Environmental Dependence of Type Ia Supernovae in Low-redshift Galaxy Clusters

We present an analysis of 102 Type Ia supernovae (SNe Ia) in nearby (z < 0.1), x-ray-selected galaxy clusters. This is the largest such sample to date and is based on archival data primarily from ZTF and ATLAS. We divide our SNe Ia into an inner cluster sample projected within r 500 of the cluster center and an outer cluster sample projected between r 500 and 2 r 500. We compare these to field samples of SNe Ia at similar redshifts in both quiescent and star-forming host galaxies. Based on SALT3 fits to the light curves, we find that the inner cluster SNe Ia have a higher fraction of fast-evolving objects (SALT3 x 1 < −1) than the outer cluster or field quiescent samples. This implies an intrinsically different population of SNe Ia occurs in inner cluster environments, beyond known correlations based on host galaxy alone. Our cluster samples show a strongly bimodal x 1 distribution with a fast-evolving component that dominates the inner cluster objects (≳75%) but is just a small fraction of SNe Ia in field star-forming galaxies (≲10%). We do not see strong evidence for variations in the color (SALT3 c) distributions among the samples and find only minor differences in SN Ia standardization parameters and Hubble residuals. We suggest that the age of the stellar population drives the observed distributions, with the oldest populations nearly exclusively producing fast-evolving SNe Ia.


INTRODUCTION
Due to their high and standardizable luminosity (Phillips 1993), type Ia supernovae (SNe Ia) are a key part of the cosmic distance ladder.Measurements of SN Ia distances led to the discovery of the accelerating expansion of the Universe (Riess et al. 1998;Perlmutter et al. 1999) and are used to determine the local value of the Hubble constant (Riess et al. 2009(Riess et al. , 2011(Riess et al. , 2016(Riess et al. , 2022;;Burns et al. 2018;Dhawan et al. 2018;Freedman et al. 2019).SNe Ia also contribute to the chemical enrichment of galaxies and are the dominant source of iron-group elements (Nomoto et al. 2013).Despite their great importance, the fundamental astrophysics of SNe Ia, including their progenitor channels and explosion mechanisms, is not well understood.Currently, the only consensus is that SNe Ia result from exploding carbon-oxygen white dwarfs (for reviews, see e.g., Jha et al. 2019;?).
The environments of supernovae provide important clues to their astrophysics.For example, the association of core-collapse supernovae with recent star-formation points to a massive star origin.SNe Ia, in contrast, occur in every type of host galaxy, though they are most common in star-forming galaxies.Because star-formation is correlated with other galaxy properties, this also means SNe Ia occur more frequently in bluer galaxies, morphologically late-type galaxies, and lower-mass galaxies (van den Bergh 1990; Mannucci et al. 2005;Sullivan et al. 2006;Brown et al. 2019).Not only is the SN Ia rate higher in certain types of host galaxies, the light curve properties of the SNe Ia are also connected to their environment (Hamuy et al. 1996(Hamuy et al. , 2000;;Branch et al. 1996;Sullivan et al. 2006;Rigault et al. 2013).This in turn means that SN Ia environments are linked to their standardization, and may impact the use of SNe Ia as cosmological probes, because host galaxy properties vary with redshift.For instance, this could introduce a bias to the dark energy equation of state parameter, w, of around its current statistical uncertainty of ∼4% (Rigault et al. 2020;Brout & Scolnic 2021;Brout et al. 2022;Dixon et al. 2022).The relationship between environment and SN Ia light curve properties also has important implications for progenitor and explosion models.
Significant evidence has accumulated for an environmental dependence to SN Ia luminosity, even after light-curve standardization.The first indications of a Hubble residual cor-related with host environment were based on the global stellar mass or the star-formation rate of the host galaxy (Kelly et al. 2010;Sullivan et al. 2010;Lampeitl et al. 2010).Often a "mass-step" is now applied in cosmological analyses to correct for this (Sullivan et al. 2011;Betoule et al. 2014;Scolnic et al. 2018;Smith et al. 2020b).Correlations with SN Ia Hubble residual have also been found using other hostgalaxy environmental attributes, including projected separation from the host nucleus, host-galaxy metallicity, and hostgalaxy dust content (D'Andrea et al. 2011;Galbany et al. 2012;?).In addition to "global" host properties, SN Ia luminosity has also been correlated with "local" measurements of stellar mass, star-formation rate, and specific star-formation rate (sSFR; Rigault et al. 2013;Roman et al. 2018;Jones et al. 2018a;Rose et al. 2019;Rigault et al. 2020;Briday et al. 2022).Furthermore, the color of the local SN environment has also been shown to correlate with SN Ia luminosity (Roman et al. 2018;Kelsey et al. 2021Kelsey et al. , 2023;;Briday et al. 2022).
Of key importance is understanding the causation behind these correlations.The light curve or luminosity of a SN Ia is surely not directly influenced by its host-galaxy stellar mass, for example citep[as noted by][]2010MNRAS.406..782S.Instead, presumably the local or host-galaxy environment is indirectly related to the kinds of white dwarf progenitor systems available to explode.The distributions of metallicity or age of the progenitor population may be the intermediaries that link the environment with the supernova explosion.In fact, it has been noted for a long time that progenitor age may be the main driver of SN Ia properties (Sullivan et al. 2010;Brandt et al. 2010;Gupta et al. 2011a), and further studies have indicated that the age of the stellar population (distinctly correlated with host-galaxy properties described above) may be the dominant factor in shaping the kinds of SNe Ia that occur (Rose et al. 2019(Rose et al. , 2020;;Lee et al. 2020;Kang et al. 2020;Wiseman et al. 2021Wiseman et al. , 2023)).
While the physical causal mechanism may not yet be conclusively known, the empirical correlations between SNe Ia and their host-galaxy (or smaller) scale environments are well established.It is intriguing to ask then whether these empirical correlations hold at even larger scales.Here we revisit the nature of SNe Ia found in clusters of galaxies.
Much work has been done on the rate of SNe Ia in cluster host galaxies, which estimates the number of SNe Ia that occur in a galaxy normalized by the galaxy's stellar mass.Early studies of SNe Ia in low-redshift galaxy cluster members show that the SN Ia rate in cluster elliptical hosts is similar to or perhaps elevated compared to the rate in elliptical hosts in the field (Sharon et al. 2007;Mannucci et al. 2008;Dilday et al. 2010;Maoz et al. 2010;Sand et al. 2012).Higher-redshift galaxy cluster studies have also measured the SN Ia rate in clusters and found similar trends (Sharon et al. 2010; Barbary et al. 2012;Freundlich & Maoz 2021;?).The uncertainties in many of these studies have been dominated by small number statistics, however.
Beyond merely the rate of SNe Ia in galaxy clusters, it is interesting to compare their light-curve properties and standardized luminosities with SNe Ia in the field.Meyers et al. (2012), using Hubble Space Telescope (HST) data of highredshift (z ≃ 1) cluster SNe Ia, found no significant differences with field SNe Ia, but with only a small sample size of six cluster SNe Ia with elliptical hosts.Xavier et al. (2013) found evidence that SNe Ia in galaxy clusters (with a sample size of 48 objects) at intermediate redshift (z ≃ 0.1-0.5)had faster-evolving light curves than those in the field, even when restricting both samples to passive galaxies.They ascribed this effect to the older average age of cluster passive galaxies compared to field passive galaxies.Recently, ?used a larger sample of 70 cluster SNe Ia at redshifts z < 0.7 and also found evidence for faster decline rates compared to field SNe Ia (though not specifically restricting to only passive galaxies).This trend appears to continue down to low redshift, but published samples are sparse (Germany et al. 2004).
Our analysis investigates the properties of nearby (z < 0.1) SNe Ia in x-ray selected galaxy clusters.The x-ray selection assures a higher fidelity cluster sample than the typically optically-selected clusters at higher redshift.Our total sample includes 102 cluster SNe Ia and hundreds of field objects for comparison, also improving statistics compared to previous work.The advent of large-area time-domain surveys, e.g., PTF (Law et al. 2009), ASAS-SN (Holoien et al. 2017), ATLAS (Tonry et al. 2018), and ZTF (Bellm et al. 2019), allows us to build a large sample of nearby cluster SNe Ia with multicolor light curves through archival research, rather than requiring a dedicated observing program (e.g., Reiss et al. 1998;Gal-Yam et al. 2008).

