# The Dependence of the Type Ia Supernova Host Bias on Observation or Fitting
Technique

Jared Hand Pittsburgh Particle Physics, Astrophysics, and Cosmology Center
(PITT PACC). Department of Physics and Astronomy, University of Pittsburgh,
Pittsburgh, PA 15260, USA  Shu Liu  Pittsburgh Particle Physics, Astrophysics,
and Cosmology Center (PITT PACC). Department of Physics and Astronomy,
University of Pittsburgh, Pittsburgh, PA 15260, USA  Lluís Galbany Institute
of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, E-08193
Barcelona, Spain.  Daniel Perrefort Pittsburgh Particle Physics, Astrophysics,
and Cosmology Center (PITT PACC). Department of Physics and Astronomy,
University of Pittsburgh, Pittsburgh, PA 15260, USA  W. M. Wood-Vasey
Pittsburgh Particle Physics, Astrophysics, and Cosmology Center (PITT PACC).
Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA
15260, USA  Chris Burns Observatories of the Carnegie Institution for Science,
813 Santa Barbara St, Pasadena, CA, 91101, USA

###### Abstract

More luminous Type Ia supernovae (SNe Ia) prefer less massive hosts and
regions of higher star formation. This correlation is inverted during width-
color-luminosity light curve standardization resulting in step-like biases of
distance measurements with respect to host properties. Using the PISCO
supernova host sample and SDSS, GALEX, and 2MASS photometry, we compare host
stellar mass and specific star formation rate (sSFR) from different
observation methods, including local vs. global, and fitting techniques to
measure their impact on the host step biases. Mass step measurements for all
our mass samples are consistent within a 1$\sigma$ significance from
-0.03$\pm$0.02 mag to -0.04$\pm$0.02 mag. Including or excluding UV
information had no effect on measured mass step size or location. Specific SFR
(sSFR) step sizes are more significant than mass step measurements and varied
from $0.05\pm 0.03$ mag (H$\alpha$) and $0.06\pm 0.02$ mag (UV) for a 51 host
sample. The sSFR step location is influenced by mass sample used to normalize
star formation and by sSFR tracer choice. The step size is reduced to
0.04$\pm$0.03 mag when using all available 73 hosts with H$\alpha$
measurements. This 73 PISCO host subsample overall lacked a clear step signal,
but here we are searching for whether different choices of mass or sSFR
estimation can create a step signal. We find no evidence that different
observation or fitting techniques choice can create a distance measurement
step in either mass or sSFR.

methods: observational; techniques: image processing

††software:  FAST++888https://github.com/cschreib/fastpp,
STARLIGHT999http://www.starlight.ufsc.br, ZPEG101010http://imacdlb.iap.fr/cgi-
bin/zpeg/zpeg.pl, Python111111http://python.org, AstroPy (Astropy
Collaboration et al., 2013)121212http://www.astropy.org,
NumPy131313http://www.numpy.org, SciPy141414http://www.scipy.org,
STAN151515https://mc-stan.org/, pandas161616https://pandas.pydata.org/

##  1 Introduction

The discovery of dark energy using Type Ia Supernovae (SNe Ia) nearly 20 years
ago established SN cosmology as a key field in observational cosmology (Riess
et al., 1998; Perlmutter et al., 1999). SNe Ia are often used as
standardizable candles where empirical relationships are used to further
reduce the already low observed intrinsic scatter at peak luminosity. In
particular, the width-luminosity relationship accounts for a correlation in
peak luminosity with SN Ia duration (referred to as width or stretch) while
the color-luminosity relationship accounts for a correlation between peak
luminosity and color (Phillips, 1993; Riess et al., 1996). By applying these
corrections, recent analyses have been able to reduce scatter to within
$\sigma<0.1$ mag (Conley et al., 2011; Betoule et al., 2014; Scolnic et al.,
2018; Brout et al., 2019), achieving a level of precision comparable other
cosmology probes such as CMB polarization, CMB temperature power spectrum
decomposition, and lensing (Planck Collaboration et al., 2018).

Given the growing tension between $H_{0}$ measurements by competing probes
(Freedman, 2017), high precedence is placed on further improving measurement
precision. Considering the rate and brightness of SNe Ia, coupled with the
expected detection rate of next-generation facilities such as the Vera C.
Rubin Observatory (Ivezić et al., 2019) and Nancy Grace Roman Space Telescope
(Spergel et al., 2015), the utility of these transient events to constrain the
properties of dark energy remains high. Multiple concerted efforts to increase
the number of SN Ia observations across ever larger redshift and wavelength
ranges have already reduced random error to the point that systematic errors
have become the dominant source of uncertainty (Wood-Vasey et al., 2007;
Kessler et al., 2009; Conley et al., 2011; Betoule et al., 2014; Scolnic et
al., 2018; Brout et al., 2019). It is paramount to understand and reduce these
uncertainties in order to maximize the utility of upcoming surveys.

Brighter (dimmer) SNe Ia prefer less (more) massive and star-forming
(quiescent) host galaxies — this trend is reversed post-standardization. The
most commonly used host property to quantify this bias is stellar mass (see
Section 2 for details), with recent SN Ia analyses incorporating a luminosity
correction term for host mass during standardization (Conley et al., 2011;
Betoule et al., 2014; Scolnic et al., 2018). This effect is typically
quantified against Hubble residuals $\mu_{\rm SN}-\mu_{\rm mod}(z_{\rm SN})$,
or the difference between the standardized brightness and that predicted by
the best-fit cosmology. The ubiquitous host bias measured post-standardization
is the mass step, but similar step-like trends between specific star formation
rate (sSFR) and Hubble residuals for both global and local 1 kpc apertures
have been observed (D’Andrea et al., 2011; Rigault et al., 2020). As dust,
age, and metallicity correlate with mass and sSFR, similar trends have been
observed for they properties; all trends are more pronounced when compared to
stretch (see 2 for more details). The existence of these biases in historical
data sets is not ubiquitous, though. Variation in trends between SFR and SN Ia
properties based on SFR calibration was observed in D’Andrea et al. (2011),
and no mass step was found in the initial analysis of DES SNe Ia (Brout et
al., 2019); subsequent DES analyses have measured a mass step (Smith et al.,
2020; Kelsey et al., 2021). This prompts the question: does the measured host-
property bias depend on the chosen observation method and fitting technique
used to estimate host galaxy properties?

Any attempt to explain the relationship between SNe Ia and their host galaxy’s
properties should begin with quantifying whether the significance of observed
trends vary between choice of observation method and fitting technique. The
host bias extends from the local 1 kpc environment to the entirety to a global
aperture; integral field spectroscopy (IFS) samples such as PISCO (Galbany et
al., 2018), in providing resolved spectral information of a galaxy, are an
ideal tool to measure the host bias. Pragmatism has necessitated the use of
photometry to constrain host properties in nearly all cosmology analyses. We
considered the following questions:

  1. 1.

Does observational technique have a significant effect on measured global and
local host bias?

  2. 2.

Does the fitting technique used to estimate host properties effect the
measured host bias?

We here built a set of of host galaxy samples and then inferred galaxy
properties using different observational and fitting techniques. We compared
stellar mass and SFR estimates from the PISCO sample. Using the PISCO SN Ia
subsample, we then compared different stellar mass and sSFR estimate samples
to SN Ia properties, looking primarily for differences in the resulting host-
SN Ia property trends between mass/sSFR estimate samples. Finally, the larger
observed size and strength of the sSFR host bias relationship relative to the
stellar mass host bias is both presented and discussed.

In Section 2 we summarize SN Ia host studies up to the present followed by a
summary of the considered data set in Section 3. Section 4 provides an
overview of our methodology, including summaries of fitting techniques used.
Our results are provided and discussed in Section 5, and concluding remarks
presented in Section 6.

##  2 Summary of Host Galaxy Bias Literature

The presence of an observed correlation between the properties of SNe Ia and
their host’s properties is common in the literature. Parameters of light curve
width variation (such as $x_{1}$ in SALT2 Guy et al. (2007)) see lower $x_{1}$
values prefer more massive hosts, older stellar populations, and environments
of larger SFR (Sullivan et al., 2010; Kelly et al., 2010; Gupta et al., 2011;
Conley et al., 2011; Betoule et al., 2014; Scolnic et al., 2018). Both
Sullivan et al. (2010) and Gupta et al. (2011) saw a relationship between the
SALT2 color parameter $c$ and host mass and host age, respectively, albeit at
a lower significance than $x_{1}$; Scolnic et al. (2018) found no significant
color trend. Recently, Pruzhinskaya et al. (2020) found a statistically
significant dependence of SALT2 $x_{1}$ on host galaxy morphology, with lower
$x_{1}$ SNe Ia preferring elliptical and lenticular galaxies.

The observed correlation between SNe Ia and host properties are not explicitly
included nor accounted for with a canonical Tripp standardization model
(Tripp, 1998), resulting in an apparent over-correction of the host bias post-
standardization. For example, both the SN Legacy Survey (SNLS; Sullivan et
al., 2010) and SDSS SN Survey (Sako et al., 2018) found a ‘mass step’, where
SNe Ia with brighter Hubble residuals were on average hosted by more massive
galaxies (Kelly et al., 2010; Lampeitl et al., 2010; Gupta et al., 2011). In
comparing residuals in the fitted distance modulus of SNe Ia with respect to
cosmological prediction to their host masses, both SDSS and SNLS samples
observed a sudden step-like change in Hubble residual vs mass near
$10^{10}M_{\odot}$. Conley et al. (2011), Betoule et al. (2014), and Scolnic
et al. (2018) also observed this mass step at $10^{10}M_{\odot}$ in their
combined SN Ia sample analyses. Initial analysis by Brout et al. (2019) of
Dark Energy Survey (DES) SN Ia found no evidence for a mass step post-
standardization, although more thorough methodology for an updated SN Ia
sample did indeed recover a mass step (Smith et al., 2020; Kelsey et al.,
2021). Using SNIFS spectrophotometry from SNFactory, Rigault et al. (2013) and
Rigault et al. (2020) found that Hubble residuals are strongly dependent upon
SFR and sSFR, respectively, the latter having observed a $5\sigma$
relationship between Hubble residual and sSFR and confirming the tentative
findings of D’Andrea et al. (2011). Recently, Jones et al. (2019) compared
$u-g$ color of SN Ia 1.5 kpc local environment apertures against randomly
selected 1.5 kpc apertures within the host, finding that the SN Ia environment
correlates with SN Ia distance slightly more than random apertures, and found
a local stellar mass step after the global mass step had been corrected for.
Hayden et al. (2013) used both mass and metallicity to reduce Hubble residual
scatter. Roman et al. (2018) used $U-V$ as a proxy for stellar age and found
an age mass step of similar magnitude and significance as the fiducial mass
step, and found a $7\sigma$ relationships between local $U-V$ measurement and
distance. Rose et al. (2019), using principal component analysis, found a
strong relationship between a linear combination of host galaxy properties and
Hubble residuals. Brout & Scolnic (2020) presented a model that explain the
mass step post-light curve standardization via SALT2 resulting from improper
treatment of host dust, which was further expanded by Popovic et al. (2021).
In contrast, Uddin et al. (2020) found a clear dependence on Hubble residuals
calculated from light curves fit with SNooPy with host mass calculated for
visible and NIR light curves that was inconsistent with the model presented by
Brout & Scolnic (2020). Both Gonzalez-Gaitan et al. (2020) and Ponder et al.
(2020) found tentative evidence for a host mass step for SNooPy-fit NIR light
curves for SN Ia.

