CONFIRMATION OF A STAR FORMATION BIAS IN TYPE Ia SUPERNOVA DISTANCES AND ITS EFFECT ON THE MEASUREMENT OF THE HUBBLE CONSTANT

In order to confirm the LSF bias previously detected in the SNfactory sample we need an independent nearby Hubble-flow sample for which it is possible to compare SALT2-standardized magnitudes between SNe Ia from locally SF and passive environments. The compilation of H09 has been used previously for a number of cosmological analyses (e.g., H09; Kessler et al. 2009; Rest et al. 2014; Riess et al. 2009, 2011) and only six of the SNe Ia have been studied in R13 already. For the nearby Hubble flow range of 0.023 < z < 0.1 (as used, e.g., by SH0ES11), we find that the H09 compilation contains 110 such Hubble-flow SNe Ia. Because the H09 sample was constructed for cosmological applications, peculiar SNe Ia or those with large extinction or poor lightcurve fits have already been removed. Thus, the H09 compilation appears to be quite suitable for an independent measurement of the LSF bias, provided a suitable set of local star-formation measurements can be obtained. A 0.14 ± 0.07 mag offset between E/S0 and Sc/Sd/Irr morphological types in this sample was identified by H09, thus a first comparison between bias revealed by morphological versus local star-formation indicators will be possible.

In the case of R13, it was possible to obtain sensitive measurements of the local Hα surface brightness as a direct by-product of the SuperNova Integral Field Spectrograph (SNIFS) observations conducted by the SNfactory. Conventional slit spectroscopy or imaging photometry, as employed for the SN Ia follow-up programs compiled in H09, does not afford any robust parallel quantitative measurement of local star formation. Furthermore, archival Hα imaging is quite limited for the galaxies in the H09 compilation. Thus, suitable Hα data for measuring the LSF bias in the H09 sample are not currently available.

The far-ultraviolet (FUV) luminosity is another well-established SF indicator. Previously, we used this along with optical data to characterize the global star formation activity of SNfactory SNe Ia host galaxies (Childress et al. 2013a, 2013b), while Neill et al. (2009) did the same for many host galaxies in the H09 sample.

This led us to investigate the availability of sufficiently deep GALEX FUV imaging for the H09 host galaxies. We found that 92 out of the 110 H09 Hubble-flow SN Ia host galaxies have UV coverage from the GALEX GR6/7 data release in the MAST archive,¹⁷ and that these data have sensitivity sufficient to classify SN Ia environments following the scheme of R13 for most hosts. (Observations from the CAUSE phase of the GALEX mission were not considered due to their inhomogeneous nature.) We also investigated the available coverage from SWIFT. There the overlap with the H09 Hubble-flow subsample was too small to be useful and all but two cases had GALEX coverage already, and thus we decided not to use the SWIFT data at this time. We therefore proceed to examine the LSF bias using a combination of the nearby Hubble-flow SN Ia subset from H09 and UV data from GALEX.

As a start, we examine any biases that may arise from excluding the subset of SNe Ia lacking GALEX coverage. GALEX was ostensibly an all-sky imaging survey (AIS) reaching a 5 σ point source depth of m_FUV = 19.9 AB mag (Morrissey et al. 2007). However, partway through the mission the FUV detector failed to function, leading to incomplete FUV coverage. In addition, bright stars were avoided in order to prevent damage to the GALEX detectors, leaving coverage gaps concentrated toward the Galactic plane region, which SN surveys avoid anyway. GALEX also conducted deeper surveys—the Medium Imaging Survey (MIS) covering 1000 deg² to m_FUV = 23.5 AB mag and the Deep Imaging Survey (DIS) covering 80 deg² to m_FUV = 25.0 AB mag—in fields coincident with other extragalactic surveys. These solid angles are much smaller than the sky coverage typical of nearby SN surveys, and thus constitute a fairly random sampling. Since these variations in GALEX coverage with respect to sky location or proximity to bright stars are completely decoupled from characteristics of nearby SN searches, there is no a priori expectation for a bias between SNe Ia in hosts with and without GALEX coverage. Indeed, application of Kolmogorov–Smirnov tests indicates that lightcurve stretch, color and standardized Hubble residual distributions of the 18 SNe Ia without GALEX observations are completely compatible with those having GALEX coverage, giving similarity probabilities greater than 16% for all comparisons.

Next we apply the selection criteria used in R13, which we follow in order to provide the best possible comparison to that study. In R13 we eliminated SNe Ia spectroscopically classified as 91T-like according to Scalzo et al. (2012) due to the possibility that they may be so-called super-Chandrasekhar SNe Ia and therefore not representative of SN cosmology samples. In Appendix B.1 we provide details of this selection process, which resulted in the elimination of three 91T-like SNe Ia, one of which lacked GALEX FUV coverage anyway. R13 also removed highly inclined hosts; as discussed in more detail in Appendix B.2, for FUV observations this helps avoid both potential false-positive and false-negative environmental associations. We identified seven SN host galaxies with i > 80°; SN 1992ag, SN 1995ac, SN 1997dg, SN 1998eg, SN 2006ak, SN 2006cc and SN 2006gj, and removed them from our baseline analysis.

As a result of these sample selection procedures, which are summarized in Table 1, our baseline analysis will utilize 77 hosts when using Hubble residuals based on SALT2 and 83 hosts when using MLCS2k2 (Jha et al. 2007) Hubble residuals. This sample size compares favorably with the sample of 82 hosts used in R13 to discover the LSF bias.

2.2.1. FUV and Hα as Star-formation Indicators

Massive short-lived O and early B type stars with ≳ 17 M_☉ are responsible for the ionizing radiation that generates Hα emission, while FUV emission is produced by O- through late-B stars with ≳ 3 M_☉. Detection of UV light is therefore an indication of star formation within the preceding 100 Myr (see Calzetti 2013 for a detailed review) and FUV and Hα emission are strongly coupled. This makes them consistent and commonly used star formation indicators (see, e.g., Sullivan et al. 2000; Bell & Kennicutt 2001; Salim et al. 2007 and generally Lee et al. 2009, 2011 and references therein).

Like Hα, the FUV flux drops dramatically with the age of the stellar population. In simple stellar-population instantaneous-burst models that account for the late-time contribution of hot subdwarfs, the FUV flux drops by ∼1.4 dex between 10 Myr and 100 Myr, and then another ∼3 dex from 100 Myr to 1 Gyr (Han et al. 2007; Leitherer et al. 1999). While this is an exceptionally strong signal, it is complicated by dust extinction that is stronger in the FUV than for Hα. This not only weakens the ability to detect star formation, but adds non-negligible uncertainty arising from the extinction correction.

There is also a diffuse FUV component, analogous to the diffuse Hα commonly observed in nearby spiral galaxies. In Appendix D we provide further details concerning this diffuse emission source, along with our examination of its potential impact. For the equivalent star-formation threshold set in R13 (see below), we find that this component should only marginally affect our classification of SN Ia environments.

After correcting for Galactic and interstellar dust extinction, details of which are discussed in Section 2.2.2, both Hα and FUV indicators can be converted to a star formation rate (SFR) surface density, Σ_SFR (in M_☉ yr⁻¹ kpc⁻²):

$$\begin{eqnarray} \Sigma _{\mathrm{SFR}}&= \kappa _{1} \times {L^0_{\mathrm{FUV}}}/{\mathcal {S}} \nonumber\\ \Sigma _{\mathrm{SFR}}&= \kappa _{2} \times \Sigma _{\mathrm{H}\alpha } \end{eqnarray} \tag{ 1 }$$

In this equation, $L^0_{\mathrm{FUV}}$ is the dust-corrected FUV luminosity (in erg s⁻¹ Hz⁻¹) summed over an aperture centered at the SN location having area $\mathcal {S}\ \mathrm{kpc^{2}}$. Σ_Hα is the local Hα surface brightness (in erg s⁻¹ kpc⁻²). The redshifts considered here are small (z ∼ 0.03), so the FUV and NUV K-corrections are negligible—typically smaller than the measurement errors (Chilingarian & Zolotukhin 2012). Here we use the usual conversion factors κ₁ = 1.08 × 10⁻²⁸ and κ₂ = 5.5 × 10⁻⁴², as in, e.g., Salim et al. (2007); Kennicutt et al. (2009); Calzetti (2013). Modifications to the initial mass function, metallicity, etc., can alter these conversion factors by ±0.2 dex; see Table 2 of Hao et al. (2011) for examples. As in R13, we do not attempt to perform corrections to face-on quantities due to uncertainty concerning the three-dimensional distribution of star formation in local regions. Even for the extreme case of SNe in the planes of pure disks viewed at random inclinations below our limit of $i<80\deg$, only ∼0.2 dex of additional scatter is introduced.

In R13 we used an Hα surface density threshold of log (Σ_Hα) = 38.35 dex, corresponding to log (Σ_SFR) = −2.9 dex, to split the SNfactory sample into two equal-sized groups. Below this threshold SNe Ia were classified as having a locally passive environment, Ia, and above this threshold they were classified as having a locally SF environment, Iaα. The R13 threshold also happened to be that ensuring a minimum 2σ detection over the SNfactory redshift range, and it was also high enough to limit the impact of miscategorization caused by diffuse Hα emission.

We retain this threshold for the current analysis for consistency with R13. For FUV measurements this threshold is also sufficient to minimize miscategorization due to the aforementioned diffuse FUV light; Boquien et al. (2011) found that for log (Σ_SFR) > −2.75 dex interarm regions in M33 are largely suppressed and our threshold is only slightly below this. The mildly non-linear relation observed between Hα and FUV (Lee et al. 2009; Verley et al. 2010) does not affect the placement of this threshold by more than ∼0.1 dex.