Galaxy cluster catalog
For this study, we use the Meta Catalog of X-ray Detected Clusters of Galaxies (MCXC; Piffaretti et al. 2011) to select a sample of 663 galaxy clusters within our redshift range of interest, z < 0.1.The catalog also includes information about the cluster sizes, x-ray luminosities, and inferred masses.Specifically, we rely on the catalog r 500 measurement, the radius of the cluster at which the mass density is 500 times the critical density of the Universe at the cluster redshift.The MCXC r 500 values depend on assumptions about cluster relations that are detailed by Piffaretti et al. (2011), and the catalog adopts a flat ΛCDM cosmology with H 0 = 70 km s −1 Mpc −1 , Ω M = 0.3, and Ω Λ = 0.7.We adopt this cosmological model in our analysis for consistency.

Supernova samples
To build our SN Ia samples, we select SNe projected within 2r 500 of each cluster, converting the MCXC tabulated r 500 from a physical to angular size using the angular diameter distance appropriate for the cluster redshift.We split the cluster SN Ia sample into an inner cluster sample, for SNe Ia within r 500 , and an outer cluster sample between r 500 and 2r 500 .The inner cluster sample probes the centers of our clusters, typically including the extent of observed x-ray emission, and populated by mainly early-type, quiescent galaxies (Giovanelli & Haynes 1985).The outer cluster sample includes SNe Ia that extend out to approximately the virial radius of the clusters (Reiprich et al. 2013;Walker et al. 2019).An example of one of the clusters in our sample, hosting two SNe Ia, is shown in Figure 1.We reiterate that our sample division is based on the projected separation; we discuss below how we estimate cluster membership and contamination below and in Section 3.1.
We identify our supernova samples by querying the Transient Name Server1 (for objects discovered after 2016) and the IAU List of Supernovae2 for older objects.We restrict our sample to SNe that have been spectroscopically classified as regular SNe Ia, and we check the classification by manually inspecting light curves (see Section 2.3).
We use the "directional light radius" (DLR; Sullivan et al. 2006;Gupta et al. 2016) method and the Galaxies HOsting Supernova Transients (GHOST) database (Gagliano et al. 2021) to associate each potential cluster SN Ia with a host galaxy matched against the NASA Extragalactic Database (NED)3 or SIMBAD (Wenger et al. 2000).These account for ∼75% and 67% of our inner and outer cluster sample host identifications respectively.For the remainder, we lack the requisite imaging data to measure the galaxy photometry and light profiles, but can unambiguously identify the host by visual inspection.In our inner cluster sample, there were two supernovae, SN 2020wcj and SN 2020yji, that did not have obviously identifiable hosts, while in our outer cluster sample, there were three such supernovae: SN 2020ags, SN 2020vnr, and SN 2022rdt.
Each SN Ia that had an identifiable host was associated with a NED source: either the host galaxy itself, or absent that, a WISE source (Cutri et al. 2021), from which we collated photometry.We adopted the NED host-galaxy spectroscopic redshift if available (the majority of objects), or else we used the redshift from the SN spectrum as reported in the supernova discovery or classification.Following Carr et al. (2022), we adopt redshift uncertainties of σ z = 0.0001 or σ z = 0.005 for host-galaxy spectroscopic redshifts or SN spectrum redshifts, respectively.If only a host photometric redshift was available, we adopt σ z = 0.01.
We use these redshifts to verify that each SN host galaxy is a member of its cluster.We follow Xavier et al. (2013) and calculate the membership probability with where z SN and σ SN are the redshift and redshift uncertainty of the supernova (given by σ z above), z CL and σ CL are the redshift and redshift uncertainty of the cluster, and z d is three times the velocity dispersion of the cluster in redshift space.We adopt the cluster redshifts as tabulated in the MCXC catalog and set σ CL = 0 as this uncertainty is negligible compared to σ SN .We use the cluster scaling relation given by Zhang et al. (2011) to map the catalogued r 500 to a cluster velocity dispersion that is used to calculate z d .We assume cluster membership for any supernova that yields p > 0.5.In order to compare our cluster supernova samples to the field, we construct samples of SNe Ia in quiescent field galaxies and star-forming field galaxies.For our purposes, the "field" includes any 0.01 < z < 0.1 galaxies outside of our rich x-ray clusters: we do not attempt to eliminate galaxies in groups, in poorer clusters (e.g., optically selected), or in otherwise overdense environments.To identify quiescent and star-forming field galaxies, we use the catalog from Chang et al. (2015), which contains star formation rates (SFRs) and stellar masses for around 850,000 galaxies based on Sloan Digital Sky Survey (SDSS) + WISE photometry (York et al. 2000;Wright et al. 2010).SN host galaxy associations for the field sample use the DLR method (Sullivan et al. 2006;Gupta et al. 2016).We base our quiescent or star-forming classification on Chang et al. (2015), except with slightly stricter criteria 4 to avoid the ambiguity of galaxies that lie in the "green valley" of star formation (Salim 2014).
While we can create large enough field supernova samples even restricting the sky area to the SDSS footprint, our cluster SNe Ia cover the whole sky.For the cluster SN host galaxies with SDSS photometry (just under half of the sample; Chang et al. 2015), we use the same quiescent/starforming classification as the field galaxies above. 5For the cluster host galaxies without SDSS photometry, we rely on WISE colors alone, classifying such galaxies as star-forming if W 2 − W 3 = [4.6µ]− [12µ] > 1.4, and quiescent otherwise (see Figure 12 of Wright et al. 2010).
A few special cases were handled separately: SN 2019ulw (in our outer cluster sample) had an identifiable host, but lacked either WISE or SDSS photometry, so we exclude it from our cluster star-forming and quiescent samples.The hosts of SN 2007fr and SN 2019gwn (in our inner cluster sample) also lacked the requisite photometry, but we were able to acquire slit spectra centered on the host galaxy using the Robert Stobie Spectrograph (RSS; Smith et al. 2006) on the Southern African Large Telescope.The spectral reductions were performed using a custom pipeline based on PySALT (Crawford et al. 2010).The spectrum of SN 2007fr's host showed prominent narrow emission lines of Hα, Hβ, and [O III], so we categorize this galaxy as starforming.The host galaxy of SN 2019gwn was faint and while its spectrum showed hints of an Hα emission line, we could not confidently classify categorize it, and so we exclude SN 2019gwn from the star-forming or quiescent samples.

