# A Systematic Study of Ia-CSM Supernovae from the ZTF Bright Transient Survey

Yashvi Sharma Division of Physics, Mathematics and Astronomy, California
Institute of Technology, Pasadena, CA 91125, USA  Jesper Sollerman Department
of Astronomy, The Oskar Klein Center, Stockholm University, AlbaNova, 10691
Stockholm, Sweden  Christoffer Fremling Division of Physics, Mathematics and
Astronomy, California Institute of Technology, Pasadena, CA 91125, USA
Shrinivas R. Kulkarni Division of Physics, Mathematics and Astronomy,
California Institute of Technology, Pasadena, CA 91125, USA  Kishalay De MIT-
Kavli Institute for Astrophysics and Space Research, Cambridge, MA 02139, USA
Ido Irani Department of Particle Physics and Astrophysics, Weizmann Institute
of Science, 234 Herzl St, 76100 Rehovot, Israel  Steve Schulze Department of
Physics, The Oskar Klein Center, Stockholm University, AlbaNova, 10691
Stockholm, Sweden  Nora Linn Strotjohann Department of Particle Physics and
Astrophysics, Weizmann Institute of Science, 234 Herzl St, 76100 Rehovot,
Israel  Avishay Gal-Yam Department of Particle Physics and Astrophysics,
Weizmann Institute of Science, 234 Herzl St, 76100 Rehovot, Israel  Kate
Maguire School of Physics, Trinity College Dublin, the University of Dublin,
College Green, Dublin, Ireland  Daniel A. Perley Astrophysics Research
Institute, Liverpool John Moores University, Liverpool Science Park, 146
Brownlow Hill, Liverpool L35RF, UK  Eric C. Bellm DIRAC Institute, Department
of Astronomy, University of Washington, 3910 15th Avenue NE, Seattle, WA
98195, USA  Erik C. Kool Department of Astronomy, The Oskar Klein Center,
Stockholm University, AlbaNova, 10691 Stockholm, Sweden  Thomas Brink
Department of Astronomy, University of California, Berkeley, CA 94720-3411,
USA  Rachel Bruch Department of Particle Physics and Astrophysics, Weizmann
Institute of Science, 234 Herzl St, 76100 Rehovot, Israel  Maxime Deckers
School of Physics, Trinity College Dublin, the University of Dublin, College
Green, Dublin, Ireland  Richard Dekany Caltech Optical Observatories,
California Institute of Technology, Pasadena, CA 91125, USA  Alison Dugas
Institute for Astronomy, University of Hawai’i, Honolulu, HI 96822, USA
Samantha Goldwasser  Department of Particle Physics and Astrophysics, Weizmann
Institute of Science, 234 Herzl St, 76100 Rehovot, Israel  Matthew J. Graham
Division of Physics, Mathematics and Astronomy, California Institute of
Technology, Pasadena, CA 91125, USA  Melissa L. Graham DIRAC Institute,
Department of Astronomy, University of Washington, 3910 15th Avenue NE,
Seattle, WA 98195, USA  Steven L. Groom IPAC, California Institute of
Technology, 1200 E. California Blvd, Pasadena, CA 91125, USA  Matt Hankins
Arkansas Tech University, Russellville, AR 72801, USA  Jacob Jencson Steward
Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ
85721-0065, USA  Joel P. Johansson Department of Physics, The Oskar Klein
Center, Stockholm University, AlbaNova, 10691 Stockholm, Sweden  Viraj
Karambelkar Division of Physics, Mathematics and Astronomy, California
Institute of Technology, Pasadena, CA 91125, USA  Mansi M. Kasliwal Division
of Physics, Mathematics and Astronomy, California Institute of Technology,
Pasadena, CA 91125, USA  Frank J. Masci IPAC, California Institute of
Technology, 1200 E. California Blvd, Pasadena, CA 91125, USA  Michael S.
Medford Department of Astronomy, University of California, Berkeley, Berkeley,
CA 94720  Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., Berkeley, CA
94720  James D. Neill Division of Physics, Mathematics and Astronomy,
California Institute of Technology, Pasadena, CA 91125, USA  Guy Nir
Department of Astronomy, University of California, Berkeley, CA 94720-3411,
USA  Reed L. Riddle Caltech Optical Observatories, California Institute of
Technology, Pasadena, CA 91125, USA  Mickael Rigault  Université Clermont
Auvergne, CNRS/IN2P3, Laboratoire de Physique de Clermont, 63000 Clermont-
Ferrand, France  Tassilo Schweyer Department of Astronomy, The Oskar Klein
Center, Stockholm University, AlbaNova, 10691 Stockholm, Sweden  Jacco H.
Terwel School of Physics, Trinity College Dublin, the University of Dublin,
College Green, Dublin, Ireland  Isaac Newton Group (ING), Apt. de correos 321,
E-38700, Santa Cruz de La Palma, Canary Islands, Spain  Lin Yan Division of
Physics, Mathematics and Astronomy, California Institute of Technology,
Pasadena, CA 91125, USA  Yi Yang (杨轶)  Department of Astronomy, University of
California, Berkeley, CA 94720-3411, USA  Yuhan Yao Division of Physics,
Mathematics and Astronomy, California Institute of Technology, Pasadena, CA
91125, USA Yashvi Sharma<EMAIL_ADDRESS>
###### Abstract

Among the supernovae (SNe) that show strong interaction with the circumstellar
medium, there is a rare subclass of Type Ia supernovae, SNe Ia-CSM, that show
strong narrow hydrogen emission lines much like SNe IIn but on top of a
diluted over-luminous Type Ia spectrum. In the only previous systematic study
of this class (Silverman et al., 2013), 16 objects were identified, 8 historic
and 8 from the Palomar Transient Factory (PTF). Now using the successor survey
to PTF, the Zwicky Transient Facility (ZTF), we have classified 12 additional
objects of this type through the systematic Bright Transient Survey (BTS). In
this study, we present and analyze the optical and mid-IR light curves,
optical spectra and host galaxy properties of this sample. Consistent with
previous studies, we find the objects to have slowly evolving light curves
compared to normal SNe Ia with peak absolute magnitudes between $-19.1$ and
$-21$, spectra having weak H$\beta$, large Balmer decrements of $\sim 7$ and
strong Ca NIR emission. Out of 10 SNe from our sample observed by NEOWISE, 9
have $3\sigma$ detections, along with some showing a clear reduction in red-
wing of H$\alpha$, indicative of newly formed dust. We do not find our SN Ia-
CSM sample to have significantly different distribution of equivalent width of
He I $\lambda 5876$ than SNe IIn as observed in Silverman et al. (2013). The
hosts tend to be late-type galaxies with recent star formation. We also derive
a rate estimate of 29${}^{+27}_{-21}$ Gpc-3 yr-1 for SNe Ia-CSM which is
$\sim$0.02–0.2% of the SN Ia rate. This work nearly doubles the sample of well
studied Ia-CSM objects in Silverman et al. (2013), increasing the total number
to 28.

circumstellar matter – supernovae: general – supernovae: individual (SN
1997cy, SN 2002ic, SN 2005gj, SN 2005ip, SN 2006jc, SN 2008J, SN 2009ip, SN
2010jl, PTF11kx, SN 2012ca, SN 2013dn, SN 2018crl, SN 2018gkx, SN 2018evt, SN
2019agi, SN 2019ibk, SN 2019rvb, SN 2020onv, SN 2020qxz, SN 2020uem, SN
2020xtg, SN 2020abfe, SN 2020aekp)

††software: LAMBDAR (Wright et al., 2016), Prospector (Johnson et al., 2021),
pySEDM (Rigault et al., 2019), IRAF (Tody, 1986, 1993), pyNOT
(https://github.com/jkrogager/PyNOT), LPipe (Perley, 2019), pypeit (Prochaska
et al., 2020), extinction (Barbary, 2016), pyraf-dbsp (Bellm & Sesar, 2016),
FPipe (Fremling et al., 2016), DBSP_DRP (dbs, 2021), ztfquery (Rigault, 2018),
astropy (Astropy Collaboration et al., 2013, 2018, 2022), matplotlib (Hunter,
2007)

##  1 Introduction

When it comes to supernovae (SNe) interacting with circumstellar material
(CSM), a number of sub-types of core-collapse SNe (CCSNe) show signs of strong
interaction, like SNe IIn (Schlegel, 1990; Filippenko, 1997), SNe Ibn
(Pastorello et al., 2008; Foley et al., 2007; Chugai, 2009; Hosseinzadeh et
al., 2017) and most recently SNe Icn (Gal-Yam et al., 2021, 2022; Perley et
al., 2022). SN IIn progenitors are generally thought to be massive stars (like
Luminous Blue Variables, LBVs) that lose their hydrogen envelopes to wind-
driven mass loss and outbursts (Gal-Yam et al., 2007; Gal-Yam & Leonard, 2009;
Kiewe et al., 2012; Taddia et al., 2013; Smith, 2014). Helium-rich but
hydrogen-deficient CSM in the case of SNe Ibn (Pastorello et al., 2008; Foley
et al., 2007; Chugai, 2009) and both hydrogen and helium deficient CSM in SNe
Icn (Gal-Yam et al., 2022; Perley et al., 2022; Pellegrino et al., 2022) are
thought to arise from high-velocity wind mass loss or stripping of the
envelope in binary configurations of massive Wolf-Rayet (WR) like stars. For
SNe IIn in most cases, the mass-loss rate derived from the CSM velocity is
consistent with estimates from LBV-like eruptive mass loss.

However, there exists a rare sub-type of thermonuclear supernovae (SNe Ia)
which also interacts strongly with CSM i.e. SNe Ia-CSM. This class poses a
challenge to the progenitor debate of SNe Ia. There is some consensus on there
being at least two major progenitor channels for SNe Ia; the double-degenerate
(DD) channel (Webbink, 1984; Iben & Tutukov, 1984) which is the merging of two
C/O white dwarfs and the single-degenerate (SD) channel (Whelan & Iben, 1973)
where the white dwarf accretes enough material from a non-degenerate companion
to explode. Although there are more arguments for the DD scenario from
observations of nearby SNe Ia (Nugent et al., 2011; Li et al., 2011; Brown et
al., 2012; Bloom et al., 2011), the strongest observational evidence for the
SD scenario are SNe Ia with CSM.

Indications of CSM around SNe Ia ranges from detection of time varying narrow
Na ID absorption lines (Patat et al., 2007; Blondin et al., 2009; Simon et
al., 2009) in high-resolution spectra (found in at least 20% of SNe Ia in
spiral hosts, Sternberg et al. 2011; Maguire et al. 2013; Clark et al. 2021),
to strong intermediate and narrow Balmer emission features in the spectra and
large deviations of the light curves from the standard shape. The latter
phenomena have been named SNe Ia-CSM (Silverman et al., 2013), but were
earlier referred to as “SNe IIna” or “SNe Ian” due to the strong similarity
between their spectra and those of SNe IIn. The first two examples of this
class studied in detail were SNe 2002ic (Hamuy et al., 2003; Deng et al.,
2004; Wang et al., 2004; Wood-Vasey et al., 2004; Kotak & Meikle, 2005; Chugai
et al., 2004) and 2005gj (Aldering et al., 2006; Prieto et al., 2007), but for
a long time there was ambiguity regarding their thermonuclear nature (Benetti
et al., 2006). These SNe were dominated by interaction from the first spectrum
and were quite over-luminous compared to normal SNe Ia. The first clear
example of a thermonuclear SN Ia-CSM was PTF11kx (Dilday et al., 2012;
Silverman et al., 2013). It looked like a luminous SN Ia (99aa-like) at early
phases but started showing interaction at $\sim 60$ days from explosion and
thereafter strongly resembled SNe 2002ic and 2005gj at late times. Higher
resolution spectra taken at early times indicated multiple shells of CSM with
some evacuated regions in between. Dilday et al. (2012) suggested a symbiotic
nova progenitor involving a WD and a red giant (similar to RS Ophiuchi) could
produce such CSM distribution, however later studies argued that the massive
CSM of PTF11kx was inconsistent with the mass-loss rates from symbiotic nova
systems (Silverman et al., 2013; Soker et al., 2013).

Ever since, a handful of SNe of this class have been studied in detail to
investigate their progenitors and to distinguish them from their spectroscopic
cousins, the Type IIn SNe. Both SN Ia-CSM and SN IIn spectra share a blue
quasi-continuum, a strong H$\alpha$ feature with an intermediate and a narrow
component, and often a broad Ca NIR triplet feature, but they differ with
regards to the line strength of H$\beta$, strength/presence of helium and
presence of emission lines from intermediate mass elements often found in
CCSNe. There are some individual SNe with unclear type often referred to as SN
Ia-CSM/IIn, like SN 2012ca for which some papers argue for core-collapse
(Inserra et al., 2014, 2016) and others for a thermonuclear origin (Fox et
al., 2015). This ambiguity becomes more dominant as the underlying SN flux
gets smaller compared to the interaction power (Leloudas et al., 2015).
Silverman et al. (2013, hereafter S13) is the only study to analyze a sample
of SNe Ia-CSM, 16 objects in total including 6 previously known, 3 re-
discovered (re-classified SNe IIn) and 7 new from the Palomar Transient
Factory (PTF). Their paper presents the common properties of optical light
curves, spectra and host galaxies and contrast them against SN IIn properties.
In this paper, we present 12 new SNe Ia-CSM discovered as part of the Zwicky
Transient Facility’s (ZTF; Bellm et al., 2019; Graham et al., 2019; Dekany et
al., 2020) Bright Transient Survey (BTS; Fremling et al., 2020; Perley et al.,
2020) and analyze their optical light curves, spectra, hosts and rates.
Throughout this paper, we have compared the results derived from our sample to
the ones in S13.

This paper is organised as follows; we first discuss the sample selection
criteria, the photometric and spectroscopic data collection in §2, then the
analysis of light- and color-curves and the bolometric luminosities is done in
§3.1. The analysis of early and late-time spectra and emission line
identification is presented in §3.2, and analysis of the host galaxies is
provided in §3.3. The rates are estimated from the BTS survey in §3.4. We end
with a discussion about the nature of SN Ia-CSM progenitors and a summary in
§4 and §5.

##  2 Observations and Data reduction

In this section, we outline our selection criteria, and present the optical
photometry and spectroscopic observations of the 12 SNe Ia-CSM in our sample.

