# Circumstellar Medium Constraints on the Environment of Two Nearby Type Ia
Supernovae: SN 2017cbv and SN 2020nlb

D. J. Sand Steward Observatory, University of Arizona, 933 North Cherry
Avenue, Tucson, AZ 85721-0065, USA  S. K. Sarbadhicary Department of Physics
and Astronomy, Michigan State University, East Lansing, MI 48824, USA  C.
Pellegrino Las Cumbres Observatory, 6740 Cortona Drive, Suite 102, Goleta, CA
93117-5575, USA  Department of Physics, University of California, Santa
Barbara, CA 93106-9530, USA  K. Misra  Aryabhatta Research Institute of
Observational Sciences, Manora Peak, Nainital 263 001, India  R. Dastidar
Millennium Institute of Astrophysics, Nuncio Monsenor Sotero Sanz 100,
Providencia, Santiago, Chile  P. J. Brown Department of Physics and Astronomy,
Texas A&M University, 4242 TAMU, College Station, TX 77843, USA  George P. and
Cynthia Woods Mitchell Institute for Fundamental Physics & Astronomy  K.
Itagaki  Itagaki Astronomical Observatory, Yamagata 990-2492, Japan  S.
Valenti Department of Physics and Astronomy, University of California, 1
Shields Avenue, Davis, CA 95616-5270, USA  Jonathan J. Swift Thacher
Observatory, Thacher School, 5025 Thacher Rd. Ojai, CA 93023, USA  J. E.
Andrews Gemini Observatory/NSF’s NOIRLab, 670 N. A’ohoku Place, Hilo, Hawai’i,
96720, USA  K. A. Bostroem Department of Physics and Astronomy, University of
California, 1 Shields Avenue, Davis, CA 95616-5270, USA  J. Burke Department
of Physics, University of California, Santa Barbara, CA 93106-9530, USA  Las
Cumbres Observatory, 6740 Cortona Drive, Suite 102, Goleta, CA 93117-5575, USA
L. Chomiuk Department of Physics and Astronomy, Michigan State University,
East Lansing, MI 48824, USA  Y. Dong Department of Physics and Astronomy,
University of California, 1 Shields Avenue, Davis, CA 95616-5270, USA  L.
Galbany Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can
Magrans, s/n, E-08193 Barcelona, Spain  M. L. Graham DiRAC Institute,
Department of Astronomy, University of Washington, Box 351580, U.W., Seattle,
WA 98195, USA  D. Hiramatsu Department of Physics, University of California,
Santa Barbara, CA 93106-9530, USA  Las Cumbres Observatory, 6740 Cortona
Drive, Suite 102, Goleta, CA 93117-5575, USA  D. A. Howell Las Cumbres
Observatory, 6740 Cortona Drive, Suite 102, Goleta, CA 93117-5575, USA  E. Y.
Hsiao Department of Physics, Florida State University, 77 Chieftan Way,
Tallahassee, FL 32306, USA  D. Janzen Department of Physics and Engineering
Physics, University of Saskatchewan, 116 Science Pl, Saskatoon, SK S7N 5E2,
Canada  J. E. Jencson Steward Observatory, University of Arizona, 933 North
Cherry Avenue, Tucson, AZ 85721-0065, USA  M. J. Lundquist Steward
Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ
85721-0065, USA  C. McCully Department of Physics, University of California,
Santa Barbara, CA 93106-9530, USA  Las Cumbres Observatory, 6740 Cortona
Drive, Suite 102, Goleta, CA 93117-5575, USA  D. Reichart Department of
Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel
Hill, NC 27599, USA  Nathan Smith Steward Observatory, University of Arizona,
933 North Cherry Avenue, Tucson, AZ 85721-0065, USA  Lingzhi Wang Chinese
Academy of Sciences South America Center for Astronomy, National Astronomical
Observatories, CAS, Beijing 100101, People’s Republic of China  CAS Key
Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese
Academy of Sciences, Beijing 100101, People’s Republic of China  S. Wyatt
Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson,
AZ 85721-0065, USA

###### Abstract

We present deep Chandra X-ray observations of two nearby Type Ia supernovae,
SN 2017cbv and SN 2020nlb, which reveal no X-ray emission down to a luminosity
$L_{X}$$\lesssim$5.3$\times$1037 and $\lesssim$5.4$\times$1037 erg s-1 (0.3–10
keV), respectively, at $\sim$16–18 days after the explosion. With these
limits, we constrain the pre-explosion mass-loss rate of the progenitor system
to be $\dot{M}$$<$7.2$\times$10-9 and $<$9.7$\times$10-9 M⊙ yr-1 for each (at
a wind velocity $v_{w}$=100 km s-1 and a radius of $R$$\approx$1016 cm),
assuming any X-ray emission would originate from inverse Compton emission from
optical photons up-scattered by the supernova shock. If the supernova
environment was a constant density medium, we find a number density limit of
nCSM$<$36 and $<$65 cm-3, respectively. These X-ray limits rule out all
plausible symbiotic progenitor systems, as well as large swathes of parameter
space associated with the single degenerate scenario, such as mass loss at the
outer Lagrange point and accretion winds. We also present late-time optical
spectroscopy of SN 2020nlb, and set strong limits on any swept up hydrogen
($L_{H\alpha}$$<$2.7$\times$1037 ergs s-1) and helium ($L_{He,\lambda
6678}$$<$2.7$\times$1037 ergs s-1) from a nondegenerate companion,
corresponding to $M_{H}$$\lesssim$0.7–2$\times$10-3 M⊙ and
$M_{He}$$\lesssim$4$\times$10-3 M⊙. Radio observations of SN 2020nlb at 14.6
days after explosion also yield a non-detection, ruling out most plausible
symbiotic progenitor systems. While we have doubled the sample of normal type
Ia supernovae with deep X-ray limits, more observations are needed to sample
the full range of luminosities and sub-types of these explosions, and set
statistical constraints on their circumbinary environments.

Type Ia Supernovae (1728), Circumstellar matter(241)

††facilities: CXO (ACIS), Las Cumbres Observatory (Sinistro), FTN (FLOYDS),
MMT (Blue Channel spectrograph), Swift (UVOT), VLA††software:  astropy
(Astropy Collaboration et al., 2013; The Astropy Collaboration et al., 2018),
The IDL Astronomy User’s Library (Landsman, 1993), CIAO (Fruscione et al.,
2006), Supernova IDentification software package (SNiD; Blondin & Tonry,
2007), Astrometrica (Raab, 2012), SNooPy (Burns et al., 2011, 2014), HEASoft
(Nasa High Energy Astrophysics Science Archive Research Center (2014),
Heasarc), lcogtsnpipe (Valenti et al., 2016), DoPHOT (Schechter et al., 1993)

##  1 Introduction

Despite their critical use for cosmology, the exact progenitor systems and
explosion mechanisms for Type Ia supernovae (SNe Ia) are still being
determined (e.g., Jha et al., 2019, for a recent review). There are two
general categories of SN Ia progenitors which can plausibly explain how the
carbon-oxygen white dwarf accretes the necessary mass to cause an explosion:
the single degenerate (SD) and double degenerate (DD) scenarios. In the DD
scenario a second degenerate companion (i.e. another white dwarf) is in the
binary system (Iben & Tutukov, 1984; Webbink, 1984), while in the SD scenario
there is a nondegenerate companion star (Whelan & Iben, 1973). Within these
two broad categories, the exact triggering mechanism for the thermonuclear
explosion is a topic of current research.

There are several observational techniques that have been developed to shed
light on the progenitor system, although we only mention a few here. For
instance, models predict that the very early light curves of SNe Ia may
exhibit a ‘blue bump’ in the UV-optical in the days after explosion due to the
ejecta shocking the nondegenerate companion (Kasen, 2010). A similar signature
has been observed in a handful of instances (e.g. Cao et al., 2015; Marion et
al., 2016; Hosseinzadeh et al., 2017a; Miller et al., 2018; Shappee et al.,
2019; Dimitriadis et al., 2019; Miller et al., 2020; Tucker et al., 2020a;
Burke et al., 2021, and strongly constrained in other instances, e.g. Hayden
et al. 2010; Bianco et al. 2011; Ganeshalingam et al. 2011; Brown et al. 2012;
Olling et al. 2015), although the interpretation of these early light curves
are still a matter of debate. Meanwhile, another prediction of the SD scenario
is that material stripped from the companion star is swept up by the SN Ia
ejecta, detectable as a narrow emission line of hydrogen or helium at late
times (most recently, Botyánszki et al., 2018; Dessart et al., 2020). While
most searches have only led to limits on the amount of stripped hydrogen
and/or helium (Mattila et al., 2005; Leonard, 2007; Shappee et al., 2013;
Lundqvist et al., 2013, 2015; Maguire et al., 2016; Graham et al., 2017;
Shappee et al., 2018; Holmbo et al., 2018; Tucker et al., 2019; Dimitriadis et
al., 2019; Sand et al., 2016, 2018, 2019; Tucker et al., 2020b), three recent
detections from fast-declining SNe Ia (Kollmeier et al., 2019; Vallely et al.,
2019a; Prieto et al., 2020; Elias-Rosa et al., 2021) indicate that a broader
search for such features may prove fruitful. Presumably, if an early light
curve bump was due to interaction with a nondegenerate companion, then at late
times a hydrogen or helium emission line should be visible. Such important
cross-checks between early light curve and nebular signatures of the
progenitor are essential, as has recently been carried out for SN 2017cbv
(early light curve: Hosseinzadeh et al. 2017a; nebular spectra: Sand et al.
2018) and SN 2018oh (early light curve: Dimitriadis et al. 2019; Shappee et
al. 2019; Li et al. 2019; nebular spectra: Dimitriadis et al. 2019; Tucker et
al. 2019). In these recent examples, even though the early light curves may
point to a single degenerate progenitor, the nebular spectra do not
necessarily corroborate this picture, suggesting that further progenitor
probes are necessary to understand these systems.

One powerful probe of the immediate SN Ia environment, and thus the progenitor
system, utilizes X-ray observations around the time of maximum light (Margutti
et al., 2012; Horesh et al., 2012a; Margutti et al., 2014; Russell & Immler,
2012; Shappee et al., 2018, 2019; Stauffer et al., 2021). X-ray emission in
the weeks after a SN Ia explosion originates from the upscattering of optical
photons off relativistic particles accelerated at the SN shock (i.e. inverse
Compton emission; Chevalier & Fransson, 2006a; Margutti et al., 2012). This
circumstellar medium was in turn shaped by the mass loss of the progenitor
star system leading up to the explosion. Broadly speaking, in the SD scenario
the white dwarf accretes material from a nondegenerate stellar companion,
either through direct Roche lobe overflow (RLOF; Nomoto, 1982) or from a wind
from the secondary star (the ‘symbiotic channel’; e.g. Patat et al. 2011) – it
thus is expected to have residual CSM in its immediate environment either from
the donor star wind or from non-conservative mass loss from the RLOF transfer.
By contrast, a standard DD scenario involving two white dwarfs inspiraling due
to angular momentum loss should have a ‘cleaner’ CSM environment.

Deep Chandra X-ray limits have been reported for only two normal SNe Ia thus
far – the nearby and well studied SN 2011fe (Margutti et al., 2012) and SN
2014J (Margutti et al., 2014). Both resulted in strong X-ray upper limits
which ruled out a symbiotic giant star companion and large portions of
parameter space associated with accretion winds and Lagrangian losses from a
main sequence or subgiant companion. Despite these strong results, deep X-ray
data for two SNe Ia is insufficient to draw wider conclusions about the SN Ia
population, and ultimately a statistical data set of deep X-ray limits on SNe
Ia is needed (along with other tracers) to constrain SN Ia progenitor
properties.

Here we present Chandra X-ray data of two nearby type Ia SNe – SN 2017cbv and
SN 2020nlb – to constrain the circumstellar environment associated with the
progenitor system, doubling the sample with deep X-ray limits. The study of SN
2017cbv is particularly interesting given the ‘blue bump’ observed in its
early light curve, which may be due to interaction with a nondegenerate
companion. Meanwhile, we couple deep X-ray data of SN 2020nlb with radio data
from the Very Large Array (VLA) and nebular spectroscopy to constrain any
hydrogen or helium emission – these complementary probes are essential for
narrowing in on the SN Ia progenitor. We end this paper with our X-ray derived
CSM constraints and a discussion of the donor star and allowed progenitor
configuration for SN 2017cbv and SN 2020nlb.