To account for measurement errors, rather than simply dividing the SNe Ia into two groups as in R13, we will estimate a probability for each SN, $\mathcal {P}\mathrm{(Ia\epsilon)}$, giving the chance that its local environment is locally passive. To do so we use the Poisson errors on the measurements of FUV flux and extinction, A_FUV (see Section 2.2.2), and calculate the fraction of the resulting log (Σ_SFR) distribution that has $\Sigma _{\mathrm{SFR}}^{\lim } \le 10^{-2.9}\ \mathrm{{M}_\odot \ yr^{-1}\ kpc^{-2}}$. We have confirmed the appropriateness of using Poisson uncertainties by measuring aperture fluxes for 10⁴ blank sky regions and checking that the results were Poisson-distributed.

2.2.2. Local Dust Correction

Dust is associated with star formation (e.g., Charlot & Fall 2000; Simones et al. 2014; Verley et al. 2010) and so can have a strong impact on the observed UV light around the SN location. The amount of dust depends on many factors such as the geometry, the quantity of metals available to form dust, and dust production and destruction mechanisms and timescales. Nevertheless, for SF galaxies there is a good correlation between FUV−NUV color and the amount of FUV dust-absorption, A_FUV. Here we use the relation given in Equation (5) of Salim et al. (2007) to estimate A_FUV. (See Conroy et al. 2010 for examples of several alternative extinction relations.) Since this correction is only appropriate for SF environments, we face the need to assess whether an environment is SF before knowing whether to correct for extinction.

We start by examining the global SF properties of the SN host galaxies. The association of dust with star-formation suggests that locally passive environments should not require extinction correction, and in R13 we found that globally passive host galaxies are also locally passive. Thus, in most cases it would be inappropriate to apply extinction corrections to the local environments for SNe in globally passive galaxies. One very useful quantitative measure of star-formation activity is the global specific star-formation rate (sSFR). sSFR measurements are available for ∼60% of the host galaxies in our sample. These are based primarily on UV and optical colors (Neill et al. 2009), plus NIR for some (Childress et al. 2013b). Using sSFR, we categorize host galaxies with conclusively low sSFR as globally passive and those with conclusively high sSFR as globally SF. Specifically, to be considered conclusively low or high, we require that the measured sSFR be, respectively, one standard deviation below or above a boundary set at sSFR = −10.5 dex. In Table 2, we designate these as having host types of Pa and SF, respectively. Cases where the sSFR is within one standard deviation of the threshold are designated as ∼Pa and ∼SF, depending on whether their sSFR is, respectively, below or above −10.5 dex.

