# The Early Ultraviolet Light-Curves of Type II Supernovae and the Radii of
Their Progenitor Stars

Ido Irani Department of Particle Physics and Astrophysics, Weizmann Institute
of Science, 234 Herzl St, 7610001 Rehovot, Israel<EMAIL_ADDRESS>Jonathan
Morag  Department of Particle Physics and Astrophysics, Weizmann Institute of
Science, 234 Herzl St, 7610001 Rehovot, Israel  Avishay Gal-Yam Department of
Particle Physics and Astrophysics, Weizmann Institute of Science, 234 Herzl
St, 7610001 Rehovot, Israel  Eli Waxman  Department of Particle Physics and
Astrophysics, Weizmann Institute of Science, 234 Herzl St, 7610001 Rehovot,
Israel  Steve Schulze Department of Physics, The Oskar Klein Center, Stockholm
University, AlbaNova, SE-10691 Stockholm, Sweden  Jesper Sollerman Department
of Astronomy, The Oskar Klein Center, Stockholm University, AlbaNova, SE-10691
Stockholm, Sweden  K-Ryan Hinds  Astrophysics Research Institute, Liverpool
John Moores University, IC2 Liverpool Science Park, 146 Brownlow Hill,
Liverpool L3 5RF, UK  Daniel A. Perley  Astrophysics Research Institute,
Liverpool John Moores University, IC2 Liverpool Science Park, 146 Brownlow
Hill, Liverpool L3 5RF, UK  Ping Chen Department of Particle Physics and
Astrophysics, Weizmann Institute of Science, 234 Herzl St, 7610001 Rehovot,
Israel  Nora L. Strotjohann Department of Particle Physics and Astrophysics,
Weizmann Institute of Science, 234 Herzl St, 7610001 Rehovot, Israel  Ofer
Yaron Department of Particle Physics and Astrophysics, Weizmann Institute of
Science, 234 Herzl St, 7610001 Rehovot, Israel  Erez A. Zimmerman Department
of Particle Physics and Astrophysics, Weizmann Institute of Science, 234 Herzl
St, 7610001 Rehovot, Israel  Rachel Bruch  Department of Particle Physics and
Astrophysics, Weizmann Institute of Science, 234 Herzl St, 7610001 Rehovot,
Israel  Eran O. Ofek Department of Particle Physics and Astrophysics, Weizmann
Institute of Science, 234 Herzl St, 7610001 Rehovot, Israel  Maayane T.
Soumagnac Department of Physics, Bar Ilan University, Ramat-Gan, 52900, Israel
Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720,
USA  Yi Yang Department of Astronomy, University of California, Berkeley, CA
94720-3411, USA  Bengier-Winslow-Robertson Postdoctoral Fellow  Steven L.
Groom IPAC, California Institute of Technology, 1200 E. California Blvd,
Pasadena, CA 91125, USA  Frank J. Masci IPAC, California Institute of
Technology, 1200 E. California Blvd, Pasadena, CA 91125, USA  Marie Aubert
Université Clermont Auvergne, CNRS/IN2P3, LPC, F-63000 Clermont-Ferrand,
France  Reed Riddle  Caltech Optical Observatories, California Institute of
Technology, Pasadena, CA 91125, USA  Eric C. Bellm DIRAC Institute, Department
of Astronomy, University of Washington, 3910 15th Avenue NE, Seattle, WA
98195, USA  David Hale  Caltech Optical Observatories, California Institute of
Technology, Pasadena, CA 91125

###### Abstract

Observations during the first few days of a supernova (SN) explosion are
required in order to (1) accurately measure the blackbody evolution, (2) to
discriminate between shock-cooling and circumstellar material (CSM)
interaction as the primary mechanism for powering the light-curve rise and (3)
in order to constrain the progenitor radius and explosion energy. Here we
present a sample of 34 normal SNe II detected with the Zwicky Transient
Facility, with multi-band UV light-curves starting at $t\leq 4$ days after
explosion, as well as X-ray detections and upper limits. We characterize the
early UV-optical colors and provide prescriptions for empirical host-
extinction corrections. We show that the $t>2\,$days UV-optical colors and the
blackbody evolution of the sample are consistent with the predictions of
spherical phase shock cooling, independently of the presence of ‘flash
ionization” features. We present a framework for fitting shock-cooling models,
and validate it by fitting a set of multi-group simulations. Our fitting is
capable of reproducing the simulation parameters without a significant bias up
to 20% in radius and velocity. Observations of about half of the SNe II in the
sample are well-fit by models with breakout radii $<10^{14}\,$cm. The other
half are typically more luminous, with observations from day 1 onward that are
better fit by a model with a large $>10^{14}\,$cm breakout radius. However,
these fits predict an early rise during the first day that is too slow. We
suggest these large-breakout events are explosions of stars with an inflated
envelope or a confined CSM with a steep density profile, at which breakout
occurs. Using the 4 X-ray detections and upper limits of our sample, we derive
constraints on the extended ($\sim 10^{15}$ cm) CSM density independent of
spectral modeling, and find most SNe II progenitors lose
$\dot{M}<10^{-4}M_{\odot}\,\rm yr^{-1}$ a few years before explosion. This
provides independent evidence the CSM around many SNe II progenitors is
confined. We show that the overall observed breakout radius distribution is
skewed to higher radii due to a luminosity bias. Given this bias, we argue
that the $66^{+11}_{-22}\%$ of red supergiants (RSG) explode as SNe II with
breakout radii consistent with the observed distribution of field RSG, with a
tail extending to large radii, likely due to the presence of CSM.

##  1 Introduction

The progenitor stars of the majority of spectroscopically regular (Gal-Yam,
2017) supernovae (SNe) II are red super-giants (RSG), as confirmed by pre-SN
detections (see Smartt, 2009, 2015; Van Dyk, 2017, and references therein).
While this is the case, we do not yet know if all RSG stars explode as SNe,
and the details of the latest stages of stellar evolution are not accurately
known. As we cannot know which star will explode as a SN ahead of time, the
only way of systematically observing the short-lasting final stages of stellar
evolution are through their terminal explosions as SNe. Using this approach,
the properties of a progenitor star immediately prior to explosion can be
connected to its observed supernova. Connecting the progenitors to the SN
explosions they create has been a long-lasting goal of supernova studies (Gal-
Yam et al., 2007; Smartt, 2015; Modjaz et al., 2019). In the last decade,
large statistical studies of SNe have become commonplace. While these can
place some constraints on the progenitor properties, the progenitor radius,
ejected mass and explosion energy have degenerate effects on the SN light
curves (Goldberg et al., 2019; Dessart & Hillier, 2019). Acquiring independent
estimates of these properties through their peak and plateau properties
remains a difficult and unsolved problem.

Measuring the progenitor radius is possible by observing the earliest phase of
the SN explosion. The first photons emitted from the SN explosion will be the
result of shock breakout of the radiation-mediated shock from the stellar
surface - the breakout pulse. The photons that were captured in the shock
transition region escape on a timescale of
$\max(R_{bo}/c,\frac{c}{v_{bo}^{2}\,\kappa\,\rho_{bo}})$, where
$R_{bo},v_{bo},\rho_{bo}$ are the breakout radius, velocity and density,
$\kappa$ is the opacity and $c$ is the speed of light. Typically, this allows
us to constrain the progenitor radius directly from the duration of the
breakout pulse (for a review on the subject, see Waxman & Katz, 2017, and
references therein). The shocked material, which has been compressed and
heated, is then ejected and quickly reaches a state of homologous expansion
(Matzner & McKee, 1999). From the moment of shock-breakout and in the absence
of interaction with pre-existing material above the photosphere, the dominant
emission mechanism is the cooling of this heated envelope, which evolves
according to simple analytic solutions until hydrogen recombination becomes
significant.

This stage, called the shock-cooling phase, typically lasts a few days for
normal SNe II, and less than a day for stripped-envelope supernovae and
1987A-like SNe II. During this time, the temperature and luminosity evolution
are highly sensitive to the progenitor radius and to the shock velocity -
allowing to constrain these parameters (Chevalier, 1992; Nakar & Sari, 2010;
Rabinak & Waxman, 2011). Since the first generation of models, theoretical
advancements have extended the applications of shock-cooling models to low-
mass envelopes (Piro, 2015; Piro et al., 2021) and later times (Sapir &
Waxman, 2017). Recently, Morag et al. (2022, hereafter M22) interpolated
between the planar and spherical phases, extending the validity of the model
of Sapir & Waxman (2017) to earlier times, and treated the suppression of flux
in UV due to line absorption (Morag et al., 2023, M23).

In the past decade, high-cadence and wide-field surveys have enabled the early
time detection and multi-band followup of SNe. The Palomar Transient Factory
(PTF; Law et al. 2009; Kulkarni 2013), the Astroid-Terrestrial impact Last
Alert System (ATLAS; Tonry et al. 2018), the Zwicky Transient Facility (ZTF;
Bellm et al. 2019; Graham et al. 2019), the Distance Less than 40 Mpc Survey
(DLT40; Tartaglia et al., 2018), and most recently the Young Supernovae
Experiment (YSE; Jones et al. 2021) have been conducting 1–3 day cadence wide-
field surveys and regularly detect early phase SNe (e.g. Hachinger et al.,
2009; Gal-Yam et al., 2011; Arcavi et al., 2011; Nugent et al., 2011; Gal-Yam
et al., 2014; Ben-Ami et al., 2014; Khazov et al., 2016; Yaron et al., 2017;
Hosseinzadeh et al., 2018; Ho et al., 2019; Soumagnac et al., 2020; Bruch et
al., 2021; Gal-Yam et al., 2022; Perley et al., 2022; Terreran et al., 2022;
Jacobson-Galán et al., 2022; Tinyanont et al., 2022; Hosseinzadeh et al.,
2022).

Previous attempts to model the early-phase emission of SNe II yield mixed
results. Many studies fit the analytical shock cooling models of Nakar & Sari
(2010) or Rabinak & Waxman (2011). These models require multiband photometry
extending to the early time and the UV, as the model parameters are highly
sensitive to the temperature $\sim$1 day after explosion. Many works find
radii that are small compared to the observed RSG distribution from the Small
and Large Magellanic Clouds (SMC,LMC). For example, González-Gaitán et al.
(2015) and Gall et al. (2015) compile large optical light curve samples,
fitting $ugriz$ and $r$ band photometry respectively, and adopt a constant
validity domain for the models. While Rubin et al. (2016); Rubin & Gal-Yam
(2017) demonstrated that adopting a fixed validity introduces a bias in the
parameter inference, a fixed validity remains commonplace (e.g., Hosseinzadeh
et al., 2018). Recent attempts by Soumagnac et al. (2020); Ganot et al. (2022)
and Hosseinzadeh et al. (2023) find large RSG radii $\sim 1000\,R_{\odot}$ by
fitting early UV-optical light-curves, in tension with previous results, while
Vallely et al. (2021) fit single band high-cadence Transiting Exoplanet Survey
Satellite (TESS; Ricker et al., 2014) light curves and find unrealistically
small RSG progenitor radii, which they calibrate to numerical simulations.

While some large samples by Valenti et al. (2016); Faran et al. (2017) fit the
luminosities and temperatures of SNe II using multi-band UV-optical datasets,
these did not extend to the very early times. However, these studies
demonstrate that the blackbody evolution is in agreement with the expectations
of the shock-cooling framework of a cooling blackbody with $T\sim t^{-0.5}$
(Faran et al., 2017).