Supernova photometry
4 For galaxies with (r − z)rest < 0.625, we classify those with (u − r)rest ≥ 2.1 as quiescent, and those with (u − r)rest ≤ 1.9 as star-forming.For galaxies with (r − z)rest ≥ 0.625, our quiescent galaxies have (u − r)rest ≥ 1.6 (r − z)rest + 1.1 and star-forming galaxies have (u − r)rest ≤ 1.6 (r − z)rest + 0.9.See Figure 2 of Chang et al. (2015). 5One supernova in our outer cluster sample, SN 2020jny, has a host that falls in the green valley between our SDSS color regions, so we do not include its host in either the cluster quiescent or cluster star-forming samples.We use archival photometry for our cluster and field supernova samples.The bulk of these data is drawn from the Zwicky Transient Facility (ZTF; Bellm et al. 2019) and the Asteroid Terrestrial-impact Last Alert System (ATLAS; Tonry et al. 2018).For the ZTF data we used the forced photometry service (Masci et al. 2019) to obtain gri magnitudes6 .We also used the ATLAS forced photometry service (Smith et al. 2020a;Shingles et al. 2021) to gather oc (the wide orange and cyan ATLAS passbands) supernova light curves.We also made extensive use of the ALeRCE broker (Förster et al. 2021) to examine light curves and compare photometric data.For supernovae with both ZTF and ATLAS photometry, we confirmed consistency in SN Ia light curve fits (see Section 2.4) compared to ZTF data alone.Because we have a large field supernova sample, we restrict it to exclusively use photometry from ZTF, ATLAS, or both.
Our cluster samples included 10 supernovae with Pan-STARRS1 (Tonry et al. 2012) photometric data from the Young Supernova Experiment (YSE; Jones et al. 2021) first light-curve data release (?).We included these gri photometry in our analysis (but we did not include the z-band).For cluster SNe Ia that predated these surveys (before 2016), we retrieved available Johnson-Cousins BVRI (Bessell 1990) and SDSS gri (York et al. 2000) photometry from varied sources via the Open Supernova Catalog (Guillochon et al. 2017).

Supernova light curve fitting
We employ the SALT3 model to fit our SN Ia light curves (Guy et al. 2007;Kenworthy et al. 2021) Tripp (1998) standardization, using the SNCosmo package (Barbary et al. 2016).Recent work has shown that the switch to SALT3 over SALT2 causes negligible difference in cosmological parameter estimation but reduces calibration errors (Taylor et al. 2023).SALT3 fits a multicolor SN Ia light curve with three parameters: x 0 , which captures the peak flux in the B band; x 1 , which parameterizes the light-curve decline (and rise) rate; and c, which measures the supernova color (corresponding approximately to B−V).A smaller x 1 indicates a faster-evolving light curve and a larger c denotes a redder color.
From the SALT3 fits we can define a peak B magnitude where by convention m B = 10.5 corresponds to x 0 = 1 (Kenworthy et al. 2021).We can then derive a standardized magnitude and distance modulus with a light-curve width and color correction: where µ obs represents the inferred distance modulus, and α, β, and M B are fit parameters that we describe in Section 3.2.We exclude any SNe that have less than five photometric measurements in total.We correct for effects of Milky Way dust extinction in our SALT3 model fits, with an assumed Milky Way R V = 3.1 and E(B − V ) values along the line of sight to our SNe from the dust maps of Schlegel et al. (1998), recalibrated in Schlafly & Finkbeiner (2011).We make use of the NED extinction calculator tool through an existing Python script. 7o create our final supernova samples, we apply light curve quality and fit parameter cuts.As is typical in cosmological analyses, we require SALT3 fits with |x 1 | < 3.0 and |c| < 0.3, and uncertainties σ(x 1 ) < 1.0 and σ(c) < 0.2.We also require a fit uncertainty on the time of maximum light σ(t 0 ) < 0.5 days.Similar cuts were introduced by Betoule et al. ( 2014) and have been used in other SN Ia cosmological studies (Jones et al. 2018b(Jones et al. , 2019;;Brout et al. 2019;Brout & Scolnic 2021;Peterson et al. 2022).For our cluster samples, we further manually inspect the light curve fits and demand that the light curves have both pre-maximum and postmaximum data.

