THE LOCAL HOSTS OF TYPE Ia SUPERNOVAE

For our local sample, we start with the low-z literature sample summarized in Conley et al. (2008). We supplement this with more recent SN photometry from Hicken et al. (2009a). The nearby SNe Ia that we consider here are required to have modern CCD photometry with error bars, and are required to have phase coverage beyond 3 days after maximum light and prior to 7 days after maximum light. They are also required to have one rest-frame B-band magnitude between 8 days before and 13 days after maximum light and one rest-frame U- or V-band magnitude in the same phase range. In addition, the wavelength range of the filters must be between 2700 and 7200 Å.

To be consistent with H09, we adopt the SN Ia light-curve fitting method from Conley et al. (2008). This method fits the SN light-curve data to produce the stretch, s (Perlmutter et al. 1997), a peak rest-frame B-band apparent magnitude, m_Bmax, and a SN color, $\mathcal {C}$, which is somewhat like (B − V)_Bmax in the sense that redder SNe have higher $\mathcal {C}$ values. Briefly, the stretch parameter is a time-axis scale factor that is applied to the light curve that aligns its shape with a “canonical” SN Ia light curve. The sense of the stretch parameter is such that faster, fainter SNe Ia have low-stretch values, and brighter, slower SNe Ia have higher-stretch values. The sense of the SN color parameter is such that bluer SNe at maximum are brighter. The corrected peak brightness of the SN Ia used for cosmology is determined by a linear combination of s, $\mathcal {C}$, and m_Bmax (Astier et al. 2006; Conley et al. 2008). Conley et al. (2008) present a much more detailed description of this method including comparisons with other popular fitting routines. These comparisons demonstrate that, at least for this study, our results are not dependant on the fitting technique.

Figure 1 shows distributions of the fitted SN light-curve properties for all the low-redshift SNe passing the previously described criteria in hosts with sufficient integrated host photometry to provide good SED fits (168 SNe Ia, filled histograms). This is the base sample we will examine in this work. The figure shows the distributions in stretch, peak color, absolute B magnitude (uncorrected for stretch-color), and recession velocity. The light-curve fit properties of this sample are given in Table 1, which lists the SN name, the host galaxy, the recession velocity, the light-curve stretch, the fitted apparent B magnitude at maximum light, and a status column which is described below. More details of the light-curve fits for these SNe can be found in A. Conley et al. (2010, in preparation).

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Low-luminosity SNe Ia are generally better represented in lower-redshift samples for multiple reasons. The spectra and the stretch–luminosity and color–luminosity relations for low-stretch SNe Ia differ enough from higher-stretch SNe (Garnavich et al. 2004; Taubenberger et al. 2008) to increase the errors in fitting their light curves beyond the error-budget requirement for cosmological parameter determination. This, combined with their faintness, makes low-stretch SNe less appealing targets for the spectroscopic follow-up required for cosmological surveys. As a result, the SN Ia training set derived for cosmology in Conley et al. (2008) contains no SNe with s < 0.70, and very few below s = 0.75. At lower redshifts where even faint SNe are relatively easy to follow up, the unusual objects tend to attract attention and acquire spectroscopy.

The break in the stretch–luminosity relation appears to be at s ∼ 0.80 (S. Gonzalez-Gaitan et al. 2010, in preparation). For this paper, we define the set of low-luminosity SNe Ia based on stretch to be those with s < 0.80 (to the left of the dashed vertical line in Figure 1(a)). The training set from Conley et al. (2008) allows us to extend this limit slightly to s = 0.75 when we apply corrections for stretch–luminosity.

Our local sample contains 29 SNe with s < 0.80 of which 12 are below s = 0.70. Since we are using a light-curve method developed for cosmology, this means our fitting can only tell that an object with s < 0.70 is low stretch, but cannot accurately measure the stretch. We have increased the error bars by a factor of 3 for objects with s < 0.70. The sample used in H09 was derived from the Supernova Legacy Survey (SNLS; Astier et al. 2006), which was optimized for cosmology. Either due to the fact that such objects are very rare beyond z = 0.2, or because the spectroscopic follow-up was biased against them or both, there are no objects with s < 0.75 in the H09 sample (see also Bronder et al. 2008). The low-stretch SNe Ia in our sample are indicated with an “L” in the status column in Table 1.

A similar situation exists for the peak color, $\mathcal {C}$. SNe Ia with colors greater than $\mathcal {C} \sim 0.7$ (see Figure 1(b)) are also unappealing objects for cosmological surveys because they are fainter and because they have larger fitting errors. These red SNe Ia should not be excluded when examining host properties, however. Our sample contains six SNe Ia with $\mathcal {C}>0.7$. These SNe are indicated with an “R” in the status column of Table 1. We have increased the peak color errors by a factor of 10 for these SNe to reflect the higher uncertainty in this parameter.

We emphasize that while the local sample assembled here is appropriate for exploring the link between host and SN properties, many of the SNe in our sample are too local (cz < 4000 km s⁻¹, z < 0.013, to the left of the vertical dashed line in Figure 1(d)) or have stretch errors or colors large enough to exclude them from use in cosmological fits. We indicate the cosmology status of our sample SNe Ia in the last column of Table 1 where an H indicates a SN Ia in the Hubble flow (cz > 4000 km s⁻¹), and a C indicates a SN Ia that is eligible for cosmological fitting based on the light-curve fit quality and having parameters within the range where the light-curve fitting has reasonably low errors.