A different approach to analytic cooling models is the use of numerical
hydrodynamical simulations. Motivated by the fact that narrow features from
CSM interaction are commonly observed in SNe II (Gal-Yam et al., 2014; Khazov
et al., 2016; Yaron et al., 2017; Bruch et al., 2021, 2023), these models
include a dense shell of CSM, ejected from the progenitor before explosion.
This results in an extended non-polytropic density profile extending to few
$10^{14}\,\rm cm$ from the progenitor star prior to explosion. Morozova et al.
(2018) shows the early time multi-band evolution of a sample of SNe II is
better explained by models with dense CSM compared to models which do not
include CSM. The breakout radii in this case are typically at the edge of the
CSM, at large radii ($\lesssim 3000R_{\odot}$). Dessart et al. (2017); Dessart
& Hillier (2019) fit the early ($>$ few days) spectroscopic and photometric
sequence of SNe with a grid of non-LTE simulations, and find a small amount of
CSM improves the match of the models with the early time photometry. Förster
et al. (2018) fit a sample of 26 optical SNe to a grid of hydrodynamical
models and argue that they observe a delayed rise in the majority of SNe II,
and argue it is explained by the presence of CSM, extending the rise.

In this paper we present a sample of spectroscopically regular SNe II with
well-sampled UV-optical light curves. We present our sample selection strategy
in $\S$ 2, and the details of our photometric and X-ray follow-up in $\S$ 3.
In $\S$ 4 we analyze the color evolution ($\S$ 4.1), and blackbody evolution
($\S$ 4.2) of the SNe. In $\S$ 4.3 we model the light curves during the shock
cooling phase. We discuss our results and their implications to the SN
progenitors in $\S$ 5.

Throughout the paper we use a flat $\Lambda$CDM cosmological model with
H${}_{0}=67.4$ km s-1 Mpc-1, $\Omega_{M}=0.315$, and $\Omega_{\Lambda}=0.685$
(Planck Collaboration et al., 2018).

##  2 Sample

###  2.1 Observing strategy

In Bruch et al. (2021), we described the selection process of infant SNe from
the ZTF alert stream. Using a custom filter, we select transient in
extragalactic fields ($|b|>14$ deg), with a non detection-limit $<2.5$ days
from the first detection, and from a non-stellar origin. These candidates are
routinely manually inspected by a team of duty astronomers in Europe and
Israel during California night-time in order to reject false positives (such
as stellar flares, galactic transients, and active galactic nuclei).
Management of follow-up resources and candidates was performed through the
GROWTH marshal (Kasliwal et al., 2019) and Fritz/SkyPortal platforms (van der
Walt et al., 2019; Coughlin et al., 2023). Promising candidates rising by at
least $0.5$ mag from the previous non-detection are followed-up with optical
spectroscopy, optical photometry (various instruments) and UV photometry using
the UV-Optical Telescope (UVOT) onboard the Neil Gehrels Swift Observatory
(Gehrels et al., 2004; Roming et al., 2005). We also followed-up publicly
announced infant SNe II which pass our criteria, with ZTF data during the
first week. For this paper, we consider all ZTF infant SNe with UV photometry
in the first 4 days after estimated explosion and which are classified as
spectroscopically regular SNe II at peak light. We consider SNe which are
detected until Dec 31st, 2021. Classification references are listed in Table
1.

Table 1: List of 34 SNe included in this study

SN | ZTF ID |  $\alpha$ (J2000) |  $\delta$ (J2000) | z |  $d^{a}$ [Mpc] |  $t_{ND}$ [JD] |  $t_{exp}$ [JD] |  $\tau_{flash}^{b}$ [days] | Referencec
---|---|---|---|---|---|---|---|---|---
SN 2018cxn | ZTF18abckutn | 237.026897 | 55.714855 | 0.0401 | 186.6 | 2458289.7490 | $2458289.76\pm 0.01$ | $<0.0$ | [1]
SN 2018dfc | ZTF18abeajml | 252.032360 | 24.304095 | 0.0365 | 170.0 | 2458302.7103 | $2458303.8\pm 0.009$ | $6.2\pm 2.8$ | [1]
SN 2018fif | ZTF18abokyfk | 2.360629 | 47.354083 | 0.0172 | 76.5 | 2458349.8973 | $2458350.874\pm 0.002$ | $1.6\pm 1.0$ | [1.2]
SN 2019eoh | ZTF19aatqzim | 195.955635 | 38.289155 | 0.0501 | 229.6 | 2458601.7817 | $2458606.683\pm 0.031$ | $<0.0$ | [3]
SN 2019gmh | ZTF19aawgxdn | 247.763189 | 41.153961 | 0.0307 | 141.3 | 2458633.8250 | $2458634.324\pm 0.444$ | $<1.4$ | [3]
SN 2019nvm | ZTF19abqhobb | 261.411100 | 59.446730 | 0.0181 | 86.4 | 2458713.7416 | $2458714.69\pm 0.007$ | $1.9\pm 1.0$ | [3,4]
SN 2019omp | ZTF19abrlvij | 260.142987 | 51.632780 | 0.0450 | 206.9 | 2458717.7910 | $2458718.713\pm 0.0$ | $<0.0$ | [3]
SN 2019oxn | ZTF19abueupg | 267.803290 | 51.382550 | 0.0200 | 90.3 | 2458723.7895 | $2458724.342\pm 0.129$ | $<0.4$ | [3]
SN 2019ozf | ZTF19abulrfa | 279.817010 | 54.287872 | 0.0480 | 221.2 | 2458723.7900 | $2458724.728\pm 0.005$ | $<0.0$ | [3]
SN 2019ust | ZTF19acryurj | 13.593396 | 31.670182 | 0.0220 | 96.0 | 2458799.8053 | $2458800.04\pm 0.177$ | $5.0\pm 0.5$ | [3]
SN 2019wzx | ZTF19aczlldp | 37.782326 | 4.311291 | 0.0275 | 124.9 | 2458833.7282 | $2458835.506\pm 0.092$ | $<1.1$ | [11]
SN 2020cxd | ZTF20aapchqy | 261.621953 | 71.094063 | 0.0039 | 23.7 | 2458896.0296 | $2458896.671\pm 0.671$ | $<2.4$ | [5,6]
SN 2020dyu | ZTF20aasfhia | 184.913047 | 33.040393 | 0.0500 | 230.7 | 2458911.9254 | $2458912.814\pm 0.021$ | $<0.0$ | [3]
SN 2020fqv | ZTF20aatzhhl | 189.138576 | 11.231654 | 0.0075 | 15.0 | 2458936.9007 | $2458939.43\pm 0.16$ | $<0.9$ | [7]
SN 2020jfo | ZTF20aaynrrh | 185.460355 | 4.481697 | 0.0052 | 14.7 | 2458971.7751 | $2458975.231\pm 0.424$ | $<0.5$ | [8]
SN 2020lfn | ZTF20abccixp | 246.737033 | 20.245906 | 0.0440 | 202.2 | 2458995.8154 | $2458996.701\pm 0.018$ | $4.2\pm 1.5$ | [3]
SN 2020mst | ZTF20abfcdkj | 281.793965 | 60.496802 | 0.0590 | 274.0 | 2459012.8161 | $2459013.689\pm 0.067$ | $<0.1$ | [3]
SN 2020nif | ZTF20abhjwvh | 196.057282 | -10.351002 | 0.0104 | 50.5 | 2459021.7334 | $2459023.783\pm 0.765$ | $<0.9$ | [11]
SN 2020nyb | ZTF20abjonjs | 29.783900 | 86.676205 | 0.0155 | 72.1 | 2459026.9709 | $2459033.849\pm 0.014$ | $<0.0$ | [11]
SN 2020pni | ZTF20ablygyy | 225.958184 | 42.114032 | 0.0169 | 83.2 | 2459045.7542 | $2459046.638\pm 0.004$ | $5.0\pm 1.0$ | [9]
SN 2020pqv | ZTF20abmoakx | 220.498180 | 8.462724 | 0.0338 | 160.2 | 2459046.7104 | $2459048.646\pm 0.023$ | $5.2\pm 2.5$ | [3]
SN 2020qvw | ZTF20abqkaoc | 250.983335 | 77.879897 | 0.0500 | 230.7 | 2459065.8438 | $2459066.222\pm 0.417$ | $<0.6$ | [11]
SN 2020afdi | ZTF20abqwkxs | 224.868111 | 73.898678 | 0.0239 | 110.9 | 2459069.7995 | $2459070.277\pm 0.341$ | $1.3\pm 0.5$ | [3]
SN 2020ufx | ZTF20acedqis | 322.652706 | 24.673752 | 0.0500 | 230.7 | 2459116.8338 | $2459117.752\pm 0.015$ | $4.9\pm 1.0$ | [3]
SN 2020uim | ZTF20acfdmex | 28.188740 | 36.623160 | 0.0185 | 80.5 | 2459117.8602 | $2459118.823\pm 0.0$ | $<0.1$ | [3]
SN 2020xhs | ZTF20acknpig | 30.742868 | 45.020286 | 0.0244 | 106.6 | 2459138.8669 | $2459138.936\pm 0.301$ | $<1.8$ | [3]
SN 2020xva | ZTF20aclvtnk | 263.035128 | 53.653989 | 0.0240 | 108.7 | 2459141.7258 | $2459142.69\pm 0.69$ | $<1.0$ | [3]
SN 2020aavm | ZTF20acrinvz | 116.681975 | 18.113551 | 0.0450 | 227.2 | 2459168.9788 | $2459169.935\pm 0.746$ | $<1.0$ | [11]
SN 2020abue | ZTF20acvjlev | 121.084598 | 56.302082 | 0.0280 | 126.9 | 2459188.0078 | $2459189.663\pm 0.118$ | $<0.2$ | [11]
SN 2020acbm | ZTF20acwgxhk | 40.074159 | 2.427067 | 0.0217 | 93.1 | 2459192.7093 | $2459193.654\pm 0.022$ | $<0.1$ | [11]
SN 2021apg | ZTF21aafkwtk | 205.330192 | 24.495531 | 0.0269 | 128.4 | 2459228.0064 | $2459230.722\pm 0.186$ | $<1.2$ | [11]
SN 2021ibn | ZTF21aasfseg | 132.558710 | 37.026990 | 0.0442 | 197.2 | 2459306.7862 | $2459307.252\pm 0.295$ | $<0.4$ | [11]
SN 2021skn | ZTF21abjcjmc | 246.204167 | 39.734653 | 0.0297 | 139.5 | 2459397.8203 | $2459398.735\pm 0.743$ | $<1.1$ | [11]
SN 2021yja | ZTF21acaqdee | 51.088215 | -21.565626 | 0.0053 | 22.6 | 2459459.4000 | $2459464.4\pm 0.06$ | $<2.3$ | [10]

aafootnotetext: Corrected for Virgo, Great Attractor, and Shapley supercluster
infall.

bbfootnotetext: In rest-frame days, calculated using the last spectrum showing
flash features or by taking the first spectrum as an upper limit.

ccfootnotetext: [1] Bruch et al. (2021), [2] Soumagnac et al. (2020), [3]
Bruch et al. (2023), [4] Vallely et al. (2021), [5] Yang et al. (2021), [6]
Valerin et al. (2022), [7] Tinyanont et al. (2022), [8] Sollerman et al.
(2021), [9] Terreran et al. (2022)

, [10] Hosseinzadeh et al. (2022), [11] TNS classification reports: Perley
(2019); Hiramatsu et al. (2020); Perley et al. (2020); Dahiwale & Fremling
(2020a); Weil et al. (2020); Dahiwale & Fremling (2020b); Pessi et al. (2020);
Delgado et al. (2021); Deckers et al. (2021); Siebert et al. (2021).
ddfootnotetext: This table is available in machine-readable format.

