[ Article ]
Journal of the Korean Astronomical Society - Vol. 52, No. 5, pp.181-205
ISSN: 1225-4614 (Print) 2288-890X (Online)
Print publication date 31 Oct 2019
Received 10 Apr 2019 Accepted 06 Aug 2019

# ENVIRONMENTAL DEPENDENCE OF TYPE IA SUPERNOVA LUMINOSITIES FROM THE YONSEI SUPERNOVA CATALOG

YOUNG-LO KIM1, 2 ; YIJUNG KANG2 ; YOUNG-WOOK LEE2
1Universit´e de Lyon, F-69622, Lyon, France; Universit´e de Lyon 1, Villeurbanne; CNRS/IN2P3, Institut de Physique Nucl´eaire de Lyon y.kim@ipnl.in2p3.fr
2Center for Galaxy Evolution Research and Department of Astronomy, Yonsei University, Seoul 03722

Correspondence to: Y.-L. Kim

Published under Creative Commons license CC BY-SA 4.0

## Abstract

There is evidence that the luminosities of Type Ia supernova (SN Ia) depend on their environments. While the impact of this trend on estimating cosmological parameters is widely acknowledged, the origin of this correlation is still under debate. In order to explore this problem, we first construct the YONSEI (YOnsei Nearby Supernova Evolution Investigation) SN catalog. The catalog consists of 1231 spectroscopically confirmed SNe Ia over a wide redshift range (0.01 < z < 1.37) from various SN surveys and includes light-curve fit data from two independent light-curve fitters, SALT2 and MLCS2k2. For a sample of 674 host galaxies, we use the stellar mass and the star formation rate data in Kim et al. (2018). We find that SNe Ia in low-mass and star-forming host galaxies are 0.062 ± 0.009 mag and 0.057 ± 0.010 mag fainter than those in high-mass and passive hosts, after light-curve corrections with SALT2 and MLCS2k2, respectively. When only local environments of SNe Ia (e.g., locally star-forming and locally passive) are considered, this luminosity difference increases to 0.081 ± 0.018 mag for SALT2 and 0.072 ± 0.018 mag for MLCS2k2. Considering the significant difference in the mean stellar population age between the two environments, this result suggests that the luminosity evolution of SNe Ia with redshift is most likely the origin of the environmental dependence.

## Keywords:

cosmology: observations, distance scale, supernovae: general

## 1. INTRODUCTION

Observations of distant Type Ia supernovae (SNe Ia) revealed the accelerating expansion of the universe (Riess et al. 1998; Perlmutter et al. 1999). The use of SNe Ia as a distance indicator is based on two fundamental ideas. Firstly, SN Ia luminosities can be empirically standardized (Phillips 1993; Tripp 1998). This is achieved with empirical light-curve fitters, such as SALT2 (Guy et al. 2007) and MLCS2k2 (Jha et al. 2007), that correct the observed “brighter-slower” and the “brighter-bluer” relations. This light-curve standardization reduces the scatter of SN Ia peak luminosity from ~0.3 mag to ~0.14 mag (Guy et al. 2007; Jha et al. 2007).

Secondly, the standardization does not evolve with redshift or SN environment. This idea was initially supported by small samples of SNe Ia and their host galaxies: no clear dependence of SNe Ia luminosity, after light-curve shape and color or extinction corrections, on their host morphology was shown (Riess et al. 1998; Schmidt et al. 1998). However, more recent studies with larger numbers of SNe Ia have revealed ~2σ trends between the corrected SN luminosity and host galaxy morphology. SNe Ia in early-type galaxies are brighter than those in late-type galaxies, both at low and high redshift (Hicken et al. 2009b; Suzuki et al. 2012).

The correlations between corrected luminosity of SNe Ia and host galaxy properties are being investigated intensively, both observationally (Gallagher et al. 2008; Kelly et al. 2010; Lampeitl et al. 2010; Sullivan et al. 2010; D’Andrea et al. 2011; Gupta et al. 2011; Childress et al. 2013; Johansson et al. 2013; Pan et al. 2014; Campbell et al. 2016; Wolf et al. 2016) and theoretically (Höflich et al. 1998; Timmes et al. 2003; Kasen et al. 2009). All these studies conclude that SNe in latetype, star-forming, low-mass, and low-metallicity hosts are ~0.1 mag fainter than those in early-type, passive, high-mass, and high-metallicity galaxies. Likewise, recent studies focused on the “local” environment at the SN explosion site (Rigault et al. 2013, 2015, 2018; Jones et al. 2018b; Kim et al. 2018; Roman et al. 2018) find a systematic luminosity difference which is of the same order of magnitude.

Considering the intrinsic scatter of ~0.14 mag on the SN Ia luminosity after empirical light-curve corrections, a systematic ~0.1 mag difference implies that there are physical processes operating in SNe Ia, such as different SN Ia populations and/or different explosion mechanisms, that we do not fully understood yet. It is therefore important to investigate the origin of the environmental dependence of SN Ia luminosities to understand the underlying physics of SNe, not least to make SNe more accurate standard candles. Some studies suggest that the environmental dependence arises from differences in the physical properties of progenitor stars or of the stellar populations in the host galaxy, for example in age or metallicity (Timmes et al. 2003; Kasen et al. 2009; Johansson et al. 2013; Childress et al. 2014; Pan et al. 2014; Kang et al. 2016). However, most of the previous works are limited in sample size and the redshift range because they only include SNe found in specific surveys (e.g., SDSS-II SNe survey or SN Legacy survey) and analyzed the data with one specific lightcurve fitter (especially SALT2). In order to investigate the origin of the luminosity difference and the underlying physics in detail, we have to combine data from several surveys to increase the sample size. As part of the YOnsei Nearby SN Evolution Investigation (YONSEI; Kim et al. 2015; Kang et al. 2016) project, we present in this article the YONSEI SN catalog which provides a sample of 1231 spectroscopically confirmed SNe Ia and 674 host galaxies and which utilizes two independent light-curve fitters, SALT2 and MLCS2k2. Using our catalog, we present an extensive study of the depndence of SN Ia luminosities on the global and local host properties.

## 2. THE YONSEI SUPERNOVA CATALOG

For the YONSEI project, we constructed our own catalog of SNe Ia. We employed the SALT2 and MLCS2k2 light-curve fitters implemented in the SuperNova ANAlysis software (hereafter SNANA; Kessler et al. 2009b) package version 10 34. We included 1231 SNe Ia with redshifts 0.01 ≤ z ≤ 1.37, which makes our catalog a superset of all SN Ia surveys adopted by the SNANA package.

### 2.1. Datasets

We took SN Ia light-curve data from several surveys compiled in the SNANA package except of the Pan- STARRS SN Ia data (hereafter PS, 146 SNe; Rest et al. 2014). Rest et al. (2014) provides the PS lightcurves in the SNANA format, allowing us to add the PS sample to the SNANA light-curve archive. For the “LOWZ” SNe Ia in SNANA (see Table 1), we use the JRK07 compilation of SNe collected from Calan/Tololo (29 SNe; Hamuy et al. 1996a,b), CfA1 (22 SNe; Riess et al. 1999a), CfA2 (44 SNe; Jha et al. 2006), and other sources (38 SNe; Jha et al. 2007). We also include CfA3 (185 SNe; Hicken et al. 2009a), CfA4 (94 SNe; Hicken et al. 2012), CSP DR1/2 (hereafter CSP, 85 SNe; Contreras et al. 2010; Stritzinger et al. 2011) into our LOWZ sample. In addition, the full three-year SDSS-II SNe survey (hereafter SDSS, 500 SNe; Sako et al. 2018), ESSENCE survey (60 SNe; Miknaitis et al. 2007), the first three years of the Supernova Legacy survey (hereafter SNLS, 281 SNe; Guy et al. 2010), and the HST sample (37 SNe; Riess et al. 2004, 2007) are used to construct our intermediate- and high-redshift SN samples. In total, we included 1521 SNe Ia into our light-curve analysis (see Table 2). Whenever a specific SN has been covered by more than one survey, we use the dataset with the most observations (see e.g., Rest et al. 2014).

Contributions to the LOWZ sample in the YONSEI SN catalog

Sample sizes and cuts for each sample in the YONSEI SN catalog

### 2.2. Light-Curve Analysis

2.2.1. The SALT2 and MLCS2k2 Light-Curve Fitters

The SNANA package was originally developed for the analysis of SDSS SNe data and later adopted for simulating and fitting the SN Ia light-curves obtained by different surveys and from different telescopes. SNANA contains a light-curve simulator, a light-curve fitter, and a cosmology fitter for all types of SNe. The primary goal of the SNANA package is to use SNe Ia as distance indicators to derive cosmological parameters. In addition, it can be employed to study the SN rate taking into account selection efficiencies, estimate the non-Ia contamination, and optimize future SN surveys. In the SNANA package, most of the current SN models and non-Ia models are included. For the YONSEI catalog, we employed the most up-to-date SALT2 (version 2.4 from Betoule et al. (2014)) and MLCS2k2 (with RV = 2.2) light-curve fitters. For the MLCS2k2, we select a flat prior allowing negative AV values, and RV = 2.2 for the dust reddening parameter, which is the same value as in Kessler et al. (2009a).

Th light-curve fitters SALT2 and MLCS2k2 determine the luminosity distance (μSN) by means of a linear function of light-curve shape and color or extinction parameters (Tripp 1998)

 (1)

where mB is the observed rest-frame peak apparent magnitude in B-band, MB is the absolute magnitude determined from the SN intrinsic luminosity, and α and β are global parameters that characterize the brighter–slower and brighter–bluer relations, respectively. SALT2 and MLCS2k2 fit each observed lightcurve for the peak magnitude, the shape parameter (X1 for SALT2 and ∆ for MLCS2k2), and the color (C for SALT2) or host galaxy extinction value (AV for MLCS2k2), under the implicit assumption that SNe Ia light-curves at low and high redshifts, for given shapes and colors, are intrinsically identical. However, these fitters have different ways of estimating model parameters from light-curve data, use different approaches to training the models, and employ different assumptions about the treatment of color variations in SNe Ia. SALT2 is calibrated with data from SNe across all redshifts, while MLCS2k2 is calibrated solely using SNe at low redshifts (see e.g., Guy et al. 2010; Betoule et al. 2014; Jones et al. 2015). At high redshift, young progenitors might be dominant, while young and old progenitors are expected to be mixed at low redshift. Therefore, a luminosity evolution effect would be more diluted in SALT2 than in MLCS2k2, making MLCS2k2 potentially more powerful for constraining the luminosity evolution of SNe Ia. We hence use both fitters, analyze their results separately, and compare the results afterwards.

2.2.2. Initial Cut Criteria

We analyzed our 1521 SN light-curves with SALT2 and MLCS2k2 fitters after an initial cut. The criteria used for the initial cut are based on 1) the light-curve data quality, 2) the light-curve fit quality, and 3) the redshift, which are similar to the criteria adopted in Betoule et al. (2014), Rest et al. (2014), and Sako et al. (2018). Out of the 1521 SNe, 1182 and 1188 pass the initial test when using SALT2 andMLCS2k2, respectively. We detail the selection criteria below; the number of sources from each dataset is listed in Table 2.

Our light-curve data quality criteria are the following:

1-1. At least 1 measurement with −20 days < t < +10 days, where t is the rest-frame phase relative to the time of maximum light in B-band.

1-2. At least 1 measurement with 0 days < t < +50 days.

1-3. At least 3 measurements between 20 days < t < +50 days.

1-4. 2 or more filters with signal-to-noise ratio ≥ 3.

Our light-curve fit quality and redshift criteria are:

2-1. Pfit ≥ 0.01, where Pfit is the SNANA light-curve fit probability based on the χ2 per degree of freedom.

2-2. Visual inspection of the SN light-curve fit.

3-1. z ≥ 0.01, to include only SNe Ia in the Hubble flow.

Conley et al. (2011) pointed out that automatic quality cuts based on goodness-of-fit χ2 statistics (e.g., Pfit) are frequently misleading, especially in case of the LOWZ sample. Many SNe light-curves in the LOWZ sample show outliers which have little or no effect on the light-curve fitting but cause large χ2 values. We therefore used visual inspection together with the value of Pfit to assess the light-curve fit quality.

2.2.3. Bias Correction and Error Analysis

Before attempting to derive cosmological parameters from our data, we need to assess selection biases and the uncertainties in distance modulus. SN samples from flux-limited surveys are affected by the Malmquist bias (Malmquist 1936): intrinsically brighter and slowly declining SNe Ia remain above a given detection threshold for a longer time than intrinsically fainter and fast declining SNe, and hence are easier to observe. This leads to the incorrect impression that SN Ia luminosities increase with distance and results in SN luminosity distance estimates being systematically too small. Since the level of bias differs among surveys, we need to correct for it survey by survey. We take correction terms for LOWZ, SDSS, and SNLS samples from Betoule et al. (2014), who use a sample very similar to our catalog. For the PS and ESSENCE samples, we take correction terms from Rest et al. (2014) and Wood-Vasey et al. (2007), respectively. We do do apply a bias correction to the HST sample; Strolger et al. (2004) argued that the HST images are sufficiently deep to avoid significant Malmquist bias out to the maximum redshift where SN are discovered (see also Conley et al. 2011). We interpolate the correction value for each SN at a given redshift (Figure 1) and subtract this value from all rest-frame peak magnitudes in the B-band for SALT2 and all distance moduli for MLCS2k2.

