of Richmond & Smith (2012) and Munari et al. (2013) as compared to our synthetic BVRI photometry from the spectra for illustrative purposes. Figure  2 presents our calibrated spectra with obvious telluric features marked. Finally, we compare our nebular phase spectrum to the spectra presented in Leonard (2007), which provided the previous best limits on Hα. As can be seen in Figure 2, our spectrum has a substantially higher S/N than the previous studies. These observations allow us to place even stronger limit on Hα emission as we discuss in §3. Note. -Observational and derived properties of our time series spectra of SN 2011fe. Days since maximum B brightness assume JD t Bmax = 2455816.0 ± 0.3 (Richmond & Smith 2012). P.A. is the position angle of the spectrograph slit. Par. P.A. and airmass give the range of parallactic angles and airmasses at the start of each separate observation, respectively. Standard stars were observed on the same night as science observations and, when multiple standards were available, the computed response functions from each standard were averaged. Seeing gives the FWHM for the red / blue channels of the spatial profile in the combined 2d spectra. Exposure times are given for the red / blue channels separately. r ′ magnitude is derived from the acquisition images. Each flux calibrated spectra was multiplied by a scale factor derived in the R-or r ′ -band to place it on an absolute flux scale. a SN 2011fe was saturated in this epoch's acquisition images, so no reliable photometry was obtained.  (2012) and Munari et al. (2013), respectively. Our synthetic BV RI photometry are represented by filled stars. The first epoch is calibrated to an absolute flux scale using the Richmond & Smith (2012) R-band light curve so good agreement is expected. The rest of our spectra are calibrated using our r ′band acquisition images and SDSS DR7 photometry. From the second epoch we estimate that our absolute flux calibration is accurate to better than 10% in the R-band.   Leonard (2007) which previously provided the best limits on Hα emission from the stripped material. Our spectra are binned to match the resolution of Leonard (2007). The rest wavelength of Hα is indicated by the vertical red line and the shaded gray region shows where hydrogen emission would be expected ( ±1000 km s −1 = ±22 Å about Hα). Our spectrum has a substantially higher S/N due to the proximity of SN 2011fe, allowing us to place a substantially stronger limit on Hα emission in Section 3.

The Search for Hydrogen
In our search for Hα emission in the spectrum of SN 2011fe, we closely follow the methods presented in Leonard (2007). We define a continuum by smoothing our spectra on scales large compared to expected Hα feature, then subtract off this continuum and examine the residuals. We searched for Hα emission within ±1000 km s −1 (±22 Å) about Hα at the redshift of M101, 0.000804±0.000007 (de Vaucouleurs et al. 1991). We smoothed the spectrum with a second-order Savitsky-Golay smoothing polynomial (Press et al. 1992) with a width of 60 Å. Our data requires this smaller smoothing scale than that employed by Leonard (2007) for a good continuum fit. It is, however, still significantly larger than the expected velocity width of any Hα feature. Additionally, we smoothed over the telluric feature at 6510 − 6525 Å before smoothing the rest of the spectrum, because the feature was affecting the continuum determination near Hα.
Our nebular phase spectrum and continuum fit are shown in the top panel of Figure 4 in the vicinity of Hα and are binned to their approximate spectral resolution.
We then subtracted the continuum from the binned spectrum and examined the residuals, shown in the bottom panel of Figure 4, for narrow Hα emission. There is no evidence for any Hα emission in the spectrum. The closest possible emission is the hump in the smoothed continuum at ∼6575−6595 Å which is discussed in Section 3.2. More broadly, we found no narrow emission lines at any wavelength, including regions around Hβ, [O I]