###  2.2 Distance

We adopt Hubble-flow distances using the NASA Extragalactic Database
(NED)111https://ned.ipac.caltech.edu/ and using their online calculator to
correct the redshift-distance for Virgo, Great Attractor, and Shapley
supercluster infall (based on the work of Mould et al., 2000). The top panel
of Fig. 1 shows the distribution of distances in our sample compared to that
of a magnitude-limited and spectroscopically complete sample from ZTF Bright
Transient Survey (Fremling et al., 2020; Perley et al.,
2020).222http://sites.astro.caltech.edu/ztf/rcf/explorer.php

###  2.3 Extinction

We correct for foreground Galactic reddening using the Schlafly & Finkbeiner
(2011) recalibration of the Schlegel et al. (1998) extinction maps, and
assuming a Cardelli et al. (1989) Milky Way extinction law with $R_{V}=3.1$.
These corrections are applied to all photometry data appearing in this paper.
We do not correct the photometry for host-galaxy extinction, and treat this
effect separately in $\S$ 4.3.

###  2.4 Time of zero flux

We acquire an initial estimate of the time of zero flux $t_{0}$ using a power-
law extrapolation of the forced-photometry flux to 0. Using both $g$-band and
$r$-band data, we fit a function $f_{\lambda}=f_{0}(t-t_{0})^{n}$ with a slope
of $0<n<5$, and allow values of $t_{0}$ between the first detection of the SN
and the last non-detection. We then estimate the error on $t_{0}$ as the
scatter in $t_{0,best}$ over all allowed values of $n$, and choose to use the
band with the best constraint on $t_{0}$. In Fig. 2, we show the distribution
of first detection times relative to the estimated time of zero flux in both
UV and optical bands. We find a large fraction of the SNe have $t_{0}$ close
to their first detections. Most of these are SNe where first detection in the
forced photometry light-curve are recovered from a non-detection in the alert
photometry - resulting in a sharp rise. As the SN time of zero flux should not
correlate with the time of first detection, we expect a uniform distribution
in $t_{0}$. $t_{first}-t_{0}$ should then be a rising and falling
distribution, similar to that observed in $t_{UV,first}-t_{0}$. The fact that
our results deviate from such a distribution indicates a systematic deviation
from a power-law rise in flux - a model which is not physically motivated.
Hosseinzadeh et al. (2023) fit the early light curve of the recently
discovered Type II SN 2023ixf (Itagaki, 2023), and show that the rise is
comprised from 2 phases - a slower phase followed by a sharply rising phase.
For such a light curve, extrapolating based on the sharply rising phase would
result in a time of first light too late by several hours, and the first point
on the rise would be close to the fit $t_{0}$. Our fit provides preliminary
evidence this is the case for the majority of SNe II.

###  2.5 Flash feature timescale

Bruch et al. (2021) define flash-features based on the presence of the
$\lambda 4686$ He II feature before broad H recombination features appear. The
flash feature duration $\tau_{flash}$ is defined through the half-time between
the last spectrum showing $\lambda 4686$ He II emission and the subsequent
epoch (Bruch et al., 2023). We adopt these definitions and the measurements of
Bruch et al. (2023) throughout our paper. We extend the estimation to the SNe
not included in Bruch et al. (2023) using all available spectroscopy, which
will be released in a future publication.

In Table 1 we list the 34 SNe in our sample, as well as their median alert
coordinates, redshifts, distance estimates, non-detection limits, estimated
time of zero flux and their flash feature timescales, if applicable.

###  2.6 RSG radiation-hydrodynamic simulations

When comparing data to semi-analytic models, which are calibrated to numerical
simulations, it is unclear how the calibration scatter and theoretical
uncertainties will propagate to observed fluxes. These could potentially
manifest as correlated residuals when the model is compared to the data, and
subsequently create biases in the fit parameters. In order to demonstrate and
account for such effects in our analysis, we repeat some of the analysis we
perform throughout the paper to a set of 28 multi-group radiation-
hydrodynamical simulations of RSG described in detail in M23. These
simulations are generated by relaxing the assumption of local thermal
equilibrium (LTE) and instead solving the radiation transfer using multiple
photon groups and a realistic opacity table with free-free, bound-free and
bound-bound opacities at different densities, temperatures, and compositions.
The simulations allow us to generate synthetic data sets with arbitrary
sampling in time with any set of filters. Unless mentioned otherwise, we use
the sampling, filters, and error-bars of the light curves of SN 2020uim,
arbitrarily chosen from our sample as a representative SN. We do not add
simulated noise, and all points are assumed to be detected regardless of
luminosity unless otherwise mentioned.

##  3 Observations

###  3.1 Optical photometry

ZTF photometry in the gri bands were acquired using the ZTF camera (Dekany et
al., 2020) mounted on the 48 inch (1.2 m) Samuel Oschin Telescope at Palomar
Observatory (P48). These data were processed using the ZTF Science Data System
(ZSDS; Masci et al., 2019). Light curves were obtained using the ZTF forced-
photometry service333See ztf_forced_photometry.pdf under
https://irsa.ipac.caltech.edu/data/ZTF/docs on difference images produced
using the optimal image subtraction algorithm of Zackay, Ofek and Gal-Yam
(ZOGY; Zackay et al., 2016) at the position of the SN, calculated from the
median ZTF alert locations which are listed in Table 1. We removed images that
have flagged difference images (with problem in the subtraction process), bad
pixels close to the SN position, a large standard deviation in the background
region, or a seeing of more than 4″. We performed a baseline correction to
ensure the mean of the pre-SN flux is zero. We report detections above a
$3\sigma$ threshold, and use a $5\sigma$ threshold for upper limits.

In addition to the ZTF photometry, we also used the following instruments to
collect early multi-band light-curves:

  * •

The Optical Imager (IO:O) at the 2.0 m robotic Liverpool Telescope (LT; Steele
et al., 2004) at the Observatorio del Roque de los Muchachos. We used the
Sloan Digital Sky Survey (SDSS; York et al., 2000) $u$, $g$, $r$, $i$ and $z$
filters. Reduced images were downloaded from the LT archive and processed with
custom image-subtraction and analysis software (K. Hinds and K. Taggart et
al., in prep.) Image stacking and alignment is performed using SWarp (Bertin,
2010) where required. Image subtraction is performed using a pre-explosion
reference image in the appropriate filter from the Panoramic Survey Telescope
and Rapid Response System 1 (Pan-STARRS1; Chambers et al., 2016) or SDSS. The
photometry are measured using PSF fitting methodology relative to Pan-STARRS1
or SDSS standards and is based on techniques in Fremling et al. (2016). For
SDSS fields without u-band coverage, we returned to these fields after the SN
had faded on photometric nights to create deep stacked u-band reference
imaging. We then calibrated these field using IO:O standards taken on the same
night at varying airmasses and used these observations to calibrate the
photometry (Smith et al., 2002).

  * •

The Rainbow Camera (Blagorodnova et al., 2018) on the Palomar 60 inch (1.5 m)
telescope (P60; Cenko et al. 2006). Reductions were performed using the
automatic pipeline described by Fremling et al. (2016).

In addition to the above, we use early optical light curves from the
literature. These include the multi-band light curves covering the rise of SN
2021yja (Hosseinzadeh et al., 2022) and light curves from the TESS for SN
2020fqv (Tinyanont et al., 2022) and SN 2020nvm Vallely et al. (2021).

Figure 1: In the top panel, we show the distribution of distances to the SNe
in our sample, compared to the distribution of BTS SNe II. We truncate the
plot at 400 Mpc for clarity. In the bottom panel, we show the distribution of
peak $r$-band magnitude compared to BTS SNe II. In both panels, we show
histograms and the cumulative distributions.

###  3.2 UV photometry

UV photometry were acquired from all SNe using UVOT onboard the Neil Gehrels
Swift Observatory (Gehrels et al., 2004; Roming et al., 2005). We reduced the
images using the Swift
HEAsoft444https://heasarc.gsfc.nasa.gov/docs/software/heasoft/ v. 6.26.1.
toolset. Individual exposures comprising a single epoch were summed using
uvotimsum. Source counts were then extracted using uvotsource from the summed
images using a circular aperture with a radius of 5″. The background was
estimated from several larger regions surrounding the host galaxy. These
counts were then converted to fluxes using the photometric zero points of
Breeveld et al. (2011) with the latest calibration files from September 2020,
and including a small scale sensitivity correction with the latest map of
reduced sensitivity regions on the sensor from March 2022. A UV template image
was acquired for all SNe and for all bands after the SN had faded, with an
exposure time twice as long as used for the deepest image of the SN. These
images were then summed with any archival images of the site and used to
estimate the host flux at the SN site. We remove the local host-galaxy
contribution by subtracting the SN site flux from the fluxes from individual
epochs. In Fig. 3 we show the early $g,r$ and $UVW2$ light curves of the SNe
in our sample. In Fig. 4 we show a representative example of the multi-band
light curves in our sample. We make the multi-band light curve figures of
individual SNe available through the journal website and WISeREP. Finally, we
show the full ZTF forced photometry light curves in Fig. 23.

Figure 2: The times of first detection relative to the estimated time of zero
flux, in UV and in optical bands. Both a histogram and a cumulative
distribution is shown.
Figure 3: UVW2 (magenta stars), $g$ and $r$ (green and red stars) light curves
for all of the objects in our samples. The latest upper limits before
discovery are marked with a downward facing triangle. We note that some points
which are marked as limits in the alert photometry became detections using
forced photometry.
Figure 4: A representative example of the multi-band light curves of SN
2019nvm in the first 40 days. The individual light curves of the rest of the
sample are available through the journal website.

###  3.3 X-ray observations

While the SNe were monitored with UVOT, Swift also observed the field between
0.3 and 10 keV with its onboard X-ray telescope (XRT) in photon-counting mode
(Burrows et al., 2005). We analyzed these data with the online tools provided
by the UK Swift team.555https://www.swift.ac.uk/user_objects These online
tools use the methods of Evans et al. (2007, 2009) and the software package
HEASoft v. 6.29 to generate XRT light curves and upper limits, perform PSF
fitting, and provide stacked images.

In most cases, the SNe evaded detection at all epochs. We derive upper limits
by calculating the median $3\sigma$ count-rate limit of each observing block
in the 0.3–10 keV band, determined from the local background. We stack all
data, and converting the count-rates to unabsorbed flux by assuming a power-
law spectrum with a photon index of 2, and taking into account the Galactic
neutral hydrogen column density at the location of the SN (HI4PI Collaboration
et al., 2016).

In several cases (SN 2020jfo, SN 2020nif and SN 2020fqv) we find spurious
detections which are likely associated with a nearby constant source,
identified by inspecting co-added X-ray images over all epochs, and by
comparing to archival survey data through the HILIGT server (Saxton et al.,
2022). We treat the measured flux as upper limits on the SN flux.