Table 2. FUV Measurements of the Hubble-flow SN Ia Sample

Name	$\Delta M_B^{\mathrm{corr}}$ (mag)			z	GALEX data			Local	Global	Local	log (ΣSFR)	$\mathcal {P}\mathrm{(Ia\epsilon)}$	Cuts
	SALT	MLCS2k2			Exp.	FUV	NUV	AFUV	Host	Dust
		RV = 1.7	RV = 2.5		(s)	(mag)	(mag)	(mag)	Class	Corr.	(M☉ kpc−2 yr−1)	(%)	Applied
1990O	−0.14 ± 0.19	−0.02 ± 0.16	−0.02 ± 0.16	0.031	145	22.77 ± 0.64	24.73 ± 1.68	1.9 ± 0.6	SF	Y	$-2.53_{-0.53}^{+0.10}$	22
1990af	−0.13 ± 0.18	−0.28 ± 0.19	−0.25 ± 0.20	0.050	489	27.35 ± 10.11	>21.8	2.0 ± 0.6	Pa	N	$-4.68_{-\infty }^{+0.35}$	100
1991U	−0.35 ± 0.20	⋅⋅⋅	⋅⋅⋅	0.033	219	21.43 ± 0.36	20.63 ± 0.10	2.2 ± 0.6	∼SF	Y	$-1.83_{-0.68}^{+0.23}$	6
1992J	−0.27 ± 0.19	⋅⋅⋅	⋅⋅⋅	0.046	218	26.61 ± 7.93	24.22 ± 0.80	2.0 ± 0.6	Pa	N	$-4.47_{-\infty }^{+0.56}$	100
1992P	+0.10 ± 0.20	+0.11 ± 0.17	+0.14 ± 0.18	0.026	⋅⋅⋅	no image	no image	⋅⋅⋅	∼SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
1992ae	−0.08 ± 0.18	−0.08 ± 0.19	−0.08 ± 0.20	0.075	558	24.00 ± 0.83	23.47 ± 0.24	2.0 ± 0.6	Pa	N	$-2.98_{-0.86}^{+0.29}$	61
1992ag	−0.30 ± 0.20	−0.21 ± 0.18	−0.23 ± 0.19	0.026	184	19.38 ± 0.11	19.20 ± 0.05	1.3 ± 0.3	∼SF	Y	$-1.58_{-0.13}^{+0.04}$	0	Incl.
1992bg	⋅⋅⋅	−0.01 ± 0.17	+0.00 ± 0.17	0.036	199	22.23 ± 0.45	22.78 ± 0.38	1.7 ± 0.5	SF	Y	$-2.25_{-0.35}^{+0.07}$	10
1992bh	+0.12 ± 0.18	+0.26 ± 0.16	+0.24 ± 0.17	0.045	175	22.78 ± 0.54	22.51 ± 0.28	1.9 ± 0.6	SF	Y	$-2.18_{-0.43}^{+0.09}$	11
1992bk	+0.15 ± 0.28	−0.05 ± 0.23	−0.03 ± 0.22	0.058	1021	26.28 ± 1.64	25.40 ± 0.62	2.0 ± 0.6	Pa	N	$-4.12_{-\infty }^{+0.17}$	100
1992bl	−0.05 ± 0.20	−0.08 ± 0.18	−0.04 ± 0.17	0.043	109	23.79 ± 1.08	27.78 ± 15.79	2.0 ± 0.6	∼Pa	N	$-3.48_{-\infty }^{+0.43}$	96
1992bp	−0.27 ± 0.17	−0.16 ± 0.15	−0.13 ± 0.14	0.079	106	>20.6	27.41 ± 9.45	2.0 ± 0.6	Pa	N	< − 3.0	66
1992br	+0.11 ± 0.21	−0.63 ± 0.22	−0.51 ± 0.24	0.088	⋅⋅⋅	no image	no image	⋅⋅⋅	Pa	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
1992bs	+0.20 ± 0.17	+0.23 ± 0.18	+0.23 ± 0.19	0.063	216	22.45 ± 0.40	23.13 ± 0.32	1.6 ± 0.5	SF	Y	$-1.87_{-0.29}^{+0.07}$	5
1993B	−0.11 ± 0.17	+0.07 ± 0.17	+0.10 ± 0.17	0.071	192	23.14 ± 0.61	22.14 ± 0.21	2.1 ± 0.6	SF	Y	$-1.84_{-0.54}^{+0.10}$	11
1993H	⋅⋅⋅	−0.25 ± 0.17	−0.22 ± 0.17	0.025	137	23.05 ± 0.88	22.34 ± 0.35	2.0 ± 0.6	SF	Y	$-2.78_{-0.83}^{+0.12}$	39
1993O	+0.02 ± 0.17	+0.11 ± 0.14	+0.16 ± 0.14	0.052	215	>21.1	25.08 ± 1.34	2.0 ± 0.6	Pa	N	< − 3.8	99
1993ac	+0.05 ± 0.19	+0.06 ± 0.19	+0.05 ± 0.21	0.049	224	26.19 ± 6.78	24.36 ± 0.78	2.0 ± 0.6	Pa	N	$-4.24_{-\infty }^{+0.30}$	98
1993ag	−0.05 ± 0.18	+0.23 ± 0.16	+0.22 ± 0.16	0.050	⋅⋅⋅	no image	no image	⋅⋅⋅	Pa	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
1994M	+0.03 ± 0.20	−0.01 ± 0.18	−0.02 ± 0.18	0.024	109	>22.5	24.97 ± 2.68	2.0 ± 0.6	∼Pa	N	< − 4.3	100
1994T	−0.02 ± 0.19	−0.28 ± 0.16	−0.20 ± 0.16	0.036	136	>21.8	25.05 ± 1.93	2.0 ± 0.6	Pa	N	< − 4.3	100
1995ac	−0.32 ± 0.17	−0.23 ± 0.13	−0.27 ± 0.14	0.049	211	23.99 ± 0.91	22.83 ± 0.30	2.1 ± 0.6	SF	Y	$-2.53_{-0.90}^{+0.12}$	26	Incl.
1996C	+0.20 ± 0.20	+0.32 ± 0.16	+0.34 ± 0.17	0.028	⋅⋅⋅	no image	no image	⋅⋅⋅	SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
1996bl	−0.12 ± 0.18	−0.00 ± 0.15	−0.01 ± 0.16	0.035	221	22.15 ± 0.35	22.18 ± 0.21	1.7 ± 0.5	SF	Y	$-2.24_{-0.30}^{+0.07}$	7
1997dg	+0.41 ± 0.19	+0.38 ± 0.16	+0.38 ± 0.16	0.030	488	21.63 ± 0.22	21.96 ± 0.13	1.2 ± 0.4	∼SF	Y	$-2.38_{-0.32}^{+0.08}$	5	Incl.
1998ab	−0.31 ± 0.19	−0.32 ± 0.16	−0.37 ± 0.16	0.028	316	20.52 ± 0.23	20.36 ± 0.07	1.6 ± 0.4	SF	Y	$-1.84_{-0.69}^{+0.41}$	2	91T
1998dx	−0.10 ± 0.18	−0.15 ± 0.14	−0.16 ± 0.14	0.054	153	>21.3	26.29 ± 3.72	2.0 ± 0.6	∼Pa	N	< − 3.7	97
1998eg	+0.07 ± 0.21	+0.09 ± 0.18	+0.08 ± 0.18	0.024	166	22.87 ± 0.69	23.88 ± 0.96	1.9 ± 0.6	∼Pa	N	$-3.56_{-0.44}^{+0.06}$	100	Incl.
1999awb	+0.07 ± 0.18	⋅⋅⋅	⋅⋅⋅	0.039	322	27.66 ± 19.96	>22.4	2.0 ± 0.6	SF	Y	< − 3.5	75
1999cc	−0.03 ± 0.18	−0.05 ± 0.15	−0.06 ± 0.15	0.032	137	21.93 ± 0.40	20.92 ± 0.14	2.2 ± 0.6	SF	Y	$-2.03_{-0.40}^{+0.09}$	9
1999ef	+0.24 ± 0.19	+0.33 ± 0.16	+0.37 ± 0.16	0.038	112	23.98 ± 1.31	23.14 ± 0.52	2.0 ± 0.6	SF	Y	$-2.78_{-\infty }^{+0.16}$	40
1999gp	+0.01 ± 0.19	⋅⋅⋅	⋅⋅⋅	0.026	⋅⋅⋅	no image	no image	⋅⋅⋅	SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	91T UV
2000bh	−0.12 ± 0.21	+0.00 ± 0.20	+0.02 ± 0.20	0.024	⋅⋅⋅	no image	no image	⋅⋅⋅	SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
2000ca	−0.16 ± 0.20	−0.15 ± 0.16	−0.11 ± 0.16	0.025	3362	20.93 ± 0.07	20.21 ± 0.02	2.6 ± 0.2	SF	Y	$-1.72_{-0.40}^{+0.26}$	0
2000cf	+0.18 ± 0.18	+0.17 ± 0.14	+0.18 ± 0.15	0.036	204	21.76 ± 0.46	21.22 ± 0.13	2.0 ± 0.6	SF	Y	$-1.93_{-0.76}^{+0.28}$	8
2001ah	−0.10 ± 0.18	−0.03 ± 0.17	+0.02 ± 0.16	0.058	⋅⋅⋅	no image	no image	⋅⋅⋅	SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
2001az	+0.05 ± 0.18	−0.04 ± 0.15	+0.00 ± 0.15	0.041	⋅⋅⋅	no image	22.62 ± 0.28	⋅⋅⋅	SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
2001ba	+0.10 ± 0.19	+0.08 ± 0.15	+0.13 ± 0.14	0.030	107	22.38 ± 0.63	22.53 ± 0.42	1.9 ± 0.6	SF	Y	$-2.39_{-0.48}^{+0.09}$	16
2001eh	−0.05 ± 0.18	+0.12 ± 0.13	+0.14 ± 0.13	0.036	⋅⋅⋅	no image	no image	⋅⋅⋅	SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
2001gb	⋅⋅⋅	+0.04 ± 0.23	⋅⋅⋅	0.027	⋅⋅⋅	no image	no image	⋅⋅⋅	SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
2001ic	⋅⋅⋅	−0.10 ± 0.21	⋅⋅⋅	0.043	208	>21.8	23.89 ± 0.66	2.0 ± 0.6	Pa	N	< − 5.8	100
2001ie	−0.02 ± 0.20	−0.03 ± 0.18	−0.04 ± 0.20	0.031	103	>22.0	25.22 ± 2.40	2.0 ± 0.6	Pa	N	< − 3.9	100
2002G	+0.04 ± 0.24	−0.40 ± 0.35	−0.41 ± 0.38	0.035	173	23.36 ± 0.72	22.07 ± 0.22	2.1 ± 0.6	SF	Y	$-2.55_{-0.65}^{+0.11}$	24
2002bf	−0.20 ± 0.21	+0.13 ± 0.18	+0.11 ± 0.19	0.025	112	22.04 ± 0.47	20.40 ± 0.12	2.5 ± 0.6	∼SF	Y	$-2.18_{-0.48}^{+0.10}$	12
2002bz	+0.11 ± 0.24	−0.01 ± 0.18	⋅⋅⋅	0.038	⋅⋅⋅	no image	no image	⋅⋅⋅	SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
2002ck	+0.02 ± 0.19	+0.02 ± 0.17	+0.03 ± 0.17	0.030	⋅⋅⋅	no image	no image	⋅⋅⋅	∼SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
2002de	+0.06 ± 0.20	+0.12 ± 0.16	+0.08 ± 0.18	0.028	110	20.51 ± 0.23	19.80 ± 0.09	2.2 ± 0.5	SF	Y	$-1.58_{-0.29}^{+0.07}$	3
2002hd	−0.31 ± 0.19	−0.34 ± 0.17	−0.33 ± 0.18	0.036	112	23.10 ± 0.80	21.59 ± 0.22	2.1 ± 0.6	Pa	N	$-3.28_{-0.51}^{+0.09}$	94
2002he	+0.08 ± 0.21	−0.08 ± 0.19	−0.06 ± 0.19	0.025	110	25.01 ± 3.10	23.28 ± 0.68	2.0 ± 0.6	∼SF	N	$-4.37_{-\infty }^{+0.35}$	100
2002hu	−0.11 ± 0.18	−0.03 ± 0.13	+0.00 ± 0.13	0.038	128	25.03 ± 2.68	22.90 ± 0.44	2.0 ± 0.6	∼SF	N	$-4.00_{-\infty }^{+0.27}$	100
2003D	⋅⋅⋅	−0.26 ± 0.19	−0.32 ± 0.20	0.024	168	24.11 ± 1.60	21.76 ± 0.22	2.1 ± 0.6	Pa	N	$-4.10_{-\infty }^{+0.16}$	100
2003U	−0.04 ± 0.22	−0.12 ± 0.16	−0.08 ± 0.16	0.028	170	21.73 ± 0.34	21.16 ± 0.15	2.0 ± 0.5	SF	Y	$-2.15_{-0.33}^{+0.08}$	7
2003ch	+0.14 ± 0.19	+0.25 ± 0.16	+0.24 ± 0.16	0.030	204	26.17 ± 7.04	24.56 ± 1.44	2.0 ± 0.6	Pa	N	$-4.67_{-\infty }^{+0.45}$	100
2003cq	−0.04 ± 0.21	+0.00 ± 0.20	−0.06 ± 0.24	0.034	81	22.11 ± 0.56	21.78 ± 0.28	2.0 ± 0.6	SF	Y	$-2.15_{-0.45}^{+0.09}$	11
2003fa	−0.11 ± 0.18	+0.03 ± 0.13	+0.04 ± 0.12	0.039	128	26.09 ± 5.75	24.95 ± 1.70	2.0 ± 0.6	∼SF	N	$-4.40_{-\infty }^{+0.53}$	100
2003hu	−0.28 ± 0.22	−0.15 ± 0.17	−0.13 ± 0.18	0.075	294	23.70 ± 0.64	22.86 ± 0.24	2.1 ± 0.6	SF	Y	$-2.03_{-0.54}^{+0.10}$	12	91T
