TYPE Ia SUPERNOVA CARBON FOOTPRINTS

SNIFS observed SN 2005di on 10 occasions between August 14 and September 22.²⁰ The first three spectra of SN 2005di appear in Figure 2. The −8.6 day spectrum used here is a co-addition of two consecutive exposures on the same night. Close examination of the time series reveals the presence of narrow rest-frame Na i D absorption (see Figure 3(a)). This and the relatively red appearance of the spectral energy distribution lead us to conclude that SN 2005di is heavily extinguished by line-of-sight dust in its host galaxy or circumstellar environment. Since SNIFS exposure times were generally not adjusted to compensate for high extinction, the spectra of SN 2005di have lower S/N than typical SNe Ia observed by SNIFS at the same redshift. Still, C ii λ6580 is detected in the first spectrum and possibly in the second.

Initial spectroscopic classifications of SN 2005di were published by two groups. Salvo et al. (2005) reported that a spectrum obtained on August 16 resembles the spectrum of another SN Ia a few days past peak, and Gal-Yam et al. (2005) state that their August 14 spectrum suggests that SN 2005di is "young," but neither report discusses C ii. The SNIFS quick-reduction pipeline classification indicated that SN 2005di was an SN Ia about 1 week before maximum and highly extinguished with an estimated E(B − V) ∼ 0.5. Revisiting our quick-reduction spectrum we find that the C ii λ6580 absorption notch could have been identified, but its significance was not obvious at the time.

SN 2005di was used in the SNfactory spectral flux ratio luminosity indicator study (Bailey et al. 2009). That study found the ratio of flux measured at 642 nm to that at 443 nm at maximum light ($\mathcal {R}_{642/443}$) to be a good predictor of relative luminosity. SN 2005di is the object in that study with the largest value of $\mathcal {R}_{642/443}$, owing primarily to its red color. Any possible effect of C ii λ6580 emission near 642 nm either as a possible source of signal or noise in the relationship between $\mathcal {R}_{642/443}$ and Hubble diagram residual was not discussed, since at the time of publication the presence of C ii had not been noticed. We expect our C ii λ6580 detection to have no implication for the flux ratio result, since that study was restricted to spectra obtained within 2.5 days of maximum, when the carbon signature is gone.

Nineteen SNIFS visits of SN 2005el were conducted between September 26 and November 20. Figure 2 includes the spectra from the first two of these. The −6.9 day observation is a co-addition of the two observations obtained that night. In this case, C ii λ6580 is only positively detected by SYNAPPS on the first date of observation. However, it is clearly present in both high S/N spectra taken that night and the co-add.

SN 2005el is a very well observed SN (Wood-Vasey et al. 2008; Hicken et al. 2009; Contreras et al. 2010). Its spectroscopic normality has been remarked upon in the literature previously (e.g., Phillips et al. 2007; Höflich et al. 2010). Initial classification reports indicated that SN 2005el was discovered a few to several days prior to maximum (Wong et al. 2005; Morrell et al. 2005) but until now no remarks have been made in the literature regarding the presence of C ii in the spectra. These classification spectra were obtained the same night as the first SNIFS observations. The SNIFS quick-reduction pipeline in use during the SN 2005el campaign failed to properly correct for a cosmic-ray hit coincident with the C ii λ6580 notch in one spatial element of the two spectra obtained on the first night. Subsequent improvements to the pipeline later revealed the clear C ii λ6580 notch in both spectra.

SNIFS follow-up of SN 2005ki was triggered on November 20. Six nights of observations were obtained in all, ending on December 2, around the time of maximum brightness. Follow-up ended prematurely due to equipment failure at the UH 2.2 m telescope that forced an extended offline period for SNIFS. Therefore, we adopt the date of maximum and light curve fit parameters from a SALT2 fit to more complete photometry published by Hicken et al. (2009) and Contreras et al. (2010). The first three spectra of SN 2005ki are presented in Figure 2. Relatively weak C ii λ6580 absorption is detected in the first spectrum and very marginally in the second. Returning to the first two SNIFS quick-reduction spectra of this object, the presence of C ii λ6580 now seems obvious in retrospect. Our classification announcement made no mention of it (SNfactory 2005).

Twenty nights of spectroscopy of SNF20080514-002 were obtained with SNIFS, starting on May 16 and ending on July 9. The first four spectra of SNF20080514-002 appear in Figure 2. The −7.9 day and −5.0 day spectra are co-additions of three consecutive observations on each respective night. C ii λ6580 is clearly detected in the first two spectra of this object and probably in the third. Though the emission peak visible at the position of the notch in the fourth spectrum looks flattened, we hesitate to posit a flux depression due to C ii opacity in this case. At this point, SYNAPPS is able to convincingly fit the feature with or without a weak C ii λ6580 line.