For SN 2020acbm and SN 2020uim, we report $>3\sigma$ X-ray detections from the
binned exposures.666We note that while the detection significance
$S/\sqrt{(}B)>3$, where $S$ is the source flux and $B$ is the background
level, taking into account the source flux in the error calculation results in
a $<3\sigma$ measurement error, since the measurement signal-to-noise is
$S/\sqrt{(}B+S)$. These approximations for the signal to noise hold in the
Gaussian limit, which is approximately correct in our case. For both SNe, the
SN location is within 90% error region of the source PSF. In the case of SN
2020pqv we report a detection 11” from the SN where the source 90%
localization region is $8\farcs 5$. We lack constraining limits on the
quiescent flux at the location of all three SNe when comparing to archival
ROSAT data or compared to the late-time XRT exposures. For SN 2021yja, we
report a source 2$\farcs$6 from the SN site from observations in the first 10
days, brighter by a factor $4.2\pm 1.8$ than the derived $3\sigma$ upper limit
from observation in subsequent epochs - robustly indicating the emission is
related to the SN. We report our measurements in Table 2, and show our results
in Fig. 5.

Table 2: XRT photometry for SNe included in this study

SN |  $t$ [day] | $t_{\rm max}$ [day] |  $t_{\rm min}$ [day] | XRT count rate [s-1] | Flux [$10^{-14}$ erg s-1 cm-2] | Luminosity [$10^{40}$ erg s-1]
---|---|---|---|---|---|---
SN 2018cxn | 7.2 | 10.0 | 1.6 | $<0.002$ | $<7.1$ | $<28.3$
SN 2018dfc | 1.5 | 5.2 | 1.5 | $<0.0011$ | $<4.3$ | $<14.08$
SN 2018fif | 2.1 | 16.8 | 1.2 | $<0.0015$ | $<6.4$ | $<4.56$
SN 2019eoh | 11.6 | 20.0 | 1.4 | $<0.0015$ | $<5.3$ | $<33.68$
SN 2019gmh | 479.9 | 480.4 | 1.9 | $<0.0009$ | $<3.2$ | $<7.41$
SN 2019nvm | 7.6 | 230.2 | 0.3 | $<0.0006$ | $<2.3$ | $<1.85$
SN 2019omp | 2.6 | 11.2 | 1.8 | $<0.0019$ | $<6.9$ | $<35.07$
SN 2019oxn | 2.3 | 10.6 | 0.7 | $<0.0018$ | $<6.8$ | $<6.6$
SN 2019ozf | 196.6 | 391.3 | 1.9 | $<0.0005$ | $<1.9$ | $<10.9$
SN 2019ust | 20.5 | 325.5 | 2.1 | $<0.0005$ | $<2.2$ | $<2.55$
SN 2019wzx | 28.7 | 692.5 | 2.1 | $<0.0008$ | $<2.9$ | $<5.39$
SN 2020aavm | 4.3 | 6.2 | 2.4 | $<0.0016$ | $<6.2$ | $<31.65$
SN 2020abue | 1.7 | 11.3 | 0.4 | $<0.0018$ | $<7.0$ | $<13.45$
SN 2020acbm | 5.7 | 22.8 | 0.3 | $0.0011\pm 0.0004$ | $4.0\pm 1.5$ | $4.56\pm 1.71$
SN 2020afdi | 3.2 | 4.0 | 2.3 | $<0.0027$ | $<10.1$ | $<14.05$
SN 2020cxd | 5.0 | 14.9 | 2.9 | $<0.0028$ | $<10.7$ | $<0.38$
SN 2020dyu | 9.6 | 476.7 | 2.3 | $<0.0008$ | $<2.9$ | $<18.22$
SN 2020fqv | 1.7 | 59.0 | 0.0 | $<0.0072$ | $<43.1$ | $<5.79$
SN 2020jfo | 1.4 | 84.5 | 0.0 | $<0.0017$ | $<6.3$ | $<0.41$
SN 2020lfn | 4.0 | 119.5 | 1.4 | $<0.0004$ | $<1.7$ | $<8.03$
SN 2020mst | 2.4 | 13.5 | 1.4 | $<0.0013$ | $<5.2$ | $<46.13$
SN 2020nif | 3.3 | 16.8 | 0.0 | $<0.006$ | $<22.9$ | $<5.87$
SN 2020nyb | 4.2 | 12.3 | 1.2 | $<0.0012$ | $<5.3$ | $<3.05$
SN 2020pni | 6.9 | 103.1 | 0.6 | $<0.0006$ | $<2.1$ | $<1.41$
SN 2020pqv | 12.6 | 31.3 | 1.5 | $0.0005\pm 0.0002$ | $1.8\pm 0.9$ | $5.2\pm 2.42$
SN 2020qvw | 3.7 | 484.5 | 2.6 | $<0.0016$ | $<6.2$ | $<39.45$
SN 2020ufx | 2.7 | 267.2 | 1.7 | $<0.0007$ | $<2.8$ | $<17.74$
SN 2020uim | 272.2 | 272.5 | 272.0 | $<0.0036$ | $<14.7$ | $<12.14$
SN 2020uim | 10.0 | 271.8 | 1.6 | $0.0008\pm 0.0004$ | $3.1\pm 1.5$ | $2.6\pm 1.26$
SN 2020xhs | 17.5 | 256.7 | 2.6 | $<0.0014$ | $<6.3$ | $<9.06$
SN 2020xva | 2.0 | 18.3 | 1.9 | $<0.0009$ | $<3.5$ | $<4.92$
SN 2021apg | 8.1 | 14.3 | 1.9 | $<0.0014$ | $<4.8$ | $<8.53$
SN 2021ibn | 129.6 | 257.3 | 1.9 | $<0.0008$ | $<2.8$ | $<13.54$
SN 2021skn | 2.8 | 12.1 | 1.4 | $<0.0015$ | $<5.4$ | $<11.68$
SN 2021yja | 4.3 | 8.0 | 2.3 | $0.0013\pm 0.0003$ | $4.8\pm 1.2$ | $0.32\pm 0.08$
SN 2021yja | 46.9 | 83.2 | 15.9 | $<0.0006$ | $<2.1$ | $<0.14$

aafootnotetext: All times are reported in rest-frame days

bbfootnotetext: We report 3$\sigma$ upper limits, or measurements with a
significance of 3$\sigma$ above the background level.

ccfootnotetext: Fluxes are corrected for galactic neutral hydrogen column
density, and converted from count-rates assuming a power-law spectrum with a
photon index of 2.

ddfootnotetext: For SN 2020jfo, SN 2020fqv and SN 2020nif we report quiescent
host-galaxy detections as upper limits on the SN flux.

Figure 5: The right panel shows the XRT binned detections and upper limits for
the SNe in our sample. Measurements were binned over the duration of the Swift
observations, and the time of detections and upper limits is set to the mean
photon arrival time. The left panel shows upper limits on the emission for the
SN location for the 4 XRT detections from archival ROAST survey data. We also
show the XRT light curve of the nearby Type II SN 2023ixf (Zimmerman et al.,
2023).

##  4 Results

###  4.1 Color evolution

Before recombination begins, and although the external layers of the SN ejecta
are not in LTE, the spectrum of a SN II is expected to be well approximated by
a blackbody (Baron et al., 2000; Blinnikov et al., 2000; Nakar & Sari, 2010;
Rabinak & Waxman, 2011; Morag et al., 2023). However, several reasons exists
to expect deviations of the spectrum from a perfect blackbody:

  * •

Extinction can contribute significantly to deviations from blackbody. While
the exact applicable extinction law has a modest effect on the optical colors,
it can create major differences in the UV and UV-optical colors. Large $R_{V}$
values will cause bluer UV-optical colors compared to an $R_{V}=3.1$ MW
extinction law. Many star-forming galaxies lack the characteristic “bump” at
220 nm, which will mostly affect the UVM2-band photometry (Calzetti et al.,
2000; Salim & Narayanan, 2020). For both SNe Ia and stripped-envelope SNe,
sample color-curves have been used to derive a “blue edge” where the amount of
extinction is assumed to be zero (Phillips et al., 1999; Stritzinger et al.,
2018). This is in turn used to estimate the host-galaxy extinction in the line
of sight to the SN, typically performed at phases for which the intrinsic
scatter in color is minimal.

  * •

While a frequency-independent opacity is expected to yield a blackbody
continuum, a frequency-dependent opacity will create deviations. These will
manifest as emission and absorption features - particularly line blanketing in
the UV, as well as broad deviations from blackbody in the continuum. M23
characterize these deviations using multi-group radiation hydrodynamical
simulations, and these are included in their latest analytical model. Line
blanketing in the UV is observed in the few early time UV spectra of SNe II
(Valenti et al., 2016; Vasylyev et al., 2022, 2023a; Bostroem et al., 2023b;
Zimmerman et al., 2023).

  * •

CSM interaction is suggested to create bluer UV-optical colors, to be
associated with a higher luminosity, and with spectral signatures indicating
the presence of CSM (Ofek et al., 2010; Katz et al., 2011; Chevalier & Irwin,
2011; Hillier & Dessart, 2019). CSM interaction is typically accompanied by
strong line emission (Yaron et al., 2017), possibly in the UV, which can
create deviations from blackbody.

Figure 6: The color evolution of SNe II in our sample in the UVW2 – $r$ bands
(left panel) and UVW2 – UVW1 (right panel) bands. Each curve represents a
single SN. The dashed lines are the colors of blackbodies at various
temperatures. The arrows show the color difference due to extinction with
$\rm{E(B-V)}=0.2\ \rm{mag}$ (red arrow) and with $\rm{E(B-V)}=0.4\ \rm{mag}$
(black arrow), assuming a Milky Way extinction curve with $R_{\rm V}=3.1$. The
outlier in the left plot is the highly extinguished SN 2020fqv.
Figure 7: The mean colors of a sample of SNe II at (a) $t=2$ d and (b) $t=4$
d. The solid points and gray shaded regions show the mean color and the
scatter of each color. The transparent points are individual SN colors. Both
the mean and individual SN colors are color-coded by wavelength. The gray
points demonstrate the effect of applying $E(B-V)=0.2$ mag with an $R_{V}=3.1$
Cardelli et al. (1989) extinction law to the bluest colors, demonstrating the
extinction in our sample is smaller than this value. The colored plus are the
colors of the highly reddened SN 2020fqv. The red curve shows the effect of
reddening the mean colors using the best fit extinction curve, which
reproduces the colors of SN 2020fqv to within the errorbars for all
wavelengths.

Using our well sampled light curves, we constrain the deviations from a
blackbody spectral energy distribution (SED) in our sample, as well as attempt
to isolate their main source (i.e., physical or extinction).

First, we consider the effect of extinction. In Fig. 6, we show the $UVW2-r$
and $UVW2-UVW1$ color curves for our sample. On both plots, we illustrate the
effect of applying galactic extinction with $E(B-V)$ of $0.2,0.4$ mag with red
and black arrows respectively. We show dashed lines showing the expected
colors of a blackbody with various temperatures in the background. The scatter
in the color curves represents the variance in temperature and in extinction.
A significant variance in temperature (and thus in color) is expected if these
SNe are powered by shock-cooling, as the temperature evolution is sensitive to
the shock-breakout radius. Despite this, all SNe in our sample besides the
highly extinguished SN 2020fqv (Tinyanont et al., 2022) fall within
$E(B-V)=0.2$ mag of the bluest SN in the sample. We consider this value an
upper limit on the reddening affecting these SNe.777Our sample does not
include other extinguished SNe since we require a blue color to trigger UVOT.
In the case of SN 2020fqv, UVOT was triggered by another group, and thus had
early UV and is included in this study.