The use of simple stellar population (SSP) templates and stellar population
synthesis (SPS) libraries has been a central part any endeavor to estimate a
galaxy properties; these properties include stellar mass (Courteau et al.,
2014), stellar age, star formation rate (Kennicutt, 1998; Kennicutt & Evans,
2012), and gas-phase/stellar metallicity (Tremonti et al., 2004; Gallazzi et
al., 2005; Kewley & Ellison, 2008). Likewise, complex systematic uncertainties
in modeling and from observational limitations propagate into uncertainties in
derived property estimates. Past SN Ia cosmology analyses have generally
treated SSP/SPS libraries and fitting software as black boxes when estimating
host properties, and frequently relied on few data points from photometry
spanning a narrow wavelength range. Redshift, stellar mass, stellar age, dust
extinction, metallicity, and star formation rate are often degenerate with
each other and large systematic covariances complicate fitting methods
(Kauffmann et al., 2003; Brinchmann et al., 2004; Tremonti et al., 2004;
Gallazzi et al., 2005). Such degeneracies, together with systematic
uncertainties, result in dramatic uncertainties for some best fit parameters
(see section 3 introduction for more information).

Although optical multi-wavelength photometry of host galaxies has been the
primary tool used to estimate host mass and SFR (Sullivan et al., 2010; Kelly
et al., 2010; Childress et al., 2013; Betoule et al., 2014; Scolnic et al.,
2018; Brout et al., 2019), optical wavelength spectra (D’Andrea et al., 2011;
Johansson et al., 2013), UV or IR photometry in addition to optical spectra or
photometry (Gupta et al., 2011; Anderson et al., 2015), and IFS (Rigault et
al., 2013, 2020; Galbany et al., 2018) have been used. Childress et al. (2013)
and Gupta et al. (2011) both found stellar mass estimates using optical, IR,
and UV photometry changes little from mass estimates using optical photometry
only, consistent with the results of Bell & de Jong (2001). D’Andrea et al.
(2011) used sSFR estimates from SDSS II spectra and two different mass
estimates: one from SPS model best fits using SDSS II spectra and one from
Gupta et al. (2011). Hayden et al. (2013) directly compared three different
mass estimates for a set of SDSS host galaxies using metallicity estimates
from the Fundamental Metallicity Relation (Mannucci et al., 2010) to further
reduce Hubble residual scatter.

##  3 Data

We consider 319 galaxies observed as part of the PMAS/PPak Integral-field
Supernova Hosts Compilation (PISCO Galbany et al., 2018).

These observations were complemented by optical ugriz photometry from the
Sloan Digital Sky Survey (SDSS), near-infrared (NIR) JHKS photometry from the
Two Micron All Sky Survey (2MASS), and ultraviolet (UV) NUV+ and FUV
photometry from the Galaxy Evolution Explorer (GALEX). Figure 1 shows the
redshift distribution of the sample, which spans a range of
$0.00013<z<0.0875$. These 319 galaxies host 375 SNe, of which 198 are SNe Ia.

PanSTARRS DR1 (Chambers et al., 2016) was considered to expand coverage, but
added complexity with overlapping visible wavelength photometry and our
constraint to northern hemisphere targets resulted in its disregarding in
favor of SDSS. Follow up analyses will likely make use of PanSTARRs DR2,
especially if our observation footprint extends into the southern hemisphere.

Figure 1: Distribution of redshifts for galaxies considered by this paper.
This includes a total of 319 galaxies selected from the PISCO sample with
supplementary observations from 2MASS, SDSS DR12, and GALEX. All considered
targets were observed by PISCO and detected in 2MASS.

###  3.1 PISCO Supernova Sample

PISCO is a compilation of SN host galaxies observed with integral field unit
(IFU) spectroscopy using the same instrument PMAS/PPak (Roth et al., 2005;
Kelz et al., 2006) mounted to the 3.5 m Calar Alto telescope. PISCO was built
from an initial sample of SN host galaxies obtained by the CALIFA survey
(Sánchez et al., 2016; Galbany et al., 2014, 2016) and extended with new
observations of SN hots based on different science goals (see Galbany et al.
2018 for details).

The PISCO SN Ia subsample had 198 objects. When calculating distance moduli
all 14 peculiar SNe Ia were ignored (e.g., SN 1991bg and 1991T-like objects),
while 83 normal SNe Ia lacked available optical photometry, with many only
having NIR light curves. SN 2014J was excluded due to its extremely low
redshift and host galaxy M82’s mass estimation difficulties. We used the SALT2
output fits for 30 unpublished SNe Ia from Carnegie Supernova Project II
(CSPII, Suntzeff et al, in prep), bringing the sample to 101. During SALT2
fitting we removed SN 2006lf, which had an very high Milky Way color excess of
$E(B-V)=0.821$, giving a final total of 100 SNe Ia used. SDSS coverage reduced
this count to 76, while mutual SDSS and GALEX coverage further reduced the
number to 66 (Section 5.2). Four SN Ia hosts lacked H$\alpha$ flux
measurements and 11 host galaxies had unavailable GALEX FUV or NUV flux
measurements. These too were all excluded, bringing the total SN Ia count to
51 for sSFR analysis (Section 5.4). See Tables 1 and 2 for a summary of sample
reductions.

Table 1: Summary of SNe Ia sample size reductions. Details on specific SN Ia removal is provided in Section 3.1 Each row defines a subgroup of the row described above. SN Ia Subsample Condition | SN Ia Count
---|---
Total PISCO SNe Ia | 198
Normal SNe Ia | 184
Available visible photometry + CSPII | 101
Excluding specific SNe Ia | 100
Available STARLIGHT mass estimates | 97
Table 2: Summary of mass and sSFR step analyses subsample sizes starting with 97 available STARLIGHT mass estimates. SN Ia Subsample | SN Ia Count
---|---
SDSS coverage | 76
SDSS+GALEX coverage | 66
Available H$\alpha$ measurements | 73
Available H$\alpha$ and SDSS+GALEX coverage | 51

###  3.2 PISCO Host Galaxy Global Parameters

Stellar mass estimates and integrated H$\alpha$ flux measurements of all PISCO
galaxies were taken from Galbany et al. (2018) with mass estimates made using
STARLIGHT (Cid Fernandes et al., 2005). Mass estimates were calculated using a
SSP library built using Bruzual & Charlot (2003) (BC03) with a Chabrier
(2003a) initial mass function (IMF). Galbany et al. (2018) used a more complex
set of basis templates instead of just BC03 used here (see Galbany et al.
(2018), Section 3.2.1 for more details) — otherwise, the methodology we used
to estimate masses with STARLIGHT was identical.

###  3.3 SDSS DR12 Optical Photometry

The Sloan Digital Sky Survey (SDSS) is a multi-year, multi-program survey
performed at the Apache Point Observatory (APO) using the SDSS 2.5 m telescope
(York et al., 2000; Gunn et al., 2006). We used observations from SDSS Data
Release 12 (DR12 Alam et al., 2015) to provide imagining data for host
galaxies in the ugriz filters Doi et al. (2010). Mutual coverage between SDSS
and PISCO is available for 239 of the 319 galaxies (74.9%).

All SDSS fields were selected using the nearest neighbor search functions
built into the DR12 CASJOBS
database111http://skyserver.sdss.org/CasJobs/SchemaBrowser.aspx and downloaded
from the Science Archive Server (SAS)222https://dr12.sdss.org/.

###  3.4 2MASS IR Photometry

The Two Micron All Sky Survey (2MASS) was a three-year program run at the
Whipple Observatory and Cerro Tololo Inter-American Observatory (Skrutskie et
al., 2006). 2MASS observed 99.998% of the sky with three near infrared (NIR)
passbands JHKs, resulting in all PISCO galaxies having corresponding 2MASS
images. Optimal operations result in a 2.5–3.4″PSF with a Pixel size of
$2.0$″. Images were obtained using the Infrared Science Archive
(IRSA).333https://irsa.ipac.caltech.edu/frontpage/

###  3.5 GALEX Photometry

The Galaxy Evolution Explorer (GALEX) is a space-based observatory with a 1.2
degree diameter circular field of view that observed through two ultra-violet
(UV) bands, FUV (135–175 nm) and NUV (175–280 nm), (Martin et al., 2005). A
total of 287 PISCO galaxies reside within GALEX’s footprint for a mutual
coverage of 90.0%, although only 203 were also within SDSS coverage. Images
were downloaded from the four primary GALEX surveys using STSci MAST services
444https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html, with
precedent placed on exposure time when choosing fields. Where possible we used
“Deep Imaging Survey” fields (DIS: 30,000 s exposure), followed by “Medium
Imaging Survey” fields (MIS: 1500 s exposure), and finally the “All-sky
Imaging Survey” fields (AIS: 100$\times$10 s exposures Martin et al. (2005).
If available, Nearby Galaxy Survey (NGS) fields were used instead of AIS
fields. Guest investigator fields were also used when necessary. 2.2% of PISCO
galaxies had DIS coverage, 5.1% had NGS coverage, 14.4% had MIS coverage, and
80.9% had AIS coverage or were observed as part of the guest investigator
program.

##  4 Methodology

We performed our global photometry and combined that with corresponding PISCO
IFS to estimate host galaxy properties. For details on PISCO data reduction we
refer the reader to Galbany et al. (2018). As one brief note, the PISCO IFS
apertures were hexagonal, while the apertures on the imaging data we analyzed
here are elliptical.

###  4.1 Photometric Image Preparation

Foreground objects in images from each data set were removed by masking. The
position and appropriate aperture size of foreground objects in SDSS images
were determined using Source Extractor (Bertin & Arnouts, 1996) on r-band
images. All identified objects were visually reviewed and assigned a
proportion factor ($\alpha_{\rm SDSS}$) which corrected the Kron radius
calculated by Source Extractor ($r_{k}$)

$r_{k}^{\rm cor}=\alpha_{\rm SDSS}~{}r_{k}$ (1)

This factor was used to decrease the area of measured foreground objects so to
not compromise the shape of the host galaxy. Pixel values within the scaled
aperture were masked and replaced using an interpolation to account for lost
photons in the masked region.

For SDSS, we replaced all foreground objects within a circular region of the
host less than $A\times r_{k}^{\rm cor}$ using a two-dimensional linear
interpolation. With GALEX and 2MASS, we instead masked foreground objects due
to lower field signal-to-noise leading to unrealistic interpolation results.
All foreground objects outside this radius but within a radius of $2.8(A\times
r_{k}^{\rm cor})$ were simply masked and unused. For 2MASS and GALEX we masked
all foreground objects within a radius of $2.8(A\times r_{k}^{\rm cor})$. SDSS
images were provided background-subtracted with FITS header information for
background reconstruction. Background images were provided with GALEX field
downloads and were used directly in background subtraction. Zero pixels in
both image and provided background fields were masked for GALEX NUV and FUV
data sets. As both fields were masked, this did not increase our background
estimation.

###  4.2 Galaxy Parameter Estimation

To explore how the host galaxy bias varies with fitting technique, we required
host property estimates from multiple techniques. To this end, we used three
fitting programs to estimate host properties two for photometry and one for
IFS. These fitting techniques make use of simple stellar population (SSPs)
libraries, or use stellar population synthesis (SPS) libraries built by
convolving a set of SSPs with a star formation history (SFH) parameterization
and a recipe to handle dust extinctions to produce a library of composite
stellar populations (CSPs) (Walcher et al., 2011; Conroy, 2013). It is
important to explicitly note that simple stellar population (SSP) or stellar
population synthesis (SPS) libraries contain numerous sources of systematic
uncertainties and that even with high-quality observations, systematic model
uncertainties endemic to SPS libraries are larger than what is expected from
observational errors alone (Conroy et al., 2009).

Figure 2: Systematic variation in estimated mass (left column) from variation
in SFH (top), IMF (middle), and SPS library (bottom). Along the x-axes are the
base template sets with a delayed-$\tau$ SFH (top), a Chabrier IMF (middle),
and a BC03 library (bottom). Along the y-axes are (top) an exponential decay
$\tau$ model, (middle) a Salpeter IMF, (bottom) FSPS.