Malmquist bias correction as function of redshift and survey. We subtract the appropriate values from the rest-frame peak magnitudes in B-band and the distance moduli for SALT2 and MLCS2k2, respectively.

The total uncertainty follows from the propagation of statistical and systematic uncertainties. Systematic uncertainties are associated with the calibration, the light-curve model uncertainty, the host dependency, and so on. As our purpose is to investigate a specific systematic effect – the dependence on the host – we consider only the statistical uncertainties in the following.

Following Conley et al. (2011) and Betoule et al. (2014), the (statistical) uncertainty for each SN is propagated like

 ${\sigma }_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}^{2}={\sigma }_{\mathrm{f}\mathrm{i}\mathrm{t}}^{2}+{\sigma }_{\mathrm{z}}^{2}+{\sigma }_{\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{s}}^{2}+{\sigma }_{\mathrm{i}\mathrm{n}\mathrm{t}}^{2},$ (2)

where σfit is the error on the best-fit light-curve parameters estimated from SALT2 and MLCS2k2, σz accounts for the redshift determination uncertainty, σlens represents the statistical variation of magnitudes caused by gravitational lensing, and σint is the intrinsic scatter of SNe Ia luminosities that is required to arrive at χ2/d.o.f. = 1 (unity reduced ${\chi }_{\mathrm{r}\mathrm{e}\mathrm{d}}^{2}$) for the best-fit cosmology. Our approximation of the redshift uncertainty follows Equation (5) of Conley et al. (2011), and the random, uncorrelated scatter due to lensing follows the suggestion by Jönsson et al. (2010): σlens = 0.055 × z. We do not include an intrinsic scatter term into our analysis, as our study is based on the presumption that a physical, systematic variation in SN Ia luminosities as function of host galaxy properties may be present (D’Andrea et al. 2011; Gupta et al. 2011; Pan et al. 2014).

### 2.3. YONSEI Supernova Catalog and Systematic Tests

After applying bias correction and error propagation we have the YONSEI SN Catalog (see Table 3). This catalog provides either the rest-frame peak magnitude in B-band or the distance modulus, a light-curve shape parameter, and either a color or a host extinction value for each SN. Because both normal and peculiar SNe Ia are included, we refer to this catalog as the YONSEI “All” sample to distinguish it from the YONSEI “Cosmology” sample, which only comprises normal SNe (described in the next section). The redshift distribution of the YONSEI All sample is shown in Figure 2.

Redshift distribution of the YONSEI All sample. Histogram colors indicate the various surveys. The first bin of the LOWZ sample contains 268 SNe Ia.

2.3.1. Light-Curve Shape and Color or Extinction Values as Function of Redshift

In Figures 3 and 4, we show the distributions of best-fit shapes (for both SALT2 and MLCS2k2) and either colors (for SALT2) or host extinctions (for MLCS2k2), as function of redshift. At high redshifts, we do not find faint and red (or highly reddened) SNe Ia. However, it is unclear whether this is because of the flux limits of the surveys or the luminosity evolution of SNe Ia. Since we choose a flat prior for the distribution of extinction values, thus allowing for negative AV , in MLCS2k2 (see Section 2.1), we find multiple SNe with AV < 0 in the right panel of Figure 4. However, the negative-AV distribution has little effect on the ∆ distribution (Kessler et al. 2009a).

Distribution of SALT2 fit parameters found for the YONSEI All sample: X1 (left panel) and C (right panel) versus redshift. Faint (low X1) and red (high C) SNe Ia are not found at the higher redshifts. Colors distinguish surveys. The dashed lines indicate our cosmology cut criteria for SALT2 (−3 < X1 < 3 and −0.3 < C < 0.3).

Same as Figure 3, but for MLCS2k2 fit parameters: ∆ (left panel) and AV (right panel). Faint (high ∆) and highly reddened (high AV ) SNe Ia are not found at the higher redshifts. The dashed lines indicate our cosmology cut criteria for MLCS2k2 (−0.4 < ∆ < 0.7 and AV < 0.5).

Considering the SNe Ia at high redshifts and the criteria adopted in Betoule et al. (2014) and Hicken et al. (2009b), we here preliminarily define one of our cosmology cut criteria (see Section 2.4.1). For SALT2, we employ −3 < X1 < 3 and −0.3 < C < 0.3, and for MLCS2k2 we use −0.4 < ∆ < 0.7 and AV < 0.5. As shown in Figures 3 and 4, most of SNe at the higher redshifts are included, except the highly reddened ones in MLCS2k2.

2.3.2. Comparison between SALT2 and MLCS2k2 Light-Curve Fit Parameters

We now compare the light-curve fit parameters of SALT2 and MLCS2k2 to check if they are consistent. In Figure 5, SALT2 X1 is compared to MLCS2k2 ∆ in the upper panel, and SALT2 C is compared to MLCS2k2 AV in the lower panel. There is a strong correlation between the SALT2 and MLCS2k2 fit parameters, albeit with some scatter and a few outliers. X1 and ∆ are correlated non-linearly, while C and AV are correlated linearly, as demonstrated by Hicken et al. (2009b) and Sako et al. (2018). Due to the non-linear correlation of the shape parameters, ∆ spans a wide range in the vicinity of X1 = −2 (fast decline), and the brightest SNe (negative ∆) span a wide range in X1. Our cosmology cut criteria exclude most of the SNe in those regions of the parameter space. We note that there is a zeropoint offset for the color between the fitters, C ≈ −0.1 when AV = 0. Overall, the best-fit lightcurve parameters of SALT2 and MLCS2k2 are in good agreement.

Comparison of SALT2 and MLCS2k2 light-curve fit parameters. Top panel: Comparison of light-curve shape parameters, SALT2 X1 versus MLCS2k2 ∆. Bottom panel: Comparison of reddening parameters, SALT2 C versus MLCS2k2 AV . Strong correlations, as discussed by Hicken et al. (2009b) and Sako et al. (2018), are evident. The dashed lines indicate our cosmology cut criteria for both fitters, which also lead to the exclusion of several outliers.

2.3.3. Distribution of Shape and Color or Extinction Values for SALT2 and MLCS2k2

We show the distribution of shape and color or host extinction values for SALT2 and MLCS2k2 in Figure 6 to investigate potential systematics in the YONSEI All sample. By construction of the fitters, SNe Ia data cluster around zero in both parameter spaces (e.g., Campbell et al. 2013). Our cosmology cut criteria discard most of the outlying (i.e., peculiar) SNe Ia.

Distribution of shape and color or host extinction for SALT2 (upper panel) and MLCS2k2 (lower panel). The dashed lines indicate our cosmology cut criteria which remove most of peculiar (outlying) SNe.

### 2.4. YONSEI Hubble–Lemaître Diagrams

2.4.1. YONSEI Cosmology Sample

For a reliable derivation of cosmological parameters, we have to restrict our analysis to well-fitted normal SNe Ia from the YONSEI All sample. We thus apply additional “cosmology cut” criteria to obtain the “YONSEI Cosmology” sample. Building upon the cut criteria established in the previous section and adopted in Betoule et al. (2014) and Hicken et al. (2009b), the “cosmology cuts” are based on the 1) the Milky Way extinction E(BV)MW; 2) the uncertainty on the time of maximum B-band flux (t0), σ(t0); 3) the uncertainty on the light-curve shape parameter σ(shape), and 4) the bestfit shape and color or extinction parameters from each light-curve fitter. The numbers of SNe Ia affected by the cosmology cuts in each original sample are given in Table 2.

Our cosmology cut criteria are:

1. E(BV)MW < 0.15 mag;

2. σ(t0) < 2;

3. σ(shape) < 1;

4. −3 < X1 < 3 and −0.3 < C < 0.3 for SALT2, and −0.4 < ∆ < 0.7 and AV < 0.5 for MLCS2k2.

We use the JLA likelihood code (Betoule et al. 2014) to fit a flat ΛCDM cosmological model to the redshift– distance modulus distribution of the YONSEI Cosmology sample. The best-fit cosmological parameters are ΩM = 0.30, α = 0.15, β = 3.69, and MB = −19.06 for SALT2, and H0 = 63 kms−1Mpc−1 and ΩM = 0.43 for MLCS2k2.1 While estimating cosmological parameters, we applied Chauvenet’s criterion (Taylor 1997) to reject outliers, removing SNe whose probability of being members of the underlying (assumed to be Gaussian) distribution of intrinsic luminosities is less than 1/(2×sample size). This corresponds to rejecting data more than 3.5σ and more than 3.4σ away from the mean for SALT2 and MLCS2k2, respectively. The outlier rejection is not sensitive to the choice of cosmological model, the same SNe are excluded in all cases. The number of sources affected by Chauvenet’s criterion is listed in Table 2. Eventually, our Cosmology samples contain 1049 sources in case of SALT2 and 821 SNe for MLCS2k2.

2.4.2. Hubble–Lemaître Diagrams for the YONSEI Cosmology Sample

We present the Hubble–Lemaître diagrams derived from the YONSEI Cosmology sample in Figures 7 and 8 for SALT2 and MLCS2k2, respectively. Hubble residuals HR ≡ μSNμmodel(z) (where μmodel(z) is the distance modulus predicted by the cosmological model) are shown below the Hubble–Lemaître diagrams.

YONSEI Hubble–Lemaître diagram (top panel) and Hubble residuals (bottom panel) for the SALT2 sample. The solid line represents the best-fit flat ΛCDM cosmology model based on SNe Ia only. The best-fit values are ΩM = 0.30, α = 0.15, β = 3.69, and MB = −19.06. Colors distinguish surveys.

Same as Figure 7, but for the MLCS2k2 sample. The best-fit flat ΛCDM cosmology parameters are H0 = 63 kms−1Mpc−1 and ΩM = 0.43.

Table 4 shows the weighted mean and rms scatter of the Hubble residuals for each dataset. The average weighted mean of the HR for the YONSEI Cosmology sample is 0.00± 0.01 mag, the rms scatter is 0.19 mag. We note that the mean value of the HR of the HST sample is substantially shifted toward negative values. This means that the SNe in the HST sample are brighter, after light-curve corrections, than those in the other samples. As discussed in Section 2.3.1, it is not clear whether this is due to selection bias or intrinsic differences in SNe Ia. Because of larger photometric uncertainties, the HST and ESSENCE samples show rather large rms scatters. The rms values we find for both samples are similar to those found by previous studies (see the rms values for the high-z sample in Hicken et al. 2009b; Kessler et al. 2009a; Conley et al. 2011; Suzuki et al. 2012).

Weighted mean and root-mean-squared (rms) scatter of Hubble residuals in each dataset

2.4.3. Systematic Trends in the Hubble Residuals

Systematics trends in the Hubble residuals, if any, can effect our results described in the following sections. In Figure 9, we compare the HRs obtained from SALT2 and MLCS2k2 fitters. They are in good agreement, with a mean offset of 0.02 mag and a correlation coefficient of 0.86. Given that SALT2 and MLCS2k2 characterize SN Ia light-curves in a consistent manner (see Section 2.3.2), most of the residual scatters might be due to the different methods the fitters used for determining distance moduli.

Comparison of Hubble residuals from SALT2 and MLCS2k2, for 718 SNe Ia that are present in both datasets. The mean offset is 0.02 mag, the correlation coefficient is 0.86. There is one outlier, 06D2cb in the SNLS sample, for which only one filter is used when MLCS2k2 estimates lightcurve fit parameters. The dashed line indicates one-to-one correspondence.

Figure 10 shows HRs as function of the light-curve shape parameters for SALT2 and MLCS2k2, respectively. No significant systematic trends are found for either fitter. Outliers, supposedly peculiar SNe Ia, are removed by our cosmology cut criteria. In the region of ∆ > 0.7 for MLCS2k2, the residuals have mostly negative values as pointed out by Hicken et al. (2009b). They discussed that this “dip” is most likely due to 1991-bg like SNe Ia, which are fainter than normal SNe Ia.

Hubble residuals as function of light-curve shape parameters. Top panel: X1, from SALT2. Bottom panel: ∆, from MLCS2k2. The diagrams show no significant systematic trends. Outliers (mostly peculiar SNe Ia; cross marks) are removed by our cosmology cuts (dashed lines), including a group of 1991bg-like SNe Ia located at ∆ > 0.7.

Finally, we plot the HRs versus C and AV for SALT2 and MLCS2k2 in Figure 11. The HRs appear to be systematically smaller for higher values of C or AV . Even though the redder (C > 0.3 for SALT2) and highly reddened (AV > 0.5 for MLCS2k2) SNe, which have mostly negative residuals, are removed by our cosmology cut criteria, trends still remain. To investigate this, we plot the HRs versus C and AV separately for different surveys that cover specific redshift ranges in Figures 12 and 13, respectively. The declining trends turn out to be present in all samples and thus redshift ranges. Hicken et al. (2009b) showed that the cuts on C and AV make this trend have little effect on the SN cosmology. Nevertheless, we consider the possibility that this trend hints at a dependence of SN luminosities on properties of their host galaxies. For example, hosts which have highly reddened SNe might be related to star-forming environments (young populations), while those with low extinction values are related to passive environments (old populations).

