SPECTROSCOPY OF TYPE Ia SUPERNOVAE BY THE CARNEGIE SUPERNOVA PROJECT^*

The CSP carried out follow-up campaigns to obtain optical and near-infrared (NIR) light curves and optical spectroscopy of nearby (z ≲ 0.08) SNe of all types. Between 2004 September and 2009 May over 250 objects were monitored, among which 129 were SNe Ia. High-quality optical and NIR light curves of 36 of these were published by Contreras et al. (2010), and their analysis was presented in the work of Folatelli et al. (2010). Light curves of additional 50 SNe Ia were made available by Stritzinger et al. (2011).

Along with well-sampled light curves, the CSP collected spectra for most of the SNe. However, due to the relative scarcity of spectroscopy time, the temporal sampling obtained was more sporadic than that of the photometry. In this work, we have collected the spectra of the SNe Ia with light curves published by Contreras et al. (2010) and Stritzinger et al. (2011) plus several SNe observed more recently for which clean photometry was obtained without performing subtraction of the host-galaxy light—i.e., because they were bright enough and isolated from their hosts. Note that we do not include SN 2005hk—a 2002cx-like object observed by the CSP (Phillips et al. 2007)—in the analysis due to the lack of CSP spectra near maximum light.

Table 1 lists the sample of SNe Ia selected for this work along with the amount and span of spectroscopy epochs, and spectral classification as defined in Section 4. Additional information in Table 1 includes redshift and photometric parameters. The sample includes a large variety of SNe Ia, as can be inferred from the wide distribution of light-curve decline rates parameterized by Δm₁₅(B) and shown in the top left panel of Figure 1.

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For most of the objects in the sample, the heliocentric redshifts given in Table 1 were obtained from the NASA/IPAC Extragalactic Database (NED). Whenever possible, we have used CSP spectra to verify the quoted values by measuring host-galaxy lines. For 55 spectra of 34 SNe, we obtained a very good agreement with an average difference in z of 0.00009 and a dispersion of 0.00055 (165 km s⁻¹). For SNe 2005ag, 2006is, and 2006lu, no information on the host galaxies or their redshifts is available in NED, so we have adopted our measured values, as indicated in Table 1. These redshift values were used to put the spectra in the rest frame. As shown in Figure 1, the SN sample covers a range of redshifts up to z = 0.083, with ≈80% of the objects closer than z = 0.04.

The procedures followed by the CSP for spectroscopic observations and reductions were described by Hamuy et al. (2006). As mentioned there, most of the data were obtained with the 2.5 m du Pont Telescope at Las Campanas Observatory, using the Wide Field CCD Camera (WFCCD) in long-slit spectroscopy mode. Other instruments used to improve our spectroscopic time coverage were the Las Campanas Modular Spectrograph at the du Pont, the Low Dispersion Survey Spectrograph (LDSS2; Allington-Smith et al. 1994) on the Magellan Clay 6.5 m telescope, and the Ritchey-Chrétien spectrograph at the 1.5 m CTIO telescope, operated by the SMARTS consortium. In addition to these, more recently we have also employed, at Las Campanas: LDSS3 on the Magellan Clay telescope (an upgrade of LDSS2, with new grisms and different long slits); the Inamori Magellan Areal Camera and Spectrograph (IMACS; Dressler et al. 2011) on the Magellan Baade 6.5 m telescope, in its long (f/4) and short (f/2) camera modes, with different combinations of gratings/grisms and slits; the Boller and Chivens spectrograph at the du Pont telescope; and finally, a few spectra have been obtained using the Magellan Echellette (MagE; Marshall et al. 2008) spectrograph on the Magellan Clay telescope. We have also obtained single nights with the New Technology Telescope (NTT) and the 3.6 m Telescope at ESO-La Silla, using the ESO Multi-Mode Instrument (EMMI; Dekker et al. 1986) in medium resolution spectroscopy mode (at the NTT) and the ESO Faint Object Spectrograph and Camera (EFOSC; Buzzoni et al. 1984) at the 3.6 m and NTT telescopes. A few spectra have been obtained with the Gemini Multi-Object Spectrograph (GMOS; Hook et al. 2004) mounted on the Gemini South Telescope.

About 80% of our spectra were obtained with the WFCCD, with most of the remaining 20% secured with EMMI, LDSS2/3, and IMACS. In Table 2, we provide a complete journal of the spectroscopic observations considered in this work, giving for each spectrum the spectral coverage, FWHM resolution, exposure time, and airmass in the middle of the observation. UT and Julian dates are also provided along with the estimated rest-frame phase with respect to maximum light in the B band.¹⁹

In its spectroscopic monitoring, the CSP obtained at least one spectrum of the vast majority of the SNe which were selected for photometric follow-up. Among the 36 SNe Ia included in Contreras et al. (2010), only SN 2005ir at z = 0.076 was not observed spectroscopically by our program. Among the additional 50 objects published by Stritzinger et al. (2011), no spectra were obtained for only five SNe, namely 2005hj, 2005mc, 2006bt, 2007hx, and 2007mm. As can be seen in the bottom left panel of Figure 1 which shows the distribution of the number of spectroscopic epochs for all the SNe in the present sample, for most of the objects we obtained between 2 and 5 spectroscopic epochs. Moreover, several SNe were followed more intensively and for longer intervals, which allowed us to gather spectra at 10–15 different epochs.

We tried to concentrate our spectroscopic observations around the time of maximum light. For most SNe we obtained the first spectrum before or around maximum light. Specifically, for 72 out of the 93 SNe, the first spectrum was obtained earlier than 5 days after B-band maximum light (see Figure 1). In many cases the monitoring was extended up to ∼50 days after the time of B-band maximum. For the brightest objects we were able to obtain spectra to approximately +150 days.

Although most of the observations were performed without order-sorting filters, the effect of second-order contamination is negligible in most cases because SNe Ia in general do not show extremely blue colors. The flux calibration was generally performed using several spectrophotometric standards to reduce the risk of introducing second-order contamination in the calibration of the red part of the spectrum. We have evaluated the effect of second-order contamination by comparing spectra obtained with and without order-sorting filter using the Boller and Chivens spectrograph at the du Pont telescope. We have done this with several SNe observed between 2007 and 2009. In all cases, the results are in agreement within a few percent between the two instrumental setups. Unfortunately, the WFCCD spectrograph does not allow observations to be made with order-sorting filters. However, the results of the Boller and Chivens spectrograph—which has significantly greater sensitivity in the blue—indicate that the effect is negligible also in the case of the WFCCD.

Telluric features were removed from almost all the spectra using appropriate standards observed each night with the same slit used for the SN observations. Note that this procedure often left residuals from the strongest telluric bands which were not further corrected, as explained in detail in Hamuy et al. (2006). Only 22 of the total of 604 CSP spectra were not telluric-corrected because the necessary standards were not obtained.