##  2 Background

###  2.1 SN 2017cbv

SN 2017cbv (RA
$14\overset{\mathrm{h}}{\phantom{.}}32\overset{\mathrm{m}}{\phantom{.}}34\overset{\mathrm{s}}{.}38$
& Dec
$-44\overset{\circ}{\phantom{.}}08\overset{\prime}{\phantom{.}}03\overset{\prime\prime}{.}1$
J2000) was discovered in the outskirts of the nearby galaxy NGC 5643 on 2017
March 10 UT (MJD 57822.14) at a magnitude of $r$$\approx$16 by the Distance
Less Than 40 Mpc survey (DLT40; Tartaglia et al., 2018). Within hours of
discovery, the transient was classified as a very young SN Ia (Hosseinzadeh et
al., 2017b), and an intense multiwavelength follow-up campaign was begun. The
early light curve of SN 2017cbv displayed a clear, blue excess, lasting
$\sim$3 days (Hosseinzadeh et al., 2017a). Such excess emission is predicted
in the single degenerate scenario, when the SN ejecta shock a nondegenerate
companion star (Kasen, 2010). While the observed optical light curve of SN
2017cbv is well fit to this model, it overpredicts the observed flux in the
ultraviolet bands (possibly due to line blanketing or other physics not
currently accounted for in the models; see, Hosseinzadeh et al., 2017a).
Nebular phase spectroscopy did not detect any narrow hydrogen or helium
features (Sand et al., 2018), as might be expected in the single degenerate
scenario (e.g. Botyánszki et al., 2018; Dessart et al., 2020), although
further modeling is needed. The uncertain origin for the early blue excess
emission makes SN 2017cbv an excellent target for a deep X-ray search for CSM
interaction, as a complementary probe of the progenitor system.

We adopt an explosion epoch of MJD 57821.0, as found by Hosseinzadeh et al.
(2017a) based on the early Si II velocity evolution (using the technique
described in Piro & Nakar, 2014). We also adopt a distance of $\mu$=30.58 mag
($D$$\approx$13.1 Mpc), the value used by Wang et al. (2020) for presenting
their SN 2017cbv bolometric light curve, which we adopt for our analysis as
well. This distance is in agreement with other recent light curve analyses of
SN 2017cbv (e.g. Sand et al., 2018; Burns et al., 2020), and a tip of the red
giant branch distance to SN 2017cbv’s host galaxy, NGC 5643 (Hoyt et al.,
2021). We also use the epoch of $B$-band maximum from Wang et al. 2020 for
reference, MJD 57840.87.

The Galactic neutral hydrogen column density in the direction of SN 2017cbv is
NH = 8.014$\times$1020 cm-2 (Kalberla et al., 2005). The hydrogen column
associated with the host galaxy is likely negligible, as no significant host
galaxy extinction is evident (see discussions in Ferretti et al., 2017; Sand
et al., 2018); we therefore adopt NH = 8.014$\times$1020 cm-2 as the total
hydrogen column density to SN 2017cbv in this work.

###  2.2 SN 2020nlb

SN 2020nlb was discovered on 2020 June 25.25 UT (MJD 59025.25) by the ATLAS
survey (Tonry et al., 2018) with an orange magnitude of 17.44. The last non-
detection from ATLAS was two days earlier (2020 June 23.28). The field of SN
2020nlb was also monitored by the Itagaki Astronomical Observatory’s 0.35-m
telescope in Okayama, Japan who obtained a tighter nondetection epoch of 2020
June 24.57 (MJD 59024.57), with a limiting magnitude of $<$18.5 mag, before
also detecting the SN on 2020 June 26.56 at 16.1 mag. The unfiltered Itagaki
photometry was extracted using Astrometrica (Raab, 2012) and calibrated to the
Fourth US Naval Observatory CCD Astrograph Catalog (UCAC4; Zacharias et al.
2013). We adopt the midpoint between the Itagaki non-detection and the first
detection by the ATLAS survey as the explosion epoch (MJD 59024.91). Our X-ray
analysis is not sensitive to the exact epoch adopted.

SN 2020nlb (RA
$12\overset{\mathrm{h}}{\phantom{.}}25\overset{\mathrm{m}}{\phantom{.}}24\overset{\mathrm{s}}{.}18$
& Dec
$+18\overset{\circ}{\phantom{.}}12\overset{\prime}{\phantom{.}}12\overset{\prime\prime}{.}5$
J2000) exploded in the halo of M85 ($v_{\odot}$=729 km s-1,
$z_{\odot}$=0.002432; Smith et al., 2000), an early type galaxy in the Virgo
Cluster. Many distance measurements to M85 have been made, but we will utilize
the surface brightness fluctuation measurement from the ACS Virgo Cluster
Survey, which found a distance modulus of $\mu$=31.26$\pm$0.05 mag ($D$=17.9
Mpc; Mei et al., 2007). We adopt a Milky Way extinction of $E(B-V)$=0.026 mag
based on the dust maps of Schlafly & Finkbeiner (2011).

No results on SN 2020nlb have been published in the literature, and so we
present UV/optical photometry and a maximum-light spectrum to characterize
this SN Ia. We also present a nebular spectrum to constrain narrow hydrogen or
helium emission from any companion or CSM interaction to complement the X-ray
CSM constraints. A more comprehensive optical-infrared analysis of SN 2020nlb
will be presented in a future work. The Galactic neutral hydrogen column
density in the direction of SN 2020nlb is NH = 2.49$\times$1020 cm-2 (Kalberla
et al., 2005).

####  2.2.1 Light Curve

We display a $UBVgri$ light curve of SN 2020nlb in the left panel of Figure 1,
taken with the 0.4- and 1.0-m telescope network of Las Cumbres Observatory
(Brown et al., 2013) as part of the Global Supernova Project (e.g. Szalai et
al., 2019). These data were reduced in a standard way using the PyRAF-based
photometric pipeline lcogtsnpipe (Valenti et al., 2016). An additional, high
cadence data set was obtained by the 0.7m Thacher Observatory (Swift & Vyhnal,
2018) in the $g,r,i,z$ bands. The data was reduced in a standard way, and the
PSF photometry tool DoPHOT (Schechter et al., 1993) was used in conjunction
with photometric calibration from Pan-STARRS DR1 (Flewelling et al., 2020) to
produce the final light curve. Since the SN was offset from the host galaxy,
no image subtraction was performed, and we expect host galaxy contamination to
be minimal.

Observations from the Neil Gehrels Swift Observatory (Swift; Gehrels et al.,
2004a) Ultra-Violet Optical Telescope (UVOT; Roming et al., 2005) were also
obtained and reduced using the pipeline associated with the Swift Optical
Ultraviolet Supernovae Archive (SOUSA; Brown et al., 2014) and the zeropoints
of Breeveld et al. (2010). The Swift data is also displayed in Figure 1.

We fit a fourth order polynomial to the $B$ and $V$-band light curve of SN
2020nlb around maximum light, resampling the data based on the photometric
uncertainties over 1000 trials. We find a peak $B$-band apparent magnitude of
$B_{max}$=12.11$\pm$0.02 mag on MJD = 59041.8 $\pm$ 0.2 (UT 2020 July 11.8),
which we adopt throughout this work. The $V$-band light curve peaked at
$V_{max}$=12.04$\pm$0.03 mag on MJD = 59043.9 $\pm$ 0.3, which is 2.1 d after
the $B$-band peak. The $B$-band decline rate $\Delta$m15($B$) is measured to
be 1.29$\pm$0.06 mag, based on the polynomial fit.

One way to constrain host galaxy extinction is to measure the color at maximum
light, $B_{max}$$-$$V_{max}$, which was parameterized as a function of the
decline rate parameter, $\Delta$$m_{15}$$(B)$, in Phillips et al. (1999).
After applying a Milky Way extinction of $E(B-V)_{MW}$=0.026 mag, we find
$B_{max}$$-$$V_{max}$=0.04$\pm$0.04 mag from the polynomial fits described in
the previous paragraph. This is close to the expectation from the Phillips et
al. (1999) relation ($B_{max}$-$V_{max}$=$-$0.05$\pm$0.03 mag), and so we
consider host extinction to be minimal for this work. Any underestimate of the
extinction would lead to a corresponding underestimate of the luminosity of
the supernova, which ultimately would yield slightly weaker constraints on the
CSM from our X-ray limits. Applying only Milky Way extinction to the observed
$B_{max}$, and using a distance of 17.9 Mpc, yields a peak absolute $B$-band
magnitude of $M_{B}$=$-$19.25 mag, which is in line with SNe Ia with similar
decline rates (Blondin et al., 2012; Folatelli et al., 2013).

####  2.2.2 Spectroscopy

In the right panel of Figure 1, we show a spectrum taken with the FLOYDS
robotic spectrograph (Brown et al., 2013) at Faulkes Telescope North on
2020-07-12 06:32 UTC (+0.5 d with respect to $B$-band maximum), reduced with
the pipeline described in Valenti et al. (2014). Using the Supernova
IDentification software package (SNID; Blondin & Tonry, 2007) we find that all
reasonable matches correspond to SNe Ia near maximum light. A particularly
good match to SN 2004eo at +2 d with respect to $B$-band maximum was found,
with similar Si II and O I strengths between the two events. SN 2004eo also
has a similar, relatively fast light curve decline rate ($\Delta$m15($B$)=1.45
mag; Pastorello et al. 2007) as SN 2020nlb ($\Delta$m15($B$)=1.29 mag). We
also compare the SN 2020nlb spectrum to the canonical ‘normal’ SN Ia 2011fe at
maximum light in Figure 1 for illustrative purposes.

We measure a Si II $\lambda$6355 velocity of 10,400$\pm$100 km s-1 near
maximum light, as well as pseudo-equivalent width (pEW) values of 118 Å and 24
Å for the Si II $\lambda$6355 and $\lambda$5972 features, respectively, from
the +0.5d FLOYDS spectrum. In the standard Branch classification scheme
(Branch et al., 2006), SN 2020nlb is a Core Normal supernova, and belongs to
the Normal Velocity class of SNe Ia as described in Wang et al. (2009).

An additional low resolution optical spectrum was obtained with the Blue
Channel spectrograph (Schmidt et al., 1989) at the MMT on 2021-01-28 21:06 UTC
(+179 d), using the 300 l/mm grating and an exposure time of 3$\times$900 s.
We display this spectrum in Figure 4, and use it in Section 5 to constrain any
hydrogen or helium in the nebular phase. To account for slit losses, we scale
this spectrum to an $r$-band magnitude of 17.92, based on an interpolation of
the Zwicky Transient Facility (ZTF; Bellm et al., 2019) light curve at late
times (similar to Sand et al., 2018).

Figure 1: Left: Swift UVOT, Thacher and Las Cumbres Observatory optical
photometry of SN 2020nlb, spanning out to $\sim$30 days after $B$-band
maximum. The light curves have not been corrected for Milky Way extinction in
this plot. The light curve will be made available in electronic format upon
publication. Right: The +0.5 day spectrum of SN 2020nlb, along with spectra of
SN 2004eo (+2 d; Pastorello et al., 2007) and the canonical ‘normal’ type Ia
SN 2011fe (+0 d; Pereira et al., 2013).

##  3 X-Ray Observations And Analysis

###  3.1 Swift-XRT

The Swift (Gehrels et al., 2004b) X-Ray Telescope (XRT; Burrows et al., 2005)
observed both SN 2017cbv and SN 2020nlb extensively and we report flux limits
here. All XRT data was analyzed using HEASoft (v6.28) and corresponding
calibration files. Standard filtering and screening criteria were applied.

We gathered Swift XRT data of SN 2017cbv taken between 2017 March 10.5 and
April 15.46, corresponding to $\approx$1.5d and 37.5d from our adopted
explosion epoch, with a total accumulated exposure time of 62.2 ks. SN 2017cbv
sits in a region of low background, and we obtain an unabsorbed (accounting
for Galactic absorption) 3-$\sigma$ flux limit of $F$$<$7.7$\times$10-15 ergs
cm-2s-1 in the 0.3–10 keV energy range, corresponding to a 3-$\sigma$
luminosity limit of $L$ $<$ 1.6$\times$1038 ergs s-1 at a distance of 13.1
Mpc.

A sequence of Swift XRT data was taken of SN 2020nlb (alongside the UVOT data
described in Section 2.2), starting on 2020 June 25.76 UTC. We gathered all
data taken through 2020 August 07.2 UTC ($\sim$43 days after our adopted
explosion epoch), a total of 27.5 ks. Unresolved, diffuse X-ray emission from
the host elliptical galaxy M85 is apparent in the combined XRT data, which
largely resolves into point sources in the Chandra data presented below. At
the position of SN 2020nlb, we find an unabsorbed 3-$\sigma$ flux limit of
$F$$<$1.4$\times$10-14 ergs cm-2s-1 in the 0.3–10 keV energy range,
corresponding to a 3-$\sigma$ luminosity limit of $L$ $<$ 5.5$\times$1038 ergs
s-1 at a distance of 17.9 Mpc.