####  4.2.1 ZPEG

ZPEG estimates galaxy redshifts by fitting photometry against a library of
CSPs constructed from the theoretical spectral library PEGASE.2. The best-fit
template is determined using maximum likelihood analysis with a $\chi^{2}$
function for the difference between synthetic photometry computed from
templates and observed photometry. Specifically, $\chi^{2}$ values are
calculated for each point along a four-dimensional grid of parameters
($E(B-V)$, $t_{*}$, redshift, and template), with the best-fit model being the
minimal $\chi^{2}$ value on the grid

$\chi^{2}_{Z}=\sum^{N}_{i}\frac{\big{[}F_{\lambda,i}-\alpha
F_{\lambda,\text{mod}}\big{(}t_{*},E(B-V),z\big{)}\big{]}^{2}}{\sigma^{2}_{i}}$
(2)

where $N$ is the number of filters, $F_{\text{mod}}$ is the model flux density
from given template of age $t_{*}$ and color excess $E(B-V)$, $\sigma^{2}_{i}$
is the measured observation variance for data point $i$, and $\alpha$ is a
scaling parameter to match normalized template SEDs to the observed flux.
Uncertainty in the best-fit model is determined by calculating the reduced
$\chi^{2}$ ($\chi^{2}_{r}$) value of the best-fit model and finding the
corresponding model parameters whose model $\chi^{2}$ ($\chi^{2}_{\rm err}$)
satisfy $\chi^{2}_{\rm err}\leq\chi^{2}_{r}+1$. Spectroscopic redshifts can be
provided for each object to simplify fitting.

With ZPEG, we used the PEGASE.2 library, a Salpeter IMF, included nebular
emissions, and averaged SFR over 500 million years starting at present. We
used the default 200-ages Salpeter library of 15 galaxy templates provided
with ZPEG, excluding the starburst template due to its extremely nonphysical
description of galaxy evolution. A foreground dust screen with color excess
$E(B-V)$ with values ranging from $0$ to $0.4$ mags in intervals of $0.2$ mags
was added for each template when fitting. There is a setting “AGE_CONSTR_Z0”
for ZPEG that when turned off can result in dramatic underestimation of mass,
especially if the starburst template is included. We kept the default setting
of “T” to keep it enabled.

####  4.2.2 FAST++

FAST++ is a C++ implementation of FAST (Kriek et al., 2009) with added
functionality (Schreiber, 2019; Schreiber et al., 2018). Given photometry or
spectra, FAST++ determines a best-fit SED from a provided SPS library on a
five-dimensional grid, with each grid point corresponding to a CSP SED with
age $t_{*}$, SFH time scale $\tau$, $V$ band extinction $A_{V}$, and stellar
metallicity $Z_{*}$ at some redshift $z$. Note that the CSP is constructed
using the selected SFH parameterization and dust extinction model. The
redshift parameter can be fixed by providing a spectroscopic redshift value as
input for fitting. At each point on the grid a $\chi^{2}$ value is calculated:

$\chi^{2}_{F}=\sum^{N}_{i}\frac{\big{[}F_{\lambda,i}-F_{\lambda,\text{mod}}(t_{*},\tau,A_{V},Z_{*},z)\big{]}^{2}}{\sigma^{2}_{i}}$
(3)

where $N$ is the number of combined photometric and spectroscopic data points
and $\sigma^{2}_{i}$ is the observation variance for data point $i$.
Confidence intervals for parameters and derived quantities (such as stellar
mass and SFR) are determined using Monte Carlo sampling of the grid around the
lowest $\chi^{2}$.

SFR was averaged over the last 500 million years as done with ZPEG. Unless
otherwise stated, we used a Calzetti dust law with a uniform and constant
foreground dust screen with the BC03 SPS library calculated using a delayed
exponential (delayed-$\tau$) SFH and a Chabrier IMF (Calzetti et al., 2000;
Chabrier, 2003b).

Using FAST++ we compared the systematic effects of changing different SPS
library components (Figure 2). Mass estimates varied uniformly with variation
in IMF (Chabrier vs. Salpeter) and were unchanged for different SFH models
(exponential or $\tau$ vs. delayed-$\tau$). The global shift from changing to
a Salpeter IMF was 0.24 dex. Leaving IMF and SFH fixed, when then compared
mass estimates for the SPS libraries from BC03 to the newer FSPS (Conroy et
al., 2009). The particular FSPS library used was the default provided by
FAST/FAST++ as described in Aird et al. (2017), Appendix A. FSPS estimated
systematically higher mass at $0.12$ dex with a standard deviation of $0.12$
dex — a higher scatter than that due to changing IMF or SFH but well within
the average error in mass estimates and the expected 0.3 dex template
uncertainty.

####  4.2.3 Fitting IFS with STARLIGHT

STARLIGHT fits observations to linear combinations of SSPs attenuated by a
given dust law in a process called spectral inversion fitting (Cid Fernandes
et al., 2005). This differs from FAST++ and ZPEG which instead fit
observations to a library of composite stellar populations, themselves built
from SSPs using some star formation history and dust law.

STARLIGHT fits spectra by masking emission lines. A Fitzpatrick dust model
with $R_{V}=3.1$ was used for dust correction (Fitzpatrick, 1999). The best-
fit SED is determined by minimizing the resulting $\chi^{2}$ value against the
model SED $M_{\lambda}$ using an implementation of the Metropolis algorithm
(Cid Fernandes et al., 2005), with:

$M_{\lambda}=M_{\lambda,0}10^{-0.4(A_{\lambda}-A_{\lambda,0})}\Bigg{[}\sum^{N_{\ast}}_{i}x_{i}F_{\lambda,i}\Bigg{]}\odot\mathcal{N}(v_{\ast},\sigma_{v_{\ast}})$
(4)

where $x_{i}$ and $F_{\lambda,i}$ are the fractional contribution and
synthetic flux density of $i$th SSP SED, respectively, $\odot$ is the
convolution operator, and the normal distribution $\mathcal{N}$ models
velocity dispersion due to stellar motion $v_{*}$. $M_{\lambda,0}$ is the
normalized synthetic flux density. The population vector elements $x_{i}$
serve as weights for each $F_{\lambda,i}$, from which one can infer SFH,
metallicity, and other properties as a weighted sum of the properties of each
contributing $F_{\lambda,i}$. To improve consistency with FAST++’s BC03 and
the Chabrier IMF template library described above, the PISCO mass estimates
used here were recalculated using a SPS library constructed from the BC03
library and Chabrier IMF as well.

###  4.3 Hubble Residuals

Hubble residuals are the difference between the measured distance modulus and
that predicted by the assumed cosmology at a given redshift $z_{\text{CMB}}$:
$\mu-\mu_{\text{mod}}(z_{\text{CMB}};H_{0},\Omega_{\Lambda})$. To better
facilitate comparison with existing literature, Hubble residuals were
estimated in a similar fashion to the Joint Light-Curve Analysis, or JLA
(Betoule et al., 2014) using the light curve fitter SALT2.

70 of 100 used PISCO SNe Ia had light curves fit with the SNCOSMO
implementation of SALT2 using the Betoule et al. (2014) fiducial light curve
template (Guy et al., 2007; Barbary et al., 2016). In particular, we fit for
the scaling parameter ($x_{0}$), the effective stretch parameter ($x_{1}$),
and the color parameter ($c$). Milky Way dust extinction was taken into
account during fitting using Schlegel et al. (1998) dust maps with a Cardelli
dust law Cardelli et al. (1989). If a light curve was observed by more than
one survey, then each set of observations were fit separately. The light curve
fits were then visually inspected and the better fit was used.

The 30 remaining SNe Ia were observed as part of the unpublished CSPII
(Suntzeff et al, in prep). Preliminary SALT2 parameters were provided by CSPII
for this analysis, as many low-mass PISCO SN Ia hosts consisted primarily of
CSPII hosts.

To standardize fitted SN Ia luminosity, cosmological parameters were held
fixed assuming a flat $\Lambda$CDM cosmology with $H_{0}=70$ and
$\Omega_{\Lambda}=0.7$ using astropy’s cosmology suite (Astropy Collaboration
et al., 2013). The distance modulus per SN is calculated assuming a linear
relationship between both SALT2 color parameter $c$ and SALT2 stretch
parameter $x_{1}$ versus absolute $B$-band magnitude $M_{B}$ with slopes
$\alpha$ and $\beta$, respectively (Tripp, 1998):

$\mu_{B}=m_{B}+\alpha x_{1}-\beta c-M_{B}$ (5)

Here, $\alpha$ and $\beta$ are nuisance variables calculated using a maximum
likelihood analysis akin to Conley et al. (2011):

$\chi^{2}_{H}=\sum^{N_{\text{SN}}}_{i}\frac{\big{(}\mu_{B,i}-\mu_{\rm
mod}(z_{\text{CMB},i};H_{0},\Omega_{\Lambda})\big{)}^{2}}{\sigma^{2}_{i}+\sigma^{2}_{\text{int}}}$
(6)

We ignored covariance between SNe for simplicity and fixed intrinsic
dispersion to $\sigma^{2}_{\text{int}}=0.1$ to be consistent with Pantheon
(Scolnic et al., 2018). We did not decompose intrinsic scatter into components
incorporating dependencies on $\alpha$ and $\beta$ (Marriner et al., 2011).
Given this project’s focus on studying the host bias before and after
standardization, no attempt was made to incorporate host properties into
equation 6. Magnitude uncertainty due to peculiar velocity was estimated using
an empty-universe approximation with a peculiar velocity of $\sigma_{v}=300$
km s-1 for each SN (Davis et al., 2011, , Eq. A4):

$\sigma_{\mu}=\frac{\sigma_{v}}{c}\frac{5}{\ln(10)}\bigg{[}\frac{1+z_{\rm
CMB}}{z_{\rm CMB}(1+\frac{z_{\rm CMB}}{2})}\bigg{]}.$ (7)

Figure 3: (top) Hubble diagram comparing SALT2-standardized PISCO SN Ia
distance moduli to a predicted flat $\Lambda$CDM cosmology with H${}_{0}=70$
km s-1 Mpc-1 and $\Omega_{\Lambda}=0.7$ given as the dashed line. Nuisance
parameters $M_{B}$, $\alpha$, and $\beta$, and the fixed intrinsic SN Ia
scatter $\sigma_{\text{int}}$ are given at the top of the top plot. (bottom)
Hubble residuals $\mu^{*}-\mu_{\text{mod}}(z)$ against redshift, with a dashed
line at $\mu^{*}-\mu_{\text{mod}}(z)=0$ for reference.

###  4.4 Linear Regression and STAN

When comparing SFR estimates we used a Bayesian linear regression mixture
model LinMix developed and described by Kelly (2007)
555https://github.com/jmeyers314/linmix. This model takes into account
uncertainties in both dependent and independent variables by modeling the true
values of said variables as latent parameters described by a Gaussian mixture
model. Otherwise, Ordinary Least Squares (OLS) linear regression implemented
with SciPy666https://www.scipy.org/ was used where noted (Virtanen et al.,
2020).

We used Stan777https://mc-stan.org/ to sample the posterior of a model between
Hubble residuals and host property in place of a step function. The built-in
Stan Hamiltonian Monte Carlo sampler approximates the Jacobian of model
parameters, and since a step function features an undefined derivative at the
step location, we instead used a shifted and scaled hyperbolic tangent (tanh)
model:

$[\mu^{*}-\mu_{\text{mod}}(z)](x)=\Delta\mu\tanh{\frac{x-x_{s}}{\alpha}}+\Delta\mu_{0}$
(8)

where $x$ is the host property of interest (mass or sSFR). $\Delta\mu$ and
$x_{s}$ parameterized the step size and step location, respectively with
$x_{s}(M_{\odot})\doteq M_{s}$ and $x_{s}(sSFR)\doteq sSFR_{s}$ for the mass
and sSFR step location parameters. Parameter $\Delta\mu_{0}$ accounted for any
systematic y-axis offset. Parameter $\alpha$ determined the transition scale
and was fixed to $\alpha=0.01$ to enforce a step-like trend, akin to the
logistics model used by Scolnic et al. (2018), Brout & Scolnic (2020), and
Popovic et al. (2021). Appendix B details priors used and their respective
motivations.

##  5 Results and Analysis

The robustness of stellar mass estimates is why a mass step is the most common
characterization of the host-correlated bias in SN Ia distance standardization
(Conley et al., 2011; Betoule et al., 2014; Scolnic et al., 2018). But given
that all host properties are is correlated with other host properties, it is
not surprising that both SFR and sSFR step-like biases have also been detected
(D’Andrea et al., 2011; Rigault et al., 2013, 2015, 2020). In this work we use
our available H$\alpha$ flux and UV photometry alongside optical spectra and
photometry to estimated various mass and sSFR samples to determine if any
chosen observation method or fitting technique leads to a significant change
in the measured host bias.