###  2.1 Selection Criteria

To carefully curate our sample of SNe Ia-CSM, we used the BTS sample and its
publicly available BTS Sample
Explorer111https://sites.astro.caltech.edu/ztf/bts/explorer.php website to
obtain the list of all classified Type Ia sub-types during the period
2018-05-01 to 2021-05-01. We then filter out oddly behaving Type Ia SNe based
on their light-curve properties. We used two criteria; the primary being rest-
frame duration considering flux above 20% of peak flux, and the second being
change in magnitude after 30 days from peak ($\Delta m_{30}$). We calculated
these two properties from either $g$ or $r$-band light curves (whichever had
maximum number of detections) grouped into 3-day bins and used Gaussian
Process Regression222Pedregosa et al. (2011) https://scikit-
learn.org/stable/modules/gaussian_process.html to interpolate the light curves
where coverage was missing. For the first filtering, we calculated the mean
($\mu\approx 35$ days) and standard deviation ($\sigma\approx 16$ days) of the
duration distribution and selected everything that had a duration greater than
$\mu+3\sigma$. Given the large sample size ($N=3486$), the standard error on
the mean is $\sim 0.5$ days, hence our duration cut of $3\sigma$ is suitable.
This filtering selected 41 out of 3486 BTS SNe Ia. Then from these 41 SNe, we
calculated the mean and standard deviation of the $\Delta m_{30}$ distribution
and removed SNe that were more than 1$\sigma$ away from the mean on the higher
side to reject the relatively steeply declining long SNe, which resulted in 35
SNe being kept. Again, the mean and standard deviation of $\Delta m_{30}$
distribution of these 41 long duration SNe are 0.48 mag and 0.27 mag
respectively and the standard error on mean is $\sim 0.04$, making our
$1\sigma$ cut suitable. Finally, we manually inspected the 35 selected SNe Ia
to confirm their classification. 20 out of the 35 SNe that passed the above
filtering criteria were just normal SNe Ia either caught late or missing some
post-peak coverage in ZTF or had spurious detections that resulted in long
duration estimates, 2 had incorrect duration estimate due to an interpolation
error and were recalculated and 1 (AT2020caa; Soraisam et al., 2021) had some
detections before the SN explosion which could be connected to a different SN
(i.e. a sibling; Graham et al., 2022).

The remaining 12 long-duration SNe Ia all turned out to be spectroscopically
classified SNe Ia-CSM in BTS, and none of the classified BTS SNe Ia-CSM were
missed in this filtering. No other SNe apart from these stood out in
particular, indicating the classification reliability of the BTS sample.
During the same period, 9 SNe Ia-CSM were reported to the Transient Name
Server (TNS), out of which 7 are already in our sample, 1 was detected by ZTF
but did not meet the BTS criteria, and 1 was not detected in ZTF as the
transient location fell too close to the field edges and was masked by the
automated image subtraction pipeline. Yao et al. (2019) presented early
photometric observations of one SN Ia-CSM in our sample, SN 2018crl. Table 1
summarizes the coordinates, redshifts, peak absolute magnitudes, durations,
host galaxy information and Milky Way extinction for the 12 SNe Ia-CSM in our
sample.

Furthermore, we re-checked the classifications of 142 SNe IIn classified in
BTS during the same period as above, in case any SN Ia-CSM was masquerading
among them and found 6 to have ambiguous classifications. These are discussed
further in Appendix A.

Table 1: Properties of the 12 BTS SNe Ia-CSM

ZTF Name | IAU Name | z | $M_{r}^{\rm{peak}}$ | Duration1 | Host Name | Host Mag2
---|---|---|---|---|---|---
|  |  | (mag) | (days) |  | ($m_{r}$)
ZTF18aaykjei | SN 2018crl | 0.097 | -19.66 | 130 | SDSS J161938.90+491104.5 | 18.89
ZTF18abuatfp | SN 2018gkx | 0.1366 | -20.07 | 322 | SDSS J135219.22+553830.2 | 18.23
ZTF18actuhrs | SN 2018evt | 0.02378 | -19.10 | 447 | MCG-01-35-011 | 14.07
ZTF19aaeoqst | SN 2019agi | 0.0594 |  $<$-18.76 |  $>$303 | SDSS J162244.06+240113.4 | 17.82
ZTF19abidbqp | SN 2019ibk | 0.04016 |  $<$-17.55 |  $>$576 | SDSS J014611.93-161701.1 | 15.55
ZTF19acbjddp | SN 2019rvb | 0.1835 | -20.74 | 172 | WISEA J163809.90+682746.3 | 20.44
ZTF20abmlxrx | SN 2020onv | 0.095 |  $<$-20.36 |  $>$154 | WISEA J231646.31-231839.9 | 17.95
ZTF20abqkbfx | SN 2020qxz | 0.0964 | -20.00 | 166 | WISEA J180400.99+740050.0 | 17.65
ZTF20accmutv | SN 2020uem | 0.041 |  $<$-20.17 |  $>$279 | WISEA J082423.32-032918.6 | 15.88
ZTF20aciwcuz | SN 2020xtg | 0.0612 |  $<$-19.60 |  $>$336 | SDSS J153317.64+450022.8 | 15.42
ZTF20acqikeh | SN 2020abfe | 0.093 | -20.24 | 171 | SDSS J200003.30+100904.2 | 20.18
ZTF21aaabwzx | SN 2020aekp | 0.046 | -19.62 | 458 | SDSS J154311.45+174843.7 | 18.41

  * 1

Rest frame duration above 20% of $r$-band peak flux, uncertainty of $\pm 2-3$
days from ZTF cadence.

  * 2

Corrected for Galactic extinction.

###  2.2 Discovery

All SNe Ia-CSM were detected by the ZTF (Bellm et al., 2019; Graham et al.,
2019; Dekany et al., 2020) and passed the criteria for the BTS (Fremling et
al., 2020; Perley et al., 2020) automatic filtering, i.e. extra-galactic real
transients with peak magnitudes brighter than 19 mag. These were saved and
classified as part of BTS which aims to classify all transients brighter than
18.5 magnitude, and reported to the Transient Name Server333https://www.wis-
tns.org/ (TNS) during the period 2018-05-01 to 2021-05-01. Out of the 12 SNe,
6 were first reported to TNS (i.e. discovered) by ZTF (AMPEL, Nordin et al.
2019; Soumagnac & Ofek 2018 and BTS), 3 were first reported by GaiaAlerts
(Hodgkin et al., 2021), 2 by ATLAS (Smith et al., 2020) and 1 by ASAS-SN
(Shappee et al., 2014). For classification, 9 were classified by the ZTF
group, 1 by ePESSTO (Smartt et al., 2015; Stein et al., 2018a), 1 by SCAT
(Tucker et al., 2018; Payne et al., 2019) and 1 by the Trinity College Dublin
(TCD) group (Prentice et al., 2020). The follow-up spectral series for these
SNe were obtained as part of the BTS classification campaign as many were
difficult to classify with the ultra-low resolution spectrograph P60/SEDM
(Blagorodnova et al., 2018) and hence were followed up with intermediate
resolution spectrographs. The SEDM spectra were helpful in determining an
initial redshift but the template matches were unclear (matched to SN IIn as
well as SN Ia-CSM and SN Ia-pec templates, some matched poorly to SN Ia/Ic at
early times). SNe 2019agi (classification and spectrum taken from TNS),
2019rvb, 2020onv, 2020qxz and 2020uem were classified as Ia-CSM $\sim 1-2$
month after discovery using spectra at phases of 42, 26, 38, 45 and 51 days
respectively. SNe 2018crl, 2018gkx and 2019ibk were classified $\sim 2-3$
months after discovery using spectra at phases of 92, 75 and 103 days
respectively. SNe 2018evt, 2020abfe and 2020aekp were classified $\sim 4-5$
months after discovery using the spectra at phases of 144, 146 and 132 days
respectively. SN 2020xtg immediately went behind the sun after its first
detection in ZTF therefore its first spectrum (using SEDM) was taken at 91
days since explosion which was dominated by strong H$\alpha$ emission, and
thus SN 2020xtg was initially classified as a Type II. As this SN was
exhibiting a long lasting light curve, an intermediate resolution spectrum was
taken at 340 days which matched very well to SN Ia-CSM and therefore its
classification was updated. SNe 2020uem and 2020aekp showed peculiar features
and were followed up for more optical spectroscopy for single object studies
(to be presented in future papers).

###  2.3 Optical photometry

To assemble our sample light curves, we obtained forced PSF photometry via the
ZTF forced-photometry service (Masci et al., 2019; IRSA, 2022) in $g$, $r$ and
$i$ bands and also added data from ATLAS (Tonry et al., 2018; Smith et al.,
2020) forced-photometry service in $c$ and $o$ bands. The high cadence ZTF
partnership survey in $i$ band contributed some photometry to SNe 2018crl,
2018gkx, 2019agi, 2019ibk and 2019rvb. The ZTF and ATLAS data were
supplemented with data from the Rainbow camera (RC, Ben-Ami et al. 2012) on
the robotic Palomar 60-inch telescope (P60, Cenko et al., 2006) and the
Optical wide field camera (IO:O) on the Liverpool telescope (LT, Steele et
al., 2004). The P60 data was processed with the automatic image subtraction
pipeline FPipe (Fremling et al., 2016) using reference images from SDSS when
available, and otherwise from Pan-STARRS1. The IO:O data was initially reduced
with their standard
pipeline444https://telescope.livjm.ac.uk/TelInst/Pipelines/ then image
subtraction was carried out using the method outlined in Taggart (2020). For
SN 2018evt, some early time data available from ASAS-SN (Shappee et al., 2014;
Kochanek et al., 2017) in the $V$ band was obtained through their Sky
Patrol555https://asas-sn.osu.edu/ interface.

We corrected all photometry for Milky Way extinction with the Python package
extinction (Barbary, 2016) using the dust extinction function from Fitzpatrick
(1999), the Schlafly & Finkbeiner (2011) dust map, and an RV of 3.1. Then we
converted all measurements into flux units for analysis and considered
anything less than a 3$\sigma$ detection an upper limit. There is moderate to
good coverage in $g$, $r$, $c$ and $o$ bands for all SNe in our sample. Figure
1 shows a multi-paneled figure of the light curves of the objects in our
sample.

Figure 1: Optical light curves of the ZTF BTS SN Ia-CSM sample. The SNe Ia-CSM
have longer duration than the average SN Ia, with some variety like bumpy
light curves or long plateaus. The one SN marked with an asterisk (SN 2020uem)
has an unconstrained explosion time estimate ($\sim\pm 50$ d). The decline
rate from Cobalt decay is marked with black dashed line, the light curve
decline rates measured from $r$-band data are shown in the subplot legends.

###  2.4 Mid-IR photometry

The transients were observed during the ongoing NEOWISE all-sky mid-IR survey
in the $W1$ ($3.4$ $\mu$m) and $W2$ ($4.5$ $\mu$m) bands (Wright et al.,
2010a; Mainzer et al., 2014). We retrieved time-resolved coadded images of the
field created as part of the unWISE project (Lang, 2014a; Meisner et al.,
2018). To remove contamination from the host galaxies, we used a custom code
(De et al., 2020) based on the ZOGY algorithm (Zackay et al., 2016) to perform
image subtraction on the NEOWISE images using the full-depth coadds of the
WISE and NEOWISE mission (obtained during 2010-2014) as reference images.
Photometric measurements were obtained by performing forced PSF photometry at
the transient position on the subtracted WISE images until the epoch of the
last NEOWISE data release (data acquired until December 2021). Further
analysis of the mid-IR photometry is presented in §3.1.4

###  2.5 Optical spectroscopy

The main instruments used for taking spectra and the software used to reduce
the data are summarized in Table 2. Additionally, the spectrum Reguitti (2020)
obtained using the Asiago Faint Object Spectrograph and Camera (AFOSC) on the
1.8 m telescope at Cima Ekar, and the spectrum Stein et al. (2018b) obtained
using the ESO Faint Object Spectrograph and Camera version 2 (EFOSC2) on ESO
New Technology Telescope (NTT) were taken from TNS.

Table 2: Description of spectrographs used for follow-up and the corresponding
data reduction pipelines

Inst. | Telescope | Reduction Software
---|---|---
SEDM1 | Palomar 60-inch (P60) | pySEDM2
ALFOSC3 | Nordic Optical Telescope |  IRAF4, PyNOT14, pypeit
DBSP5 | Palomar 200-inch (P200) |  IRAF6, DBSP_DRP7
KAST8 | Shane 3-m | IRAF
LRIS9 | Keck-I |  LPipe10
SPRAT11 | Liverpool Telescope | Barnsley et al. (2012)
DIS12 |  APO13 | IRAF

  * 1

Spectral Energy Distribution Machine (Blagorodnova et al., 2018)

  * 2

Rigault et al. (2019)

  * 3

Andalucia Faint Object Spectrograph and Camera

  * 4

Tody (1986, 1993)

  * 5

Double Beam Spectrograph (Oke & Gunn, 1982)

  * 6

Standard pipeline by Bellm & Sesar (2016) used prior to Fall 2020

  * 7

pypeit (Prochaska et al., 2020) based pipeline
(https://github.com/finagle29/dbsp_drp) used since Fall 2020

  * 8

Kast Double Spectrograph (Miller & Stone, 1987)

  * 9

Low Resolution Imaging Spectrometer (Oke et al., 1995)

  * 10

IDL based automatic reduction
pipeline666https://sites.astro.caltech.edu/~dperley/programs/lpipe.html
(Perley, 2019)

  * 11

Spectrograph for the Rapid Acquisition of Transients (Piascik et al., 2014)

  * 12

Dual Imaging Spectrograph

  * 13

Astrophysics Research Consortium telescope at the Apache Point Observatory

  * 14

https://github.com/jkrogager/PyNOT

The details for all optical spectra (61 for the sample in total) presented in
this paper are provided in Table 3. Furthermore, all spectra were corrected
for Milky Way extinction using extinction and the same procedure as for the
photometry. The SN redshifts were derived using narrow host lines for the
objects which did not already have a host redshift available in the NASA/IPAC
Extragalactic Database777https://ned.ipac.caltech.edu/ (NED). Photometric
calibration was done for all spectra i.e. they were scaled such that the
synthetic photometry from the spectrum matched the contemporaneous host-
subtracted ZTF $r$-band data. For SN 2018crl, a host galaxy spectrum taken
using P200/DBSP was available, which was subtracted from the P200/DBSP SN
spectrum taken at +92 days. For SN 2020aekp, more spectra beyond $\sim 350$
days were obtained but will be presented in a future study of the object (34
additional spectra up to $\sim$600 day).

These processed spectra were used for the rest of the analysis as detailed in
$\S\ref{sec:specanalysis}$ and will be available on
WISeREP888https://www.wiserep.org/ (Yaron & Gal-Yam, 2012).

