THE SUBLUMINOUS AND PECULIAR TYPE Ia SUPERNOVA PTF 09dav

Following the initial WHT classification spectrum, two further spectra were taken during the photospheric phase of the SN. The first was taken with the Palomar Hale 200 inch telescope (P200) plus Double Beam Spectrograph (DBSP; Oke & Gunn 1982) on 2009 August 20.5. The 600l/4000 Å (blue) and 158l/7500 Å (red) gratings, and D55 dichroic, were used, giving a wavelength coverage of ∼3500–9500 Å. The second spectrum was taken using the Keck I telescope and the Low-Resolution Imaging Spectrometer (Oke et al. 1995) on 2009 August 25.5—a wavelength coverage of ∼3400–10000 Å was achieved using the 400l/3400 Å grism (blue), 400l/8500 Å grating (red), and the 560 dichroic. A final spectrum taken during the nebular phase of the SN was taken on 2009 November 11.4 and will be presented in a companion paper (M. M. Kasliwal et al. 2010, in preparation).

The three photospheric spectra were reduced using the same custom-written pipeline based on standard procedures in IRAF and IDL broadly following the reduction procedures outlined in Ellis et al. (2008), including flux calibration and telluric feature removal. All spectra were observed at the parallactic angle in photometric conditions. "Error" spectra are derived from a knowledge of the CCD properties and Poisson statistics and are tracked throughout the reduction procedure. The spectra are also rebinned (in a weighted way) to a common dispersion and joined across the dichroic. The three spectra are shown in Figures 2 and 3.

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The host galaxy of PTF 09dav is somewhat ambiguous (Figure 1). PTF 09dav lies 568 (projected) SE of a potential host galaxy (r ≃ 17.6; α = 22^h46^m529, δ = +21°38'216, J2000). A Lick spectrum taken on 2009 October 25 shows this galaxy to have strong nebular emission lines (Hα, Hβ, O iii, O ii) and be located at a heliocentric redshift z_hel = 0.0371 ± 0.0002 (well within the Hubble flow), consistent with the estimated SN redshift. At the position of the SN, z_hel = 0.0371 corresponds to z = 0.0359 in the cosmic microwave background (CMB) rest-frame (z_cmb) or a distance modulus of 35.99 ± 0.06 (the error assumes a host galaxy peculiar velocity uncertainty of 300 km s⁻¹). This would give a projected physical separation between PTF 09dav and the center of this galaxy of 40.6 kpc.

There is no evidence for a host galaxy at the position of the SN. Using 129 "DeepSky"¹⁵ (Nugent et al. 2009) images taken with the Palomar-QUEST survey over of the field of PTF 09dav, we have constructed a deep RG610 image (a longpass r + i + z filter). Using a 4'' diameter aperture at the position of the SN, we detect no host galaxy with a 3σ limiting magnitude of m = 23.2 in the RG610 or M = −12.8 at z = 0.0359. Such a faint absolute magnitude would be lower than any detected host galaxy of a core collapse SN found by PTF (Arcavi et al. 2010). Deeper Keck imaging at the position of PTF 09dav is underway (M. M. Kasliwal et al. 2011, in preparation).

Photometric monitoring in gri filters commenced using the robotic Palomar 60 in (P60) telescope (Cenko et al. 2006) on 2009 August 15.3 and on the robotic Faulkes Telescope North (FTN) on 2009 August 18.4, complementing the rolling PTF search on the Samuel Oschin 48 inch telescope (P48) in R band. The resulting multi-color light curve of PTF 09dav is shown in Figure 4. As PTF 09dav has no detected host galaxy at the position of the SN, no subtraction of a reference image is required, simplifying the light curve measurement. We measure the SN photometry using a point-spread function (PSF) fitting method. In each image frame, the PSF is determined from nearby field stars, and this average PSF is then fit at the position of the SN event weighting each pixel according to Poisson statistics, yielding an SN flux and flux error.