Hubble residuals versus C (for SALT2, top panel) and AV (for MLCS2k2, bottom panel). Both diagrams show systematic decreases of HRs with increasing parameter values (blue lines with ±1σ ranges). The black dashed lines indicate our cosmology cut criteria which remove the redder (C > 0.3) and highly reddened (AV > 0.5) SNe, which have mostly negative residuals.

SALT2 HRs versus C, separated by SN dataset. Declining trends are observed in every sample. Blue lines indicate the best-fit linear trends with ±1σ ranges.

Same as Figure 12, but for MLCS2k2 Hubble residuals and AV .

### 2.5. Host Galaxy Data

Quantification of host galaxy properties, specifically morphological type, stellar mass (Mstellar), and global specific star formation rate (sSFR; star formation rate per unit stellar mass), is required to explore the environmental dependence of SN Ia luminosities. Morphological types for the LOWZ sample (194 SNe out of 218) are drawn from the NASA Extragalactic Database (NED)2 and the HyperLeda database (Makarov et al. 2014).3 Data for the SDSS sample (55 out of 392) are from the Korea Institute for Advanced Science Value-Added Galaxy Catalog (Choi et al. 2010, KIAS-VAGC)4 and Han et al. (2010).

Host Mstellar and sSFR are taken from Kim et al. (2018) who provide data for the LOWZ, SDSS, and SNLS samples.5 They employ the P´EGASE.2 galaxy spectral evolution code (Fioc & Rocca-Volmerange 1997; Le Borgne & Rocca-Volmerange 2002; Le Borgne et al. 2004) to determine host galaxy properties, following the method described in detail in Sullivan et al. (2006, 2010). They use a set of 14 exponentially declining star formation histories (SFHs) and foreground dust screens ranging from E(BV) = 0 to 0.30mag in steps of 0.05mag. Then, they fit the host galaxy data from Smith et al. (2012) and Sako et al. (2018) (for the SDSS sample), and Sullivan et al. (2010) (for the SNLS sample). Host galaxy properties for the LOWZ sample are taken from Neill et al. (2009) who use the same P´EGASE.2 approach. For SALT2 data, in total 89 hosts (out of 218) for LOWZ, 355 (out of 392) for SDSS, and 213 (out of 262) for SNLS, are matched with the YONSEI Cosmology sample. For MLCS2k2, 73 hosts (out of 174) for LOWZ, 292 (out of 328) for SDSS, and 147 (out of 170) for SNLS are collected. The data and sample sizes used in our analysis are listed in Tables 3 and 5, respectively. As discussed in Sullivan et al. (2010) and Kim et al. (2018), we restrict the SNLS sample to z ≤ 0.85, where the SNLS sample has the highest signal-to-noise ratio and the smallestMalmquist corrections.

Figures 14 and 15 show the number of YONSEI SNe as fuction of host galaxy morphology, Mstellar, and sSFR. Evidently, SNe Ia are preferentially observed in late-type, star-forming, and more massive (high-mass; log(Mstellar) > 10.0) systems. We note that the fraction of high-mass hosts in the LOWZ sample is much higher than that in other samples (see the blue histogram in the upper panel of Figure 15). This is because many SNe in the LOWZ sample were discovered in host-targeted surveys which prefer more luminous and massive galaxies, while the SDSS and SNLS samples were drawn from untargeted rolling surveys without selection biases (see also Neill et al. 2009; Kelly et al. 2010; Sullivan et al. 2010; Pan et al. 2014). In the distribution with sSFR (lower panel of Figure 15), the various samples are not significantly different, as already pointed out by Neill et al. (2009).

Distribution of YONSEI SNe host galaxy morphologies. Only LOWZ (blue histogram) and SDSS (red histogram) samples have host morphology information (see text). Top panel: Division of hosts into early- and latetype galaxies. Bottom panel: Detailed morphological type information, only for the LOWZ sample. SNe Ia are preferentially observed in late-type galaxies.

Same as Figure 14, but as function of Mstellar (top panel) and sSFR (bottom panel). The LOWZ sample (blue histogram) has a higher fraction of high-mass (log(Mstellar) > 10.0) hosts than the other samples. In sSFR, the distributions are fairly similar each other.

We also investigated the distribution of our host galaxies in the MstellarsSFR plane in Figure 16. Most of the high-mass host galaxies have relatively low sSFR values, while the low-mass hosts in general show strong star formation activity, as expected.

Mstellar versus sSFR for the YONSEI host sample. Most high-mass galaxies have low sSFR values, while low-mass galaxies show strong star formation activity. The black horizontal line indicates the value log(sSFR) = −10.4 where we split galaxies into star-forming and passive. The black vertical line indicates log(Mstellar) = 10.0) where we split hosts into high- and low-mass galaxies.

In the following sections, we investigate relationships between various SN Ia properties and properties of their host galaxies. Firstly, we divide galaxies into early- and late-type galaxies. In case of the LOWZ sample, we can divide the hosts by morphological types E–S0, S0a–Sc, and Scd/Sd/Irr, following the scheme presented in Hicken et al. (2009b). Secondly, we divide hosts into high- and low-mass galaxies, using log(Mstellar) = 10.0 as dividing line (the black vertical line in Figure 16; see Sullivan et al. 2010; Childress et al. 2013; Pan et al. 2014). Thirdly, we divide galaxies by specific star formation rate, with the division between passive and star-forming environments being log(sSFR) = −10.4 (the black horizontal line in Figure 16; for similar criteria, see Sullivan et al. 2010; Childress et al. 2013; Rigault et al. 2013, 2015; Pan et al. 2014; Jones et al. 2015).

2.5.1. Kim et al. (2018) Method to Infer the Local Environments of SNe Ia

Recent studies of SN Ia host galaxies have focused on the local environments at SN explosion sites (e.g., Rigault et al. 2013, 2015, 2018; Jones et al. 2015, 2018b). However, measurements of the local environments are challenging, and therefore only SNe at the low-redshift range (z < 0.1) were available for those studies. In order to cover a wider redshift range, Kim et al. (2018) introduced an empirical method to infer the local environments, only based on the global properties of host galaxies, such as Mstellar and global sSFR. The main idea is that SNe Ia in locally star-forming environments are located in globally star-forming and low-mass galaxies. SNe Ia in globally passive host galaxies are all located in locally passive environments, as demonstrated by Rigault et al. (2013). We apply this method to infer the local environments of our sample, and the local sample sizes are listed in Table 5.

Numbers of SNe for which specific host galaxy data are available

## 3. SN IA LUMINOSITIES VS. HOST GALAXY PROPERTIES6

### 3.1. Light-Curve Fit Parameters as Function of Host Galaxy Properties

In Figures 17 and 18, we plot the SN Ia light-curve fit parameters as function of global host galaxy properties for SALT2 and MLCS2k2, respectively. The weighted means of light-curve parameters for SNe in different environments are summarized in Table 6.

SALT2 light-curve fit parameters X1 (top panels) and C (bottom panels), as function of host galaxy properties for the YONSEI host sample. The red squares represent the weighted means of light-curve fit parameter, with one mean value for each host galaxy parameter bin.

Same as Figure 17, but for the MLCS2k2 parameters ∆ (top panels) and AV (bottom panels).

Weighted means of best-fit light-curve parameters vs. host galaxy properties

3.1.1. Light-Curve Shape: X1 and ∆

We examine the distribution of SN Ia light-curve shape parameters as function of host properties in the top panels of Figures 17 and 18. Overall, we recover the trends found in previous works (e.g., Filippenko 1989; Hamuy et al. 1995, 1996a, 2000; Gallagher et al. 2005; Sullivan et al. 2006; Howell et al. 2009; Neill et al. 2009; Lampeitl et al. 2010; Smith et al. 2012; Childress et al. 2013; Pan et al. 2014).

First, we regard the light-curve shape parameters as function of host galaxy morphology in the first two panels of the top panels of Figures 17 and 18. The lightcurves of SNe Ia in late-type host galaxies are significantly (>6.0σ) broader and decline slower than those in early-type hosts (see also Table 6). The faintest SNe Ia are found in early-type hosts, while the brightest SNe are found in late-type hosts. When regarding more specific morphological types (the first panel in each figure), the differences in the light-curve shape parameters are most obvious between SNe in E-S0 on the one hand and Scd/Sd/Irr hosts on the other hand; the difference is ~ 55% larger than the value found from dividing the hosts into early and late types. Considering the stellar population age difference between those morphological types, this result indirectly shows that SN progenitors are located in populations of different ages.

The light-curve shape parameters as function of host Mstellar and global sSFR are shown in the third and fourth panels of the top panels of Figures 17 and 18. SNe with broader, more slowly declining light-curves are more likely to be found in low-mass and globally star-forming hosts with a statistical confidence >6.5σ (see also Table 6). Note that, in low-mass and high sSFR hosts, narrower and faster-declining SN lightcurves are rarer, while SNe in high-mass and low sSFR hosts span a much wider range of light-curve shapes. We also see evidence that the light-curve shape parameter is a continuous variable of Mstellar and global sSFR, as pointed out by Sullivan et al. (2010).

3.1.2. Supernova Color and Host Extinction: C and AV

he lower panels of Figures 17 and 18 show SN Ia color (for SALT2) and extinction (for MLCS2k2) as function of host properties. Interpreting the SN color is complicated, as C is a single parameter that captures both SN intrinsic color and reddening by dust. Even though several studies discussed this issue (e.g., Hicken et al. 2009b; Neill et al. 2009; Sullivan et al. 2010; Childress et al. 2013; Pan et al. 2014), there is no conclusive result yet. For the MLCS2k2 AV , our work is the first to investigate its relationship with host Mstellar and sSFR.

The SN color as function of host properties is displayed in the lower panels of Figure 17. A priori, we expect that SNe Ia in late-type and globally star-forming host galaxies are redder, because these galaxies are thought to contain more dust than early-type and globally passive galaxies in general. However, there appears to be no correlation between C and host morphological types or global sSFR. We do, however, find a trend with host galaxy stellar mass. SNe Ia in high-mass hosts are slightly bluer than those in low-mass hosts: the difference in the weighted mean of C is 0.030 ± 0.008 (3.8σ, Table 6). The reddest SNe Ia (i.e., C ≥ 0.2) prefer high-mass and globally star-forming hosts.

In the lower panels of Figure 18, we plot the dust extinction value for host galaxies, estimated from MLCS2k2, as function of host properties. As expected, we find that late-type and globally star-forming host galaxies show 0.117±0.032mag (3.7σ) and 0.035±0.017 mag (2.1σ) higher extinction values than early-type and globally passive hosts, respectively (see Table 6). The difference is largest (0.191 ± 0.045 mag, 4.2σ) when we split the hosts into more specific morphological types. Contrary to the case for SALT2 C, there is no trend with Mstellar.

### 3.2. Dependence of SN Ia Luminosities on Host Galaxy Properties

As noted in the previous section, trends between lightcurve fit parameters and host properties need to be corrected for light-curve shape and color or extinction. In the ideal case of perfect correction, we would not be able to observe a dependence of corrected luminosity of SNe Ia on the properties of host galaxies. In order to investigate environmental effects, we plot the corrected luminosity of SNe Ia as a function of host global properties in Figures 19 through 25. The weighted mean and rms scatter of HRs with host properties for our sample are listed in Table 7. We define Hubble residuals as HR ≡ μSNμmodel(z), for the corrected luminosity of SNe Ia. Thus, a negative residual means that the distance determined from the SN is less than the distance derived from the host galaxy redshift within the given cosmological model. In general, the brighter SNe have, after light-curve corrections, negative HRs, and vice versa for the fainter SNe. When calculating a weighted mean of HRs in each host group, we rescale errors such that ${\chi }_{\mathrm{r}\mathrm{e}\mathrm{d}}^{2}$ = 1. We also apply Chauvenet’s criterion to reject outliers, corresponding to the rejection of data points more than 2.9σ (for SALT2) and 2.8σ (for MLCS2k2) away from the mean.

Weighted mean and rms scatter of Hubble residuals for various host galaxy properties

3.2.1. Host Stellar Mass

We begin with the well-established correlation between SN Hubble residuals and host Mstellar. In Figure 19, the dependence of SN Ia luminosity on the host Mstellar is shown for SALT2 (top panel) and MLCS2k2 (bottom panel). We find that SNe Ia in low-mass hosts are fainter than those in high-mass hosts: the difference in the weighted mean of HRs is 0.057 ± 0.014 mag (4.1σ) for SALT2 and 0.065 ± 0.015 mag (4.3σ) for MLCS2k2 (see Table 7). Our findings are quantitatively and qualitatively in good agreement with previous studies (e.g., Kelly et al. 2010; Lampeitl et al. 2010; Sullivan et al. 2010).

Hubble residuals for SALT2 (top panel) and MLCS2k2 (bottom panel) versus host Mstellar. SNe Ia in low-mass hosts are ~0.06 mag fainter than those in highmass hosts. Red squares represent the weighted means of HRs in bins of host Mstellar. The vertical dotted line (log(Mstellar) = 10.0) indicates the boundary between highmass and low-mass host galaxies. The histograms on the right show the HR distributions.