The analysis is presented with each subsection having both a summary of
results followed by a discussion to make our analysis more digestible for the
reader.

###  5.1 Mass Estimate Comparisons

Figure 4: A comparison of stellar mass estimates between ZPEG and FAST++ for
SDSS-only and SDSS+GALEX photometry. Error bars are taken directly from the
respective fitting technique. A diagonal one-to-one grey line is included for
reference. Figure 5: A comparison of mass estimate techniques. We found an
offset of 0.47 dex between ZPEG and STARLIGHT mass estimates. Standard
deviation between mass estimate differences were 0.28 dex for ZPEG (with the
16 erroneous estimates excluded) and 0.33 dex for FAST++.

Figure 4 compares fit mass estimates from FAST++ and ZPEG using SDSS and
SDSS+GALEX photometry. There was a median offset of -0.43 dex (for SDSS only)
and -0.54 dex (for SDSS+GALEX), largely consistent with that expected from
differences between the Chabrier and Salpeter IMFs ($\sim$0.2 dex) and the
stellar libraries BC03 and PEGASE.2 ($\sim$0.1 dex) (Moustakas et al., 2013).
The increase in median offset after including GALEX was likely driven by
discrepancies between handling of young, massive stars in the respective
libraries.

We compared mass estimates from FAST++ and ZPEG using SDSS optical ugriz to
STARLIGHT mass estimates using PISCO optical spectra. Only 308 of 319 PISCO
hosts had BC03+Chabrier IMF STARLIGHT mass estimates. Of those 308 PISCO
targets, very low redshift hosts Andromeda, M82, and NGC 6946 had failed mass
estimates. Low redshift NGC 2276 was observed as three targets, each with
failed mass estimates and were excluded. This reduced the usable STARLIGHT
mass sample to 302 galaxies with STARLIGHT mass estimates. Our requirement for
mutual SDSS coverage reduced our working sample to 237 hosts. In comparing
mass estimates, we measured an average offset of 0.03 dex between the FAST++
and STARLIGHT mass samples with a standard deviation of 0.33 dex (Figure 5).
This small offset stemmed from the FAST++ SPS library and the SSP basis used
by STARLIGHT both being constructed with a BC03 library and a Chabrier IMF. A
global median offset of 0.47 dex towards larger ZPEG mass estimates was caused
by use of a Salpeter IMF and the PEGASE.2 spectral library for ZPEG (Moustakas
et al., 2013). Mass offset standard deviation between the ZPEG and STARLIGHT
mass samples was $0.28$ dex, slightly less than that measured for FAST++ mass
values.

Mass estimates from optical photometry and IFS were mostly consistent with
predicted global offsets. ZPEG mass estimates made with only SDSS photometry
had systemically $\sim$0.15 dex higher values than their STARLIGHT or FAST++
counterparts — this could be from the choice in library or dust model of ZPEG
being biased towards older red stellar populations without UV constraints.
Random variation was consistent with SPS library uncertainties of $\sim$0.3
dex, with some further scatter arising from different aperture size and shape
between PISCO IFS and our in-house photometry.

Figure 6: Absolute change in BC03 FAST++ stellar mass estimates after
including GALEX photometry for 211 hosts. Three outliers exhibit mass
increases of $>0.6$ dex, which would shift them over the fiducial mass step
location marked with the vertical solid line. However we don’t have light
curves for the corresponding SNe Ia and thus these hosts aren’t actually used
in the host galaxy bias analysis present here. No mass shift magnitude greater
than 0.2 dex was observed for massive hosts with $\log_{10}(M/M_{\odot})>11$,
marked with the vertical dotted line. Note the correlation between differences
in the best-fit $A_{V}$ and mass — an example of the mass-age-dust degeneracy.
Figure 7: A comparison between K–band absolute magnitude and FAST++ mass
estimates determined using 2MASS+SDSS photometry for our PISCO sample. The
dashed black line references $\log_{10}(M/M_{\odot})=10$, the approximate
location of the canonical mass step. The standard deviation of residual in
mass estimates for galaxies above the dotted line is 0.35 dex compared to 0.46
dex for those below. The solid black line is the linear OLS fit.

####  5.1.1 Effects of Incorporating UV Information

With FAST++ we compared mass estimates with and without GALEX NUV and FUV
photometry. This required GALEX coverage and limited our sample to 211
galaxies from 237. Adding UV information helped better constrain FAST++’s
$A_{V}$ dust parameter, with average $A_{V}$ uncertainty decreasing by a
factor of 2 from 0.6 mag to 0.3 mag. There was an appreciable anti-correlation
between the change in fit $A_{V}$ and the change in fit mass (Pearson’s r
score of -0.74). Figure 6 shows three clear outliers where mass increased by
more than 0.6 dex once UV information was included: UGC 02134 and UGC 09165,
both inclined spiral galaxies with clear UV signals, and 2MASXJ02305208, the
smallest of a triple elliptical cluster. Note that both SN Ia hosts UGC 09165
and 2MASXJ02305208 had mass estimates shift from above to below the canonical
mass step location $\log_{10}(M/M_{\odot})=10$, but that these SNe Ia lacked
optical light curves and were not used in our mass step analysis (Section
5.2).

UV flux comes from active or recent star formation. An elliptical galaxy
incorrectly described with a star forming model SED using only optical
photometry can be correctly identified as elliptical once UV information is
included, as was the case for 2MASXJ02305208. For UGC 02134 and UGC 09165, UV
information provided further information about dust-obscured star formation,
resulting in a lower stellar mass estimate after UV addition. Apart from these
these outliers, remaining shifts in mass were within the 0.4 dex, with 52
estimates shifting with absolute value greater than 0.2 dex. All but five of
theses 52 hosts with absolute value shifted from higher to lower mass with UV
information included. This information helped break the color degeneracy for
these 47 objects, with redness instead attributed to dust-obscured young stars
with lower mass-to-light ratios as opposed to older red dwarf stars with high
mass-to-light ratios, reducing mass estimates.

Nonetheless, aside from identifying galaxies that are forming no stars, mass
estimation is largely insensitive to dust effects (Conroy, 2013). This means
that including UV information does not significant change mass estimates the
vast majority of our sample (1.4% of our 211 hosts for this subsample). No
hosts with SDSS mass $\log_{10}(M/M_{\odot})>11$ changed by more than 0.2 dex
after including UV information. Overall, we do recommend including UV
information when estimating mass given its ability to partially break the
color degeneracy by distinguishing old stellar populations from dust-obscured
young stars, but it does not significant change mass estimates for the sample.

####  5.1.2 Mass from NIR

We also experimented with including 2MASS NIR information with SDSS
photometry, finding mass estimates effectively unchanged. Average fit mass
estimate uncertainty decreased for hosts with $\log_{10}(M/M_{\odot})>10$,
though. NIR photometry provided insufficient new information to constrain
stellar mass beyond that already provided by optical photometry.

We considered the linear relationship between 2MASS K-band magnitudes and
FAST++ mass estimates using 2MASS and SDSS photometry, akin to the methodology
used in Betoule et al. (2014) (Figure 7). Two trends were present: (1) a
linear relationship between absolute magnitude and mass estimate, with
brighter absolute magnitudes being correlated with larger masses; and (2) an
increase in the typical magnitude uncertainty for dimmer objects. The standard
deviation of mass estimate residual was 0.35 dex below
$\log_{10}(M/M_{\odot})=10$ and 0.46 dex above. Neither relationship was
surprising, but we explicitly mention these as the resulting trend is visibly
and logically heteroscedastic — dimmer objects will have larger observational
errors, thus biasing lower-mass galaxies towards greater mass estimate
uncertainties. This should have no influence upon a step function model for a
host bias correction, as the ordering of mass estimates would be effectively
unchanged given the K-mag trend with mass is clearly linear: a change in slope
would have no impact upon said step model.

###  5.2 Host Mass Bias Comparison

Figure 8: Comparison of 76 PISCO Hubble residuals to three sets of stellar mass estimates. SDSS ugriz photometry was used to calculate FAST++ and ZPEG mass estimates. The bias towards high-mass SN Ia hosts in the PISCO sample is apparent. Tanh function fit results are given as a solid orange line for FAST++, a dashed green line for ZPEG, and a dotted purple line for STARLIGHT. The bottom panel is a comparison of 66 mass estimates from FAST++ excluding (orange diamonds) and including (purple x’s) GALEX photometry from the base SDSS ugriz. Despite noted shifts from high to low mass, both samples measured the same step function size, despite 10 fewer data points. Dotted lines in both plots are for reference. Table 3: Tanh model parameter results for mass samples. Mass Sample | $M_{s}$ | $\Delta\mu$ | $\Delta\mu_{0}$
---|---|---|---
76 FAST++ | $9.78\pm 0.37$ | $-0.04\pm 0.02$ | $0.02\pm 0.02$
66 FAST++ | $9.73\pm 0.39$ | $-0.04\pm 0.03$ | $0.02\pm 0.02$
66 FAST++ & UV | $9.76\pm 0.35$ | $-0.05\pm 0.03$ | $0.02\pm 0.02$
76 ZPEG | $10.06\pm 0.53$ | $-0.03\pm 0.02$ | $0.02\pm 0.02$
76 STARLIGHT | $9.91\pm 0.56$ | $-0.03\pm 0.02$ | $0.01\pm 0.02$
97 STARLIGHT | $9.83\pm 0.33$ | $-0.04\pm 0.02$ | $0.02\pm 0.02$

Hubble residuals for 76 SNe Ia were compared against three mass estimates
samples: FAST++ using SDSS, ZPEG using SDSS, and STARLIGHT using PISCO IFS.
These SN Ia hosts had both SDSS coverage and available STARLIGHT mass
estimates. The decision to use only visible wavelength SDSS photometry for
FAST++ mass estimates here were to maximize our usable sample and because
PISCO SED only covers visible wavelengths. Linear OLS regressors fit for all
three mass samples found slope values consistent with a zero slope. Using our
tanh step model implemented with Stan, we found $M_{s}=9.78\pm 0.37$ and
$\Delta\mu=-0.04\pm 0.02$ mag for the FAST++ mass sample. For the STARLIGHT
mass sample we found $M_{s}=9.91\pm 0.56$ and $\Delta\mu=-0.03\pm 0.02$ mag.
With all available 97 STARLIGHT mass estimates the fit step size and location
were more consistent with the 76 FAST++ mass sample at $M_{s}=9.83\pm 0.33$
and $\Delta\mu=-0.04\pm 0.02$ mag. ZPEG fit parameters for the 76-host sample
saw a less than 1$\sigma$-significant shift of 0.23 dex to $M_{s}=10.06\pm
0.53$ with a slightly reduced step size of $\Delta\mu=-0.03\pm 0.02$ mag. This
shift toward a higher mass step location relative to the FAST++ mass sample
was consistent with an expected $\sim$0.3 dex bias towards higher mass due to
ZPEG’s using the PEGASE.2 library and a Saltpeter IMF (Section 5.1). Also, the
ZPEG and STARLIGHT step locations coincided with center of our mass step
location bounds, $[9,11]$, albeit with ZPEG’s step location being 0.15 dex
higher than STARLIGHT’s. These parameter uncertainties were higher than their
FAST++ counterpart by 0.16 dex and 0.19 dex for ZPEG and STARLIGHT,
respectively, and were sufficient to span the allowed step location parameter
space. See Table 3 for a summary of $\tanh$ model results for our used mass
subsamples.