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We perform a flux calibration to the Sloan Digital Sky Survey (SDSS) photometric system, close to the AB system (Oke & Gunn 1983), using P48 and P60 observations of SDSS fields made on the same night as observations of PTF 09dav. We use an average calibration from photometric nights in 2009 August and September, which provides calibrated tertiary standards in the field of PTF 09dav. This calibration is then transferred to other epochs and to the FTN observations, using aperture photometry of these tertiary standards to determine an relative flux-scaling factor for each epoch, typically measured to <1%. In the P60/FTN g, r, and i filters the color terms to the SDSS system are very small. The P48 color term is larger, and we include color, extinction, and color–extinction terms. The rms of the color term fits is 0.02–0.03 mag (with a color term in r − i of ∼0.22 mag), although we present magnitudes in the natural P48 system and do not apply this color term to our photometry. Finally, we fit the same PSF used for the SN flux measurement to the calibrating field stars, and apply a correction to go from the aperture in which the flux calibration is determined, to the PSF fit in which the SN is measured.

Although we could perform our entire analysis using magnitudes defined in the AB system, rest-frame SN Ia properties in the literature are typically given in the Vega system. For ease of comparison to previous work, we convert our calibrated light curves into this system when performing the light curve analysis, and all quoted magnitudes are given in the Vega system. The offsets from Vega (m_vega) to AB (m_AB) magnitudes are −0.12, 0.13, 0.19, and 0.35 for the g, r, R, and i filters, respectively (m_vega = m_AB − offset). Our light curve data can be found in Table 1, presented in counts rather than magnitudes to preserve information on non-detections.

Estimating the peak luminosity of SNe in a given bandpass requires an interpolation between observed data points at the time of maximum light, followed by a k-correction back to some standard rest-frame filter of interest. The interpolation step is best performed using a smooth light curve template in the observed filter which is believed to represent the photometric evolution of the SN; the k-correction requires a time series spectral energy distribution (SED; e.g., Nugent et al. 2002; Hsiao et al. 2007). To parametrize the light curve of PTF 09dav, we fit a time series SED to the observed photometry using the SiFTO light curve fitter (Conley et al. 2008) developed for SN Ia cosmology studies. We replace the standard SN Ia spectral template¹⁶ with one based on the subluminous SN Ia events SN1991bg (Filippenko et al. 1992; Leibundgut et al. 1993) and SN1999by (Garnavich et al. 2004). Ideally, one would use an SED template which exactly matches the spectral class of the object under study. For PTF 09dav, the first object of its type, no such template exists, so we use our subluminous template which has many common spectral features and similar broadband colors.

SiFTO works in flux space, manipulating a model of the SED and synthesizing an observer-frame light curve from a given spectral time series in a set of filters at a given redshift, allowing an arbitrary normalization in each observed filter (i.e., the absolute colors of the template being fit are not important and do not influence the fit). The time-axis of the template is adjusted by a dimensionless relative "stretch" (s) factor (where the input template is defined to have s = 1) to fit the data. Once the observer-frame SiFTO fit is complete, it can be used to estimate rest-frame magnitudes in any given set of filters, provided there is equivalent observer-frame filter coverage and at any epoch. This is performed by adjusting the template SED at the required epoch to have the correct observed colors from the SIFTO fit, correcting for extinction along the line of sight in the Milky Way, de-redshifting, and integrating the resultant SED through the required filters. This process is essentially a cross-filter k-correction, with the advantage that all the observed data contribute to the SED shape used. As an illustration, the size of the k-correction for an SN1991bg-like SN Ia to go from observer g (r) at z = 0.0371 to rest-frame B (V) is ∼−0.16 mag (∼−0.24 mag) at maximum light and ∼−0.28 mag (∼−0.48 mag) at 10 days after maximum.