The XRT limits we obtain are a factor of $\sim$3–10 less stringent than the
Chandra data we present in the next section, and for this reason we do not
consider this data further as we constrain the circumbinary environment of SN
2017cbv and SN 2020nlb.

Figure 2: False color Chandra X-ray images of both SN 2017cbv (left;
$\delta$t=17.89 days after explosion) and SN 2020nlb (right; $\delta$t=15.79
days after explosion). Red, green, and blue colors refer to soft (0.3–1.4
keV), medium (1.4–3 keV) and hard (3–10 keV) photons, respectively. The
greyscale zoom-in on each panel is the full 0.3-10 keV Chandra energy range.

###  3.2 Chandra

Deep X-ray follow-up of both SN 2017cbv and SN 2020nlb were obtained with the
Chandra X-ray Observatory under Director’s Discretionary Time proposals. All
data were reduced within a conda CIAO (v4.12) environment using relevant
calibration files (CALDB v4.9.1) and standard ACIS data filtering. All X-ray
count limits and confidence bounds are calculated assuming Poisson statistics,
as described in Primini & Kashyap (2014). We present false color X-ray images,
and zoom-ins on each SN location, in Figure 2.

Observations of SN 2017cbv began on March 27, 2017 (PI: Drout; Proposal
1850876; Obs ID 20055), and the total exposure time was 51 ks. The midtime of
the observations (MJD = 57839.789) corresponds to $\delta$t = 17.89 days with
respect to the explosion epoch, or $-$1.1 days with respect to $B$-band
maximum. No X-ray source is detected with a 3–$\sigma$ upper limit of
1.8$\times$10-4 counts s-1 in the 0.3–10 keV energy band, which corresponds to
a flux limit of $F$$<$2.2$\times$10-15 ergs cm-2 s-1, assuming a power law
model with spectral photon index $\Gamma$=2. The unabsorbed flux limit is then
$F$$<$2.6$\times$10-15 ergs cm-2 s-1 (NH = 8.014$\times$1020 cm-2; 0.3–10 keV
energy band), corresponding to a 3-$\sigma$ luminosity limit of $L$ $<$
5.4$\times$1037 ergs s-1 at a distance of 13.1 Mpc.

Chandra observations of SN 2020nlb (PI: Sand; Proposal 21508740; Obs ID 23314,
23315)111https://doi.org/10.25574/23314, https://doi.org/10.25574/23315,
respectively were split into two blocks for a total exposure time of 75 ks.
The first observation (totaling 63 ks) began on 2020 July 09 23:58 (UT), while
the second observation (12 ks) began $\sim$1.5 days after the end of the first
on 2020 July 12 04:15. We take the weighted average time of these two
exposures as the effective epoch of the observations, MJD 59040.7, which
corresponds to $\delta t$=15.79 days with respect to the assumed explosion
epoch, or $-$1.10 days with respect to $B$-band maximum. For our analysis, we
extract the individual source spectra and use the CIAO/specextract task for
combination of the spectra and appropriate response files. We have also
combined the two observations into a single event map using the CIAO/merge_obs
task for illustrative purposes in Figure 2, to show that no source is present.
For the combined spectrum, at the position of SN 2020nlb, we find a 3-$\sigma$
flux limit of $F$$<$1.3$\times$10-15 ergs cm-2 s-1 in the 0.3–10 keV energy
range, assuming a power law model with spectral photon index $\Gamma$=2. The
unabsorbed flux limit is then $F$$<$1.4$\times$10-15 ergs cm-2 s-1 (NH =
2.49$\times$1020 cm-2; 0.3–10 keV energy band), and the 3-$\sigma$ luminosity
limit is $L$ $<$ 5.4$\times$1037 ergs s-1 at a distance of 17.9 Mpc.

We place the Chandra X-ray luminosity limits of SN 2017cbv and SN 2020nlb in
context in Figure 3, in comparison to the majority of X-ray limits in the
literature. The data on SN 2017cbv and SN 2020nlb are amongst the most
constraining obtained for any SNe Ia, just behind the very nearby SNe 2011fe
and 2014J. We use these limits in Section 7 to constrain any CSM associated
with these SNe.

Figure 3: X-ray luminosity limits of normal SNe Ia from the compilation of
Russell & Immler (2012), along with deep Chandra observations of SN 2011fe
(Margutti et al., 2012) and SN 2014J (Margutti et al., 2014). The new Chandra
X-ray limits for SN 2020nlb and SN 2017cbv are also shown as blue stars, and
are the deepest data taken of SNe Ia beyond D=10 Mpc. Note that the data from
Russell & Immler (2012) is generally derived from the combination of Swift XRT
data taken across many epochs over $\sim$30 days, which is not well-
represented by the points in the plot.

##  4 The Bolometric Luminosity

X-ray emission in low density, hydrogen stripped progenitor systems in the
first $\sim$1–2 months after explosion is dominated by Inverse Compton
scattering of photospheric photons by relativistic electrons accelerated by
the SN shock (Chevalier & Fransson, 2006a; Margutti et al., 2012). The Inverse
Compton X-ray luminosity is proportional to the bolometric luminosity of the
SN, and so bolometric luminosity is a key ingredient of our analysis, which we
discuss here.

We adopt the pseudo-bolometric light curve of SN 2017cbv published in Wang et
al. (2020, see their Table 7), who combined UV+optical+NIR photometry to
construct a pseudo-bolometric light curve using the SNooPy light curve package
(Burns et al., 2011, 2014); we refer the reader to that work for details.
Interpolating the Wang et al. (2020) bolometric light curve to the Chandra
X-ray epoch yields $L_{bol}$=1.46$\times$1043 ergs s-1 at our adopted distance
of 13.1 Mpc.

Based on our UV+optical light curve of SN 2020nlb presented in Section 2.2.1,
we construct a pseudo-bolometric light curve using the ‘direct’ method in the
SNooPy light curve package. We use the $UVW1$ and $UVW2$ filters from Swift
and the Las Cumbres $UBVgri$ light curves for our analysis (which encompasses
a broad wavelength range on one telescope system), ignoring the $UVM2$ filter
as its light curve was lower signal to noise and sparser, making interpolation
between epochs difficult. The ‘direct’ method takes the flux in each filter
and integrates over all filters, interpolating when necessary when a given
filter is missing. The program also takes into account the extinction (where
we are only considering Milky Way extinction, see Section 2.2.1) and distance
to the supernova. We extrapolate the flux in the near infrared by assuming a
Rayleigh-Jeans tail, although this only has a small effect on our results. We
also experimented with the ‘SED’ method in SNooPy, using the Hsiao et al.
(2007) spectral energy distribution templates, and obtained results consistent
with the direct method to within $\sim$4%. Given this, we utilize the ‘direct’
results and find $L_{bol}$=1.0$\times$1043 ergs s-1 at the epoch of the
Chandra X-ray observations (MJD 59040.7).

We plot both of the bolometric light curves in the bottom panels of Figure 5,
and highlight the luminosity at the epoch of the Chandra observations.

Figure 4: Top – Nebular-phase spectrum of SN 2020nlb, flux calibrated and
corrected for MW extinction. We mark the locations of the A- and B- band
telluric features. Bottom – Zoom in on the region around H$\alpha$ and He I
$\lambda$6678 (left) as well as He I $\lambda$5875 (right), where we constrain
any narrow emission feature by implanting simulated lines. The black histogram
is the data binned to the resolution of the spectrum, while the blue shows the
data smoothed by a second order Savitsky-Golay filter. The bottom panel on
each plot shows the difference between the original spectrum and the smoothed
version. The red histogram is an implanted emission line feature with a peak
flux four times the rms, representing the detection limit for an hydrogen or
helium emission line. The gray shaded regions correspond to 1000 km s-1 around
the rest wavelength of the hydrogen and helium lines.

Figure 5: Top panels – Expected maximum inverse Compton X-ray luminosity in
the case of wind (green, with an assumed $v_{w}$=100 km s-1) and ISM-like
(blue) environments for SN 2017cbv (left) and SN 2020nlb (right), based on the
Chandra X-ray limits (red upper limits) for each. Bottom panels – Bolometric
light curves for SN 2017cbv (data from Wang et al. 2020) and SN 2020nlb (this
work). The interpolated bolometric luminosity of the SN at the epoch of the
Chandra observations is marked with a star symbol.  Figure 6: X-ray
constraints on a wind-like CSM for SN 2017cbv (blue line) and SN 2020nlb
(solid black line) with respect to other prominent results in the literature.
Regions of parameter space not ruled out are towards the upper left of the
plot, in the direction of the arrows. The color blocked regions represent
areas of parameter space where plausible SN Ia progenitors and their expected
CSM would inhabit, which we discuss further in Section 8. Limits obtained for
other prominent SNe Ia include SN 2011fe (Margutti et al., 2012), SN 2014J
(Margutti et al., 2014), SN 2012cg (Shappee et al., 2018) and SN 2018oh
(Shappee et al., 2019). The data from Russell & Immler (2012), as seen in
Figure 3, all lie to the right of SN 2012cg in this plot. We also plot our
radio CSM constraints for SN 2020nlb (dotted lines; Section 6) assuming
$\epsilon_{b}$=0.01 and 0.1 for the fraction of shock energy shared by the
amplified magnetic field; these observations alone rule out portions of the
parameter space occupied by symbiotics and accretion winds.

##  5 SN 2020nlb Progenitor Constraints from Nebular Spectroscopy

We measure complementary constraints on the progenitor system and environment
of SN 2020nlb using the flux calibrated, extinction and redshift-corrected
nebular spectrum (+179d with respect to $B$-band maximum, and +196d with
respect to our adopted explosion epoch of MJD 59024.91) presented in Section
2.2.2 and shown in Figure 4, to go along with our primary X-ray results in the
next section. We remind the reader that we have scaled this spectrum to
$r$=17.92 mag to match the late time ZTF photometry to account for
nonphotometric conditions and slit losses. Using similar techniques, strong
constraints on H and He emission have already been placed on SN 2017cbv, using
the models of Botyánszki et al. (2018), with limits of $M_{\rm H}<1\times
10^{-4}$ $\rm M_{\odot}$ and $M_{\rm He}<5\times 10^{-4}$ $\rm M_{\odot}$,
respectively; this is $\sim$3 orders of magnitude below expectations for the
single degenerate scenario (Sand et al., 2018).

If the progenitor system of SN 2020nlb had a nondegenerate companion star,
then models predict that the SN ejecta will impact the companion, and manifest
as narrow hydrogen (or helium) emission lines with FWHM$\approx$1000 km s-1 at
late times (e.g., Marietta et al., 2000; Mattila et al., 2005; Pan et al.,
2010, 2012; Liu et al., 2012, 2013; Lundqvist et al., 2013; Botyánszki et al.,
2018; Dessart et al., 2020, among others). The models for the emission from
stripped material expect $\gtrsim$0.1 $M_{\odot}$ of stripped hydrogen, but
have considerable diversity in the strength and shape of the observed emission
line, and depend on the details of the explosion and radiative transfer
physics employed. Here we will rely on the latest radiative transfer modeling
and predictions from Botyánszki et al. (2018) and Dessart et al. (2020), and
refer the reader to those works for details.

Careful visual inspection of Figure 4 reveals no hydrogen or helium emission
features, including from the host galaxy. To set quantitative limits on narrow
H$\alpha$ as well as He I $\lambda$5875 Å and $\lambda$6678 Å emission, we
mimic the methodology of Sand et al. (2018, 2019), which we briefly describe
here. We take the flux-calibrated, extinction and redshift-corrected spectrum
and bin to the native resolution, $\approx$6.5 Å. We then establish a
‘continuum level’ around the hydrogen and helium line wavelengths by smoothing
the spectrum on scales larger than the expected emission (FWHM$\approx$1000 km
s-1) using a second-order Savitsky-Golay filter with a width of 190 Å. We
experimented with various filter widths in order to best recover simulated
emission line features in our data. Any hydrogen or helium emission line
feature of the width we are interested in would be apparent in the difference
between the smoothed and un-smoothed spectrum, which we refer to as the
residual spectrum.