We assembled host integrated photometry in the ultraviolet (UV) and optical to characterize the SN Ia host SEDs. For our low-redshift host galaxy sample, the addition of the Galaxy Evolution Explorer (GALEX) UV photometry improves the estimation of short-term star formation (e.g., Martin et al. 2005, Figure 1), and provides similar constraints on recent star formation when compared with the higher-redshift samples from the SNLS, whose blue optical photometry corresponds to the rest-frame UV. All host magnitudes are total magnitudes using matched elliptical apertures having the standard D25 diameter, to be compatible with the RC3. All host magnitudes are corrected for Milky Way (foreground) extinction using the dust maps of Schlegel et al. (1998).

In the UV, we generated host integrated magnitudes as part of the preliminary efforts to produce the GALEX Large Galaxy Atlas (GLGA; M. Seibert et al. 2010, in preparation). This atlas will measure ∼20,000 galaxies imaged by the GALEX UV-imaging satellite (Martin et al. 2005) having diameters in the UV greater than 1 arcmin. The GALEX imaging mode has two bandpasses, one in the far-UV (FUV; λ_eff = 1539 Å, Δλ = 442 Å) and another in the near-UV (NUV; λ_eff = 2316 Å, Δλ = 1060 Å). We use a technique similar to that used to generate the Nearby Galaxy Atlas (Gil de Paz et al. 2007) with which we cross-checked our integrated UV magnitudes. This method will be described in detail in M. Seibert et al. (2010, in preparation), but to summarize, we perform surface photometry in elliptical apertures on sky-subtracted images that have had foreground point sources and background galaxies masked.

For optical photometry, we used the RC3 (de Vaucouleurs et al. 1991) and/or images obtained from the Sloan Digital Sky Survey (SDSS;¹⁵ York et al. 2000) in the five SDSS bands: u, g, r, i, and z. Our sample required either SDSS coverage or an integrated magnitude from the RC3. The RC3 total integrated Johnson ultraviolet, blue, visual (UBV) magnitudes were obtained directly from NASA/IPAC Extragalactic Database (NED).¹⁶ For the larger hosts in our sample, we found the SDSS catalog data to be inaccurate for a number of reasons. Some of these hosts spanned multiple image strips and many were broken up into sub-regions making the determination of a total flux problematic. In order to enforce consistency across wavelengths, we decided to coadd and mosaic the SDSS image data for each SN host and derive the integrated photometry ourselves. To achieve this, we adapted our integrated photometry methods developed for the GLGA to SDSS image data. The major difference between GALEX and SDSS data is in the treatment of the sky background, which is extremely low in GALEX data. We checked the consistency of our integrated SDSS magnitudes by comparing them with RC3 magnitudes and found them to agree within the errors. All UV and optical integrated galaxy magnitudes are presented in M. Seibert et al. (2010, in preparation).

Sullivan et al. (2006) fit optical photometry to galaxy SED models produced with the PEGASE.2 SED galaxy spectral evolution code (Fioc & Rocca-Volmerange 1997; Le Borgne & Rocca-Volmerange 2002; Le Borgne et al. 2004). We adopted this method to allow a direct comparison with the higher-redshift host studies of Sullivan et al. (2006) and H09. As with these studies, all redshifts are known from the hosted SNe. This has the benefit of eliminating redshift degeneracies in the SED fits. The average internal extinction was allowed to vary in the fits over the range 0.0 < E(B − V)_HOST < 0.7 in increments of 0.05 mag using a Calzetti et al. (1994) dust model (see Fioc & Rocca-Volmerange 1997). We point out that the stellar mass derived from PEGASE.2 models is an estimate of the current mass in stars and is not the integral of the star formation history for a given galaxy (Sullivan et al. 2006). We also emphasize that our ages are strongly influenced by the flux produced by ongoing star formation yielding a fairly tight correlation between our derived host ages and specific SFRs. Thus, we should keep in mind that our luminosity-weighted properties might be different from those produced with mass-weighted measurements. The details of the galaxy modeling and SED fitting method employed here can be found in Section 3 of Sullivan et al. (2006).

To select the sample with good SED fits, we first require that a unique solution be found. This reduced our initial host sample from 258 down to 209, mostly due to the rejected SED having too few photometric points. We next require SED coverage in both the UV and optical bands, further reducing our sample down to 174 hosts. At this point we examined the distribution of χ²_ν and eliminated an additional six hosts that had extreme values (χ²_ν > 30; see Figure 2 and Le Borgne & Rocca-Volmerange 2002) leaving a total sample of 168. The 90 hosts that did not pass these criteria had no or limited optical photometry mostly due to not being members of any of the major galaxy catalogs (i.e., anonymous) and not being in the SDSS footprint which would allow us to derive the integrated flux from SDSS imaging. A subset of these also had no UV coverage because of proximity to a UV-bright star, which precludes GALEX observations due to detector safety. Table 2 lists the host T-type (de Vaucouleurs 1959) and the SED fit derived properties for the 166 unique hosts in our sample.