The function used to adjust the template SED can either be an interpolating spline (in which case a perfect match in color is attained) or, if the reason for the physical difference in the colors between the SN and the template is understood, a function such as a standard dust law (e.g., Cardelli et al. 1989) or other wavelength-dependent color law (e.g., Guy et al. 2007). The latter case is more useful when extrapolating beyond the wavelength range of the observed filters, although it gives a poorer match between observed and fit colors.

Our SiFTO light curve fit is in Figure 4. The fit is good—the reduced χ² of the fit is 1.02 for 40 degrees of freedom (i.e., χ² = 40.8/40)—using a standard SN Ia template in SiFTO gives a substantially worse reduced χ² of 4.3. Maximum light in the rest-frame B band was on 2009 August 08.9 ± 0.3 days (or an MJD of 55051.9), i.e., the SN was discovered some 3 days after maximum light. Interestingly, although the fit to the data around maximum light is excellent, at phases beyond ∼+30 days there appears to be significant excess i-band flux in the SN compared to the simple prediction of the template with the i-band light curve appearing to plateau, while the decay in the other filters continues to follow the subluminous template. This could be due to emerging nebular emission from the [Ca ii] doublet at λ7291 and λ7323, with stronger lines at that phase than in our SN1991bg-like subluminous template, and more similar to later time spectra of calcium-rich SNe (Perets et al. 2010).

As PTF 09dav has no detected host galaxy at the SN position, we can cross-check our photometric calibration using photometry synthesized from our WHT spectrum. At the time of the WHT spectrum (+4.9 days), SiFTO gives a light curve color of g − R = 1.17 ± 0.05, compared to a spectral color from the WHT spectrum of g − R = 1.26. Given the uncertainties in flux-calibrating long-slit spectra (e.g., differential slit losses which will redden the SED) as well as in the P48 R and P60 g filter responses used for synthetic photometry, this is an excellent level of agreement suggesting an accurate photometric flux calibration. A similar agreement is found for the later P200 spectrum.

Our reported magnitudes are in the Vega system, taking our BVR filter responses from Bessell (1990) and correcting for Milky Way extinction assuming R_V = 3.1 and a color excess of E(B − V)_mw = 0.044 (Schlegel et al. 1998) with a Cardelli et al. (1989) extinction law. We measure peak rest-frame absolute magnitudes at the time of B-band maximum light of M_B = −15.44 ±  0.05, M_V = −16.01 ±  0.05, and M_R = −16.26 ±  0.05 (errors are statistical uncertainties propagated through the light curve fit only) using a CCM law in SiFTO to match the template to the observed fit colors; we adopt these numbers throughout this paper. For comparison, using a spline in SIFTO in place of the CCM law gives M_B = −15.54 ±  0.05, M_V = −15.98 ±  0.09, and M_R = −16.24 ±  0.05.

One potential concern in the light curve fit is that the P60/FTN g coverage, corresponding to rest-frame B, did not start until ≃6 days after maximum light—and so the B-band (and V-band) maximum light estimate is an extrapolation (based on the light curves synthesized from the SED template) rather than an interpolation as with the P48 R band. Our key assumption is that the light curve of PTF 09dav is well represented by a "stretched" version of our subluminous spectral template. While this is clearly true in the P48 R data where the fit before and after maximum light is robust, in g the data are not sufficient to test this assumption.

A comparison of PTF 09dav to other SN1991bg-like subluminous SN Ia events can be found in Table 2 and Figure 5. With no commonly accepted definition for what constitutes an SN1991bg-like event, we fit a combination of events matching the cool classification from Branch et al. (2009), events with ΔM₁₅(B)>1.8 from Taubenberger et al. (2008) and (Hicken et al. 2009), and other individual events from the literature (e.g., Kasliwal et al. 2008). We fit all the public SN Ia photometry with SiFTO and the same subluminous template to ensure a consistent comparison. All magnitudes are corrected for Milky Way extinction, and we have assumed distance moduli either calculated from z_cmb when z_cmb ⩾ 0.01 or taken from a redshift-independent estimate (together with an uncertainty) from the NASA/IPAC Extragalactic Database (NED¹⁷) in other cases. We have also propagated through a 300 km s⁻¹ peculiar velocity error for those SNe Ia in the Hubble flow. We only consider SNe with adequate photometry for a reliable light curve fit, and those with M_B> − 18 at maximum light, in our analysis.