2003ica	−0.29 ± 0.18	−0.27 ± 0.16	−0.28 ± 0.16	0.054	2511	24.70 ± 0.36	24.06 ± 0.17	2.1 ± 0.6	Pa	N	$-3.56_{-0.18}^{+0.05}$	100
2003it	+0.13 ± 0.21	+0.04 ± 0.19	+0.02 ± 0.19	0.024	1613	21.84 ± 0.12	21.52 ± 0.06	1.6 ± 0.3	SF	Y	$-2.51_{-0.15}^{+0.04}$	4
2003iv	+0.18 ± 0.20	+0.24 ± 0.16	+0.22 ± 0.16	0.034	301	24.54 ± 1.39	23.48 ± 0.44	2.0 ± 0.6	Pa	N	$-3.92_{-\infty }^{+0.13}$	100
2004L	+0.04 ± 0.20	+0.11 ± 0.17	+0.02 ± 0.19	0.033	385	21.00 ± 0.23	20.65 ± 0.07	1.8 ± 0.4	SF	Y	$-1.80_{-0.61}^{+0.31}$	2
2004as	+0.16 ± 0.19	+0.27 ± 0.15	+0.27 ± 0.16	0.032	106	21.20 ± 0.32	21.38 ± 0.20	1.6 ± 0.5	SF	Y	$-1.98_{-0.26}^{+0.07}$	4
2005eq	+0.08 ± 0.19	+0.21 ± 0.15	+0.26 ± 0.15	0.028	1693	23.74 ± 0.35	22.73 ± 0.12	2.3 ± 0.6	∼SF	Y	$-2.82_{-0.38}^{+0.08}$	38
2005eu	+0.01 ± 0.19	+0.10 ± 0.15	+0.14 ± 0.14	0.034	3352	22.30 ± 0.10	22.07 ± 0.05	1.3 ± 0.3	SF	Y	$-2.48_{-0.13}^{+0.04}$	2
2005hca	+0.08 ± 0.17	+0.11 ± 0.14	+0.18 ± 0.14	0.045	3269	22.89 ± 0.13	22.67 ± 0.07	1.4 ± 0.3	∼SF	Y	$-2.42_{-0.15}^{+0.04}$	2
2005hf	+0.06 ± 0.20	+0.10 ± 0.16	+0.09 ± 0.16	0.042	190	26.13 ± 4.19	23.47 ± 0.48	2.0 ± 0.6	Pa	N	$-4.35_{-\infty }^{+0.47}$	100
2005hj	+0.15 ± 0.18	+0.09 ± 0.14	+0.15 ± 0.13	0.057	1675	24.32 ± 0.37	23.90 ± 0.19	1.9 ± 0.5	SF	Y	$-2.58_{-0.35}^{+0.08}$	18
2005iq	+0.21 ± 0.18	+0.18 ± 0.15	+0.22 ± 0.15	0.033	112	21.89 ± 0.43	21.88 ± 0.26	1.8 ± 0.5	∼SF	Y	$-2.15_{-0.34}^{+0.07}$	8
2005ir	+0.45 ± 0.19	+0.24 ± 0.14	+0.28 ± 0.14	0.075	121	23.13 ± 0.73	22.22 ± 0.27	2.1 ± 0.6	SF	Y	$-1.81_{-0.62}^{+0.11}$	12
2005lz	+0.18 ± 0.18	+0.18 ± 0.15	+0.16 ± 0.16	0.040	⋅⋅⋅	no image	>22.4	⋅⋅⋅	SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
2005mca	+0.17 ± 0.20	+0.01 ± 0.16	−0.03 ± 0.16	0.026	1616	23.49 ± 0.28	22.06 ± 0.08	2.9 ± 0.5	∼Pa	Y	$-2.54_{-0.31}^{+0.07}$	14
2005ms	+0.09 ± 0.19	+0.20 ± 0.16	+0.23 ± 0.16	0.026	216	>22.4	24.26 ± 0.99	2.0 ± 0.6	SF	Y	< − 3.6	98
2005na	−0.07 ± 0.19	−0.14 ± 0.16	−0.08 ± 0.16	0.027	⋅⋅⋅	no image	no image	⋅⋅⋅	SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
2006S	+0.11 ± 0.18	+0.10 ± 0.14	+0.15 ± 0.15	0.033	96	21.53 ± 0.39	21.57 ± 0.23	1.8 ± 0.5	SF	Y	$-2.03_{-0.33}^{+0.08}$	6
2006ac	−0.06 ± 0.20	+0.01 ± 0.17	+0.03 ± 0.17	0.024	213	20.19 ± 0.14	19.99 ± 0.07	1.4 ± 0.4	SF	Y	$-1.92_{-0.16}^{+0.05}$	1
2006ak	+0.00 ± 0.22	−0.04 ± 0.19	+0.01 ± 0.18	0.039	198	22.03 ± 0.46	21.93 ± 0.19	1.8 ± 0.5	∼SF	Y	$-2.04_{-0.61}^{+0.17}$	8	Incl.
2006al	+0.02 ± 0.18	+0.19 ± 0.14	+0.21 ± 0.14	0.069	1575	26.37 ± 1.20	>21.7	2.0 ± 0.6	Pa	N	$-4.00_{-\infty }^{+0.13}$	100
2006anb	−0.05 ± 0.17	+0.18 ± 0.14	+0.21 ± 0.13	0.065	93	>21.1	24.05 ± 0.83	2.0 ± 0.6	SF	Y	< − 2.2	23
2006az	−0.06 ± 0.18	−0.08 ± 0.14	−0.05 ± 0.14	0.032	187	23.19 ± 0.64	22.08 ± 0.22	2.1 ± 0.6	Pa	N	$-3.43_{-0.39}^{+0.07}$	100
2006bd	⋅⋅⋅	+0.14 ± 0.17	+0.16 ± 0.19	0.026	1607	25.73 ± 1.16	23.60 ± 0.19	2.1 ± 0.6	Pa	N	$-4.50_{-\infty }^{+0.12}$	100
2006bt	−0.01 ± 0.18	+0.05 ± 0.14	−0.07 ± 0.15	0.033	205	>22.0	>22.7	2.0 ± 0.6	∼SF	N	< − 4.2	100
2006bu	+0.07 ± 0.23	−0.10 ± 0.14	−0.06 ± 0.13	0.084	1675	>20.4	26.17 ± 0.65	2.0 ± 0.6	SF	Y	< − 3.7	99
2006bw	−0.04 ± 0.21	−0.15 ± 0.18	−0.14 ± 0.19	0.031	1696	>22.1	25.62 ± 0.95	2.0 ± 0.6	Pa	N	< − 4.9	100
2006bz	⋅⋅⋅	−0.20 ± 0.16	−0.24 ± 0.18	0.028	25656	25.45 ± 0.27	23.95 ± 0.06	3.1 ± 0.4	Pa	N	$-4.45_{-0.27}^{+0.10}$	100
2006cc	+0.27 ± 0.18	+0.25 ± 0.14	+0.01 ± 0.15	0.033	904	22.97 ± 0.26	22.26 ± 0.11	2.2 ± 0.5	∼SF	Y	$-2.45_{-0.31}^{+0.07}$	11	Incl.
2006cf	−0.03 ± 0.20	−0.01 ± 0.15	+0.04 ± 0.15	0.042	108	21.48 ± 0.36	21.29 ± 0.19	1.8 ± 0.5	SF	Y	$-1.77_{-0.31}^{+0.07}$	5
2006cg	−0.50 ± 0.26	−0.55 ± 0.18	−0.51 ± 0.20	0.029	1391	24.97 ± 0.67	23.47 ± 0.19	2.2 ± 0.6	Pa	N	$-4.22_{-0.41}^{+0.07}$	100
2006cj	+0.29 ± 0.18	+0.20 ± 0.13	+0.23 ± 0.13	0.068	25656	23.85 ± 0.08	23.39 ± 0.03	1.8 ± 0.3	∼SF	Y	$-2.29_{-0.26}^{+0.10}$	0
2006cq	+0.05 ± 0.18	+0.18 ± 0.16	+0.21 ± 0.17	0.049	1660	23.77 ± 0.27	23.01 ± 0.11	2.2 ± 0.5	SF	Y	$-2.39_{-0.32}^{+0.08}$	10
2006cs	⋅⋅⋅	−0.00 ± 0.18	−0.03 ± 0.21	0.024	106	23.57 ± 1.10	23.51 ± 0.75	2.0 ± 0.6	Pa	N	$-3.79_{-0.70}^{+0.13}$	100
2006en	+0.10 ± 0.19	+0.12 ± 0.17	+0.12 ± 0.19	0.031	265	21.04 ± 0.19	20.08 ± 0.07	2.7 ± 0.5	SF	Y	$-1.51_{-0.27}^{+0.07}$	2
2006gj	+0.27 ± 0.20	+0.09 ± 0.17	−0.12 ± 0.17	0.028	224	24.21 ± 1.44	23.84 ± 0.73	2.0 ± 0.6	∼Pa	N	$-3.96_{-\infty }^{+0.16}$	100	Incl.
2006gr	+0.09 ± 0.18	+0.19 ± 0.14	+0.19 ± 0.15	0.034	⋅⋅⋅	no image	no image	⋅⋅⋅	SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
2006gt	⋅⋅⋅	+0.14 ± 0.17	+0.18 ± 0.18	0.044	102	>21.5	23.85 ± 0.80	2.0 ± 0.6	Pa	N	< − 3.5	95
2006mo	+0.17 ± 0.20	−0.01 ± 0.16	+0.02 ± 0.17	0.036	1704	24.44 ± 0.49	23.21 ± 0.14	2.3 ± 0.6	Pa	N	$-3.81_{-0.27}^{+0.04}$	100
2006nz	+0.21 ± 0.22	−0.20 ± 0.18	−0.18 ± 0.18	0.037	3007	24.41 ± 0.32	23.06 ± 0.09	2.7 ± 0.6	Pa	N	$-3.77_{-0.17}^{+0.04}$	100
2006oa	−0.00 ± 0.17	+0.01 ± 0.14	+0.06 ± 0.14	0.059	3121	23.64 ± 0.19	23.63 ± 0.12	1.4 ± 0.4	SF	Y	$-2.50_{-0.20}^{+0.05}$	7
2006ob	+0.02 ± 0.17	−0.11 ± 0.14	−0.10 ± 0.13	0.058	3279	25.44 ± 0.48	24.49 ± 0.19	2.1 ± 0.6	SF	Y	$-2.93_{-0.45}^{+0.09}$	53
2006on	−0.02 ± 0.20	−0.03 ± 0.18	−0.09 ± 0.19	0.069	3934	>20.8	25.36 ± 0.32	2.0 ± 0.6	Pa	N	< − 4.7	100
2006os	−0.11 ± 0.19	−0.11 ± 0.18	−0.36 ± 0.19	0.032	110	23.31 ± 1.05	22.41 ± 0.38	2.0 ± 0.6	∼SF	N	$-3.47_{-1.09}^{+0.11}$	99
2006qo	−0.03 ± 0.19	−0.04 ± 0.16	−0.14 ± 0.16	0.030	⋅⋅⋅	no image	no image	⋅⋅⋅	SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
2006te	+0.10 ± 0.18	+0.11 ± 0.15	+0.15 ± 0.15	0.032	196	21.96 ± 0.34	20.88 ± 0.12	2.4 ± 0.6	SF	Y	$-1.97_{-0.39}^{+0.08}$	7
2007F	+0.10 ± 0.20	+0.11 ± 0.16	+0.16 ± 0.16	0.024	205	20.35 ± 0.21	20.29 ± 0.09	1.5 ± 0.4	SF	Y	$-1.94_{-0.48}^{+0.22}$	2
2007H	+0.14 ± 0.27	⋅⋅⋅	⋅⋅⋅	0.044	⋅⋅⋅	no image	no image	⋅⋅⋅	∼SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
2007O	−0.08 ± 0.18	−0.03 ± 0.15	+0.04 ± 0.15	0.036	183	20.78 ± 0.20	20.27 ± 0.09	2.0 ± 0.5	SF	Y	$-1.57_{-0.24}^{+0.06}$	2
2007R	+0.22 ± 0.20	+0.07 ± 0.16	+0.12 ± 0.16	0.031	211	21.01 ± 0.21	20.26 ± 0.08	2.3 ± 0.5	∼SF	Y	$-1.66_{-0.28}^{+0.07}$	3
2007ae	−0.20 ± 0.18	−0.16 ± 0.15	−0.13 ± 0.14	0.064	185	23.40 ± 0.70	23.96 ± 0.56	1.9 ± 0.6	∼SF	N	$-2.88_{-0.44}^{+0.07}$	47
2007ai	+0.03 ± 0.20	+0.11 ± 0.18	+0.10 ± 0.19	0.032	⋅⋅⋅	no image	no image	⋅⋅⋅	SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
2007ar	⋅⋅⋅	−0.53 ± 0.18	⋅⋅⋅	0.053	⋅⋅⋅	no image	no image	⋅⋅⋅	SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
2007ba	⋅⋅⋅	−0.52 ± 0.15	−0.46 ± 0.15	0.039	2857	23.70 ± 0.23	23.39 ± 0.12	1.8 ± 0.5	Pa	N	$-3.64_{-0.11}^{+0.03}$	100
2007bd	−0.09 ± 0.19	−0.16 ± 0.17	−0.09 ± 0.16	0.032	109	21.37 ± 0.35	21.09 ± 0.17	1.8 ± 0.5	∼SF	Y	$-1.95_{-0.31}^{+0.07}$	5
2007cg	−0.18 ± 0.21	−0.30 ± 0.20	⋅⋅⋅	0.034	111	21.76 ± 0.43	21.31 ± 0.19	2.0 ± 0.6	∼SF	Y	$-2.01_{-0.37}^{+0.09}$	8
2007co	−0.03 ± 0.19	−0.08 ± 0.16	−0.11 ± 0.16	0.027	⋅⋅⋅	no image	no image	⋅⋅⋅	SF	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	UV
2007cq	−0.25 ± 0.20	−0.25 ± 0.17	−0.20 ± 0.18	0.025	435	21.51 ± 0.19	21.05 ± 0.09	1.9 ± 0.4	∼Pa	Y	$-2.22_{-0.23}^{+0.06}$	4
2008af	−0.12 ± 0.19	−0.03 ± 0.17	+0.03 ± 0.17	0.034	73	25.69 ± 5.21	26.38 ± 7.58	2.0 ± 0.6	Pa	N	$-4.37_{-\infty }^{+0.57}$	100
2008bf	−0.35 ± 0.20	−0.25 ± 0.16	−0.20 ± 0.16	0.026	104	>22.4	23.53 ± 0.80	2.0 ± 0.6	Pa	N	< − 4.3	100