Light-Curve Properties
In our inner cluster sample, we have 54 SNe Ia with adequate light curves and SALT3 parameter values that fall within our cutoff ranges and our outer cluster sample contains 48 SNe that pass these cuts.Our field quiescent and field star-forming samples have 346 and 395 SNe, respectively, that pass the cuts.Figure 2 shows a histogram of the redshifts for these SN Ia samples.The median redshifts for the field quiescent, field star-forming, inner cluster, and outer cluster samples are: 0.062, 0.060, 0.044, and 0.045, respectively.The lower median redshifts of the cluster samples is likely a result of the cluster redshift distribution in the fluxlimited x-ray selection for the MCXC catalog (Piffaretti et al. 2011).We explore potential effects of the slightly different redshift distributions below.The cosmic age difference between the field quiescent sample median redshift (z = 0.062) and the inner cluster sample median (z = 0.044) is about 230 Myr for our adopted cosmology.
Figure 3 shows the distributions of the SALT3 x 1 and c parameters for our inner cluster and outer cluster samples, compared with the field quiescent and field star-forming samples.The most striking differences are seen in x 1 .In SALT2 (and SALT3) model training this light-curve shape parameter is created to have zero mean and unit standard deviation (Guy et al. 2007;Kenworthy et al. 2021) across the train- ing set.However, here we see a strong environmental dependence in the x 1 distribution.A statistical summary of these distributions is given in the "unimodal" columns of Table 1.While the field star-forming sample is not far from a mean of zero and standard deviation of one, the other samples are markedly different.Fast-declining (lower x 1 ) SNe Ia have long been known to preferentially occur in quiescent galaxies (Hamuy et al. 1996(Hamuy et al. , 2000;;Branch et al. 1996), and this is borne out comparing our field quiescent and field starforming samples.Moreover, fast-declining SNe Ia dominate the inner cluster sample, where the x 1 distribution is strongly peaked approximately two standard deviations lower than the mean of the training data.To be clear, when we refer to "fastdeclining" SNe Ia, we mean any SNe Ia with low x 1 values, not just traditionally fast-evolving SN Ia sub-types.
To better understand the environmental dependence in supernova properties, it is useful to control for the host galaxy type.In Figure 4 we limit the cluster samples to comprise quiescent host galaxies only and compare these with the field quiescent sample.Our inner cluster and outer cluster quiescent samples consist of 43 SNe Ia and 28 SNe Ia, respectively.The outer cluster quiescent x 1 distribution is similar to the field quiescent one, whereas the inner cluster quiescent distribution is even more strongly peaked with fast-declining SNe.
To quantitatively compare these distributions, we employ a two-sample Anderson-Darling (A-D) test, which tests the null hypothesis whether two empirical samples are drawn from the same distribution (Pettitt 1976).Calculating the test statistic between our inner cluster and outer cluster quiescent x 1 samples, we find p < 0.001, indicating a clear difference in these populations.We similarly find p < 0.001 for the inner cluster quiescent and field quiescent samples, but for the outer cluster quiescent and field quiescent samples we do not find evidence for different x 1 distributions, p > 0.25.This suggests the inner cluster sample is the standout among quiescent host galaxies.
Performing a similar analysis for star-forming host galaxies is hampered by small number statistics.Our radius and outer cluster star-forming samples consist of only 8 and 15 SNe Ia, respectively.If we combined these to form a cluster star-forming host sample, we find p = 0.031 for the A-D test between the cluster star-forming and field star-forming x 1 distributions.There is thus only marginal evidence for a population difference between cluster and field SNe Ia in star-forming hosts.
In contrast to the x 1 distributions, the right panels of Figure 3 show relatively similar SALT3 c across all of our cluster and field samples.A-D tests confirm this impression; we find no evidence for significant population differences in the color distributions of these SNe.
Distinct from the field star-forming sample, the x 1 distributions for the quiescent hosts (field or cluster) are bimodal, supported by sample statistics.Two-population models for SNe Ia, driven by their x 1 distributions, have been explored before (e.g., recently by ?, who fit such a model to a full sample of SNe Ia; see section 4), but isolating objects in quiescent hosts (and especially our inner cluster sample), brings out the bimodality clearly.We investigate a twopopulation x 1 distribution by running a Markov-Chain Monte Carlo (MCMC) fit to a double Gaussian model.The fit parameters are µ 1 and µ 2 , the x 1 means of faster and slower declining populations, respectively; σ 1 and σ 2 , the widths of the two populations; and f 1 , the fraction of the sample in the faster-declining population (so that the fraction of the slowerdeclining population is 1 − f 1 ).
The results of these fits are summarized in Table 1.In all samples we find a fast-declining population centered at Here we fix the double Gaussian parameters (µ1, σ1, µ2, σ2) to fit the full cluster sample (upper left).The fast-declining population is shown in coral and the slower-declining population is shown in blue.Using this fixed model, in each of the other panels we fit only f1, the fraction of objects in the fast-declining population, for the inner cluster (upper right), field quiescent (lower left), and field star-forming (lower right) samples.
x 1 ≃ −2 that is narrower in width8 than a broader, slowerdeclining population centered at x 1 ≃ +0.3, with slight variations between samples.There is a strong environmental variation in the fraction of objects in the fast-declining population, from approximately 76% in the inner cluster sample (and 86% if we restrict to inner cluster quiescent hosts) all the way down to just 7% in the field star-forming sample.
We illustrate these results visually in Figure 5. Different than in Table 1, in Figure 5, we fix the two population Gaussians (µ 1 , σ 1 , µ 2 , σ 2 ) as fit to the full cluster sample (upper left panel).Then for the other three samples displayed (inner cluster, field quiescent, and field star-forming), we only re-fit for f 1 , to better isolate the changing fraction of fast-declining supernovae.We obtain f 1 values of 76 ± 6%, 44% ± 3%, and 8±2% for these three samples, respectively.Not only is there a vast difference compared to the field star-forming sample, there is even a nearly 5σ difference in f 1 between the inner cluster and field quiescent samples.Clearly, the inner cluster environment produces a different population of SNe Ia than would be predicted for similar host galaxies in the field.Some of the differences between the full double Gaussian fits in Table 1 and the model fixed to the full cluster sample can also be seen in Figure 5.The inner cluster sample fastdeclining population is even slightly faster than the full cluster sample.The peaks in the field quiescent data are broader and not as well separated as in the full cluster sample, and the slower-declining peak in the field star-forming sample is also somewhat broader than the corresponding population in the cluster samples.
The difference in the x 1 distribution between our inner cluster SNe Ia sample and the outer cluster leads us to examine how this varies as a function of the projected distance from the center of the cluster.In Figure 6, we see a clear paucity of slowly-declining SNe Ia near the cluster centers.There is also a hint that the fast-declining population may become slightly slower-declining in the outskirts of the clusters.
We note that we only observe the projected separation of the supernova and its host galaxy within the cluster, so some of our inner cluster sample objects may physically be part of our outer cluster sample (or even further out).We use a cluster galaxy number density model (Carlberg et al. 1997) to estimate that up to ∼28% of our inner cluster sample could be contaminants.For 54 total inner cluster SNe Ia, this means up to ∼15 could be projected from further out.If those objects follow the outer cluster x 1 distribution (Table 1), approximately 61% (9) of those should be from the slowlydeclining population, with about 6 in the fast-declining population.Subtracting these out of our inner cluster sample would leave 41 − 6 = 35 fast-decliners (x 1 < −1) and just 13 − 9 = 4 slower-decliners (x 1 > −1), corresponding to a projection-corrected inner cluster f 1 approaching 90% (35 out of 39)!If we apply a similar projection correction for just the inner cluster quiescent galaxies, we would find that it could account for all of the slow-decliners in the sample.While these would imply an extreme population skew for inner cluster SNe Ia, we can rule out the possibility that all inner cluster objects are fast-decliners: SN 2018bgs is in the brightest cluster galaxy (BCG) and is in the slower-declining population.We further caution that our inner cluster and outer cluster separation is a simplification based on assuming a spherical geometry can adequately describe the clusters.
Though we have constructed a nearby, z < 0.1, sample, we can still investigate trends with redshift.In Figure 7 we show the inner cluster quiescent sample x 1 distribution as a function of redshift, comparing it to the field quiescent sample.Note that at redshifts z < 0.06, there is only one SN with x 1 > 0 in the inner cluster quiescent sample: SN 2008bf.All of the other slower-declining SNe in this sample are at higher redshifts.
Both the inner cluster quiescent sample and the field quiescent sample in Figure 7 show a trend towards larger x 1 as redshift increases, even in the faster-declining population.This could be a result of Malmquist bias, as slower-evolving SNe Ia tend to be more luminous before standardization.Such a luminosity bias could not be used to explain the lack of slower-declining SNe Ia at low redshift in the inner cluster quiescent sample, however, as these brighter SNe should be most easily detected, and they are clearly present in the field quiescent sample.