Table 3: Summary of optical spectra SN | JD | Epoch | Telescope/Instrument | Int | SN | JD | Epoch | Tel./Instr. | Int
---|---|---|---|---|---|---|---|---|---
|  ($-2450000$) | (days) |  | (sec) |  |  ($-2450000$) | (days) |  | (sec)
SN 2018crl | 8282 | 9 | APO/DIS | 2400 | SN 2020uem | 9128 | 11 | P60/SEDM | 1800
| 8288 | 15 | P60/SEDM | 2700 |  | 9136 | 18 | P60/SEDM | 1800
| 8295 | 21 | P60/SEDM | 2700 |  | 9170 | 51 | Ekar/AFOSC | 1200
| 8306 | 31 | P60/SEDM | 2700 |  | 9222 | 101 | Lick-3m/KAST | 3600
| 8373 | 92 | P200/DBSP | 600 |  | 9252 | 130 | Lick-3m/KAST | 2700
(Host) | 8627 | 324 | P200/DBSP | 900 |  | 9263 | 140 | Lick-3m/KAST | 2400
SN 2018gkx | 8457 | 75 | Keck1/LRIS | 300 |  | 9291 | 167 | NOT/ALFOSC | 900
SN 2018evt | 8343 | 9 | NTT/EFOSC2 | 300 |  | 9481 | 349 | P60/SEDM | 2160
| 8465 | 127 | P60/SEDM | 1200 |  | 9492 | 360 | Keck1/LRIS | 600
| 8481 | 143 | P60/SEDM | 1200 |  | 9583 | 448 | P60/SEDM | 2160
| 8481 | 144 | LT/SPRAT | 1000 |  | 9586 | 451 | P60/SEDM | 2160
| 8534 | 195 | P60/SEDM | 1200 | SN 2020xtg | 9226 | 91 | P60/SEDM | 2160
SN 2019agi | 8547 | 42 | UH88/SNIFS | 1820 |  | 9491 | 340 | Keck1/LRIS | 600
SN 2019ibk | 8691 | 35 | P60/SEDM | 2250 |  | 9606 | 448 | Keck1/LRIS | 1200
| 8695 | 39 | P60/SEDM | 2250 | SN 2020abfe | 9189 | 27 | P60/SEDM | 2700
| 8697 | 41 | P60/SEDM | 2250 |  | 9319 | 146 | Keck1/LRIS | 400
| 8748 | 90 | P60/SEDM | 2250 | SN 2020aekp | 9224 | 19 | P60/SEDM | 2160
| 8761 | 103 | P200/DBSP | 600 |  | 9342 | 132 | P60/SEDM | 2160
SN 2019rvb | 8766 | 14 | P60/SEDM | 2250 |  | 9343 | 132 | NOT/ALFOSC | 1200
| 8780 | 26 | P200/DBSP | 600 |  | 9362 | 151 | P60/SEDM | 2700
SN 2020onv | 9058 | 23 | P60/SEDM | 1800 |  | 9381 | 169 | NOT/ALFOSC | 2400
| 9062 | 27 | P60/SEDM | 1800 |  | 9404 | 191 | P60/SEDM | 2700
| 9069 | 33 | P60/SEDM | 1800 |  | 9425 | 211 | NOT/ALFOSC | 1800
| 9070 | 34 | LT/SPRAT | 750 |  | 9434 | 220 | P60/SEDM | 2700
| 9073 | 37 | P60/SEDM | 1800 |  | 9448 | 233 | P60/SEDM | 2700
| 9074 | 38 | NOT/ALFOSC | 450 |  | 9468 | 252 | P60/SEDM | 2700
SN 2020qxz | 9076 | 13 | P60/SEDM | 2250 |  | 9569 | 348 | P60/SEDM | 2700
| 9087 | 22 | P60/SEDM | 2250 |  |  |  |  |
| 9092 | 26 | NOT/ALFOSC | 1800 |  |  |  |  |
| 9098 | 32 | P60/SEDM | 2250 |  |  |  |  |
| 9101 | 34 | NOT/ALFOSC | 1200 |  |  |  |  |
| 9107 | 40 | P200/DBSP | 900 |  |  |  |  |
| 9112 | 45 | Keck1/LRIS | 300 |  |  |  |  |
| 9121 | 53 | P60/SEDM | 2250 |  |  |  |  |
| 9141 | 71 | Keck1/LRIS | 399 |  |  |  |  |

##  3 Analysis

###  3.1 Photometry

####  3.1.1 Explosion epoch estimates

For the purpose of this paper, the ‘explosion time’ simply refers to the time
when optical flux rises above the zero-point baseline (i.e. first light). We
used pre-peak $g,r,i$-band ZTF photometry and $c,o$-band ATLAS photometry
(binned in 1-day bins), when available, for our analysis. For each SN, the
light curve was interpolated using Gaussian process regression to obtain the
peak flux epoch, then a power-law (PL) model was fit using epochs from
baseline to 60% of peak brightness in each band following Miller et al.
(2020). The PL fits converged in at least one band for 6 out of 12 BTS SNe Ia-
CSM. For the rest, we simply took the middle point between the first $5\sigma$
detection and the last upper limit before this detection as the explosion
epoch with half of the separation between these two points as the uncertainty.

The explosion time estimates, light curve bands used for the PL fits and the
$1\sigma$ uncertainties on explosion times are listed in Table 4. The unfilled
‘PL fit filters’ column in the table are the SNe for which the PL fit did not
converge and averages were used. For the PL fits this typically constrains the
time of explosion to within a fraction of a day. Given the high cadence of the
ZTF survey, even in the cases where we use only the last non-detection the
uncertainty range is typically less than 3 days. Only for SN 2020uem is the
date of explosion virtually unconstrained ($\pm 57$ days) as it was behind the
sun at the time of explosion.

Although for SN 2019ibk the explosion time is formally constrained with a $\pm
3$ day uncertainty, this estimate was derived using only ATLAS $o$-band data
right after the SN emerges from behind the sun. There is not a clear rise
observed over a few epochs but two non-detections before a 5$\sigma$
detection. It is possible that the actual peak of this SN occurred earlier
while it was behind the sun and the rising $o$-band points after it emerged
are due to a second peak or bump (similar to SN 2018evt, in that case the
actual rise was caught before the SN went behind the sun in ASAS-SN data). If
the former explosion epoch estimate from $o$-band is to be believed then SN
2019ibk would be the most sub-luminous among the SNe Ia-CSM, peaking at
$-17.5$.

Table 4: Explosion time epoch estimates derived from pre-peak multi-band light curves. For 6 out of 12 SNe Ia-CSM, we were able to fit a power-law model to multi-band data following Miller et al. (2020). For the remaining 6 SNe, the explosion epoch was estimated by taking the mean of the first $5\sigma$ detection and last upper-limit before the first detection. IAU Name | PL fit filters | $t_{o}$ |  $1\sigma$ interval
---|---|---|---
|  | (MJD) | (days)
SN 2018crl | $g,r,o$ | 58271.83 | [$-$0.48,$+$0.38]
SN 2018gkx | $r,o$ | 58371.34 | [$-$0.64,$+$0.53]
SN 2018evt | - | 58334.26 | [$-$2.00,$+$2.00]
SN 2019agi | - | 58502.48 | [$-$1.51,$+$1.51]
SN 2019ibk | - | 58654.61 | [$-$2.99,$+$2.99]
SN 2019rvb | $g,r,i,o$ | 58749.16 | [$-$0.79,$+$0.60]
SN 2020onv | $o$ | 59032.75 | [$-$2.49,$+$1.10]
SN 2020qxz | $g,r,o$ | 59063.05 | [$-$0.51,$+$0.45]
SN 2020uem | - | 59117.03 | [$-$56.63,$+$56.63]
SN 2020xtg | - | 59130.14 | [$-$0.04,$+$0.04]
SN 2020abfe | $g,r,o$ | 59159.36 | [$-$2.16,$+$2.23]
SN 2020aekp | - | 59204.53 | [$-$5.50,$+$5.50]

####  3.1.2 Duration and absolute magnitudes

Figure 2 shows the SNe Ia-CSM (colored squares) in our sample in the duration-
luminosity and duration-$\Delta m_{30}$ phase space. In the top panel, the
x-axis is duration above half-max and the y-axis is the peak absolute
magnitude (see Table 1) when we have photometric coverage both pre-peak and
post-peak. For SNe missing the pre-peak coverage, their discovery magnitude is
taken to be the upper limit to peak absolute magnitude and the duration from
discovery the lower limit to duration above half-max (marked by arrows in
Figure 2). The BTS SN Ia sample is shown in gray points, and we also show the
SNe Ia-CSM presented in S13 with empty triangles for comparison in the top
panel. In the bottom panel, the x-axis is duration above 20% of peak flux
($\Delta t_{20}$) and the y-axis is $\Delta m_{30}$, the two parameters used
in the selection criteria. Most of the SNe Ia-CSM lie on the longer duration
and brighter luminosity side, and are even more distinctly separated in the
$\Delta t_{20}$-$\Delta m_{30}$ phase space. This makes the SN initial decline
rate and duration useful tools for identifying thermonuclear SNe potentially
interacting with CSM, if they have not revealed themselves already in their
early time spectra. The gray points lying in the same phase space as SNe Ia-
CSM are the false positive cases described in §2.1. Also worth noting is that
the duration calculated by taking the flux above half of peak flux value does
not capture the true duration of the light curve when the plateau phase falls
below half-max as is the case for SN 2020aekp ($>500$ days light curve) but
$\Delta t_{20}$ and $\Delta m_{30}$ do.

Figure 2: Top: Location of our 12 SNe Ia-CSM in the peak absolute magnitude
vs. rest-frame duration above half max phase space. The colored points are the
BTS SNe Ia-CSM and the gray points are the rest of the BTS SNe Ia. Also shown
with empty triangles are the SNe Ia-CSM from S13. The vertical arrows mark the
upper limits to peak absolute magnitudes and horizontal arrows mark the lower
limits to durations of SNe not having pre-peak coverage. Bottom: Change in
magnitude 30 days after peak ($\Delta m_{30}$) vs. rest-frame duration above
20% of peak-flux for BTS SNe Ia and SNe Ia-CSM. These criteria were used to
filter out potential SNe Ia-CSM from all SNe Ia and demonstrate that SNe Ia-
CSM occupy a distinct portion in this phase space. However some gray points
(not SN Ia-CSM) remain on the longer duration side and are the false positive
cases described in §2.1.

####  3.1.3 Light and color curves

We have good pre-peak coverage in ZTF data for 8 of the 12 SNe in our
sample999except for SNe 2018evt, 2019ibk, 2020onv and 2020uem.. SN 2018evt was
discovered by ASAS-SN on JD 2458341.91 (Nicholls & Dong, 2018) and classified
by ePESSTO the next day (Stein et al., 2018a), around 115 days before the
first detection in ZTF when the SN came back from behind the sun. Hence we
have only one epoch of pre-peak photometry and one early spectrum for SN
2018evt.

Our mixed bag of SNe Ia-CSM show post-maximum decline rates ranging from 0.5
to 2.0 mag 100d-1 in the $r$ band from peak to $\sim 100$ days post peak. The
median decline rate is 1.07 mag 100d-1, which is much slower than the decline
rates of normal SNe Ia. We see a variety of changes in decline rates after
around 100 days from peak. Two SNe (2020onv and 2020abfe) show no change and
have a constant slow decline throughout. Four SNe (2018gkx, 2019agi, 2019ibk
and 2019rvb) evolve to a shallower slope going from $\sim 0.6$–1 mag 100d-1 to
$\sim 0.2$–0.5 mag 100d-1. Three SNe (2018crl, 2020qxz and 2020aekp) show a
major change in decline rate with the light curves becoming almost flat, and
SN 2020aekp shifts back to a slow decline from this plateau after $\sim 200$
days. In three cases, the decline rate actually becomes steeper, SN 2018evt
goes from 0.52 mag 100d-1 to 1.4 mag 100d-1, SN 2020uem goes from 0.52 mag
100d-1 to 1.25 mag 100d-1 and SN 2020xtg seems to go from 0.61 mag 100d-1 to
1.35 mag 100d-1 (even though there is only one epoch at late times to measure
this change). The 3 SNe with fastest initial decline rates ($\gtrsim 1.5$ mag
100d-1 in the $r$ band) are similar to SN 2002ic (initial decline of 1.66 mag
100d-1 in $V$) and PTF11kx (initial decline of 3.3 mag 100d-1 in $R$) and
coincidentally are also the ones that evolve into a plateau. The rest of the
sample have initial decline rates comparable to SN 1997cy (0.75 mag 100d-1)
and SN 2005gj (0.88 mag 100d-1) (Inserra et al., 2016). From these
observations, we can conclude that SNe Ia-CSM exhibit a range of slow
evolution indicating that there exists a continuum of phases at which strong
CSM interaction begins to dominate the powering of the light curves for these
SNe. It is, however, difficult to pinpoint the exact phase when interaction
starts from the light curve without modeling. CSM interaction could be
affecting the peak brightness significantly even in cases where interaction
only appears to dominate after a few weeks (SNe 2018crl, 2020qxz 2020aekp).
Considering the average peak phase to be $\sim 20$ days past explosion from
the light curves and assuming an ejecta velocity of $\sim 20000$ km s-1, the
CSM is located at $\sim 3.5\times 10^{15}$ cm. This estimate can be refined by
considering the phase of the earliest spectrum that shows interaction
signatures (see §3.2). At late times, all the decline rates are slower than
that expected from Cobalt decay (0.98 mag 100d-1), confirming that the power
from CSM interaction dominates the light curve behaviour for a long time.

Figure 3: Color evolution ($g-r$) of BTS SNe Ia-CSM from $r$-band maximum
(plotted in black) compared with SNe 2005gj, 1997cy, 1999E (Ia-CSM), SN 2012ca
(IIn/Ia-CSM), SN 2010jl (IIn), SN 1991T (SN Ia) and ZTF SNe Ia (gray lines).
As can be seen for up to $\sim 150$ days, our SNe Ia-CSM tend to be redder
than SNe Ia and at late times develop a plateau similar to other interacting
SNe (IIn/Ia-CSM).

Figure 3 shows the $g-r$ color evolution of our sample SNe as a function of
phase (rest-frame days from $r$-band maximum), comparing them with some famous
SNe Ia-CSM (SNe 2005gj, 1997cy, 1999E), and SNe 2012ca (Ia-CSM/IIn), 2010jl
(IIn) and 1991T (over-luminous Type Ia). The color evolution of normal SNe Ia
from ZTF (Dhawan et al., 2022) is shown in grey lines. We use $g-r$ colors
when available, otherwise we estimate the $g-r$ color by fitting Planck
functions to estimate the black-body temperatures from the $V-R$ colors. Our
SNe Ia-CSM show similar color evolution as the older Type Ia-CSM/IIn
interacting SNe, i.e. the $g-r$ color increases gradually for about 100 days
and then settles onto a plateau or slowly declines, and one object (SN
2019ibk) becomes redder at late times similar to SN 2012ca. The interacting
SNe are redder at late times compared to the normal SNe Ia.

####  3.1.4 Mid-IR brightness comparison

Out of 12 SNe in our sample, only one observed (SN 2020abfe) did not have
3$\sigma$ detections post explosion in the unWISE difference photometry light
curves and two (SNe 2019rvb and 2020qxz) did not have coverage post explosion.
The unWISE light curves for the rest of the SNe Ia-CSM having $>3\sigma$
detections in W1 (3.3 $\mu$m) and W2 (4.6 $\mu$m) bands are shown in Figure 4
(black and red stars) along with Spitzer IRAC survey data of SN 2008cg (indigo
and magenta empty triangles), SN 2008J (indigo and magenta empty squares)
(both Ia-CSM) and some SNe IIn (blue and orange crosses) taken from Fox et al.
(2011). The most nearby SN in our sample, SN 2018evt, is among the brightest
($\sim 17$ AB mag) in MIR at least until $\sim$1000 days after explosion and
has a bumpy light curve. SNe 2019ibk and 2018crl however are the most luminous
with an absolute magnitude of $-18.7$ mag in the W1 band. The brightness of
the BTS SNe Ia-CSM is comparable with other interacting SNe and span a similar
range ($-16$ to $-19$). However, SNe IIn have been detected until even later
epochs (up to 1600 days) than SNe Ia-CSM, probably due to the larger number of
SNe IIn at closer distances. SN 2020abfe has upper limits around $\sim-18$ in
W1 band and $\sim-18.5$ in W2 band up to $\sim$300 days post explosion shown
with upside down filled triangles. As the mid-IR luminosity can be fainter
than these limits for SNe Ia-CSM (as can be seen for other nearby SNe in this
sample) and SN 2020abfe is at a redshift of 0.093, it might just be out of
reach for WISE.