In Fig. 7, we show the $M_{n}-M_{r}$ color distributions in our sample at
$t=2$ and $t=4$ days (panels (a) and (b), respectively), where
$n\in\\{UVW2,UVM2,UVW1,U,g,i\\}$. For each band, the transparent data points
show the interpolated color, the solid diamonds and black dashed lines show
the average color, and the error bars and gray shaded regions show the
standard deviation of the color. A extinction corresponding to a galactic
extinction curve with $E(B-V)=0.2$ mag applied to the bluest color
(transparent points with highest $M_{n}-M_{r}$) is indicated by the gray
transparent data points. For UV colors, which are most sensitive to
extinction, this mild amount of extinction is sufficient to account for the
full dispersion of colors in all SNe besides SN 2020fqv. Assuming that SN
2020fqv is well represented by our sample in its intrinsic SED, we use the
average colors to calculate its extinction curve. In each curve, we determine
$E(n-r)$ from the color difference at $t=2$ days, and fit a Cardelli et al.
(1989) extinction curve with free $R_{V}$ and $A_{V}$. In Fig. 7 we show both
the colors of SN 2020fqv (solid plus) and the best fit extinction curve
applied to the average SED (red points), which match well at both times. Here
and in the rest of the paper, we assign wavelengths to filters using the pivot
wavelength for a flat spectrum $\lambda_{piv}=\sqrt{\frac{\int
T\left(\lambda\right)\lambda d\lambda}{\int
T\left(\lambda\right)\frac{d\lambda}{\lambda}}}$, where $T$ is the filter
transmission curve, downloaded from the Spanish Virtual Observatory (SVO;
Rodrigo et al., 2012; Rodrigo & Solano, 2020).

In Fig. 8, we show the calculated $E(n-r)$ for SN 2020fqv along with the best
fitting extinction curves. The computed posterior probability distribution in
the $A_{V}-R_{V}$ plane is shown in the inset. Using our results, we can
determine extinction to $E(B-V)=0.1$ mag on average, and with a maximum
systematic uncertainty of $E(B-V)=0.2$ mag. The case of SN 2020fqv
demonstrates that for highly extinguished SNe, a tight constraint can be
acquired on $R_{V}$. As UVM2 measurement for SN 2020fqv were not acquired, we
cannot discriminate between extinction curves with and without the 220 nm
feature. However, these can likely be distinguished if such measurements were
available. For mildly extinguished SNe, one may limit the extinction using
these data. In Table 5, we report the color for $t=1$ to $t=5$ days. When
using this method to measure the extinction, we caution against using a single
epoch to estimate the extinction, as it can be degenerate with a temperature
difference from the SN II population.

We next consider intrinsic deviations from blackbody. In Fig. 9, we show
color-color plots of the SNe in our sample at the first UV epoch. In panel (a)
we plot the $W2-r$ and $g-r$ colors, and in panel (b) the $UVW2-UVM2$ and
$g-r$ colors. Data points indicate the colors of the SNe II at their first
UVOT visit, where blue and red colors represent SNe with and without flash
features in their early spectra, respectively. The solid black line
corresponds to a blackbody with 0 extinction between $10,000\,$K and
$100,000\,$K. The red dashed lines indicate the effect of extinction between
$E(B-V)=0$ and $0.4$ mag with $R_{V}=3.1$ at the same temperatures. The green
dashed lines demonstrate the effect of extinction with the same $E(B-V)$ range
with different values of $R_{V}$.

The positions that various SNe occupy in the Fig. 9 demonstrate a clear
deviation from a non-extinguished blackbody (black curve). SNe with and
without flash features occupy the same area in the parameter space, indicating
that this deviation from blackbody is not related to the presence of optically
thin CSM. Pure reddening can explain some of the deviation, but requires
$R_{V}>3.1$, a high temperature close to $100,000\,$K, and $E(B-V)$ of up to
$0.4$ mag for some of the objects - more than the 0.2 mag that we infer based
on the scatter in color curves. A difference in $R_{V}$ seems a good
explanation for at least some of the deviation from blackbody. It is
consistent with the colors of the various SNe in both the $W2-r$ color, where
the value of $R_{V}$ has a large effect on the color and the $W2-M2$ color,
which is relatively unaffected by the value of $R_{V}$.

In panels (c) and (d) we show the expected color-color values from the
analytic shock cooling models of M23, at $E(B-V)=0-0.4$ mag, including time-
dependent deviations from blackbody. Colored points represent a subset of SNe
from our sample and their evolution in their first week. The time-dependent
nature of the color curves (evolving from blue to red) conclusively indicates
some of the deviation is intrinsic. For many of the objects, the color
evolution is similar to the expected color evolution in the shock cooling
models, and a combination of mild $E(B-V)<0.2$ mag, intrinsic deviations from
blackbody, and in some cases $R_{V}>3.1$, can fully explain all SN colors. The
color evolution of SN 2020pni (blue stars) stands out in our sample. Its $g-r$
color becomes bluer in the first few days of its evolution. Terreran et al.
(2022) argue the early light curve of this SN is powered by a shock breakout
in an extended wind, rather than cooling of a shocked envelope. This non-
monotonic color evolution was also observed for the nearby SN 2023ixf
(Zimmerman et al., 2023; Jacobson-Galan et al., 2023; Hiramatsu et al., 2023),
also suspected as a wind breakout.

To conclude, 33 of 34 SNe in our sample show $UVW2-r$ colors that become
redder with time, consistent with a cooling behaviour. Using the mean colors,
the extinction of any SNe can be constrained to better than $E(B-V)=0.2$ mag.
The early UV-optical colors of SNe II indicate deviations from blackbody that
are consistent with the expected deviations due to extinction and the expected
intrinsic deviations from blackbody in a cooling envelope, with no additional
CSM interaction required.

Figure 8: The best fit extinction curve we find for SN 2020fqv by correcting
it to the mean colors of SNe II. In each band, the downward (upward) pointing
blue (red) triangle shows the limits of the value of $A_{\lambda}$ from the
bluest (reddest) objects in the sample. The black points show the color
difference from the sample. The purple points are the best fit extinction
curve, applied on a flat spectrum, and integrated over the filter bandpass.
The purple curve is the best fit extinction laws, and the gray transparent
curves are 50 randomly drawn curves from the posterior distribution. In the
inset, we show the posterior distribution of our fit, with colors indicating
the 95,68,50 percentile regions.
Figure 9: (a) Color-color diagram of the UVW2-$r$ and the optical $g-r$ color.
The data points represent different SNe at their 1st UV epoch with (blue
circles) and without (red squares) flash features. The solid black curve
represent the colors of a blackbody with temperatures between 100 kK and 5 kK.
The green dashed line and red dot-dashed lines illustrate the effects of
extinction on this curve: the red dot-dashed lines show increasing $E(B-V)$
from 0 to 0.4 mag, applied to the cooling blackbody curve. The green dashed
lines show the 100 kK colors extinguished with increasing $E(B-V)$ from 0 to
0.4 mag, using extinction laws with different $R_{V}$. The green arrow shows
the direction of increasing $E(B-V)$. (b) is similar to (a), but for
$UVW2-UVM2$. (c) and (d) are similar to (a) and (b), but showing the color
evolution of 4 SNe before $t<7$ days. We also show model Shock-cooling curves
using the models of M23 with increasing $E(B-V)$ using a MW extinction law
with $R_{V}=3.1$. The distance from the black line corresponds to the
deviation from blackbody, which is present in all SNe studied in this work.
Table 3: Early-time blackbody fits of SNe included in this work (truncated)

SN | t [rest-frame days] | $\rm T_{eff}\ [K]$ | $\rm R_{BB}\ [10^{14}\rm cm]$ | $\rm L_{pseudo}\ [10^{42}\rm erg\ \rm s^{-1}]$ | $\rm L_{pseudo,extrap}\ [10^{42}\rm erg\ \rm s^{-1}]$ | $\chi^{2}/dof$
---|---|---|---|---|---|---
SN2018cxn | 1.6 | $23500\pm 1500$ | $2.15\pm 0.16$ | $3.75\pm 3.75$ | $10.01\pm 0.7$ | 1.36
SN2018cxn | 2.19 | $20800\pm 1400$ | $2.58\pm 0.22$ | $3.77\pm 3.77$ | $8.69\pm 0.54$ | 2.22
SN2018cxn | 5.6 | $12700\pm 600$ | $5.3\pm 0.42$ | $3.5\pm 3.5$ | $5.08\pm 0.13$ | 2.0
SN2018cxn | 9.59 | $10500\pm 300$ | $6.82\pm 0.34$ | $2.83\pm 2.83$ | $3.88\pm 0.04$ | 0.57
SN2018dfc | 1.58 | $22000\pm 800$ | $4.31\pm 0.2$ | $13.18\pm 13.18$ | $31.38\pm 1.18$ | 1.0
SN2018dfc | 3.19 | $17000\pm 500$ | $5.99\pm 0.25$ | $12.46\pm 12.46$ | $21.67\pm 0.37$ | 1.01
SN2018dfc | 4.1 | $15000\pm 300$ | $6.92\pm 0.21$ | $10.69\pm 10.69$ | $17.05\pm 0.16$ | 0.46
SN2018dfc | 5.03 | $13300\pm 200$ | $8.19\pm 0.29$ | $9.88\pm 9.88$ | $14.7\pm 0.12$ | 0.55
SN2018fif | 1.22 | $20600\pm 1500$ | $1.68\pm 0.14$ | $1.67\pm 1.67$ | $3.69\pm 0.27$ | 2.66
SN2018fif | 1.25 | $20100\pm 1100$ | $1.73\pm 0.12$ | $1.65\pm 1.65$ | $3.54\pm 0.18$ | 2.13
SN2018fif | 2.1 | $15600\pm 500$ | $2.7\pm 0.15$ | $1.85\pm 1.85$ | $3.08\pm 0.06$ | 1.65
SN2018fif | 2.65 | $15100\pm 700$ | $2.87\pm 0.21$ | $1.81\pm 1.81$ | $2.96\pm 0.07$ | 2.87
SN2018fif | 4.57 | $12000\pm 600$ | $4.22\pm 0.3$ | $1.98\pm 1.98$ | $2.65\pm 0.05$ | 3.6
SN2018fif | 6.15 | $11200\pm 600$ | $4.86\pm 0.42$ | $2.04\pm 2.04$ | $2.68\pm 0.05$ | 4.41
SN2018fif | 6.17 | $11100\pm 600$ | $4.87\pm 0.42$ | $2.04\pm 2.04$ | $2.68\pm 0.05$ | 4.41
SN2018fif | 7.31 | $10600\pm 600$ | $5.33\pm 0.46$ | $2.04\pm 2.04$ | $2.66\pm 0.04$ | 4.21
SN2018fif | 8.33 | $10000\pm 500$ | $5.86\pm 0.49$ | $2.0\pm 2.0$ | $2.6\pm 0.04$ | 3.5

aafootnotetext: A full version of this table is made available through the
journal website.

bbfootnotetext: A 0.1 mag systematic error was adopted for the fitting.

###  4.2 Blackbody evolution

We linearly interpolate the UV-optical light curves of the sample SNe to the
times of UV observations and construct an SED. Using the Scipy curve_fit
package (Virtanen et al., 2020), we fit this SED to a Planck function and
recover the evolution of the blackbody temperature, radius, and luminosity
parameters $T_{\rm eff}$, $R_{\rm BB}$, and $L_{\rm BB}$, respectively. We
assume a $0.1$ mag systematic error in addition to the statistical errors to
account for imperfect cross-instrument calibration. In addition to the best-
fit blackbody luminosity, we calculate a pseudobolometric luminosity by
performing a trapezoidal integration of the interpolated SED and extrapolating
it to the UV and infrared (IR) using the blackbody parameters. The fit results
are reported in Table 3.