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The number of unique hosts is two less than the number of SNe Ia because two galaxies hosted two SNe Ia each: NGC 1316 hosted SN1980N and SN1981D, and NGC 5468 hosted SN1999cp and SN2002cr. In NGC 1316, the SNe Ia produced are low stretch (s ∼ 8.5) with values that differ by only 3%, while the two SNe Ia produced in NGC 5468 are normal stretch (s ∼ 0.98) and differ by 11%. This is certainly not a conclusive test of using integrated host magnitudes for comparison with stretch values, but it gives no cause to doubt this method, as would be the case if these pairs of SNe Ia differed by greater amounts.

Figure 3 shows the distributions of derived host properties for the local (solid line histograms) and H09 (dot-dashed line histograms) samples. There are some interesting differences between the two samples. The discrepancy in the mass distributions (Figure 3(b)) can be explained because local SNe are discovered in host-targeted surveys which prefer more massive hosts, while the SNLS is an areal survey without a mass bias and therefore includes lower-mass hosts. The discrepancy in the SFR distributions (Figure 3(c)) could be due to a luminosity bias from the host-targeted low-redshift surveys. Here the higher-redshift areal survey does not prefer luminous, and therefore higher SFR, hosts. These differences are reinforced if there is a correlation between mass and SFR. In this case, the same bias that produces the deficit of low-mass hosts in the local mass distribution produces the deficit of lower SFR hosts in the local SFR distribution. Figure 3(d) shows that when considering the specific star formation (sSFR), defined as SFR divided by stellar mass, our distributions are fairly similar. Thus, from here on we consider sSFR in preference over SFR.

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We start by examining correlations in host properties with SN Ia light-curve stretch. In the following discussion, it is good to keep in mind that higher-stretch SNe Ia are brighter and lower-stretch SNe Ia are fainter. In these plots, we highlight the transition between the low-luminosity (i.e., low-stretch) and normal SNe with an horizontal dashed line at s = 0.80.

Figure 4 plots the log of the sSFR against hosted SN Ia light-curve stretch. For this plot and plots following, the symbols indicate the host's sSFR: filled circles indicate hosts with no detected star formation (sSFR ⩽10⁻¹² yr⁻¹), filled stars indicate strongly star-forming hosts (sSFR >10^−9.5 yr⁻¹), and filled squares indicate hosts with intermediate sSFR. Typically, one would expect elliptical galaxies to belong in the lowest sSFR group and spiral galaxies to belong to the intermediate and high sSFR groups. Our aim here is to use a metric that is more physical than morphology; hence we do not use morphological classifications to examine these SN Ia hosts.

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We notice several interesting features in this diagram. We see that the sensitivity threshold of our models is just above ∼10⁻¹² yr⁻¹. We set all hosts with no detected sSFR to this value and consider these to be “dead” hosts. At the high end, we see the timescale limit which is determined by the lifetime of stars with SEDs that peak in the UV, ∼3 × 10⁸ yr. Since all of our hosts are essentially at zero redshift, this limit appears as a line. The triangles show the average stretch in three sSFR bins indicated by the vertical dashed lines. Note that low-stretch SNe are rare in high sSFR hosts (the one exception is SN1993H, as indicated in the plot), but common in intermediate and low sSFR hosts.

Figure 5 plots the luminosity-weighted host age against stretch, with the same symbol coding as in Figure 4. This plot shows that age and sSFR are well correlated with all the high sSFR galaxies having ages less than 1 Gyr and all the low sSFR hosts having ages greater than 4 Gyr as expected (see Section 2.2). The averages (filled triangles) were derived from three age bins (divided at 3 × 10⁸ and 2 × 10⁹ yr) and show a downward trend of stretch with age beyond 1 Gyr. Here we find the low-stretch SNe to be evenly distributed between host luminosity-weighted ages older than 5 × 10⁸ yr, but rare below this age with SN 1993H again being the sole exception.

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Figure 6 plots host stellar mass, M_*, against light-curve stretch and shows that hosts of the lowest stretch SNe Ia tend to have stellar masses higher than 10¹⁰ M_☉. The higher-stretch SNe Ia hosts have a much wider mass range (10⁸–10¹² M_☉).

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There is a major challenge in interpreting SN Ia peak color because of the unknown mix of two potential sources of the color: intrinsic SN Ia color from the details of the explosion itself and host galaxy line-of-sight reddening. In other words, the host extinction is not accounted for in the fitting process, which means that the peak color contains an intrinsic component and a host extinction component. This difficulty manifests itself when the color–luminosity relation is converted into a dust extinction law. In most cases, the resulting R_V is much lower than what is found in the Milky Way or other galaxies (Tripp 1998). However, it is clearly not appropriate to assume Milky-Way-like dust is responsible for SN Ia residual color (Conley et al. 2007).