We also investigate the difference in HRs for the LOWZ (low-redshift), SDSS (intermediate-redshift), and SNLS (high-redshift) samples separately. In Figures 20 and 21, the dependence of SN Ia luminosity on the host Mstellar, separately for each dataset, is shown for SALT2 and MLCS2k2, respectively. All subsample (which cover different redshift ranges) follow the trend we found with the YONSEI sample, and their HR differences are consistent within ~1σ (see Table 8). This indicates that the dependence of SN Ia luminosity on the host Mstellar is a global phenomenon which is present over the whole redshift range covered by our study. As pointed out in Section 2.5, the LOWZ sample was obtained from host-targeted surveys which prefer more luminous and massive galaxies. Therefore, high-mass host galaxies are over-abundant compared to the other samples, the ratio of low to high-mass galaxies being 15:85 compared to 31:69 for other samples on average. This may affect the trend observed in the LOWZ sample.

SALT2 Hubble residuals versus Mstellar, separately for each survey. Each subsample, covering a different redshift range, follows the trend found with the YONSEI sample.

Same as Figure 20, but for MLCS2k2 Hubble residuals.

Hubble residual differences in each dataset

Finally, we compare the rms scatters for SNe Ia in high-mass and low-mass samples. SNe in low-mass hosts show ~5% and ~16% smaller rms scatter than those in high-mass hosts for SALT2 and MLCS2k2, respectively (see Table 7). This result suggests that SNe Ia in low-mass hosts are better standard candles than those in high-mass hosts.

3.2.2. Host Global Specific Star Formation Rate

We plot SN Ia luminosity as function of host global sSFR in Figure 22. We find that SNe Ia in the globally star-forming hosts are 0.049 ± 0.015 mag (3.3σ) and 0.033 ± 0.016 mag (2.1σ) fainter than those in the globally passive hosts for SALT2 and MLCS2k2, respectively (see Table 7). Our result is qualitatively consistent with previous results, but the HR differences we find are smaller (other studies found up to ~ 0.1 mag, see Lampeitl et al. 2010; Sullivan et al. 2010; D’Andrea et al. 2011). The weighted mean HR for SNe Ia in globally star-forming hosts is ~0.0 mag, which implies that those SNe can be a good anchor for the Hubble– Lemaître diagram.

Same as Figure 19, but for global sSFR of host galaxies. SNe Ia in globally star-forming hosts are ~0.04 mag fainter than those in globally passive hosts. The vertical dotted line (log(sSFR) = −10.4) indicates the limit separating passive and star-forming host galaxies in our sample. The histograms on the right show the HR distributions.

In Figures 23 and 24, SN Ia luminosity vs. host global sSFR is shown separately for each SN dataset for SALT2 and MLCS2k2, respectively. The trends in all subsamples agree with the trend observed in the YONSEI sample, even though their statistical significance is slightly lower (see Table 8). As the mean sSFR is known to increase with redshift (e.g., Madau & Dickinson 2014; Driver et al. 2018), the fraction of globally star-forming hosts in our sample increases by up to ~10% with increasing redshift. In addition, the overall SN Ia occurrence rate for globally star-forming hosts in the YONSEI sample is ~2.3 times larger than that for globally passive hosts, which is qualitatively consistent with the results of Sullivan et al. (2006) and Smith et al. (2012).

SALT2 HRs versus global sSFR of host galaxies separately for each survey. The trends in all subsamples agree well with the trend observed in the YONSEI sample.

Same as Figure 23, but for MLCS2k2 HRs.

The rms of HRs for SNe Ia in globally star-forming hosts is ~7% smaller than for globally passive hosts when using SALT2. However, we see no difference in the rms values in the MLCS2k2 global sSFR sample. Previous studies likewise reached different conclusions; for example, Kelly et al. (2015), Uddin et al. (2017), and Kim et al. (2018) concluded that SNe Ia in the star-forming sample show less scatter, while Lampeitl et al. (2010), Sullivan et al. (2010), and Jones et al. (2015) found the opposite result.

3.2.3. Host Morphology

Figure 25 shows SN Ia luminosity versus host galaxy morphology for SALT2 (upper panel) and MLCS2k2 (lower panel). We observe no significant systematic trends for our LOWZ and intermediate-redshift SDSS samples. More quantitatively, the HR difference is 0.011 ± 0.029 mag and 0.028 ± 0.027 mag on average for SALT2 and MLCS2k2, respectively (see Table 7). The values we find are substantially smaller than those reported by previous studies which found HR differences of 0.144 ± 0.070 mag for the low-redshift sample (z < 0.1; Hicken et al. 2009b) and 0.180±0.090 mag for the high-redshift sample (z > 0.9; Suzuki et al. 2012).

Same as Figure 19, but for the host galaxy morphology. We observe no significant trend.

We also find that SNe Ia in Scd/Sd/Irr hosts have the lowest rms scatter (~0.084 mag, see Table 7), which is consistent with the result of Hicken et al. (2009b). These SNe show a 46% and 74% smaller rms scatter than those in E-S0 hosts for SALT2 and MLCS2k2, respectively. This may imply that SNe Ia in Scd/Sd/Irr hosts can provide more robust results in estimating cosmological parameters.

3.2.4. Comparison with Previous Studies

In this section, we summarize our results of the analysis of SN Ia HRs as function of different host galaxy properties and compare them with the results reported in previous studies. We present a summary of our findings and previous results in Table 9 and Figure 26. We note that we compare our results only to works which used corrections for both the light-curve shape and SN color or host extinction (after 2007, when Guy et al. 2007 and Jha et al. 2007 released the SALT2 and MLCS2k2 fitters, respectively).

Comparison of Hubble residual differences between previous studies

Comparison of HR differences reported by previous studies. Our results are consistent with those of many previous studies. See Table 9 for more information about each study.

We first compare our results with previous studies with respect to host Mstellar. As shown in Table 9, there are many studies using samples that cover large redshift ranges. These studies found that SNe Ia in high-mass hosts appear brighter than those in low-mass hosts, after light-curve corrections with several lightcurve fitters. The HR difference is 0.08 mag on average and the transition mass is around 1010 M. Our result is thus fully consistent with previous studies within the ~1σ level.

Several points regarding the mass comparison are worth noting here. Firstly, some of the recent studies tried to include photometrically classified SNe Ia in their sample (e.g., Campbell et al. 2016; Uddin et al. 2017; Jones et al. 2018a). With this inclusion, their sample size is ~2 times larger than other studies. The error of the HRs, however, is not as small as expected from the sample size, because of the contamination from other types of SNe. Secondly, the light-curve fitting method for the results of Jones et al. (2018a) and Scolnic et al. (2018). They employed the same equation for the SALT2 SN distance modulus we used (see Equation 1), but they included two extra terms: ∆M for the host mass dependence correction and ∆B for the simulated selection bias correction (see Equation 3). Interestingly, even though they considered the HR difference among different host masses prior to estimating the distance modulus of SNe, a dependence of SN Ia luminosity on the host mass is still observed at a ~5.2σ level. Thirdly, Scolnic et al. (2014) found no trend between HRs and host stellar mass. However, with a ~10 times larger sample which includes Scolnic et al. (2014) data, the trend is recovered in Scolnic et al. (2018).

We now turn to our analysis of HRs as function of host global sSFR. Our result is consistent with previous studies; SNe Ia in passive hosts are brighter than those in star-forming hosts. The magnitude of the HR difference is 0.06 mag on average. This difference, however, is smaller and statistically less significant than the value found when analyzing HRs as function of host Mstellar.

Assuming that host Mstellar and sSFR are closely related to the galaxy morphology, we expect from our observations summarized above that brighter SNe Ia preferentially occur in early-type host galaxies. However, we find no HR difference between SNe Ia in earlytype hosts and those in late-type hosts, while previous studies found such a discrepancy at the ~2σ level. This may be because our LOWZ sample, which is dominant in the host morphology study (~80%), is drawn from a host-targeted survey, as pointed out in Section 2.5. As a result, most of the hosts in the LOWZ sample are high-mass galaxies (see the second panels of Figures 20 and 21); thus, there would be no HR difference between SNe in early-type hosts and those in late-type hosts.

Finally, we look at the trends with local environments of SNe Ia. Our findings, which include analysis of a sample at high-redshifts, show good agreement with previous studies. These works concluded that SNe Ia occurring locally passive and redder, in local UV color, environments are brighter than those in locally star-forming and bluer environments, with exception of the results of Jones et al. (2015).7 The magnitude of the HR difference is ~0.1 mag, which is larger than the value found when using host global properties. As the local environment is more directly linked to the SN progenitor, the results strongly suggest that there are different populations of SN Ia progenitors.

From this comparison, we conclude that our results are consistent with the results reported by many previous studies. However, our findings are an independent confirmation based on the spectroscopically confirmed SNe Ia from a combined sample of LOWZ, SDSS, and SNLS data, together with two different light-curve fitters.

## 4. ESTIMATING COSMOLOGICAL PARAMETERS FROM SNE IA IN DIFFERENT ENVIRONMENTS

We observed in the previous section that the luminosity of SNe Ia varies with their host properties. This might imply that using a sample of SNe Ia without considering different host environments can cause a bias in estimates of cosmological parameters; for example, a ~10% shift in w and a 3.3% correction for H0 (Lampeitl et al. 2010; Sullivan et al. 2010, 2011; Rigault et al. 2013, 2015; Campbell et al. 2016; Uddin et al. 2017). In order to investigate this potential bias in the YONSEI Cosmology sample, we split here the SN Ia sample according to the host environments as described the previous section (e.g., see Table 7), and then estimate cosmological parameters separately.

We use the JLA likelihood code described in Section 2.4.1 to estimate the best-fit cosmological parameters from SALT2 SNe Ia alone. For our baseline cosmology, we assume the flat ΛCDM model. Else than in Section 2.4.1, we simultaneously calculate σint, instead of setting σint = 0. As σint is the uncertainty that makes ${\chi }_{\mathrm{r}\mathrm{e}\mathrm{d}}^{2}$ unity, this uncertainty is required when we determine the best-fit cosmological parameters. The best-fit parameters estimated from the YONSEI Cosmology sample in different environments are listed in Table 10.

The table shows that shifts in M and α are negligible, as pointed out by Sullivan et al. (2011) and Uddin et al. (2017). However, in β, we can see a significant shift, except when dividing the sample by host Mstellar. The value of β in passive environments is lower than that in star-forming environments. This trend is also observed by Lampeitl et al. (2010) for the SDSS sample and Sullivan et al. (2010) for the SNLS sample.

Best-fit flat ΛCDM parameters estimated from SNe Ia in different host environments

In terms of σint (Table 10) and rms scatter of HRs (Table 7), SNe Ia in low-mass and star-forming environments provide more robust results when estimating cosmological parameters. For example, SNe in locally star-forming environments have a ~18% smaller rms scatter, and also require a ~15% smaller intrinsic scatter than those in the full YONSEI Cosmology sample. From this, we can conclude that SNe Ia in low-mass and star-forming environments have similar progenitor ages and thus form the most homogeneous sample (see also Childress et al. 2014; Kelly et al. 2015; Kim et al. 2018).

From the results described in this section, we conclude that cosmological parameters appear to be biased when not considering the SN Ia environments. With additionals SNe Ia surveys providing ever larger samples, we may expect to see significant differences in cosmological parameters estimated from SNe Ia (Uddin et al. 2017). This means that we may need a host-relatedcorrection (see e.g., Sullivan et al. 2011; Suzuki et al. 2012; Scolnic et al. 2018). However, before making attempts at correcting the environmental dependence of SN Ia luminosity, its origin should be understood – which may, eventually, lead to a more accurate cosmology.

## 5. DISCUSSION

The purpose of this study is to investigate the dependence of SNe Ia luminosity on global and local properties of host galaxies, explore the origin of the dependence, and predict its impact on the SN cosmology. For this, we have constructed an independent SN Ia catalog comprising 1231 spectroscopically confirmed SNe Ia and 674 host galaxy datasets over the redshift range 0.01 < z < 1.37 and applying two independent lightcurve fitters, SALT2 and MLCS2k2. From this catalog, we find that SNe Ia in low-mass and star-forming environments are 0.062 ± 0.009 mag and 0.057 ± 0.010 mag fainter than those in high-mass and passive environments, after empirical light-curve corrections with SALT2 and MLCS2k2, respectively (see Table 7 for our main results). When only local environments of SNe Ia are considered, the luminosity difference increases to 0.081±0.018 mag for SALT2 and 0.072±0.018 mag for MLCS2k2. Our finding is consistent with previous studies (see Table 9). However, our result is an independent confirmation based on a combined sample of SNe Ia from LOWZ, SDSS, and SNLS surveys (0.1 < z ≤ 0.85), by using two different light-curve fitters.

### 5.1. Origin of the Environmental Dependence of SN Ia Luminosity

As shown in Section 4, the dependence of SN luminosity on environment can affect estimates of cosmological parameters. It is therefore important to investigate the origin of the dependence in order to use SNe Ia as accurate standard candles. The trends remaining after empirical light-curve corrections indicate that 1) there are intrinsic physical processes that we do not understand yet, or 2) we simply require a “third parameter” when we analyze SN Ia light-curves. The latter case was investigated intensively by Scolnic et al. (2018).