In Fig. 10 we show the blackbody evolution for our sample SNe, as well as the
mean blackbody evolution of the population. To do so, we interpolate the
temperatures, radii and luminosities with 0.5 day intervals, and take the
population mean separately for SNe with and without flash ionization features
as determined by Bruch et al. (2021) and Bruch et al. (2023). We estimate the
error on the population mean through a bootstrap analysis (Efron & Tibshirani,
1993). We draw 34 SNe, allowing for repetitions. We then draw samples from the
blackbody parameters of each SN assuming a Gaussian distribution for every fit
point. We then interpolate to the same time grid and calculate the population
mean at every time step. The blue histogram shows the fraction of SNe in our
sample with blackbody fit as a function of time.

We find that SNe with flash features have a blackbody temperature
$6.3\%\pm{4.1\%}$ cooler and a radius (or photospheric velocity)
$28\%\pm{11\%}$ larger than SNe without flash features. This difference is
highlighted in Fig. 11 where we show the radius and temperature distribution
of SNe with and without flash features, interpolated to $t=2$ days after
explosion. At all times where a significant $>50\%$ fraction of the sample
have measurements, the mean blackbody properties are well described by the
predictions of spherical phase shock cooling. Our results indicate that the
population of SNe II is well described by a cooling blackbody following shock-
breakout at the edge of a shell of material with a steep density profile.

Figure 10: The blackbody evolution of a sample of SNe II during the first 10
days. The transparent points represent individual SNe, color coded according
to the presence of flash features (black) or lack thereof (red). The blue
curve indicates the fraction of the sample with blackbody fits at each time
step. The solid points show the population mean, and the dashed curves show
the predicted evolution according to spherical phase shock cooling. Panels
(a)-(c) shows the blackbody temperature, radius and luminosity, respectively.
The match between the predictions of spherical phase shock-cooling models and
the population blackbody evolution motivates the use of these models to fit
individual SN light curves.
Figure 11: The distribution of blackbody temperature and radius, interpolated
to $t=2$ days. Black and red points are SNe II with and without flash
features, respectively. The dashed lines and shaded regions show the
population mean and standard error. The red and blue colored regions show the
area occupied by simulated progenitors with $<10^{14}$ cm and $>10^{14}$ cm
respectively. These are generated by fitting a blackbody to synthetic datasets
constructed from the MG simulations of M23. Of the 23 SNe with a measurement
at this time, 7 are only consistent with simulations that have a breakout
radii $>10^{14}$ cm, or with a shock velocity parameter $v_{s*}\gtrsim
6000{\rm km\,s^{-1}}$

###  4.3 Shock-cooling fitting

####  4.3.1 Method and validation

As the population blackbody evolution is well described by shock cooling, we
fit individual SN light-curves to shock-cooling models. We do this using the
model presented in M22 and M23, which interpolated between the planar phase
(i.e., when $r\approx R_{bo}$) and spherical phase (i.e., when $vt\gtrsim
R_{bo}$) of shock cooling, and predicts the deviations of the SED from
blackbody as a function of model parameters. The full model is described in
Morag et al. (2022, 2023) and is briefly summarized in $\S$ A.1.

The model has four independent physical parameters: The progenitor radius
$R=R_{13}\,10^{13}\ \rm cm$, the shock velocity parameter
$v_{s*}=v_{s*,8.5}\,10^{8.5}\,\rm{cm\,s}^{-1}$, the product of density numeric
scale factor $f_{\rho}$ and the progenitor mass $M_{*}=M\,M_{\odot}$ (treated
as a single parameter) and the envelope mass
$M_{env}=M_{env,\odot}\,M_{\odot}$. In addition to these parameters, we also
fit for the extinction curve, parameterized as a Cardelli et al. (1989) law
with free $R_{V}$ and $E(B-V)$, and the breakout time $t_{0}$.

As demonstrated in Rubin et al. (2016), adopting a fixed validity domain will
create a bias against some large radius models. For every model realization,
we calculate the validity domain, omitting the points outside this validity
range from consideration. In order to properly compare between models with a
different number of valid points, we we adopt a likelihood function based on
the $\chi^{2}$ probability density function (PDF), as described in detail in
Soumagnac et al. (2020).

Shock cooling models are expected to have residuals in temperature on order 5%
– 10% from model predictions (Rabinak & Waxman, 2011; Sapir & Waxman, 2017)
when an average opacity is assumed, and additional systematics due to the
presence of lines. M23 expect the residuals on the flux to be of order 20% –
40%, which will be correlated in time and wavelength. These residuals
determine the appropriate covariance matrix to use in the $\chi^{2}$
statistic. They will also provide a criterion through which we can reject fits
to a given data set. Indeed, when comparing the light curves of our sample of
hydrodynamical simulations to the analytical model predictions, we find that
in 50% of the data points have residuals extending to $0.17$ mag and 95% have
residuals extending to $0.45$ mag. To incorporate the correlation between
residuals into our analysis, we construct a likelihood function using the
following steps:

  * •

Given a set of light curves, we construct a set of synthetic measurements from
the set of hydrodynamical simulations of M23 at the same times and photometric
bands, by integrating the simulated SED with the appropriate transmission
filters.

  * •

From each simulation, we construct a set of residuals from the analytic model
predicted by the physical parameters of each simulation.

  * •

For each light-curve point, we calculate the covariance term as the mean over
all simulations, taking into account only simulations which are valid at that
time.

  * •

Since the covariance matrix has too many parameters to be accurately estimated
in full, we take the singular value decomposition (SVD) of the mean covariance
and keep the top 3 eigenvalues.888This choice accounts for $>80\%$ of the
variance, while preventing negative eigenvalues for any sampling used in our
work. We then add this covariance matrix with a diagonal covariance matrix
constructed from the observational errors in each data point, and add a 0.1
mag systematic error for cross-instrument calibration.

  * •

The likelihood of a model given the data is taken to be
$\mathcal{L}=PDF(\chi^{2},\nu)$ where
$\chi^{2}=(d_{i}-m_{i})cov^{-1}_{ij}(d_{j}-m_{j})$, where $\vec{d},\vec{m}$
are the data and the model respectively, $\nu$ is the number of points where
the model is valid, and PDF is the $\chi^{2}$ distribution PDF.

Using this likelihood, we fit the model to the photometry using the nested-
sampling (Skilling, 2006) package dynesty (Higson et al., 2019; Speagle,
2020). We validate our method by testing that even in the presence of such
residuals, we can still recover the true model parameters from simulated data
sets. We fit all simulated data sets using this method, and compare the fit
parameters with the physical parameters used in the simulations. In Fig. 12,
we show an example of such a fit for a simulation generated with $R_{13}=0.3$,
$v_{s*,8.5}=1.33,M_{env}=1\,M_{\odot}$ with $E(B-V)=0.1$ mag extinction added.
We recover $R_{13}=0.3\pm 0.05$, $v_{s*,8.5}=0.9\pm 0.13,M_{env}=16\pm
7.8\,M_{\odot}$ and $E(B-V)=0.04\pm 0.03$ mag.

In Fig. 13 we show the fit and true radii $R_{13}$ and shock velocity
parameter $v_{s*,8.5}$, compared to the parameters used in the simulations.
The 90% confidence intervals for parameter recovery are $30\%$ for $R_{13}$,
$26\%$ for $v_{s*,8.5}$ and better than $0.05$ mag in $E(B-V)$ over the entire
parameters space of our simulations. However, we cannot recover $M_{env}$ or
$f_{\rho}M_{tot}$ to better than an order of magnitude, and our fit results
are highly sensitive to our choice of prior in those parameters, indicating
they cannot be effectively constrained from shock-cooling modelling.

Our results demonstrate that even given significant residuals, one may still
fit these analytic models and recover the shock velocity, progenitor radius
and the amount of dust reddening with no significant biases. Our results also
demonstrate that rejecting shock-cooling as the main powering mechanism of the
early light curves requires residuals larger than $\sim 0.5$ mag.

Figure 12: Example of shock-cooling fits to a multi-band synthetic dataset,
compared to the models generated from the physical simulation parameters. The
solid lines are the average fits from the posterior, and the dot-dashed lines
are model generated from the physical simulation parameters. The model light
curve typically deviate by up to 20% (calibration uncertainty) from the
simulations, and are expected to deviate by up to 40% in band specific flux
due to theoretical uncertainty. We show the model until to its upper validity
time. The best fit model accurately reproduces the breakout radius, velocity
and finds a similar $E(B-V)$, but cannot reproduce the envelope mass or other
model parameters.
Figure 13: Parameter recovery when fitting a sample of synthetic light curves
with analytic shock-cooling models. In panels (a) and (b), we show the fit and
true parameters for $R_{13}$ and $v_{s*,8.5}$, respectively. In panel (c), we
show the recovery accuracy of $E(B-V)$. The dashed line represents a perfect
recovery, and the shaded regions represent the $68\%$ interval over the full
parameter space.
Figure 14: (a) An example of a fit to a SN dataset from our sample. The dot-
dashed curves are the best fits in each band. The transparent curves are 50
random samples from the posterior distribution. The vertical dashed lines
indicate the best fit lower validity domain (gray) and the transition from
planar to spherical phase (orange). (b) An example of a fit which misses the
rise (the first $g$-band point) for the best fit model
($R_{13}=22.2,v_{s*,8.5}=1.7$, dot-dashed lines), but to which a reasonable
lower radius fit exists ($R_{13}=4.0,v_{s*,8.5}=3.3$, solid lines).
Figure 15: Best fit shock-cooling models to the early time TESS light curve of
SN 2020nvm. The blue curve shows the best fit M23 model to the multi-band
light curve, which misses the rise during the planar phase. The green curve
shows the best fit for a narrow radius prior, and the red curve shows the same
model as the blue curve but accounting only for the spherical phase with the
model of Sapir & Waxman (2017). While the spherical phase only can reproduce
the full light curve, taking the planar phase into account results in
different early time light curve. When including the planar phase, no good fit
is found which can describe the entire light curve.

####  4.3.2 Light-curve fits

We ran our fitting routine on all sample SNe. We used log-uniform priors for
$R_{13}\in[0.1,30]$, $v_{s*,8.5}\in[0.1,6]$, $f_{\rho}M\in[0.1,200]$,
$M_{env,\odot}\in[0.3,30]$. We also fit $t_{exp}\in[t_{ND}-1,t_{first}]$ with
a uniform prior, where $t_{ND}$ is the last non-detection and $t_{first}$ is
the first detection, respectively (relaxing the prior on $t_{ND}$ does not
significantly impact our fit). Motivated by our analysis in $\S$ 4.1 we also
fit for host-galaxy extinction by assuming a Cardelli et al. (1989) reddening
law with uniform priors on $E(B-V)$ and $R_{V}$ in the range
$E(B-V)\in[0,0.25]$ mag and $R_{V}\in[2,5]$. For SN 2020fqv, we fit with a
wide prior of $E(B-V)\in[0.25,1]$ mag, given the high host-extinction we
inferred from its color evolution.