As initially reported (SNfactory 2008a), the early spectra of SNF20080514-002 are quite blue, indicative of an SN Ia at or before a week prior to maximum light. Both spectra exhibit absorption lines attributed to C ii λ6580, but C ii λ7234 is not as readily apparent as in, say, SN 2005el. C ii λ4745 was also mentioned, but is a much weaker and more blended line than the others.

Like SN 2005di, SNF20080514-002 was used in the Bailey et al. (2009) flux ratio study. In marked contrast to SN 2005di, this target has an extremely blue color but is well within the core of the Hubble residual versus $\mathcal {R}_{642/443}$ distribution (their Figure 2). As with SN 2005di, the use of the at-maximum spectrum for the flux ratio study limits the influence of C ii λ6580 on those results.

SNIFS observed SN 2005cf on 12 nights from June 3 to July 8. The first two spectra are shown at the bottom of Figure 2. A small C ii λ6580 absorption notch is visible in the −9.4 day spectrum but becomes absent or nearly absent 2 days later. Our selection guidelines require detection in two distinct SNIFS spectra, so we should technically disqualify SN 2005cf from further consideration. However, SN 2005cf is an object with extensive previously published spectroscopy (Garavini et al. 2007; Wang et al. 2009b). Neither previous spectroscopic study nor the original classification announcement (Modjaz et al. 2005) discussed the putative C ii λ6580 notch visible in the spectra. When considering those observations, Parrent et al. (2011) placed SN 2005cf into their "uncertain" C ii detection category. But given three independent data sets showing the same feature at roughly the same phase, it now seems difficult to overlook the presence of C ii in the case of SN 2005cf.

The detailed evolution of the carbon features in the pre-maximum spectra of SNe 2005di, 2005el, 2005ki, and SNF20080514-002 is depicted in Figure 3. SN 2005cf and a non-detection case for comparison (SNF20071021-000) appear in Figure 4. The C ii λ6580 notch is readily apparent, situated at or quite near the rest-frame emission peak of the Si ii λ6355 feature. The detailed evolution of the feature in each case is described in the Appendix.

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In the first four cases, the notch is strongest in the earliest spectrum. It weakens gradually with time and without appreciable wavelength shift. Generally, the notch is centered on an apparent blueshift of 12, 000 km s⁻¹ relative to rest-frame C ii λ6580 (also roughly the same velocity as observed in SN 2006D). In SN 2005cf, the notch disappears between the first and second spectrum.

Excluding SN 2005cf, we see that while the notch dissipates, the shape of the spectrum just redward evolves as well. The slope of the decline in flux on the red side of the Si ii λ6355 emission feature becomes steeper while the notch weakens and the underlying Si ii λ6355 emission peak rises. In some cases (SNe 2005di, 2005ki, and SNF20080514-002), the earlier spectra may even exhibit a mild "flux plateau" morphology. Along with an absorption notch, such an emission plateau could be a signature of a "detached" distribution of C ii line opacity in a shell separated somewhat from the photosphere (Jeffery & Branch 1990). However, under spherical symmetry, such a plateau should be roughly symmetric about the line rest wavelength. Visually, this does not seem to be the case here.

The notch in the spectrum of SN 2005cf is morphologically distinct from the other cases and appears to span a slightly smaller range in blueshift (10, 000–13, 000 km s⁻¹). When the notch disappears, there is at most only a small amount of evolution in the flux slope just redward.

Confident identification of C ii λ7234 is problematic. Almost none of the cases presented shows a clear absorption feature at the same blueshift as the C ii λ6580 notch. At most, there is only an inflection visible around 6900–7000 Å and a slight emission "bump" around 7100 Å. Visual inspection alone would seem to be insufficient to draw more firm conclusions about the presence or absence of C ii λ7234 in general.

To examine the extent to which the selected targets are spectroscopically normal SNe Ia, we again use SYNAPPS, this time to fit the full wavelength range of each pre-maximum spectrum of each selected SN (detailed commentary is provided in the Appendix). Close examination of the C ii features in the full fits may also enable some explosion-model independent statements about the distribution of carbon in the SN ejecta. Two selected fits for each SN appear in Figures 5 and 6: one fit to the first available spectrum and another fit to the first spectrum where C ii is absent. In general, the opacity profiles for C ii lines decrease with time as expected. Wavelengths of major ion contributors to the spectra are marked at the top of either figure. Except for the presence of C ii, the spectra of the first four carbon-positive SNe Ia are anything but extraordinary—typical SN Ia ions at normal pre-maximum ejection velocities. SN 2005cf is another matter, since HV Si ii and Ca ii components are mandatory for a good fit, as discussed previously (Garavini et al. 2007; Wang et al. 2009b).