Scolnic et al. (2018) analyzed the SN light-curves using a modified version of SALT2. As we briefly described in Section 3.2.4, they included two extra terms in their SALT2 analysis, ∆M and ∆B, such that

 $\mu SN={m}_{B}-{M}_{B}+\alpha {X}_{1}-\beta C+{∆}_{M}+{∆}_{B}$ (3)

where ∆M is a distance correction based on the observed trend between SN Ia luminosity and host mass, and ∆B is another distance correction based on the predicted bias estimated from SN survey simulations (Kessler & Scolnic 2017). Furthermore, they considered distance biases due to intrinsic scatter, introduced by Scolnic & Kessler (2016). However, even after these extra corrections they still observed a HR difference of 0.053±0.009mag (5.9σ, see Table 9). They argued that not including these additional corrections increases the HR difference to 0.071 ± 0.010 mag (7.1σ). This indicates that corrections using various functional forms are not appropriate to capture the remaining trends in SN Ia luminosity as functions of host galaxy properties. Instead, we require a better understanding of the detailed physics of SNe Ia.

Since host Mstellar and sSFR cannot directly affect the SN luminosity, theoretical studies suggested that the leading candidates for the observed trends are the progenitor age and the progenitor metallicity (Timmes et al. 2003; Kasen et al. 2009). Both are empirically known to correlate with the host Mstellar and sSFR (e.g., Tremonti et al. 2004; Gallazzi et al. 2005; Kang et al. 2016).

Explore these issues more directly, several studies have dealt with the host galaxy age and (gas-phase or stellar) metallicity (e.g., Neill et al. 2009; Sullivan et al. 2010; Gupta et al. 2011; Johansson et al. 2013; Pan et al. 2014; Campbell et al. 2016; Wolf et al. 2016). Most of these studies used SED fitting technique or analysis of emission lines. However, there are well-known limitations of those methods such as the age-metallicity degeneracy and attenuation by dust (see Worthey et al. 1994; Walcher et al. 2011). Therefore, Balmer absorption lines have been widely used in estimating the age and the metallicity of early-type galaxies during the last two decades (Faber et al. 1992;Worthey et al. 1994; Worthey 1998; Trager et al. 2000; Thomas et al. 2005; Kuntschner et al. 2006; Graves et al. 2007, 2009; Conroy & Gunn 2010). The recent study of Kang et al. (2016) employed Balmer absorption lines to determine reliable population ages and metallicities for 27 earlytype host galaxies. From high signal-to-noise observed spectra (≥100 per pixel), they suggested that the stellar population age is mainly responsible for the relation between SN Ia luminosities and host properties, at the ~3.9σ level. Even though more data are required to confirm this result, this kind of study can reveal the origin of the environmental dependence and the evolution of SN Ia luminosity.

Furthermore, we suggest another indirect approach to explore the origin of the environmental dependence of SN Ia luminosities. Our results and many previous studies showed that SN Ia luminosities change systematically at log(Mstellar) = 10 (Section 3.2). Furthermore, the Kim et al. (2018) method to infer the local environments from the global host properties requires this mass scale (Section 2.5.1). The mass scale of 1010M occupies a unique position in galaxy studies. Numerous observational studies found that a transition in the assembly histories of galaxies for both early- and latetypes and a transition of galaxy morphology occur near this mass scale (e.g., Kauffmann et al. 2003; Balcells et al. 2007; Hopkins et al. 2009; Cappellari et al. 2013; Bernardi et al. 2014). In addition, several recent simulations predict a transition between SN feedback and AGN feedback around this mass (e.g., Crain et al. 2015; Bower et al. 2017; Taylor et al. 2017), and those studies have been tested with observations (Martín-Navarro & Mezcua 2018). Taken all information together, the origin of the luminosity difference in SNe Ia might be related to the suspected physical transitions. As the average mass, metallicity, and the population age of host galaxies change with these transitions, the SN progenitor properties and environments would change as well. This, in turn, affects the SN explosion mechanism, and therefore leads to the SN Ia luminosity difference.

### 5.2. Luminosity Evolution of SNe Ia?

Since the discovery of the accelerated expansion of the universe, many studies investigated the luminosity evolution of SNe Ia. Earlier works mostly used photometric information, such as the host morphology (Riess et al. 1998; Schmidt et al. 1998) and the SN rise time (Riess et al. 1999b). With more SN Ia spectroscopic data becoming available, recent studies have compared averaged spectra of high-redshift SNe with those at low redshifts (Bronder et al. 2008; Foley et al. 2008; Balland et al. 2009; Sullivan et al. 2009). Several theoretical studies constructed SN explosion models to explore luminosity evolution (Höflich et al. 1998; Timmes et al. 2003; Kasen et al. 2009). Interestingly, most of these studies suggested that the magnitude of luminosity evolution is ~0.2 mag.

In this paper, we suggested that the stellar population age of host galaxies might be the origin of the environmental dependence of SN Ia luminosity. As the mean population age of host galaxies is known to evolve with redshift, so should the mean luminosity of SNe Ia. In order to investigate this, we split the YONSEI Cosmology sample into several redshift bins, and calculate the weighted-mean HRs in each bin. Figure 27 shows the mean SNe Ia luminosity as function of redshift. We see indication for luminosity evolution even after the standard light-curve corrections on a scale of <0.1 mag, which is a smaller than the value suggested in previous theoretical studies (see previous paragraph). This is because the light-curve corrections dilute the luminosity evolution, as the light-curve correction models use an average SN Ia at an average redshift as references (see Guy et al. 2007). To examine this, we also plot the mean SN Ia luminosity from SALT2 and MLCS2k2 without the light-curve corrections in Figure 27. The magnitude of the luminosity evolution without lightcurve correction is larger than that with light-curve correction: ~0.4 mag for the SALT2 sample and ~0.2 mag for the MLCS2k2 sample. Interestingly, the luminosity evolution is similar up to intermediate redshifts, while at high redshifts the SALT2 data without light-curve correction differ. Further data, especially for the highredshift range, are required to confirm the luminosity evolution of SNe Ia.

Luminosity evolution of SNe Ia with redshift. Data points are weighted mean HRs in given redshift bins from the YONSEI Cosmology sample for SALT2 (red) and MLCS2k2 (blue). Filled circles are values with light-curve corrections, while open circles are estimated without lightcurve corrections. Error bars in redshift indicate bin sizes.

In order to investigate the impact of the luminosity evolution of SNe Ia on observational cosmology, several studies constructed cosmological models taking into account a term for the luminosity evolution (e.g., Drell et al. 2000; Linden et al. 2009; Tutusaus et al. 2017, 2018). The latest study of Tutusaus et al. (2018) concluded that a non-accelerated universe was able to correctly fit all the main cosmological probes if SN Ia luminosity evolution is allowed. Riess et al. (1999b) noted that an unexpected luminosity evolution would be sufficient to nullify their cosmological conclusions. Therefore, in order to confirm whether the luminosity evolution of SNe Ia is important or not, we require more SN data at z > 1 (see Figure 27), where the effect of dark energy can be distinguished from luminosity evolution.

### 5.3. FutureWork

Current data are sufficient to open a discussion on the origin and luminosity evolution of SNe Ia, albeit more observations of SNe Ia and their host galaxies are required. Especially, as investigated by Kang et al. (2016) (see Section 5.1), we need more – at least 100 – earlytype host galaxies to derive robust conclusions on the origin of the environmental dependence and the evolution of SNe Ia at sufficient confidence levels. From ongoing SN surveys covering low redshifts, such as the Zwicky Transient Facility (Bellm et al. 2019; Graham et al. 2019), the Korea Microlensing Telescope Network (Kim et al. 2016), and the Foundation SN Survey (Foley et al. 2018), a multitude of early-type host galaxy high signal-to-noise ratio spectra will be obtained to determine more reliable population ages and metallicities. Furthermore, in the era of 30-meter class telescopes, we can expect an expansion of the redshift range to 0.5 or above. The Dark Energy Survey (Flaugher et al. 2015) SN program expects ~270 early-type host galaxies to be observed up to aredshift of 1.0. At such high redshifts, the morphological classification of galaxies is challenging. In order to more reliably select early-type host galaxies in this redshift range, we need to develop or improve the methods for morphology classification, as done before for the SDSS sample (e.g., Park & Choi 2005; Choi et al. 2010) and the HST Cluster SN Survey sample (see Meyers et al. 2012; Suzuki et al. 2012).

## Acknowledgments

We thank the referees for helpful comments. This work was supported by the National Research Foundation of Korea through grant programs 2017R1A5A1070354 and 2017R1A2B3002919. Y.-L.K. acknowledges support from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No. 759194 – USNAC). This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. We also utilized the HyperLeda database (http://leda.univ-lyon1.fr).

Notes
1This is most likely due to a lack of recent calibration of MLCS2k2 with high-redshift SNe Ia (see e.g., Guy et al. 2010; Betoule et al. 2014; Jones et al. 2015).
5Since Kim et al. (2018) do not provide the host data for PS, ESSENCE, and HST samples, we do not include those samples in our host analysis.
6In this paper, we only present HR values related to the local en- vironmental dependence of SN Ia properties. A detailed study of local environments is presented in Kim et al. (2018).
7This is because of the effect of the redshift cut they applied for their sample. Kim et al. (2018) recovered the Jones et al. (2015) and Rigault et al. (2015) results, which show an apparent discrepancy, by applying the same redshift cut used by each of them.

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### Figure 1.

Malmquist bias correction as function of redshift and survey. We subtract the appropriate values from the rest-frame peak magnitudes in B-band and the distance moduli for SALT2 and MLCS2k2, respectively.

### Figure 2.

Redshift distribution of the YONSEI All sample. Histogram colors indicate the various surveys. The first bin of the LOWZ sample contains 268 SNe Ia.

### Figure 3.

Distribution of SALT2 fit parameters found for the YONSEI All sample: X1 (left panel) and C (right panel) versus redshift. Faint (low X1) and red (high C) SNe Ia are not found at the higher redshifts. Colors distinguish surveys. The dashed lines indicate our cosmology cut criteria for SALT2 (−3 < X1 < 3 and −0.3 < C < 0.3).

### Figure 4.

Same as Figure 3, but for MLCS2k2 fit parameters: ∆ (left panel) and AV (right panel). Faint (high ∆) and highly reddened (high AV ) SNe Ia are not found at the higher redshifts. The dashed lines indicate our cosmology cut criteria for MLCS2k2 (−0.4 < ∆ < 0.7 and AV < 0.5).

### Figure 5.

Comparison of SALT2 and MLCS2k2 light-curve fit parameters. Top panel: Comparison of light-curve shape parameters, SALT2 X1 versus MLCS2k2 ∆. Bottom panel: Comparison of reddening parameters, SALT2 C versus MLCS2k2 AV . Strong correlations, as discussed by Hicken et al. (2009b) and Sako et al. (2018), are evident. The dashed lines indicate our cosmology cut criteria for both fitters, which also lead to the exclusion of several outliers.

### Figure 6.

Distribution of shape and color or host extinction for SALT2 (upper panel) and MLCS2k2 (lower panel). The dashed lines indicate our cosmology cut criteria which remove most of peculiar (outlying) SNe.

### Figure 7.

YONSEI Hubble–Lemaître diagram (top panel) and Hubble residuals (bottom panel) for the SALT2 sample. The solid line represents the best-fit flat ΛCDM cosmology model based on SNe Ia only. The best-fit values are ΩM = 0.30, α = 0.15, β = 3.69, and MB = −19.06. Colors distinguish surveys.

### Figure 8.

Same as Figure 7, but for the MLCS2k2 sample. The best-fit flat ΛCDM cosmology parameters are H0 = 63 kms−1Mpc−1 and ΩM = 0.43.

### Figure 9.

Comparison of Hubble residuals from SALT2 and MLCS2k2, for 718 SNe Ia that are present in both datasets. The mean offset is 0.02 mag, the correlation coefficient is 0.86. There is one outlier, 06D2cb in the SNLS sample, for which only one filter is used when MLCS2k2 estimates lightcurve fit parameters. The dashed line indicates one-to-one correspondence.

### Figure 10.

Hubble residuals as function of light-curve shape parameters. Top panel: X1, from SALT2. Bottom panel: ∆, from MLCS2k2. The diagrams show no significant systematic trends. Outliers (mostly peculiar SNe Ia; cross marks) are removed by our cosmology cuts (dashed lines), including a group of 1991bg-like SNe Ia located at ∆ > 0.7.

### Figure 11.

Hubble residuals versus C (for SALT2, top panel) and AV (for MLCS2k2, bottom panel). Both diagrams show systematic decreases of HRs with increasing parameter values (blue lines with ±1σ ranges). The black dashed lines indicate our cosmology cut criteria which remove the redder (C > 0.3) and highly reddened (AV > 0.5) SNe, which have mostly negative residuals.

### Figure 12.

SALT2 HRs versus C, separated by SN dataset. Declining trends are observed in every sample. Blue lines indicate the best-fit linear trends with ±1σ ranges.