This brightness of SNe Ia-CSM in mid-IR can be indicative of existing or newly
formed dust. A clear signature of new dust is reduced flux in the red wing of
the H$\alpha$ emission line at late phases as the new dust formed in the cold
dense shell behind forward shock absorbs the far-side (redshifted)
intermediate and narrow line emission (see bottom panel of Fig. 7). For our
sample, this reduction in H$\alpha$ red wing is the most pronounced for SN
2018evt.

Figure 4: unWISE detections in the W1 and W2 bands of BTS SNe Ia-CSM. The W1
and W2 points are marked with black and red filled stars respectively. Spitzer
IRAC photometry of SNe IIn (blue and orange crosses) and two SNe Ia-CSM from
Fox et al. (2011) (SNe 2008cg and 2008J in empty triangle and square) are also
shown for comparison. 9 out of 12 BTS SNe Ia-CSM are as bright in mid-IR as
other interacting SNe ($\sim-16$ to $\sim-19$). The upper limits for SN
2020abfe are shown in black and red filled upside down triangles.

####  3.1.5 Bolometric luminosity

As the SN Ia-CSM luminosity is dominated by CSM interaction, their spectra
comprise of a pseudo-continuum on the blue side and strong H$\alpha$ emission
on the red side, hence a blackbody fit to multi-band photometric data is not
appropriate to estimate the bolometric luminosity. Instead we calculate a
pseudo-bolometric luminosity from the available multi-band optical data by
linearly interpolating the flux between the bands and integrating over the
optical wavelength range spanned by the ATLAS and ZTF bands. The individual
band light curves are first interpolated using Gaussian process regression to
fill in the missing epochs. This estimate places a strict lower limit on the
bolometric luminosity.

In Figure 5 we show the pseudo-bolometric luminosity of our SN Ia-CSM sample
in comparison with SN 1991T (Type Ia), SNe 1997cy, 1999E, 2002ic, 2005gj,
2013dn and PTF11kx (Ia-CSM). Multi-band photometric data were taken from the
Open Supernova Catalog (Guillochon et al., 2017) for SN 1991T (Filippenko et
al., 1992; Ford et al., 1993; Schmidt et al., 1994) to generate the bolometric
luminosity light curve through black body fitting. The pseudo-bolometric
luminosity light curve for SN 1997cy was obtained from Germany et al. (2000),
for SN 2013dn from Fox et al. (2015) and for SNe 2002ic, 2005gj, 1999E and
PTF11kx from Inserra et al. (2016).

All BTS SNe Ia-CSM show a slow evolution in bolometric luminosity,
inconsistent with the decay of 56Co to 56Fe. The sample’s overall luminosity
decline rates are comparable to those of SNe 1997cy and 2013dn, as shown in
Figure 5. Only SNe 2018crl and 2020aekp seem to show early decline in their
pseudo-bolometric light curves similar to SN 1991T for about 40 days after
peak like SN 2002ic and PTF11kx. Another BTS interacting SN Ia, ZTF20aatxryt
(Kool et al., 2022), was found to follow the PTF11kx light-curve evolution
very closely and as its light curve fell into a plateau the SN started showing
signs of interaction with a helium-rich CSM and evolved into a helium-rich SN
Ia-CSM. We have excluded ZTF20aatxryt from the sample as we focus on typical
SNe Ia-CSM interacting with hydrogen-rich CSM in this study. At late phases
($\sim 300$ days), the SNe Ia-CSM are approximately 100 times brighter than
normal SNe Ia at the same epoch. Therefore, at these late phases, the
luminosity and spectral features of SNe Ia-CSM are entirely dominated by CSM-
interaction with little emergent SN flux. From the pseudo-bolometric light
curves, we place a lower limit on the total radiated energy for SNe Ia-CSM to
be 0.1–1.5 $\times 10^{50}$erg. This is well below the thermonuclear budget
(E${}_{kin}\sim 10^{51}$ erg), but as this is a lower limit and some SNe in
the sample have unconstrained peaks, the true total radiative energy might
come close to the thermonuclear budget, requiring high conversion efficiency
to achieve their luminosity.

Figure 5: Pseudo-bolometric luminosity light curves of BTS SNe Ia-CSM compared
with pseudo-bolometric light curves of SNe 1991T, 1997cy, 1999E, 2002ic,
2005gj, 2013dn, and PTF11kx from literature. The light curves in each filter
having more than 10 epochs were interpolated using Gaussian process regression
to fill in the missing epochs, and at each epoch the fluxes between the bands
were linearly interpolated and integrated over the optical wavelength range
spanned by ZTF and ATLAS filters to get the pseudo-bolometric luminosity. For
BTS SNe, the phases are with respect to the estimated explosion epochs, while
for comparison SNe the phases are with respect to discovery.

###  3.2 Spectroscopy

Figure 6 displays the spectral series obtained for the BTS SNe Ia-CSM. Most of
the early time spectra were taken with the SEDM, the BTS workhorse instrument
(R $\sim$100), which is not able to resolve the narrow CSM lines. Therefore,
these SNe were followed up with higher resolution instruments to get more
secure classifications. For each spectrum in Figure 6, the phase is provided
with respect to the explosion epoch estimate given in Table 4. We have spectra
ranging from a few to around 470 days from explosion. Considering the well
constrained explosion times of SN 2018evt, presence of narrow H$\alpha$ in its
first spectrum at 8 days since explosion and assuming a typical ejecta
velocity of $\sim$20000 km s-1, this implies that the CSM interaction start as
close as $\sim$1.4$\times 10^{15}$ cm.

Figure 6: Spectral series of all SNe Ia-CSM presented in this paper. The rest-
frame phases are shown alongside the spectra in each subplot and have been
calculated using the explosion epoch estimate. The colors depict different
instruments used to obtain this data. Major emission lines are marked with
vertical dashed lines.

Figure 7 shows the early time (left) and late time (right) spectral behaviour
of the BTS SNe Ia-CSM together with a few historical SNe for comparison,
namely SNe Ia-CSM SN 2011jb (Silverman et al., 2013), SN 2005gj and PTF11kx,
the Type Ia SN 1991T and the well-observed Type IIn SN 2010jl. Vertical gray
regions mark typical SN Ia absorption features and [Fe II/III] line regions,
and vertical dashed lines mark the Balmer emission lines. The sample spectra
have been multiplied by a constant factor to magnify relevant spectral
features. In the following paragraphs, we compare the observations of some of
the spectral features with previous analysis of this class (Silverman et al.,
2013; Fox et al., 2015; Inserra et al., 2016).

A few of our early time SNe Ia-CSM show underlying SN Ia absorption features
like PTF11kx and SN 2002ic (most are, however, quite diluted and also affected
by the low resolution and signal-to-noise ratio (SNR) of the SEDM spectra),
the most notable being SNe 2018evt, 2020qxz and 2020aekp. SNe 2020qxz and
2020aekp also have among the fastest initial post-peak decline rates in the
sample, similar to PTF11kx, while coverage around peak is not available for SN
2018evt. On the other hand, SNe with slower decline rates similar to SN 1997cy
and SN 2005gj have more SN IIn-like early time spectra dominated by blue
pseudo-continuum and Balmer emission. The faster decline rate suggests we are
still seeing some of the emission from the ejecta at those phases. To unveil
the nature of the progenitor of interacting SNe, it is therefore necessary to
obtain some spectroscopic follow-up before peak light. Spectroscopic data at
the phase of transition to interaction-dominated luminosity would also help in
deducing the extent and density structure of the optically thick CSM.

Late time spectra of SNe Ia-CSM look very similar to those of SNe IIn, heavily
dominated by H$\alpha$ emission. The CSM interaction masks the underlying SN
signature and we instead see late-time spectra riddled with photoionized CSM
lines. In some cases, the photosphere might lie in an optically thick cold
dense shell (CDS) formed between the forward and reverse shocks which obscures
the ejecta completely (Smith et al., 2008; Chugai et al., 2004). The continuum
is also enshrouded under a blue quasi-continuum from a forest of iron-group
element lines (S13) as identified and analyzed for SNe 2012ca and 2013dn by
Fox et al. (2015).

The blue quasi-continuum blend of iron lines ([Fe III] lines around $\sim$4700
Å and [Fe II] around $\sim$5200 Å) in the spectra of the BTS SN Ia-CSM sample
(see Figure 7 top right panel) is the dominant feature blue-ward of 5500 Å but
the ratio of [Fe III]/[Fe II] is much weaker compared to for SNe Ia (like SN
1991T). This feature is more apparent in the SNe Ia-CSM like PTF11kx and SN
2002ic that became interaction-dominated later than for other SNe Ia-CSM such
as SNe 1997cy, 1999E and SN 2012ca (SN Ia-CSM/IIn, for which a clear type has
not been established). Inserra et al. (2014) argues for a core-collapse origin
for SN 2012ca given this low amount of [Fe III] along with the detection of
blueshifted Carbon and Oxygen lines (which however, were later argued to be
[Fe II] lines by Fox et al. 2015). S13 instead argues in favor of a
thermonuclear origin given the presence of this blue quasi-continuum, despite
[Fe III] being weaker. Fox et al. (2015) points out that a similarly
suppressed ratio of [Fe III]/[Fe II] is observed in some SNe Ia, particularly
the super-Chandra candidate SN 2009dc, for which the explanation was suggested
to be a low ionization nebular phase owing to high central ejecta density and
low expansion velocities (Taubenberger et al., 2013). Fox et al. (2015) argue
that in the case of SNe Ia-CSM, a lower ionization state could arise owing to
the deceleration of ejecta by the dense CSM explaining the Fe line ratio
suppression. Since Ca has lower first and second ionization potentials than
Fe, the detection of [Ca II] $\lambda\lambda$7291, 7324 would be consistent
with this low ionization, which Fox et al. (2015) confirms for SNe 2012ca and
2013dn. Indeed, we find clear evidence of [Ca II] emission for 8 out of 12 SNe
in our sample and moderate to weak signal for the remaining 4. Although this
does favor the argument for a thermonuclear origin, a similar blue quasi-
continuum is also observed in other interacting SN types like SNe Ibn (SN
2006jc, Foley et al. 2007) and SNe IIn (SNe 2005ip and 2009ip), making Fe an
incomplete indicator of the progenitor nature (see detailed discussion in Fox
et al. 2015).

We do not find strong evidence of O I $\lambda 7774$ or [O I]
$\lambda\lambda$6300, 6364 emission in our sample, although they might be
present at very weak levels in some SNe (e.g. SN 2020uem). SN 2020uem has
strong emission lines at 6248, 7155 and 7720 Å which are consistent with being
iron lines and were also observed in SNe 2012ca, 2013dn and 2008J. S13 note
that the very broad emission around 7400 Å can be due to a blend of [Ca II]
$\lambda\lambda$7291, 7324 and [O II] $\lambda\lambda$7319, 7330, however we
note that this broad emission is likely to be from calcium as O II is harder
to excite than O I which is either very weak or absent in our spectra. The
broad Ca NIR triplet feature resulting from electron scattering is the next
strongest feature after the Balmer emission and is present in all mid to late-
time spectra of the SNe in our sample where the wavelength coverage is
available. We observe it increasing in relative strength with phase, at least
for a year, after which we no longer have spectral coverage.

Figure 7: Top left: Early-time spectra of BTS SNe Ia-CSM with phases between 0
and 30 days since explosion compared to spectra of SNe 2011jb, 2005gj, 1991T
and PTF11kx (phases in days since discovery). Top right: Late-time spectra of
BTS SNe Ia-CSM (phases ranging from 40 to 370 days since explosion) compared
to spectra of SNe 2011jb, 2005gj, 2010jl and PTF11kx (phases in days since
discovery).

Bottom left and right: H$\alpha$ line profiles (post continuum removal) with
the blue side reflected across the peak flux, marked by dashed lines. SNe
2020aekp, 2020abfe, 2020xtg and 2020uem in the right panel, and SNe 2018crl,
2018gkx, 2018evt, 2019agi, 2019ink, 2019rvb, 2020onv, 2020qxz in left panel.

The bottom panel of Figure 7 shows the line profile of H$\alpha$, with the
blue side reflected over the red side at the maximum flux after continuum
removal. We do see evidence of diminished flux in the red wing of H$\alpha$ at
late phases in some SNe (most notable in SNe 2018evt and 2020uem), which can
indicate formation of new dust in the post-shock CSM. S13 claim to observe
this for all non-PTF SNe Ia-CSM in their sample starting at $\sim$75–100 days,
while for the PTF SNe Ia-CSM they do not have spectra available post that
phase range. For some BTS SNe Ia-CSM, we also do not have spectra available
post 100 days which limits any analysis of this phenomenon for a large enough
sample.

The spectra were reduced and processed as outlined in §2.5 for the emission
line analysis, the results of which are described in the next section. We used
only good SNR SEDM spectra and intermediate resolution spectra for line
identification and analysis.

####  3.2.1 H$\alpha$, H$\beta$ and He I emission lines

To analyze the H$\alpha$ line emission, we first fit the continuum level using
the fit_continuum function of the specutils Python package, where the
continuum is estimated by a cubic function fitted on regions on each side of
the line. We remove this continuum level and then fit the H$\alpha$ line with
a broad and a narrow component Gaussian function using the fit_lines function
of specutils which returns the best fit Gaussian model and the $1\sigma$
uncertainty on the model parameters. We generate 1000 sample models within
$1\sigma$ uncertainties of the parameters centered around the best-fit values
and calculate the intensity, flux and velocity (FWHM) of the broad and narrow
components for each model. Then we take the median and standard deviation of
the intensity, flux and velocity FWHM distributions to get their final best
value and $1\sigma$ uncertainty. The equivalent width was also calculated for
the H$\alpha$ line using the model fit as well as directly from the data, and
the difference between the values derived from model and data is reported as
the error on the EW. All values are reported in Table 5. For 3 SNe in our
sample, we have a series of intermediate resolution spectra through which we
can trace the evolution of the H$\alpha$ line with phase. Figure 8 shows this
trend of the H$\alpha$ line parameters (integrated flux in the top panel and
equivalent width in the bottom panel) versus phase for all SNe in our sample.
The un-filled markers represent the narrow emission while the filled markers
represent the broad emission. For SNe where this analysis could be done on
multiple spectra, we see that the H$\alpha$ equivalent width generally
increase over time, with some SNe showing fluctuations up to 100 days possibly
due to interaction of ejecta with multiple CSM shells of varying density. For
SN 2018evt, Yang et al. (2022) analyzed H$\alpha$ line properties from a
comprehensive spectral series data, which are plotted in Figure 8 in gray
circles and seem to agree well with our analysis at comparable epochs.

From the Gaussian profile line fitting analysis of the H$\alpha$ emission
line, we found that the broader component has velocities ranging from
$\sim$1000 to $\sim$4000 km s-1 (intermediate width) and the narrow component
has velocities of about $\sim$200 km s-1 to $\sim$1000 km s-1 (see Figure 9).
The narrow component could only be resolved down to $\sim$300 km s-1 limited
by the mediocre resolution of the spectrographs used (KeckI/LRIS R$\sim$800,
P200/DBSP R$\sim$1000, NOT/ALFOSC has R$\sim$360). While we know that the
narrow lines originate in the unshocked ionized CSM, the exact origin of the
intermediate components is uncertain. They could arise from the post-shock gas
behind the forward shock or from the shocked dense clumps in the CSM (Chugai &
Danziger, 1994).