Standardization and Cosmological Distances
We now turn our attention to examining whether these environmental differences among the samples persist through SN Ia standardization and inferred distances for cosmology.As mentioned in Section 2.4, in order to do a cosmological analysis with the Tripp (1998) standardization, we need to fit for the fit parameters α, β, and M B .We also fit for σ int , a measure of the intrinsic scatter that exists within our SN samples.For our fits, we use an MCMC implemented through the emcee package (Foreman-Mackey et al. 2013).Our log-likelihood function, ln L, is defined via the relation where µ cosmo is the distance modulus derived from our assumed cosmology, and σ obs is the distance modulus uncertainty for each SN.This uncertainty comprises the variances and covariances of the SALT3 fit parameters, redshift uncertainty, and a negligible contribution from lensing effects (given our low-redshift sample; Jönsson et al. 2010).
For our cluster samples, we use the cluster redshifts as the cosmological redshifts, converted to the cosmic microwave background (CMB) frame.We make no correction for cluster peculiar velocities and include a 300 km s −1 peculiar velocity contribution to the redshift uncertainty (Léget et al. 2018), and further restrict the sample to z > 0.01.For our field samples, we convert host redshifts to the CMB frame and also correct for peculiar velocities, following Peterson et al. (2022) and Carr et al. (2022), and using the velocity fields of Carrick et al. (2015) and Said et al. (2020).We assume a peculiar velocity uncertainty of 150 km s −1 for our field objects.For the fit parameters, we adopt uniform priors on α, β, and M B , and a logarithmic prior on σ int with p ∝ 1/σ int .We iterate our fit twice, removing 2σ outliers in Hubble residual (µ obs − µ cosmo ) after the first pass and rerunning to obtain our final values.The results of this analysis for all of our samples are summarized in Table 2.
In Figure 8, we show the corner plot for the inner cluster and outer cluster distributions from our MCMC analysis.The results between the two samples are largely consistent, though there is a hint of a 1.5σ offset in M B : 0.083 ± 0.053 mag.The inner cluster sample and, to a lesser extent, the outer cluster sample also show covariance between M B and α that can largely be ascribed to the x 1 distributions in these samples.For the inner cluster sample especially, the average x 1 is far from x 1 = 0 that defines M B , inducing a correlation with the slope α.
In Figure 9, we show the inferred distances to our cluster SNe Ia compared to the assumed cosmological model.The SN distance moduli and their uncertainties depend upon the fit parameters (α, β, M B , and σ int ) and the individual SN light-curve parameters.The redshifts are taken to be the CMB-frame cluster redshifts.Though the inner cluster and outer cluster samples have different light curve properties, there are not major differences in the inferred distances.Both cluster samples give residual RMS of approximately 0.17 mag, matching, for example, the RMS seen in a ZTF sample (Dhawan et al. 2022).
Comparing our cosmological fits from the cluster samples to the field samples, we see in Table 2 the field sample RMS is slightly lower than the cluster SNe Ia, with RMS of 0.144 mag for the field quiescent sample and 0.134 mag for the field star-forming samples.Based on Figure 7, we noted the possibility of Malmquist bias affecting the field quiescent sample at z > 0.06.If we restrict the field quiescent sample to z < 0.06, Table 2 shows a higher RMS residual of 0.172 mag, comparable to the cluster samples.
The small sizes of our cluster samples mean that the best-fit parameters α, β, and M B are uncertain enough to be consistent with both the field quiescent and field star-forming samples.However, the best-fit values diverge between the field quiescent and star-forming samples themselves, with ∼3σ differences for each parameter.The field host star-formation rate is highly correlated with host stellar mass.In Figure 10 we show the Hubble residual for the field samples as a func- tion of stellar mass, using fit parameters from the combined "full field" sample tabulated in Table 2, and color-coding the galaxies as either quiescent or star-forming.Adopting a host stellar mass division at log(M ⋆ /M ⊙ ) = 10, as typically used in SN Ia cosmology (Sullivan et al. 2010;Rigault et al. 2013;Jones et al. 2019;Smith et al. 2020b), we see that nearly all of the field quiescent hosts are in the higher-mass bin.The differences in the population parameters α, β, and M B manifest themselves as a Hubble residual offset.We recover a mass step of 0.049±0.012mag, consistent with other low-redshift measurements (Betoule et al. 2014;Jones et al. 2018a), including recent investigations using SALT3 (?).Alternatively, we could derive a "specific star-formation step" of 0.049 ± 0.011 mag between the field quiescent and starforming host SNe Ia in Figure 10.If we allow for different α, β, and σ int for these two samples and marginalize over them, the star-formation step is 0.057 ± 0.013 mag, given by the M B offset between the field quiescent and field star-forming galaxies in Table 2.It is reassuring that these slightly different approaches give a robust estimate of the step.
Figure 10 also shows the weighted means of the Hubble residual of our inner cluster sample with the same host stellar mass division as the full field sample.We estimate the host masses of our inner cluster SNe Ia hosts using massto-light scaling relations of either their 2MASS Ks or WISE W 1 photometry (Burns et al. 2018;Dettman et al. 2021;Jarrett et al. 2023), finding good consistency for objects with  2023), there is a clear steepening in the slope, representing the parameter α, towards faster-declining SNe Ia.On the right, we show the same plot but for three increasing host stellar mass bins.We find this steepening in α to be consistent across all three mass bins.both 2MASS and WISE data.The lower mass bin inner cluster weighted mean Hubble residual is quite similar to the respective field sample weighted mean, while the higher mass bin inner cluster weighted average differs from the respective field sample mean by 0.045 ± 0.029 mag, i.e., consistent to within 2σ.One interesting trend to note is that our inner cluster quiescent hosts extend to lower mass than the field quiescent sample; we postulate that this may be due to stronger quenching of low-mass galaxies within clusters in the local Universe (Bolzonella et al. 2010;Moutard et al. 2018).Garnavich et al. (2023) recently suggested that fastdeclining SN Ia may have a steeper dependence of luminosity on x 1 , i.e., an α that varied with x 1 .In Figure 11 we examine this possibility with our inner cluster and field samples, plotting the SALT3 color-corrected SN Ia absolute magnitudes (with β = 2.395 fixed from the field sample) versus x 1 .We then perform a weighted linear regression for both fasterand slower-decliners separately (x 1 < −1 and x 1 > −1 respectively).We find α = −0.203± 0.020 for the faster-decliners and α = −0.087± 0.014 for the slower-decliners.These values are consistent to those from Garnavich et al. (2023) to within 1σ, confirming their finding favoring a nonlinear x 1 correction rather than a single fixed α.We also perform this same fit in three separate mass bins, shown in the right column panels of Figure 11.Here we do not confirm the sugges-tion of Garnavich et al. (2023) that the steepening in α for x 1 < −1 is stronger for higher stellar masses.Our α values for both the faster-and slower-declining samples are consistent to within 1σ across the mass bins.Nevertheless, we concur with Garnavich et al. (2023) that a nonlinear correction in place of a single α value would benefit cosmological samples that contain SNe Ia with a wide range of x 1 .