### Figure 13.

Same as Figure 12, but for MLCS2k2 Hubble residuals and AV .

### Figure 14.

Distribution of YONSEI SNe host galaxy morphologies. Only LOWZ (blue histogram) and SDSS (red histogram) samples have host morphology information (see text). Top panel: Division of hosts into early- and latetype galaxies. Bottom panel: Detailed morphological type information, only for the LOWZ sample. SNe Ia are preferentially observed in late-type galaxies.

### Figure 15.

Same as Figure 14, but as function of Mstellar (top panel) and sSFR (bottom panel). The LOWZ sample (blue histogram) has a higher fraction of high-mass (log(Mstellar) > 10.0) hosts than the other samples. In sSFR, the distributions are fairly similar each other.

### Figure 16.

Mstellar versus sSFR for the YONSEI host sample. Most high-mass galaxies have low sSFR values, while low-mass galaxies show strong star formation activity. The black horizontal line indicates the value log(sSFR) = −10.4 where we split galaxies into star-forming and passive. The black vertical line indicates log(Mstellar) = 10.0) where we split hosts into high- and low-mass galaxies.

### Figure 17.

SALT2 light-curve fit parameters X1 (top panels) and C (bottom panels), as function of host galaxy properties for the YONSEI host sample. The red squares represent the weighted means of light-curve fit parameter, with one mean value for each host galaxy parameter bin.

### Figure 18.

Same as Figure 17, but for the MLCS2k2 parameters ∆ (top panels) and AV (bottom panels).

### Figure 19.

Hubble residuals for SALT2 (top panel) and MLCS2k2 (bottom panel) versus host Mstellar. SNe Ia in low-mass hosts are ~0.06 mag fainter than those in highmass hosts. Red squares represent the weighted means of HRs in bins of host Mstellar. The vertical dotted line (log(Mstellar) = 10.0) indicates the boundary between highmass and low-mass host galaxies. The histograms on the right show the HR distributions.

### Figure 20.

SALT2 Hubble residuals versus Mstellar, separately for each survey. Each subsample, covering a different redshift range, follows the trend found with the YONSEI sample.

### Figure 21.

Same as Figure 20, but for MLCS2k2 Hubble residuals.

### Figure 22.

Same as Figure 19, but for global sSFR of host galaxies. SNe Ia in globally star-forming hosts are ~0.04 mag fainter than those in globally passive hosts. The vertical dotted line (log(sSFR) = −10.4) indicates the limit separating passive and star-forming host galaxies in our sample. The histograms on the right show the HR distributions.

### Figure 23.

SALT2 HRs versus global sSFR of host galaxies separately for each survey. The trends in all subsamples agree well with the trend observed in the YONSEI sample.

### Figure 24.

Same as Figure 23, but for MLCS2k2 HRs.

### Figure 25.

Same as Figure 19, but for the host galaxy morphology. We observe no significant trend.

### Figure 26.

Comparison of HR differences reported by previous studies. Our results are consistent with those of many previous studies. See Table 9 for more information about each study.

### Figure 27.

Luminosity evolution of SNe Ia with redshift. Data points are weighted mean HRs in given redshift bins from the YONSEI Cosmology sample for SALT2 (red) and MLCS2k2 (blue). Filled circles are values with light-curve corrections, while open circles are estimated without lightcurve corrections. Error bars in redshift indicate bin sizes.

### Table 1

Contributions to the LOWZ sample in the YONSEI SN catalog

SN
Data
Redshift
Range
Total SALT2 MLCS2k2
“Cosmology” sample “All” sample “Cosmology” sample “All” sample
JRK07 0.01–0.09 133 59 69 46 69
CFA3 0.01–0.07 185 73 89 62 96
CFA4 0.01–0.08 94 46 59 35 66
CSP 0.01–0.09 85 40 49 31 62
LOWZ 0.01–0.09 497 218 266 174 293

### Table 2

Sample sizes and cuts for each sample in the YONSEI SN catalog

Light-curve
Fitter
SN
Data
Redshift
Range
Total Final
(= “Cosmology” sample)
Initial
Cut
Cosmology
Cut
Chauvenet’s
Criterion
The columns “intitial cut”, “cosmology cut”, and “Chauvenet’s criterion” give the number of SNe removed by the corresponding cut.
The columns “total” and “final” give the sample sizes before and after applying all cuts, respectively.
SALT2 YONSEI 0.01–1.37 1521 1049 339 129 4
LOWZ 0.01–0.09 497 218 231 45 3
SDSS 0.03–0.41 500 392 64 43 1
PS 0.03–0.64 146 108 23 15 0
ESSENCE 0.15–0.70 60 51 0 9 0
SNLS 0.12–1.06 281 262 9 10 0
HST 0.21–1.37 37 18 12 7 0
MLCS2k2 YONSEI 0.01–1.37 1521 821 333 362 5
LOWZ 0.01–0.09 497 174 204 116 3
SDSS 0.03–0.41 500 328 82 90 0
PS 0.03–0.64 146 98 21 27 0
ESSENCE 0.15–0.70 60 41 1 18 0
SNLS 0.12–1.06 281 170 9 100 2
HST 0.21–1.37 37 10 16 11 0