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In each case, we find compelling evidence for opacity from C ii, O i, Mg ii, Si ii and Si iii, S ii, Ca ii, singly ionized ions of Ti through Co, and Fe iii. For both Si ii and Ca ii, we enable two-component fits: one for a photospheric (undetached) component and another for an HV (detached) component. The opacity profiles of all other ions are undetached from the photosphere. Optimal values for the velocity at the photosphere are found in the range 12, 000–13, 000 km s⁻¹. Including some Na i opacity does seem to improve the fit morphology around the Si ii 5800 Å absorption feature—however, this identification is not unprecedented (e.g., Branch et al. 2005). In all cases, we were able to reconstruct the basic structure redward of 3500 Å quite well and at times had reasonable success fitting the ultraviolet (UV, where lines from iron-peak elements dominate). We do not expect exceptional agreement in the UV, as the underlying assumptions of SYNAPPS (in particular the treatment of line opacity) begin to break down here. In general, the strengths of the features evolve smoothly with time and no abrupt changes are observed as the C ii becomes optically thin.

SYNAPPS accounts for the C ii λ6580 feature, including the region just redward of the notch, rather well (see Figure 7, red curve). Variations with and without detached C ii were tried, but again SYNAPPS tended to set the lower velocity of the C ii region to the velocity at the photosphere, making the need for detachment uncompelling. Analysis of the fit residuals indicates that the SYNAPPS model has insufficient fidelity for achieving a reduced χ² of 1, but we find no strong indications of persistent residual structure.

In Figure 7, the 5800–7500 Å region of the first spectrum of each carbon-positive SN is overlaid with the converged, all-ions, full-wavelength SYNAPPS fits (shown in red). The blue curve results when the fully converged synthetic spectrum is recomputed with the C ii opacity deactivated, while all other settings retain their converged values. The blue curves are thus not re-fits without C ii included, in contrast to the example plots shown in Figure 1. Thus, the change from the blue curve to the red one illustrates what role C ii plays in the formation of the spectrum quite clearly. Not only is C ii λ6580 responsible for the absorption notch, it "screens" emission from bluer Si ii λ6355 effectively enough that some emission relative to the C ii-free spectrum (centered around 6600 Å) is visible in the top four cases. Finally, Figure 7 indicates that the flux depression around 6900–7000 Å may indeed be influenced by C ii λ7234 to some extent.

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It is interesting that three of the five carbon-positive SNe Ia have relatively narrow light curves, with low SALT2 x₁ values around −2 (s ∼ 0.87, or Δm₁₅(B) ∼ 1.47, see Table 1). These same targets also have bluer than normal colors. SNF20080514-002 is also among the SNe Ia observed by Swift/Ultraviolet and Optical Telescope (UVOT) (Gehrels et al. 2004; Roming et al. 2005) with largest UV excesses (Immler & Brown 2008), as shown in Figure 8 (adapted from Milne et al. 2010). Swift/UVOT photometry for SNe 2008hv and SNF20080514-002 will be presented in Brown et al. (2011). Figure 9 is a plot of SALT2 fit parameters for all SNe Ia with SNIFS light curve fits and a spectrum before −5 days, the latest phase for which any C ii λ6580 is positively detected in this sample. SNe 2005el, 2005ki, and SNF20080514-002 form a relatively tight "cluster" at the fast declining (low x₁) but blue corner of this plot. Other published results for SN 2005el have a somewhat larger value for x₁ (Hicken et al. 2009; Contreras et al. 2010), though all measurements indicate that x₁ is negative and this SN belongs in this group of relatively narrow light curves with blue colors. Thus, the quantitative results for SN 2005el may be further refined, but our qualitative conclusions should remain unchanged.

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Neither SN 2005cf nor SN 2005di fit into the fast-decliner/blue-color family. In the case of SN 2005cf, this may not be surprising since the Si ii and Ca ii features quite robustly trace out HV ejecta more dramatically than in the other SNe at the same phases, indicating real physical differences between SN 2005cf and the others. However, as described in Section 3 there is evidence that SN 2005di is extrinsically reddened. Since our data do not resolve the Voigt profiles of the possible multiple velocity components comprising the Na i D absorption line, we are unable to apply a quantitative correction for extinction using Na i D equivalent width (Poznanski et al. 2011). Instead, we use a different procedure to investigate whether SN 2005di could simply be a reddened member of the fast-decliner/blue-color subclass.