To avoid light loss due to differential refraction, we carried out the vast majority of the observations by aligning the slit at the parallactic angle, especially when observing at low elevation. Also, special care was taken to fit and subtract the underlying emission from the host galaxy in order to obtain a clean SN spectrum. In order to assess the quality of the spectrophotometry, we compared synthetic photometry computed through different bandpasses with the corresponding broadband photometry. For most of the spectra the wavelength range covered allows comparison with several bandpasses. In general we find an agreement within a few percent between synthetic and observed fluxes after removal of a constant flux term. In the last column of Table 2, we provide the rms of the differences in magnitudes between the bandpasses. In some cases we were not able to perform the comparison, either because the spectrum had a wavelength coverage that was too restricted, or because the photometric data did not cover the epoch of the spectrum. When the rms was larger than ≈0.15 mag among at least three bandpasses we used a low-order polynomial function to correct the overall shape of the spectrum. As a further consistency check, we compared synthetic colors obtained from the spectra with corresponding colors measured from the photometry and interpolated to the same epochs of the spectra. The comparison is shown in Figure 2. The figure shows that the majority of the spectra show color deviations within ±0.15 mag. Most of the spectra that show larger deviations in any given color are the ones that were corrected by the procedure described above. A few spectra with a large deviation in one color index were not corrected because their wavelength span did not cover other bandpasses.

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Figure 3 shows examples of spectral time-series for some of the SNe in the current sample. The complete set of plots are provided as online-only material and will be made available together with the spectroscopic data in the CSP Web site (http://csp.obs.carnegiescience.edu).

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View extended figure (94 panels)

A number of non-CSP spectra have been included in this paper. Some of them are unpublished, including: a total of 30 spectra of SNe 2006dd, 2006ef, 2006ej, 2006et, 2006gj, 2006hb, 2006is, 2006kf, 2006lu, and 2006mr obtained with the Boller & Chivens CCD spectrograph at the Hiltner 2.4 m Telescope of the MDM Observatory; 4 spectra of SNe 2005hc, 2005ku, and 2006fw obtained during the SDSS-II Supernova Survey (Frieman et al. 2008) with the Boller & Chivens CCD spectrograph mounted on the McGraw-Hill 1.3 m Telescope of the MDM Observatory, and EMMI at the NTT telescope of ESO-La Silla; and 1 spectrum of SN 2005A obtained with the Double Spectrograph (DBSP; Oke & Gunn 1982) mounted on the Hale 200 inch Telescope at Palomar Observatory. In addition to this, 84 spectra of SN 2004dt (Altavilla et al. 2007), SN 2004eo (Pastorello et al. 2007), SN 2005bl (Taubenberger et al. 2008), SN 2005hj (Quimby et al. 2007), and SN 2006X (Wang et al. 2008; Yamanaka et al. 2009) were retrieved from The Online Supernova Spectrum Archive (SUSPECT, http://suspect.nhn.ou.edu/~suspect/). Near-maximum spectra of the SNe included in this work were added from the CfA Supernova Program and the BSNIP. This comprises 106 spectra from the CfA sample (Blondin et al. 2012), and 38 from the BSNIP sample (Silverman et al. 2012a). The SUSPECT, CfA, and BSNIP spectra are not listed in Table 2.

The shift of the absorption minimum of a line with respect to the rest wavelength of the corresponding transition provides an estimate of the average expansion velocity of the material producing the absorption. Wavelength shifts can be converted to velocities via the Doppler formula. We adopted the relativistic Doppler formula (see Equation (6) of Blondin et al. 2006). Accurately measuring the absorption minimum is not always easy in the case of SNe because the large speed of the material broadens the lines and often makes them blend together. We have selected a number of multiplets which are the most easily identifiable and isolated in the spectra of SNe Ia around maximum light. For these, effective rest-frame wavelengths were computed based on air wavelengths and oscillator strengths given by the NIST Atomic Spectra Database (ver. 3.1.5; available from http://physics.nist.gov/asd3). These ions and resulting effective wavelengths are as follows: Ca ii H&K λ3945.02 and the IR triplet λ8578.79; Si ii λ4129.78 (4130), λ5971.89 (5972), and λ6356.08 (commonly referred to as 6355); S ii λ5449.20 (5449) and λ5622.46 (5622), where numbers between parentheses will be used as line identifications in what follows. The O i λλ7772, 7775 doublet is commonly found in SN-Ia spectra. We have, however, not included it in this analysis because its absorption can be affected by residuals of the telluric A-band.

The observed line positions were derived via Gaussian fitting of the absorption minimum performed with the IRAF routine splot²⁰ after removing the redshift introduced by the host-galaxy recession velocity. Since the Gaussian function is generally not a good approximation of the complete absorption profile, the fits were restricted to the core of the lines. This way we were able to obtain the location of the absorption minimum in a reproducible way. In cases when the minimum presented a flat shape the Gaussian provided an approximation of the central position. Whenever there was a double profile, we found the location of both minima using two local Gaussians. In the following analysis we consider the velocity of the redder component (with lower velocity) whenever the line had a double minimum.

Measurement uncertainties, which are very much dependent on the width of the line, its signal-to-noise ratio (S/N), and spectral resolution, were estimated by performing repeated Gaussian fits around the originally measured value. The limits of the fitting regions on each side of the measured minimum were allowed to vary between 40 and 70 Å for the weakest lines (Si ii λ4130, S ii λ5449, and λ5622), and between 40 and 100 Å for the rest of the lines. The limiting points of the fitting range were varied by three pixels between repetitions, which implies that the number of Gaussian fits was determined by the spectral sampling. The median absolute deviation (MAD) of all Gaussian minima was adopted as an estimate of the measurement uncertainty. In a conservative approach, we also compared the median central wavelength of all the Gaussian fits with the originally measured position derived from splot. In cases where these values differed by more than the computed MAD, we adopted the absolute value of the difference as the uncertainty.

In the following sections we will use values of expansion velocities at the time of B-band maximum light, as listed in Table 3. Since the observations very rarely coincided with that exact phase, we have derived such values using data obtained near maximum. In cases when there were several observations within one week before and after maximum, we performed low-order (first or second) polynomial fits. When only two observations encompassing maximum light were available, we interpolated to the time of maximum. If the observations did not encompass the time of maximum light, we allowed for an extrapolation if there was at least one measurement obtained in the range of [ − 1, 1] day. Otherwise, we extrapolated any measurement obtained within four days from maximum using average slopes for the velocity evolution obtained for well-sampled SNe. These slopes are summarized in Table 4. If more than one such extrapolation was done for a given SN, then the results were combined using a weighted average.

We tested the robustness of the fits and interpolations to maximum light by repeating the calculations described above after removing data points from the best-observed SNe. Such tests confirmed that the derived velocities at maximum light are stable and that median deviations from the originally fit values are smaller than ≈300 km s⁻¹ for any number of data points down to two. In the end, we were able to obtain expansion velocities at maximum light for 78 of the SNe in our sample.