### Table 3

Name Survey zCMB SALT2 MLCS2k2 Morph. Host Mass Global sSFR
mB
(mag)
Error X1 Error C Error μSN
(mag)
Error Error AV
(mag)
Error log(Mstellar)
(M)
δ +δ log(sSFR)
(yr−1)
δ +δ
The entire catalog is available from the corresponding author, Y.-L. Kim, upon request. “Morph.” is the host galaxy morphology.
1990O LOWZ 0.0306 16.230 0.035 0.541 0.180 -0.056 0.030 35.839 0.121 -0.202 0.074 0.067 0.090 Sa ... ... ... ... ... ...
1990af LOWZ 0.0502 17.777 0.032 2.132 0.141 -0.043 0.044 36.846 0.111 0.651 0.156 -0.195 0.161 S0 ... ... ... ... ... ...
1991ag LOWZ 0.0139 14.438 0.046 0.843 0.144 -0.050 0.030 34.082 0.111 -0.228 0.068 0.050 0.104 Sd 9.07 0.03 0.03 -8.66 0.06 0.08
1992P LOWZ 0.0263 16.074 0.034 0.217 0.277 -0.073 0.041 35.596 0.118 -0.171 0.086 0.120 0.078 Sb 10.34 0.10 0.14 -9.98 0.88 0.63
1992ae LOWZ 0.0748 18.459 0.043 0.729 0.153 -0.024 0.051 37.703 0.168 0.128 0.114 0.116 0.147 E ... ... ... ... ... ...
1992ag LOWZ 0.0259 16.372 0.036 0.640 0.094 0.212 0.041 35.095 0.107 0.084 0.073 0.465 0.062 Sc 10.02 0.10 1.04 -9.88 1.23 0.93
1992al LOWZ 0.0141 14.469 0.033 0.256 0.083 -0.112 0.026 34.109 0.074 -0.025 0.064 -0.062 0.053 Sc ... ... ... ... ... ...
1992aq LOWZ 0.1009 19.317 0.041 1.375 0.219 -0.089 0.056 ... ... ... ... ... ... Sa ... ... ... ... ... ...
1992bc LOWZ 0.0198 15.121 0.031 0.881 0.072 -0.115 0.026 34.960 0.050 -0.261 0.043 -0.078 0.040 Sc 9.72 0.53 0.70 -9.62 0.94 1.12
1992bh LOWZ 0.0451 17.625 0.035 0.003 0.148 0.044 0.044 36.840 0.076 -0.102 0.068 0.276 0.060 Sbc ... ... ... ... ... ...
1992bk LOWZ 0.0579 18.119 0.045 1.668 0.150 -0.091 0.052 37.146 0.159 0.644 0.248 -0.208 0.163 E ... ... ... ... ... ...
1992bl LOWZ 0.0429 17.333 0.040 1.703 0.085 -0.050 0.044 36.533 0.122 0.493 0.138 -0.206 0.109 Sa 11.81 0.65 0.46 10.85 0.71 1.58
1992bo LOWZ 0.0181 15.782 0.033 1.980 0.064 -0.045 0.028 ... ... ... ... ... ... S0 12.13 1.20 0.14 11.18 0.82 1.69
1992bp LOWZ 0.0789 18.310 0.031 0.952 0.133 -0.104 0.048 37.846 0.087 0.089 0.105 -0.061 0.074 E/S0 ... ... ... ... ... ...
1992br LOWZ 0.0878 19.202 0.076 2.389 0.198 -0.141 0.071 38.418 0.198 0.552 0.140 -0.262 0.224 E ... ... ... ... ... ...
1992bs LOWZ 0.0634 18.299 0.040 0.241 0.129 -0.027 0.046 37.544 0.134 -0.051 0.082 0.208 0.118 Sc ... ... ... ... ... ...
1993B LOWZ 0.0707 18.467 0.048 0.331 0.166 0.047 0.051 37.668 0.113 -0.022 0.093 0.172 0.091 Sb ... ... ... ... ... ...
1993H LOWZ 0.0248 16.656 0.035 2.042 0.060 0.075 0.029 ... ... ... ... ... ... Sab 10.51 0.38 0.56 -8.63 1.74 0.49
1993O LOWZ 0.0519 17.640 0.032 0.614 0.100 -0.082 0.043 37.114 0.073 0.038 0.063 0.031 0.054 E/S0 ... ... ... ... ... ...
1993ag LOWZ 0.0500 17.834 0.034 0.832 0.136 0.057 0.045 37.001 0.098 0.098 0.086 0.176 0.068 E/S0 ... ... ... ... ... ...
1994M LOWZ 0.0243 16.294 0.035 1.405 0.090 0.055 0.028 35.235 0.068 0.293 0.079 0.141 0.073 E 11.04 0.11 0.19 10.88 1.12 1.01
1994S LOWZ 0.0160 14.778 0.035 0.376 0.152 -0.079 0.027 34.429 0.076 -0.124 0.081 -0.024 0.068 Sab 10.50 0.11 0.03 -9.68 0.04 0.14
1994T LOWZ 0.0357 17.254 0.032 1.439 0.112 0.055 0.030 ... ... ... ... ... ... S0/a ... ... ... ... ... ...
1995ac LOWZ 0.0488 17.078 0.029 0.788 0.089 -0.045 0.026 36.494 0.053 -0.303 0.047 0.276 0.038 Sa ... ... ... ... ... ...
1995ak LOWZ 0.0220 16.024 0.039 1.037 0.109 0.075 0.031 34.912 0.086 0.038 0.067 0.372 0.077 Sbc ... ... ... ... ... ...
1996C LOWZ 0.0275 16.643 0.034 0.741 0.132 0.061 0.029 35.867 0.070 -0.162 0.051 0.265 0.062 Sa 9.99 0.03 0.17 -9.98 0.39 0.60
1996ab LOWZ 0.1242 19.557 0.045 0.018 0.375 -0.156 0.055 ... ... ... ... ... ... S ... ... ... ... ... ...
1996bl LOWZ 0.0348 16.710 0.031 0.110 0.110 -0.001 0.027 36.048 0.079 -0.139 0.065 0.237 0.061 Sc ... ... ... ... ... ...
1996bv LOWZ 0.0167 15.341 0.032 0.746 0.103 0.158 0.026 ... ... ... ... ... ... Scd 10.15 0.98 0.30 -9.76 0.89 1.33
1997E LOWZ 0.0133 15.114 0.029 1.702 0.087 0.016 0.022 34.152 0.063 0.244 0.103 0.182 0.073 S0 11.52 0.09 0.81 10.03 0.98 1.63
1997Y LOWZ 0.0166 15.329 0.029 0.940 0.138 -0.015 0.023 34.583 0.081 0.059 0.077 0.137 0.059 Sb 10.42 0.28 0.01 10.26 0.67 1.16
1997dg LOWZ 0.0297 16.837 0.027 0.348 0.173 -0.038 0.023 36.183 0.076 -0.048 0.095 0.149 0.064 S ... ... ... ... ... ...
1997do LOWZ 0.0105 14.383 0.034 0.384 0.111 0.092 0.022 33.537 0.101 -0.135 0.093 0.338 0.071 Sbc 9.30 0.14 0.09 -8.65 0.24 0.24
1998ab LOWZ 0.0279 16.100 0.027 0.220 0.073 0.054 0.022 35.204 0.067 -0.162 0.054 0.403 0.045 Sbc 10.59 0.04 0.23 -9.67 0.64 0.72
1998bp LOWZ 0.0102 15.308 0.034 2.492 0.092 0.194 0.024 ... ... ... ... ... ... E ... ... ... ... ... ...
1998dx LOWZ 0.0537 17.542 0.036 1.575 0.288 -0.129 0.027 37.018 0.074 0.371 0.154 -0.230 0.154 Sb 11.72 0.55 0.87 12.00 0.00 4.00
1998ef LOWZ 0.0167 14.846 0.030 1.122 0.106 -0.070 0.023 34.098 0.126 0.231 0.169 0.029 0.108 S ... ... ... ... ... ...
1998eg LOWZ 0.0235 16.114 0.027 0.507 0.210 -0.005 0.023 35.335 0.078 0.021 0.126 0.209 0.086 Scd 11.32 0.75 0.47 11.10 0.69 2.94
1999aa LOWZ 0.0153 14.720 0.027 1.190 0.034 -0.091 0.020 34.474 0.034 -0.304 0.022 0.015 0.024 Sc 10.72 0.10 0.24 10.23 0.32 1.39
1999aw LOWZ 0.0392 16.797 0.029 2.264 0.075 -0.038 0.027 ... ... ... ... ... ... ... ... ... ... ... ... ...
1999cc LOWZ 0.0315 16.779 0.025 1.546 0.073 -0.012 0.022 35.892 0.050 0.268 0.083 0.108 0.058 Sc 10.99 0.05 0.04 10.02 0.27 0.42
1999cp LOWZ 0.0104 13.947 0.035 0.334 0.083 -0.087 0.026 33.556 0.099 -0.116 0.119 0.014 0.086 Scd 9.48 0.09 0.29 -8.65 0.39 0.40
1999dk LOWZ 0.0139 14.867 0.030 0.555 0.109 0.048 0.022 34.174 0.067 -0.258 0.049 0.283 0.058 Sc 10.20 0.16 0.09 -9.77 0.37 0.52
1999dq LOWZ 0.0135 14.375 0.028 0.889 0.034 0.021 0.020 33.687 0.033 -0.315 0.023 0.369 0.022 Sc 10.78 0.06 0.21 -9.77 0.83 0.61
1999ef LOWZ 0.0380 17.075 0.056 0.297 0.161 -0.042 0.027 36.621 0.105 -0.119 0.125 -0.075 0.128 Scd ... ... ... ... ... ...
1999ej LOWZ 0.0128 15.339 0.052 1.485 0.223 -0.032 0.031 34.506 0.104 0.321 0.181 -0.045 0.144 S0/a ... ... ... ... ... ...
1999gp LOWZ 0.0260 16.029 0.024 1.705 0.038 0.008 0.021 ... ... ... ... ... ... Sb ... ... ... ... ... ...
2000bh LOWZ 0.0242 15.937 0.034 0.136 0.073 0.006 0.026 35.276 0.114 -0.065 0.059 0.159 0.061 S ... ... ... ... ... ...
2000ca LOWZ 0.0245 15.561 0.025 0.534 0.071 -0.115 0.021 35.340 0.055 -0.154 0.057 -0.089 0.047 Sbc 10.04 0.34 0.23 -9.00 0.35 0.51
2000cf LOWZ 0.0365 17.051 0.029 0.512 0.084 -0.040 0.023 36.367 0.066 -0.001 0.071 0.112 0.061 Sbc* ... ... ... ... ... ...
2000cn LOWZ 0.0232 16.549 0.027 2.485 0.149 0.085 0.022 ... ... ... ... ... ... Scd ... ... ... ... ... ...
2000dk LOWZ 0.0164 15.364 0.027 2.047 0.077 -0.023 0.022 ... ... ... ... ... ... E 11.54 1.37 0.02 11.24 0.56 1.61
2000fa LOWZ 0.0218 15.889 0.028 0.490 0.082 0.043 0.022 35.000 0.085 -0.137 0.074 0.368 0.064 Im 9.82 0.17 0.28 -8.65 0.46 0.47
2001V LOWZ 0.0583 17.632 0.055 1.354 0.622 -0.052 0.030 ... 0.109 -0.230 0.060 -0.040 0.077 Sbc ... ... ... ... ... ...
2001ah LOWZ 0.0406 16.923 0.029 0.903 0.233 -0.084 0.025 37.355 0.084 0.003 0.113 -0.032 0.083 S 10.68 0.13 0.14 -9.38 1.02 0.51
2001az LOWZ 0.0305 16.192 0.031 0.197 0.093 -0.170 0.039 36.523 0.053 -0.087 0.047 -0.145 0.041 Sbc 10.98 0.50 0.43 -8.94 1.38 0.77
2001ba LOWZ 0.0153 14.717 0.030 0.459 0.084 -0.032 0.022 36.004 0.066 -0.289 0.073 0.325 0.052 ... ... ... ... ... ... ...
2001bf LOWZ 0.0144 15.281 0.032 0.906 0.052 0.157 0.026 34.037 ... ... ... ... ... Sbc ... ... ... ... ... ...
2001bt LOWZ 0.0154 15.277 0.030 0.537 0.040 0.123 0.022 ... 0.056 0.026 0.050 0.381 0.052 Sc ... ... ... ... ... ...
2001cn LOWZ 0.0163 15.055 0.031 0.146 0.061 0.049 0.026 34.123 0.067 -0.107 0.054 0.288 0.053 Sc ... ... ... ... ... ...
2001cz LOWZ 0.0363 16.604 0.026 1.582 0.166 -0.044 0.023 34.261 0.058 -0.351 0.048 0.121 0.050 Sb ... ... ... ... ... ...
2001eh LOWZ 0.0155 15.111 0.030 1.071 0.054 0.018 0.024 36.248 0.081 0.128 0.075 0.122 0.068 Sbc* 10.38 0.15 0.15 10.45 0.26 0.89
2001en LOWZ 0.0129 14.887 0.030 1.026 0.061 0.056 0.021 34.248 0.056 0.140 0.083 0.328 0.059 Sb 10.37 0.25 0.04 10.22 0.24 0.98
2001ep LOWZ 0.0144 14.657 0.030 0.634 0.094 -0.056 0.023 33.832 0.083 -0.156 0.069 0.129 0.059 Sa 10.22 0.11 0.12 -9.72 0.87 0.63
2001fe LOWZ 0.0312 16.666 0.042 0.588 0.119 -0.024 0.027 34.155 0.122 0.039 0.114 0.327 0.097 E 10.99 0.07 0.21 10.88 1.12 0.20
2001ie LOWZ 0.0162 14.556 0.026 0.917 0.042 -0.050 0.020 35.732 ... ... ... ... ... Sb 10.78 0.09 0.19 10.43 0.50 0.35
2002G LOWZ 0.0247 16.326 0.047 0.307 0.131 0.144 0.031 ... 0.096 -0.182 0.074 0.449 0.088 Sb 10.62 0.07 0.12 10.49 0.34 0.32
2002bf LOWZ 0.0302 16.295 0.041 0.101 0.089 -0.069 0.024 35.355 0.093 -0.084 0.079 0.084 0.068 Sb 10.97 0.08 0.22 10.16 0.78 0.69
2002ck LOWZ 0.0103 14.201 0.034 0.495 0.062 -0.037 0.022 35.826 0.074 0.027 0.072 0.192 0.059 Scd 9.48 0.09 0.29 -8.65 0.39 0.40
2002cr LOWZ 0.0281 16.654 0.027 0.422 0.359 0.092 0.023 33.457 0.073 -0.066 0.175 0.440 0.110 S 10.83 0.12 0.03 -9.68 0.22 0.17
2002de LOWZ 0.0104 13.955 0.033 0.006 0.129 0.063 0.023 35.626 0.075 -0.161 0.143 0.352 0.069 E 11.34 0.13 0.03 10.76 0.48 0.16
2002dj LOWZ 0.0105 14.570 0.034 0.317 0.209 0.063 0.023 33.152 0.062 -0.065 0.130 0.426 0.082 Sc 10.40 0.36 0.35 -9.38 0.99 0.57
2002dp LOWZ 0.0346 17.584 0.058 1.538 0.390 0.208 0.041 33.584 ... ... ... ... ... E ... ... ... ... ... ...
2002ha LOWZ 0.0134 14.702 0.030 1.354 0.073 -0.086 0.023 34.040 0.067 0.216 0.104 -0.007 0.081 Sab 11.09 0.13 0.14 10.43 0.36 0.76
2002he LOWZ 0.0248 16.257 0.037 1.756 0.168 -0.035 0.026 ... ... ... ... ... ... E 11.12 0.48 0.90 -8.61 3.39 0.57
2002hu LOWZ 0.0382 16.613 0.024 0.320 0.095 -0.110 0.022 36.297 0.058 -0.218 0.054 0.043 0.048 S 10.27 1.44 0.66 -9.68 1.27 1.68
2002jy LOWZ 0.0187 15.730 0.029 0.865 0.107 -0.039 0.022 35.217 0.062 -0.221 0.067 0.167 0.057 Sc 10.46 0.14 0.11 -9.43 0.46 0.48
2002kf LOWZ 0.0195 15.666 0.030 1.111 0.078 -0.053 0.023 35.059 0.070 0.195 0.066 -0.100 0.063 ... ... ... ... ... ... ...
2003U LOWZ 0.0279 16.482 0.033 2.156 0.315 -0.031 0.028 35.558 0.081 0.433 0.131 0.039 0.113 Scd 10.74 0.30 0.13 -9.93 0.33 0.91
2003W LOWZ 0.0211 15.877 0.026 0.091 0.065 0.111 0.021 34.828 0.055 -0.042 0.051 0.451 0.041 Sc 10.55 0.40 0.25 -9.44 1.18 1.10
2003ch LOWZ 0.0256 16.675 0.028 1.347 0.155 -0.039 0.023 36.019 0.075 0.169 0.112 -0.015 0.085 S0 ... ... ... ... ... ...
2003cq LOWZ 0.0337 17.194 0.052 0.797 0.165 0.118 0.044 ... ... ... ... ... ... Sbc ... ... ... ... ... ...
2003fa LOWZ 0.0391 16.679 0.025 1.474 0.098 -0.071 0.022 36.401 0.048 -0.318 0.045 0.022 0.042 S 10.81 0.78 0.61 -9.57 1.46 1.13
2003ic LOWZ 0.0542 17.607 0.030 1.999 0.203 -0.066 0.029 ... ... ... ... ... ... S0 11.70 0.03 0.27 10.76 1.24 0.07
2003it LOWZ 0.0240 16.353 0.032 1.648 0.168 0.021 0.029 35.315 0.098 0.410 0.140 0.106 0.110 S ... ... ... ... ... ...
2003iv LOWZ 0.0335 16.973 0.028 2.157 0.188 -0.095 0.027 36.354 0.092 0.596 0.159 -0.362 0.133 E* ... ... ... ... ... ...
2003kc LOWZ 0.0343 17.157 0.033 0.660 0.181 0.110 0.017 ... ... ... ... ... ... Sc 10.67 0.14 0.09 -9.38 0.61 0.31
2004L LOWZ 0.0334 17.391 0.039 1.165 0.240 0.188 0.031 ... ... ... ... ... ... S 10.35 0.15 0.21 -9.90 0.59 1.35
2004as LOWZ 0.0321 16.980 0.028 0.294 0.142 0.058 0.024 36.171 0.069 -0.199 0.064 0.381 0.061 Irr 9.28 0.13 0.08 -9.23 0.35 0.44
2004bg LOWZ 0.0219 15.628 0.044 0.509 0.119 -0.043 0.029 35.217 0.089 -0.175 0.069 0.014 0.106 Scd ... ... ... ... ... ...

### Table 4

Weighted mean and root-mean-squared (rms) scatter of Hubble residuals in each dataset

SN Data SALT2 MLCS2k2
NSN HRWM
(mag)
Error
(mag)
rms
(mag)
Error
(mag)
NSN HRWM
(mag)
Error
(mag)
rms
(mag)
Error
(mag)
Parameters: NSN: number of SNe; HRWM: weighted mean value of Hubble residual.
YONSEI 1049 0.000 0.006 0.194 0.004 821 0.006 0.006 0.182 0.004
LOWZ 218 0.020 0.015 0.206 0.010 174 0.011 0.015 0.188 0.010
SDSS 392 −0.006 0.008 0.165 0.006 328 −0.003 0.008 0.153 0.006
PS 108 −0.022 0.017 0.172 0.012 98 0.056 0.016 0.156 0.011
ESSENCE 51 0.016 0.033 0.235 0.023 41 0.049 0.036 0.230 0.026
SNLS 262 −0.006 0.012 0.197 0.009 170 −0.014 0.015 0.191 0.010
HST 18 −0.116 0.069 0.294 0.051 10 −0.054 0.072 0.227 0.053

### Table 5

Numbers of SNe for which specific host galaxy data are available

SN Data SALT2 MLCS2k2
NSN Morph. Mass & sSFR Local
Environment
NSN Morph. Mass & sSFR Local
Environment
Parameters: NSN: total number of SNe in the sample; “Morph.”: morphology.
LOWZ 218 194 89 40 174 152 73 29
SDSS 392 55 355 203 328 45 292 164
SNLS 262 0 213 130 170 0 147 96
YONSEI 872 249 657 373 672 197 512 289