There is potentially important information about the SN Ia explosion contained in the intrinsic color, if we could quantify and remove the line of sight, or host extinction part. Unfortunately, there are no observable signatures that allow these two sources to be disentangled, although extending the light-curve data to the near infrared may minimize the problem (Kasen 2006; Wood-Vasey et al. 2008). Our host data show no correlations between host proporties and SN peak color. The only feature worth noting, shown in Figure 7, is that all of the reddest SNe appear in hosts with intermediate age (∼1 Gyr). The low-stretch SNe with s < 0.80, indicated in the plot with the large open circles, are not the reddest SNe as might be expected from the color–luminosity relation (Tripp 1998; Tripp & Branch 1999; Parodi et al. 2000).

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Another way to examine this issue is to look at SN color as a function of host extinction, as shown in Figure 8. We see an average trend in sSFR with host extinction such that hosts with higher sSFR also have higher host extinction, a finding that gives us encouragement that the extinction estimates from PEGASE.2 are robust. The average SN peak color (filled triangles) shows no trend with host extinction, and the reddest SNe appear in hosts covering a substantial range of host extinctions. This could be due to the clumpiness of host extinction which makes an average host extinction irrelevant for the specific line of sight to the SN.

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In an effort to mitigate the difficulty of untangling host extinction and intrinsic SN color, Gallagher et al. (2008) made a study of local SNe Ia in hosts that were morphologically classified as early-type and thus thought to be low-extinction hosts. They used spectroscopic line diagnostics to determine metallicities and ages. We have the opportunity to select hosts with low extinction inferred from our SED fits, without the assumption that early-type galaxies all have low extinction and without possible host classification errors.

To test the impact of host extinction on cosmological fitting, we look for residual trends in the cosmologically corrected peak SN Ia brightness as a function of host luminosity-weighted age. We calculate the peak absolute B-band brightness for our SNe Ia, corrected for stretch and color using

$$\begin{equation} M_B = m_{B{\rm max}} + \alpha (s-1.0) - \beta \mathcal {C} - \mu _B(z_{\rm spec}), \end{equation} \tag{ 1 }$$

where α = 1.2, β = 2.9 (Sullivan et al. 2009), and μ_B(z_spec) is the distance modulus based on the spectroscopic redshift (A. Conley et al. 2010, in preparation). Since we are testing cosmological fitting, we eliminate low-stretch (s < 0.75) and red $(\mathcal {C}>0.7)$ SNe Ia. The distance modulus, μ_B, is only accurate if the SNe Ia are in the Hubble flow so we also eliminate hosts with z < 0.013. After applying these cuts, we are left with a sample of 85 SNe Ia.

We plot the stretch–color-corrected absolute peak B magnitude against the luminosity-weighted host age for this sample in the bottom panel of Figure 9 using the previously defined symbols based on sSFR. In the top panel of Figure 9, we plot the same values for a low host extinction subsample (N = 22), with E(B − V)_HOST ⩽ 0.05 according to our SED fits. The bottom panel plot shows no obvious residual trend with age for the larger sample. The residual trend apparent in the low host extinction subset has a correlation of −0.68. To determine the significance of this correlation, we selected 22 hosts at random from the full set of 85 hosts 10,000 times, and ran the same linear regression analysis on each randomly selected sample. The low host extinction sample is a 2.1σ outlier when compared with the resulting distribution of random correlations.

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Here we complement the higher-redshift (0.2 < z < 0.75) sample of H09 by using our nearby (0.013 < z < 0.06) sample of SNe Ia. This local sample, in addition to testing the Timmes et al. (2003) model in the nearby universe, will provide a test of the method developed in H09 for deriving Ni masses and host metallicities.

3.4.1. Host Metallicities from Host Masses

H09 point out the difficulties in using spectroscopic line indices (Hamuy et al. 2000; Gallagher et al. 2008) or line ratios (Gallagher et al. 2005) to derive host metallicities to compare with SN Ia intrinsic luminosity or ⁵⁶Ni mass. Instead, they use the mass–metallicity relation of Tremonti et al. (2004). There are drawbacks to using this trend, which uses gas-phase metallicity, on all galaxies regardless of gas content. However, as pointed out in H09, there are good reasons for assuming this method is accurate enough for the purposes here (see H09, Section 3.2). We also repeat the caution from H09 that gas-phase metallicity is not the same as stellar metallicity, although they should be correlated (Fernandes et al. 2005). The apparent scatter in the Tremonti relationship is 0.1 dex, which we add in quadrature to our errors when we estimate host metallicities. For consistency, we use host masses derived using the same technique applied in H09 and outlined in Sullivan et al. (2006).

We test the use of the Tremonti et al. (2004) mass–metallicity relation for low-z SN hosts by using the SN host metallicity data from Prieto et al. (2008). Their metallicities come from the SDSS as were those used in Tremonti et al. (2004). A comparison of the two results should reveal any biases in the low-z SN host sample. We have sufficiently good photometry for 170 SN hosts in the Prieto et al. (2008) catalog to perform this comparison. These data are also from the GLGA and will be published in M. Seibert et al. (2010, in preparation). We do not place any requirements on the SNe in this sample other than that they have metallicities from Prieto et al. (2008), and that we have enough host photometry for a good SED fit. Figure 10 plots our SED-fit stellar masses against the metallicities from Prieto et al. (2008). The relation from Tremonti et al. (2004) is shown as the solid line and the low-metallicity extension from Lee et al. (2006) is shown as the dashed line for comparison with the host data. The hosts with masses in the range 9 < log M_* < 11 appear to follow the Tremonti relation well, while hosts with log M_* < 9 appear to follow the Lee relation, albeit with a sparser sampling.