To estimate the maximum H$\alpha$ (or helium) emission that could go
undetected, we directly implant emission lines into our data. We assume a line
width of FWHM$\approx$1000 km s-1 and a peak flux that is four times the root
mean square of the residual spectrum. This results in an H$\alpha$ flux limit
of 7.1$\times$10-16 erg s-1 cm-2, and a luminosity limit of 2.7$\times$1037
ergs s-1 at a distance of D=17.9 Mpc. Similarly, we find a He I $\lambda$6678
Å ($\lambda$5875 Å) flux limit of 7.1$\times$10-16 erg s-1 cm-2
(7.9$\times$10-16 erg s-1 cm-2), leading to a luminosity limit of
2.7$\times$1037 ergs s-1 (3.0$\times$1037 ergs s-1). Dessart et al. (2020)
suggest that limits on the equivalent width of the H$\alpha$ line may also be
an effective way to obtain stripped-mass limits. Given this, we have also
followed the Dessart et al. (2020) prescription for obtaining equivalent width
limits (using their Equation B.1), and find EQW(H$\alpha$)$<$5.3 Å. We
illustrate our detection limits in the bottom panels of Figure 4.

The recent 3D radiation transport results of Botyánszki et al. (2018)
presented simulated SN Ia spectra at 200 days after explosion (well-matched to
our spectrum at +196 days after explosion, which we make no further
adjustments to) derived from the SN Ia ejecta-companion interaction
simulations of Boehner et al. (2017), which utilized a spherically symmetric
W7 explosion model (Nomoto et al., 1984; Thielemann et al., 1986). These
simulated spectra show strong hydrogen and helium nebular emission
(FWHM$\approx$1000 km s-1, shifted by up to $\sim$10 Å from rest) with
$L_{H\alpha}$$\approx$4.5–15.7$\times$1039 ergs s-1 for their main sequence,
subgiant and red giant companion star models, corresponding to $M_{\rm
strip}$$\sim$0.2–0.4 $M_{\odot}$. Given our H$\alpha$ luminosity limit of
2.7$\times$1037 ergs s-1, we rule out the basic predictions of Botyánszki et
al. (2018) in SN 2020nlb by over two orders of magnitude. To approximate the
effects of smaller stripped hydrogen masses (due to weaker explosions, wider
companion separations or inhomogeneities in the ejecta structure), Botyánszki
et al. (2018) varied the hydrogen density in their fiducial main sequence
companion model, fitting a quadratic to the relation between stripped hydrogen
mass and the H$\alpha$ luminosity (see their Equation 1, but note the
typographical error corrected in Sand et al. 2018). Using this formula, we
derive a stripped hydrogen mass limit of $M_{\rm strip}$=7$\times$10-4 M⊙.

Further radiative transfer calculations of SN Ia ejecta enclosing stripped
material from a nondegenerate companion star were recently performed by
Dessart et al. (2020). These 1D calculations include several different delayed
detonation models (DDC0, DDC15, and DDC25; Blondin et al., 2013) and a sub-
Chandrasekhar model (SCH3p5; Blondin et al., 2017), expanding beyond the focus
on W7 explosions in previous work. They also include non-LTE physics and
optical depth effects, and cover stripped hydrogen masses from $M_{\rm
strip}$$\sim$0.001–0.5 M⊙ (although we note that masses in the $M_{\rm
strip}$$\sim$0.1–0.5 M⊙ range are what is seen in multi-dimensional
hydrodynamic simulations, as mentioned above). We estimate hydrogen mass
limits of $M_{\rm strip}$=1–2$\times$10-3 M⊙ based on these models, where the
range includes the three explosion models with tabulated results in the
Appendix of Dessart et al. (2020). When we use our equivalent width limit for
H$\alpha$ (EQW(H$\alpha$)$<$5.3 Å) instead of our luminosity limit, we obtain
nearly identical hydrogen mass limits of $M_{\rm strip}$=1–3$\times$10-3 M⊙.
All of these mass limits are $\sim$2 orders of magnitude lower than
expectations from single degenerate models.

Helium stars are also plausible white dwarf companions (e.g. Iben & Tutukov,
1984), and models predict that such progenitor systems should yield $M_{\rm
strip}$$\approx$0.002–0.06 M⊙ of stripped helium-rich material which
ultimately may be visible in nebular spectra (e.g. Pan et al., 2012; Liu et
al., 2013). Unfortunately, few radiative transport simulations of the helium
star scenario have been done, and so it is difficult to translate helium
luminosity limits to stripped helium masses. As an approximate solution, we
utilize the Botyánszki et al. (2018) model where they replaced hydrogen with
helium in their simulations, and assume that the helium mass falls off with
luminosity with the same quadratic form as for the stripped hydrogen models
(see also Sand et al. 2018). From this we infer a limit of $M_{\rm
strip}$$\sim$4$\times$10-3 M⊙, although this value should be treated with
caution. We note that the recent radiative transfer work of Dessart et al.
(2020) produce weak or ambiguous helium lines in their simulated spectra,
aside from the stronger He I $\lambda$10830 Å line. Thus, our helium limits
correspond to the lower end of expectations for helium companion stars in the
single degenerate model, but further work is needed to produce robust helium
line predictions.

In summary, our limits on stripped hydrogen from the single degenerate
scenario are $\sim$2–3 orders of magnitude below expectations, setting a
strong constraint on this scenario, modulo current model limitations. We
further rule out most helium companion star scenarios, although our helium
limit of $M_{\rm strip}$$\sim$4$\times$10-3 M⊙ does overlap with some
predictions, so we cannot completely rule out this channel. Our hydrogen
limits are similar to or stronger than the H$\alpha$ recently seen in the fast
declining SNe Ia ASASSN-18tb ($L_{H\alpha}$=2.2$\times$1038 ergs s-1;
Kollmeier et al. 2019), SN 2018cqj ($L_{H\alpha}$=3.8$\times$1037 ergs s-1;
Prieto et al. 2020), and SN 2016jae ($L_{H\alpha}$=1.6–3.0$\times$1038 ergs
s-1; Elias-Rosa et al. 2021). As an aside, our hydrogen limits also rule out
any hydrogen-rich CSM (although the model expectations are less clear here)
which may be interacting with the ejecta at this epoch. Outside of the single
degenerate scenario, such CSM may plausibly be associated with a giant planet
(Soker, 2019) or a nondegenerate tertiary star (Thompson, 2011; Kushnir et
al., 2013; Vallely et al., 2019b), which does not seem to be the case for SN
2020nlb.

##  6 SN 2020nlb Constraints on Circumstellar Interaction from Radio
Observations

Radio emission can independently probe the presence of circumstellar material
(CSM) because interaction of the SN ejecta with this CSM accelerates electrons
to relativistic energies and amplifies the ambient magnetic field, producing
radio synchrotron emission (Chevalier, 1982, 1984, 1998). Simple models of
radio emission have provided constraints on the CSM environment and progenitor
properties for both core-collapse (e.g. Ryder et al., 2004; Soderberg et al.,
2006a; Chevalier & Fransson, 2006b; Weiler et al., 2007; Salas et al., 2013;
Bostroem et al., 2019) and Type Ia SNe (Panagia et al., 2006; Chomiuk et al.,
2016). Radio emission is yet to be detected from a Type Ia SN, but non-
detections have provided stringent constraints on their progenitor scenarios
(Chomiuk et al., 2016), particularly for nearby events (Horesh et al., 2012b;
Chomiuk et al., 2012; Pérez-Torres et al., 2014; Pellegrino et al., 2020;
Lundqvist et al., 2020; Burke et al., 2021).

Below we describe our VLA observations of SN 2020nlb. SN 2017cbv is outside
the declination limit of the VLA, and we are not aware of any radio
observations that were associated with this SN.

###  6.1 Observation

A radio observation of SN 2020nlb was obtained with the Karl G. Jansky Very
Large Array (VLA) on 2020 July 7 at 21:49, which is 14.6 days since explosion
(derived in Section 2.2). The observation block was 1-hr long, with 37.5 mins
on-source time for SN 2020nlb. Observations were taken in C-band (4–8 GHz) in
the B-configuration of the VLA (DDT: 20A-577, PI: S. Sarbadhicary). The
observations were obtained in wide-band continuum mode, yielding 4 GHz of
bandwidth sampled by 32 spectral windows, each 128 MHz wide sampled by 1 MHz-
wide channels with two polarizations. We used 3C286 as our flux, delay and
bandpass calibrator, and J1224+2122 as our complex gain calibrator. Data were
calibrated with the VLA CASA calibration pipeline (version 5.6.1-8), which
iteratively flags corrupted measurements, applies corrections from the online
system (e.g. antenna positions), and applies delay, flux density, bandpass and
complex gain calibrations. We then imaged the calibrated visibility dataset
with tclean in CASA. We used multi-term, multi-frequency synthesis as our
deconvolution algorithm (set with deconvolver=‘mtmfs’ in tclean), which
approximates the full 4-8 GHz wide-band spectral structure of the sky
brightness distribution as a Taylor-series expansion about a reference
frequency (in our case, 6 GHz) in order to reduce frequency-dependent
artifacts during deconvolution (Rau & Cornwell, 2011). We set nterms=2 which
uses the first two Taylor terms to create images of intensity (Stokes-I) and
spectral index. We sampled the synthesized beam with 3-4 pixels, and imaged
out to 11.2′ (about 12$\%$ sensitivity level of primary beam) to deconvolve
any outlying bright sources and mitigate their sidelobes at the primary beam
center. Gridding was carried out with the W-projection algorithm
(gridder=wproject) with 16 w-planes. Images were weighted with the Briggs
weighting scheme (weighting=briggs) using a robust value of 0 to balance
point-source sensitivity with high angular resolution and low sidelobe
contamination between sources. The final image has a spatial resolution of
0.9″$\times$ 0.8″(or roughly $79\times 70$ pc), and an RMS of about 5
$\mu$Jy/bm, which is within 25$\%$ of the expected thermal noise level of our
observation.222https://obs.vla.nrao.edu/ect/

No radio source was detected at the site of SN 2020nlb in the cleaned,
deconvolved 6-GHz image at the 3$\sigma$ level. The flux at the SN location is
$6.4~{}\mu$Jy/beam, and the RMS noise in a circular region 7″ across around
the SN location is $4.5~{}\mu$Jy/beam. We therefore assume a flux density
upper limit of 19.7 $\mu$Jy/beam, which is equal to the flux density at the SN
location plus three times the RMS noise. At a distance of 17.9 Mpc, this
corresponds to a 6 GHz luminosity of $7.6\times 10^{24}$ ergs s-1 Hz-1.

###  6.2 Analysis

The luminosity upper limit can shed some light on the CSM around SN 2020nlb
similar to the methodology in Chomiuk et al. (2012) and Chomiuk et al. (2016).
We assume SN 2020nlb was surrounded by the Chevalier (1982) model of a CSM,
produced by steady mass loss from the progenitor, i.e.
$\rho_{csm}=\dot{M}/4\pi r^{2}v_{w}$ (where $\rho_{csm}$ is the CSM density in
g cm-3, $\dot{M}$ is the mass-loss rate from the progenitor, $r$ is the
distance from the progenitor and $v_{w}$ is the wind velocity). Assuming a
standard SN Ia explosion with 1051 ergs kinetic energy and 1.4 M⊙ ejecta mass,
we obtain a mass-loss rate upper limit of $\dot{M}<(3.7-16.7)\times 10^{-9}$
M⊙ yr-1, assuming $v_{w}$=10 km s-1. The range of mass-loss rates reflect the
uncertainty in the parameter $\epsilon_{B}$, the fraction of shock energy
shared by the amplified magnetic field, with typical values in the range
0.01–0.1 for SNe (Chomiuk et al., 2012). These limits are compared with the
mass-loss rate parameter space of single-degenerate models as defined in
Chomiuk et al. (2012) in Figure 6. We find that our limits are deep enough to
rule out red-giant companions (symbiotic systems), characterized by slow winds
of 10-100 km s-1 and mass-loss rates of 10-6–10-8 M⊙ yr-1 (Seaquist & Taylor,
1990). Symbiotic systems have also been ruled out for the majority of SNe Ia
based on their radio upper limits (Horesh et al., 2012b; Chomiuk et al., 2012;
Pérez-Torres et al., 2014; Chomiuk et al., 2016; Pellegrino et al., 2020;
Lundqvist et al., 2020; Burke et al., 2021). Many models involving main-
sequence companions however are still allowed within our limits of SN 2020nlb
(see colored regions in Figure 6).