We found no evidence that using optical spectra versus optical photometry
created any biased mass step. All step size variation between the 76-host mass
samples were within 1$\sigma$ of each other. Despite these two mass samples
having different observation method and fitting technique, using all 97
STARLIGHT mass estimates produced fits results clearly consistent with the
76-host FAST++ mass sample fit parameters. We interpreted the increased step
location uncertainty and reduced step size of the 76-host STARLIGHT sample fit
as an artifact of our reduced sample size. The ZPEG mass step location was
predicted to be greater than that fit for STARLIGHT and FAST++ mass samples
(Section 5.1), but its reduced step size relative to FAST++ results and a less
constrained step location could have affected the best-fit ZPEG step location.
A similar weakness in mass step signal for the 76-host ZPEG and STARLIGHT
samples relative to the FAST++ sample was partly due to the lower scatter
between ZPEG and STARLIGHT mass estimates as presented in Section 5.1. Again,
our reduced statistics were likely to blame for weak signal detection.

####  5.2.1 Effects of Incorporating UV Information

The 66 SN Ia hosts with both SDSS and GALEX coverage had mass estimates
compared both with and without UV photometry. As seen in Figure 6, below
$\log_{10}(M/M_{\odot})<11$ there was a preferred shift to lower mass for a
substantial portion of the PISCO sample once UV information was included. This
trend carried over for these 66 hosts, with arrows in the bottom plot of
Figure 8 predominately pointing towards lower mass. In particular, eight mass
estimates changed by $2\sigma=0.28$ dex, with seven of the eight shifting to a
lower mass once UV information was included. For the 66 mass estimates fit
with GALEX information we found $M_{s}=9.73\pm 0.39$ and $\Delta\mu=-0.04\pm
0.03$ mag; mass estimates made only SDSS only fit for parameter values
$M_{s}=9.76\pm 0.35$ and $\Delta\mu=-0.05\pm 0.3$ mag. These were both
relatively consistent and consistent with the previously discussed 76-host
SDSS sample results.

None of the three PISCO hosts with mass changes greater than 0.6 dex were used
in our mass step analysis, thus preventing an extreme shift in mass over the
mass step location. We observed an asymmetry in mass change direction after
including UV information for many of our SN Ia, but these mass changes were
relatively small at $\sim 0.4$ dex and did not translate to notable
qualitative change in the step model parameter values or uncertainties. Adding
UV information caused an insignificant 0.33-$\sigma$ change in mass step from
-0.04 mag to -0.05 mag. Although we cannot rule out the possibility of
occasional SN Ia host galaxies being misidentified when UV information is
excluded, the majority of hosts had largely stable mass estimates with or
without UV information (98.5% in our 211 sample). Regardless, we recommend
mass estimates be made with UV information included where possible to prevent
potentially large mass estimate errors.

Figure 9: A comparison of global aperture SFR estimates using various
techniques. The left-hand plot compares FUV and NUV SFR estimates, which show
very clear agreement with each other. The right-hand plot compares FUV and NUV
SFR estimates to H$\alpha$ SFR estimates. The orange dotted line corresponds
to NUV LinMix mean fit, while the purple dot-dashed line corresponds to FUV
LinMix mean fit. Note that UV-calibrated SFR estimates include two sources of
error: one from UV flux uncertainty and another 15% fractional error from
calibration uncertainty. Open circles correspond to the PISCO SN Ia subsample.

###  5.3 SFR Comparison

H$\alpha$ SFR estimates were calculated using a linear relationship provided
by Calzetti (2013). For consistency, a similar linear relationship for UV
luminosity was also used to estimate UV SFR values. Using a single parameter
star formation history for both ZPEG and FAST++ resulted in poorly constrained
template SFR values. As such, we excluded template SFR samples from the
remainder of our analysis.

H$\alpha$ and UV SFR values were estimated using relationships from Leitherer
et al. (1999) recalibrated for a Chabrier IMF. H$\alpha$ SFRs were calibrated
for a stellar mass range of 0.1–100 M⊙ and star forming timescale $\tau\geq 6$
Myr. Type-B recombination was assumed with $T_{e}=10^{4}$K and $n_{e}=100$
cm-1:

$\text{SFR}({\text{H}\alpha})=(0.88)~{}5.5\times 10^{-42}L(\text{H}\alpha)$
(9)

where the factor of 0.88 accounts for our use of a Chabrier IMF instead of a
Salpeter IMF and $L(\text{H}\alpha)$ is the luminosity calculated from the
observed flux and luminosity distance. Galbany et al. (2018) corrected
H$\alpha$ flux for nebular host attenuation using measured versus theoretical
H$\alpha$/H$\beta$ ratios.

We used a UV SFR calibration valid for stellar mass range of 0.1-100 M⊙ and
star forming timescale $\tau=10$ Myr:

$\text{SFR}({\text{UV}_{i}})=(0.88)~{}4.3\times
10^{-47}\lambda_{i}L(\text{UV}_{i})$ (10)

where $i$ indexes the NUV and FUV effective wavelengths. For both equations,
$L$ has units ergs s-1. STARLIGHT $A_{V}$ values were used to dust-correct UV
flux via a Fitzpatrick dust extinction law with $R_{V}=3.1$, consistent with
STARLIGHT’s dust treatment described in Subsection 4.2.3 (Fitzpatrick, 1999).
Note that UV-calibrated SFR estimates carried a further 15% fractional error
added in quadrature with luminosity uncertainty (Calzetti, 2013).

Four SN Ia hosts lacked H$\alpha$ flux measurements, excluding these from
further analysis. We also note that SN Ib SN2003i’s host IC2481 had
erroneously large FUV flux uncertainty, as seen in both plots of Figure 9.

The left-hand plot from Figure 9 demonstrated expected consistency between our
NUV and FUV SFR estimates. There was a global median offset of 0.22 dex
towards higher NUV SFR estimates, an artifact in the chosen SFR calibration’s
explicit linear dependence on wavelength that is partly accounted for by the
mentioned 15% fractional error added to our estimates. Indeed, the offset
remained unchanged when UV SFR estimates uncorrected for attenuation were
instead used.

In the right-hand plot of Figure 9, we compared UV-calibrated SFR estimates to
H$\alpha$-calibrated SFR estimates from PISCO spectra. To account for
uncertainties along both axes we used LinMix to regress these UV samples
against our H$\alpha$ sample. Said regressions both had fit slopes less than
one; OLS linear regression results were nearly identical to the mean LinMix
model parameters. When UV photometry was uncorrected for dust, UV-H$\alpha$
SFR regression slopes were shallower at a 2.5$\sigma$ significance . An
physical source of the observed scatter resulted from UV flux tracing SFR
timescales of 10-100 Myr; nebular emissions such as H$\alpha$ trace a near-
instantaneous ($<10$ Myr) SFR timescale (Kennicutt, 1998). We attempted to
alleviate this by using a UV SFR relationship recalibrated for a shorter star
formation timescale ($\approx 10$ Myr), but such recalibration translates to
only a global offset in $\log_{10}(SFR)$ estimates. Readily apparent in Figure
10 is said star formation timescale reducing the fit slope in SFR sample
comparison, with UV SFR values being consistently larger than H$\alpha$ SFR
estimates in the range $\log_{10}\text{SFR}(\text{H}\alpha)<-1$
$M_{\odot}yr^{-1}$. This was consistent with H$\alpha$ and UV flux both
capturing very early star formation, but only UV flux capturing B-type stellar
flux contribution after ionizing O-type stars have died out. Difference in our
elliptical UV photometry apertures and PISCO’s hexagonal apertures contributed
to the observed scatter as well.

Figure 10: The top plot compares sSFR to stellar mass for all three flux-
calibrated SFR samples for global aperture for our 51 host SN Ia subsample.
The bottom plot similarly compares SFR to stellar mass. The lack of UV sSFR
values below -12 dex is apparent. Dashed lines are for reference.

###  5.4 sSFR Bias Comparison

Table 4: Tanh model results for sSFR samples. sSFR Sample | $sSFR_{s}$ | $\Delta\mu$ | $\Delta\mu_{0}$
---|---|---|---
51 H$\alpha$ | $-10.96\pm 0.48$ | $0.05\pm 0.03$ | $0.03\pm 0.02$
73 H$\alpha$ | $-10.83\pm 0.73$ | $0.02\pm 0.03$ | $0.02\pm 0.02$
51 H$\alpha$ & FAST++ | $-10.42\pm 0.41$ | $0.06\pm 0.03$ | $0.03\pm 0.02$
51 FUV | $-10.28\pm 0.52$ | $0.06\pm 0.02$ | $0.04\pm 0.02$
51 NUV | $-10.14\pm 0.42$ | $0.06\pm 0.02$ | $0.04\pm 0.03$

In the top plot of Figure 11 we took 51 Hubble residuals of SNe Ia with PISCO
H$\alpha$ and GALEX FUV+NUV photometry coverage to three sSFR samples: FUV and
NUV SFRs normalized by FAST++ mass estimates, and H$\alpha$ SFR normalized by
STARLIGHT mass estimates. FAST++ mass estimates were calculated with GALEX and
SDSS photometry. Linear OLS fits gave consistent slopes relative to each sSFR
sample and were each statistically consistent with a zero slope. With our
Stan-implemented tanh model we found all three 51 host sSFR samples fit for
slightly larger (and positive) step sizes than our mass step results with
H$\alpha$ giving $\Delta\mu=0.05\pm 0.02$, NUV giving $\Delta\mu=0.06\pm
0.02$, and FUV giving $\Delta\mu=0.06\pm 0.02$. NUV and FUV step locations
were $\text{sSFR}_{s}=-10.14\pm 0.42$ and $\text{sSFR}_{s}=-10.28\pm 0.52$,
respectively. The fit H$\alpha$ step location was at a 0.5 dex lower sSFR with
$\text{sSFR}_{s}=-10.96\pm 0.41$. Normalizing H$\alpha$ sSFR values with
FAST++ mass estimates gave a step location closer to its UV sSFR counterparts
with $\text{sSFR}_{s}=-10.48\pm 0.52$ and $\Delta\mu=0.06\pm 0.03$ mag. Using
instead all available 73 SN Ia hosts with global H$\alpha$ flux to fit
H$\alpha$ sSFR values against Hubble residuals saw the step size inexplicably
drop a 1$\sigma$-significant shift by 0.03 mag to only $\Delta\mu=0.02\pm
0.02$, with the step location parameter fitting for $\text{sSFR}_{s}=-10.83\pm
0.73$. This step location was effectively unconstrained within the bounds
enforced on the sampler. See Table 4 for a summary of all sSFR tanh model
results.

Figure 11: The top plot is a comparison of differing sSFR estimates to Hubble
residuals for 51 SNe Ia. The bottom plot is a comparison the H$\alpha$ sSFR
estimates using STARLIGHT or FAST++ mass estimates (consistent and
inconsistent apertures, respectively). sSFR tanh model fits are given in the
top plot for H$\alpha$ (solid orange), NUV (dotted purple), and FUV (dashed
green). The bottom plot compares H$\alpha$ sSFR normalized using STARLIGHT
(orange diamonds) and FAST++ (purple x’s) masses. The solid orange line is the
best fit tanh model for sSFR values from STARLIGHT mass estimates, the dotted
purple line is the tanh model result instead using FAST++ mass values.  Figure
12: A comparison of global sSFR estimates to SALT2 parameters $x_{1}$ (top)
and $c$ (bottom) for 51 SNe Ia. Best-fit Hubble residual step locations are
given by the vertical lines: H$\alpha$ corresponds to solid orange, NUV
corresponds to dotted purple, and FUV corresponds to dashed green. FUV and NUV
step locations overlap. The discrepancy in lower sSFR values between H$\alpha$
and UV sSFR values is clear in both plots.

In Figure 12 we compared SALT2 parameters $x_{1}$ and $c$ to the same three
sSFR samples, marking with vertical lines the best-fit sSFR step location for
each of the three samples. Obvious in this plot were the lowest H$\alpha$ sSFR
estimates being less than the lowest UV sSFR estimates by an order of
magnitude. To see if the SN Ia host bias was dependent on SFR tracer, we
calculated the rank correlations coefficient Spearman’s $\rho$ of the three
sSFR samples against SALT2 $x_{1}$. A relative comparison of these $\rho$
values demonstrated uniformity with modest rank correlation with $\rho=0.61$
for H$\alpha$, $\rho=0.66$ for NUV, and $\rho=0.62$ for FUV sSFR samples,
providing tempered support for star formation epoch (10 Myr versus 100 Myr)
being an insignificant factor in our host bias measurement. Interestingly,
when repeated with UV SFR estimates uncorrected for dust, both NUV and FUV
Spearman’s $\rho$ values decreased to $\rho=0.55$ and $\rho=0.54$,
highlighting the important of dust corrections when measuring the SN Ia host
bias.