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The SNe show expected trends between stretch, color, and M_B (Figure 5) which are consistent with previous studies (Garnavich et al. 2004; Taubenberger et al. 2008; Gonzalez-Gaitan et al. 2011): fainter SNe are redder and with smaller values of stretch. (Note that the stretches here are measured relative to our subluminous template and are not on the same system as stretches of normal SNe Ia.) Clearly PTF 09dav is an outlier in these relations, being considerably fainter for its color and stretch than other subluminous events: PTF 09dav is ∼3.5 mag underluminous compared to normal SNe Ia (M_B ≃ −19.1), ∼1.5 mag fainter than a typical subluminous SN Ia, and around ∼0.5 mag fainter than SN2007ax, the faintest subluminous SN Ia identified (Kasliwal et al. 2008).

No correction for host extinction (if any is present) has been applied to the magnitudes of PTF 09dav (or the other SNe in Table 2), and thus host extinction will impact Figure 5. For PTF 09dav, (B − V)_max = 0.57 ± 0.08, and when using the CCM law in SiFTO to match the subluminous template to the fit colors for PTF 09dav, a small additional E(B − V) of 0.08 ± 0.04 is required. Though it may be tempting to interpret this at face value as a reddening for the SN (and derive similar corrections for the other SNe in Table 2), such an approach is likely to be dangerous. Generally, the color–luminosity variation in SNe Ia is poorly understood. There is considerable evidence for an intrinsic color–luminosity relation which is currently impossible to disentangle from the effects of dust unless the SN is particularly well observed. Thus, interpreting a red color as evidence of extinction may not be correct. A second consideration is that our subluminous template may not be appropriate for zero extinction, as it is based on real SN photometry. Therefore, we simply note that the broadband colors of PTF 09dav are similar to other subluminous SN Ia events and show no evidence for significant host galaxy extinction.

We also estimate the value of the Phillips (1993) decline rate parameter Δm₁₅(B) (the amount in magnitudes in the rest-frame B band that the SN declines in the 15 days following maximum light) as Δm₁₅(B) = 1.87 ± 0.06. The error is a combination of propagating the error in the stretch parameter, combined with the uncertainty in peak B-band brightness. Numerous studies have fit the relation between Δm₁₅(B) and M_B for subluminous SNe Ia (e.g., Garnavich et al. 2004; Taubenberger et al. 2008). According to the relation of Taubenberger et al. (2008), our Δm₁₅(B) = 1.87 should correspond to a peak B absolute magnitude of −17.44, nearly two magnitudes brighter than we observe (M_B ≃ −15.5 corresponds to Δm₁₅(B) ≃ 2.15 according to the Taubenberger relation). This is consistent with PTF 09dav as an outlier in Figure 5. However, Δm₁₅(B), unlike stretch, can be misleading in these comparisons. In the fainter examples of subluminous SNe Ia, the transition from the fast initial decline to the slower late-time decline occurs before −15 days, which distorts the relation (e.g., Kasliwal et al. 2008).

The subluminous template we used in the SiFTO fit has a rise time (τ_r) from explosion of 13.0 days to B-band maximum light and 14.0 days to bolometric maximum light. PTF 09dav has a light curve "stretch" factor of 0.86 ± 0.02 compared to this template, giving a rise time to bolometric peak of 12.0 ± 0.3 days (statistical error only). We also estimate the rise time by fitting the P48 R data in the early rise-time region using the analytical equation f(t) = α(τ + τ_r)² (Riess et al. 1999). Here, τ = t/(1 +  z), where t is the observed time and α is a normalizing constant. We find rise times of 12.0 ± 2.9 when fitting the first two epochs (including the first non-detection) and 14.5 ± 1.1 when including the next epoch. These are consistent with our estimates from the template light curve fit. The latter measure includes data from near-maximum light, where the assumption of the simple rise-time model may no longer hold, and should be considered a strong upper limit.