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We will be looking for average trends in ⁵⁶Ni mass with metallicity, therefore we want to be sure to sample the range of the scatter in the Tremonti relation so we are not biased toward one side or the other by observational effects. The host mass range for our low-z SNe Ia with well-fit light curves is primarily above log M_* = 9 (see Figure 6). The scatter in the mass–metallicity relation for SN hosts appears to be well sampled above this mass; thus, we should be less subject to observational biases that could be in effect below this host mass. We also need not use the low-metallicity extension from Lee et al. (2006) for our base sample of SN Ia hosts.

3.4.2. SN Ia ⁵⁶Ni Masses

H09 present a technique for estimating the SN Ia ⁵⁶Ni mass using Arnett's Rule (Arnett 1979, 1982) to convert bolometric luminosity and SN Ia rise time to ⁵⁶Ni mass. We use the identical technique on the well-sampled light curves for our local SNe Ia. Because the estimate of the bolometric luminosity assumes the luminosity distance is accurate, we use only the SNe in the Hubble flow (see Table 1).

The lowest stretch SNe Ia are also excluded from this experiment because they produce inaccurate ⁵⁶Ni masses using our technique. As previously stated, low-luminosity SNe Ia deviate from the normal trend of luminosity versus light-curve shape (Garnavich et al. 2004; Taubenberger et al. 2008), thus the bolometric luminosity is inaccurate. The SN Ia spectral templates currently available are also not representative of SNe Ia with s < 0.75 (Conley et al. 2008). A higher-order relation between light-curve shape and luminosity that properly accounts for low-luminosity SNe Ia and better spectral templates would allow us to use these SNe to test this model (S. Gonzalez-Gaitan et al. 2010, in preparation). They will be quite useful because the strongest effect from metallicity should occur in the faintest SNe. For our plots of Ni mass, we exclude objects with s < 0.75. To preclude inaccuracies due to excessive extinction we include only SNe Ia with $\mathcal {C} < 0.4$. The final sample of 74 SNe that pass these cuts is presented in Table 3, where the host and the derived ⁵⁶Ni masses and host metallicities are listed.