##  7 X-ray Constraints on Circumstellar Material

Deep X-ray observations can constrain the density of the circumstellar
environment in the region around the supernova, which has inevitably been
shaped by any mass loss in the progenitor system prior to explosion. Within
$\delta t$$\lesssim$40 days of explosion, the X-ray emission in low density
environments, such as that expected from SNe Ia, is dominated by inverse
Compton scattering of photospheric photons by relativistic electrons
accelerated by the SN shock (Chevalier & Fransson, 2006a). A generalized
formalism for the inverse Compton luminosity was developed by Margutti et al.
(2012), building off of Chevalier & Fransson (2006a), which depends on the
bolometric luminosity of the SN ($L_{IC}$$\propto$$L_{bol}$), the SN ejecta
mass ($M_{ej}$) and explosion energy ($E$), the density structure of the SN
ejecta ($\rho_{SN}$), the density structure of the CSM ($\rho_{CSM}$), and the
number of electrons and their energy distribution ($p$ and $\epsilon_{e}$),
which is responsible for the upscattering of the optical photons to X-ray
energies. Here we adopt this formalism for determining the X-ray inverse
Compton luminosity, using many of the assumptions made in that work which have
been utilized to constrain the low density CSM around several other nearby SNe
Ia – most stringently for SN 2011fe (Margutti et al., 2012) and SN 2014J
(Margutti et al., 2014), but also SN 2012cg (Shappee et al., 2018), SN 2018oh
(Shappee et al., 2019), and the SN Iax 2014dt (Stauffer et al., 2021). We also
use the bolometric luminosities discussed in Section 4 for our results here.

As in previous work, we assume the outer density of the SN scales as
$\rho_{SN}$$\propto$$R^{-n}$ with n=10 (see e.g., Matzner & McKee, 1999, for
compact progenitors). The electrons are assumed to be distributed like a
power-law distribution dependent on the Lorentz factor ($\gamma$),
$n_{e}(\gamma)$$\propto$$\gamma^{-p}$ with index $p$=3; this value is
supported by observations of SN Ib/c shocks (e.g. Soderberg et al., 2006b). We
assume the fraction of post-shock energy density in relativistic electrons is
$\epsilon_{e}$=0.1, as other SN shocks have indicated (Chevalier & Fransson,
2006a); CSM density limits scale as ($\epsilon_{e}$/0.1)-2 for any variation
in this parameter (Margutti et al., 2012). Unlike similar radio constraints on
the CSM, X-ray observations do not require any assumptions about magnetic
field-related parameters (see dotted lines in Figure 6). As both SN 2017cbv
and SN 2020nlb appear to be ‘normal’ SNe Ia we adopt an ejecta mass of
$M_{ej}$=1.4 M⊙ and explosion energy of $E$=1051 erg for each; these are the
same values adopted in the X-ray analysis for SN 2011fe and SN 2014J (Margutti
et al., 2012, 2014).

We explore two different scenarios for the CSM environment: 1) a constant-
density ISM-like CSM ($\rho_{CSM}$=constant) and 2) a wind-like CSM
($\rho_{CSM}$$\propto$$R^{-2}$). In a simple case, a star that has been losing
material at a constant rate, $\dot{M}$, with wind velocity, $v_{w}$, has a
‘wind-like’ CSM with $\rho_{CSM}$ = $\dot{M}/(4\pi R^{2}v_{w})$, and would be
a signature of the single degenerate scenario. Double degenerate scenarios
would have ‘clean’ environments with no CSM or a low density ISM-like CSM
(although see discussion below). We do not consider asymmetric or CSM
configurations with cavities explicitly here with our observational
constraints, although we discuss a wide variety of CSM geometries in the
following section.

For an ISM-like medium, and using the Margutti et al. (2012) formalism along
with the bolometric luminosities in Section 4, we derive limits of
$n_{CSM}$$<$ 35.8 cm-3 and $<$65 cm-3 for SN 2017cbv and SN 2020nlb,
respectively. Given the epoch that the X-ray data were taken, they probe radii
of $R_{ISM}$=1.4$\times$1016 cm and 1.2$\times$1016 cm, respectively, for SN
2017cbv and SN 2020nlb. These contraints are within an order of magnitude of
those from SN 2011fe ($<$166 cm-3) and SN 2014J ($<$3.5 cm-3).

Similarly, for a wind-like medium and fiducial wind velocity of $v_{w}$=100 km
s-1, we constrain the progenitor mass loss rate to be
$\dot{M}$$<$7.2$\times$10-9 M⊙ yr-1 and $\dot{M}$$<$9.7$\times$10-9 M⊙ yr-1
for SN 2017cbv and SN 2020nlb, respectively. At the epoch of the Chandra
observations, these correspond to radii of 1.9$\times$1016 cm and
1.6$\times$1016 cm for the two SNe. These constraints are weaker than those of
SN 2011fe ($\dot{M}$$\lesssim$2$\times$10-9 M⊙ yr-1) and SN 2014J
($\dot{M}$$\lesssim$1$\times$10-9 M⊙ yr-1), but are the same order of
magnitude.

In Figure 5 we plot the time evolution of the expected Inverse Compton X-ray
emission corresponding to the limits obtained for both the ISM and wind-like
CSM scenarios described above, alongside our Chandra X-ray limits. In the
following section we discuss the physical implications for the SN progenitor
systems that these constraints provide.

##  8 Discussion

We have presented deep Chandra X-ray observations of SN 2017cbv and SN 2020nlb
around optical maximum light in order to constrain the environment around
these SN Ia explosions. In addition to this data, we have presented VLA radio
observations and a deep nebular spectrum of SN 2020nlb to further constrain
the progenitor of this nearby SN. The X-ray observations double the sample of
normal SNe Ia with such deep limits, and regardless of the assumed circumburst
density profile, they imply a ‘clean’ environment at distances of
$R$$\lesssim$1016 cm from the explosion. We focus our discussion on the
constraints that these data provide on the progenitor system in this section.

###  8.1 Single Degenerate Scenarios with Near-Steady Mass Loss

In the single degenerate scenario, where a white dwarf near the Chandrasekhar
mass is accreting from a companion star (at a rate of
$\dot{M}_{acc}$$\gtrsim$3$\times$10-7 $M_{\odot}$ yr-1 for steady hydrogen
burning; Shen & Bildsten 2007), material can be lost to the surrounding
environment via donor star winds, non-conservative mass transfer through Roche
lobe overflow or even winds from the accreting white dwarf itself – inverse
Compton X-ray emission around maximum light can probe all of these scenarios.

Symbiotic binary systems are plausible SN Ia progenitor systems, where the
white dwarf accretes wind material from an evolved giant star. Mass-loss rates
range from $\dot{M}$$\approx$5$\times$10-9 to 5$\times$10-6 $M_{\odot}$ yr-1
with wind velocities $v_{w}$$\lesssim$100 km s-1 (e.g. Seaquist & Taylor,
1990; Patat et al., 2011; Chen et al., 2011, see also discussion in Meng & Han
2016), as illustrated in the appropriate block of Figure 6. Our new X-ray
observations (complemented by our radio observations of SN 2020nlb) can rule
out all plausible symbiotic systems. While the sample size is still small,
combining the current X-ray results with those from SN 2014J and SN 2011fe
suggest that symbiotic-like CSM is uncommon around SN Ia systems. Using their
much larger sample of SNe Ia with radio observations, Chomiuk et al. (2016)
similarly conclude that $\lesssim$10% of SNe Ia are in symbiotic systems.

It is also possible that lower mass, nondegenerate companions (main sequence,
subgiant or helium stars) are influencing the CSM environment through non-
conservative mass transfer. Here the nondegenerate secondary star fills its
Roche lobe and some material is lost to the environment at the outer Lagrange
point. We estimate the typical velocity of this lost and ejected material to
be a few hundred km s-1, the same order as the orbital velocity of the white
dwarf, with an upper limit of $\sim$600 km s-1, corresponding to the limit
seen in stable nuclear burning white dwarfs (Deufel et al., 1999). The
fraction of material lost is unknown, but is often assumed to be
$\epsilon_{\rm loss}$$\approx$1%, thus leading to the expected mass loss range
of $\dot{M}$$\approx$0.3–3$\times$10-8 $M_{\odot}$ yr-1 shown in Figure 2. Our
new observations of SN 2017cbv and SN 2020nlb cut into this region of
parameter space (see Figure 6), but do not completely rule out this
‘Lagrangian Losses’ scenario. Indeed, if the real fraction of material lost at
the outer Lagrange points is significantly less than $\epsilon_{\rm
loss}$$\approx$1%, than this scenario would remain plausible for all X-ray
constraints published thus far, and it is likely that a next-generation X-ray
mission is necessary to fully rule out this scenario.

If the accretion rate from a nondegenerate companion is high enough, optically
thick winds from the white dwarf are expected to develop, which happens around
a critical value of $\dot{M}_{\rm acc}$$\sim$7$\times$10-7 $M_{\odot}$ yr-1
depending on the hydrogen mass fraction and white dwarf mass (Hachisu et al.,
1999; Han & Podsiadlowski, 2004; Shen & Bildsten, 2007), leading to the range
of allowed mass losses associated with the ‘Accretion Winds’ scenario in
Figure 6 (although see the recent models of Dragulin & Hoeflich 2016 which
suggest a low density cavity near the progenitor system which would lead to
weaker limits). The associated white dwarf wind velocities can be up to a few
thousand km s-1 (Hachisu et al., 1999), similar to the outflows seen in X-ray
luminous, nuclear burning white dwarfs (Cowley et al., 1998). Our X-ray
constraints on SN 2017cbv and SN 2020nlb largely rule out this single
degenerate progenitor scenario (as have the X-ray observations of SN 2011fe
and SN 2014J), although a small region of the allowed parameter space (at high
velocities, $\gtrsim$1000 km s-1, and low mass loss rates, $\sim$10-7
$M_{\odot}$ yr-1) are still viable.

###  8.2 Non-steady mass loss in the single degenerate scenario

Our X-ray analysis is most sensitive to progenitor scenarios with continuous
mass loss up until the point of the SN explosion, although there are many
instances where this may not be the case, even within the single degenerate
scenario. If there is non-continuous mass loss in the time period just
preceding explosion, our observations would be insensitive to any material
inside or outside of $R$$\approx$1016 cm.

Recurrent nova systems are plausible SN Ia progenitors, with a high mass white
dwarf ($>$1.3 M⊙) accreting at 10-8–10-7 M⊙ yr-1 (Livio & Truran, 1992; Yaron
et al., 2005), and experiencing repeated nova explosions due to unsteady
hydrogen burning. The recurrent nova system RS Oph is a prominent example of
this class of objects (Patat et al., 2011), where the white dwarf increases in
mass with time (Hachisu & Kato, 2001) unlike in classical nova systems. The SN
Ia PTF11kx, for instance, showed clear evidence of nova shells in multi-epoch
high resolution spectroscopy and is suggested to have a recurrent nova
progenitor system (Dilday et al., 2012), as have other SNe Ia with signs of
interaction (e.g. SN 2002ic; Wood-Vasey & Sokoloski, 2006).

The CSM for recurrent nova systems is expected to be complex, and may include
relatively high density nova shells, with nearly evacuated regions or wind
material from the donating star in between; it is also possible there is a
central cavity with no material as well (see discussion in Dimitriadis et al.,
2014; Darnley et al., 2019). The exact geometry of the CSM will depend on the
time since the last nova outburst, and the outbursting history. In this
scenario, we would need to be very lucky to perform our X-ray observations at
the time when the blast wave is interacting with a nova shell, as in between
the CSM density would be $<$10-2 cm-3 (e.g., see Figure 9 in Dimitriadis et
al., 2014), far below our constraints of $\lesssim$36–65 cm-3. In any case,
neither SN 2017cbv or SN 2020nlb show any signs of interaction in their
spectra (see the high resolution optical spectroscopic sequence of Ferretti et
al., 2017, in particular).

Other scenarios where the mass loss stops prior to explosion would also yield
non-detections in our X-ray data if the material is all at $\gtrsim$1016 cm,
or if the delay between the cessation of mass loss and explosion were
$t$$\gtrsim$30$\times$(vw/100 km s-1)-1 yr. One model where this can occur is
the so-called spin-up/spin-down scenario, where the accreting white dwarf
gains enough angular momentum during the accretion process that it will not
explode at the Chandrasekhar mass, and must spin down before it explodes (Di
Stefano et al., 2011; Justham, 2011). Another scenario with potentially long
delays between mass loss and the explosion is the core degenerate scenario,
where the white dwarf merges with the core of an asymptotic giant branch star
at the end of the common envelope phase (Kashi & Soker, 2011; Ilkov & Soker,
2012); here again, the rapid rotation of the white dwarf may prevent it from
exploding immediately. In both cases, the key unknown is the delay time
between the completion of mass transfer and explosion, and is difficult to
assess because the physical mechanism of the spin-down is not certain although
calculations have suggested delays ranging from $\lesssim$105 yr to
$\gtrsim$109 yr (Lindblom et al., 1999; Yoon & Langer, 2005; Ilkov & Soker,
2012; Hachisu et al., 2012); if one of these single degenerate scenarios were
responsible for a sizable proportion of SNe Ia, it would be difficult to
discern with X-ray observations.