3.1.1. Velocity Decline Rate

A convenient way of quantifying spectral properties of SNe Ia is to use pseudo-equivalent widths (pW) of apparent absorption features. The prefix "pseudo" is used to indicate that the reference "continuum" level adopted is generally not the actual continuum emission. We have measured pW for eight spectral features defined by Folatelli (2004) following the prescriptions given by Garavini et al. (2007). Examples of the pW features are shown in Figure 4. Feature definitions are summarized in Table 5. The first column gives the names that will be used throughout the text. The second column provides the main lines that are associated with each absorption feature near the time of maximum light. Although these line identifications are generally not unique and they vary with SN phase, we adopt them for the feature names to help the reader follow our analysis. Nevertheless, the association of features 1 and 8 with Ca ii lines is persistent with phase, although near maximum light feature 1 may include a significant contribution of Si ii λ3858 (see Blondin et al. 2012). Features 3 and 4 are blends of lines due to Fe and intermediate-mass elements; for convenience, we call these "pW3 (Mg ii)" and "pW4 (Fe ii)" in reference to the ions that produce the strongest absorptions at maximum light. Feature 5 corresponds to the W-shaped absorption due to S ii that is observed until about 10 days after maximum light. Finally, features 2, 6, and 7 are associated with Si ii λ4130, λ5972, and λ6355, respectively, although other ions also contribute. The former two features are weak and can only be identified until about ten days after maximum. Feature 7 is measured until approximately two months post-maximum, although its identification with Si ii λ6355 is only valid until day ≈+10. We have left aside the absorption around 7500 Å that is mostly due to the O i λλ7772, 7775 doublet because it lies near the telluric A-band absorption. Even though most of the spectra were corrected for telluric absorption, the residuals of such correction can be large enough to affect the measurement of the O i doublet.

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Each pW measurement is obtained by defining a straight "continuum" level between two flux peaks and computing the integral of the spectrum flux relative to the continuum (with positive sign for simplicity). The flux peaks that define each feature are selected within a fixed spectral range so that the maximum allowed spectral range is spanned. Columns 3 and 4 of Table 5 provide the wavelength ranges allowed for the location of the flux peaks on each side of the eight features (see Garavini et al. 2007). Note that the definition of pW3 (Mg ii) permits it to cover the wavelength range of pW2 (Si ii 4130). This generally happens at times after maximum light or for the subtype of CL SNe Ia (see Section 4), and in those cases feature 2 is not measured.

Because pW measurements involve an integration over a relatively wide wavelength region of ∼100 Å, statistical uncertainties, in relative terms, are usually several times to one order of magnitude smaller than the uncertainties in the flux in a wavelength resolution bin. A significant contribution to the measurement uncertainty arises from systematic errors in the definition of the continuum points, variations in the flux peak levels due to an imprecise flux calibration, to contamination by host-galaxy light or even to noise. Most of our spectra have high signal-to-noise ratios (S/N ≳ 30 per 10 Å bins for over 90% of the spectra), so we have focused on other possible sources of systematic error. In our measurement procedure we have included a contribution to the uncertainty estimated by randomly varying the regions used for the continuum fit and for the integration (see Garavini et al. 2007).

The effect of reddening is to smoothly modify the shape of the continuum and thus its slope around the absorption features. Nordin et al. (2011a) find that this effect reduces the pW of some features, with a magnitude of <5%, for E(B − V) < 0.3 mag, and assuming the reddening law of Cardelli et al. (1989) with R_V = 1.7. Garavini et al. (2007) find similar results adopting a law with R_V = 3.1. To avoid this possible systematic error, we corrected the spectra of SNe with E(B − V) > 0.3 mag using the same reddening law and R_V = 1.7 (this choice of R_V is supported by the results of Section 5.3 and those of, e.g., Folatelli et al. 2010; Foley & Kasen 2011; Mandel et al. 2011).

Contamination by the host galaxy adds flux to the continuum and therefore produces systematically lower pW. Host-galaxy contamination is not important in our sample because most of the SNe are nearby and isolated from the bright regions of their hosts. As explained in Section 2.2, special care was taken to subtract the underlying emission from the host galaxies, and synthetic photometry from the resulting spectra was compared with broadband photometry in order to check the quality of the subtraction. For most of the spectra, the rms of the differences between synthetic and observed photometry was <0.1 mag (see Table 2), which indicates low degrees of contamination. Garavini et al. (2007) estimated roughly 10% decrease in pW for every 10% of contamination from host-galaxy light in the observed flux. Based on this, the effect of contamination is negligible for most of the spectra in the present sample.

In a similar way as was done for the line expansion velocities (Section 3.1), we derived pW values at B-band maximum light. Table 6 lists these values for 78 SNe. When several measurements were available within one week before and after the time of maximum, a smooth polynomial fit was used. If only two data points were obtained encompassing maximum light within −4 and +4 days, then an interpolation was performed. In a few cases, only data before or after maximum were available within [ − 7, +7] days. In those cases, an extrapolation was allowed if the closest point to maximum light was not farther than one day. For SNe which only had one measurement in the range [ − 4, +4] days or when measurements in that range did not encompass maximum light, average slopes determined from the best observed SNe were used for correcting the pW value to the time of maximum light. Table 7 provides the average pW slopes used for this purpose (see Section 4 for a detailed definition of SN-Ia subtypes). Similarly to the velocity fits, we performed tests by removing data points from the best-observed SNe and found that the resulting values at maximum light are robust. Median deviations were estimated to be within 5 Å for all pW parameters.

Blondin et al. (2012) published spectroscopic measurements of line velocities and pseudo-equivalent widths for an expanded sample of SNe Ia collected by the Centre for Astrophysics (CfA) Supernova Program (see their Table 4). We compared the measurements for 37 objects in common with our sample. Figure 5 shows the comparison of pW6 (Si ii 5972), pW7 (Si ii 6355), and v (Si ii 6355), all evaluated at maximum light. We can see that in general there is a good agreement in the pW values. A systematic shift of ≈3 ± 2 Å in is observed which indicates that the measurements of Blondin et al. (2012) are slightly smaller than our own. Straight-line fits to the pW measurements yield pW6 (Si ii 5972)_CSP = 2.73(± 0.53) + 1.06(± 0.02) × pW6 (Si ii 5972)_CfA and pW7 (Si ii 6355)_CSP = 7.8(± 1.4)  +  0.97(± 0.01) × pW7 (Si ii 6355)_CfA. The differences may be due to a larger incidence of host-galaxy contamination in the CfA spectra, or by a systematically different measurement procedure. The largest discrepancies are found for SNe 2007al and 2007ux. The CfA spectra of these objects show systematically redder continua as compared with the CSP spectra at similar epochs. This may be due to host-galaxy contamination which produces a systematic decrease in the pW of both Si ii lines.

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In the case of Si ii velocities, the agreement is very good. A weighted average of the differences yields Δv ≡ v_CfA − v_CSP = 78 ± 63 km s⁻¹. A fit to the velocity measurements, considering uncertainties in both axes, yields v_CSP = 90 (± 260) + 0.99 (± 0.02) × v_CfA km s⁻¹. The absolute values of the differences are <600 km s⁻¹ for all SNe except for SNe 2005bl and 2007ux, for which we get velocities at maximum that are ≈750 km s⁻¹ lower and ≈1300 km s⁻¹ higher than those measured by the CfA team, respectively. These differences can be explained by the fact that the CfA spectra were obtained at −2.9 days and 5.8 days relative to maximum light for each SN, respectively. In fact, when we compare measurements from spectra at similar epochs for these SNe, in all cases the velocities agree within the uncertainties with those of the CfA.