In addition to the flat priors on the parameters, we include non-rectangular
priors through the model validity domain. This is done to prevent fits that
exclude most data points from the validity range for parameter combinations
with high $v_{s*,8.5}$ and low $M_{env}$. We assign 0 probability to models
that have no photometry data within their validity domain. While this does not
impact our results in this work, fitting models without good non-detection
limits shortly before explosion, or that are expected to have short validity
times (e.g., due to small radii, or high velocity to envelopes mass ratios),
might be affected by this demand. In Soumagnac et al. (2020), we assigned
priors on the recombination time at $0.7~{}\rm{eV}=8120$ K ($t_{0.7\ \rm
eV}\sim R_{13}^{0.56}v_{s*,8.5}^{0.16}$) of the SN through it spectral
sequence. However, in some of the simulations of M23, we start seeing signs of
hydrogen emission already at $20,000$ K. Instead, we use priors derived from
the blackbody sequence of the SN. Since there are residuals in color between
the simulations and models, and since the effect of host galaxy extinction is
known to better than $0.2$ mag, the fit temperature assuming $E(B-V)=0$ mag
might not always be accurately used to determine the true photospheric
temperature. We quantify the maximal effect of these systematics on the
photospheric temperature near $0.7~{}\rm{eV}=8120$ K. We fit all synthetic
datasets (with an extinction of up to $E(B-V)=0.2$ mag) with blackbody SEDs
assuming no host extinction, and find that demanding that $T>10,700$ K is
enough to determine that $t>t_{0.7eV}$, and $T<5500$ is enough to determine
that $t<t_{0.7eV}$ for any combination of parameters, as long as $E(B-V)\leq
0.2$ mag. These physically motivated priors on the recombination time have a
significant effect on our fitting process.

Due to the peculiar temperature and luminosity evolution of SN 2020pni, which
does not fit the general predictions of spherical phase shock cooling, we omit
this SN from the fitting process. We will treat the modelling of this SN in
detail in Zimmerman et al. (in perp.).

In Table 4 we report the parameters of our posterior sampling at the 16th,
50th and 84th percentiles. In all cases, we find good fits for the light
curves at $t>1$ days after explosion. Our fits divide into 2 cases: (1) For 15
SNe, we find good fits to the UV-optical SN light curves throughout the
evolution. These models are characterized by a radius under $10^{14}$ cm, and
residuals better than 0.42 mag (95%) throughout the first week. (2) For the
remaining 18 SNe, the early optical light curve points do not match the rise
of the models - either pushing it out of the model validity domain or missing
it completely by more than 1 mag. These models are exclusively characterized
by a large radius ($>10^{14}$ cm) required to account for a high luminosity,
but do not show the shallow rise or double peaked feature expected for planar
phase shock cooling of such a star.999In the Rayleigh-Jeans limit, this can be
intuitively understood as $f_{\lambda}\propto T_{BB}R_{BB}^{2}$, resulting in
$f_{\lambda}\propto t^{-}{1/3}$ in the planar phase, and $f_{\lambda}\propto
t^{1.15}$ early in the spherical phase. After the first day from estimated
explosion, these fits have comparable residuals to group (1). If forced to fit
a radius of $<10^{14}$ cm - a reasonable fits achieved in about half of the
cases. For the rest of the objects in this group, forcing a small radius
results in a bad overall fit.

Since the spherical phase luminosity $L_{{\rm RW}}\sim R_{13}v_{{\rm
s*,8.5}}^{1.91}$, these fits are characterized by a higher $v_{\rm s*,8.5}$
and more host-galaxy extinction to decrease the temperature as $T_{{\rm
ph,t=1\ \rm d}}\sim R_{13}^{1/4}v_{{\rm s*,8.5}}^{0.07}$. We show examples of
fits of both cases in Fig. 14, and make all figures of all light curve fits
available as online figures through the journal website upon publication. In
Fig 15, we show the illuminating example of SN 2020nvm, which was observed by
TESS throughout its rise. We show that a model accounting only for the
spherical phase will artificially create a much sharper rise compared to a
model which fits the peak. In this case, our best small-radius fit did not
match the observed light curve well, and the large radius model (one of the
largest values in our sample) misses the rise. The clear first peak expected
in planar phase cooling is not observed even at early times.101010We note some
features are present in the very early light curve. These are also present in
some of the simulations of M23, and could be the result of lines. This is
likely not the shock breakout signal, which is expected to be very faint in
this band (Sapir et al., 2013; Katz et al., 2013; Sapir & Halbertal, 2014) The
Sapir & Waxman (2017) model fits the rise much better, although it is not
physical at early times.

In Fig. 16, we present the posterior probability for the radius of best-fit
models that miss the rise, and those that match the rise. We find no
statistically significant difference between SNe with and without flash
features (which could perhaps be detected given a larger sample).

We summarize the different categories our objects fall into in Fig. 17. Most
SNe II are cooling at early times, showing constant or reddening UV-optical
colors. We refer to these as “II-C”. SNe II which are heating and showing a
bluer UV-optical color with time are referred to as “II-H”. We further
subdivide the II-C group into SNe with small fit radius (“II-C+”), which are
well fit at early times, and those with large fit radius (“II-C-”), which are
not well fit by shock cooling models at early times.

Figure 16: (a) Posterior probability distribution of the breakout radius, for
SNe whose fit misses the rise and SNe whose best fit does not miss the rise.
(b) A scatter plot showing the correlation between the best fit radius and the
$r$-band magnitude at $t=2$ days. A large fit radius is strongly associated
with with missing the rise during the first day, and is associated with a
brighter $r$-band light curve. Table 4: Best fit parameters for shock cooling
fitting

SN | $R_{13}$ | $v_{s*,8.5}$ | $f_{M}$ |  $E(B-V)$ [mag] | $R_{V}$ |  $t_{0}$ [JD] |  $t_{0.7}$ [days] |  $t_{tr}$ [days]
---|---|---|---|---|---|---|---|---
SN2019eoh | $7.7^{+0.9}_{-0.9}$ | $2.0^{+0.3}_{-0.3}$ | $0.5^{+0.5}_{-0.4}$ | $0.0^{+0.0}_{-0.0}$ | $4.0^{+0.9}_{-1.3}$ | $-0.02^{+0.05}_{-0.06}$ | 26.7 | 16.3
SN2020aavm | $13.4^{+4.1}_{-4.3}$ | $0.9^{+0.3}_{-0.3}$ | $83.7^{+85.7}_{-70.8}$ | $0.1^{+0.1}_{-0.1}$ | $3.9^{+1.0}_{-1.2}$ | $0.19^{+0.45}_{-0.50}$ | 22.2 | 47.1
SN2020fqv | $3.4^{+1.6}_{-1.7}$ | $1.0^{+0.4}_{-0.3}$ | $99.4^{+76.4}_{-75.7}$ | $0.8^{+0.0}_{-0.0}$ | $2.8^{+0.5}_{-0.5}$ | $0.40^{+0.26}_{-0.28}$ | 13.8 | 47.4
SN2019oxn | $5.4^{+0.8}_{-0.8}$ | $0.7^{+0.1}_{-0.1}$ | $1.4^{+1.7}_{-1.2}$ | $0.0^{+0.0}_{-0.0}$ | $3.9^{+0.9}_{-1.2}$ | $0.01^{+0.18}_{-0.21}$ | 20.2 | 46.8
SN2020ufx | $15.2^{+3.8}_{-4.2}$ | $2.2^{+0.5}_{-0.4}$ | $83.0^{+81.7}_{-64.5}$ | $0.0^{+0.0}_{-0.0}$ | $3.6^{+1.1}_{-1.2}$ | $-0.33^{+0.27}_{-0.33}$ | 27.7 | 4.6
SN2019ozf | $16.5^{+2.8}_{-3.4}$ | $0.7^{+0.2}_{-0.2}$ | $94.5^{+77.6}_{-71.0}$ | $0.0^{+0.0}_{-0.0}$ | $3.7^{+1.0}_{-1.2}$ | $-0.44^{+0.33}_{-0.33}$ | 20.6 | 30.9
SN2018cxn | $13.7^{+3.2}_{-3.1}$ | $0.6^{+0.1}_{-0.1}$ | $109.7^{+68.1}_{-69.8}$ | $0.1^{+0.1}_{-0.1}$ | $3.8^{+1.0}_{-1.2}$ | $-0.00^{+0.01}_{-0.01}$ | 16.7 | 38.9
SN2020cxd | $3.5^{+1.3}_{-1.0}$ | $0.3^{+0.1}_{-0.0}$ | $53.0^{+77.3}_{-47.4}$ | $0.1^{+0.1}_{-0.1}$ | $3.7^{+1.0}_{-1.2}$ | $0.48^{+0.53}_{-0.60}$ | 12.4 | 32.9
SN2019nvm | $17.2^{+2.1}_{-2.2}$ | $0.7^{+0.1}_{-0.1}$ | $111.2^{+68.4}_{-70.3}$ | $0.1^{+0.0}_{-0.0}$ | $3.6^{+1.1}_{-1.1}$ | $-0.51^{+0.38}_{-0.34}$ | 25.6 | 38.2
SN2020lfn | $17.5^{+2.1}_{-2.6}$ | $1.5^{+0.3}_{-0.2}$ | $98.5^{+72.3}_{-67.1}$ | $0.0^{+0.0}_{-0.0}$ | $3.8^{+1.0}_{-1.2}$ | $-0.24^{+0.22}_{-0.24}$ | 27.0 | 8.8
SN2020jfo | $6.3^{+1.3}_{-1.3}$ | $0.6^{+0.1}_{-0.1}$ | $72.3^{+76.8}_{-56.8}$ | $0.0^{+0.0}_{-0.0}$ | $3.6^{+1.1}_{-1.2}$ | $0.11^{+0.23}_{-0.27}$ | 14.3 | 28.5
SN2020nyb | $14.8^{+3.1}_{-3.0}$ | $0.4^{+0.1}_{-0.1}$ | $60.0^{+81.4}_{-53.1}$ | $0.1^{+0.1}_{-0.1}$ | $3.9^{+0.9}_{-1.1}$ | $-0.55^{+0.47}_{-0.60}$ | 21.9 | 60.6
SN2019wzx | $14.0^{+4.9}_{-6.2}$ | $1.0^{+0.4}_{-0.3}$ | $92.6^{+79.7}_{-73.3}$ | $0.0^{+0.0}_{-0.0}$ | $3.6^{+1.1}_{-1.2}$ | $-0.26^{+0.51}_{-0.55}$ | 20.2 | 31.2
SN2019gmh | $14.9^{+4.6}_{-6.6}$ | $0.8^{+0.3}_{-0.2}$ | $132.4^{+55.0}_{-68.5}$ | $0.1^{+0.0}_{-0.0}$ | $4.1^{+0.7}_{-0.9}$ | $-0.30^{+0.20}_{-0.16}$ | 24.5 | 10.1
SN2020afdi | $8.0^{+1.7}_{-1.6}$ | $0.4^{+0.1}_{-0.1}$ | $49.1^{+77.2}_{-45.2}$ | $0.0^{+0.0}_{-0.0}$ | $3.8^{+1.0}_{-1.2}$ | $-0.07^{+0.27}_{-0.28}$ | 21.8 | 48.5
SN2020pqv | $17.3^{+2.2}_{-2.7}$ | $0.8^{+0.2}_{-0.2}$ | $80.0^{+83.6}_{-64.6}$ | $0.0^{+0.0}_{-0.0}$ | $3.7^{+1.0}_{-1.2}$ | $-0.61^{+0.46}_{-0.50}$ | 29.5 | 13.5
SN2020mst | $14.7^{+4.2}_{-4.5}$ | $0.9^{+0.2}_{-0.2}$ | $90.1^{+80.7}_{-72.2}$ | $0.1^{+0.1}_{-0.1}$ | $3.6^{+1.1}_{-1.2}$ | $-0.35^{+0.31}_{-0.33}$ | 24.6 | 23.6
SN2020dyu | $16.0^{+3.2}_{-3.4}$ | $1.2^{+0.3}_{-0.2}$ | $105.0^{+71.6}_{-70.4}$ | $0.0^{+0.0}_{-0.0}$ | $3.6^{+1.1}_{-1.1}$ | $-0.54^{+0.28}_{-0.24}$ | 26.0 | 14.0
SN2021apg | $14.9^{+3.9}_{-4.7}$ | $0.6^{+0.2}_{-0.2}$ | $87.9^{+80.8}_{-70.7}$ | $0.1^{+0.1}_{-0.1}$ | $3.7^{+1.0}_{-1.2}$ | $-0.31^{+0.76}_{-0.83}$ | 23.0 | 12.9
SN2020xva | $10.6^{+3.0}_{-2.7}$ | $0.5^{+0.1}_{-0.1}$ | $66.8^{+84.8}_{-58.6}$ | $0.1^{+0.1}_{-0.1}$ | $4.0^{+0.8}_{-1.2}$ | $0.22^{+0.40}_{-0.46}$ | 18.6 | 44.5
SN2020nif | $13.0^{+5.1}_{-5.0}$ | $1.6^{+0.4}_{-0.3}$ | $87.7^{+81.4}_{-70.5}$ | $0.1^{+0.0}_{-0.0}$ | $3.6^{+1.1}_{-1.2}$ | $-0.07^{+0.41}_{-0.46}$ | 23.1 | 9.0
SN2020acbm | $15.5^{+2.3}_{-2.4}$ | $0.7^{+0.1}_{-0.1}$ | $92.6^{+77.5}_{-70.7}$ | $0.0^{+0.0}_{-0.0}$ | $3.7^{+1.1}_{-1.2}$ | $-0.46^{+0.33}_{-0.33}$ | 26.7 | 10.8
SN2021yja | $15.2^{+3.8}_{-4.6}$ | $0.6^{+0.2}_{-0.1}$ | $90.2^{+80.7}_{-72.7}$ | $0.0^{+0.0}_{-0.0}$ | $3.6^{+1.1}_{-1.2}$ | $0.39^{+1.08}_{-1.08}$ | 21.7 | 54.2
SN2019omp | $13.5^{+4.9}_{-5.0}$ | $0.8^{+0.2}_{-0.2}$ | $105.5^{+72.9}_{-74.3}$ | $0.1^{+0.1}_{-0.1}$ | $3.7^{+1.0}_{-1.2}$ | $-0.48^{+0.33}_{-0.31}$ | 24.4 | 33.1
SN2021ibn | $8.0^{+2.8}_{-2.6}$ | $1.9^{+0.5}_{-0.5}$ | $89.1^{+80.3}_{-69.5}$ | $0.0^{+0.0}_{-0.0}$ | $3.7^{+1.0}_{-1.2}$ | $0.19^{+0.15}_{-0.18}$ | 17.6 | 6.8
SN2020qvw | $15.2^{+3.7}_{-4.4}$ | $1.4^{+0.3}_{-0.3}$ | $90.1^{+80.7}_{-70.3}$ | $0.0^{+0.0}_{-0.0}$ | $3.6^{+1.1}_{-1.2}$ | $-0.10^{+0.25}_{-0.21}$ | 24.0 | 6.5
SN2018fif | $12.2^{+3.5}_{-3.3}$ | $0.7^{+0.1}_{-0.1}$ | $63.8^{+79.4}_{-54.2}$ | $0.2^{+0.1}_{-0.1}$ | $4.2^{+0.6}_{-0.9}$ | $-0.25^{+0.22}_{-0.29}$ | 20.6 | 47.2
SN2020pni | $14.8^{+4.2}_{-5.1}$ | $1.4^{+0.5}_{-0.4}$ | $92.3^{+79.0}_{-71.1}$ | $0.0^{+0.0}_{-0.0}$ | $3.7^{+1.0}_{-1.2}$ | $0.14^{+0.73}_{-0.68}$ | 25.5 | 10.8
SN2021skn | $12.8^{+5.4}_{-5.0}$ | $1.1^{+0.4}_{-0.3}$ | $105.7^{+71.5}_{-73.3}$ | $0.0^{+0.0}_{-0.0}$ | $3.6^{+1.1}_{-1.2}$ | $-0.48^{+0.38}_{-0.32}$ | 23.3 | 10.8
SN2020uim | $13.4^{+1.8}_{-1.7}$ | $0.4^{+0.1}_{-0.1}$ | $52.7^{+79.2}_{-47.6}$ | $0.0^{+0.0}_{-0.0}$ | $3.7^{+1.1}_{-1.2}$ | $-0.24^{+0.30}_{-0.37}$ | 20.7 | 55.0
SN2018dfc | $15.1^{+4.0}_{-4.7}$ | $1.4^{+0.5}_{-0.4}$ | $105.5^{+71.7}_{-72.1}$ | $0.0^{+0.0}_{-0.0}$ | $3.6^{+1.1}_{-1.2}$ | $-0.76^{+0.29}_{-0.23}$ | 27.8 | 13.7
SN2020xhs | $14.1^{+3.3}_{-3.7}$ | $0.5^{+0.2}_{-0.1}$ | $96.4^{+78.4}_{-75.3}$ | $0.1^{+0.1}_{-0.0}$ | $3.6^{+1.1}_{-1.2}$ | $0.59^{+0.61}_{-0.51}$ | 19.5 | 49.9
SN2019ust | $10.0^{+2.2}_{-2.1}$ | $2.1^{+0.4}_{-0.4}$ | $17.1^{+24.9}_{-15.7}$ | $0.2^{+0.0}_{-0.0}$ | $4.1^{+0.7}_{-0.9}$ | $0.57^{+0.12}_{-0.14}$ | 23.1 | 4.8
SN2020abue | $13.9^{+3.0}_{-3.0}$ | $0.6^{+0.1}_{-0.1}$ | $97.0^{+77.3}_{-73.6}$ | $0.0^{+0.0}_{-0.0}$ | $3.7^{+1.1}_{-1.2}$ | $-0.86^{+0.50}_{-0.48}$ | 22.5 | 26.8