### Table 6

Weighted means of best-fit light-curve parameters vs. host galaxy properties

Property Group SALT2 MLCS2k2
NSN X1,WM Error CWM Error NSN WM Error AV,WM Error
Morphology E–S0 44 −1.515 0.079 −0.011 0.014 32 0.213 0.040 −0.024 0.029
S0a–Sc 134 −0.238 0.083 0.007 0.009 106 −0.117 0.019 0.144 0.018
Scd/Sd/Irr 16 0.420 0.194 0.013 0.018 14 −0.163 0.041 0.167 0.035
Difference Scd/Sd/Irr − E–S0) 1.935 0.209 0.024 0.023 0.376 0.057 0.191 0.045
Morphology Early-type 68 −1.426 0.079 −0.003 0.011 51 0.113 0.038 0.042 0.028
Late-type 181 −0.180 0.070 0.011 0.007 146 −0.130 0.015 0.159 0.015
Difference 1.246 0.106 0.014 0.013 0.243 0.041 0.117 0.032
Mass High-mass 469 −0.383 0.046 −0.014 0.004 369 −0.111 0.011 0.168 0.009
Low-mass 188 0.410 0.048 0.016 0.007 143 −0.213 0.011 0.166 0.013
Difference 0.793 0.066 0.030 0.008 0.102 0.016 0.002 0.016
sSFR Globally Passive 196 −0.844 0.070 −0.009 0.007 155 −0.021 0.020 0.140 0.015
Globally Star-Forming 461 −0.016 0.041 −0.003 0.004 357 −0.169 0.011 0.175 0.009
Difference 0.828 0.081 0.006 0.008 0.148 0.023 0.035 0.017
sSFR Locally Passive 196 −0.844 0.070 −0.009 0.007 155 −0.021 0.020 0.140 0.015
Locally Star-Forming 177 0.455 0.046 0.017 0.007 134 −0.219 0.011 0.167 0.013
Difference 1.299 0.084 0.026 0.010 0.198 0.023 0.027 0.020

### Table 7

Weighted mean and rms scatter of Hubble residuals for various host galaxy properties

Host Property Group SALT2 MLCS2k2
NSN HRWM
(mag)
Error
(mag)
rms
(mag)
Error
(mag)
NSN HRWM
(mag)
Error
(mag)
rms
(mag)
Error
(mag)
Mass High-mass 464 −0.022 0.008 0.172 0.006 366 −0.023 0.009 0.166 0.006
Low-mass 184 0.035 0.012 0.164 0.009 138 0.042 0.012 0.140 0.008
Difference 0.057 0.014 0.065 0.015
sSFR Globally Passive 194 −0.043 0.013 0.180 0.009 152 −0.034 0.013 0.162 0.009
Globally Star-Forming 455 0.006 0.008 0.167 0.006 354 −0.001 0.009 0.163 0.006
Difference 0.049 0.015 0.033 0.016
sSFR Locally Passive 194 −0.043 0.013 0.180 0.009 152 −0.034 0.013 0.162 0.009
Locally Star-Forming 174 0.038 0.013 0.172 0.009 129 0.038 0.012 0.138 0.009
Difference 0.081 0.018 0.072 0.018
Morphology E-S0 44 0.036 0.036 0.220 0.022 32 0.038 0.036 0.187 0.024
S0a-Sc 131 0.001 0.018 0.191 0.012 103 −0.014 0.019 0.176 0.012
Scd/Sd/Irr 16 0.018 0.038 0.119 0.013 14 0.073 0.028 0.049 0.010
Difference Scd/Sd/Irr - E-S0) 0.018 0.052 0.035 0.046
Morphology Early-type 66 −0.012 0.023 0.178 0.016 50 −0.019 0.024 0.164 0.017
Late-type 177 −0.009 0.014 0.173 0.009 143 0.001 0.015 0.162 0.010
Difference 0.003 0.027 0.020 0.028

### Table 8

Hubble residual differences in each dataset

SN Data SALT2
Mass sSFR
NSN NLow : NHigh HR Difference
(mag)
NSN NPas : NSF HR Difference
(mag)
YONSEI 648 184:464 0.057 ± 0.014 (4.1σ) 649 194:455 0.049 ± 0.015 (3.3σ)
LOWZ 88 12:76 0.002 ± 0.072 (0.0σ) 86 28:59 0.054 ± 0.044 (1.2σ)
SDSS 350 87:263 0.088 ± 0.018 (4.9σ) 350 122:228 0.040 ± 0.019 (2.1σ)
SNLS 207 85:122 0.074 ± 0.023 (3.2σ) 207 45:162 0.069 ± 0.031 (2.2σ)
SN Data MLCS2k2
Mass sSFR
NSN NLow : NHigh HR Difference
(mag)
NSN NPas : NSF HR Difference
(mag)
YONSEI 504 138:366 0.065 ± 0.015 (4.3σ) 506 152:354 0.033 ± 0.016 (2.1σ)
LOWZ 71 11:60 0.124 ± 0.068 (1.8σ) 72 18:54 0.013 ± 0.042 (0.3σ)
SDSS 288 69:219 0.066 ± 0.019 (3.5σ) 287 99:188 0.042 ± 0.019 (2.2σ)
SNLS 140 57:83 0.102 ± 0.025 (4.1σ) 141 36:105 0.061 ± 0.037 (1.6σ)

### Table 9

Comparison of Hubble residual differences between previous studies

Study SN Data NSN Redshift
Range
HR Difference
(mag)
LC Fitter
a. 581 photometrically classified SNe Ia.
b. 755 photometrically classified SNe Ia are included in their SDSS and SNLS samples.
c. 1035 photometrically classified SNe Ia are included in their PS sample.
d. ∆M is a distance correction based on the host mass and ∆B is another distance correction based on the predicted selection bias estimated from SN survey simulations.
Mass
This Work YONSEI 648 0.01 < z < 0.85 0.057 ± 0.014 (4.1σ) SALT2
This Work YONSEI 504 0.01 < z < 0.85 0.065 ± 0.015 (4.3σ) MLCS2k2 (RV = 2.2)
Kelly et al. (2010) CfA 62 0.015 < z < 0.08 0.094 ± 0.045 (2.1σ) SALT2
Kelly et al. (2010) CfA 60 0.015 < z < 0.08 0.083 ± 0.046 (1.8σ) MLCS2k2
Lampeitl et al. (2010) SDSS 162 0.05 < z < 0.21 0.100 ± 0.025 (4.0σ) SALT2
Sullivan et al. (2010) SNLS 195 0.01 < z < 0.85 0.080 ± 0.020 (4.0σ) SALT2+SiFTO
Gupta et al. (2011) SDSS 206 0.01 < z < 0.42 0.096 ± 0.028 (3.4σ) SALT2
Childress et al. (2013) SNf 115 0.03 < z < 0.08 0.085 ± 0.028 (3.0σ) SALT2
Rigault et al. (2013) SNf 82 0.03 < z < 0.08 0.098 ± 0.031 (3.2σ) SALT2
Betoule et al. (2014) JLA 740 0.01 < z < 1.4 0.061 ± 0.012 (5.1σ) SALT2
Pan et al. (2014) PTF 50 0.01 < z < 0.09 0.085 ± 0.047 (1.8σ) SiFTO
Scolnic et al. (2014) PS 110 0.03 < z < 0.65 0.019 ± 0.025 (0.8σ) SALT2
Campbell et al. (2016) SDSS 581a 0.05 < z < 0.55 0.091 ± 0.045 (2.0σ) SALT2
Wolf et al. (2016) SDSS 144 0.05 < z < 0.3 0.082 ± 0.030 (2.7σ) SALT2
Uddin et al. (2017) CfA+CSP+SDSS+SNLS 1338b 0.01 < z < 1.1 0.050 ± 0.009 (5.6σ) SALT2
Jones et al. (2018a) CfA+CSP+PS 1369c 0.01 < z < 0.7 0.092 ± 0.021 (4.4σ) SALT2 with ∆M and ∆Bd
Jones et al. (2018b) Pantheon+Foundation 216 0.01 < z < 0.1 0.049 ± 0.018 (2.7σ) SALT2 with ∆Bd
Rigault et al. (2018) SNf 141 0.02 < z < 0.08 0.119 ± 0.026 (4.6σ) SALT2
Roman et al. (2018) CfA+CSP+SDSS+SNLS 666 0.01 < z < 0.8 0.070 ± 0.013 (5.4σ) SALT2
Scolnic et al. (2018) Pantheon 1023 0.01 < z < 2.3 0.053 ± 0.009 (5.9σ) SALT2 with ∆M and ∆Bd
Global sSFR
This Work YONSEI 649 0.01 < z < 0.85 0.049 ± 0.015 (3.3σ) SALT2
This Work YONSEI 506 0.01 < z < 0.85 0.033 ± 0.016 (2.1σ) MLCS2k2 (RV = 2.2)
Lampeitl et al. (2010) SDSS 162 0.05 < z < 0.21 0.100 ± 0.040 (2.5σ) SALT2
Sullivan et al. (2010) SNLS 195 0.01 < z < 0.85 0.080 ± 0.031 (2.6σ) SALT2+SiFTO
D'Andrea et al. (2011) SDSS 55 z < 0.15 0.100 ± 0.033 (3.0σ) SALT2
Childress et al. (2013) SNf 115 0.03 < z < 0.08 0.050 ± 0.029 (1.7σ) SALT2
Pan et al. (2014) PTF 48 0.01 < z < 0.09 0.070 ± 0.041 (1.7σ) SiFTO
Wolf et al. (2016) SDSS 144 0.05 < z < 0.3 0.013 ± 0.031 (0.5σ) SALT2
Uddin et al. (2017) CfA+CSP+SDSS+SNLS 1338c 0.01 < z < 1.1 0.030 ± 0.014 (2.1σ) SALT2
Morphology
This Work YONSEI 243 0.01 < z < 0.2 0.003 ± 0.027 (0.1σ) SALT2
This Work YONSEI 193 0.01 < z < 0.2 0.020 ± 0.028 (0.7σ) MLCS2k2 (RV = 2.2)
Hicken et al. (2009b) CfA 97 0.01 < z < 0.1 0.144 ± 0.070 (2.1σ) SALT2+MLCS2k2
Suzuki et al. (2012) Union2.1 28 0.9 < z < 1.5 0.180 ± 0.090 (2.0σ) SALT2
Local Environments
This Work YONSEI 281 0.01 < z < 0.85 0.072 ± 0.018 (4.0σ) MLCS2k2 (RV = 2.2)
Rigault et al. (2013) SNf 82 0.03 < z < 0.08 0.094 ± 0.031 (4.5σ) SALT2
Jones et al. (2015) CfA+CSP+CT+SDSS+SNLS+PS1 179 0.01 < z < 0.1 0.000 ± 0.018 (0.0σ) SALT2
Jones et al. (2015) CfA+CSP+CT+SDSS+SNLS+PS1 156 0.01 < z < 0.1 0.029 ± 0.027 (1.1σ) MLCS2k2 (RV = 2.5)
Rigault et al. (2015) CfA 77 0.023 < z < 0.1 0.094 ± 0.037 (2.5σ) SALT2
Rigault et al. (2015) CfA 81 0.023 < z < 0.1 0.155 ± 0.041 (3.8σ) MLCS2k2 (RV = 2.5)
Jones et al. (2018b) Pantheon+Foundation 195 0.01 < z < 0.1 0.040 ± 0.020 (2.0σ) SALT2 with ∆Bd
Kim et al. (2018) YONSEI 368 0.01 < z < 0.85 0.081 ± 0.018 (4.5σ) SALT2
Rigault et al. (2018) SNf 141 0.02 < z < 0.08 0.163 ± 0.029 (5.6σ) SALT2
Roman et al. (2018) CfA+CSP+SDSS+SNLS 666 0.01 < z < 0.8 0.091 ± 0.013 (7.0σ) SALT2

### Table 10

Best-fit flat ΛCDM parameters estimated from SNe Ia in different host environments

Group SNe ΩM α β MB σint χ2/D.O.F.
High-Mass 464 ${0.32}_{-0.08}^{+0.12}$ ${0.15}_{-0.02}^{+0.01}$ 3.26 ± 0.20 ${-19.07}_{-0.02}^{+0.03}$ 0.112 458.23/460
Low-Mass 184 ${0.29}_{-0.06}^{+0.09}$ 0.15 ± 0.03 ${3.28}_{-0.34}^{+0.36}$ ${-19.03}_{-0.04}^{+0.05}$ 0.098 179.37/180
Globally Passive 194 ${0.33}_{-0.10}^{+0.09}$ ${0.18}_{-0.02}^{+0.03}$ ${2.96}_{-0.29}^{+0.31}$ ${-19.12}_{-0.05}^{+0.04}$ 0.104 190.62/190
Globally Star-Forming 455 0.30 ± 0.05 ${0.13}_{-0.01}^{+0.02}$ ${3.28}_{-0.20}^{+0.19}$ ${-19.12}_{-0.03}^{+0.02}$ 0.105 450.08/451
Locally Passive 194 ${0.33}_{-0.10}^{+0.09}$ ${0.18}_{-0.02}^{+0.03}$ ${2.96}_{-0.29}^{+0.31}$ ${-19.12}_{-0.05}^{+0.04}$ 0.104 190.62/190
Locally Star-Forming 174 0.31 ± 0.09 ${0.14}_{-0.03}^{+0.04}$ ${3.40}_{-0.37}^{+0.40}$ −19.02 ± 0.05 0.111 170.58/170
YONSEI Cosmology 1049 ${0.32}_{-0.04}^{+0.03}$ ${0.14}_{-0.00}^{+0.01}$ ${3.07}_{-0.15}^{+0.14}$ ${-19.06}_{-0.02}^{+0.01}$ 0.131 1038.15/1045