BSNIP recently published a series of papers with their SN-Ia spectroscopic sample. Silverman et al. (2012c) presented spectroscopic measurements of 432 near-maximum spectra of 261 SNe Ia. Among those SNe, 52 objects are in common with our sample. We used the data in their Tables B1–B9 to compare velocity and pW measurements. We compared each of their measurements with an average of all available measurements of the same SN from spectra obtained by the CSP within four days of the BSNIP spectrum. This was done for all eight of our pW features and for the velocities of Si ii, Ca ii, and v (S ii 5622) (the latter corresponds to their S ii "W" velocity.) The agreement for the velocities is good, with no significant deviations between the two samples. However, the weighted rms scatter of the differences was ≈500 km s⁻¹ for the Si ii and S ii lines, and ≈1000 km s⁻¹ for the Ca ii lines. These dispersions indicate that assuming flat uncertainties of 100 km s⁻¹ for individual measurements may be an underestimation.

For the pW measurements, the agreement is again good within the quoted uncertainties for pW1 (Ca ii H&K), pW2 (Si ii 4130), pW5 (S ii W), pW6 (Si ii 5972), and pW8 (Ca ii IR). The weighted dispersion of the differences is 2–3 Å for the weak Si ii features, and 15 Å and 33 Å for pW1 (Ca ii H&K) and pW8 (Ca ii IR), respectively. These values provide an indication of the actual measurement uncertainties. The relative dispersion of pW5 (S ii W) values is large (about 15 Å) and may be due to differences in the continuum-fitting regions that define the pW measurements (compare Table 5 in this paper with Table 1 of Silverman et al. 2012c). Non-negligible systematic differences of 3σ–4σ appear in the cases of pW3 (Mg ii), pW4 (Fe ii), and pW7 (Si ii 6355). Our pW are larger on average than those of Silverman et al. (2012c) by 18.5 ± 4.7 Å for pW3 (Mg ii), 15.5 ± 4.3 Å for pW4 (Fe ii), and 7.0 ± 2.4 Å for pW7 (Si ii 6355), based on 28, 37, and 52 measurements, respectively. In the first two cases, we suspect that the discrepancy arises from differences in the regions of continuum fitting (our regions are wider and may thus lead to larger pW values). Although the discrepancy in pW7 (Si ii 6355) is smaller, we could not find a clear explanation for it. Since this parameter measured at maximum light is useful for characterizing SNe Ia as will be shown in the following sections, we performed the comparison with measurements obtained only within one week of maximum and found a still-significant, although smaller, discrepancy of 5.6 ± 2.1 Å among 30 measurements.

Figure 9 shows the Si ii λ6355 line expansion velocity as a function of phase relative to B-band maximum light. Similar plots can be found in Figure 1 of Foley et al. (2011), Figure 15 of Blondin et al. (2012), and Figure 5 of Silverman et al. (2012c). We have shaded the 1σ region about the average of normal SNe Ia in the classification system of Wang et al. and overplotted the data of individual objects of different Branch subtypes. For normal SNe Ia, an almost constant decrease is seen between −10 and +30 days, going from about 12,000 to 10,000 km s⁻¹. While for the non-HV CN SNe the dispersion at any given epoch is about 1000 km s⁻¹, for the complete sample this increases to over 5000 km s⁻¹. BL SNe show the largest velocities and span a range of 5000–7000 km s⁻¹ depending on the epoch. They also show the largest velocity decline rates. CL SNe show similar velocities and dispersions than CN objects, and somewhat larger velocity gradients after maximum light. The evolution of SS SN velocities is rather flat. Among these, SN 2005M shows the lowest velocity in the whole sample, with v (Si ii 6355) ≈8000 km s⁻¹ at maximum light, which is about 1500 km s⁻¹ below the minimum value of the rest of the sample. The CN SN 2006is stands out by showing substantially higher Si ii velocity at maximum light than the rest of the subtype, and shallower evolution than that of BL SNe with similar v (Si ii 6355). SNe 2005M and 2006is will be analyzed separately in Section 4.3.

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Figure 10 shows the time evolution of the expansion velocities for the other two Si ii lines, plus the S ii and Ca ii lines near maximum light (cf. Figure 4 of Silverman et al. 2012c). For the weak Si ii and S ii lines, the range of epochs shown is the interval when these features are clearly distinguishable in the spectra. A continuously declining behavior is observed for all SNe Ia, with the exception of v (Si ii 5972) after maximum light when the absorption may become contaminated by Na i D lines. The smallest velocities correspond to the weakest of these lines, namely Si ii λ4130, and the two S ii absorptions. The relative behavior of different subtypes is similar to that of v (Si ii 6355) shown in Figure 9. Ca ii velocities show the largest dispersions. Part of this may be due to the difficulty of measuring a velocity based on the absorption minimum of these very broad lines that, as pointed out by Foley et al. (2011) and Blondin et al. (2012), commonly present composite profiles. As will be shown in Section 4.2, the dispersion of Ca ii velocities is not correlated with variations in the velocity of other species.

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Figure 11 shows the evolution of the eight pW parameters in the range of epochs where they can be measured (cf. Figures 7 and 8 of Silverman et al. 2012c). This extends to about +10 days for the weakest features, namely pW2 (Si ii 4130), pW5 (S ii W), and pW6 (Si ii 5972). The rest of the features are defined until about two months after maximum light, although their association with specific species is no longer valid—with the possible exception of the Ca ii absorptions. The evolution of pW3 (Mg ii), pW4 (Fe ii), pW7 (Si ii 6355), and pW8 (Ca ii IR) is roughly similar, i.e., a phase of nearly constant or slightly decreasing pW before maximum light, followed by an increase, and a subsequent flattening. The increase is the fastest for pW3 (Mg ii), lasting for about 15 days, while it lasts for about 25 days for pW4 (Fe ii), pW7 (Si ii 6355), and pW8 (Ca ii IR). pW1 (Ca ii H&K), as opposed to all the other features, decreases almost continuously with time. For pW5 (S ii W), there is a steep decrease that occurs after about day +5.

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CL SNe are clearly distinguished by their higher than normal pW6 (Si ii 5972) values. They also show large pW2 (Si ii 4130), pW3 (Mg ii), and pW8 (Ca ii IR), and small pW5 (S ii W) values. For eCL SNe, the increase of pW3 (Mg ii) occurs earlier than for normal SNe Ia, even as early as −10 days. The subgroup of SS SNe shows relatively low values of pW for all features. The rise of pW3 (Mg ii) for SS objects occurs at later times as compared with the rest of the subgroups.