H$\alpha$ sSFR step size parameters had uncertainties within 2$\sigma$
significance of a zero step fit, but FUV and NUV sSFR step size parameters fit
with a 3$\sigma$ significance from a zero step. Despite a modest sample size
of 51 hosts, this 3$\sigma$ significance was the the best of any step models
we fit in our analysis. The combination of SFR and stellar mass provided a
stronger and larger step signal than mass alone, consistent with both Rose et
al. (2020) and Rigault et al. (2020). The mass sample chosen to normalize
H$\alpha$ SFR values influenced sSFR step location, with H$\alpha$ SFR
normalized by FAST++ mass values having a step location closer to UV sSFR
estimates by 0.05 dex. This observed sSFR step location shift was an order of
magnitude larger than the corresponding 0.05 dex median mass offset between
these 51 FAST++ and STARLIGHT mass values. The lower minimum H$\alpha$ SFR (as
seen in Figures 10 and 12) explained the remaining difference between the the
H$\alpha$ and UV sSFR step locations. The observed step location change for
NUV and FUV sSFR samples was a consequence of an explicit wavelength
dependence in our SFR UV calibration. There was only a slight increase in step
size from H$\alpha$ to UV sSFR samples. This less than 1$\sigma$ change was
statistically insignificant and provided no evidence that tracing differing
star formation timescales influenced sSFR step size. Using all available 73
H$\alpha$ sSFR values normalized by STARLIGHT did result in weak step size
detection well within 1$\sigma$ of a zero step. When fitting for the mass step
using only these 73 PISCO hosts, we found an unconstrained mass step location,
evidence that this particular PISCO host subset simply had a weak to
nonexistent mass step signal.

We found no evidence that observation method nor fitting technique influenced
sSFR step size. Lending support to this conclusion, the host bias strength
inferred from Spearman’s $\rho$ rank correlations between $x_{1}$ and sSFR
samples were very similar. The sSFR step location was partly influenced by SFR
tracer choice. Different SFR tracers measure different star formation ages
H$\alpha$-based SFR tracks young O-type stars, while UV-based SFR includes a
wider range massive stars.

##  6 Conclusion

This project sought to determine whether different observation methods or
fitting techniques create or change the observed SN Ia host bias in the SN Ia
standardized magnitudes. When we examined subsets with more complete
complementary photometry, the reduced statistics resulted in all mass step
sizes being at or within a 2$\sigma$ significance with respect to a zero step,
ranging from -0.03$\pm$0.02 mag to -0.04$\pm$0.02 mag. Mass step size values
for our three optical wavelength mass samples (FAST++ and ZPEG with SDSS,
STARLIGHT with PISCO) were all relatively consistent, being within a 1$\sigma$
significance of each other (Table 3). The mass step location, but not size,
varied under different IMF and stellar spectra choice. Including GALEX UV when
fitting for photometric mass estimates with FAST++ led to an insignificant
0.33$\sigma$ change in mass step size and no discernible change in
corresponding step location. Not including UV information could ostensibly
influence mass step measurement, but that was not the case for our used PISCO
subsample. Given that this could matter, including available UV information
during SPS fitting is the best practice.

The dust-corrected sSFR samples were fit against Hubble residuals for a
51-host subsample with both UV and SDSS coverage alongside available H$\alpha$
flux measurements (Table 4). Physically different star formation timescales
traced by H$\alpha$ and UV flux sourced a H$\alpha$ sSFR step location
$\sim$0.7 dex lower than UV sSFR step locations. Step size parameter values
for these sSFR samples were all within 1$\sigma$ of each other. The sSFR steps
from both FUV or NUV sSFR samples were the most statistically significant of
all our step model runs at 3$\sigma$, with a step size of 0.06$\pm$0.02 mag.
Alternatively, using all available 73 PISCO SN Ia hosts with H$\alpha$ flux
produced the smallest step size of any model fit, being more than a factor of
two less than the corresponding 51 host sample H$\alpha$ step size parameter
value and within a 1$\sigma$ significance of a zero step. With the 51 PISCO
sample across all three sSFR samples the sSFR step sizes were clearly
consistent for all observation methods and fitting techniques. Thus, we
concluded that the methodology or technique choice had no significant effect
on sSFR step size measurements. Indeed, for this project only a particular
change in sample size led to a discernible change in sSFR step parameter value
for our particular data set.

We undertook this study expecting to find that these differences would matter
for the current state of SN Ia cosmology. We found that they did not in the
presently available sample, but we nevertheless urge continued attention by
the SN cosmology community to advances in our understanding of galaxy
properties. Given the complex nature of the SN Ia host bias problem, it is
paramount that galaxy community resources be researched and utilized to reach
a resolution in the future and to be mindful of coming developments in both
SED fitting and SPS research.

This work was supported in part by the US Department of Energy Office of
Science under DE-SC0007914. The authors thank the referee for their time,
patience, and valued input in reviewing this paper in its submissions. The
authors thank the Carnegie Supernova Project II for generously sharing the
SALT-2 fits for unpublished SNe Ia whose hosts were part of the PISCO sample.
The authors would also like to thank Dr. Alex Kim for both the introduction to
and guidance using Stan. L.G. acknowledges financial support from the Spanish
Ministry of Science, Innovation and Universities (MICIU) under the 2019 Ramón
y Cajal program RYC2019-027683 and from the Spanish MICIU project
PID2020-115253GA-I00. Based on observations collected at the Centro
Astronómico Hispano-Alemán (CAHA) at Calar Alto, operated jointly by Junta de
Andalucía and Consejo Superior de Investigaciones Científicas (IAA-CSIC).
Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the
Participating Institutions, the National Science Foundation, and the U.S.
Department of Energy Office of Science. The SDSS-III web site is
http://www.sdss3.org/. SDSS-III is managed by the Astrophysical Research
Consortium for the Participating Institutions of the SDSS-III Collaboration
including the University of Arizona, the Brazilian Participation Group,
Brookhaven National Laboratory, Carnegie Mellon University, University of
Florida, the French Participation Group, the German Participation Group,
Harvard University, the Instituto de Astrofisica de Canarias, the Michigan
State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence
Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max
Planck Institute for Extraterrestrial Physics, New Mexico State University,
New York University, Ohio State University, Pennsylvania State University,
University of Portsmouth, Princeton University, the Spanish Participation
Group, University of Tokyo, University of Utah, Vanderbilt University,
University of Virginia, University of Washington, and Yale University. This
publication makes use of data products from the Two Micron All Sky Survey,
which is a joint project of the University of Massachusetts and the Infrared
Processing and Analysis Center/California Institute of Technology, funded by
the National Aeronautics and Space Administration and the National Science
Foundation. Both pandas and NumPy were constantly utilized throughout this
project (Harris et al., 2020; pandas development team, 2020).

##  Appendix A Issues with 1 kpc Photometry with GALEX

We initially planned to perform 1 kpc circular aperture photometry around our
SNe Ia to compare local UV and H$\alpha$ SFR estimates, but the large GALEX
PSF proved cumbersome to work with. For pulse height bin values above 10 the
PSF FWHM averaged at 5.3” or the NUV band and 4.2” for the FUV band (Morrissey
et al., 2007). The PSF for GALEX NUV and FUV images was notably asymmetric for
many observations. Thus, we excluded local 1 kpc aperture photometry from this
project as these apertures’ angular sizes were almost always less than average
PSF as shown in Figure 13.

To get an idea of flux loss, we assumed a Gaussian profile for the PSF of a
centralized point source and calculated the fractional flux loss as 1 kpc
apertures decreased in size with increasing redshift. The left and right teal
curves in Figure 13 correspond to point source NUV and FUV flux loss fraction
with redshift, respectively. Such calculations were crude approximations of
extended structure, but the rapid blurring of UV flux with increasing redshift
was dramatically evident — only targets with $z<0.025$ did not simultaneously
suffer from $\sim 50$% point source flux loss and $\sim 50$% flux contribution
from outside the 1 kpc aperture. By $z=0.05$, you are effectively capturing
none of the true flux originating from the 1 kpc aperture, instead almost
entirely capturing photons originating from outside your aperture. This
approximation for a point source at the center of the aperture ignored the far
more complex flux blurring for a resolved host.

Motivating our use of 1 kpc aperture photometry was to better approximate
local properties such as SFR and stellar mass. This was partly in response to
GALEX’s use in past SN Ia host galaxy studies using apertures with radii as
large as 4 kpc (Rigault et al., 2015; Jones et al., 2015; Roman et al., 2018).
To treat UV flux measured from such an aperture as a proxy for local UV SFR is
not physical. Indeed, even a 1 kpc radius aperture is nearly four times the
radius of the largest molecular clouds. With these issues, it was obvious that
GALEX could not be used to reasonably estimate SFR rates smaller than the
entire host galaxy for all but the closest targets with $z<0.01$.

Figure 13: The solid monotonically-decreasing curve is the angular size of 1
kpc circular apertures in arc-seconds as a function of redshift $z$. Black
diamonds correspond to the PISCO SNe Ia with ‘usable’ 1 kpc GALEX photometry.
The horizontal orange dotted line is GALEX NUV average PSF size of 5.3″, while
the horizontal purple dashed line is GALEX FUV average PSF of 4.2″. The
monotonically-ascending teal dot-dashed curves approximates a central point
source’s NUV or FUV flux loss fraction as the 1 kpc aperture size decreases
with redshift. Teal shaded regions cover apertures with less than 50% NUV
(light+dark) and FUV (dark-only) point source flux loss.

##  Appendix B Tanh Model

Stan’s HMC sampler calculates a numerical Jacobian matrix of model parameters.
A true step function such as a Heaviside function has an undefined derivative
at the specified step location which prevented model convergence for nearly
all data sets we used. Some works form the literature instead used a logistics
function with a rapidly transitioning curve (Scolnic et al., 2018; Brout &
Scolnic, 2020; Popovic et al., 2021). We chose to use a hyperbolic tangent
function in place of a logistics function since $\tanh(0)=0$ and its
antisymmetry, although such properties were lost when adding the y-axis offset
parameter $\Delta\mu_{0}$. You can derive a a shifted tanh from a logistics
function:

$\frac{1}{1+e^{-2x}}=\frac{1}{2}+\frac{1}{2}\tanh{x}$ (B1)

A relatively loose prior was placed on $\Delta\mu$ to prevent the sampler from
getting lost at extreme $\Delta\mu$ values:

$\Delta\mu\sim\mathcal{N}(0,0.5)$ (B2)

The measured host bias step size in the literature is on the order of 0.1 mag
or less. Physically-motivated bounds were set to limit the sign of the step
based on the host galaxy property being used: $\Delta\mu\in(-\infty,0]$ and
$\Delta\mu\in[0,\infty)$ for mass and sSFR, respectively. The direction of the
host bias post-standardization is established, hence bounding the step
direction.

For both The mass and sSFR step size parameters $x_{s}(M_{\odot})\doteq M_{s}$
and $x_{s}(sSFR)\doteq sSFR_{s}$ both had a modest prior to deter the sampler
from becoming stuck at parameter boundaries:

$x_{s}\sim\mathcal{N}(c,1)$ (B3)

where $c=10$ for $M_{s}$ and $c=-11$ for $sSFR_{s}$. Values for $c$ were the
midpoints for the boundaries $M_{s}\in[9,11]$ and $sSFR_{s}\in[-12.5,-9.5]$.
These bounds were placed to keep the fit step location within the actual mass
or sSFR distribution for our subsamples used.