The luminosities of the H$\alpha$ line measured from the BTS SNe Ia-CSM lie in
the range 2.5–37$\times 10^{40}$ erg s-1 which are comparable to the values
from S13 who reported most of their SNe in the 1–10$\times 10^{40}$ erg s-1
range except one object that had a luminosity of 39$\times 10^{40}$ erg s-1.
From the broad H$\alpha$ luminosity, we did a simple estimate of the mass-loss
rate assuming spherically symmetric CSM deposited by a stationary wind
$\rho\propto r^{-2}$ having velocity $v_{w}$ (Chugai, 1991; Salamanca et al.,
1998). The mass-loss rate $\dot{M}$ can be related to the broad H$\alpha$
luminosity $L_{H\alpha}^{Broad}$ as (Salamanca et al., 1998, their Eq. 2)

$L_{H\alpha}^{Broad}=\frac{1}{4}\epsilon_{H\alpha}\frac{\dot{M}}{v_{w}}v_{s}^{3}$

where $v_{s}$ is the shock velocity (obtained from the broad component
velocity of the H$\alpha$ line). We used a value of 100 km s-1 considering
previous high resolution spectral studies of SNe Ia-CSM (Kotak & Meikle, 2005;
Aldering et al., 2006; Dilday et al., 2012) for $v_{w}$ as we cannot fully
resolve the narrow component and a maximum value of 0.1 for the efficiency
factor $\epsilon_{H\alpha}$ (Salamanca et al., 1998). The mass-loss rates were
estimated from the available spectra and are shown in Figure 10 as a function
of years before explosion ($t_{w}=\frac{v_{s}t}{v_{w}}$, where $t$ is the
phase of the spectra). For most SNe in the sample, the mass-loss rates lie
between 0.001–0.02 $M_{\odot}$ yr-1, except for SN 2019rvb which has
$\sim$0.07 $M_{\odot}$ yr-1 lost within 2 years prior the explosion. These
rates are much higher than what could be attained from a red giant superwind
($\sim 3\times 10^{-4}$ $M_{\odot}$ yr-1) but are comparable to previous
estimates (calculated through multiple methods) for SNe Ia-CSM and require
some unusual mechanism to reach such persistently higher mass-loss rates in
the decades prior to explosion. Also to consider is that the simplistic
assumption of spherical symmetry likely does not apply for SNe Ia-CSM.
Evidence of multiple thin shells and asymmetric CSM was observed for PTF11kx
(Dilday et al., 2012) and light curve modeling of SNe 1997cy and 2002ic
suggested a better fit to a flat density profile rather than stationary wind
(Chugai & Yungelson, 2004). An asymmetric or clumpy CSM might be the norm for
SNe Ia-CSM (and some SNe IIn) rather than the exception.

Table 5: Summary of H$\alpha$ line properties obtained from two-component Gaussian fitting. SN Name | Phase | Broad Flux | Narrow Flux | Total Flux | Broad Velocity | Narrow Velocity
---|---|---|---|---|---|---
| (days) | ($10^{-16}$ erg s-1 cm-2) | ($10^{-16}$ erg s-1 cm-2) | ($10^{-16}$ erg s-1 cm-2) | FWHM (km s-1) | FWHM (km s-1)
SN 2018crl | 92 | 135.4$\pm$10.0 | 32.8$\pm$2.0 | 168.2$\pm$12.0 | 4137$\pm$312 | $<214$
SN 2018gkx | 75 | 9.9$\pm$0.7 | 3.9$\pm$0.2 | 13.7$\pm$0.9 | 2640$\pm$398 | $<375$
SN 2018evt | 144 | 2020.3$\pm$128.5 | 1247.4$\pm$52.8 | 3267.7$\pm$181.3 | 6465$\pm$997 | 1816$\pm$973
SN 2019agi | 42 | 52.7$\pm$3.6 | 23.7$\pm$1.1 | 76.4$\pm$4.7 | 3836$\pm$349 | 464$\pm$301
SN 2019ibk | 103 | 85.6$\pm$1.7 | 17.0$\pm$0.5 | 102.6$\pm$2.3 | 2431$\pm$217 | 272$\pm$214
SN 2019rvb | 26 | 22.0$\pm$3.0 | 10.4$\pm$1.0 | 32.5$\pm$4.1 | 2321$\pm$298 | 374$\pm$216
SN 2020onv | 38 | 32.8$\pm$5.2 | 33.3$\pm$2.0 | 66.1$\pm$7.2 | 2714$\pm$879 |  $<$834
SN 2020qxz | 26 | 76.6$\pm$6.2 | 13.8$\pm$1.7 | 90.4$\pm$7.9 | 11294$\pm$1106 | $<836$
SN 2020qxz | 34 | 55.1$\pm$5.0 | 10.8$\pm$1.8 | 65.9$\pm$6.8 | 8252$\pm$1039 | 1070$\pm$845
SN 2020qxz | 40 | 12.9$\pm$1.7 | 7.6$\pm$0.5 | 20.5$\pm$2.2 | 2049$\pm$284 | 245$\pm$215
SN 2020qxz | 45 | 20.7$\pm$1.6 | 9.1$\pm$0.4 | 29.8$\pm$2.1 | 3429$\pm$419 | $<375$
SN 2020qxz | 71 | 39.1$\pm$1.3 | 10.4$\pm$0.4 | 49.5$\pm$1.7 | 5013$\pm$395 | 400$\pm$375
SN 2020uem | 51 | 246.3$\pm$47.2 | 151.1$\pm$16.8 | 397.4$\pm$64.0 | 6520$\pm$1163 | 1178$\pm$840
SN 2020uem | 101 | 655.2$\pm$28.9 | 241.2$\pm$9.6 | 896.4$\pm$38.4 | 7456$\pm$309 | 1066$\pm$217
SN 2020uem | 130 | 552.9$\pm$17.6 | 281.8$\pm$6.2 | 834.8$\pm$23.8 | 7465$\pm$265 | 1269$\pm$215
SN 2020uem | 140 | 545.4$\pm$20.0 | 283.4$\pm$6.8 | 828.8$\pm$26.7 | 7457$\pm$275 | 1308$\pm$216
SN 2020uem | 167 | 424.3$\pm$19.0 | 312.0$\pm$7.7 | 736.3$\pm$26.6 | 6852$\pm$854 | 1439$\pm$834
SN 2020uem | 360 | 179.8$\pm$4.0 | 77.4$\pm$1.4 | 257.2$\pm$5.4 | 5377$\pm$382 | 1170$\pm$375
SN 2020xtg | 340 | 129.2$\pm$4.2 | 52.1$\pm$1.6 | 181.3$\pm$5.8 | 4242$\pm$382 | 1258$\pm$376
SN 2020xtg | 448 | 131.7$\pm$7.7 | 96.3$\pm$3.2 | 228.0$\pm$10.9 | 4452$\pm$395 | 1566$\pm$377
SN 2020abfe | 146 | 33.6$\pm$1.1 | 3.0$\pm$0.3 | 36.6$\pm$1.4 | 4411$\pm$389 | $<376$
SN 2020aekp | 132 | 149.5$\pm$4.0 | 33.0$\pm$1.0 | 182.5$\pm$5.0 | 7728$\pm$846 | $<833$
SN 2020aekp | 169 | 231.0$\pm$4.5 | 32.3$\pm$1.3 | 263.3$\pm$5.8 | 6775$\pm$839 | $<834$
SN 2020aekp | 211 | 251.0$\pm$9.5 | 58.6$\pm$3.4 | 309.6$\pm$12.8 | 7422$\pm$852 | 1342$\pm$836
Figure 8: Integrated fluxes and equivalent widths of H$\alpha$ emission line
with respect to SN phases for the BTS SN Ia-CSM sample. Broad component values
are shown with filled markers and narrow component values with un-filled
markers. SN 2018evt H$\alpha$ luminosities and EWs presented in Yang et al.
(2022) are also shown in gray circles. Figure 9: Velocity of H$\alpha$
emission line with respect to SN phases for the BTS SN Ia-CSM sample. Broad
component values are shown with filled markers and narrow component values
with un-filled markers. Figure 10: Mass-loss rates estimated from the
luminosity of the broad component of H$\alpha$ for the BTS SNe Ia-CSM. A value
of 100 km s-1 was assumed for the wind velocity.

The same analysis as for the H$\alpha$ line was also carried out for H$\beta$
and He I $\lambda$5876 with a one component Gaussian fit. For cases where a
Gaussian model could not fit the data, we integrate the flux value in a 100 Å
region centered at 5876 Å for He I. The Na ID absorption lines are also
prevalent in some spectra and blend with the He I line, resulting in positive
EWs for some SNe. The cumulative distributions of H$\beta$ and He I equivalent
widths are shown in the top and bottom panels of Figure 11 respectively.

The H$\beta$ median EW measured from the BTS SN Ia-CSM sample is 7.1 Å , close
to the S13 value of $\sim$6 Å and quite weak compared to what S13 measured for
SNe IIn ($\sim$13 Å ). The overall cumulative distribution of H$\beta$ EW is
also comparable to the S13 SNe Ia-CSM rather than to the S13 SNe IIn. For the
He I $\lambda$5876 line, the median EW measured for our BTS SN Ia-CSM sample,
considering only significant emission features, is 2.4 Å . This is close to
the value of $\sim$2 Å reported in S13, and again significantly different from
their SN IIn value of $\sim$6 Å ($\sim$4 Å with upper limits), however the
overall distribution seems to be closer to the S13 SNe IIn (but still weaker)
rather than to the S13 SNe Ia-CSM. This indicates that perhaps He I is not as
good a discriminant between the populations compared to H$\beta$. Among the
most He-rich SNe in our sample are SNe 2019ibk, 2020uem, 2020xtg, 2020aekp and
2018evt, and these SNe also have the higher H$\alpha$ equivalent widths in the
sample.

Figure 11: Cumulative distributions of equivalent width of H$\beta$ and He I
$\lambda$5876 emission lines calculated from the BTS SNe Ia-CSM (in grey)
compared with the respective distributions presented in S13 for SNe Ia-CSM
(blue) and SNe IIn (red). Vertical dashed lines mark the median EW of the
distributions.

Figure 12 plots the cumulative distribution of the Balmer decrements
($\frac{F_{H\alpha}}{F_{H\beta}}$) measured for our sample SNe. The higher
Balmer decrement values ($>$15) have large errors associated to them because
of low SNR of the spectra from which they were derived, particularly near the
H$\beta$ line. Consistent with the results of S13, the SNe Ia-CSM from this
sample also have a high median Balmer decrement value of $\sim$7 ($\sim$5 in
S13), indicating that the emission line mechanism is probably collisional
excitation or self-absorption rather than recombination, from which the
expected Balmer decrement value is $\sim$3\. In the case of SNe Ia-CSM, if the
CSM distribution consists of multiple shells as suggested for PTF11kx,
moderately high densities could be created when fast moving ejecta overtake
slowly moving thin dense CSM shells creating large enough optical depth in the
H$\alpha$ line which results in the H$\beta$ transition decaying as Pa$\alpha$
$+$ H$\alpha$ (Xu et al., 1992). For some individual SNe where multiple
spectra are available, the Balmer decrement is observed to first increase and
later on decrease with phase.

Figure 12: Cumulative distribution of $H\alpha/H\beta$ intensity ratio (Balmer
decrement) calculated from intermediate resolution spectra of BTS SN Ia-CSM
sample (grey shaded region). The red line is the distribution of Balmer
decrement of SNe IIn measured in S13, the blue line is the SN Ia-CSM Balmer
decrement distribution from S13. The black circles are a few representative
points indicating the high Balmer decrement values and the uncertainties on
them. The vertical dashed line is the median Balmer decrement measured from
BTS SNe Ia-CSM.

###  3.3 Host galaxies

We retrieved science-ready co-added images from the Galaxy Evolution Explorer
(GALEX) general release 6/7 (Martin et al., 2005), the Sloan Digital Sky
Survey DR 9 (SDSS; Ahn et al. 2012), the Panoramic Survey Telescope and Rapid
Response System (Pan-STARRS, PS1) DR1 (Chambers et al., 2016), the Two Micron
All Sky Survey (2MASS; Skrutskie et al., 2006), and preprocessed WISE images
(Wright et al., 2010b) from the unWISE archive (Lang,
2014b)101010http://unwise.me.

We used the software package LAMBDAR (Lambda Adaptive Multi-Band Deblending
Algorithm in R) (Wright et al., 2016) and tools presented in Schulze et al.
(2021), to measure the brightness of the host galaxy. The spectral energy
distribution (SED) was modelled with the software package
Prospector111111https://github.com/bd-j/prospector version 0.3 (Johnson et
al., 2021). We assumed a linear-exponential star-formation history, the
Chabrier (2003) initial mass function, the Calzetti et al. (2000) attenuation
model, and the Byler et al. (2017) model for the ionized gas contribution. The
priors were set as described in Schulze et al. (2021).

Figure 13 shows the log of star formation rate (SFR) as a function of stellar
mass for hosts of BTS SNe Ia-CSM. We also use a Galaxy-zoo (Lintott et al.,
2011) sample of elliptical and spiral galaxies (randomly sampled in the
redshift range $z=0.015-0.05$), and BTS SN Ia hosts as comparison samples
collected by and used for comparison in Irani et al. (2022). We find the SN
Ia-CSM host galaxy population to be consistent with late-type spirals and
irregulars with recent star formation history. 4 out of 12 SNe have clearly
spiral hosts, 3 have edge-on host galaxies, 4 seem to have irregulars as hosts
and 1 has an unclear host type. Host galaxies of 10 out of 12 SNe have $w2-w3$
measurements available which are all $>1$ mag, putting them in late-type
category (Irani et al., 2022), 1 (SN 2019rvb) does not have W3 measurement but
has $NUV-PS1_{r}\ \sim 1$ mag again putting it towards late-type and 1 (SN
2020abfe) does not have any of the above information available except the
$PS1_{r}$ band magnitude of 20.766, which is the faintest host galaxy
(absolute SDSS $r$-band magnitude of $-17.4$) in our BTS SN Ia-CSM sample. As
noted in S13, the SN Ia-CSM hosts of their sample had generally low
luminosities ($-19.1<M_{r}<-17.6$) except MW like spiral hosts. Our BTS SN Ia-
CSM host luminosities lie in the range of $-21.8<M_{r}<-17.4$ covering low to
MW like luminosities.

Figure 13: Host galaxies of BTS SN Ia-CSM (black circles) on SFR vs stellar
mass plot with Galaxy-zoo spiral (blue contours) and elliptical (red contours)
galaxies for comparison. BTS SN Ia hosts are also shown for comparison in
green circles. Equal sSFR lines are marked with grey dashed lines.