###  8.3 White dwarf – white dwarf progenitors

In the double degenerate scenario, two white dwarfs coalesce and lead to the
final SN Ia explosion. The general prediction for this scenario is for a
‘clean’ circumbinary environment on scales greater than $R$$\gtrsim$1014 cm
(Fryer et al., 2010; Shen et al., 2012; Raskin & Kasen, 2013), similar to the
ISM. Despite this, there are several ways in which a white dwarf – white dwarf
merger can enrich the circumbinary environment. We briefly discuss these
scenarios in the context of our X-ray limits at $\sim$1016 cm.

One feature of white dwarf–white dwarf merger calculations is the tidal
stripping and ejection of mass just prior to coalescence, consisting of
10-4–10-2 M⊙ of material moving at $\sim$2000 km s-1 in the equatorial region
(Dan et al., 2011; Raskin & Kasen, 2013), equivalent to an effective mass loss
rate of $\dot{M}$$\approx$10-2–10-5 $M_{\odot}$ yr-1 (Raskin & Kasen, 2013).
If this CSM, produced during the coalescence, is at appropriate radii at
explosion ($\sim$1016 cm) then it could lead to detectable inverse Compton
emission in the X-ray regime. The key parameter is the time between
coalescence (and tidal tail ejection), and the SN explosion, which needs to be
$\sim$108 s to reach the radii that X-ray observations are sensitive to. Our
observations rule out such delays between coalescence and explosion, although
we cannot comment on explosions that occur on a dynamical ($\sim$102–103 s) or
viscous timescale ($\sim$104–108 s); longer timescales ($\gg$108 s) are also
not excluded by our data.

One variant of the double degenerate scenario, the ‘double detonation’ model,
posits a progenitor configuration with a carbon oxygen white dwarf accreting
from a helium white dwarf companion (e.g. Nomoto, 1982; Livne, 1990; Woosley &
Weaver, 1994). In certain scenarios, hydrogen rich material on the surface of
the helium white dwarf accretes onto the carbon-oxygen white dwarf until
convective hydrogen burning is ignited (akin to a classical nova), causing the
envelope on the carbon-oxygen white dwarf to expand and overflow its Roche
radius, ejecting material at $\sim$1500 km s-1 (Shen et al., 2013), typically
$\approx$3–6$\times$10-5 M⊙. Unfortunately, such a shell ejection must occur
$\sim$2-3 years prior to the final explosion in order for it to be detectable
by our X-ray observations (assuming $\sim$1500 km s-1 ejected velocity), which
are probing $\sim$1016 cm; the simulations presented by Shen et al. (2013)
indicate that the time scales for these nova-like shell ejections are more
like hundreds to thousands of years prior to explosion, depending on the
details of the white dwarf progenitors. Thus, while our X-ray observations can
rule out short ‘ejection to explosion’ delay times, they are not a stringent
test of this double detonation prediction.

Other double degenerate scenarios with some circumstellar material are also
plausible, including mass outflows during rapid accretion events (e.g.
Guillochon et al., 2010; Dan et al., 2011) and disk winds from white dwarf
mergers that do not promptly detonate (Ji et al., 2013), although these both
require specific timing between the mass ejection and eventual explosion of
roughly a few years to have material at $\sim$1016 cm where we have X-ray
constraints. Our observations of SN 2017cbv and SN 2020nlb (along with SN
2011fe and SN 2014J) largely rule out these ejection to explosion time scales.

##  9 Summary & Future Outlook

In this work, we have presented deep Chandra X-ray observations of two nearby
type Ia SNe around maximum light, SN 2017cbv and SN 2020nlb. X-ray
observations of SNe Ia in the time period around maximum light are sensitive
to inverse Compton emission, which is caused by interaction between the SN
blastwave and accelerated particles in the CSM surrounding the explosion. As
this CSM was shaped by the mass loss history of the progenitor star system
leading up to the explosion, X-ray observations are a sensitive probe of the
pre-explosion SN environment, and ultimately the progenitor system itself. The
analysis of deep X-ray data for two additional, normal SNe Ia doubles the
sample studied in this way, adding to the ground-breaking work on SN 2011fe
(Margutti et al., 2012) and SN 2014J (Margutti et al., 2014).

The Chandra data lead to X-ray luminosity limits of
$L_{X}$$\lesssim$5.4$\times$1037 and $\lesssim$5.4$\times$1037 erg s-1 (0.3–10
keV) at 17.9 and 15.8 days after explosion for SN 2017cbv and SN 2020nlb,
respectively. Using the inverse Compton formalism of Margutti et al. (2012)
(see also Chevalier & Fransson, 2006b), which is appropriate for SNe Ia in low
density environments in the weeks after explosion, this corresponds to
nCSM$<$36 and $<$65 cm-3 at a radius of $R$=1.4$\times$1016 cm and
1.2$\times$1016 cm for the two SNe, assuming a constant density ISM-like
circumstellar medium. If we assume a wind-like medium (where $\rho_{CSM}$ =
$\dot{M}/(4\pi R^{2}v_{w})$), we obtain mass loss limits of
$\dot{M}$$<$7.2$\times$10-9 and $<$9.7$\times$10-9 M⊙ yr-1 for a fiducial wind
velocity of $v_{w}$=100 km s-1 at a radius of $R$=1.9$\times$1016 cm and
1.6$\times$1016 cm. These limits rule out several prospects for the single
degenerate scenario, including all symbiotic progenitor star systems, as well
as large portions of the parameter space associated with mass loss at the
outer Lagrange point and white dwarf accretion winds. It is difficult for
current X-ray observations to rule out double degenerate scenarios as the
expectation is for a generally ‘clean’ environment around the SN, unless the
timing between the ejection of tidal tails (or other material) is properly
timed with the subsequent explosion such that there is significant material at
$\sim$1016 cm (which the X-ray observations probe).

In addition to our X-ray analysis, we have also presented other complementary
constraints on the progenitor system of SN 2020nlb, and complementary
constraints have already been published for SN 2017cbv. Using a nebular phase
spectrum of SN 2020nlb, we set strong constraints on any swept up hydrogen or
helium from a nondegenerate companion star in the single degenerate scenario,
obtaining limits that were $\sim$2–3 orders of magnitude below expectations
for that channel; our data would have also detected the H$\alpha$ features
recently observed in three fast declining SN Ia (Kollmeier et al., 2019;
Prieto et al., 2020; Elias-Rosa et al., 2021). We also obtained VLA data of SN
2020nlb around 15 days after the explosion, and the nondetection allowed us to
rule out most plausible symbiotic progenitor systems, in agreement with the
X-ray data. These complementary constraints on the progenitor of SN 2020nlb
stand alongside the other SN studied in X-rays in this paper, SN 2017cbv.
Although SN 2017cbv had an early, blue light curve bump that may have
signalled interaction with a nondegenerate companion star (Hosseinzadeh et
al., 2017a), neither nebular spectroscopy (Sand et al., 2018) nor the X-ray
constraints in the current work yield any further hints of the single
degenerate scenario.

Future directions for X-ray constraints on the CSM around nearby SNe Ia are
clear. Even with the current study, only four nearby SNe Ia have been studied
to sufficient depths to rule out some standard single degenerate scenarios
which predict winds or accretion losses. X-ray CSM constraints on a
statistical sample are necessary to make population-level statements about the
SN Ia progenitor system and its diversity, and it is vital to have
observations spanning the range of SN Ia properties (including luminosity,
light curve parameters, and sub-type). We also advocate for multiple
observational probes of the SN Ia progenitor system be made for each nearby SN
Ia (e.g. high cadence early light curves to search for ‘bumps’, late time
search for narrow hydrogen and helium lines, radio CSM constraints, etc), as
each technique has its own strengths, dependence on modeling and systematic
uncertainties. By combining probes for the few SNe Ia that are near enough,
progress can be made.

The scientific results reported in this article are based to a significant
degree on observations made by the Chandra X-ray Observatory (Obs ID: 20055,
23314, 23315. We thank H. Tananbaum and the entire Chandra team for making the
X-ray observations possible. Support for this work was provided by the
National Aeronautics and Space Administration through Chandra Award Number
DDO-21119X issued by the Chandra X-ray Center, which is operated by the
Smithsonian Astrophysical Observatory for and on behalf of the National
Aeronautics Space Administration under contract NAS8-03060. This work makes
use of observations from the Las Cumbres Observatory network. The LCO team is
supported by NSF grants AST-1911225 and AST-1911151 and NASA Swift grant
80NSSC19K1639. Research by SV is supported by NSF grants AST–1813176 and AST-
2008108. Time domain research by D.J.S. is also supported by NSF grants
AST-1821987, 1813466, 1908972, & 2108032, and by the Heising-Simons Foundation
under grant #2020-1864. S.K.S. and L.C. are supported by NSF grant NSF
AST-1907790 and the Packard Foundation. L.G. acknowledges financial support
from the Spanish Ministry of Science, Innovation and Universities (MICIU)
under the 2019 Ramón y Cajal program RYC2019-027683 and from the Spanish MICIU
project PID2020-115253GA-I00. LW is sponsored (in part) by the Chinese Academy
of Sciences (CAS) through a grant to the CAS South America Center for
Astronomy (CASSACA) in Santiago, Chile. Observations reported here were
obtained at the MMT Observatory, a joint facility of the University of Arizona
and the Smithsonian Institution. The National Radio Astronomy Observatory is a
facility of the National Science Foundation operated under cooperative
agreement by Associated Universities, Inc. We are grateful to C. Burns for his
help with the SNooPy software package.