Using our light curve fits, we can also estimate the bolometric luminosity, L_bol, of PTF 09dav. Estimating the bolometric luminosity is never straightforward as full ultraviolet through infrared (or UVOIR) light curves are rarely observed. Instead, we measure the luminosity in a given band together with the colors from our light curve fits and use the template to derive a bolometric luminosity estimate (effectively a bolometric correction). Such techniques work well for SNe Ia events near maximum light as the peak of the luminosity output is in the optical. Again, as with the light curve fit, we use the template spectrum to calculate our bolometric light curve. In principle we could use the observed spectra, but the lack of an observation at maximum light, and the lack of λ>7700 data in the spectrum nearest maximum, makes this difficult. Our technique broadly matches that of Howell et al. (2009). We take the template spectrum on the day of maximum light, adjust it using a CCM law to have the correct color, normalize to the peak B-band absolute magnitude, and integrate the resulting spectrum. The peak bolometric luminosity (occurring ≃1 day after B-band peak) is estimated to be L^B_bol = 5.6 ±  0.4 × 10⁴¹erg s⁻¹ (Table 2). The implicit bolometric correction, defined as BC = M_bol − M_V, where M_bol is the bolometric magnitude, is ≃0.2 mag, comparable to other subluminous events SN Ia events (Contardo et al. 2000).

The ejecta mass M_ej and kinetic energy E_kin of PTF 09dav can be estimated from its rise time and ejecta velocity v_ej using M_ej ∝ v_ejτ²_r and E_kin ∝ v³_ejτ²_r (e.g., Arnett 1982; Foley et al. 2009). Comparing PTF 09dav to a "typical" SN Ia with a kinetic energy of 10⁵¹ erg, a rise time of 17.4 days (Hayden et al. 2010), and a photospheric velocity of 11,000 km s⁻¹ (Benetti et al. 2005), and assuming the opacities of both are the same, we estimate an ejecta mass of 0.36 M_☉ and kinetic energy of 8 × 10⁴⁹ erg. (Here, we have used an ejecta velocity of 6000 km s⁻¹ for PTF 09dav estimated from the spectral fitting in Section 4.) These are low values; a typical ejecta mass for an SN Ia ranges from ≃0.5 M_☉ for an SN1991bg-like event up to the Chandrasekhar mass (1.4 M_☉) for normal SNe Ia (e.g., Stritzinger et al. 2006; Mazzali et al. 2007). A similar low ejecta mass was derived for the calcium-rich SN Ib SN2005E (Perets et al. 2010), and even lower ejecta masses have been estimated for faint examples of SN2002cx-like events (Foley et al. 2009; McClelland et al. 2010) and for SN2002bj (Poznanski et al. 2010) and SN2010X (Kasliwal et al. 2010).