Notes. The asymetric errors on log (Σ_SFR) indicate the 16% and 64% boundaries of the Σ_SFR cumulative probability distribution functions; a lower boundary of zero is indicated by −∞ when in log  space. For cases with no GALEX FUV counts we only indicate the upper boundary. The uncertainties on the FUV and NUV magnitudes have been symmetrized for readability but are not directly used. The "Cuts Applied" column indicates reasons why an SN Ia was removed from the main analysis; UV stands for no GALEX data, Incl. for inclined host, and 91T for 91T-like SN (see Appendix B). The "Global Host Type" column gives the global star formation classification, as defined in Section 2.2.2. The "Local" A_FUV column lists the FUV extinction, regardless of whether it is applied (as indicated by the "Local Dust Corr" column). The "Exp." column indicates the GALEX exposure time in seconds. ^aSee Appendix C.1. ^bSee Appendix C.2.

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When an sSFR measurement is not available, we rely on morphology. Gil de Paz et al. (2007) have shown that morphological type is another useful means of selecting those galaxies that follow the SF UV color relation. Host galaxies with E/S0 morphological classifications are considered to be globally passive, while later morphological types are considered to be globally SF. Again, in Table 2 these are designated as Pa or SF, respectively.

Once these global designations are assigned, we consider the local environments of SNe in globally passive host galaxies to be ineligible for extinction correction. That is, those local environments for SNe in host galaxies with conclusively low sSFR, or, when sSFR is not available, E/S0 morphology, are not corrected for extinction. Those local environments for SNe in host galaxies that have conclusively high sSFR, or, when sSFR is not available, non-E/S0 morphology, are corrected using the relation from Salim et al. (2007). For cases with a global sSFR measurement that is inconclusively passive or SF, in accordance with the association of dust with star formation, we apply an extinction correction if the local FUV signal is detected at greater than 2σ. We have checked that using our morphological criterion in place of sSFR for cases where the sSFR is poorly measured does not change which cases are corrected for dust. Finally, the hosts of SN 2005hc and SN 2005mc were cases of early type galaxies with inconclusive sSFR measurement where local star-formation was detected (see Appendix C.1); extinction corrections were applied in these cases.

With this procedure we can be fairly certain that an extinction correction is being applied only when appropriate. Since the uncertainty on the FUV−NUV color is sometimes large, we include a prior on the resulting A_FUV based on the A_FUV versus color distribution measured for spiral galaxies by Salim et al. (2007). This prior leads to a typical A_FUV = 2.0 ± 0.6 mag for large FUV−NUV uncertainties (see also Salim et al. 2005). For completeness, we report in Table 2 our best estimate of A_FUV based on FUV−NUV color and the Salim et al. (2007) relation, whether or not it was actually applied. With this, the interested reader can examine the impact of making slightly different choices regarding the extinction correction. The maximum A_FUV allowed in the relation of Salim et al. (2007) is 3.37 mag; thus extinction correction can increase log (Σ_SFR) by at most 1.35 dex, and 0.8 dex will be more typical. Therefore, proper extinction correction is important, but can only affect the classification of SN hosts whose star-formation surface density is already near our threshold.

To obtain our final values of Σ_SFR, we combine the uncertainties on the FUV fluxes with the uncertainties on A_FUV by convolving the two probability distribution functions. The local extinction-corrected FUV flux is then converted into Σ_SFR using Equation (1). In Section 2.4 we explore the effect of applying a blanket correction to the local environments of all globally SF hosts.

2.2.3. Local Aperture Size Appropriate for GALEX FUV Data

2.2.4. SN Ia Local FUV Measurements

In Figure 1 we show the SALT2-standardized Hubble residuals, $\Delta M_B^{\mathrm{corr}}$, from H09 as a function of our measurement of log (Σ_SFR) for the 77 SNe Ia of the H09/GALEX sample. We find that the SNe Ia from locally passive environments are $\delta \langle M_B^{\mathrm{corr}}\rangle _{\mathrm{SF}}=$ 0.094 ± 0.037 mag brighter. This is the difference between the means of the Hubble residuals for the two environmental subsamples, derived from a maximum likelihood calculation in which each SN has a chance $\mathcal {P}\mathrm{(Ia\epsilon)}$ or $1-\mathcal {P}\mathrm{(Ia\epsilon)}$ of belonging to the Ia or Iaα population, respectively. The variances on the Hubble residuals from H09 (which includes the intrinsic dispersion they assigned) as listed in Table 2, are used in the likelihood calculation. Because the log-likelihood involves the logarithm of sums unique for each SN, it must be solved computationally. The summed probability for the number of Ia is 38, representing 48.9% of the sample.

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This measurement constitutes an independent confirmation, at the 2.5σ confidence level, of the LSF bias previously observed in the SNfactory data set ($\delta \langle M_B^{\mathrm{corr}}\rangle _{\mathrm{SF}}=$ 0.094 ± 0.031 mag; R13). The amplitude of the bias is in remarkable agreement between the two samples. It is similar to the 0.14 ± 0.07 mag offset between E/S0 and Sc/Sd/Irr galaxies found by H09, but has a higher statistical significance.

We also tested for the presence of this bias in the H09 data set when using the MLCS2k2 lightcurve fitter for three commonly used values of R_V, again taking Hubble residuals directly from H09. H09 found that MLCS2k2 with R_V = 1.7 produced the smallest dispersion, and this case gives an observed bias of $\delta \langle M_B^{\mathrm{corr}}\rangle _{\mathrm{SF}}=$0.136 ± 0.040 mag. Similar results are found for R_V = 3.1 and R_V = 2.5. From this we conclude that the LSF bias found in the H09 data set is only mildly dependent on which of the two lightcurve fitters is used, differing by only ∼1 σ after taking into account the covariance between SNe Ia in common. (See Kim et al. 2014 for additional discussion of sensitivity to host environment with different lightcurve fitters.) A deeper knowledge of what is driving the LSF bias will help in understanding such variation between lightcurve fitters. Table 3 summarizes these results (also see Figure 3), while Figure 2 shows how the results depend on various analysis choices, as detailed in Section 2.4.

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Table 3. The Local Star-formation Bias and Environmental Variations in the H09/GALEX Sample

Light-curve fitter	Star-formation Bias			SN Hubble Residual dispersiona
	Fraction of	$\delta \langle M_B^{\mathrm{corr}}\rangle _{\mathrm{SF}}$	Bias	SNe Ia	SNe Iaα	SNe Ia
	SNe Ia (ψ)	(mag)	Signifiance	(mag)	(mag)	(mag)
SALT2	48.9%	0.094 ± 0.037	2.5σ	0.147 ± 0.019	0.144 ± 0.024	0.144 ± 0.026
MLCS2k2 RV = 1.7	52.2%	0.136 ± 0.040	3.4σ	0.165 ± 0.011	0.127 ± 0.019	0.180 ± 0.014
MLCS2k2 RV = 2.5	52.1%	0.155 ± 0.041	3.8σ	0.166 ± 0.012	0.122 ± 0.020	0.181 ± 0.015
MLCS2k2 RV = 3.1	52.4%	0.171 ± 0.040	4.2σ	0.183 ± 0.011	0.137 ± 0.018	0.202 ± 0.013

Note. ^aWeighted rms with noise due to small-scale galaxy peculiar velocities (300 km s⁻¹) removed.

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Finally, for use with Equation (A.14) in Appendix A of R13, which details the relation between the local star-formation bias and the host mass step, we report the fraction of high mass hosts, F_H, in the H09/GALEX sample. We find F_H = 89% for the H09 sample studied here, and expect it to be representative of most nearby samples currently in use. This compares with a high-mass fraction of only ∼55% for the SNfactory (Childress et al. 2013b), SDSS (Gupta et al. 2011) or PTF (Pan et al. 2014) samples.

In this section, we test the influence of the various criteria used in performing this portion of the analysis. These include the sample selection, the radius chosen to represent the local environment, and the dust correction. The effects of changing each of these selections in turn are illustrated in the lower two panels of Figure 2, and are discussed in the following paragraphs. Two key ideas to keep in mind here are that (1) while the specific values of Σ_SFR can change with the details of the measurement technique, only SNe Ia near the Σ_SFR threshold can have much effect, and (2) any errors made in categorizing the local environment are most likely to decrease the measured size of any real LSF bias by mixing SNe Ia from different environments.

Sample construction. In the main analysis, we made two sample selections (see Table 1). As in R13, we removed 91T-like SNe and the SNe from highly inclined host galaxies. Alterations in these selection criteria change the LSF bias by less than 0.015 mag, as illustrated in Figure 2.