## References

  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068
  * Bellm et al. (2019) Bellm, E. C., Kulkarni, S. R., Graham, M. J., et al. 2019, PASP, 131, 018002, doi: 10.1088/1538-3873/aaecbe
  * Bianco et al. (2011) Bianco, F. B., Howell, D. A., Sullivan, M., et al. 2011, ApJ, 741, 20, doi: 10.1088/0004-637X/741/1/20
  * Blondin et al. (2013) Blondin, S., Dessart, L., Hillier, D. J., & Khokhlov, A. M. 2013, MNRAS, 429, 2127, doi: 10.1093/mnras/sts484
  * Blondin et al. (2017) —. 2017, MNRAS, 470, 157, doi: 10.1093/mnras/stw2492
  * Blondin & Tonry (2007) Blondin, S., & Tonry, J. L. 2007, ApJ, 666, 1024, doi: 10.1086/520494
  * Blondin et al. (2012) Blondin, S., Matheson, T., Kirshner, R. P., et al. 2012, AJ, 143, 126, doi: 10.1088/0004-6256/143/5/126
  * Boehner et al. (2017) Boehner, P., Plewa, T., & Langer, N. 2017, MNRAS, 465, 2060, doi: 10.1093/mnras/stw2737
  * Bostroem et al. (2019) Bostroem, K. A., Valenti, S., Horesh, A., et al. 2019, MNRAS, 485, 5120, doi: 10.1093/mnras/stz570
  * Botyánszki et al. (2018) Botyánszki, J., Kasen, D., & Plewa, T. 2018, ApJ, 852, L6, doi: 10.3847/2041-8213/aaa07b
  * Branch et al. (2006) Branch, D., Dang, L. C., Hall, N., et al. 2006, PASP, 118, 560, doi: 10.1086/502778
  * Breeveld et al. (2010) Breeveld, A. A., Curran, P. A., Hoversten, E. A., et al. 2010, MNRAS, 406, 1687, doi: 10.1111/j.1365-2966.2010.16832.x
  * Brown et al. (2014) Brown, P. J., Breeveld, A. A., Holland, S., Kuin, P., & Pritchard, T. 2014, Ap&SS, 354, 89, doi: 10.1007/s10509-014-2059-8
  * Brown et al. (2012) Brown, P. J., Dawson, K. S., Harris, D. W., et al. 2012, ApJ, 749, 18, doi: 10.1088/0004-637X/749/1/18
  * Brown et al. (2013) Brown, T. M., Baliber, N., Bianco, F. B., et al. 2013, PASP, 125, 1031, doi: 10.1086/673168
  * Burke et al. (2021) Burke, J., Howell, D. A., Sarbadhicary, S. K., et al. 2021, arXiv e-prints, arXiv:2101.06345.  https://arxiv.org/abs/2101.06345
  * Burns et al. (2011) Burns, C. R., Stritzinger, M., Phillips, M. M., et al. 2011, AJ, 141, 19, doi: 10.1088/0004-6256/141/1/19
  * Burns et al. (2014) —. 2014, ApJ, 789, 32, doi: 10.1088/0004-637X/789/1/32
  * Burns et al. (2020) Burns, C. R., Ashall, C., Contreras, C., et al. 2020, ApJ, 895, 118, doi: 10.3847/1538-4357/ab8e3e
  * Burrows et al. (2005) Burrows, D. N., Hill, J. E., Nousek, J. A., et al. 2005, Space Sci. Rev., 120, 165, doi: 10.1007/s11214-005-5097-2
  * Cao et al. (2015) Cao, Y., Kulkarni, S. R., Howell, D. A., et al. 2015, Natur, 521, 328, doi: 10.1038/nature14440
  * Chen et al. (2011) Chen, X., Han, Z., & Tout, C. A. 2011, ApJ, 735, L31, doi: 10.1088/2041-8205/735/2/L31
  * Chevalier (1982) Chevalier, R. A. 1982, ApJ, 259, 302, doi: 10.1086/160167
  * Chevalier (1984) —. 1984, ApJ, 285, L63, doi: 10.1086/184366
  * Chevalier (1998) —. 1998, ApJ, 499, 810, doi: 10.1086/305676
  * Chevalier & Fransson (2006a) Chevalier, R. A., & Fransson, C. 2006a, ApJ, 651, 381, doi: 10.1086/507606
  * Chevalier & Fransson (2006b) —. 2006b, ApJ, 651, 381, doi: 10.1086/507606
  * Chomiuk et al. (2012) Chomiuk, L., Soderberg, A. M., Moe, M., et al. 2012, ApJ, 750, 164, doi: 10.1088/0004-637X/750/2/164
  * Chomiuk et al. (2016) Chomiuk, L., Soderberg, A. M., Chevalier, R. A., et al. 2016, ApJ, 821, 119, doi: 10.3847/0004-637X/821/2/119
  * Cowley et al. (1998) Cowley, A. P., Schmidtke, P. C., Crampton, D., & Hutchings, J. B. 1998, ApJ, 504, 854, doi: 10.1086/306123
  * Dan et al. (2011) Dan, M., Rosswog, S., Guillochon, J., & Ramirez-Ruiz, E. 2011, ApJ, 737, 89, doi: 10.1088/0004-637X/737/2/89
  * Darnley et al. (2019) Darnley, M. J., Hounsell, R., O’Brien, T. J., et al. 2019, Nature, 565, 460, doi: 10.1038/s41586-018-0825-4
  * Dessart et al. (2020) Dessart, L., Leonard, D. C., & Prieto, J. L. 2020, A&A, 638, A80, doi: 10.1051/0004-6361/202037854
  * Deufel et al. (1999) Deufel, B., Barwig, H., Šimić , D., Wolf, S., & Drory, N. 1999, A&A, 343, 455.  https://arxiv.org/abs/astro-ph/9811285
  * Di Stefano et al. (2011) Di Stefano, R., Voss, R., & Claeys, J. S. W. 2011, ApJ, 738, L1, doi: 10.1088/2041-8205/738/1/L1
  * Dilday et al. (2012) Dilday, B., Howell, D. A., Cenko, S. B., et al. 2012, Science, 337, 942, doi: 10.1126/science.1219164
  * Dimitriadis et al. (2014) Dimitriadis, G., Chiotellis, A., & Vink, J. 2014, MNRAS, 443, 1370, doi: 10.1093/mnras/stu1249
  * Dimitriadis et al. (2019) Dimitriadis, G., Foley, R. J., Rest, A., et al. 2019, ApJ, 870, L1, doi: 10.3847/2041-8213/aaedb0
  * Dimitriadis et al. (2019) Dimitriadis, G., Rojas-Bravo, C., Kilpatrick, C. D., et al. 2019, The Astrophysical Journal, 870, L14, doi: 10.3847/2041-8213/aaf9b1
  * Dragulin & Hoeflich (2016) Dragulin, P., & Hoeflich, P. 2016, ApJ, 818, 26, doi: 10.3847/0004-637X/818/1/26
  * Elias-Rosa et al. (2021) Elias-Rosa, N., Chen, P., Benetti, S., et al. 2021, arXiv e-prints, arXiv:2106.15340.  https://arxiv.org/abs/2106.15340
  * Ferretti et al. (2017) Ferretti, R., Amanullah, R., Bulla, M., et al. 2017, ApJ, 851, L43, doi: 10.3847/2041-8213/aa9e49
  * Flewelling et al. (2020) Flewelling, H. A., Magnier, E. A., Chambers, K. C., et al. 2020, ApJS, 251, 7, doi: 10.3847/1538-4365/abb82d
  * Folatelli et al. (2013) Folatelli, G., Morrell, N., Phillips, M. M., et al. 2013, ApJ, 773, 53, doi: 10.1088/0004-637X/773/1/53
  * Fruscione et al. (2006) Fruscione, A., McDowell, J. C., Allen, G. E., et al. 2006, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 6270, Proc. SPIE, 62701V, doi: 10.1117/12.671760
  * Fryer et al. (2010) Fryer, C. L., Ruiter, A. J., Belczynski, K., et al. 2010, ApJ, 725, 296, doi: 10.1088/0004-637X/725/1/296
  * Ganeshalingam et al. (2011) Ganeshalingam, M., Li, W., & Filippenko, A. V. 2011, MNRAS, 416, 2607, doi: 10.1111/j.1365-2966.2011.19213.x
  * Gehrels et al. (2004a) Gehrels, N., Chincarini, G., Giommi, P., et al. 2004a, ApJ, 611, 1005, doi: 10.1086/422091
  * Gehrels et al. (2004b) —. 2004b, ApJ, 611, 1005, doi: 10.1086/422091
  * Graham et al. (2017) Graham, M. L., et al. 2017, Mon. Not. Roy. Astron. Soc., 472, 3437, doi: 10.1093/mnras/stx2224
  * Guillochon et al. (2010) Guillochon, J., Dan, M., Ramirez-Ruiz, E., & Rosswog, S. 2010, ApJ, 709, L64, doi: 10.1088/2041-8205/709/1/L64
  * Hachisu & Kato (2001) Hachisu, I., & Kato, M. 2001, ApJ, 558, 323, doi: 10.1086/321601
  * Hachisu et al. (1999) Hachisu, I., Kato, M., & Nomoto, K. 1999, ApJ, 522, 487, doi: 10.1086/307608
  * Hachisu et al. (2012) Hachisu, I., Kato, M., Saio, H., & Nomoto, K. 2012, ApJ, 744, 69, doi: 10.1088/0004-637X/744/1/69
  * Han & Podsiadlowski (2004) Han, Z., & Podsiadlowski, P. 2004, MNRAS, 350, 1301, doi: 10.1111/j.1365-2966.2004.07713.x
  * Hayden et al. (2010) Hayden, B. T., Garnavich, P. M., Kasen, D., et al. 2010, ApJ, 722, 1691, doi: 10.1088/0004-637X/722/2/1691
  * Holmbo et al. (2018) Holmbo, S., et al. 2018.  https://arxiv.org/abs/1809.01359
  * Horesh et al. (2012a) Horesh, A., Kulkarni, S. R., Fox, D. B., et al. 2012a, ApJ, 746, 21, doi: 10.1088/0004-637X/746/1/21
  * Horesh et al. (2012b) —. 2012b, ApJ, 746, 21, doi: 10.1088/0004-637X/746/1/21
  * Hosseinzadeh et al. (2017a) Hosseinzadeh, G., Sand, D. J., Valenti, S., et al. 2017a, ApJ, 845, L11, doi: 10.3847/2041-8213/aa8402
  * Hosseinzadeh et al. (2017b) Hosseinzadeh, G., Howell, D. A., Sand, D., et al. 2017b, The Astronomer’s Telegram, 10164, 1
  * Hoyt et al. (2021) Hoyt, T. J., Beaton, R. L., Freedman, W. L., et al. 2021, arXiv e-prints, arXiv:2101.12232.  https://arxiv.org/abs/2101.12232
  * Hsiao et al. (2007) Hsiao, E. Y., Conley, A., Howell, D. A., et al. 2007, ApJ, 663, 1187, doi: 10.1086/518232
  * Iben & Tutukov (1984) Iben, Jr., I., & Tutukov, A. V. 1984, ApJS, 54, 335, doi: 10.1086/190932
  * Ilkov & Soker (2012) Ilkov, M., & Soker, N. 2012, MNRAS, 419, 1695, doi: 10.1111/j.1365-2966.2011.19833.x
  * Jha et al. (2019) Jha, S. W., Maguire, K., & Sullivan, M. 2019, Nature Astronomy, 3, 706, doi: 10.1038/s41550-019-0858-0
  * Ji et al. (2013) Ji, S., Fisher, R. T., García-Berro, E., et al. 2013, ApJ, 773, 136, doi: 10.1088/0004-637X/773/2/136
  * Justham (2011) Justham, S. 2011, ApJ, 730, L34, doi: 10.1088/2041-8205/730/2/L34
  * Kalberla et al. (2005) Kalberla, P. M. W., Burton, W. B., Hartmann, D., et al. 2005, A&A, 440, 775, doi: 10.1051/0004-6361:20041864
  * Kasen (2010) Kasen, D. 2010, ApJ, 708, 1025, doi: 10.1088/0004-637X/708/2/1025
  * Kashi & Soker (2011) Kashi, A., & Soker, N. 2011, MNRAS, 417, 1466, doi: 10.1111/j.1365-2966.2011.19361.x
  * Kollmeier et al. (2019) Kollmeier, J. A., Chen, P., Dong, S., et al. 2019.  https://arxiv.org/abs/1902.02251
  * Kushnir et al. (2013) Kushnir, D., Katz, B., Dong, S., Livne, E., & Fernández, R. 2013, ApJ, 778, L37, doi: 10.1088/2041-8205/778/2/L37
  * Landsman (1993) Landsman, W. B. 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, 246
  * Leonard (2007) Leonard, D. C. 2007, ApJ, 670, 1275, doi: 10.1086/522367
  * Li et al. (2019) Li, W., Wang, X., Vinkó, J., et al. 2019, ApJ, 870, 12, doi: 10.3847/1538-4357/aaec74
  * Lindblom et al. (1999) Lindblom, L., Mendell, G., & Owen, B. J. 1999, Phys. Rev. D, 60, 064006, doi: 10.1103/PhysRevD.60.064006
  * Liu et al. (2012) Liu, Z. W., Pakmor, R., Röpke, F. K., et al. 2012, A&A, 548, A2, doi: 10.1051/0004-6361/201219357
  * Liu et al. (2013) Liu, Z.-W., Pakmor, R., Seitenzahl, I. R., et al. 2013, ApJ, 774, 37, doi: 10.1088/0004-637X/774/1/37
  * Livio & Truran (1992) Livio, M., & Truran, J. W. 1992, ApJ, 389, 695, doi: 10.1086/171242
  * Livne (1990) Livne, E. 1990, ApJ, 354, L53, doi: 10.1086/185721