We now analyze the general spectroscopic properties of SNe Ia of different subtypes in a quantitative manner, concentrating on the interrelationships between velocity and pW measurements. Figure 12 shows the Pearson correlation coefficients, ρ, between all pairs of pW (left panel) and velocity (right panel) measurements at maximum light. In each panel, the upper left triangle corresponds to the complete sample of SNe with available measurements. The lower right triangles show the coefficients for objects with low silicon velocities [v (Si ii 6355) < 12, 000 km s⁻¹] and light-curve decline rates [Δm₁₅(B) < 1.7 mag]. When all SNe Ia are considered, no strong correlations between pW parameters are found (|ρ| < 0.75). Some strong correlations stand out if we exclude HV and fast-declining SNe. Figure 13 shows the strongest of such correlations involving Si ii features, and pW8 (Ca ii IR) with pW4 (Fe ii) and pW7 (Si ii 6355). In general, the correlation coefficients between pW parameters for this restricted sample are positive. That is, the change in spectral line strengths from object to object tends to be in the same direction for all features. The exception to this is pW1 (Ca ii H&K), which shows low and sometimes negative correlation coefficients with other pW parameters.

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The right panel of Figure 12 shows that expansion velocities in general correlate positively with each other. The exceptions again involve Ca ii lines whose velocities do not correlate with those of other features. This is likely due in part to difficulty of measuring a velocity from the absorption minimum of Ca ii lines, as pointed out before and also stressed by Foley et al. (2011) and Blondin et al. (2012). Si ii and S ii line velocities correlate strongly, with coefficients near ρ = 0.9.

In Section 4.1, we pointed out the existence of two objects whose expansion velocities, as measured with the Si ii λ6355 line, were atypical. These objects are SNe 2005M and 2006is. Their spectral time-series are shown in Figure 3. As can be seen in Figure 9, the former SN shows a lower Si ii λ6355 velocity than any other object in the sample, while SN 2006is shows a large velocity, compared with the rest of the CN sample, but shallower velocity evolution than typical HV SNe. The behavior of SN 2006is is similar to the one observed for SN 2009ig after maximum light (Foley et al. 2012).

The velocity shifts in the spectra of SNe 2005M and 2006is of the other Si ii lines as well as S ii λλ5449, 5622 with respect to the measurements for the rest of the sample are notable, though less pronounced (see Figure 10). However, the shape of the spectrum outside the Si ii λ6355 line is similar to that of other SNe of the corresponding subtype (SS for SN 2005M and CN for SN 2006is). We thus studied the distribution of different species in the ejecta in order to confirm the peculiar behavior of Si ii and S ii.

For this purpose, we fit the maximum-light spectra of SNe 2005M, 2006is, and 2009ig with the automated spectrum synthesis code SYNAPPS (Thomas et al. 2011b), derived from SYNOW (Fisher 2000). SYNAPPS uses a highly parameterized, but fast spectrum synthesis technique, useful for identifying the ions that form the observed features. The best-fit synthetic spectra are compared with the observed spectra in Figure 14. The best-fit Si ii and S ii velocities for SN 2005M are 8100 km s⁻¹ and 9400 km s⁻¹, respectively. These are substantially lower than the best-fit median velocity of 10,900 km s⁻¹ for the rest of the ion species, notably Mg ii, Ca ii and Fe iii.

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The best-fit Si ii velocity for SN 2006is is 14,400 km s⁻¹. O i and S ii also show high velocities at 13,300 km s⁻¹ and 12,300 km s⁻¹, respectively. The remainder of the ion species has a median velocity of 11,300 km s⁻¹. SN 2009ig has very similar spectral features as SN 2006is, and the best-fit velocities are also very similar. The best-fit Si ii and S ii velocities are 14,800 km s⁻¹ and 12,300 km s⁻¹, respectively, while the remainder of the ions has a median velocity of 11,500 km s⁻¹. Note that for SN 2006is and SN 2009ig, constraining the velocities of all the ions to have the same value produces poor fits, especially for the Si ii λ6355 feature. Although for SN 2006is we adopted the redshift measured from our own deep spectrum of the host galaxy (see Section 2.1), the behavior of line velocities cannot be attributed to an error in the redshift as it would equally affect all lines. Moreover, the close similarity with SN 2009ig provides further confidence that the measured redshift is accurate.

The light curves of SNe 2006is and 2009ig were both more slowly declining than average, with Δm₁₅(B)  =0.80 mag (Stritzinger et al. 2011) and 0.89 mag (Foley et al. 2012), respectively. Interestingly, SN 2005M was also a slow decliner with Δm₁₅(B)  =0.82 mag (Contreras et al. 2010). We performed SNooPy (Burns et al. 2011) fits to the uBgVriYJH²² light curves of SN 2006is and found that its V −NIR colors at maximum light are bluer by about 0.2–0.3 mag than those of unreddened SNe Ia of similar decline rate. On the other hand, optical colors of this SN are normal. The NIR light curves of SN 2006is show the double-peaked shape that is typical of SNe Ia, but their brightness relative to the optical bands appears to be low as compared with template SN Ia of similar Δm₁₅(B). SNooPy fits to the uBgVriYJH light curves of SN 2005M do not reveal any obvious photometric peculiarities.

The existence of rare events like SNe 2005M and 2006is whose departure from the norm is mostly indicated by the peculiar velocities of certain intermediate-mass elements (IMEs) seems to indicate a new form of spectroscopic diversity, related to peculiar distribution of elements—notably Si ii and S ii which are the products of explosive oxygen burning—in the ejecta. An asymmetric explosion may have to be invoked in the case of SN 2005M to explain the presence of IMEs at lower velocity than that of Fe ii. The cases of SNe 2006is and 2009ig may indicate the existence of an outer silicon-rich shell. Since these objects depart from the Si ii λ6355 velocity versus velocity gradient relation at maximum light (Foley et al. 2011), they do not seem to comply with the same geometrical picture of Maeda et al. (2010a) involving asymmetric explosions.

Figure 16 shows the degrees of correlation between pW parameters and light-curve decline rates, Δm₁₅(B), considering both the pW measurements themselves and their ratios. The strongest correlation with Δm₁₅(B) among single pW parameters is that of pW6 (Si ii 5972), with a Pearson coefficient of ρ = 0.86 (both for the complete sample and when HV SNe are excluded). This relation was previously noted by Hachinger et al. (2006), and more recently by Silverman et al. (2012b). The resulting dispersion of Δm₁₅(B) about the straight-line fit is of 0.14 mag. pW2 (Si ii 4130) also depends strongly on Δm₁₅(B). Its correlation coefficient of ρ = 0.77 for the complete sample increases to ρ = 0.84 if we restrict the sample to SNe with Δm₁₅(B) < 1.7 mag. Both cases of pW2 (Si ii 4130) and pW6 (Si ii 5972) are shown in Figure 17. In general, the correlations become stronger when we discard HV SNe Ia, as can be seen in the right panel of Figure 16.