DISCUSSION
We have identified clear differences between samples of low-redshift SNe Ia in cluster and field environments.It is important to interrogate to what extent our sample selection affects our results.For example, we have only included "normal" SNe Ia, uniformly excluding any objects that were spectroscopically classified as 1991bg-like or 1991T/99aalike from all samples.These would contribute to the fastdeclining and slow-declining populations, respectively, and are further correlated with quiescent and star-forming environments.SN Ia classifiers do not always provide this level of granularity; the quality and phase of the classification spectrum can affect whether a subtype designation can be determined, and there is a continuum between normal SN Ia and these subtypes.Nevertheless, investigating the objects excluded by this selection, we find only one or two objects of each subclass for our cluster sample.Including them would not significantly alter our conclusions.
Similarly, in our analysis we also uniformly excluded objects with |x 1 | > 3, out of range of the SALT3 model.The number of objects rejected with x 1 < −3 or x 1 > +3 are 3/0, 0/0, 21/7, and 0/5, for our inner cluster, outer cluster, field quiescent, and field star-forming samples, respectively.If we assume the too-fast-declining objects are part of the fast-declining population (and conversely for the too-slow objects), our estimates of the fraction in the fast-declining population f 1 (see Figure 5) would change by +1.2%, 0.0%, +3.0%, and −0.2% for those four samples.Standardization of fast-declining objects, especially relevant to the inner cluster sample may benefit from using other light curve fitting tools like MLCS2k2 or SNooPy (Jha et al. 2007;Burns et al. 2011Burns et al. , 2014) ) that can better handle faster-evolving SNe Ia.
The x 1 distributions of the inner cluster and outer cluster samples are clearly bimodal (Figure 5), and this bimodality is also strongly suggested in the field quiescent population.Recently, ?used a hierarchical Bayesian model to similarly identify two populations of SNe Ia in the parameter space of (x 1 , c, m B − µ).As in our analysis, they find the greatest separation between the two populations in the x 1 distributions and also note the correlation with host-galaxy properties.In their model the two populations furthermore have slightly different color (c) distributions, interpreted as arising from different intrinsic colors and dust reddening.We do not find conclusive evidence for differences in the c distributions among our samples (Figure 3), but this should be explored further, especially as our cluster (and even field quiescent) samples bring the two populations into much sharper relief compared to a full sample covering all environments.
Our field quiescent x 1 distribution is consistent with other nearby samples of SNe Ia in quiescent host galaxies (Rigault et al. 2013;Kim et al. 2019), showing similar bimodality.Measurements at higher redshift tend to have more unimodal x 1 distributions (Xavier et al. 2013;Chen et al. 2022), typically with a higher mean x 1 than we find here (though perhaps excepting Lampeitl et al. 2010).This could be a result of redshift evolution in quiescent galaxies and the SNe Ia they host, but Malmquist bias may also be playing a role.
Comparing our cluster SNe Ia samples to those at higher redshift (Xavier et al. 2013; ?), we confirm the tendency of the cluster SNe Ia to be faster evolving than their field counterparts.We also confirm with higher statistics the suggestions by Xavier et al. (2013) that 1. SNe Ia closer to the cluster center have a higher fraction of fast-declining objects than farther out, 2. cluster passive galaxies have a higher fraction of faster-declining objects than field passive galaxies, and 3. the fast-declining cluster SNe Ia are slightly more extreme (even lower x 1 ) than field quiescent SNe Ia (Table 1; Figure 5).We caution that our study differs from the higher red-shift examples because we are using an x-ray selected galaxy cluster catalog, while the high-redshift studies are limited to use optically-selected clusters.The potentially different cluster physical environments may play a role in the different SN Ia populations we see and may also confound effects due to redshift evolution.
There are a few possibilities why SNe Ia from inner cluster host galaxies may have different properties than SNe Ia in the field, even restricting the samples to quiescent galaxies only.We note that whatever the cause, it must be intrinsic to the supernovae.Extrinsic factors like host-galaxy dust may affect the brightness or color of the SNe Ia, but cannot alter the light curve shape (x 1 ) distribution to the large extent we see.
Metallicity has been suggested as a factor in SN Ia variation (D'Andrea et al. 2011;Childress et al. 2013), and the deep gravitational potential well at the centers of galaxy clusters should retain metals better than field quiescent galaxies.However, studies of low-redshift cluster galaxies show they are only slightly more metal rich (≲ 0.05 dex) than field counterparts (Ellison et al. 2009;Lara-López et al. 2022).Observations of the intracluster medium do show a metal enhancement near low-z cluster centers (Lovisari & Reiprich 2019), but the metals escape the galaxies (and subsequent generations of stars) similarly to field quiescent galaxies.It is unlikely, then, that differences in progenitor stellar metallicities are driving the differences seen in our cluster SNe Ia.
The most likely explanation for the properties of the cluster SNe Ia is the age of the stellar population from which they arise.Quiescent massive galaxies host fast-declining SNe Ia, and these galaxies by definition will have preferentially older stars.A correlation between low x 1 and mean stellar age is expected and observed in field samples (Gupta et al. 2011b;Kang et al. 2020) and age is implicated as the chief driver behind supernova standardization differences with host-galaxy properties (recently in, e.g., Briday et al. 2022;Lee et al. 2022;?;Wiseman et al. 2023).Turning to galaxy clusters, Xavier et al. (2013) analyzed the ages of cluster SN Ia host galaxies and found that these hosts were older on average than field host galaxies.This is in accord with results that early type galaxies in nearby galaxy clusters are older than similar early type galaxies in the field by 1-2 Gyr (van Dokkum & Stanford 2003;Thomas et al. 2005;Renzini 2006), an effect that has also been seen at higher redshifts (Webb et al. 2020).It is further intriguing that the strong shift to a fast-declining population in clusters is seen most clearly in our nearby sample, with a less pronounced trend at high redshift (?).This suggests that the fast-evolving population is tracing the oldest SN Ia progenitors.
The bimodality in the x 1 distribution may be a hint that there is a qualitative difference between objects in the fastevolving population and others.A more gradual evolution in the progenitor population might be more compatible with a gradual shift in a unimodal x 1 distribution, but that is not what we observe.Given the wide range of possible SN Ia progenitors and explosion mechanisms, it is enticing to speculate the x 1 bimodality is a signal of the emergence of a different SN Ia progenitor scenario in the oldest stellar populations.In a single-degenerate model with a Chandrasekhar-mass C/O white dwarf, for instance, the oldest SN Ia have red giant companions (see Maoz et al. 2014, for a review).Conversely, the delay times in typical double-degenerate SN Ia models reflect the initial separation distribution for binary white dwarfs (Maoz et al. 2018); if this is a power law as conventionally assumed, the qualitatively different behavior we observe for the oldest SNe Ia might be unexpected.
Our results strengthen the case that older stellar populations produce atypical SNe Ia (Graur et al. 2017;Shen et al. 2017;Hakobyan et al. 2020Hakobyan et al. , 2021;;Karapetyan 2022;Barkhudaryan 2023).The bimodality of the x 1 distribution also suggests that caution is warranted in assuming SNe Ia from old populations (in passive galaxies, for example) are continuously connected to those from younger populations.Though we do not find evidence for large differences in SN Ia standardized luminosity that could depend on age (especially in our cluster objects; Figure 10), deriving age-dependent corrections from a passive galaxy sample (or potentially disregarding cluster versus field distinctions) may lead to results that are not applicable to the majority of SNe Ia in starforming galaxies or otherwise younger environments (Kim et al. 2019;Rose et al. 2019Rose et al. , 2020;;Kang et al. 2020;Lee et al. 2020Lee et al. , 2022;;Murakami et al. 2021;?).