Local environment measurement radius. In Section 2.2.4 we presented the rationale for our use of a 2 kpc radius aperture to define the "local" SN environments. We have tested the impact of using either a smaller (1 kpc) or larger (3 kpc) aperture, and find changes of less than 0.01 mag, regardless of which light-curve fitter Hubble residuals are used.

Dust correction. In our main analysis, when the global sSFR was not at least one standard deviation from the threshold set at −10.5 dex, an extinction correction was applied only if the FUV signal was detected at more than 2 σ in a host galaxy compatible with being SF (Section 2.2.2). Here we test the extreme case of applying dust extinction corrections to the local environment whenever the host galaxy is not globally passive. This tests the possibility that strong extinction is responsibly for pushing the observed FUV signal below the 2σ detection threshold. This test essentially consists of assigning the typical A_FUV = 2.0 ± 0.6 mag found by Salim et al. (2005, 2007) to the SNe Ia from globally SF hosts that were not corrected for extinction in the main analysis. This change to the analysis reduces the amplitude of the LSF bias by only ∼0.010–0.013 mag, as shown in Figure 2.

GALEX sensitivity. We have considered whether the limited sensitivity of some GALEX exposures might affect our results. Fortunately, almost half of the hosts considered have exposures several times longer than those of the main GALEX AIS survey (see Table 2). We find no direct correspondence between SF sensitivity and redshift or classification probability in the current data set.

In summary, the measurement of the H09 LSF bias is robust at the ∼0.015 mag level against variations in the analysis.

R13 suggested the presence of a bimodal structure in the $\Delta M_B^{\mathrm{corr}}$ distribution of the SNfactory data set (see the lower-right histogram in Figure 1 of R13). The brighter mode consisted entirely of SNe Ia from locally passive environments, Ia, while the fainter mode consisted of SNe Ia from a mix of Iaα and Ia environment. While the fainter mode extended over the full range of host galaxy masses, the brighter mode was concentrated in the high-mass half of the distribution.

As in R13 we find that the SNe Ia having locally SF environments have a ∼30% tighter dispersion than the overall sample. After removing the random noise expected due to small-scale galaxy peculiar velocities, we find that the Iaα population has a weighted rms of only 0.127 ± 0.019 mag when using MLCS2k2 Hubble residuals. See Table 3 for a summary of the weighted rms for each environmental subpopulation.

We have fitted the R13 bimodal model, without any adjustment, to the environmentally categorized Hubble residuals of our H09 subset. Here we find that the R13 model is a better fit than a single Gaussian whose dispersion is allowed to float. Specifically, we measure differences of −4.6 and −0.9 in favor of the bimodal model for the Akaike information criterion corrected for finite sample size (AICc) when using MLCS2k2 and SALT2 Hubble residuals, respectively. The result using MLCS2k2 strongly favors the R13 bimodal model, but the evidence for bimodality using the H09 SALT2 Hubble residuals is weaker than found in R13. The mixed evidence for bimodality here is not surprising given the generally larger measurement uncertainties reported by H09.

The LSF bias measured for the H09 sample is in remarkable agreement with the value determined in R13 using the SNfactory sample, both based on SALT2 Hubble residuals. Under the assumption that the LSF bias is a universal quantity, we can combine these measurements (first averaging the six SNe Ia in common). Doing so, we find a common LSF bias of $\delta \langle M_B^{\mathrm{corr}}\rangle _{\mathrm{SF}}=$ 0.094 ± 0.025 mag, which constitutes a 3.8 σ measurement of this environmental bias. Alternatively, this becomes 0.110 ± 0.024 mag when combining the R13 results with the MLCS2k2 Hubble residuals from the H09/GALEX data set.

We first examine the eight SNe Ia hosts whose distances were measured using the Cepheid period–luminosity relation by SH0ES11. We measure their $\mathcal {P}\mathrm{(Ia\epsilon)}$ in the same manner as for the H09 sample, as described in Section 2.1. The results are summarized in Table 4. The top half of the table summarizes the galaxies used by SH0ES11 to measure H₀, while the bottom half presents our measurements for additional SN Ia host galaxies whose Cepheid-based distances are anticipated. The local environments for seven of the eight are covered by both GALEX FUV and NUV observations, while SN 1998eq lacks FUV coverage.

Table 4. Local UV Environments of the Cepheid–SNe Ia Sample

Name	FUV	NUV	AFUV	Host	Dust	log (ΣSFR)	$\mathcal {P}\mathrm{(Ia\epsilon)}$
	(mag)	(mag)	(mag)	Type	Corr.	(M☉ kpc−2 yr−1)	(percent)
SN1981B	17.34 ± 0.02	16.91 ± 0.01	1.7 ± 0.1	SF	Y	−2.34 ± 0.02	0
SN1990N	18.76 ± 0.10	18.46 ± 0.04	1.5 ± 0.3	SF	Y	−2.67 ± 0.13	9
SN1994ae	18.33 ± 0.08	17.77 ± 0.04	2.1 ± 0.3	SF	Y	−2.09 ± 0.11	0
SN1995al	16.49 ± 0.03	15.87 ± 0.01	2.3 ± 0.1	SF	Y	−1.44 ± 0.03	0
SN1998aq	no image	16.29 ± 0.00	⋅⋅⋅	SF	⋅⋅⋅	> − 2.4a	0
SN2002fk	16.46 ± 0.01	15.87 ± 0.00	2.2 ± 0.0	SF	Y	−1.09 ± 0.01	0
SN2007af	17.67 ± 0.02	17.27 ± 0.01	1.6 ± 0.1	SF	Y	−2.18 ± 0.03	0
SN2007sr b	22.08 ± 0.57	20.65 ± 0.13	2.3 ± 0.6	SF	Y	−3.68 ± 0.33	50 c
SN2001el	16.85 ± 0.03	16.41 ± 0.01	1.7 ± 0.1	SF	Y	−1.98 ± 0.04	0
SN2003du	18.66 ± 0.10	18.44 ± 0.04	1.3 ± 0.3	SF	Y	−2.29 ± 0.11	0
SN2005cf b	22.29 ± 0.25	21.16 ± 0.06	2.8 ± 0.5	SF	Y	−3.34 ± 0.23	100
SN2011fe	14.95 ± 0.01	14.62 ± 0.01	1.3 ± 0.1	SF	Y	−2.26 ± 0.02	0
SN2012cg	16.67 ± 0.01	15.91 ± 0.00	2.7 ± 0.1	SF	Y	−1.62 ± 0.01	0
SN2012fr	17.54 ± 0.01	17.02 ± 0.00	2.0 ± 0.1	SF	Y	−2.15 ± 0.02	0
SN2012ht	20.42 ± 0.04	19.68 ± 0.01	2.7 ± 0.1	SF	Y	−2.20 ± 0.05	0
SN2013dy	15.64 ± 0.00	15.31 ± 0.00	1.4 ± 0.1	SF	Y	−1.87 ± 0.00	0

Notes. ^aBased on NUV magnitude, assuming FUV-NUV = 1 and A_FUV = 0. ^bTails of interacting galaxies, $\mathcal {P}\mathrm{(Ia\epsilon)}$ could be problematic. ^cSee Section 3.1.

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Although SN 1998aq does not have FUV imaging, it does have a strong NUV signal. We can use the NUV signal along with very conservative assumptions to categorize the local environment of SN 1998eq as SF. Specifically, even assuming an extreme UV color of FUV−NUV =1 (see Figure 13 of Salim et al. 2007) and no dust extinction still requires a minimum value for the local star formation density of log (Σ_SFR) > −2.46 dex.

SN 2007sr is an exceptional case, as it is located in the well-known tidal tail of the merging galaxies NGC 4038/39 (the Antennae). Tidal environments are known as sites of strong star formation (e.g., Neff et al. 2005; Smith et al. 2010; Kaviraj et al. 2012). The Antennae tidal tail is indeed quite blue (Hibbard et al. 2005), and contains star clusters with mean ages of 10–100 Myr (Whitmore et al. 1999; Fall et al. 2005). Therefore, one might presume that SN 2007sr should be classified as a Iaα. However, SN 2007sr actually lies at a projected separation of 2 kpc from the spine of the tidal tail, and Hibbard et al. (2005) estimate an age around 400 Myr along the portion of the tail projected closest to SN 2007sr. (Note that the Hibbard et al. 2005 age determinations did not include correction for possible dust extinction, and so may be too large.) An age of 400 Myr is older than the estimated dynamical time for the tidal tail, and would therefore suggest that stars near the location of SN 2007sr were originally formed in the disk of their parent galaxy. Tidal forces will act in a similar manner on the volume of stars originally local to the SN 2007sr progenitor, but it is likely that the stars are now more spread out due to dynamical evolution, having moved SN 2007sr off the spine of the tail and lowering the stellar surface density, and thus the measured Σ_SFR, compared to the original environment.

When faced with such ambiguity for the Hubble-flow sample, as with highly inclined host galaxies, the simplest avenue was to cut them from the sample. Doing that in this case would result in a value ψ^C ∼ 0, along with a slight increase in the uncertainty on H₀ due to the smaller number of calibrators, since all the remaining environments for the Cepheid-calibrated SNe Ia are SF. Given the possibility that SN 2007sr may be slightly too old to be counted as Iaα, this choice could slightly overestimate the final correction to H₀ that is needed. To better reflect the ambiguity for this calibrator, we will take a neutral value of $\mathcal {P}\mathrm{(Ia\epsilon)}=0.5$ for our main analysis. We note that SN 2005cf, listed in Table 4 as a likely future calibrator, is also located in a tidal tail. Thus, the question of the proper categorization of tidal tails will resurface when it is time to incorporate SN 2005cf into the measurement of H₀.

Combining the eight individual $\mathcal {P}\mathrm{(Ia\epsilon)}$, we find ψ^C = 7.0% as the fraction of SNe Ia in the Cepheid-calibrated SNe Ia used for the SH0ES11 measurement of the local Hubble constant. As anticipated, the local environments of this sample is predominately SF.