To see if this is at least a plausible hypothesis, we warp the spectral time series of SN 2005di according to the CCM dust law, fitting for the optimal differential E(B − V) that brings the spectra into detailed agreement above 5000 Å with each of SNe 2005el, 2005ki, and SNF20080514-002. We make no attempt to constrain the differential R_V and we assume a standard Milky Way value of 3.1. If we assume that the main difference between SN 2005di and the other SNe is the amount of dust extinction the former suffers, then correcting for it should bring the spectral time series into alignment. In the case of perfect "twin" SNe, the agreement above 5000 Å should be exquisite on a feature-by-feature basis and the extrapolated flux below 5000 Å a good match.

The warping technique and a fully developed twin SN study are the subject of a future paper (Fakhouri et al. 2011), here we briefly describe the mechanics for two given objects. Spectral observations of the objects are paired based on phase, with similar phases being matched to each other. A linear interpolation correction to the fluxes accounts for overall flux difference arising from the small phase differences. A CCM dust law with fixed R_V = 3.1 is fit to the ensemble of paired spectra, as well as an individual scale factor for each pair, to account for any small scatter. By fitting all of the pairs (extending from early epochs to late epochs) jointly for the appropriate dust law warping, we minimize the influence of any particular features on the fit at any given phase.

Figure 10 shows pairs of spectra that result when the time series of SN 2005di is warped to match the flux from another SN above 5000 Å, roughly matching by phase. The earliest pair of phases formed in each of the three cases is shown. The agreement above 5000 Å on a feature-by-feature basis is quite good, though there is a significant difference in the Si ii λ6355 absorption feature with respect to SN 2005ki—clearly an "intrinsic" difference. Blueward of the 5000 Å cut, the extrapolated color looks quite consistent. Thus, while we cannot prove definitively that SN 2005di is a dust-estranged member of the fast-decliner/blue-color family, there does seem to be a resemblance. Figure 9 includes the position of SN 2005di when corrected for the median derived differential E(B − V) = 0.40 is removed.

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Our data suggest that unburned carbon, while far from ubiquitous, is also not particularly rare—in line with the result of Parrent et al. (2011). A detailed rate calculation is beyond the scope of this article, but we can try to estimate the frequency of photospheric velocity carbon in normal SNe Ia based on the latest phase (−5.0 d) and lowest median S/N per 2.4 Å bin in the wavelength range of interest (11.7, that of SN 2005di at −11.3 days) where C ii λ6580 is detected. Thirty-one SNe Ia pass these cuts in the full SNfactory sample (which includes SN 2006D, Thomas et al. 2007), of which two are super-Chandrasekhar candidates and a further two are SN 1991T-like. Excluding these four SNe places the fraction of SNe Ia with C ii λ6580 that persists to roughly −5 days at 22⁺¹⁰ _{− 6}% (Bayesian binomial confidence interval, see Cameron 2010).

SN 2005el, SN 2005ki, SNF20080514-002, and perhaps SN 2005di could be members of a physically meaningful family of SNe Ia characterized by detectable carbon in their early spectra, relatively fast-declining light curves, and intrinsically blue colors. These four SNe were selected solely based on the presence of carbon signatures in their spectra, so we now reverse the selection and re-examine the early spectra of other objects with similar light curve or color parameters.

The most interesting results from our surveyed sample come from objects with similar light curve width. Figure 11 shows the 5800–7500 Å region of the pre-maximum spectra of SN 2006dm (Schwehr & Li 2006) and SNF20080919-002. Neither case presents a robust notch, however the Si ii λ6355 emission peak looks somewhat "squashed" in the earliest spectra. The evidence is hardly decisively in favor of photospheric velocity carbon in these two additional SNe Ia, but it is tantalizing. Carbon-positive SN 2006D (Thomas et al. 2007) is also plotted in Figure 9. It also has a SALT2 x1 around −2 but is redder than the objects uncovered by our survey here.

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Returning to the Swift/UVOT color curves in Figure 8, we identify SN 2008Q (Villi et al. 2008) and SN 2008hv (Pignata et al. 2008) as having UV colors similar to those of SNF20080514-002. All three of these targets separate from the rest of the Swift sample especially well in u–v color space. While the spectroscopic classification announcements for neither SN 2008Q (Stanishev 2008) nor SN 2008hv (Marion et al. 2008; Challis & Hora 2008; Folatelli & Forster 2008) mention C ii λ6580, the pre-maximum spectra of both objects include the absorption notch signature (V. Stanishev and G. H. Marion 2011; private communications). Both Ganeshalingam et al. (2010) and Brown et al. (2010) report a faster-than-average decline rate (corresponding roughly to x₁ of −0.92 and −1.67, respectively) for SN 2008Q, suggesting that it could also belong with the fast-decliner/blue-color family. Optical light curve analysis for SN 2008hv is yet to be published, but a preliminary decline-rate estimate from the UVOT photometry appears to be faster than average.