Table 3. ⁵⁶Ni Mass and Host Metallicity

SN	HOST	56Ni Mass	Corrected	Mass–Metal	Prieto et al. 2006
		(M☉)	56Ni Mass	12 + log (O/H)	12 + log (O/H)
			(M☉)
1999gd	NGC 2623	0.15 ± 0.02	0.34 ± 0.04	9.10	…
2006cc	UGC 10244	0.20 ± 0.02	0.68 ± 0.06	9.12	…
2007ci	NGC 3873	0.26 ± 0.02	0.31 ± 0.03	9.19	…
2001N	NGC 3327	0.27 ± 0.03	0.57 ± 0.06	9.16	…
2005kc	NGC 7311	0.27 ± 0.03	0.51 ± 0.05	9.18	…
2001da	NGC 7780	0.29 ± 0.04	0.30 ± 0.04	9.10	…
2006bq	NGC 6685	0.30 ± 0.03	0.41 ± 0.04	9.16	…
2006ar	M+11-13-36	0.30 ± 0.03	0.47 ± 0.04	8.95	9.09
2004L	M+03-27-38	0.31 ± 0.03	0.45 ± 0.05	9.10	…
2007bz	IC3918	0.31 ± 0.03	0.52 ± 0.05	8.84	…
2005ls	M+07-07-01	0.34 ± 0.03	0.79 ± 0.08	8.99	…
2008af	UGC 9640	0.35 ± 0.05	0.51 ± 0.07	9.21	…
1996bo	NGC 673	0.36 ± 0.03	0.75 ± 0.07	9.10	…
1994M	NGC 4493	0.36 ± 0.04	0.35 ± 0.04	9.19	…
2006N	M+11-08-12	0.36 ± 0.04	0.35 ± 0.03	9.17	…
1999cc	NGC 6038	0.37 ± 0.03	0.37 ± 0.03	9.18	…
2002he	UGC 4322	0.37 ± 0.03	0.36 ± 0.03	9.19	…
2006al	A103929+0511	0.38 ± 0.06	0.42 ± 0.07	9.08	…
2003U	NGC 6365A	0.38 ± 0.03	0.39 ± 0.03	9.16	…
2006ac	NGC 4619	0.38 ± 0.03	0.56 ± 0.05	9.18	…
2007bc	UGC 6332	0.38 ± 0.04	0.38 ± 0.03	9.16	…
2004as	A112539+2249	0.39 ± 0.04	0.44 ± 0.04	8.81	…
2001ie	UGC 5542	0.40 ± 0.09	0.45 ± 0.10	9.19	…
2006ej	NGC 191A	0.41 ± 0.04	0.47 ± 0.05	9.19	…
2006sr	UGC 14	0.41 ± 0.04	0.42 ± 0.04	9.15	…
2006bt	M+03-41-04	0.42 ± 0.04	0.74 ± 0.07	9.19	…
2003W	UGC 5234	0.43 ± 0.04	0.59 ± 0.05	9.13	…
2005ki	NGC 3332	0.44 ± 0.04	0.37 ± 0.03	9.20	…
2002bf	CGCG266-031	0.44 ± 0.04	0.67 ± 0.07	9.14	…
2005iq	M-03-01-08	0.45 ± 0.04	0.40 ± 0.04	9.10	…
2007bd	UGC 4455	0.45 ± 0.04	0.42 ± 0.04	9.16	…
1992bl	E291-G11	0.45 ± 0.05	0.40 ± 0.04	9.20	…
2002de	NGC 6104	0.45 ± 0.04	0.67 ± 0.07	9.17	…
1992ag	E508-G67	0.47 ± 0.05	0.61 ± 0.06	9.03	…
2006cp	UGC 7357	0.47 ± 0.04	0.59 ± 0.05	8.99	…
2006S	UGC 7934	0.48 ± 0.04	0.69 ± 0.06	9.12	…
2006en	M+05-54-41	0.50 ± 0.06	0.66 ± 0.09	9.15	…
2004eo	NGC 6928	0.50 ± 0.05	0.58 ± 0.05	9.20	…
2000fa	UGC 3770	0.51 ± 0.05	0.58 ± 0.05	8.98	…
2007O	UGC 9612	0.51 ± 0.05	0.54 ± 0.06	9.15	…
2002jy	NGC 477	0.51 ± 0.05	0.52 ± 0.05	9.12	…
2006az	NGC 4172	0.51 ± 0.04	0.47 ± 0.04	9.20	…
2002ha	NGC 6962	0.53 ± 0.05	0.47 ± 0.04	9.19	8.94
2006on	A215558-0104	0.53 ± 0.09	0.67 ± 0.11	9.09	…
1996C	M+08-25-47	0.53 ± 0.05	0.66 ± 0.06	9.02	…
2001en	NGC 523	0.54 ± 0.10	0.57 ± 0.10	9.10	…
2005ms	UGC 4614	0.54 ± 0.05	0.55 ± 0.05	9.09	9.06
1996bv	UGC 3432	0.57 ± 0.06	0.77 ± 0.08	9.06	…
2006te	A081144+4133	0.57 ± 0.07	0.50 ± 0.06	9.09	9.10
1999dk	UGC 1087	0.58 ± 0.05	0.68 ± 0.06	9.07	…
2007F	UGC 8162	0.60 ± 0.05	0.60 ± 0.05	9.04	9.05
1998dx	UGC 11149	0.61 ± 0.06	0.50 ± 0.05	9.20	…
2006ax	NGC 3663	0.62 ± 0.05	0.56 ± 0.05	9.17	…
2001fe	UGC 5129	0.64 ± 0.06	0.70 ± 0.06	9.07	…
1992P	IC3690	0.66 ± 0.08	0.54 ± 0.07	9.10	…
1998ab	NGC 4704	0.67 ± 0.06	0.72 ± 0.06	9.14	9.16
2001ba	M-05-28-01	0.67 ± 0.06	0.54 ± 0.05	9.18	…
1994S	NGC 4495	0.67 ± 0.06	0.61 ± 0.06	9.13	…
1998V	NGC 6627	0.70 ± 0.08	0.69 ± 0.08	9.17	…
1999aa	NGC 2595	0.71 ± 0.06	0.64 ± 0.05	9.16	…
1991U	IC4232	0.72 ± 0.08	0.68 ± 0.08	9.19	…
2001az	UGC 10483	0.72 ± 0.08	0.65 ± 0.07	9.15	…
2005eq	M-01-09-06	0.72 ± 0.06	0.98 ± 0.09	9.14	…
2007ae	UGC 10704	0.74 ± 0.08	0.86 ± 0.09	9.21	…
2002ck	UGC 10030	0.74 ± 0.10	0.71 ± 0.10	9.18	9.23
2008bf	NGC 4055	0.74 ± 0.06	0.94 ± 0.08	9.21	…
2002hu	M+06-06-12	0.80 ± 0.07	0.73 ± 0.06	9.08	…
2000ca	E383-G32	0.87 ± 0.08	0.76 ± 0.07	9.03	…
2001V	NGC 3987	0.88 ± 0.07	1.05 ± 0.09	9.16	…
1991ag	IC4919	0.89 ± 0.10	0.86 ± 0.09	8.73	…
1992bc	E300-G09	0.90 ± 0.08	0.71 ± 0.06	8.95	…
2003fa	M+07-36-33	0.92 ± 0.08	1.04 ± 0.09	9.17	…
2006cj	A125924+2820	0.95 ± 0.12	0.85 ± 0.11	9.11	…
1999dq	NGC 976	0.96 ± 0.09	1.22 ± 0.11	9.16	…

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Figure 11 shows the SN Ia ⁵⁶Ni mass as a function of host metallicity for our final sample. We use the same symbol coding as in Figure 4. We have taken the average Ni mass in three bins of metallicity starting at 12 + log (O/H) = 8.6 and having a width of 0.2 and plot these as filled triangles. The model from Timmes et al. (2003) altered for thin-disk O/Fe (H09) is overplotted as a thick dashed line. The average trend seen in H09 is shown by the open circles. Although our data are statistically consistent with no trend, they are also consistent with the H09 trend and the Timmes model.