###  3.4 Rates

Following the methodology for calculating the volumetric rate of transients
found in the Bright Transient Survey from Perley et al. (2020), we use their
equation 2 to calculate the SN Ia-CSM rate:

$R=\frac{1}{T}\sum_{i=1}^{N}\frac{1}{(\frac{4\pi}{3}D^{3}_{max,i})f_{sky}f_{ext}f_{rec}f_{cl,i}}$

where $T$ is the duration of the survey, $N$ is the number of transients that
pass the quality cut, $D_{max,i}$ is the distance out to which the $i^{th}$
transient with peak absolute magnitude $M_{i}$ can be detected above the
survey magnitude limit $m_{lim}$ (=19 mag for BTS SNe Ia-CSM) at peak light
without any extinction, $f_{sky}$ is the average active survey coverage as a
fraction of full sky, $f_{ext}$ is average reduction in effective survey
volume due to Galactic extinction, $f_{rec}$ is the average recovery
efficiency for a detectable transient within the survey coverage area, and
$f_{cl,i}$ is the classification efficiency dependent on apparent magnitude.

The duration of the survey in which these 12 SNe Ia-CSM were detected is from
2018-05-01 to 2021-05-01, i.e. $T=3$ years. We calculate $f_{sky}$ during this
time period by averaging the sky area coverage of the public MSIP survey
considering 3 day cadence for ZTF Phase I (2018-05-01 to 2020-10-31) and 2 day
cadence for ZTF Phase II (since 2020-11-01), which turns out to be 12505 deg2
for Phase I and 14831 deg2 for Phase II, giving a mean $f_{sky}=0.32$. We use
the same value of 0.82 for $f_{ext}$ as calculated in Perley et al. (2020)
given there has not been any change in the number and positions of ZTF fields.

To estimate $f_{rec}$, we consider SNe Ia-CSM brighter than $-18.5$ peak
absolute magnitude and brighter than 18 apparent magnitude (total 5) of which
4 pass the quality cut, giving an $f_{rec}$ of 0.8. We take classification
completeness of 0.75 at 19 mag, 0.9 at 18.5 mag and 1 at 17.2 mag and linearly
interpolate in between these values to get $f_{cl,i}$.

Then using $H_{0}=70$ km s-1 Mpc-1, ignoring cosmological
effects121212Contraction of control time window approximately compensated by
increase in the star-formation rate density in the low redshift regime for
redshift dependent SN rates. as in Perley et al. (2020) and applying a uniform
K-correction (K = 2.5$\times log_{10}(1+z)$), we get a rate of
29.35${}^{+27.53}_{-21.37}$ Gpc-3 yr-1 for SNe Ia-CSM. We also calculate a SN
Ia rate of 2.88${}^{+0.28}_{-0.25}\times 10^{4}$ Gpc-3 yr-1 from SNe Ia
observed in the same period following the same method, which is close to the
value of 2.35$\times 10^{4}$ Gpc-3 yr-1 calculated in Perley et al. (2020).
This puts SNe Ia-CSM to be 0.02–0.2% of SNe Ia. However this rate estimate
should be considered a lower limit given various caveats in the correct
identification of SNe Ia-CSM (see discussion §4.3). If the ambiguous
classification cases outlined in Appendix A are considered to be SN Ia-CSM and
included in the rate calculation, we obtain a rate upper limit of
$97.7^{+135.8}_{-77.3}$ Gpc-3 yr-1, which is 0.07–0.8% of SNe Ia.

###  3.5 Precursor rates

The ZTF precursor rates were calculated following the method in Strotjohann et
al. (2021) which studied the frequency of precursors in interacting SNe found
in ZTF. Strotjohann et al. (2021) included 6 of the SNe Ia-CSM presented in
this paper in addition to 4 other SNe Ia-CSM not in this paper (see Appendix A
for details) for their search but did not find any robust 5$\sigma$ precursor
detections. This non-detection was concluded to be due to the small sample
size of SNe Ia-CSM (or that they are more distant) compared to the SN IIn
sample, so even if the precursors were as bright or frequent as for SNe IIn,
it would be difficult to detect them.

The same search was here carried out for our larger sample by taking the ZTF
forced photometry multi-band ($g,r,i$) light curves generated by the pipeline
outlined in Masci et al. (2019) and stacking them in 1, 3 and 7-day long bins
to search for faint outbursts. There were 7389 total available pre-explosion
epochs for BTS SNe Ia-CSM, the earliest epoch being 1012 days prior to the
explosion and the median phase 340 days prior. Hence the results are valid for
typical SN Ia-CSM progenitors at about $\sim$1 year before the SN. We did not
find any robust 5$\sigma$ precursor detections. The upper limits for the
precursor rates in different bands are shown in Figure 14, where the solid
lines indicate up to what fraction of the time a precursor of a given
brightness could have been detected while being consistent with the ZTF non-
detections. A precursor of $-15$ magnitude could occur as frequently as
$\sim$10% of the time given the ZTF non-detections. A continuous search for
the precursors as more SNe Ia-CSM are found and classified and their sample
size increases could yield a detection if the precursors are as frequent and
bright as for SNe IIn. The dense and massive CSM around these objects is close
enough to have been deposited within decades prior to the SN but the lack of
precursors within 1 year indicates that there is likely no violent event that
ejects a lot of mass in that period. Probing for precursors could potentially
constrain the progenitor in at least some cases. For example, Soker et al.
(2013) predicts for their core degenerate (CD) model for PTF11kx-like SNe
release of significant energy ($\sim$1049 erg) before explosion over timescale
of several years, implying a precursor 3–7 magnitudes fainter than the SN
explosion spread over several years, peaking in the near-IR.

Figure 14: Precursor rate as a function of magnitude calculated from BTS SN
Ia-CSM pre-explosion ZTF forced photometry stacked in 7-day bins. The
different colored shaded regions correspond to different ZTF bands ($r$-red,
$g$-green, $i$-grey). The solid lines depict the upper limits on fraction of
the time a precursor of the corresponding magnitude would have been detected
which is consistent with the ZTF non-detections.

##  4 Discussion

###  4.1 Fraction of SNe Ia-CSM with delayed interaction

The fastest declining SNe in our sample (SNe 2018crl, 2020qxz and 2020aekp)
are also the ones that develop a plateau and show relatively stronger SN Ia-
like absorption features in their early spectra. They seem to have a delayed
start for the interaction like PTF11kx but not as fast a decline, and thus
bridge the gap between PTF11kx and the rest of the strongly interacting SNe
Ia-CSM. It remains to be seen how many SNe Ia are weakly interacting where the
CSM interaction starts in earnest at timescales of $\sim$year or more after
explosion, this requires searching for faint detections in carefully
calibrated forced photometry light curves (stacked to go fainter), a study
currently undertaken by Terwel et al. (in prep). From the current sample, it
appears that in addition to SNe Ia-CSM being intrinsically rare, delayed
interaction SNe Ia-CSM are even rarer and only constitute about a quarter of
all SNe Ia-CSM. This delayed interaction behaviour could also be an effect of
asymmetric or clumpy CSM wherein part of the SN ejecta shine through depending
on the viewing angle. Observational campaigns that capture the inner boundary
of the CSM and the geometry robustly could shed light on the distribution of
the inner CSM radius and reveal if it is a continuous distribution or if there
are multiple progenitor scenarios within the SN Ia-CSM class.

###  4.2 Implications for progenitor based on observed mass loss

From Figure 10, the estimated mass-loss rates from a simple spherical
treatment of the CSM and a stationary wind lie between $\sim 10^{-3}$ to
$10^{-1}$ M⊙ yr-1 over a period of less than $\sim 60$ years before explosion.
That gives a total mass loss of $\sim 0.1$ to $\sim 1$ M⊙. Dilday et al.
(2012) estimated $\sim 5$ M⊙ of CSM around PTF11kx while Graham et al. (2017)
revised it to be $\sim 0.06$ M⊙. Light curve modeling of SN 1997cy and SN
2002ic by Chugai & Yungelson (2004) resulted in $\sim 5$ M⊙ estimates for both
SNe. Inserra et al. (2016) also fit analytical models to some SNe Ia-CSM and
found the CSM mass to lie between 0.4 and 4.4 M⊙. Since from Figure 5, the
pseudo-bolometric luminosities of our SNe Ia-CSM lie somewhere between PTF11kx
and SNe 1997cy, 2002ic and 2005gj, with SN 1999E somewhere in the middle, we
can say that the total CSM mass in our sample of SN Ia-CSM should also be
several solar masses. A WD$+$AGB star system has typically been suggested for
historical SNe Ia-CSM to explain this massive CSM. The WD could either gain
mass through Roche Lobe overflow (RLOF) from the companion that drives an
optically thick wind (OTW) or merge with the core of the AGB star that then
explodes in or soon after the common envelope phase. Meng & Podsiadlowski
(2019) model WD$+$MS systems for their common envelope wind (CEW) model and
find $\sim 1$ M⊙ CSM around SNe Ia-CSM. Thus, given the large observed CSM
mass range, the nature of the companion cannot be solely determined from total
mass lost. High resolution spectroscopy that can resolve the narrow unshocked
CSM wind velocity is also needed to determine the compactness of the
companion.

###  4.3 Implications for progenitor based observed volumetric rate

Robust observed rate estimates for SNe Ia-CSM have been few and far between.
Dilday et al. (2010) found 1 interacting SN Ia (SN 2005gj) in a sample of 79
SNe Ia at $z<0.15$ in the SDSS-II SN survey, giving a rate of $\sim$1%. After
the PTF11kx discovery in the Palomar Transient Factory (PTF) survey, the SN
Ia-CSM rate was estimated to be $\sim$0.1% (1 in 1000 classified SNe Ia;
Dilday et al., 2012) but without spectroscopic completeness determination. S13
identified 7 more SNe Ia-CSM from the PTF SN IIn sample, bumping up the
estimate to $\sim$0.8%. With this sample we have improved the rate estimate,
providing a robust value (along with an uncertainty estimate on that value)
from an unbiased survey with high spectroscopic completeness up to 18.5
magnitude. However this rate quite possibly still underestimates the true
value for two reasons. The first being possible thermonuclear SNe that are
enshrouded so completely by CSM interaction that they are misclassified as SNe
IIn in the absence of good early time data. In the BTS SN IIn sample, we found
6 SNe IIn to have ambiguous classifications which could possibly be SNe Ia-CSM
and these are described in Appendix A. Including these ambiguous cases in rate
estimation results in a rate upper limit of 0.07–0.8% for strongly interacting
thermonuclear SNe, while excluding them gives an underestimated rate of
0.02-0.2%.

The second issue with the rates is if there is indeed a continuum of delayed
interaction SNe Ia-CSM like PTF11kx, interaction in SNe Ia may present itself
hundreds of days later at magnitudes fainter than ZTF’s limit ($\sim$20.5)
resulting in those SNe not being counted when they may be sharing the same
progenitor as the rest of the interacting SNe Ia-CSM. Lastly in some rare
cases, the SN might appear normal in its light curve shape and duration (and
thus would be missed by the selection criteria used in this paper) but seem to
have peculiar narrow H$\alpha$ in its spectrum or bright mid-IR flux (like in
the case of SN 2020aaym; Thévenot et al. 2021).

Han & Podsiadlowski (2006) predicted a rate of 0.1–1% for 02ic-like events for
their delayed dynamical instability SD model but could not naturally explain
the delayed interaction and multiple CSM shells in PTF11kx (which is relevant
for some SNe in our sample). A symbiotic nova-like progenitor was suggested by
Dilday et al. (2012) for PTF11kx and they quoted the theoretical rates for the
same to lie between 1–30%, however the model could not explain the massive
CSM. Soker et al. (2013) suggested a core degenerate (CD) scenario in which
the explosion is set by the violent prompt merger of the core of the giant
companion on to the WD and could naturally explain the massive CSM of PTF11kx
(Livio & Riess, 2003). Soker et al. (2013) estimated the occurrence of such
SNe (M${}_{core}+$ M${}_{WD}\gtrsim 2$ M⊙ and M${}_{env}\gtrsim 4$ M⊙) through
population synthesis and found it to be 0.002 per 1000 M⊙ stars formed.
Assuming $\sim$1–2 SNe Ia occur per 1000 M⊙ stars formed (Maoz et al., 2012),
this corresponds to 0.1–0.2%, which compares well with our observed rate
estimate.

The CEW model by Meng & Podsiadlowski (2019) predicts that the SNe Ia-CSM like
objects could arise in the SD CEE scenario when CONe White Dwarfs (WD)
steadily accrete material at the base of the CE without quickly spiraling in
due to the driving of a CEW wind (10–100 km s-1). The WD explodes when it
reaches the Chandrasekhar mass (1.38 M⊙) and could possibly explode within the
CE before it is ejected. The CEW model predicts that 25–40% of the SNe Ia from
CONe WD in Common envelope evolution with a Main Sequence (MS) companion will
show SN Ia-CSM like properties. Meng & Podsiadlowski (2019) also give the
ratio of SNe Ia from CONe WDs to normal SNe Ia from CO WDs to be between 1/9
and 1/5 (considering normal SNe Ia only come from CO WD + MS systems).
Combining that with the estimate that roughly 10–20% of all SNe Ia may come
from the SD scenario (Hayden et al., 2010; Bianco et al., 2011), SNe Ia-CSM
from CONe WD according to the CEW model should be 0.28% to 1.6% of all SNe Ia.
A spin-down before explosion of the WD (Justham, 2011; Di Stefano & Kilic,
2012) could also explain the time delay between explosion and interaction.

Soker (2022) estimated the common envelope to explosion delay time
distribution (CEEDTD) shortly after the CEE (t${}_{CEED}<10^{4}$ yr) from SN
in planetary nebula rates and SN Ia-CSM observed rates to be roughly constant
rather than having a t-1 dependence, that is the SN explosion could occur very
soon after the CEE as well. Our observed rates are on the lower side compared
to these theoretical model estimates but compare well within the observational
uncertainties, though the CEW model seems to best account for the overall SNe
Ia-CSM properties.

##  5 Summary

In this paper, we have presented optical and mid-IR photometry, optical
spectra and detailed analysis of 12 new SNe Ia-CSM identified in the Zwicky
Transient Facility Bright Transient Survey, nearly doubling the total number
of such objects discussed previously by Silverman et al. (2013). The
properties of the sample extracted in this paper agree very well with similar
analysis conducted in S13, particularly the median EW of H$\beta$ is found to
be significantly weaker in SNe Ia-CSM compared with SNe IIn and consequently
the Balmer decrements are ubiquitously higher in SNe Ia-CSM. The brightness of
SNe Ia-CSM in mid-IR is comparable to SNe IIn and observations of reduced flux
in the red side of the H$\alpha$ wing together with the mid-IR brightness
points to formation of new dust in the cooling post-shock gas. The host
galaxies of SNe Ia-CSM lie towards late-type galaxies with recent star
formation. Unlike SNe IIn, no precursors were found within $\sim$1000 days
before explosion for SNe Ia-CSM, which could be an observational bias (less
number of SNe Ia-CSM compared to SNe IIn). We provide a robust rate estimate
of 0.02–0.2% of all SNe Ia for SNe Ia-CSM on account of the BTS survey being
unbiased and spectroscopically highly complete. The simple mass-loss rate
estimates from broad H$\alpha$ luminosity of $\sim 10^{-2}$ M⊙ yr-1 are
similar to previous estimates from various methods and indicate several solar
masses of CSM around these SNe. The observed rate agrees well within the
observational uncertainties with the CEW model by Meng & Podsiadlowski (2019)
which can also explain the interaction delay and massive CSM.