If the light curve is predominantly powered by the decay of ⁵⁶Ni, the ⁵⁶Ni mass, M_Ni, can be estimated from a knowledge of the rise time τ_r and L_bol (Arnett 1982). At maximum light, M_Ni is given by M_Ni=L_bol/α$\dot{S}$(τ_r) (Arnett's rule), where $\dot{S}$ is the radioactive luminosity per solar mass of ⁵⁶Ni from the decay to ⁵⁶Co to ⁵⁶Fe evaluated at maximum light and α is the ratio of bolometric to radioactive luminosities, near unity. We adopt $\dot{S}$ as defined in Howell et al. (2009; see also Branch 1992), which includes the effect of τ_r, and take τ_r and its error from our light curve fits with a conservative additional two-day uncertainty in the rise-time error estimate to match the range found above. In practice, α is likely to deviate from unity. For normal SNe Ia, the light curve may peak at a luminosity that exceeds the instantaneous radioactive luminosity (α>1) due to a falling temperature and opacity (e.g., Branch 1992). On the other hand, for smaller ejecta masses some gamma rays may escape the ejecta without being thermalized (i.e., α < 1). Using the approach of Kasliwal et al. (2010), we estimate the optical depth of PTF 09dav at maximum light to be ∼70 indicating an effective trapping of emitted γ-rays. For simplicity, we therefore take α = 1, giving M_Ni = 0.019 ± 0.003 M_☉. Under the same assumptions, SN 2008ha produced 0.0029 M_☉ of ⁵⁶Ni, and SN 2007ax 0.038 ± 0.008 M_☉—see Table 2 for estimated M_Ni for all the 1991bg-like subluminous SNe. In these calculations, we estimated τ_r for each event by multiplying the stretch by the rise time of the subluminous template (14 days). We emphasize that this calculation assumes the entire light curve to be powered by the decay of ⁵⁶Ni.

In summary of this section, the M_B, L_bol, M_Ni,  and ejecta mass M_ej of PTF 09dav are all unusually low. PTF 09dav is one of the faintest subluminous SNe Ia yet discovered, and, while not as faint as SN2008ha, it is the faintest of the SN1991bg-like sub-class.

When no detailed ab initio SN explosion model provides an immediate explanation for observations, parametrized spectrum synthesis provides the first step toward their construction. The idea is to use simplified radiative transfer calculations to directly fit SN spectra. A good fit constrains explosion models through interpretive spectral feature identification, with the main result being the detection or exclusion of specific chemical elements. The velocity distribution of detected species within the ejecta can also be constrained.

In our analysis we make use of SYNAPPS (Thomas et al. 2011). The physical assumptions SYNAPPS uses match those of the well-known SYNOW code (Fisher 2000), so findings are restricted to identification of features and not quantitative abundances. But where SYNOW is completely interactive, SYNAPPS is automated. This relieves the user from tedious, iterative adjustment of a large number of parameters (over 50 variables) to gain fit agreement, and assures more exhaustive searching of the parameter space. SYNAPPS can be thought of as the hybridization of a SYNOW-like calculation with a parallel optimization framework, where spectral fit quality serves as the objective function to optimize.

We run SYNAPPS on our three photospheric spectra, and the resulting fits are shown in Figure 6. We identify the following lines common to subluminous SN Ia spectra: O i, Ca ii, Si ii, Ti ii, Fe ii, and Co ii. The Ti ii lines are particularly strong relative to other SN1991bg-like events. We also identify Sc ii, Na i, and Mg i, as well as evidence for Sr ii and possibly Cr ii. There was no evidence for S ii or Mg ii—both degraded the quality of the fits, S ii around 5500 Å, and Mg ii in the red.

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Though unusual, the presence of Sc ii seems robust. As well as the two features at 5400 Å and 5550 Å (caused by λ5527 and λ5658), the 6490 Å feature (caused by λ6604), together with improved fits between 4000 and 5000 Å, provides additional confirmation. S ii has strong lines in this region, but cannot be responsible for the two features at 5400 Å and 5550 Å (observer frame)—the ratio of the two line wavelengths does not match S ii and the velocity would be inconsistent with the other elements (Figure 7). S ii is common in 1991bg-like events (although the lines typically become weaker and disappear after maximum light), and its non-detection here is therefore surprising, but it does have a higher ionization energy than the other elements, which may point to lower temperatures.

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Although Sc ii has been included in the SYNOW fits of faint SN2002cx-like SNe Ia (Foley et al. 2009; McClelland et al. 2010), it has never been robustly detected in SNe Ia. Sc ii has been observed (together with the other s-process elements Ba ii and Sr ii) in SN1987A (Williams 1987; Mazzali et al. 1992) and also during the plateau phase of some lower-luminosity SNe IIP (Fassia et al. 1998; Pastorello et al. 2004). Mg i (with no indication of Mg ii) is also surprising. As both Sc ii and Mg i are only seen at low temperatures (Hatano et al. 1999), even lower than Ti ii, this provides further evidence for the low temperatures of PTF 09dav.