  * Lundqvist et al. (2013) Lundqvist, P., Mattila, S., Sollerman, J., et al. 2013, MNRAS, 435, 329, doi: 10.1093/mnras/stt1303
  * Lundqvist et al. (2015) Lundqvist, P., Nyholm, A., Taddia, F., et al. 2015, A&A, 577, A39, doi: 10.1051/0004-6361/201525719
  * Lundqvist et al. (2020) Lundqvist, P., Kundu, E., Pérez-Torres, M. A., et al. 2020, ApJ, 890, 159, doi: 10.3847/1538-4357/ab6dc6
  * Maguire et al. (2016) Maguire, K., Taubenberger, S., Sullivan, M., & Mazzali, P. A. 2016, MNRAS, 457, 3254, doi: 10.1093/mnras/stv2991
  * Margutti et al. (2014) Margutti, R., Parrent, J., Kamble, A., et al. 2014, ApJ, 790, 52, doi: 10.1088/0004-637X/790/1/52
  * Margutti et al. (2012) Margutti, R., Soderberg, A. M., Chomiuk, L., et al. 2012, ApJ, 751, 134, doi: 10.1088/0004-637X/751/2/134
  * Marietta et al. (2000) Marietta, E., Burrows, A., & Fryxell, B. 2000, ApJS, 128, 615, doi: 10.1086/313392
  * Marion et al. (2016) Marion, G. H., Brown, P. J., Vinkó, J., et al. 2016, ApJ, 820, 92, doi: 10.3847/0004-637X/820/2/92
  * Mattila et al. (2005) Mattila, S., Lundqvist, P., Sollerman, J., et al. 2005, A&A, 443, 649, doi: 10.1051/0004-6361:20052731
  * Matzner & McKee (1999) Matzner, C. D., & McKee, C. F. 1999, ApJ, 510, 379, doi: 10.1086/306571
  * Mei et al. (2007) Mei, S., Blakeslee, J. P., Côté, P., et al. 2007, ApJ, 655, 144, doi: 10.1086/509598
  * Meng & Han (2016) Meng, X., & Han, Z. 2016, A&A, 588, A88, doi: 10.1051/0004-6361/201526077
  * Miller et al. (2018) Miller, A. A., Cao, Y., Piro, A. L., et al. 2018, ApJ, 852, 100, doi: 10.3847/1538-4357/aaa01f
  * Miller et al. (2020) Miller, A. A., Magee, M. R., Polin, A., et al. 2020, ApJ, 898, 56, doi: 10.3847/1538-4357/ab9e05
  * Nasa High Energy Astrophysics Science Archive Research Center (2014) (Heasarc) Nasa High Energy Astrophysics Science Archive Research Center (Heasarc). 2014, HEAsoft: Unified Release of FTOOLS and XANADU.  http://ascl.net/1408.004
  * Nomoto (1982) Nomoto, K. 1982, ApJ, 253, 798, doi: 10.1086/159682
  * Nomoto et al. (1984) Nomoto, K., Thielemann, F. K., & Yokoi, K. 1984, ApJ, 286, 644, doi: 10.1086/162639
  * Olling et al. (2015) Olling, R. P., Mushotzky, R., Shaya, E. J., et al. 2015, Nature, 521, 332, doi: 10.1038/nature14455
  * Pan et al. (2010) Pan, K.-C., Ricker, P. M., & Taam, R. E. 2010, ApJ, 715, 78, doi: 10.1088/0004-637X/715/1/78
  * Pan et al. (2012) —. 2012, ApJ, 750, 151, doi: 10.1088/0004-637X/750/2/151
  * Panagia et al. (2006) Panagia, N., Van Dyk, S. D., Weiler, K. W., et al. 2006, ApJ, 646, 369, doi: 10.1086/504710
  * Pastorello et al. (2007) Pastorello, A., Mazzali, P. A., Pignata, G., et al. 2007, MNRAS, 377, 1531, doi: 10.1111/j.1365-2966.2007.11700.x
  * Patat et al. (2011) Patat, F., Chugai, N. N., Podsiadlowski, P., et al. 2011, A&A, 530, A63, doi: 10.1051/0004-6361/201116865
  * Pellegrino et al. (2020) Pellegrino, C., Howell, D. A., Sarbadhicary, S. K., et al. 2020, ApJ, 897, 159, doi: 10.3847/1538-4357/ab8e3f
  * Pereira et al. (2013) Pereira, R., Thomas, R. C., Aldering, G., et al. 2013, A&A, 554, A27, doi: 10.1051/0004-6361/201221008
  * Pérez-Torres et al. (2014) Pérez-Torres, M. A., Lundqvist, P., Beswick, R. J., et al. 2014, ApJ, 792, 38, doi: 10.1088/0004-637X/792/1/38
  * Phillips et al. (1999) Phillips, M. M., Lira, P., Suntzeff, N. B., et al. 1999, AJ, 118, 1766, doi: 10.1086/301032
  * Piro & Nakar (2014) Piro, A. L., & Nakar, E. 2014, ApJ, 784, 85, doi: 10.1088/0004-637X/784/1/85
  * Prieto et al. (2020) Prieto, J. L., Chen, P., Dong, S., et al. 2020, ApJ, 889, 100, doi: 10.3847/1538-4357/ab6323
  * Primini & Kashyap (2014) Primini, F. A., & Kashyap, V. L. 2014, ApJ, 796, 24, doi: 10.1088/0004-637X/796/1/24
  * Raab (2012) Raab, H. 2012, Astrometrica: Astrometric data reduction of CCD images.  http://ascl.net/1203.012
  * Raskin & Kasen (2013) Raskin, C., & Kasen, D. 2013, ApJ, 772, 1, doi: 10.1088/0004-637X/772/1/1
  * Rau & Cornwell (2011) Rau, U., & Cornwell, T. J. 2011, A&A, 532, A71, doi: 10.1051/0004-6361/201117104
  * Roming et al. (2005) Roming, P. W. A., Kennedy, T. E., Mason, K. O., et al. 2005, Space Sci. Rev., 120, 95, doi: 10.1007/s11214-005-5095-4
  * Russell & Immler (2012) Russell, B. R., & Immler, S. 2012, ApJ, 748, L29, doi: 10.1088/2041-8205/748/2/L29
  * Ryder et al. (2004) Ryder, S. D., Sadler, E. M., Subrahmanyan, R., et al. 2004, MNRAS, 349, 1093, doi: 10.1111/j.1365-2966.2004.07589.x
  * Salas et al. (2013) Salas, P., Bauer, F. E., Stockdale, C., & Prieto, J. L. 2013, MNRAS, 428, 1207, doi: 10.1093/mnras/sts104
  * Sand et al. (2016) Sand, D. J., Hsiao, E. Y., Banerjee, D. P. K., et al. 2016, ApJ, 822, L16, doi: 10.3847/2041-8205/822/1/L16
  * Sand et al. (2018) Sand, D. J., Graham, M. L., Botyánszki, J., et al. 2018, ApJ, 863, 24, doi: 10.3847/1538-4357/aacde8
  * Sand et al. (2019) Sand, D. J., Amaro, R. C., Moe, M., et al. 2019, ApJ, 877, L4, doi: 10.3847/2041-8213/ab1eaf
  * Schechter et al. (1993) Schechter, P. L., Mateo, M., & Saha, A. 1993, PASP, 105, 1342, doi: 10.1086/133316
  * Schlafly & Finkbeiner (2011) Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103, doi: 10.1088/0004-637X/737/2/103
  * Schmidt et al. (1989) Schmidt, G. D., Weymann, R. J., & Foltz, C. B. 1989, PASP, 101, 713, doi: 10.1086/132495
  * Seaquist & Taylor (1990) Seaquist, E. R., & Taylor, A. R. 1990, ApJ, 349, 313, doi: 10.1086/168315
  * Shappee et al. (2018) Shappee, B. J., Piro, A. L., Stanek, K. Z., et al. 2018, ApJ, 855, 6, doi: 10.3847/1538-4357/aaa1e9
  * Shappee et al. (2013) Shappee, B. J., Stanek, K. Z., Pogge, R. W., & Garnavich, P. M. 2013, ApJ, 762, L5, doi: 10.1088/2041-8205/762/1/L5
  * Shappee et al. (2019) Shappee, B. J., Holoien, T. W. S., Drout, M. R., et al. 2019, ApJ, 870, 13, doi: 10.3847/1538-4357/aaec79
  * Shen & Bildsten (2007) Shen, K. J., & Bildsten, L. 2007, ApJ, 660, 1444, doi: 10.1086/513457
  * Shen et al. (2012) Shen, K. J., Bildsten, L., Kasen, D., & Quataert, E. 2012, ApJ, 748, 35, doi: 10.1088/0004-637X/748/1/35
  * Shen et al. (2013) Shen, K. J., Guillochon, J., & Foley, R. J. 2013, ApJ, 770, L35, doi: 10.1088/2041-8205/770/2/L35
  * Smith et al. (2000) Smith, R. J., Lucey, J. R., Hudson, M. J., Schlegel, D. J., & Davies, R. L. 2000, MNRAS, 313, 469, doi: 10.1046/j.1365-8711.2000.03251.x
  * Soderberg et al. (2006a) Soderberg, A. M., Chevalier, R. A., Kulkarni, S. R., & Frail, D. A. 2006a, ApJ, 651, 1005, doi: 10.1086/507571
  * Soderberg et al. (2006b) Soderberg, A. M., Nakar, E., Berger, E., & Kulkarni, S. R. 2006b, ApJ, 638, 930, doi: 10.1086/499121
  * Soker (2019) Soker, N. 2019, Research Notes of the American Astronomical Society, 3, 153, doi: 10.3847/2515-5172/ab4c97
  * Stauffer et al. (2021) Stauffer, C. M., Margutti, R., Linford, J. D., et al. 2021, arXiv e-prints, arXiv:2103.10538.  https://arxiv.org/abs/2103.10538
  * Swift & Vyhnal (2018) Swift, J., & Vyhnal, C. 2018, Robotic Telescope, Student Research and Education Proceedings, 1, 281
  * Szalai et al. (2019) Szalai, T., Vinkó, J., Könyves-Tóth, R., et al. 2019, ApJ, 876, 19, doi: 10.3847/1538-4357/ab12d0
  * Tartaglia et al. (2018) Tartaglia, L., Sand, D. J., Valenti, S., et al. 2018, ApJ, 853, 62, doi: 10.3847/1538-4357/aaa014
  * The Astropy Collaboration et al. (2018) The Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, ArXiv e-prints.  https://arxiv.org/abs/1801.02634
  * Thielemann et al. (1986) Thielemann, F. K., Nomoto, K., & Yokoi, K. 1986, A&A, 158, 17
  * Thompson (2011) Thompson, T. A. 2011, ApJ, 741, 82, doi: 10.1088/0004-637X/741/2/82
  * Tonry et al. (2018) Tonry, J. L., Denneau, L., Heinze, A. N., et al. 2018, PASP, 130, 064505, doi: 10.1088/1538-3873/aabadf
  * Tucker et al. (2019) Tucker, M. A., Shappee, B. J., & Wisniewski, J. P. 2019, ApJ, 872, L22, doi: 10.3847/2041-8213/ab0286
  * Tucker et al. (2020a) Tucker, M. A., Ashall, C., Shappee, B. J., et al. 2020a, arXiv e-prints, arXiv:2009.07856.  https://arxiv.org/abs/2009.07856
  * Tucker et al. (2020b) Tucker, M. A., Shappee, B. J., Vallely, P. J., et al. 2020b, MNRAS, 493, 1044, doi: 10.1093/mnras/stz3390
  * Valenti et al. (2014) Valenti, S., Sand, D., Pastorello, A., et al. 2014, MNRAS, 438, L101, doi: 10.1093/mnrasl/slt171
  * Valenti et al. (2016) Valenti, S., Howell, D. A., Stritzinger, M. D., et al. 2016, MNRAS, 459, 3939, doi: 10.1093/mnras/stw870
  * Vallely et al. (2019a) Vallely, P. J., Fausnaugh, M., Jha, S. W., et al. 2019a, arXiv e-prints.  https://arxiv.org/abs/1903.08665
  * Vallely et al. (2019b) —. 2019b, MNRAS, 487, 2372, doi: 10.1093/mnras/stz1445
  * Wang et al. (2020) Wang, L., Contreras, C., Hu, M., et al. 2020, ApJ, 904, 14, doi: 10.3847/1538-4357/abba82
  * Wang et al. (2009) Wang, X., Filippenko, A. V., Ganeshalingam, M., et al. 2009, ApJ, 699, L139, doi: 10.1088/0004-637X/699/2/L139
  * Webbink (1984) Webbink, R. F. 1984, ApJ, 277, 355, doi: 10.1086/161701
  * Weiler et al. (2007) Weiler, K. W., Williams, C. L., Panagia, N., et al. 2007, ApJ, 671, 1959, doi: 10.1086/523258
  * Whelan & Iben (1973) Whelan, J., & Iben, Jr., I. 1973, ApJ, 186, 1007, doi: 10.1086/152565
  * Wood-Vasey & Sokoloski (2006) Wood-Vasey, W. M., & Sokoloski, J. L. 2006, ApJ, 645, L53, doi: 10.1086/506179
  * Woosley & Weaver (1994) Woosley, S. E., & Weaver, T. A. 1994, ApJ, 423, 371, doi: 10.1086/173813
  * Yaron et al. (2005) Yaron, O., Prialnik, D., Shara, M. M., & Kovetz, A. 2005, ApJ, 623, 398, doi: 10.1086/428435
  * Yoon & Langer (2005) Yoon, S. C., & Langer, N. 2005, A&A, 435, 967, doi: 10.1051/0004-6361:20042542
  * Zacharias et al. (2013) Zacharias, N., Finch, C. T., Girard, T. M., et al. 2013, AJ, 145, 44, doi: 10.1088/0004-6256/145/2/44