Next, we consider whether normal SNe Ia with previous C ii λ6580 detections in the literature have a tendency toward narrow light curves and blue colors. A revisit of Parrent et al. (2011) yields mixed results, partially because of the lack of consistent light curve fits across all the data sets. Of the two "definite" cases presented there in the low-velocity and high-velocity gradient subgroups, SN 1990N fails to fit the pattern (x₁ = 0.54 ± 0.10, c = 0.10 ± 0.01) and the other is SN 2006D. The "probable" category (where data are available) is dominated by narrower light curves than average as well, but no strong tendency toward blue colors. The exact role that host galaxy dust extinction plays in the Parrent et al. (2011) sample is unconstrained, however. Overall, it would seem that the picture for unburned carbon in SNe Ia may be a complex one, where there are multiple subclasses and considerable variation between them.

Four of the five newly identified carbon-positive SNe Ia may indeed be representative of a meaningful subclass, but SN 2005cf stands apart. Its light curve shape is less extreme and its colors more red. It also lacks the large UV excess of SNF20080514-002 seen in Figure 8. HV ejecta signatures in the spectra of SN 2005cf are much stronger than in the other carbon-positive SNe Ia considered here. Though HV Ca ii features may be "ubiquitous" (Mazzali et al. 2005), it is clear that there is considerable variation in the velocities and line strengths observed. Cases with the strongest HV Ca ii IR triplet also seem to exhibit strong Si ii λ6355 absorption early on (Stanishev et al. 2007). The origin of the HV features remains unclear. (Is it a density or composition enhancement in the ejecta or is it swept-up circumstellar material? See, e.g., Gerardy et al. 2004; Tanaka et al. 2008; Wang et al. 2009b.) Evidence for a connection between carbon and the HV features is weak. The best candidate aside from SN 2005cf with HV features and a possible C ii λ6580 notch seems to be SN 2003du (Stanishev et al. 2007; Tanaka et al. 2008). On the other hand, SN 2009ig (also with HV features) appears to be a counterexample (not a distinct notch, so Parrent et al. 2011 label it at most a "possible" detection). SNF20071021-000, the non-detection example in Figure 4 is yet another.

A number of "peculiar" SNe Ia (or SN Ia-like objects) with carbon lines have been discussed in the literature. Here we compare our sample of normal SNe Ia with those objects.

C ii features are a spectroscopic bellwether of candidate super-Chandrasekhar SNe Ia, where they seem to persist to maximum light and even beyond (Howell et al. 2006; Hicken et al. 2007; Scalzo et al. 2010; Yamanaka et al. 2009; Silverman et al. 2010). This has been interpreted as evidence supporting the super-Chandrasekhar hypothesis, where more total carbon is present in the progenitor and/or much remains after disruption. These objects are quite overluminous and have much broader than normal light curves. Their spectra, while mostly consistent with one another, are quite different from those of objects considered here. Overall, if the super-Chandrasekhar candidates form a subclass of SNe Ia, it is distinct from the one proposed here.

With varying degrees of certainty, carbon is also occasionally detected in low luminosity, short timescale or otherwise peculiar SNe Ia. Taubenberger et al. (2008) claim that C ii λ6580 is present in the spectra of SN 2005bl, a low-luminosity SN 1991bg-like SN Ia, but carbon is seldom remarked upon or observed in other members of this subclass. More unusual events like SN 2002cx (Li et al. 2003; Branch et al. 2004), SN 2005hk (Chornock et al. 2006; Phillips et al. 2007), SN 2007qd (McClelland et al. 2010), and SN 2008ha (Foley et al. 2010a) have been conjectured to represent a distinct population of peculiar, low-luminosity SNe Ia. These SNe are quite sub-luminous (peak M_B ≳ −18), have light curves that evolve more rapidly than normal SNe Ia, and have spectra that exhibit many narrow absorption lines that suggest lower kinetic energies than typical. Pure white dwarf deflagrations or failed deflagrations may provide a plausible way to account for those observations, in which case carbon signatures may also be expected (e.g., Röpke et al. 2007), but the carbon identifications in the spectra of these events have been at best tentative. Spectra of candidate "SNe .Ia" (Bildsten et al. 2007), SN 2002bj (Poznanski et al. 2010), and SN 2010X (Kasliwal et al. 2010) exhibit robust C ii detections, but so far detailed simulations of SNe .Ia (Shen et al. 2010) do not predict observable carbon. All of the above cases are much dimmer than the SNe considered here and much more exotic spectroscopically.