There are still many unanswered questions about the nature of the progenitors
and if we are accurately identifying all potential members of this class. As
ZTF Phase II continues, we are identifying more and more SNe Ia-CSM
(interacting with hydrogen rich and helium rich CSM) and looking further to
the future, if ZTF continues for a Phase III and when LSST survey operations
begins, a larger sample would further improve upon the observed rate
calculation. However, individual object studies are as important and detailed
spectroscopic and multi-wavelength follow-up is essential to capture the CSM
configuration and mass.

##  6 Acknowledgment

Based on observations obtained with the Samuel Oschin Telescope 48-inch and
the 60-inch Telescope at the Palomar Observatory as part of the Zwicky
Transient Facility project. ZTF is supported by the National Science
Foundation under Grants No. AST-1440341 and AST-2034437 and a collaboration
including current partners Caltech, IPAC, the Weizmann Institute of Science,
the Oskar Klein Center at Stockholm University, the University of Maryland,
Deutsches Elektronen-Synchrotron and Humboldt University, the TANGO Consortium
of Taiwan, the University of Wisconsin at Milwaukee, Trinity College Dublin,
Lawrence Livermore National Laboratories, IN2P3, University of Warwick, Ruhr
University Bochum, Northwestern University and former partners the University
of Washington, Los Alamos National Laboratories, and Lawrence Berkeley
National Laboratories. Operations are conducted by COO, IPAC, and UW. The ZTF
forced-photometry service was funded under the Heising-Simons Foundation grant
#12540303 (PI: Graham). This work was supported by the GROWTH project
(Kasliwal et al. 2019) funded by the National Science Foundation under PIRE
Grant No 1545949. The Oskar Klein Centre was funded by the Swedish Research
Council. Partially based on observations made with the Nordic Optical
Telescope, operated by the Nordic Optical Telescope Scientific Association at
the Observatorio del Roque de los Muchachos, La Palma, Spain, of the Instituto
de Astrofisica de Canarias. Some of the data presented here were obtained with
ALFOSC. Some of the data presented herein were obtained at the W. M. Keck
Observatory, which is operated as a scientific partnership among the
California Institute of Technology, the University of California, and NASA;
the observatory was made possible by the generous financial support of the W.
M. Keck Foundation. The SED Machine is based upon work supported by the
National Science Foundation under Grant No. 1106171. This work has made use of
data from the Asteroid Terrestrial-impact Last Alert System (ATLAS) project.
The Asteroid Terrestrial-impact Last Alert System (ATLAS) project is primarily
funded to search for near earth asteroids through NASA grants NN12AR55G,
80NSSC18K0284, and 80NSSC18K1575; byproducts of the NEO search include images
and catalogs from the survey area. The ATLAS science products have been made
possible through the contributions of the University of Hawaii Institute for
Astronomy, the Queen’s University Belfast, the Space Telescope Science
Institute, the South African Astronomical Observatory, and The Millennium
Institute of Astrophysics (MAS), Chile. This research has made use of the
NASA/IPAC Infrared Science Archive, which is funded by the National
Aeronautics and Space Administration and operated by the California Institute
of Technology. The Liverpool Telescope is operated on the island of La Palma
by Liverpool John Moores University in the Spanish Observatorio del Roque de
los Muchachos of the Instituto de Astrofisica de Canarias with financial
support from the UK Science and Technology Facilities Council.

Y. Sharma thanks the LSSTC Data Science Fellowship Program, which is funded by
LSSTC, NSF Cybertraining Grant #1829740, the Brinson Foundation, and the Moore
Foundation; her participation in the program has benefited this work.

S. Schulze acknowledges support from the G.R.E.A.T research environment,
funded by Vetenskapsrådet, the Swedish Research Council, project number
2016-06012.

This work has been supported by the research project grant “Understanding the
Dynamic Universe” funded by the Knut and Alice Wallenberg Foundation under Dnr
KAW 2018.0067,

The research of Y. Yang is supported through a Bengier-Winslow-Robertson
Fellowship.

Fritz (van der Walt et al., 2019; Duev et al., 2019) and GROWTH marshal
(Kasliwal et al., 2019) (dynamic collaborative platforms for time-domain
astronomy) were used in this work.

.

## References

  * dbs (2021) 2021, DBSP DRP, GitHub.  https://github.com/finagle29/dbsp_drp
  * Ahn et al. (2012) Ahn, C. P., Alexandroff, R., Allende Prieto, C., et al. 2012, ApJS, 203, 21
  * Aldering et al. (2006) Aldering, G., Antilogus, P., Bailey, S., et al. 2006, ApJ, 650, 510
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33
  * Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123
  * Astropy Collaboration et al. (2022) Astropy Collaboration, Price-Whelan, A. M., Lim, P. L., et al. 2022, apj, 935, 167
  * Barbary (2016) Barbary, K. 2016, extinction v0.3.0, Zenodo, doi:10.5281/zenodo.804967.  https://doi.org/10.5281/zenodo.804967
  * Barnsley et al. (2012) Barnsley, R. M., Smith, R. J., & Steele, I. A. 2012, Astronomische Nachrichten, 333, 101
  * Bellm & Sesar (2016) Bellm, E. C., & Sesar, B. 2016, pyraf-dbsp: Reduction pipeline for the Palomar Double Beam Spectrograph, Astrophysics Source Code Library, record ascl:1602.002, ,
  * Bellm et al. (2019) Bellm, E. C., Kulkarni, S. R., Barlow, T., et al. 2019, PASP, 131, 068003
  * Ben-Ami et al. (2012) Ben-Ami, S., Konidaris, N., Quimby, R., et al. 2012, in Proc. SPIE, Vol. 8446, Ground-based and Airborne Instrumentation for Astronomy IV, 844686.  http://dx.doi.org/10.1117/12.926317
  * Benetti et al. (2006) Benetti, S., Cappellaro, E., Turatto, M., et al. 2006, ApJ, 653, L129
  * Bianco et al. (2011) Bianco, F. B., Howell, D. A., Sullivan, M., et al. 2011, ApJ, 741, 20
  * Blagorodnova et al. (2018) Blagorodnova, N., Neill, J. D., Walters, R., et al. 2018, PASP, 130, 035003
  * Blondin et al. (2009) Blondin, S., Prieto, J. L., Patat, F., et al. 2009, ApJ, 693, 207.  https://doi.org/10.1088/0004-637x/693/1/207
  * Blondin & Tonry (2007) Blondin, S., & Tonry, J. L. 2007, ApJ, 666, 1024
  * Bloom et al. (2011) Bloom, J. S., Kasen, D., Shen, K. J., et al. 2011, ApJ, 744, L17.  https://doi.org/10.1088/2041-8205/744/2/l17
  * Brown et al. (2012) Brown, P. J., Dawson, K. S., de Pasquale, M., et al. 2012, ApJ, 753, 22.  https://doi.org/10.1088/0004-637x/753/1/22
  * Byler et al. (2017) Byler, N., Dalcanton, J. J., Conroy, C., & Johnson, B. D. 2017, ApJ, 840, 44
  * Calzetti et al. (2000) Calzetti, D., Armus, L., Bohlin, R. C., et al. 2000, ApJ, 533, 682
  * Cenko et al. (2006) Cenko, S. B., Fox, D. B., Moon, D.-S., et al. 2006, PASP, 118, 1396
  * Chabrier (2003) Chabrier, G. 2003, PASP, 115, 763
  * Chambers et al. (2016) Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, arXiv e-prints, arXiv:1612.05560
  * Chugai (1991) Chugai, N. N. 1991, MNRAS, 250, 513
  * Chugai (2009) —. 2009, MNRAS, 400, 866
  * Chugai et al. (2004) Chugai, N. N., Chevalier, R. A., & Lundqvist, P. 2004, MNRAS, 355, 627
  * Chugai & Danziger (1994) Chugai, N. N., & Danziger, I. J. 1994, MNRAS, 268, 173
  * Chugai & Yungelson (2004) Chugai, N. N., & Yungelson, L. R. 2004, AstL, 30, 65
  * Clark et al. (2021) Clark, P., Maguire, K., Bulla, M., et al. 2021, MNRAS, 507, 4367
  * De et al. (2020) De, K., Hankins, M. J., Kasliwal, M. M., et al. 2020, PASP, 132, 025001
  * Dekany et al. (2020) Dekany, R., Smith, R. M., Riddle, R., et al. 2020, PASP, 132, 038001.  https://doi.org/10.1088/1538-3873/ab4ca2
  * Deng et al. (2004) Deng, J., Kawabata, K. S., Ohyama, Y., et al. 2004, ApJ, 605, L37
  * Dhawan et al. (2022) Dhawan, S., Goobar, A., Smith, M., et al. 2022, MNRAS, 510, 2228
  * Di Stefano & Kilic (2012) Di Stefano, R., & Kilic, M. 2012, ApJ, 759, 56
  * Dilday et al. (2010) Dilday, B., Smith, M., Bassett, B., et al. 2010, ApJ, 713, 1026
  * Dilday et al. (2012) Dilday, B., Howell, D. A., Cenko, S. B., et al. 2012, Science, 337, 942
  * Duev et al. (2019) Duev, D. A., Mahabal, A., Masci, F. J., et al. 2019, Monthly Notices of the Royal Astronomical Society, 489, 3582
  * Filippenko (1997) Filippenko, A. V. 1997, ARA&A, 35, 309
  * Filippenko et al. (1992) Filippenko, A. V., Richmond, M. W., Matheson, T., et al. 1992, ApJ, 384, L15
  * Fitzpatrick (1999) Fitzpatrick, E. L. 1999, PASP, 111, 63
  * Foley et al. (2007) Foley, R. J., Smith, N., Ganeshalingam, M., et al. 2007, ApJ, 657, L105.  https://doi.org/10.1086/513145
  * Ford et al. (1993) Ford, C. H., Herbst, W., Richmond, M. W., et al. 1993, AJ, 106, 1101
  * Förster et al. (2021) Förster, F., Cabrera-Vives, G., Castillo-Navarrete, E., et al. 2021, AJ, 161, 242
  * Fox et al. (2011) Fox, O. D., Chevalier, R. A., Skrutskie, M. F., et al. 2011, ApJ, 741, 7
  * Fox et al. (2015) Fox, O. D., Silverman, J. M., Filippenko, A. V., et al. 2015, MNRAS, 447, 772
  * Fremling et al. (2016) Fremling, C., Sollerman, J., Taddia, F., et al. 2016, A&A, 593, A68.  https://doi.org/10.1051/0004-6361/201628275
  * Fremling et al. (2020) Fremling, C., Miller, A. A., Sharma, Y., et al. 2020, ApJ, 895, 32.  https://doi.org/10.3847/1538-4357/ab8943
  * Gal-Yam & Leonard (2009) Gal-Yam, A., & Leonard, D. C. 2009, Nature, 458, 865
  * Gal-Yam et al. (2021) Gal-Yam, A., Yaron, O., Pastorello, A., et al. 2021, TNSAN, 76, 1
  * Gal-Yam et al. (2007) Gal-Yam, A., Leonard, D. C., Fox, D. B., et al. 2007, ApJ, 656, 372
  * Gal-Yam et al. (2022) Gal-Yam, A., Bruch, R., Schulze, S., et al. 2022, Nature, 601, 201
  * Germany et al. (2000) Germany, L. M., Reiss, D. J., Sadler, E. M., Schmidt, B. P., & Stubbs, C. W. 2000, ApJ, 533, 320
  * Graham et al. (2019) Graham, M. J., Kulkarni, S. R., Bellm, E. C., et al. 2019, PASP, 131, 078001
  * Graham et al. (2017) Graham, M. L., Harris, C. E., Fox, O. D., et al. 2017, ApJ, 843, 102
  * Graham et al. (2022) Graham, M. L., Fremling, C., Perley, D. A., et al. 2022, MNRAS, 511, 241
  * Guillochon et al. (2017) Guillochon, J., Parrent, J., Kelley, L. Z., & Margutti, R. 2017, ApJ, 835, 64
  * Hamuy et al. (2003) Hamuy, M., Phillips, M. M., Suntzeff, N. B., et al. 2003, Nature, 424, 651
  * Han & Podsiadlowski (2006) Han, Z., & Podsiadlowski, P. 2006, MNRAS, 368, 1095
  * Hayden et al. (2010) Hayden, B. T., Garnavich, P. M., Kasen, D., et al. 2010, ApJ, 722, 1691
  * Hodgkin et al. (2021) Hodgkin, S. T., Harrison, D. L., Breedt, E., et al. 2021, A&A, 652, A76
  * Hosseinzadeh et al. (2017) Hosseinzadeh, G., Arcavi, I., Valenti, S., et al. 2017, ApJ, 836, 158.  https://doi.org/10.3847/1538-4357/836/2/158
  * Hunter (2007) Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90
  * Iben & Tutukov (1984) Iben, I., J., & Tutukov, A. V. 1984, ApJS, 54, 335
  * Inserra et al. (2014) Inserra, C., Smartt, S. J., Scalzo, R., et al. 2014, MNRAS, 437, L51
  * Inserra et al. (2016) Inserra, C., Fraser, M., Smartt, S. J., et al. 2016, MNRAS, 459, 2721
  * Irani et al. (2022) Irani, I., Prentice, S. J., Schulze, S., et al. 2022, ApJ, 927, 10
  * IRSA (2022) IRSA. 2022, Zwicky Transient Facility Image Service, IPAC, doi:10.26131/IRSA539.  https://catcopy.ipac.caltech.edu/dois/doi.php?id=10.26131/IRSA539
  * Johnson et al. (2021) Johnson, B. D., Leja, J., Conroy, C., & Speagle, J. S. 2021, ApJS, 254, 22
  * Justham (2011) Justham, S. 2011, ApJ, 730, L34
  * Kasliwal et al. (2019) Kasliwal, M. M., Cannella, C., Bagdasaryan, A., et al. 2019, Publications of the Astronomical Society of the Pacific, 131, 038003.  https://doi.org/10.1088%2F1538-3873%2Faafbc2
  * Kiewe et al. (2012) Kiewe, M., Gal-Yam, A., Arcavi, I., et al. 2012, ApJ, 744, 10
  * Kochanek et al. (2017) Kochanek, C. S., Shappee, B. J., Stanek, K. Z., et al. 2017, PASP, 129, 104502
  * Kool et al. (2022) Kool, E., Johansson, J., Sollerman, J., & et al. 2022,
  * Kotak & Meikle (2005) Kotak, R., & Meikle, W. P. S. 2005, in Astronomical Society of the Pacific Conference Series, Vol. 342, 1604-2004: Supernovae as Cosmological Lighthouses, ed. M. Turatto, S. Benetti, L. Zampieri, & W. Shea, 264
  * Lang (2014a) Lang, D. 2014a, AJ, 147, 108
  * Lang (2014b) —. 2014b, AJ, 147, 108
  * Leloudas et al. (2015) Leloudas, G., Hsiao, E. Y., Johansson, J., et al. 2015, A&A, 574, A61
  * Li et al. (2011) Li, W., Bloom, J. S., Podsiadlowski, P., et al. 2011, Nature, 480, 348
  * Lintott et al. (2011) Lintott, C., Schawinski, K., Bamford, S., et al. 2011, MNRAS, 410, 166
  * Livio & Riess (2003) Livio, M., & Riess, A. G. 2003, ApJ, 594, L93
  * Maguire et al. (2013) Maguire, K., Sullivan, M., Patat, F., et al. 2013, MNRAS, 436, 222
  * Mainzer et al. (2014) Mainzer, A., Bauer, J., Cutri, R. M., et al. 2014, ApJ, 792, 30
  * Maoz et al. (2012) Maoz, D., Mannucci, F., & Brandt, T. D. 2012, MNRAS, 426, 3282
  * Martin et al. (2005) Martin, D. C., Fanson, J., Schiminovich, D., et al. 2005, ApJ, 619, L1
  * Masci et al. (2019) Masci, F. J., Laher, R. R., Rusholme, B., et al. 2019, PASP, 131, 018003
  * Meisner et al. (2018) Meisner, A. M., Lang, D., & Schlegel, D. J. 2018, AJ, 156, 69
  * Meng & Podsiadlowski (2019) Meng, X., & Podsiadlowski, P. 2019, IAU Symposium, 343, 470
  * Miller et al. (2020) Miller, A. A., Yao, Y., Bulla, M., et al. 2020, ApJ, 902, 47
  * Miller & Stone (1987) Miller, J., & Stone, R. 1987, The CCD Cassegrain Spectrograph at the Shane Reflector, Santa Cruz: Lick Observatory Techical Reports No. 48
  * Nicholls & Dong (2018) Nicholls, B., & Dong, S. 2018, TNSCR, 2018-1144, 1
  * Nordin et al. (2019) Nordin, J., Brinnel, V., van Santen, J., et al. 2019, A&A, 631, A147.  http://dx.doi.org/10.1051/0004-6361/201935634
  * Nugent et al. (2011) Nugent, P. E., Sullivan, M., Cenko, S. B., et al. 2011, Nature, 480, 344
  * Oke & Gunn (1982) Oke, J. B., & Gunn, J. E. 1982, PASP, 94, 586
  * Oke et al. (1995) Oke, J. B., Cohen, J. G., Carr, M., et al. 1995, PASP, 107, 375
  * Pastorello et al. (2008) Pastorello, A., Mattila, S., Zampieri, L., et al. 2008, MNRAS, 389, 113
  * Patat et al. (2007) Patat, F., Chandra, P., Chevalier, R., et al. 2007, Science, 317, 924
  * Payne et al. (2019) Payne, A. V., Tucker, M. A., Do, A., Shappee, B. J., & Huber, M. E. 2019, TNSCR, 2019-343, 1
  * Pedregosa et al. (2011) Pedregosa, F., Varoquaux, G., Gramfort, A., et al. 2011, JMLR, 12, 2825
  * Pellegrino et al. (2022) Pellegrino, C., Howell, D. A., Terreran, G., et al. 2022, arXiv e-prints, arXiv:2205.07894
  * Perley (2019) Perley, D. A. 2019, PASP, 131, 084503
  * Perley et al. (2020) Perley, D. A., Fremling, C., Sollerman, J., et al. 2020, ApJ, 904, 35.  http://dx.doi.org/10.3847/1538-4357/abbd98
  * Perley et al. (2022) Perley, D. A., Sollerman, J., Schulze, S., et al. 2022, ApJ, 927, 180
  * Piascik et al. (2014) Piascik, A. S., Steele, I. A., Bates, S. D., et al. 2014, in Proc. SPIE, Vol. 9147, Ground-based and Airborne Instrumentation for Astronomy V, 91478H
  * Prentice et al. (2020) Prentice, S., Maguire, K., Magee, M. R., & Deckers, M. 2020, TNSCR, 2020-2285, 1
  * Prieto et al. (2007) Prieto, J. L., Garnavich, P. M., Phillips, M. M., et al. 2007, arXiv e-prints, arXiv:0706.4088
  * Prochaska et al. (2020) Prochaska, J. X., Hennawi, J. F., Westfall, K. B., et al. 2020, Journal of Open Source Software, 5, 2308.  https://doi.org/10.21105/joss.02308
  * Reguitti (2020) Reguitti, A. 2020, TNSCR, 2020-3825, 1
  * Rigault (2018) Rigault, M. 2018, ztfquery, a python tool to access ZTF data, Zenodo, vdoi, Zenodo, doi:10.5281/zenodo.1345222
  * Rigault et al. (2019) Rigault, M., Neill, J. D., Blagorodnova, N., et al. 2019, A&A, 627, A115
  * Salamanca et al. (1998) Salamanca, I., Cid-Fernandes, R., Tenorio-Tagle, G., et al. 1998, MNRAS, 300, L17
  * Schlafly & Finkbeiner (2011) Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103.  https://doi.org/10.1088/0004-637x/737/2/103
  * Schlegel (1990) Schlegel, E. M. 1990, MNRAS, 244, 269
  * Schmidt et al. (1994) Schmidt, B. P., Kirshner, R. P., Leibundgut, B., et al. 1994, ApJ, 434, L19
  * Schulze et al. (2021) Schulze, S., Yaron, O., Sollerman, J., et al. 2021, ApJS, 255, 29
  * Shappee et al. (2014) Shappee, B., Prieto, J., Stanek, K. Z., et al. 2014, in , Vol. 223, 236.03
  * Silverman et al. (2013) Silverman, J. M., Nugent, P. E., Gal-Yam, A., et al. 2013, ApJS, 207, 3.  https://doi.org/10.1088/0067-0049/207/1/3
  * Silverman et al. (2013) Silverman, J. M., Nugent, P. E., Gal-Yam, A., et al. 2013, ApJ, 772, 125
  * Simon et al. (2009) Simon, J. D., Gal-Yam, A., Gnat, O., et al. 2009, ApJ, 702, 1157.  https://doi.org/10.1088/0004-637x/702/2/1157
  * Skrutskie et al. (2006) Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163
  * Smartt et al. (2015) Smartt, S. J., Valenti, S., Fraser, M., et al. 2015, A&A, 579, A40
  * Smith et al. (2020) Smith, K. W., Smartt, S. J., Young, D. R., et al. 2020, PASP, 132, 085002
  * Smith (2014) Smith, N. 2014, ARA&A, 52, 487.  https://doi.org/10.1146/annurev-astro-081913-040025
  * Smith et al. (2008) Smith, N., Chornock, R., Li, W., et al. 2008, ApJ, 686, 467
  * Soker (2022) Soker, N. 2022, RAA, 22, 035025
  * Soker et al. (2013) Soker, N., Kashi, A., García-Berro, E., Torres, S., & Camacho, J. 2013, MNRAS, 431, 1541
  * Soraisam et al. (2021) Soraisam, M., Matheson, T., & Lee, C.-H. 2021, RNAAS, 5, 62
  * Soumagnac & Ofek (2018) Soumagnac, M. T., & Ofek, E. O. 2018, PASP, 130, 075002
  * Steele et al. (2004) Steele, I. A., Smith, R. J., Rees, P. C., et al. 2004, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 5489, Ground-based Telescopes, ed. J. Oschmann, Jacobus M., 679–692
  * Stein et al. (2018a) Stein, R., Callis, E., Kostrzewa-rutkowska, Z., Fraser, M., & Yaron, O. 2018a, TNSCR, 2018-1168, 1
  * Stein et al. (2018b) —. 2018b, TNSCR, 2018-1168, 1
  * Sternberg et al. (2011) Sternberg, A., Gal-Yam, A., Simon, J. D., et al. 2011, Science, 333, 856
  * Strotjohann et al. (2021) Strotjohann, N. L., Ofek, E. O., Gal-Yam, A., et al. 2021, ApJ, 907, 99
  * Taddia et al. (2013) Taddia, F., Stritzinger, M. D., Sollerman, J., et al. 2013, A&A, 555, A10
  * Taggart (2020) Taggart, K. 2020, PhD thesis, Liverpool John Moores University, doi:10.24377/LJMU.t.00014104.  http://researchonline.ljmu.ac.uk/id/eprint/14104/
  * Taubenberger et al. (2013) Taubenberger, S., Kromer, M., Hachinger, S., et al. 2013, MNRAS, 432, 3117
  * Thévenot et al. (2021) Thévenot, M., Kabatnik, M., & Gantier, J. M. 2021, Transient Name Server AstroNote, 212, 1
  * Tody (1986) Tody, D. 1986, in Proc. SPIE, Vol. 627, Instrumentation in astronomy VI, ed. D. L. Crawford, 733
  * Tody (1993) Tody, D. 1993, in Astronomical Society of the Pacific Conference Series, Vol. 52, Astronomical Data Analysis Software and Systems II, ed. R. J. Hanisch, R. J. V. Brissenden, & J. Barnes, 173
  * Tonry et al. (2018) Tonry, J. L., Denneau, L., Heinze, A. N., et al. 2018, PASP, 130, 064505
  * Tucker et al. (2018) Tucker, M. A., Huber, M., Shappee, B. J., et al. 2018, The Astronomer’s Telegram, 11444, 1
  * van der Walt et al. (2019) van der Walt, S. J., Crellin-Quick, A., & Bloom, J. S. 2019, Journal of Open Source Software, 4, doi:10.21105/joss.01247.  http://joss.theoj.org/papers/10.21105/joss.01247
  * Wang et al. (2004) Wang, L., Baade, D., Hflich, P., et al. 2004, ApJ, 604, L53.  https://doi.org/10.1086/383411
  * Webbink (1984) Webbink, R. F. 1984, ApJ, 277, 355
  * Whelan & Iben (1973) Whelan, J., & Iben, Icko, J. 1973, ApJ, 186, 1007
  * Wood-Vasey et al. (2004) Wood-Vasey, W. M., Wang, L., & Aldering, G. 2004, ApJ, 616, 339.  https://doi.org/10.1086/424826
  * Wright et al. (2016) Wright, A. H., Robotham, A. S. G., Bourne, N., et al. 2016, MNRAS, 460, 765
  * Wright et al. (2010a) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010a, AJ, 140, 1868
  * Wright et al. (2010b) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010b, AJ, 140, 1868
  * Xu et al. (1992) Xu, Y., McCray, R., Oliva, E., & Randich, S. 1992, ApJ, 386, 181
  * Yang et al. (2022) Yang, Y., Baade, D., Hoeflich, P., et al. 2022, MNRAS, arXiv:2211.04423
  * Yao et al. (2019) Yao, Y., Miller, A. A., Kulkarni, S. R., et al. 2019, ApJ, 886, 152
  * Yaron & Gal-Yam (2012) Yaron, O., & Gal-Yam, A. 2012, PASP, 124, 668
  * Zackay et al. (2016) Zackay, B., Ofek, E. O., & Gal-Yam, A. 2016, ApJ, 830, 27