SUMMARY AND CONCLUSIONS
Using archival data, we have constructed the largest to date sample of SNe Ia that occur within rich, nearby (z < 0.1), xray selected clusters of galaxies.We divide them into inner cluster (projected r/r 500 < 1) and outer cluster (1 < r/r 500 < 2) samples and compare these to samples of SNe Ia in field quiescent and star-forming galaxies.With SALT3 light-curve fits to archival optical photometry, the cluster samples show a strongly bimodal distribution in light curve shape (SALT3 x 1 ) and we find a significant difference in the population of fast-evolving (low x 1 < −1) SNe Ia in the clusters compared to field galaxies.Our inner cluster sample contains a much higher fraction of fast-evolving objects compared to the outer cluster sample or even a sample of field quiescent galaxies.These in turn have a higher fast-evolving fraction than field star-forming galaxies.We find no strong evidence of differences in the color (SALT3 c) distribution between the samples, and relatively small differences in standardization parameters (α, β, M B , σ int ) and standardized luminosities (Hubble residual).
A key takeaway is that environmental correlations in SN Ia properties extend beyond galactic scales: the inner cluster sample of SNe Ia is intrinsically different from outer cluster objects and this difference persists even when comparing inner cluster quiescent host galaxies with outer cluster or field quiescent hosts.We suggest that the age of the stellar population is the more direct explanatory cause of these results, with the oldest stellar populations producing almost exclusively fast-evolving SNe Ia.Future work can better clarify the galactic and local differences between low-redshift inner cluster SNe Ia and other samples.Direct measurements and comparison of stellar ages (and perhaps metallicities) at the positions of these inner cluster supernovae and for their host galaxies should yield insight.
We have shown that large samples of cluster SNe Ia provide a unique window into SN Ia populations and encourage further such observations, including extending to higher redshift.Upcoming large sky-area surveys, like the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will be transformative, allowing orders-of-magnitude increase in sample size and higher-significance determinations of sample differences.Moreover, a continued focus on nearby cluster SNe Ia will be important, not only because these can be the best studied, but also they crucially come from the oldest populations.Such objects will likely be the key to unveiling the causal mechanism at work (e.g., different progenitor scenarios).
While we do not see strong trends affecting Hubble residuals in our cluster samples, our results nevertheless have implications for SN Ia cosmology.Our cluster SNe Ia show somewhat higher scatter on the Hubble diagram than the field star-forming sample (Table 2), so excluding these (few in number) cluster objects would slightly improve cosmological samples.More worrisome are systematic uncertainties, especially if older stellar populations systematically produce different SNe Ia.The oldest supernovae at any redshift are those with delay times approaching the age of the Universe at that redshift, a clearly evolving quantity.Conversely, the youngest SNe Ia should have similar ages at all redshifts.Isolating these supernovae, by restricting samples to starforming host galaxies, for instance, may prove a helpful strategy to reduce both statistical and systematic uncertainties for cosmology.
based supernova cosmology research at Rutgers University through DOE award DE-SC0010008.L.A.K. acknowledges support by NASA FINESST fellowship 80NSSC22K1599.
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.
The SALT spectra used in this study were obtained through the Rutgers University SALT program 2023-1-MLT-008 (PI: Jha).