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Interestingly, pW8 (Ca ii IR) also shows an increasing trend with Δm₁₅(B) (ρ = 0.6–0.7). However, for a fixed Δm₁₅(B) there is a wide range of pW8 (Ca ii IR) values, with some SNe showing two or three times larger pW than their counterparts. On the contrary, the other Ca ii feature, pW1 (Ca ii H&K), shows no correlation with Δm₁₅(B), with ρ in the range between −0.1 and −0.3. Figure 18 shows example sequences of pre-maximum spectra with different pW8 (Ca ii IR) values at fixed Δm₁₅(B). Among SNe with similar Δm₁₅(B), the spectra show quite homogeneous characteristics, except at the location of the Ca ii IR triplet. The largest pW8 (Ca ii IR) values are found when a strong high-velocity component is present.

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The strongest correlations between pW ratios and Δm₁₅(B) are shown in Figure 19 (cf. Figures 13– 19 of Hachinger et al. 2006). Most of these involve Si ii features and ratios with pW4 (Fe ii) and pW5 (S ii W) (see also Silverman et al. 2012b). One of the ratios that correlates with Δm₁₅(B) is [pW6 (Si ii 5972)/pW7 (Si ii 6355)], which is similar to the line intensity ratio introduced by Nugent et al. (1995), $\cal {R}$(Si ii). This relationship is governed by the stronger dependence of pW6 (Si ii 5972) than of pW7 (Si ii 6355) on the decline rate (Hachinger et al. 2008). The dispersion is somewhat larger than that of pW6 (Si ii 5972) versus Δm₁₅(B), mostly due to BL SNe that have relatively large pW7 (Si ii 6355) and fall below the rest of the sample.

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We note that, although with fewer data points, pW1 (Ca ii H&K) is involved in some of these correlations. Interestingly, as shown in the top right panel, the relative strength of pW8 (Ca ii IR) with respect to pW1 (Ca ii H&K) increases with Δm₁₅(B). This is a consequence of the behavior noted above for pW8 (Ca ii IR) and pW1 (Ca ii H&K) versus Δm₁₅(B). A temperature effect related with Δm₁₅(B) may cause the anti-correlation of [pW1 (Ca ii H&K)/pW8 (Ca ii IR)] with Δm₁₅(B). The effect is presumably equivalent to the one described by Hachinger et al. (2008) to explain the behavior of $\cal {R}$(Si ii) with Δm₁₅(B). The most abundant ionization state of calcium in SNe Ia near maximum light is Ca iii (Tanaka et al. 2008). As temperature decreases with increasing Δm₁₅(B), the abundance of Ca ii increases. If both calcium lines are not saturated, this effect should equally increase their intensities. The observed behavior with Δm₁₅(B), however, indicates that Ca ii H&K may be saturated and so it does not react to abundance changes, while the contrary happens with the Ca ii IR triplet.

As mentioned in Section 4, SNe Ia show a wide variety of line expansion velocities. Here we study the behavior of expansion velocities of different lines at maximum light with respect to light-curve decline rate. Figure 20 shows the degree of correlation between velocity measurements at maximum light (on the diagonal) or ratios of these (off the diagonal), and Δm₁₅(B). We can see that none of the line velocities presented here correlate strongly with decline rate. The ratios of v (S ii 5449)/v (Si ii 6355), v (S ii 5622)/v (Si ii 6355), and v (S ii 5449)/v (Si ii 4130) show the largest degrees of anti-correlation with Δm₁₅(B) (ρ < −0.80).

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The lack of dependence of line velocities on Δm₁₅(B) is accompanied by a more or less clearly defined minimum expansion velocity for all decline rates. This velocity floor is about 10,000 km s⁻¹ for the strongest absorptions (Ca ii H&K and IR triplet, and Si ii λ6355), and between 6000 and 8000 km s⁻¹ for the weaker lines. In the case of v (Si ii 5972), the minimum velocity appears to be about 1000 km s⁻¹ higher for fast-declining SNe Ia [with Δm₁₅(B) ≳ 1.5 mag] than for the rest. The opposite occurs with v (S ii 5449) and v (S ii 5622)   where SNe with Δm₁₅(B) > 1.5 mag present on average lower velocities by about 1500 km s⁻¹(cf. Hachinger et al. 2006; Blondin et al. 2006). The SS SN 2005M stands out in our sample by having the lowest expansion velocities, by up to 2000 km s⁻¹ for some features (see Section 4.3).

Figure 21 shows the velocity decline rates for the Si ii λ6355 line, Δv₂₀(Si), versus Δm₁₅(B). A similar relationship was presented in the left panel of Figure 17 of Blondin et al. (2012) by adopting the velocity decline during 10 days after maximum light. The velocity gradient $\dot{v}$ as defined by Benetti et al. (2005) shows a larger dispersion in its relation with Δm₁₅(B) (see their Figure 3(b)) than the one of Δv₂₀(Si) presented here. The same happens with the instantaneous velocity decline rate defined in the right panel of Figure 17 of Blondin et al. (2012). In the case of Δv₂₀(Si), there seems to be a continuous link between CN, SS, and CL SNe Ia. Excluding BL SNe, which show the largest Δv₂₀(Si) values, a correlation coefficient as large as ρ = 0.86 is found between Δv₂₀(Si) and Δm₁₅(B).

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SN-Ia peak absolute magnitudes can be calibrated against decline rate and color (Tripp 1998) with a precision between 0.1 and 0.2 mag (Hicken et al. 2009; Folatelli et al. 2010). Given the correlation of pW2 (Si ii 4130) and pW6 (Si ii 5972) with Δm₁₅(B) shown in Figure 17 (Section 5.1), we tested the calibration of B-band peak absolute magnitudes versus (B_max − V_max) pseudo-color and these pW parameters (similar analysis can be found in Blondin et al. 2011b; Silverman et al. 2012b). For this purpose, we replaced Δm₁₅(B) by pW2 (Si ii 4130) and pW6 (Si ii 5972) in Equation (6) of Folatelli et al. (2010) for the B band. We obtained

$$\begin{eqnarray} \mu &=&B_{\mathrm{max}}-M_B(0)-a_B\,(pW\,-\,pW_0)\nonumber\\ &&-\beta _B^{BV}\,(B_{\mathrm{max}}-V_{\mathrm{max}}), \end{eqnarray} \tag{ 3 }$$

where pW corresponds to pW2 (Si ii 4130) and pW6 (Si ii 5972), and pW₀ = 15 Å and 20 Å, respectively. The redshift-based distances used for Equation (2) were supplemented with distance to the host galaxies of SNe 2005ke, 2006X, and 2006mr available in the literature. These objects were excluded from Equation (2) because they either had too large E(B − V)_Host or Δm₁₅(B), but they can be included in the luminosity calibration. For SNe 2005ke and 2006X, we adopted μ = 31.84 ± 0.08 mag and μ = 30.91 ± 0.14 mag, respectively, as given in Table 7 of Folatelli et al. (2010). For SN 2006mr, we used the latest distance modulus to its host, NGC 1316, of μ = 31.25 ± 0.05 mag provided by Stritzinger et al. (2010).