SN 2006bt (Foley et al. 2010b), however, merits specific attention. An outlier on the SN Ia light curve width/luminosity relation, SN 2006bt exhibits some spectroscopic peculiarities. Most interestingly, its earliest spectra possess a unique C ii λ6580 signature, a notch centered at 5200 km s⁻¹, apparent in at least two consecutive observations (Foley et al. 2009; Valenti et al. 2009). There is little, if any, evidence for emission to the red of the notch, and the vast difference between the apparent blueshift of the C ii λ6580 notch and the velocities of other ejected elements (12, 500 km s⁻¹ for Si ii λ6355) is quite striking. Foley et al. (2010b) suggest that the discrepancy can be accounted for by an ejected blob moving at an angle to the line of sight. The carbon identifications in the spectra of these events are irregular, tentative in most cases, though SN 2008ha presents the most clear C ii signatures (Foley et al. 2010a).

Inspired by the characteristics of multi-dimensional explosion simulations with strong asymmetries, observers have searched for spectroscopic and spectropolarimetric indications of deviation from spherical composition symmetry in SNe Ia. Spectropolarimetry offers the best means for probing the geometry of SN ejecta, but opportunities for follow-up are relatively rare and the available sample is small. Wang & Wheeler (2008) describe spectropolarimetric observations of two SNe Ia in our carbon-positive sample, SNe 2005cf and 2005el (a single epoch each). In neither case is there a particularly strong case for deviation from basically spherical composition symmetry. A dominant axis in the Stokes Q/U diagram is at least identifiable for SN 2005el, suggestive of some combination of global and smaller scale asymmetries.

While spectropolarimetry may be more definitive for constraining the geometry of the unburned material, it is interesting to consider the constraints we can set with our pure flux measurements. The comparison of synthetic spectra with and without C ii shown in Figure 7 suggests that the spatial distribution of unburned carbon in the ejecta may be quite consistent with spherical symmetry. Figure 12 demonstrates our reasoning simply, using toy model synthetic line profiles.

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The classic SN spectroscopic feature formed by a single line is plotted at the top of Figure 12: blueshifted absorption produced by material in front of the photosphere and expanding toward the observer, with an emission hump centered at the rest wavelength of the line arising from material adjacent to the photosphere in projection. For discussion purposes, we label this line "line A" and assign it a rest wavelength of 6355 Å.

Consider a second line, "line B" with rest wavelength 6580 Å, a Doppler shift of 12, 000 km s⁻¹, a shift quite similar to the cases seen in the data. If the ejecta bearing the parent ions of line B are distributed in a "blob" that only partially covers the photosphere and/or line A emissivity in projection, it is quite easy to construct a line B absorption notch blended with the line A emission component. An example of the resulting blend appears in the middle of Figure 12, overlaid on the line A profile.

Now, suppose the line B ions are distributed spherically symmetrically. In this case, a quite different blended profile results. Line B notches can be produced, but not without additional disruption of the line A profile. Flux redward of the notch is suppressed and there is even a mild red emission feature relative to the single unblended line A case. Such a blend is depicted at the bottom of Figure 12, again overlaid on the single line A profile for comparison.

Because line B opacity does not encircle the photosphere in the blob case, its effect is restricted to wavelengths corresponding roughly to where the blob is optically thick in blueshift parallel to the line of sight. However, when line B ions are distributed under spherical symmetry, the photosphere is cocooned by them, and they scatter away continuum and line A photons alike over a larger range of projected velocity. This results in the notch, the flux suppression to the red of it, and the small emission further on. Essentially, the driving factor is the projected area over which line B photons screen continuum but also line A emissivity, at a given wavelength.

The fits in Figure 7 appear more consistent with the spherically symmetric case demonstrated in Figure 12. Our toy models are quite simple, but illustrate the leading-order screening effect quite clearly. At the very least, our results highlight the critical need for detailed spectroscopy and spectropolarimetry of SNe Ia at early phases to make the most definitive conclusions about the geometry of the carbon ejecta.