If we had estimates of $\mathcal {P}\mathrm{(Ia\epsilon)}$ for all 140 nearby Hubble-flow SNe Ia used by SH0ES11 we could calculate and apply the resulting ψ^HF directly in Equation (2). However, ∼30 of the Hubble-flow SNe Ia used by SH0ES11 are not contained in H09, and in addition, we do not have $\mathcal {P}\mathrm{(Ia\epsilon)}$ estimates for another 30 due to insufficient GALEX coverage or selection cuts (see Table 1). Thus, unlike the above estimate of ψ^C, our estimate of ψ^HF will need to be statistical.

The fact that we still have ∼60% of the SNe Ia in common will reduce the uncertainty substantially since we incur a statistical error (beyond that already incorporated in the $\mathcal {P}\mathrm{(Ia\epsilon)}$ values for individual SNe) only for the ∼40% that remain unmeasured. We have shown in Section 2.1 that the H09/GALEX data set is statistically representative of the entire H09 sample, and we expect that to be true for the ∼30 SH0ES11 Hubble-flow SNe Ia not in H09.

For the H09/GALEX subset having MLCS2K2 measurements we find ψ^HF = 52.1%. For those with SALT2 measurements ψ^HF = 48.9%. This is in agreement with the value ψ^HF = 50.0% ± 5.3% in R13. More comparable is the subset of high-mass hosts in R13, for which the value is slightly higher, ψ^HF = 63.4% ± 7.5%. This may reflect differences between the untargeted SNfactory search that provided the most SNe Ia in R13 and galaxy-magnitude-limited searches that provided most of the SNe Ia in H09. It also could be due to a greater chance of false-positive associations due to the 4 × greater area covered by the larger aperture used here. Applying ψ^HF = 52.1% as a statistical estimator to the 59 SH0ES11 SNe Ia environments we were unable to measure, and combining with those we have measured, gives ψ^HF = 52.1% ± 2.3%. The variations due to the alternatives explored in Section 2.4 are within the final statistical uncertainty on ψ^HF for the SH0ES11 Hubble-flow sample, and are reflected in the calculations of the variations shown in Figure 2.

As a result of the high fraction of local SF environments for the SNe Ia in the SH0ES11 sample, they do not provide a calibration that is representative of the H09 nearby Hubble-flow sample. In Section 3.4 we will present further insights into, and explore the robustness of this measured difference in the values of ψ^HR and ψ^C.

Using Equation (2) with values ψ^HF  = 52.1% ± 2.3%, ψ^C  = 7.0%, and $\delta \langle M_B^{\mathrm{corr}}\rangle _{\mathrm{SF}}\,{=}$ 0.155 ± 0.041 mag we estimate that the Hubble constant is currently overestimated by 3.3% ± 0.7% due to the LSF bias. As will be discussed in Section 3.5, a small fraction of this bias most likely has been taken into account already because SH0ES11 applied a 0.75% correction to account for potential host-mass dependency in the SN standardized magnitudes. Since the correction for the local star-formation bias also corrects for the host-mass effect (see Section 3.5), we estimate an effective correction to H₀ of −2.6% ± 0.7% (see Table 5).

There have been several updates to the basic ingredients since the SH0ES11 analysis. Humphreys et al. (2013) reported an improved value for the distance to the NGC 4258 megamaser that served as one of the zero points for the Cepheid distance scale (along with the LMC distance and parallaxes for Milky Way Cepheids). Efstathiou (2014) re-examined the selection of Cepheids and the resulting calibration of the Cepheid period–luminosity relation for the SN host galaxies, slightly modifying those distances. Since it is the most recent, and includes the revised distance to NGC 4258, we will use the Efstathiou (2014) analysis as our baseline in quantifying how the LSF bias affects the apparent tension between direct and indirect measurements of H₀. Note that correction for the LSF bias involves a change to the luminosities assigned to SNe Ia in the Hubble flow relative to those in the Cepheid sample; we make no adjustments to the distances assigned to the Cepheid-calibrated SN Ia host galaxies.

By applying Equation (2), we calculate a value of the Hubble constant corrected for the LSF bias of $H_0^{\mathrm{corr}}$ = 70.6 ± 2.6 km s⁻¹ Mpc⁻¹ when using the LMC distance, Milky Way parallaxes, and the NGC 4258 megamaser as the Cepheid zero point as in SH0ES11 and Efstathiou (2014). If the NGC 4258 megamaser is used as the sole zero point of the Cepheid distances and the new Humphreys et al. (2013) distance is used with the Efstathiou (2014) analysis, the revised H₀ is lower, but less certain, at 68.8 ± 3.3 km s⁻¹ Mpc⁻¹. Table 6 summarizes the LSF-bias corrections for both the SH0ES11 and Efstathiou (2014) estimations of H₀, when using either the megamaser or the three Cepheid anchor(s). Details of the contributions to each correction are given, along with the new level of agreement with several recent indirect CMB-based measurements of H₀. We emphasize that the SH0ES11 analysis and our corrections both use MLCS2k2 with R_V = 2.5, and thus are fully consistent with regard to choice of lightcurve fitter. Our revised H₀ is now compatible at the 1σ level with these indirect measurement of the Hubble constant for a flat ΛCDM cosmology.

We note that this estimate can be improved in the future by the various teams who employ SNe Ia to measure H₀, by improved matching of the local SN environments between the calibrator and Hubble-flow samples.

The robustness of our correction to H₀ depends on the robustness of the inputs to Equation (2). In Section 2.4 we have already explored the robustness of the local star-formation bias to changes in our sample selection and measurement procedures. The other key ingredient for the bias on H₀ is the difference in the values of ψ^HF and ψ^C. In the upper panel of Figure 2, we show how these analysis parameters affect the measurement of the H₀ bias (see Section 2.4). None have a significant impact.

SN 2007sr classification. To further explore the difference between ψ^HF and ψ^C we consider the case where SN 2007sr is Iaα. This increases the LSF bias on H₀ by 0.4%; hence if one considers this a false-negative due to tidal dilution of the local star-formation surface density, then an extra −0.3 km s⁻¹ Mpc⁻¹ should be applied to the aforementioned revised H₀ values. The signs of these changes reverse if SN 2007sr is instead considered Ia. These changes are within our quoted uncertainty.

Simulation of distance effects. We next considered possible effects due to the redshift difference between the two samples by simulating what value of ψ^C would have resulted if the Cepheid-calibrated hosts had been observed with the same distances and exposures as the H09 Hubble-flow sample. For each of the six Iaα Cepheid-calibrated hosts having direct FUV detections, the star-formation surface densities were measured using the full set of procedures described in Section 2 after degrading the spatial resolution and increasing the noise to match each of the Hubble-flow galaxies. The net effect, averaged over all pairings, was to increase ψ^C to 15.4%. This was primarily due to changes in $\mathcal {P}\mathrm{(Ia\epsilon)}$ for the host of SN 1990N when simulated at higher redshift or with shorter GALEX exposure. The resulting change in the H₀ bias is once again well within the quoted uncertainties. This is due in part to the fact that we are already accounting for noise by using the full $\mathcal {P}\mathrm{(Ia\epsilon)}$ probability distribution functions.

Chance of low ψ^C. One might expect the Cepheid-calibrated sample to reflect the Ia fraction of 24.9% found for globally SF galaxies (as defined in Section 2.2.2) in the Hubble-flow sample. In fact the Ia fractions are consistent; application of Fisher's Exact Test²⁰, applicable to two sets of categorical data, as here, gives a 18% chance of finding no locally passive environments for the SH0ES11 sample.

Good consistency is also found when comparing based solely on morphology. The SNe Ia hosts with Cepheid calibration have Hubble types Sb—Sm. In our Hubble-flow sample we find that for SN host galaxies of these types the passive fraction is ∼26%. Application of Fisher's Exact Test for this case shows that the passive fraction in the Hubble-flow and current Cepheid-calibrated samples have a 17% probability of being the same. Even including the low locally passive fraction for the Cepheid-calibrated SNe expected to be used in the future (see Table 4), the probability of a common locally passive fraction is 14%.

Consistent, low $\Delta M_B^{\mathrm{corr}}$ dispersions. One final indicator that the SNe Ia in Cepheid hosts are of class Iaα is that they share the small dispersion that R13 found for this subclass. Using Table 3 of SH0ES11 we calculated an unbiased weighted dispersion in Cepheid-calibrated standardized SN Ia absolute magnitudes of only 0.123 ± 0.034 mag. After removing the dispersion due to Cepheid distance measurement errors, the SN Ia dispersion drops to only 0.101 mag. This agrees well with the dispersion of 0.099 ± 0.009 mag found by R13 for their SNe Ia associated with SF environments, and with the 0.122 ± 0.020 mag dispersion of the Iaα in the H09 Hubble-flow sample (see Table 3). The small dispersion of the Cepheid-calibrated SNe Ia and its similarity to the dispersion of the R13 and H09 Iaα subsets could be a coincidence, but as the overall sample dispersion is much larger, 0.166 ± 0.012 mag, the likelihood ratio strongly favors our result that these SNe Ia truly belong to the Iaα category.

SH0ES11 argued that the step in Hubble residuals occurring around a host mass of 10¹⁰ M_☉ has a small impact on their estimation of H₀ since the host masses for the Cepheid-calibrated SNe Ia are similar to those of the Hubble-flow SNe Ia from H09. Using a linear correction of Hubble residual versus host mass based on external information, the SH0ES11 estimate for H₀ is reduced by only 0.75% (see their Section 3).

Here we have shown that even for a sample such as that of H09 where almost all hosts are on the high-mass side of the mass step, there is a bias that is just as large as past studies have found for the size of the host-mass correction over the full mass range of SN Ia host galaxies (e.g., Childress et al. 2013a). These results and those of R13 indicate that star formation is a more important driver than host mass, and that in fact, the host-mass step may simply be a projection of the local star-formation bias in combination with the rapid change in the fraction of SF galaxies as a function of mass as in Figure 11 of Childress et al. (2013a).