We fitted for M_B(0), a_B, and $\beta _B^{BV}$ employing the same χ² minimization method as described in the Appendix A of Folatelli et al. (2010). Table 9 provides the results of the fits for different subsamples of SNe Ia. The table lists the fitted parameters, the estimated intrinsic dispersion σ_SN (see Appendix A of Folatelli et al. 2010), the number of SNe used, and the sample selected for each fit. The weighted rms about the fit is also listed, defined as

$$\begin{equation} \mathrm{WRMS}\;=\;\frac{\sum _i^{N_{\mathrm{SN}}}\left[\mu _i-\bar{\mu }_i\right]^2\left/\right. \left(\sigma _i^2+\sigma _{\mathrm{SN}}^2\right)}{\sum _i^{N_{\mathrm{SN}}} 1\left/\right. \left(\sigma _i^2+\sigma _{\mathrm{SN}}^2\right)}, \end{equation} \tag{ 4 }$$

where $\bar{\mu }_i$ is the distance modulus as derived from the best fit of Equation (3), σ_i is the measurement uncertainty in the distance modulus (see Appendix A of Folatelli et al. 2010), and i runs along the sample of N_SN SNe.

Table 9. Fits of Peak Magnitudes versus pW and (B − V) Pseudo-color

Fit	MB(0)	aB	$\beta _B^{BV}$	RV	σSN	WRMS	NSNe	Sample
No.				(CCM+O)	(mag)	(mag)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
pW2 (Si ii 4130) [pW0 = 15 Å]
1	−19.07 ± 0.05	0.0135 ± 0.0028	3.18 ± 0.14	1.85 ± 0.13	0.10	0.17	55	Complete
2	−19.07 ± 0.05	0.0149 ± 0.0030	3.33 ± 0.26	1.98 ± 0.24	0.09	0.17	40	Non-HV
3	−19.09 ± 0.17	0.0137 ± 0.0118	3.36 ± 0.33	2.01 ± 0.30	0.00	0.13	20	CN
4	−19.07 ± 0.07	0.0154 ± 0.0035	3.30 ± 0.40	1.96 ± 0.36	0.08	0.16	42	(B − V) < 0.2
5	−19.07 ± 0.05	0.0148 ± 0.0029	3.24 ± 0.27	1.90 ± 0.24	0.09	0.16	37	Δm15(B) < 1.7
pW6 (Si ii 5972) [pW0 = 20 Å]
6	−19.08 ± 0.04	0.0112 ± 0.0018	3.19 ± 0.12	1.86 ± 0.11	0.12	0.19	67	Complete
7	−19.09 ± 0.04	0.0108 ± 0.0021	3.18 ± 0.17	1.84 ± 0.15	0.09	0.17	49	Non-HV
8	−19.05 ± 0.15	0.0141 ± 0.0091	3.42 ± 0.42	2.07 ± 0.39	0.12	0.18	22	CN
9	−18.99 ± 0.06	0.0173 ± 0.0027	3.00 ± 0.37	1.69 ± 0.33	0.08	0.16	48	(B − V) < 0.2
10	−19.04 ± 0.04	0.0137 ± 0.0021	2.94 ± 0.25	1.64 ± 0.22	0.05	0.14	41	Δm15(B) < 1.7

Notes. Fits of the type: $\mu =B_{\mathrm{max}}-M_B(0)-a_B\,[pW\,-\,pW_0]-\beta _B^{BV}\, (B-V).$ Column 1: fit identifier; Column 2: peak absolute magnitude for pW = pW₀ and zero (B − V) pseudo-color; Column 3: luminosity–pW slope; Column 4: luminosity–color slope; Column 5: corresponding parameter R_V of the CCM+O reddening law; Column 6: resulting intrinsic dispersion of SN data; Column 7: weighted rms of fit in magnitudes (see the text); Column 8: number of SNe used in fit; Column 9: sample of SNe used in fit (see the text).

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The weighted rms scatter for the complete sample are 0.17 mag and 0.19 mag (fits 1 and 6 for pW2 (Si ii 4130) and pW6 (Si ii 5972), respectively). Similar results for pW2 (Si ii 4130) were found by Blondin et al. (2011b) and Silverman et al. (2012b). The fit and scatter remain nearly unchanged when HV SNe are removed (fits 2 and 7). When we consider only CN SNe Ia, the scatter is reduced to 0.13 mag for the case of pW2 (Si ii 4130) (fit 3). If we cut the sample of SNe Ia to exclude objects redder than (B_max − V_max) = 0.2 mag—which excludes reddened objects but also most CL SNe—the scatter is reduced to 0.16 mag (fits 4 and 9).

For comparison, the fits with exactly the same samples of SNe as in Table 9, but now with Δm₁₅(B) instead of pW, yield very similar values of WRMS. For the complete sample and (B_max − V_max) < 0.2 mag cuts, the resulting WRMS values are 0.20 mag and 0.18 mag, respectively (see also Table 8 of Folatelli et al. 2010).

The intrinsic dispersions σ_SN of the luminosity–pW fits are ≲0.1 mag in all cases. Assuming the measurement uncertainties are well constrained, this indicates that the actual dispersion not accounted for in the fits is not large. The slopes, a_B, of the relation between peak absolute magnitudes and pW for all fits are compatible within uncertainties, except for a slightly larger slope when using pW6 (Si ii 5972) and SNe with (B_max − V_max) < 0.2 mag.

The slopes, $\beta _B^{BV}$, of peak luminosity versus color are also compatible within uncertainties for all fits shown in Table 9. Such color dependence of luminosity can be interpreted as the effect of dust extinction. Nevertheless, the dependence of luminosity on color for eCL SNe—which are intrinsically red—seems to agree with that of SNe reddened by dust. This is indicated by the lack of change in $\beta _B^{BV}$ when we exclude SNe with Δm₁₅(B) > 1.7 mag—that is, basically excluding the eCL group—as shown in fits 5 and 10. Assuming the CCM+O reddening law, the color slope can be converted to the total-to-selective absorption coefficient R_V. The conversion is detailed in Appendix B of Folatelli et al. (2010). The resulting R_V values are in the range of 1.6–2.1, depending on the sample employed. This is slightly larger than the range of 1.0 < R_V < 1.5 found by Folatelli et al. (2010) when fitting versus Δm₁₅(B) on a subsample of the SNe Ia presented here. Still, the R_V values found here are smaller than the Galactic average of R_V = 3.1., with a significance of at least 3σ.

In an attempt to refine the precision of SNe Ia as distance indicators, we searched for possible correlations between spectral parameters and residuals of the luminosity calibration. B-band peak absolute magnitude residuals, ΔM_B, were calculated based on the best fit of luminosity versus Δm₁₅(B) and (B_max − V_max) pseudo-color at maximum light as in Equation (6) of Folatelli et al. (2010),

$$\begin{eqnarray} \mu &=&B_{\mathrm{max}}\;-\;M_B(0)\;-\;b_B\,\left[\Delta m_{15}(B)\,-\,1.1\right]\nonumber\\ &&-\beta _B^{BV}\,(B_{\mathrm{max}}-V_{\mathrm{max}}). \end{eqnarray} \tag{ 5 }$$

The fit included 82 SNe Ia with available distances and photometric parameters, and yielded M_B(0) = −19.16 ± 0.01 mag, b_B = 0.55 ± 0.08, and $\beta _B^{BV}=3.05\pm 0.10$ (cf. fit 1 of Table 8 in Folatelli et al. 2010). The peak absolute magnitude residuals were thus computed as

$$\begin{eqnarray} \Delta M_B &=& B_{\mathrm{max}} \;-\; \mu \;+\; 19.16 \;-\; 3.05 \, (B_{\mathrm{max}} \,-\, V_{\mathrm{max}})\nonumber\\ &&- 0.55 \, [\Delta m_{15}(B) \,-\, 1.1]. \end{eqnarray} \tag{ 6 }$$

where ΔM_B values are given in the last column of Table 1.