$\Delta\mu_{0}$ partly captured the systematic offset from zero for Hubble
residual systematic offsets. As such, we used the informative prior:

$\Delta\mu_{0}\sim\mathcal{N}\big{(}\langle\mu^{*}-\mu(z)\rangle,\text{SE}[\mu^{*}-\mu(z)]\big{)}$
(B4)

where $\text{SE}[\mu^{*}-\mu(z)]$ is the standard error of the subsample
Hubble residual mean $\langle\mu^{*}-\mu(z)\rangle$. For our 76 host SN Ia
mass subsample $\langle\mu^{*}-\mu(z)u\rangle=0.010$ mag with
$\text{SE}[\mu^{*}-\mu(z)]=0.003$ mag and for our 66 host mass subsample
$\langle\mu^{*}-\mu(z)\rangle=0.012$ mag with
$\text{SE}[\mu^{*}-\mu(z)]=0.003$ mag. For our 51 host sSFR subsample
$\langle\mu^{*}-\mu(z)\rangle=0.042$ mag with
$\text{SE}[\mu^{*}-\mu(z)]=0.004$ mag and for our 73 host sSFR subsample
$\langle\mu^{*}-\mu(z)\rangle=0.031$ mag with
$\text{SE}[\mu^{*}-\mu(z)]=0.003$ mag.

Fixing the scaling term $\alpha$ and fitting our model with values increasing
from $\alpha=0.01$ up to $\alpha=0.5$ had no appreciable effect on the sampled
posterior. If instead promoted to a free parameter and provided a uniform
prior, $\alpha$ trended to large values, resulting in a pseudo-linear
regression. Providing an informative exponential prior with $\lambda=0.3$ to
keep $\alpha$ from trending past $\alpha=1$ resulted in a near-identical
posterior to those resulting from simpler models with fixed $\alpha$.
Promoting $\lambda$ to a free hyperparameter with a inverse-gamma hyperprior
again resulted in similar results, with the data only marginally influencing
the $\lambda$ marginal posterior. We opted to leave the scaling term fixed to
$\alpha=0.01$ to provide a smooth step function approximation.