If the LSF bias is indeed the more deep-rooted cause of the mass step, then correcting for the LSF bias naturally corrects for the host-mass dependency (see also Appendix A of R13). The H09 sample was used by Kelly et al. (2010) to originally discover the SN Ia host mass bias; for our subset—having significant overlap with that of Kelly et al. (2010)—we find that the mass step calculated at their division point of 10^10.8 M_☉ drops from 0.100 ± 0.040 mag before correction for the LSF bias to 0.026 ± 0.039 mag afterward. This demonstrates that the LSF bias does in fact remove the mass step. Consequently, for our analysis to be self-consistent we remove the 0.75% offset to H₀ applied by SH0ES11, where the intent was to account for the host-mass effect, since our LSF bias correction has removed it from the data.

In Scalzo et al. (2012), we suggested that 91T-like SNe Ia are good candidates for having masses above the Chandrasekhar limit, and demonstrated that some indeed do. Because of the possibility that these might result from a different progenitor channel, they were not considered in R13. Scalzo et al. (2012) determined the rate of pure 91T-like SNe Ia—excluding those similar to the less extreme 99aa-like subclass—to be $2.6^{+1.9}_{-0.7}$% of a total SN rate for a volume-limited sample. Thus, we expect 91T-like SNe Ia to be a minor component of the H09 sample. Blondin et al. (2012) have spectroscopically classified most SNe Ia in the H09 sample, however, they did not distinguish between 91T-like and 99aa-like events. Silverman et al. (2012) present spectroscopic classifications for a large sample of nearby SNe Ia having significant overlap with the H09 sample, and they do distinguish between 91T-like and 99aa-like events. Combining those studies, we therefore exclude SN 1998ab and SN 2003hu from our baseline analysis on the basis of their 91T-like character. SN 1999gp is also 91T-like, but has no GALEX data or MLCS2k2 measurement. The resulting 91T-like fraction of 2.7% matches the result of Scalzo et al. (2012). Therefore, in this regard the parent population of the SNe Ia sample studied here is in agreement with that of R13.

In R13, highly inclined galaxies were identified as cases where a locally passive environment might incorrectly be associated with an Hα signal due to projection. In the present case, however, highly inclined galaxies are as likely to suffer suppressed FUV emission due to strong dust absorption (see, e.g., Conroy et al. 2010). Thus, it is unclear whether inclination is more likely to produce false-positive or false-negative environment categorizations.

Within the set of host galaxies studied here, SN 1992ag, SN 1995ac, SN 1997dg, SN 2006ak, and SN 2006cc are highly inclined and are classified as Iaα, and therefore may be examples where a locally passive environment has been miscategorized as a SF environment due to projection. On the other hand, SN 1998eg and SN 2006gj are examples of SNe Ia in edge-on galaxies with no FUV signal, which might be suppressed due to dust extinction. Following R13, these cases are removed from our main analysis. In Section 2.4 we examined whether including them in the main sample has any effect on our results, and found it did not. We note that such edge-on galaxies would not be suitable for Cepheid measurements either.

Another type of miscategorization can occur when the FUV signal does not directly trace star formation, namely when the signal originating from the very inner cores of E/S0 galaxies surpasses our chosen threshold simply due to the large column of stars along our line of sight (e.g., see FUV surface brightness profiles for E/S0 galaxies in Marino et al. 2011). While this problem is far worse in the NUV band, we considered it prudent to examine this in FUV as well. SNe Ia are rarely detected on E/S0 galaxy cores due to low contrast, subtraction errors, and the overall small fraction of stars projected onto the core relative to the entire galaxy, so only a dozen cases needed this special attention.

We identified two cases of SNe close to the core of E/S0 galaxies for which the GALEX FUV signal is above our threshold: SN 2005hc and SN 2005mc. These have sSFR measurements (Neill et al. 2009) that are ambiguous. In the case of SN 2005hc, there is an apparent SF disk present, which in optical light is hidden by the glare of old stars, and the SN is projected onto this disk. Therefore, the categorization of the local environment of SN 2005hc as Iaα seems correct. We note that in this case a categorization based on morphology alone—which is commonly applied in SN host studies—would produce erroneous results.

In the case of SN 2005mc, located in the (R')SB0 galaxy UGC 4414 (de Vaucouleurs et al. 1991), there is FUV light at the very core, as well as FUV light from a known SF ring. The SN lies close to the core, which is slightly bluer in FUV−NUV than the cores of normal E/S0 galaxies but not as blue as the SF ring. The SDSS spectrum of the core reveals evidence for LINER activity, with stellar-absorption-corrected Hα emission significantly weaker than [N ii] λ6583 Å or [S ii] λ6717, 6731 Å (Baldwin et al. 1981; Veilleux & Osterbrock 1987; Kewley et al. 2006). Thus, the signal in the core may be due in part to the high column density of old stars projected onto the core combined with LINER activity. To test this we remeasured the FUV flux in a 1 kpc aperture, which safely clears any light from the core. The resulting Σ_SFR did not change significantly, therefore, we retain classification of SN 2005mc as having a Iaα environment.

As part of this study we examined SN 2003ic, which has an elliptical host galaxy but where GALEX shows signs of recent star-formation. It's observed Σ_SFR, which was not corrected for extinction since the host appeared to be globally passive, is below our threshold and gives $\mathcal {P}\mathrm{(Ia\epsilon)}=100\%$. If an extinction correction had been applied, its Σ_SFR would have been slightly above our threshold, with $\mathcal {P}\mathrm{(Ia\epsilon)}\sim 30\%$. It is thus likely to be the third case of an SN Ia associated with comparatively recent star-formation hidden in an otherwise normal-looking elliptical host galaxy. Förster & Schawinski (2008) and Schawinski (2009) have also searched for such cases. This SN Ia is discussed extensively in Kelly et al. (2010) since it is in the largest host galaxy in their sample and thus helps drive some of the trends they report.

Here we consider the possibility that an actively SF environment may fall below our threshold due low stellar surface density or due to geometrical dilution. Potential examples of these situations may include low surface brightness galaxies, tidal tails, dwarf galaxies, or an aperture extending beyond the nominal edge of the SN host galaxy.

Because the vast majority of SNe Ia in the H09 sample came from searches that targeted galaxies selected from magnitude-limited catalogs, the sample contains few dwarf galaxies and no known SNe Ia in tidal tails or giant low surface brightness galaxies. Nor is the drop in surface brightness with galactocentric radius a major consideration for the galaxies considered here; inspection of the GALEX Ultraviolet Atlas of Nearby Galaxies (Gil de Paz et al. 2007) shows that for galaxies typical of those hosting SNe Ia in the H09 sample, when there is active SF it rises above our SF surface density threshold over most of the face of the galaxy. Indeed, within the canonical D₂₅ optical diameter (de Vaucouleurs et al. 1991), the azimuthally averaged FUV surface brightness range is typically only around ∼1 dex (Gil de Paz et al. 2007). Much of this variation is due to the change in filling fraction with radius rather than change in local surface brightness. This compares with the 3–4 dex amplitude of the FUV surface density signal.

However, we have identified the hosts of SN 1999aw and SN 2006an as dwarf galaxies whose sizes are smaller than the GALEX PSF. They were both found in large-area surveys unbiased toward SNe Ia in known galaxies. We estimate colors of B − V ∼ 0.4 ± 0.3 for the hosts of SN 1999aw and SN 2006an, based on photometry from Strolger et al. (2002) and SDSS, respectively. While these optical colors are not nearly as blue as those of the 125 Myr old host of SN 2007if (Childress et al. 2011), the colors for the hosts of SN 1999aw and SN 2006an are consistent with those of the blue compact dwarfs presented in Hunter et al. (2010), all of would have high star formation surface densities given FUV observations of comparable resolution and sensitivity.

In SDSS, the host of SN 2006an has a Petrosian radius of 2.4 ± 0.5 arcsec, or 1.6 ± 0.3 kpc at its redshift of z = 0.065. Thus, the effect of geometrical dilution should be small. Still, because its size is comparable to the GALEX PSF, it will be suppressed by as much as 0.3 dex since our aperture will not encompass all of the flux of a compact SF region close to SN 2006an. Thus, our current limit of log (Σ_SFR) < −2.2 dex could increase to as much as log (Σ_SFR) < −1.9 dex.

Strolger et al. (2002) find that the host of SN 1999aw is barely spatially resolved, having FWHM ∼ 0.4 arcsec, or ∼0.1 kpc at its redshift z = 0.038. Thus the geometrical dilution would be ∼0.6 dex for a 2 kpc radius aperture relative to the 1 kpc aperture used in R13. Measurement of the FUV flux from the host of SN 1999aw also will be suppressed by roughly 0.3 dex because our aperture doesn't cover the full PSF and the galaxy is unresolved by GALEX. Combining both effects, our current limit of log (Σ_SFR) < −3.5 dex could increase to roughly log (Σ_SFR) < −2.6 dex. However, if the area over which to measure SF were limited to the size of this tiny galaxy, that would raise the limit to something more like log (Σ_SFR) < −0.5 dex.

For both dwarfs, much deeper FUV data would be needed in order to turn our current upper limits into detections able to firmly classify these two dwarfs. Since the current analysis has only two such cases, their impact is negligible. However, this may become an issue given the higher fraction of SNe Ia in dwarf galaxies now being found in large-area surveys unbiased toward known galaxies.

Besides the geometrical dilution for small galaxies, there will be cases where part of our UV measurement aperture extends beyond the nominal edge of the SN host galaxy. The region outside the host will bias Σ_SFR low, though there is likely to be some compensation from inner, and often brighter, host light spread outward by the GALEX PSF. However, it is difficult to define an actual galaxy "edge,"; at UV wavelengths disks often extend 20%–40% beyond the nominal D₂₅ optical diameter (Barnes et al. 2011). Therefore, we have not implemented any compensation for this potential bias.