We investigated possible correlations between ΔM_B and spectral parameters. In general agreement with Blondin et al. (2011b) and Silverman et al. (2012b), no significant dependence was found with any of the pW parameters. On the other hand, we found that the residuals depend slightly on S ii and Si ii velocities, in particular when considering SNe Ia with Δm₁₅(B) < 1.7 mag. Figure 22 shows the strongest of such correlations. Table 10 summarizes the results of the fits. The slopes of ΔM_B versus v (Si ii 5972), v (Si ii 6355), v (S ii 5449), and v (S ii 5622) are different from zero at the ≈2σ–3σ level. Given the lack of correlations found for other SN-Ia samples by Blondin et al. (2011b) and Silverman et al. (2012b), the results presented here deserve further study using large, homogeneous samples.

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A Kolmogorov–Smirnov (K-S) test on the distribution of Hubble residuals for SNe Ia separated into the HV and normal classes of Wang et al. (2009) gives a p-value of 0.07 (for 17 HV and 31 normal SNe). There is a non-negligible probability that both distributions are consistent. However, the difference in average Hubble residuals is noticeable between HV and normal SNe Ia (or between BL and the complete sample), as shown in the last column of Table 8. In case the differences are confirmed, they may be related to the finding that the scatter in the Hubble diagram is reduced when using only normal SNe Ia, as shown by Foley & Kasen (2011). Part of the difference in Hubble residuals may be explained by differences in intrinsic colors between normal and HV SNe. If, as suggested by Foley & Kasen (2011), HV objects show redder intrinsic colors than normal SNe Ia, then they could be "overcorrected" by reddening. However, when we compared the distributions of (B_max − V_max) for both subclasses using a K-S test, the resulting p-value was of 0.85, indicating that both color distributions are consistent (cf. Foley et al. 2011).

SN colors play a key role in the determination of extinction and in the calibration of luminosity. Investigating the relation between colors and spectroscopic parameters may serve to distinguish reddening sources of intrinsic and extrinsic nature, and to understand the origin of color variations. Here we study the relationship between (B_max − V_max) and pW for different spectral features. In order to search for possible dependence of intrinsic colors (B_max − V_max)₀ on pW, a subset of "low-reddening" SNe was identified. This was done following two requirements: (1) objects with E/S0 host galaxies or isolated from nuclei and arms, and (2) no evidence of Na i D lines from the host galaxy in the spectra. To this sample, we added some objects whose late-time (B − V) colors were compatible with the intrinsic-color law given in Equation (2) of Folatelli et al. (2010). These SNe are indicated with a "Y" in Column 8 of Table 1.

It has been shown that intrinsic B−V colors of SNe Ia at maximum light depend on decline rate (Phillips et al. 1999; Altavilla et al. 2004; Folatelli et al. 2010). The dependence is slight for SNe with Δm₁₅(B) < 1.7 mag. For the fastest declining objects, however, colors are significantly redder than for the rest of SNe Ia. We thus performed straight-line fits to the intrinsic color–pW relations using low-reddening SNe with Δm₁₅(B) < 1.7 mag. This excludes the eCL SNe Ia, most of which are in the low-reddening group,²⁴ with the exception of SN 2006bd, which has Δm₁₅(B)  =1.65 ± 0.02 mag and is also significantly bluer than the rest of the eCL objects. Note that eCL SNe have no measurements of pW2 (Si ii 4130). Table 11 summarizes the fit results for all eight pW parameters. Most features show a positive dependence of intrinsic color on pW, except pW5 (S ii W). Figure 23 shows the relations for that feature along with those that yielded the strongest dependence. The slopes in these cases are different from zero at the 2σ–3σ level. Nordin et al. (2011b) showed a similar trend in the case of the Si ii λ4130 line. Based on a large sample of SNe Ia with measurements of extinction-corrected pseudo-colors at maximum light, Foley et al. (2011) found a correlation between (B_max − V_max)₀ and pW7 (Si ii 6355). In our case, we obtain a similar relation, but the fit slope is just 1.7σ from zero. It should be noted that Foley et al. (2011) obtain their intrinsic colors in a different way than the one adopted here. They define (B_max − V_max)₀ as the residuals in the color axis of the relation between light-curve shape corrected absolute magnitudes and color. This implies the underlying hypothesis that the relation between peak luminosity and light-curve shape holds exactly for all SNe. In our case, we do not resort to such an assumption but define a low-reddening sample, independently of the luminosity calibration. This procedure has the price of reducing the working sample of SNe. We confirm the lack of dependence of intrinsic color on pW1 (Ca ii H&K) also shown by Foley et al. (2011).

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An interesting case is that of pW5 (S ii W), which shows a negative slope, although with a low significance. It should be noted, however, that eCL SNe Ia seem to follow the trend found for the rest of the low-reddening sample, with redder colors and lower pW5 (S ii W), although deviating from the straight-line fit. Something of the same sort can be seen in the case of pW3 (Mg ii), with eCL SNe showing the largest colors and pseudo-equivalent widths. This is expected since the increase in pW3 (Mg ii) by the presence of strong Ti ii absorption affects the B-band magnitude and is related with a temperature effect. The explanation is not so straightforward for pW5 (S ii W).

We have also searched for correlations between (B_max − V_max)₀ and expansion velocities at maximum light based on the same sample of low-reddening SNe. Contrary to what Foley et al. (2011) presented, we find no significant relation for any of the line velocities analyzed here. In order to directly compare with the latter work, we restrict the sample to SNe with 1.0 mag ⩽ Δm₁₅(B) ⩽ 1.5 mag. For v (Si ii 6355) we find a slope of 0.012 ± 0.016 mag/10³ km s⁻¹, which is lower and less significant than the value of 0.033 ± 0.004 mag/10³ km s⁻¹ given by Foley et al. (2011). Part of the discrepancy may be due to the different definition of (B_max − V_max)₀, as was pointed out above. Blondin et al. (2012) find milder relations than Foley et al. (2011), although still with 2σ–3σ significance (see their Table 6). Our results seem to be in contradiction with the predictions of asymmetric models by Kasen & Plewa (2007) as presented in Figure 8 of Foley & Kasen (2011). Other two-dimensional models by Kasen et al. (2009) agree more with the vanishing slopes of color versus v (Si ii 6355), as shown in Figure 18 of Blondin et al. (2011a), although for those models the expansion velocities are all larger than 11,000 km s⁻¹.