The possible existence of a family of SNe Ia with similar properties to those demonstrated by SN 2005el, SN 2005ki, SNF20080514-002, and perhaps SN 2005di, is particularly intriguing. The combination of a narrow light curve, large UV excess, or at least blue colors, and the presence of photospheric velocity carbon suggests a very particular conceptual picture. A faster than average decline rate indicates lower than average luminosity for an SN Ia, in turn suggesting a lower than average mass of freshly synthesized radioactive nickel. The blue colors suggest that the amount of iron-peak elements synthesized or mixed into the outer layers is low (suppressing line-blanketing at shorter wavelengths), and these elements are limited to lower velocities. Also, a relatively high carbon abundance in the material above the photosphere indicates less efficient processing of the white dwarf progenitor material.

The above picture is somewhat consistent with a subset or region of delayed-detonation model space. Estimates of the mass fraction of photospheric carbon in SNe Ia are generally low (of order 1%, e.g., Branch et al. 2003; Marion et al. 2006; Thomas et al. 2007; Tanaka et al. 2008; Maeda et al. 2010b) and are also generally consistent with most such models. Of particular interest is the recent grid of multi-dimensional models presented by Kasen et al. (2009). In these models, a strong ignition (arising from numerous initiating sparks) raises the amount of burning that takes place during the initial sub-sonic deflagration phase. This allows the outer, unburned layers to pre-expand more relative to the weaker ignition case. When the later detonation wave passes through the pre-expanded material, nuclear burning is less efficient and the abundance of iron-peak elements is lower relative to the weak ignition case. This results in relatively lower radioactive nickel mass which is more centrally peaked in the ejecta.

However, the total amount of unburned carbon left in these models is below 1% by mass, and the S/N of the synthesized Monte Carlo spectra is too low to attempt to detect any carbon signatures in them. This result is actually at variance to earlier (one-dimensional) delayed-detonation models (e.g., Höflich et al. 2002), where some amount of unburned carbon can be left behind. Simply put, the multi-dimensional model grids may not yet be extensive enough.

In most of the carbon-positive SNe Ia discussed here, there seems to be intriguing evidence that the carbon is distributed roughly spherically symmetrically and at velocities overlapping silicon. There may still be room for deviation from spherical symmetry in the distribution of unburned material that we cannot rule out here. For example, large-scale asymmetries, such as proposed by Maeda et al. (2010a) to explain spectroscopic diversity, may allow for almost hemispherical covering of the photosphere by carbon. In that particular picture, an offset ignition in the white dwarf progenitor yields an asymmetric distribution of burning products. This scenario is proposed to explain the origin of "high-velocity gradient" (HVG) and "low-velocity gradient" (LVG) subclasses of SNe Ia, segregated by the rate of decrease in measured Si ii λ6355 blueshift with time (Benetti et al. 2005). Viewed from the side closest to the ignition, one observes an LVG SN Ia; and viewed from the other an HVG SN Ia. Detonation products are distributed in the outer layers in all directions, but it is not yet clear how complete the burning is. Interestingly, Tanaka et al. (2008) remarked that of three LVG SNe Ia they studied, all had marginally detected C ii λ6580 and blue colors. Their analysis suggests that LVG SNe Ia undergo less intense burning than their counterparts. A systematic examination of Si ii λ6355 blueshift evolution of SNfactory SNe Ia is in progress, but our preliminary results indicate that all five objects identified here are also LVG members. Whether or not a Maeda et al. (2010a) scenario is capable of explaining all the observables, and can yield carbon amounts and distributions consistent with observations, remains to be seen through detailed multi-dimensional explosion modeling and radiative transfer.

C ii. The C ii λ6580 absorption notch is clearly visible in the −11.3 day spectrum, located between roughly 9000 and 15, 000 km s⁻¹ with a minimum around 12, 000 km s⁻¹ in apparent blueshift. Almost 3 days later, the notch is barely discernible and it is clearly absent by −3.6 days. In the last spectrum, it is unlikely that the noise is obscuring a notch: the change in the shape of the spectrum between the last two spectra is overt. Examining the C ii λ7234 region, we detect an inflection in the shape of all three spectra, but its position is inconsistent across phase. This inconsistency may be a consequence of the low S/N of the observations. In the first spectrum, the flux depression is coincident with the λ6580 notch in blueshift, but this is not the case in the later spectra. However, in all three spectra, a bump in the flux centered at a λ7234 blueshift of 5000 km s⁻¹ is clearly visible. Figure 3(a) also clearly shows the narrow rest-frame Na i D absorption in the shaded rectangle.