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3.4.3. Color Correction

H09 apply a correction for the intrinsic SN Ia light-curve color to their derived Ni masses, after a color cut has been applied. Fainter SNe Ia are redder due to the intrinsic color–luminosity relation, or line-of-sight extinction, or both. Our Ni mass calculation requires the intrinsic luminosity, corrected for the dimming effects of dust, but not corrected for color–luminosity. Since the correction is based on the observed and not intrinsic color of the SN, there is bound to be some error in assuming that there is no dust dimming (uncorrected Ni masses) or that the color–luminosity relation is purely due to dust (color corrected Ni masses). Both will be inaccurate at some level. One way to examine this is to calculate and compare the χ²/dof or χ²_ν that results when comparing the corrected and uncorrected data to the Timmes model. When we apply the color correction, we find a mild improvement in the scatter as shown in Figure 12. When compared with the Timmes model, the χ²_ν is only marginally improved going from 3.93 (uncorrected) to 3.89 (color corrected).

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These values of χ²_ν greater than one imply that our errors do not reflect the expected scatter of the data points around the Timmes model, assuming it is correct. H09 found that in order to achieve χ²_ν = 1, they had to add in quadrature an extra 0.16 M_☉ to their errors in Ni mass for their uncorrected masses. We also find that we need an extra error of 0.16 M_☉ in our uncorrected ⁵⁶Ni masses to achieve χ²_ν = 1. Another measure of effectiveness of the color correction is to see how much this extra error is reduced by the correction. For H09, it was significantly reduced from 0.16 (uncorrected) to 0.12 (color corrected) M_☉. For our data there was only a marginal decrease in the extra scatter required for the color corrected ⁵⁶Ni masses (0.162–0.158 M_☉).

One possible explanation of this difference is the homogeneous light-curve photometry available for the H09 sample in contrast to the heterogeneous photometry available for our sample. The color cuts in H09 were made in a multicolor space that included wavelength regions that were not available for all the SNe in the local sample (see their Section 3.3). Consequently, our color cut here was in a single color (B − V) and may not have been as effective at removing outliers in the color corrected ⁵⁶Ni mass. We point out that there is an obvious reduction by the color correction in the scatter of Ni mass for lower-metallicity hosts, and the biggest outliers in the color-corrected plot (Figure 12) are near the highest metallicity. The fact that the color correction provides any improvement at all is consistent with the idea that at least some part of the color–luminosity relation is due to host dust extinction.

3.4.4. SN Ia ⁵⁶Ni Mass in Three Stretch Bins

Figure 13 shows the uncorrected Ni mass versus metallicity divided in three stretch bins (see H09, Figure 10). We do not sample as large a range of metallicity as H09; nonetheless, we do see similar features. The range of host metallicity for the higher-stretch SNe Ia is roughly double that for the lower-stretch group. We expect the average ⁵⁶Ni mass to increase with stretch due to stretch–luminosity, but we also see that the scatter in the masses is lowest in the lowest stretch group. The stretch cut in the low-stretch bin undoubtedly limits the Ni mass in this bin (see H09, Section 4.5), but at the low Ni mass end our local sample should be less subject to Malquist biases. Another effect is the color cut of $\mathcal {C} < 0.4$, which precludes the reddest, faintest, and therefore lowest Ni mass SNe. Nonetheless, the trends are suggestive and support the idea that lower-stretch SNe Ia appear in higher-metallicity hosts.

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Due to the age–metallicity degeneracy, we present plots of ⁵⁶Ni mass against luminosity-weighted age for the uncorrected (Figure 14) and color-corrected (Figure 15) Ni masses. We use the same symbol scheme as previous plots. We use a linear regression analysis to measure and test the correlation between age and Ni mass. The color correction slightly steepens the slope of the fit (from −0.04 ± 0.02 to −0.06 ± 0.02), and does improve the correlation from −0.10 (uncorrected) to −0.16 (color corrected).

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The age–Ni-mass slopes reported in H09 for their sample are significantly steeper: −0.15 ± 0.03 (uncorrected) and −0.11 ± 0.03 (color corrected). The correlations are also larger: −0.38 (uncorrected) and −0.37 (color corrected). Examining Figures 8 and 9 in H09, we see that a large part of the correlation seems to originate in hosts with luminosity-weighted ages beyond 3 Gyr which seem incapable of producing SNe with ⁵⁶Ni masses above 0.5 M_☉ in the uncorrected plot (their Figure 8) and above 0.6 M_☉ in the corrected plot (their Figure 9). Below 3 Gyr, there appears to be very little correlation between age and Ni mass. We see a similar feature in our data as well (Figures 14 and 15), although not quite as strong. This feature implies a threshold that is reached at a luminosity-weighted age of ∼3 Gyr, rather than a uniform trend with age.