##  Appendix A Ambiguous SN Ia-CSM/IIn in BTS

To identify potential SNe Ia-CSM hiding in the SN IIn sample classified by
BTS, we rechecked all SNe IIn classifications (total 142) using SuperNova
IDentification (SNID; Blondin & Tonry 2007) software. SNe IIn spectra were
processed through SNID, and any SN having $\geq 3$ matches to a SN Ia-CSM in
the top 10 matches were manually checked. The SNe having ambiguous
classifications are described below.

###  A.1 SN 2019smj

Discovered by ZTF and reported to TNS by ALeRCE (Förster et al., 2021) on
2019-10-13 11:28:42.000, SN 2019smj (ZTF19aceqlxc) was classified as a Type
IIn by BTS at $z=0.06$. It peaked at apparent magnitude $17.1$ in $r$ band
($\sim-20.1$) and then developed a weaker but broader bump. The spectra showed
very weak H$\beta$, barely any He I $\lambda 5876$, no O I $\lambda 7774$ or
[O I] lines but showed some iron group lines, Ca NIR emission and [Ca II].
SNID best matches were to SNe 1997cy and 2005gj. The early spectra from
P60/SEDM have some matches to SN 2005gj but are too noisy and of ultra-low
resolution to conclusively provide a Ia-CSM classification. From these
observations, SN 2019smj is most likely a Type Ia-CSM but given the lack of
confirmation we have excluded it from the main sample.

###  A.2 SN 2018dfa

Discovered and reported to TNS by ATLAS on 2018-07-05 08:51:21.000, SN 2018dfa
was classified initially as a Type IIP by BTS but later spectra revealed it to
be a Type IIn at $z=0.128$. It peaked at apparent magnitude of $17.5$ in $r$
band ($-20.2$) and showed a minor bump before main peak in the light curve.
The spectra showed weak H$\beta$ and He I $\lambda 5876$, no O I $\lambda
7774$ or [O I] lines. SNID best matches were to SNe 2002ic and 2005gj along
with SNe Ia-norm/91T. The earliest spectra with good SNR from P200/DBSP had
one match to SN 2005gj but could not provide a robust Ia-CSM classification.
From these observations, SN 2018dfa is most likely a Type Ia-CSM but given the
lack of confirmation we have excluded it from the main sample.

###  A.3 SN 2019vpk

Discovered by ZTF and reported to TNS by ALeRCE on 2019-11-25 06:33:38.000, SN
2019vpk was classified as a Type IIn by BTS at $z=0.1$. It peaked at apparent
magnitude of $\sim 18$ in $r$ band ($\sim-20.5$). The early spectra were too
noisy and the only spectrum with good SNR was obtained with P200/DBSP nearly 6
weeks after discovery which showed weak H$\beta$, no clear He I emission but
possibly Si II $\lambda 5958$ emission (which is unlike any other SN Ia-CSM).
SNID top matches were to SN 2005gj but visually did not look entirely
convincing, and some matches were also to Type IIn. We conclude SN 2019vpk
does not have enough data for a robust Ia-CSM classification.

###  A.4 SN 2019wma

Discovered by ZTF and reported to TNS by ALeRCE on 2019-12-13 13:35:26.000, SN
2019wma was classified as a Type IIn by BTS at $z=0.088$. It peaked at
apparent magnitude of $\sim 18.5$ in $r$ band ($\sim-19.5$). The spectra
obtained were either from P60/SEDM or LT/SPRAT hence of low resolution and
showed weak H$\beta$ and He I emission. SNID top matches to earliest SEDM
spectrum were to SN 2005gj at the correct redshift but given the lack of
intermediate resolution spectra and absence of late time follow-up we did not
assign a Type Ia-CSM classification to SN 2019wma and excluded it from the
main sample.

###  A.5 SN 2019kep

Discovered and reported to TNS by ATLAS on 2019-07-02 14:13:55.000, SN 2019kep
was classified as a Type IIn by BTS at $z=0.02388$. It peaked at apparent
magnitude of $18.2$ in $r$ band ($-17$). Most early spectra were too noisy for
classification but matched to SN 2005gj. A good SNR P200/DBSP spectrum showed
narrow P-Cygni H$\alpha$ with absorption minimum at $\sim 2500$ km s-1 but
overall matched to a Type II SN. From these observations, we could not
determine a robust classification for SN 2019kep and excluded it from the main
sample.

###  A.6 SN 2018ctj

Discovered and reported to TNS by ZTF on 2018-04-21 08:36:57.000, SN 2018ctj
was classified as a Type IIn by BTS at $z=0.0378$. It peaked at apparent
magnitude of $18.4$ in $r$ band ($-17.8$) and was also detected in unWISE
data. Only one P60/SEDM spectrum was obtained that matched well to SNe 1997cy
and 2005gj. Given the lack of intermediate resolution spectra this SN remains
classified as Type IIn and excluded from the main sample.