SYNAPPS fits. C ii contributes to the spectrum on −11.3 days and also in the next spectrum on −8.6 days, but on −3.6 day SYNAPPS finds no need for it. The SYNAPPS velocity at the photosphere (v_phot) fits are 12, 600, 12, 200, and 11, 900 km s⁻¹, respectively. HV Ca ii opacity is invoked (at v > 20, 000 km s⁻¹) though the signature is rather small—it is more important for fitting the IR triplet than the UV H and K feature. Ultimately, the case for HV Si ii is uncompelling, which is not surprising since the blue side of the Si ii λ6355 absorption only extends to 18, 000 km s⁻¹, in contrast to instances where HV Si ii has been previously discussed (e.g., SN 2005cf, Garavini et al. 2007) and found to extend upward of 20, 000 km s⁻¹.

C ii. A C ii λ6580 absorption notch is readily seen in the −6.9 day spectrum. As in SN 2005di, the notch is located in the apparent blueshift interval 10, 000–15, 000 km s⁻¹. There is a clear depression in the flux around 6980 Å, possibly attributable to C ii λ7234 absorption, though the blueshift is not completely consistent with that for the λ6580 notch. Both features disappear from the spectrum by the time of maximum light. As in SN 2005di, the red side of the Si ii emission feature steepens as the SN ages and the C ii λ6580 dissipates. There is also an emission bump to the red side of the λ7234 notch, centered at a rest-frame blueshift of 5000 km s⁻¹. Like the two notches, this bump disappears by maximum light.

SYNAPPS fits. SYNAPPS requires C ii only in the −6.9 day spectrum and not at maximum light. The value of v_phot changes from 12, 500 to 12, 000 km s⁻¹ from the first spectrum to the second. HV Ca ii and Si ii opacity components were enabled as was done with SN 2005di. The results were similar, with some HV Ca ii contributing to the IR triplet and the bluer feature of the H and K absorption blend, and HV Si ii making only a minor contribution to the blue wing of the Si ii λ6355 absorption in the first spectrum.

C  ii . In the −10.4 day spectrum, the C ii λ6580 notch appears slightly more blueshifted than in the first spectra of SNe 2005di and 2005el, extending just beyond 15, 000 km s⁻¹. The same is true for Si ii λ6355 absorptions. As before, the carbon signatures dissipate as the SN brightens: weaker by −8.5 days and absent by −5.5 days. Also, in the first spectrum, an emission plateau just redward of the notch is visible, asymmetric with respect to the rest wavelength of λ6580, and again it weakens in parallel with the notch. A clear association for C ii λ7234 in this spectrum is quite problematic: the fading bump at 7100 Å is again visible, but there is no clear absorption notch.

SYNAPPS fits. C ii opacity is used in the −10.4 and −8.5 day spectra, but not in the −5.5 day spectrum. SYNAPPS photospheric velocities for SN 2005ki are a bit higher than in the other SNe considered here, with v_phot fit at 13, 100, 12, 600, and 12, 500 km s⁻¹. One major difference is that a distinct HV Ca ii opacity component is not required to reproduce the Ca ii features, especially at −10.4 days: a single opacity profile extending to HV is sufficient.

C ii. The C ii λ6580 notch (apparent blueshift interval again 10, 000–15, 000 km s⁻¹) is most apparent at −10.0 and −7.9 days, still discernable at −5.0 days, and probably absent at −3.1 days. The notch is accompanied by a modest and fading emission plateau to the red which is almost symmetric about the line rest wavelength. The λ7234 blueshift region is again characterized by an inflection and bump centered blueward of 7234 Å and again the strength of this bump decreases with time.

SYNAPPS fits. C ii opacity is needed in the −10.0, −7.9, and −5.0 day fits, but not on day −3.1. The values of v_phot fit are 12, 700, 12, 400, 12, 100, and 12, 100 km s⁻¹, respectively. Only a modest amount of HV Ca ii opacity is used in these fits and HV Si ii proves to be unnecessary.

C ii. The C ii λ6580 absorption notch shape is significantly different from that seen in the other carbon-positive SNe Ia studied here. The notch is more narrow, extending in apparent blueshift from 10, 000 to 13, 000 km s⁻¹ in the −9.4 day spectrum. The notch as faded away by −7.4 days, a phase at which it is still present in the other carbon-positive SNe studied here.

SYNAPPS fits. SYNAPPS uses C ii for the −9.4 day spectrum but not for the spectrum obtained a week later. SYNAPPS determines v_phot = 12, 800 and then 12, 000 km s⁻¹, respectively. The −9.4 day spectrum requires both HV Si ii and Ca ii, though the HV Si ii feature becomes optically thin by −2.4 days. The HV component is also clearly quite important for the formation of the Ca ii H and K absorption in both spectra. The strength of the HV features in SN 2005cf distinguishes it from the other SNe Ia considered here.