Statistical Limit
Following Leonard & Filippenko (2001) and Leonard (2007), we compute a 3σ upper bound on the equivalent width as where ∆λ is the width of a resolution element (in Å), ∆I is the 1σ root-mean-square fluctuation of the flux around a normalized continuum level, W line is the full-width at half-maximum (FWHM) of the expected spectral feature (in Å), B is the number of bins per resolution element in the spectrum, and ∆X is the bin size of the spectrum (in Å). For the spectrum shown in in Figure 4, ∆I = 0.0024 Å and ∆X = 4 Åleading to W λ (3σ) = 0.067 Å for W line = 22 Å.
To translate this equivalent width constraint into a constraint on the amount of material stripped from a non-degenerate companion we follow the analysis of Mattila et al. (2005). Mattila et al. (2005) estimate that 0.5 M ⊙ of solar-abundance material 380 days after explosion produces an Hα feature with peak luminosity of ∼3.36 ×10 35 ergs s −1 Å −1 . Accounting for the distance to M101 and Galactic extinction towards M101 of E(B −V ) = 0.009 mag (Schlegel et al. 1998) and assuming R V = 3.1, the expected Hα peak flux from 0.5 M ⊙ of stripped material in SN 2011fe is 6.71 × 10 −17 erg s −1 cm −2 Å −1 . To allow for comparison with previous Fig. 4.-Nebular phase spectrum of SN 2011fe illustrating our conservative limit of 3.14 × 10 −17 erg s −1 cm −2 on the flux of Hα emission. The rest wavelength of Hα is indicated by the vertical red line and the shaded gray region shows where hydrogen emission would be expected ( ±1000 km s −1 = ±22 Å about Hα). Adopting the models of Mattila et al. (2005), these limits translate into a 0.001 M ⊙ limit on the amount of solar-abundance material stripped from the companion. Vertical dashed gray line marks a large telluric feature. Top Panel: SN spectrum binned to the approximate spectral resolution (4.0 Å; black solid); smoothed continuum (solid red); smoothed continuum with Hα limit added (dashed red); smoothed continuum with Hα limit subtracted to show what the underlying continuum would have to be to get the observed spectrum (dashed blue); and smoothed continuum with Hα limit subtracted, assuming the velocity distribution discussed in Section 3.2 (dotted blue). Middle Panel: The location of telluric water vapor absorption lines illustrated by the ESO SM-01 Sky Model Mode Version 1.3.1. Bottom Panel: SN spectrum with smoothed continuum subtracted (solid black) as compared to the Hα limit (dashed red). Horizontal solid red line marks zero.
works, we initially approximate the Hα feature as a Gaussian with FWHM 22 Å. This feature would then have an equivalent width of W λ (0.05 M ⊙ ) = 5.8 Å. Scaling linearly from the equivalent width of the Hα emission line to the amount of stripped material, we place an upper limit on the amount of solar-abundance material in SN 2011fe of 5.8 × 10 −4 M ⊙ .

Conservative Limit
Unlike the Leonard (2007) study, the main uncertainty in our Hα limit arises from the continuum determination and the Hα line profile rather than the photon noise of our spectrum. For example there is a small amplitude feature in the observed spectra at 6575 − 6595 Å. To test if this spectral feature could be attributed to material asymmetrically stripped from a companion we took the velocity distribution of stripped material from Figure 9 of Liu et al. (2012) and assumed it was narrowly distributed along a line (see Figure  11 of Liu et al. 2012). We found that a total flux of 2.20 × 10 −17 erg s −1 cm −2 and an angle between the stripped material and our line of sight of 30.0 • best reproduces the feature in our smoothed continuum. To be conservative, we take a less stringent limit on the total Hα flux of 3.14 × 10 −17 erg s −1 cm −2 , which is weaker than our statistical limit and too large to explain the spectral feature between 6575 − 6595 Å shown in Figure 4. This limit corresponds to an equivalent width of 0.12 Å, a total Hα luminosity of 1.57 × 10 35 erg s −1 , and 0.001 M ⊙ of solar-abundance material linearly scaling from the models of Mattila et al. (2005). We emphasize that whether this feature is Hα emission or clumpiness in the underlaying SN continuum, our conservative flux limit holds.

Summary
We obtained five deep, medium resolution, spectra of the nearby "plain vanilla" SN Ia 2011fe with LBT/MODS from 73 − 274 days after maximum B-band light. With the last nebular phase spectrum we place the deepest flux limits on narrow Hα emission yet for a SN Ia. Determining the late-time Hα emission in SNe Ia spectra requires difficult radiative transfer calculations, but linearly scaling from the models of Mattila et al. (2005), our limit translates into an upper limit on the mass of solar-abundance material of 0.001 M ⊙ , an order of a magnitude smaller than previous limits (Leonard 2007). However, two important theoretical questions remain. First, the opacity of the high-velocity iron-rich ejecta should be recomputed to confirm when the SN ejecta becomes optically thin. Second, the excitation of Hα emission by gammaray deposition should be modeled in detail assuming various velocity profiles with differing amounts of stripped companion material. These issues notwithstanding, our mass limit poses a significant challenge to more exotic SD models proposed to evade previous constraints. Additionally, our limit strongly rules out all MS and RG companions for which hydrodynamic simulations of the SN ejecta's impact are presented in the literature.
We thank Douglas C. Leonard for discussions and for providing the nebular phase spectra of SN