Figure 1 .
Figure 1.SDSS optical (color) and ROSAT PSPC x-ray (contours) image of the galaxy cluster MCXC J2310.4+0734 at z = 0.0424.The inner white circle corresponds to r500 = 0.73 Mpc (0.24 • radius) and the outer circle is twice that radius, roughly the virial radius of the cluster.North is up and east is to the left.The position of the type-Ia SN 2020acwj, part of our outer cluster sample, is shown in green and the position of SN 2021wyw, a fast-declining SN Ia in our inner cluster sample, is shown near the center of the cluster in pink.

Figure 2 .
Figure 2. Redshift histogram for SNe in our cluster and field samples.The cluster sample redshift values are the host cluster redshifts, while the field sample redshifts are from the host galaxy or the supernova.The counts for the field samples have been divided by 5 to bring them on the same scale as the smaller cluster samples.

Figure 3 .
Figure 3. Top: Histograms of the full SALT3 x1 and c parameter distributions for our cluster SN Ia samples.Bottom: Histograms showing the same distributions as above, but for our field quiescent and field star-forming samples.

Figure 4 .
Figure 4. Histogram of x1 parameter values for SNe in our inner cluster and outer cluster samples, restricted to quiescent host galaxies.These are compared to the field quiescent host galaxy sample (whose counts are scaled down by 5 to ease comparison).

Figure 5 .
Figure 5. Bimodal fits to the x1 distributions in different samples.Here we fix the double Gaussian parameters (µ1, σ1, µ2, σ2) to fit the full cluster sample (upper left).The fast-declining population is shown in coral and the slower-declining population is shown in blue.Using this fixed model, in each of the other panels we fit only f1, the fraction of objects in the fast-declining population, for the inner cluster (upper right), field quiescent (lower left), and field star-forming (lower right) samples.

Figure 6 .
Figure 6.Top: histogram of our full quiescent cluster sample in gray, with the fit bimodal populations overlayed in the coral and blue colors respectively.The vertical dashed lines represent the fit means for each population distribution for this sample.Bottom: the x1 parameter values of our cluster SNe Ia in quiescent hosts as a function of their projected distance from their cluster center.The inner cluster portion of the sample is represented by black diamonds.The outer cluster portion of the sample is represented by green circles.We can see that SNe closer to the center of the cluster tend to have much faster-evolving light curves.

Figure 7 .
Figure 7. Trends in the x1 parameter values of our field quiescent and inner cluster quiescent samples as a function of redshift.The black and orange points are the binned median values for our inner cluster quiescent and field quiescent samples respectively.The errors on each point are the standard error for the bin.The points are positioned at the centers of each bin.

Figure 8 .
Figure 8. Corner plot for our inner cluster (black) and outer cluster (green) sample fit parameters.The best fit values and errors are on top of each corresponding column, with the inner cluster sample values on top and the outer cluster values below them.MB and σint are in units of magnitude.

Figure 9 .
Figure 9. Inferred distances for the inner cluster and outer cluster samples, adopting best-fit values for the parameters α, β, MB, and σint for each sample separately.The blue curve shows the predicted distance moduli from our assumed cosmology.The bottom panel shows the Hubble residuals, µobs − µcosmo.The points represent the samples after the 2σ outlier removal.

Figure 10 .
Figure 10.Hubble residuals for our field quiescent and star-forming host samples versus host-galaxy stellar mass.The green line represents our adopted dividing line of 10 10 M⊙ for the low-mass and high-mass samples.The black points are the weighted average of the mass bins, while the gold stars with the black outlines represent the weighted average of our full inner cluster sample in the lower and upper mass bins .Outliers beyond 2σ have been removed from the sample.

Figure 11 .
Figure 11.Color-corrected absolute magnitudes of field quiescent, field star-forming, inner cluster quiescent, and inner cluster star-forming host SNe Ia versus x1.The black lines show weighted linear regression fits to the slower-declining (x1 > −1) and faster-declining (x1 < −1) SNe Ia from the four samples above.Confirming the result of Garnavich et al. (2023), there is a clear steepening in the slope, representing the parameter α, towards faster-declining SNe Ia.On the right, we show the same plot but for three increasing host stellar mass bins.We find this steepening in α to be consistent across all three mass bins.

Table 1 .
Number of supernovae for each sample, as well as the mean, standard deviation, median, median absolute deviation for the SALT3 x1 parameter distributions for each sample (unimodal) and double Gaussian fits (bimodal) to the x1 distribution, with f1 indicating the fraction in the fast-declining population.

Table 2 .
Fit parameters obtained through our cosmological MCMC procedure for each sample.

Table 3 continued
Table 3 (continued) In the Host SFR column, SF=star-forming, Q=quiescent, and GV=green valley.