Our results show features similar to those presented in higher-redshift host studies using the same methods (Sullivan et al. 2006; Sullivan 2009; H09). Low-stretch SNe Ia appear to be rare in high sSFR hosts, and the average stretch of SNe Ia in the lowest sSFR hosts is smaller than in hosts with higher sSFR (see Figure 4). The average stretch of SNe in hosts younger than ∼2 Gyr is close to 1 and for older hosts the average stretch appears to drop below 1 (see Figure 5). H09 were the first to plot host stellar mass against stretch, but their sample does not include SNe Ia with s < 0.75 (see their Figure 4). The interesting feature in our plot (Figure 6) is the limited mass range for lower-stretch SNe. This feature is present in the H09 figure, but it is less pronounced due to having fewer low-stretch SNe in their sample.

The apparent stellar mass threshold of 10¹⁰ M_☉ for the hosts of low-luminosity SNe Ia is fairly robust against selection effects. Our sample includes many lower-mass hosts within which it is easier to detect low-luminosity SNe. That these SNe prefer higher-mass hosts supports the idea that they arise from an older progenitor population. Figures 4–6 show that the one high sSFR host (E445-G66) of a SN Ia with s < 0.80 (SN1993H) is also massive, implying that the recently formed populations are mixed with the older populations that could be responsible for the low-stretch SN Ia. The correlation between mass and metallicity implies that metallicity could play a role as well (see Section 3.4). We see no low-mass, high sSFR hosts of low-stretch SNe Ia, and we also see few older, higher-mass hosts of the highest stretch SNe Ia. A method that can more accurately asses the star formation history of these hosts and the relative contributions from older and younger populations will produce a more definitive constraint on the progenitors of the low-luminosity SNe Ia (Schawinski 2009).

Our plot of SN peak color versus host age illustrates the difficulty of disentangling the source of the color (see Figure 7) since it shows no correlation. We are also challenged in our comparison with higher-redshift samples by the bias against SNe with very red peak colors intrinsic to cosmology surveys (see Section 2.1). Even in the local universe, our sample of six SNe Ia with $\mathcal {C}>0.7$ is too small for definitive interpretation. We point out one common feature of our figure and Figure 3 in Sullivan et al. (2009): very red SNe appear to be rare in hosts less than 0.5 Gyr in luminosity-weighted age.

Based on Figure 11, we conclude that the model of Timmes et al. (2003), relating metallicity to produced ⁵⁶Ni mass, appears consistent with the derived host metallicities and SN Ia ⁵⁶Ni masses for SNe in the local universe as well as at higher redshifts (H09), although the local data are also consistent with no trend in these properties. The degeneracy between age and metallicity makes it difficult to decide which is the more important factor in determining the ⁵⁶Ni mass of hosted SNe Ia. The apparent transition at a luminosity-weighted host age of 3 Gyr (see Figure 14, and H09, Figure 8) could place interesting constraints on progenitor scenarios given that this implies a fairly long delay time for low ⁵⁶Ni mass, hence low-luminosity and low-stretch, SNe Ia.

It is encouraging that the features in plots of light-curve properties against host properties in local hosts are similar when compared with the SNLS sample out to z = 0.75 (Astier et al. 2006; Howell et al. 2007; Sullivan et al. 2009), although a detailed comparison using Hubble diagram residuals will be needed to determine if any significant evolution of the population can be detected (A. Conley et al. 2010, in preparation; Sullivan et al. 2009). These trends do signal potential systematics for SN cosmology: as we extend the samples beyond redshift z = 0.75, we know the mix of host populations will move toward lower-mass, higher sSFR galaxies.

Our examination of low-extinction hosts suggests a trend in brightness with host age such that SNe Ia in older hosts appear brighter after correcting for stretch and color (see Figure 9). While the correlation we see is hardly significant (2.1σ), it does suggest that luminosity-weighted host age might be an interesting parameter to explore in cosmological fits of SNe Ia. A larger sample of SNe Ia from low-extinction hosts would allow a more definitive test of this correlation.

While there is no apparent trend in a similar plot in Gallagher et al. (2008, see their Figure 9), we see a trend that is marginally significant. There are several possible explanations for this difference. Since the hosts in the Gallagher et al. (2008) sample were selected morphologically, their sample may not be as free from dust extinction as originally thought. In addition, their corrections for light-curve shape are derived with a method that assumes a Milky-Way-like dust is responsible for residual color after a quadratic color-decline relation is subtracted (see comparison of fitting methods in Conley et al. 2008), which may not be appropriate for these hosts. The trend we see in Figure 9 is in the right sense to be caused by residual line-of-sight extinction since we would expect the SNe hosted by the oldest galaxies to have the least non-local extinction.

These data suggest that either the SNe Ia or the dust produced in galaxies of different host properties are different or both. Hicken et al. (2009b) showed a weak trend in the Hubble residuals when using samples divided into three host morphology bins, after removing the reddest SNe. An exploration based on more physical host properties could provide a more accurate assessment of this effect (Sullivan et al. 2009). Further progress may be made by extending host photometry farther into the infrared to help constrain the host dust content and by more detailed fitting of host star formation history to constrain the most recent episode of star formation (e.g., Schawinski 2009).