Table 5: Global mass in $\log_{10}(M/M_{\odot})$. FAST++, ZPEG masses limited to SDSS or SDSS+GALEX coverage. The first 25 entries are shown here. A full version of this table is available online. Galaxy | STARLIGHT Mass | Fast++ Mass | ZPEG Mass | Fast++ GALEX Mass
---|---|---|---|---
2MASSJ00164451 | 10.094 | 10.200 | 10.765 | –
2MASSJ00235669 | 9.653 | 9.790 | 10.192 | 9.770
2MASSJ23243021 | 10.219 | 9.910 | 10.452 | 9.890
2MASXJ22532475 | 9.891 | 9.960 | 10.348 | 10.300
2MASXJ00234829 | 10.539 | 9.850 | 10.829 | 9.860
2MASXJ01144386 | 10.434 | 10.300 | 10.723 | 10.430
2MASXJ01403375 | 10.640 | 10.760 | 11.262 | 11.000
2MASXJ02305208 | 10.013 | 9.660 | 10.787 | 10.300
2MASXJ04424248 | 11.023 | – | – | –
2MASXJ07192718 | 9.939 | – | – | –
2MASXJ08374557 | 9.387 | 9.710 | 9.436 | 9.980
2MASXJ09591230 | 9.826 | – | – | –
2MASXJ10525434 | 10.147 | 9.780 | 10.787 | –
2MASXJ12095669 | 10.285 | 10.410 | 10.816 | –
2MASXJ12385810 | 10.638 | 9.900 | 10.844 | 9.840
2MASXJ15024995 | 9.311 | 9.490 | 9.938 | –
2MASXJ15393305 | 10.996 | 11.150 | 11.530 | 11.090
2MASXJ15570268 | 9.839 | 10.080 | 10.082 | 10.080
2MASXJ16065563 | 10.163 | 10.050 | 10.500 | 10.240
2MASXJ16152860 | 9.807 | 9.950 | 10.207 | 10.030
2MASXJ16301506 | 10.725 | 10.450 | 10.910 | 10.390
2MASXJ17100856 | 10.202 | 10.170 | 10.605 | 10.160
2MASXJ18242915 | 9.475 | – | – | –
2MASXJ21352164 | 11.302 | 11.160 | 11.360 | 11.200
2MASXJ23024668 | 10.675 | 10.640 | 11.161 | 10.650
Table 6: Global SFR in $M_{\odot}\text{yr}^{-1}$. Galaxy | FAST++ SFR | H$\alpha$ SFR | NUV SFR | FUV SFR | ZPEG SFR
---|---|---|---|---|---
2MASXJ22532475 | 0.692 | 0.395 | 1.253 | 0.577 | 0.000
2MASXJ00234829 | 141.254 | 3.910 | 20.854 | 10.341 | 124.738
2MASXJ01144386 | 3.388 | 1.692 | 2.822 | 1.638 | 13.274
2MASXJ08374557 | 10.715 | 1.649 | 3.722 | 1.596 | 16.866
2MASXJ15570268 | 0.741 | 0.010 | 0.367 | 0.211 | 10.864
2MASXJ16152860 | 0.724 | 0.108 | 0.981 | 0.538 | 0.551
2MASXJ16301506 | 27.542 | 1.632 | 3.108 | 2.095 | 19.861
2MASXJ17100856 | 0.020 | 0.034 | 0.268 | 0.245 | 1.782
2MASXJ23024668 | 0.000 | 0.263 | 0.105 | 0.075 | 4.634
ARP143 | 4.898 | 1.482 | 5.137 | 3.094 | 5.383
ARP70 | 26.303 | 1.215 | 4.171 | 2.908 | 7.194
CGCG004-035 | 3.890 | 0.542 | 2.596 | 1.455 | 5.012
CGCG008-023 | 1.318 | 2.253 | 6.753 | 3.583 | 1.315
CGCG047-117 | 64.565 | 3.356 | 5.592 | 3.931 | 14.454
CGCG107-031 | 0.380 | 0.029 | 0.415 | 0.352 | 0.000
CGCG207-042 | 3.467 | 1.071 | 3.151 | 2.100 | 40.832
CGCG308-009 | 0.209 | 0.023 | 0.185 | 0.144 | 0.000
CGCG476117 | 51.286 | 1.193 | 2.242 | 1.362 | 8.433
FGC175A | 0.155 | 0.260 | 1.076 | 1.318 | 1.239
GALEXASCJ012052 | 1.202 | 0.176 | 1.806 | 1.020 | 1.622
GALEXASCJ234457 | 30.903 | 0.495 | 3.326 | 2.141 | 26.363
IC0208 | 2.291 | 0.245 | 1.071 | 0.623 | 6.180
IC0701 | 11.749 | 2.350 | 2.752 | 1.749 | 8.610
IC0758 | 4.677 | 0.044 | 0.160 | 0.116 | 6.353
IC1481 | 3.020 | 1.411 | 6.567 | 2.494 | 19.588
Table 7: Properties of SNe Ia considered in this work. Light-curve fit parameters $x_{0}$, $x_{1}$ and $c$ were determined using the SALT2 supernova model. The first 25 entries are shown here. A full version of this table is available online. SN | Survey | $\mu$ | RA | Dec | z | $x_{0}$ | $x_{1}$ | $c$ | M${}_{\text{B}}$ | $\mu_{SN}-\mu_{mod}$ | Galaxy
---|---|---|---|---|---|---|---|---|---|---|---
ASASSN-14kd | CSPII | 35.001 | 343.353 | 4.799 | 0.023 | 0.006 | 1.090 | 0.144 | 16.207 | 0.025 | 2MASXJ22532475
ASASSN-14lo | CSPII | 34.700 | 177.969 | 18.546 | 0.020 | 0.007 | -0.487 | 0.093 | 16.032 | 0.012 | UGC6837
ASASSN-14my | CSPII | 34.706 | 174.626 | -8.976 | 0.020 | 0.011 | -0.578 | -0.060 | 15.550 | -0.045 | NGC3774
ASASSN-15cb | CSPII | 36.204 | 189.959 | 3.797 | 0.040 | 0.003 | 0.918 | 0.025 | 17.049 | -0.031 | CGCG042-196
ASASSN-15cd | CSPII | 36.117 | 149.812 | 12.988 | 0.034 | 0.004 | 0.322 | -0.097 | 16.670 | 0.226 | CGCG064-017
ASASSN-15db | CSPII | 33.475 | 236.745 | 17.884 | 0.011 | 0.024 | -0.530 | 0.051 | 14.677 | 0.093 | NGC5996
ASASSN-15dd | CSPII | 34.969 | 235.995 | 19.212 | 0.024 | 0.007 | -1.314 | -0.020 | 16.083 | -0.163 | CGCG107-031
ASASSN-15ga | PS1 | 32.511 | 194.864 | 14.171 | 0.007 | 0.022 | -1.015 | 0.305 | 14.642 | 0.234 | NGC4866
ASASSN-15tz | PS1 | 34.991 | 40.287 | 43.680 | 0.024 | 0.004 | -1.620 | 0.057 | 16.418 | -0.110 | UGC2164
CSP13n | CSPII | 36.367 | 144.967 | 16.918 | 0.048 | 0.003 | 0.607 | -0.051 | 17.019 | -0.264 | CGCG092-024
iPTF13dkl | PS1 | 36.759 | 356.242 | 3.395 | 0.040 | 0.001 | 0.631 | 0.001 | 17.580 | 0.525 | GALEXASCJ234457
iPTF13dym | CSPII | 35.846 | 351.126 | 14.651 | 0.042 | 0.002 | -3.170 | 0.075 | 17.621 | -0.504 | 2MASSJ23243021
iPTF14aaf | CSPII | 37.015 | 219.211 | 6.139 | 0.059 | 0.001 | 0.524 | 0.058 | 18.043 | -0.086 | CGCG047-117
iPTF14bdn | MISC | 34.334 | 202.687 | 32.761 | 0.016 | 0.021 | 1.534 | -0.083 | 14.705 | 0.085 | UGC08503
iPTF14gnl | CSPII | 36.896 | 5.951 | -3.856 | 0.054 | 0.002 | 0.587 | -0.081 | 17.453 | 0.002 | 2MASXJ00234829
LSQ12gef | CSPII | 37.232 | 25.141 | 18.511 | 0.064 | 0.000 | 1.058 | 0.293 | 18.937 | -0.065 | 2MASXJ01403375
LSQ12hzj | CSPII | 35.821 | 149.801 | -9.003 | 0.035 | 0.004 | -0.310 | -0.091 | 16.512 | -0.089 | 2MASXJ09591230
LSQ13vy | CSPII | 36.243 | 241.732 | 3.001 | 0.042 | 0.002 | -1.105 | 0.087 | 17.671 | -0.088 | 2MASXJ16065563
LSQ14ajn | CSPII | 34.918 | 178.877 | 11.924 | 0.021 | 0.006 | -1.950 | 0.017 | 16.273 | 0.113 | PGC37426
LSQ14azy | CSPII | 36.601 | 168.145 | 12.072 | 0.046 | 0.001 | 0.182 | 0.073 | 17.742 | 0.065 | 2MASXJ11123493
LSQ14q | CSPII | 37.456 | 133.488 | 17.328 | 0.067 | 0.001 | -0.430 | -0.094 | 18.160 | 0.062 | SDSSJ08535700
LSQ15aae | CSPII | 36.755 | 247.563 | 5.931 | 0.052 | 0.001 | 1.120 | 0.127 | 17.899 | -0.049 | 2MASXJ16301506
LSQ15agh | CSPII | 37.180 | 163.226 | 23.598 | 0.060 | 0.001 | 0.958 | -0.053 | 17.760 | 0.036 | 2MASXJ10525434
PS15sv | CSPII | 35.651 | 243.299 | 1.592 | 0.033 | 0.005 | 0.319 | -0.031 | 16.423 | -0.173 | GALEXASCJ161311
SN1989a | MISC | 32.926 | 171.992 | 29.510 | 0.009 | 0.046 | -0.104 | -0.010 | 13.848 | -0.103 | NGC3687
Table 8: Galaxy coverage and fit successes. All photometry mass fits were successful.The first 25 entries are shown here. A full version of this table is available online. Galaxy | RA | Dec | $z$ | GALEX | SDSS | 2MASS | SFR | STARLIGHT Mass
---|---|---|---|---|---|---|---|---
2MASSJ00164451 | 4.185 | 15.342 | 0.070 | X | X | X |  | X
2MASSJ00235669 | 5.986 | 29.522 | 0.073 | X | X | X |  | X
2MASSJ23243021 | 351.126 | 14.651 | 0.042 | X | X | X |  | X
2MASXJ22532475 | 343.353 | 4.799 | 0.024 | X | X | X | X | X
2MASXJ00234829 | 5.951 | -3.856 | 0.054 | X | X | X | X | X
2MASXJ01144386 | 18.683 | 0.286 | 0.045 | X | X | X | X | X
2MASXJ01403375 | 25.141 | 18.511 | 0.064 | X | X | X |  | X
2MASXJ02305208 | 37.717 | 22.476 | 0.031 | X | X | X |  | X
2MASXJ04424248 | 70.677 | 18.583 | 0.016 | X | X | X |  | X
2MASXJ07192718 | 109.863 | 54.229 | 0.067 | X | X | X |  | X
2MASXJ08374557 | 129.440 | 49.478 | 0.052 | X | X | X | X | X
2MASXJ09591230 | 149.801 | -9.003 | 0.033 | X | X | X |  | X
2MASXJ10525434 | 163.226 | 23.598 | 0.060 |  | X | X |  | X
2MASXJ11123493 | 168.145 | 12.072 | 0.046 | X | X | X |  |
2MASXJ11500404 | 177.517 | 21.280 | 0.026 | X | X | X |  |
2MASXJ12095669 | 182.486 | 47.096 | 0.031 |  | X | X |  | X
2MASXJ12385810 | 189.742 | 11.131 | 0.060 | X | X | X |  | X
2MASXJ15024995 | 225.708 | 48.784 | 0.026 |  | X | X |  | X
2MASXJ15393305 | 234.888 | 32.094 | 0.054 | X | X | X |  | X
2MASXJ15570268 | 239.261 | 37.417 | 0.031 | X | X | X | X | X
2MASXJ16065563 | 241.732 | 3.001 | 0.042 |  | X | X |  | X
2MASXJ16152860 | 243.869 | 19.226 | 0.033 | X | X | X | X | X
2MASXJ16301506 | 247.563 | 5.931 | 0.052 | X | X | X | X | X
2MASXJ17100856 | 257.536 | 74.729 | 0.042 | X | X | X | X | X
2MASXJ18242915 | 276.122 | 52.444 | 0.030 | X | X | X |  | X
Table 9: In-house global photometry for SDSS and GALEX. Only GALEX photometry with SDSS coverage was measured. Given as AB magnitudes; -99 marks negative flux. The first 25 entries are shown here. A full version of this table is available online. Galaxy | $m_{u}$ | $\sigma_{m_{u}}$ | $m_{g}$ | $\sigma_{m_{g}}$ | $m_{r}$ | $\sigma_{m_{r}}$ | $m_{i}$ | $\sigma_{m_{i}}$ | $m_{z}$ | $\sigma_{m_{z}}$ | $m_{NUV}$ | $\sigma_{m_{NUV}}$ | $m_{FUV}$ | $\sigma_{m_{FUV}}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
2MASSJ00164451 | 19.522 | 0.258 | 17.730 | 0.020 | 16.919 | 0.014 | 16.485 | 0.015 | 16.128 | 0.050 | -99.000 | -99.000 | -99.000 | -99.000
2MASSJ00235669 | 17.894 | 0.054 | 16.737 | 0.005 | 16.492 | 0.007 | 16.280 | 0.009 | 16.109 | 0.028 | 18.676 | 0.048 | 19.239 | 0.106
2MASSJ23243021 | 19.010 | 0.118 | 17.363 | 0.009 | 16.539 | 0.006 | 16.119 | 0.007 | 15.930 | 0.028 | 22.980 | 0.398 | 23.196 | 0.514
2MASXJ00234829 | 16.298 | 0.046 | 15.597 | 0.006 | 15.074 | 0.007 | 14.675 | 0.008 | 14.783 | 0.030 | 17.661 | 0.034 | 18.158 | 0.064
2MASXJ01144386 | 16.983 | 0.071 | 15.902 | 0.008 | 15.286 | 0.007 | 14.940 | 0.008 | 14.734 | 0.034 | 18.174 | 0.056 | 18.523 | 0.092
2MASXJ01403375 | 17.235 | 0.092 | 15.842 | 0.008 | 15.147 | 0.007 | 14.735 | 0.007 | 14.384 | 0.018 | 18.693 | 0.090 | 18.925 | 0.135
2MASXJ02305208 | 17.268 | 0.066 | 16.119 | 0.007 | 15.248 | 0.004 | 14.721 | 0.004 | 14.591 | 0.012 | 19.920 | 0.489 | -99.000 | -99.000
2MASXJ08374557 | 17.472 | 0.077 | 16.399 | 0.011 | 15.936 | 0.011 | 15.509 | 0.011 | 15.342 | 0.033 | 18.813 | 0.097 | 19.552 | 0.212
2MASXJ10525434 | 17.080 | 0.053 | 16.179 | 0.007 | 15.638 | 0.007 | 15.341 | 0.008 | 15.151 | 0.034 | -99.000 | -99.000 | -99.000 | -99.000
2MASXJ11123493 | 17.033 | 0.052 | 16.064 | 0.007 | 15.447 | 0.006 | 15.068 | 0.007 | 14.688 | 0.025 | 18.422 | 0.050 | 19.284 | 0.163
2MASXJ11500404 | 17.178 | 0.039 | 15.635 | 0.005 | 14.875 | 0.003 | 14.513 | 0.004 | 14.262 | 0.009 | 20.588 | 0.222 | -99.000 | -99.000
2MASXJ12095669 | 17.249 | 0.048 | 15.797 | 0.005 | 14.970 | 0.004 | 14.565 | 0.004 | 14.281 | 0.012 | -99.000 | -99.000 | -99.000 | -99.000
2MASXJ12385810 | 17.352 | 0.079 | 16.419 | 0.011 | 15.782 | 0.010 | 15.459 | 0.011 | 15.080 | 0.028 | 19.298 | 0.116 | 19.734 | 0.248
2MASXJ15024995 | 17.948 | 0.092 | 16.413 | 0.012 | 15.845 | 0.009 | 15.433 | 0.010 | 15.326 | 0.030 | -99.000 | -99.000 | -99.000 | -99.000
2MASXJ15393305 | 16.579 | 0.054 | 15.286 | 0.005 | 14.449 | 0.004 | 14.054 | 0.004 | 13.822 | 0.011 | 18.930 | 0.101 | 22.090 | 1.304
2MASXJ15570268 | 17.752 | 0.083 | 16.374 | 0.008 | 15.580 | 0.006 | 15.280 | 0.007 | 14.869 | 0.025 | 20.112 | 0.295 | 20.519 | 0.546
2MASXJ16065563 | 16.311 | 0.056 | 15.230 | 0.008 | 14.891 | 0.008 | 14.522 | 0.008 | 14.502 | 0.036 | 17.177 | 0.037 | 17.599 | 0.107
2MASXJ16152860 | 18.085 | 0.134 | 16.823 | 0.012 | 16.104 | 0.010 | 15.700 | 0.012 | 15.442 | 0.032 | 20.148 | 0.189 | 21.911 | 1.727
2MASXJ16301506 | 16.960 | 0.064 | 15.789 | 0.008 | 15.144 | 0.006 | 14.761 | 0.006 | 14.468 | 0.022 | 18.730 | 0.105 | 19.668 | 0.294
2MASXJ17100856 | 17.798 | 0.076 | 16.191 | 0.006 | 15.471 | 0.005 | 15.108 | 0.005 | 14.809 | 0.019 | 21.724 | 0.668 | 20.789 | 0.429
2MASXJ21352164 | 17.328 | 0.130 | 15.943 | 0.009 | 15.062 | 0.006 | 14.499 | 0.005 | 14.250 | 0.015 | -99.000 | -99.000 | 20.613 | 1.575
2MASXJ22532475 | 17.066 | 0.077 | 15.499 | 0.005 | 14.814 | 0.005 | 14.483 | 0.005 | 14.212 | 0.020 | 18.084 | 0.059 | 19.099 | 0.163
2MASXJ23024668 | 17.992 | 0.104 | 16.219 | 0.006 | 15.345 | 0.004 | 14.902 | 0.004 | 14.561 | 0.010 | 21.219 | 0.097 | 22.513 | 0.326
ARP143 | 13.572 | 0.007 | 12.328 | 0.001 | 11.720 | 0.001 | 11.417 | 0.001 | 11.179 | 0.004 | 14.712 | 0.010 | 15.149 | 0.019
ARP70 | 15.566 | 0.047 | 14.259 | 0.004 | 13.531 | 0.003 | 13.068 | 0.003 | 12.797 | 0.010 | 17.264 | 0.033 | 18.020 | 0.075
Table 10: In-house global photometry 2MASS. Only 2MASS photometry with SDSS coverage was measured. Given as AB magnitudes. -99 marks negative flux. The first 25 entries are shown here. A full version of this table is available online. Galaxy | $m_{H}$ | $\sigma_{m_{H}}$ | $m_{J}$ | $\sigma_{m_{J}}$ | $m_{K}$ | $\sigma_{m_{K}}$
---|---|---|---|---|---|---
2MASSJ00164451 | 15.485 | 0.397 | 16.047 | 0.451 | 16.439 | 1.304
2MASSJ00235669 | 15.755 | 0.479 | 16.203 | 0.475 | 18.210 | 5.562
2MASSJ23243021 | 15.358 | 0.324 | 15.465 | 0.268 | 15.180 | 0.404
2MASXJ00234829 | 13.329 | 0.171 | 14.607 | 0.326 | 14.105 | 0.417
2MASXJ01144386 | -99.000 | -99.000 | 14.672 | 0.377 | 14.144 | 0.455
2MASXJ01403375 | 13.856 | 0.208 | 14.157 | 0.182 | 13.793 | 0.242
2MASXJ02305208 | 13.160 | 0.100 | 13.805 | 0.104 | 13.574 | 0.134
2MASXJ08374557 | 14.847 | 0.462 | 15.332 | 0.506 | 14.678 | 0.456
2MASXJ10525434 | -99.000 | -99.000 | 15.940 | 0.948 | -99.000 | -99.000
2MASXJ11123493 | 14.657 | 0.504 | 14.719 | 0.399 | 14.487 | 0.567
2MASXJ11500404 | 12.939 | 0.120 | 13.699 | 0.097 | 13.465 | 0.150
2MASXJ12095669 | 14.019 | 0.268 | 14.034 | 0.156 | 14.034 | 0.250
2MASXJ12385810 | 16.121 | 2.423 | 15.263 | 0.731 | 14.925 | 0.922
2MASXJ15024995 | 14.778 | 0.570 | 15.113 | 0.463 | 14.607 | 0.453
2MASXJ15393305 | 12.818 | 0.127 | 13.347 | 0.129 | 13.106 | 0.165
2MASXJ15570268 | 14.630 | 0.406 | 14.387 | 0.203 | 14.981 | 0.547
2MASXJ16065563 | 13.338 | 0.244 | 13.982 | 0.316 | 13.817 | 0.426
2MASXJ16152860 | 13.842 | 0.192 | 14.678 | 0.251 | 14.398 | 0.321
2MASXJ16301506 | 13.701 | 0.179 | 13.994 | 0.158 | 13.769 | 0.232
2MASXJ17100856 | 14.163 | 0.183 | 14.317 | 0.139 | 13.955 | 0.189
2MASXJ21352164 | 13.649 | 0.231 | 13.797 | 0.180 | 14.021 | 0.288
2MASXJ22532475 | 14.868 | 0.777 | 13.796 | 0.187 | 14.147 | 0.419
2MASXJ23024668 | 13.672 | 0.143 | 14.053 | 0.097 | 14.050 | 0.158
ARP143 | 11.349 | 0.082 | 10.893 | 0.035 | 11.070 | 0.066
ARP70 | 12.872 | 0.270 | 12.415 | 0.098 | 12.783 | 0.194

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