Na i λ5892 is also highly probable (Figure 7), and is typically seen in subluminous events after maximum light, although it is particularly strong in PTF 09dav—Figure 3. This feature could also be the He iλ5876 line, and we cannot unambiguously confirm Na i over He i (Figure 7). Including He i in the fits does better match the 6900 Å feature (produced by λ7065), but it introduces other features in the SYNAPPS spectra which are not seen in the data, such as 6500 Å (caused by λ6678). However, SYNAPPS does not explicitly account for non-local thermodynamic equilibrium effects which are known to be important for modeling He i features (Lucy 1991)—LTE excitation in SYNAPPS can overestimate the strength of λ6678 to λ5876 and λ7065 (Branch 2003). Thus, all we can say is that at least one of, and possibly both, Na i and He i are present in the spectra of PTF 09dav.

There is also reasonable evidence for the presence of Sr ii (via absorption near 3960 Å), with weaker evidence for Cr ii (primarily through absorption at 4770 Å), all shown in Figure 7. Sr ii is identified through a blended single line (λ4078 and λ4216), and has no other strong optical features. As with Sc ii, Sr ii is also only seen at low temperatures (Hatano et al. 1999). Cr ii is often weakly present in SN1991bg-like SNe (Mazzali et al. 1997; Taubenberger et al. 2008). Ba ii, an s-process element often seen with Sr ii, was not needed in the fits.

Given the apparent low temperatures, we also tested the inclusion of S i and Si i, but neither was required in the fits (their abundances came out to zero in SYNAPPS). Indeed, S i and Si i would add lines not seen in our spectra if their abundance were non-zero. We also experimented with V ii and C ii—there was no evidence for either in the fits, although they also did not degrade the fit results by adding extra lines not seen in the spectra.

We measure ejecta velocities from the blueshift of the absorption minima of the P-Cygni line profiles. This process can carry a number of uncertainties, particularly the blending of neighboring lines, so we use the SYNAPPS results which effectively average over several lines. The line velocities evolve from ≃6100 km s⁻¹ (+4.9 days) to ≃5100 km s⁻¹ (+11.2 days) to ≃4600 km s⁻¹ (+16.0 days), and the major lines all share a common velocity.

The strength of the Na i (or He i) line increases with time, and our tentative Sr ii detection also becomes stronger. Ti ii, already stronger than in most SN1991bg-like events, also increases in strength with phase. By contrast, the evidence for Fe ii, as well as Cr ii, has disappeared by +16 days; those lines are not needed in the later-epoch SYNAPPS fits.

We also estimate the Nugent et al. (1995) Si ii ratio, $\mathcal {R}(\mathrm{Si})$, defined as the ratio of the depth of the Si ii features at λ5972 and λ6355. We calculate this ratio as 0.35, smaller than the values typical of subluminous SNe Ia of ∼0.65 (Taubenberger et al. 2008), and naively indicating a higher temperature than in those events. However, the presence of strong emission from the Na i (or He i) line blueward of the λ5972 feature will significantly affect this measurement, decreasing the depth of the λ5972 feature and hence artificially decreasing the observed ratio. We also measure the (pseudo) equivalent widths of these two Si ii features, which can be used to differentiate sub-types of SNe Ia using the W(6100)/W(5750) plane (Branch et al. 2006, 2009). Using the notation of Branch et al. (2006), W(6100) (the λ6355 line) is 45 Å and W(5750) (the λ5972 line) is 10 Å. These measurements are both significantly lower than in SN1991bg-like events (typical values of ≃100 Å and ≃45 Å, respectively), and therefore lie well outside the region in W(6100)/W(5750) space containing other cool SNe with significant Ti ii absorption (Branch et al. 2009).