aafootnotetext: all times are in rest-frame days

bbfootnotetext: Uncertainties reflect the 10th-90th percentiles of the
posterior probability distribution

ccfootnotetext: This table will be made available in machine-readable format
through the journal website upon publication.

Figure 17: Schematic classification of the early light curves of SNe II. They
roughly divide into 2 groups: (1) SNe with increasing temperatures at early
times, which call “II-H”, and (2) with decreasing temperatures or “II-C”. We
further divide the later into 2 groups: (a) which are well fit by shock
cooling models at early times, have a good early fit, and a small fit radius.
We call these “II-C+”. (b) which are not well fit at early times, are more
luminous as a population, and have larger fit radii. We call these “II-C-”.
Next to each group we denote the number of SNe in the sample which belong to
it, as well as example SNe.
Figure 18: (a) A histogram of the distances of SNe in this work, and the
fraction of simulated SNe light curves which would be followed up with our
observations study, and in the Ultraviolet Transient Astronomy Satellite
(ULTRASAT) survey. We assume the radius distribution of Davies et al. (2013)
for the models. (b) The mean radius of the detected SNe, demonstrating a
luminosity bias at $d>70$ Mpc. (c) The unweighted posterior probability
distribution of the breakout radius, and $d$ above or below 70 Mpc. (d) The
posterior distribution of the full sample, corrected and uncorrected for the
luminosity bias. The gray histogram is a distribution of RSG radii from Davies
et al. (2013). We also shock the cumulative distribution of the observed and
corrected posterior distribution, with $68\%$ confidence intervals. While the
observed fraction of SNe with large $>1000\,R_{\odot}$ radius is
$71^{+7}_{-4}\%$, they only account for $34^{+23}_{-11}\%$ of exploding RSGs.

##  5 Discussion

###  5.1 RSG radius distribution

####  5.1.1 What can the early-time fits teach us?

In $\S$ 4.3.1, we demonstrated that with a typical set of UV-optical light
curves, we can recover the breakout radius and shock velocity parameter from
the simulations of M23 for a wide range of parameters. When applying our
method to the SNe of our sample, we found good fits to roughly half of the
SNe, with radii consistent with the observed RSG radius distribution (II-C+).
The remaining SNe systematically miss the rise and are characterized either by
a high $R_{13}$ or a high $v_{s*,8.5}$ due to the higher luminosity of this
group compared to other SNe (II-C-). Since there are acceptable fits for
roughly half of such SNe, and as the blackbody radius and temperatures of the
majority of the sample evolve according to the predictions of spherical phase
shock cooling, we cannot rule out that it is the primary powering mechanism of
these SNe. Our lack of early-time UV-optical colors and of high quality
sampling in the first hours of the SN explosions prevents us from testing
whether the blackbody evolution in the very early times evolves according to
the predictions of planar phase shock cooling. However, we note that when
optical colors are available during these first phases, the colors are
consistent with that of a hot $>15,000$ K blackbody. With this in mind, there
are several possibilities to explain the large radius fits:

  1. 1.

These SNe are powered by shock cooling only, and have a small radius. The
failure to fit the rise is due to correlated residuals not present in the
simulations, and thus is not modeled in the covariance matrix we used -
creating a bias to larger radii in some cases, or they did not cover this
particular combination of shock velocity and radius. This possibility is
likely what happens in half of the cases, where a good fit is acquired if the
fit is forced to a small radius. In other cases, the small radius fit still
misses the rise or a unrealistically high $v_{s*}$ is required.

  2. 2.

These SNe have a large progenitor radius, and their early time evolution does
not fit the predictions of planar phase shock cooling from a spherical RSG
envelope. Recent work by Goldberg et al. (2022a, b) shows that the turbulent
3D structure of the outer regions of the envelope, or a non-spherical breakout
surface could possibly extend the duration of shock breakout and affect the
early stages of shock cooling up to a timescale of $R/v\lesssim 1$ day. If
this is the case for the majority of similar fits, the large radius of the
progenitor star would be consistent with a shell of dense CSM or an inflated
envelope at $<3\times 10^{14}\,\rm cm$, with the breakout occurring at the
edge of the shell. This interpretation is also supported by
spectropolarimetric observations of SN 2021yja (Vasylyev et al., 2023b),
showing a high degree of continuum polarization during the early photospheric
phase ($t>25$ days). SN 2021yja is well fit by a large radius model during its
full evolution, but misses the rise by several magnitudes. The large radius
fit is also noted by Hosseinzadeh et al. (2022), that fit the spherical phase
model of Sapir & Waxman (2017) and acquire very similar parameters, but their
fit matches the rise at early times due to lacking an accurate description of
the planar phase. A similar case is demonstrated in Fig. 15.

  3. 3.

These SNe are the result of a breakout from the edge of a shell of dense CSM
on a several hours timescale, and the early (few days) light curve is
characterized by the subsequent cooling. The intrinsic timescale (i.e.,
ignoring light travel time) for shock breakout from any spherical density
profile is $\frac{\Delta R}{v}=\frac{c}{v_{bo}^{2}\,\kappa\,\rho_{bo}}$
$\Delta R$ is the width of the breakout shell, and $v_{bo},\rho_{bo}$ are the
velocity and density at breakout (Waxman & Katz, 2017, and references
therein). A shock breakout in a slowly declining and extended density profile
will be characterized by a density of $\lesssim 10^{-12}\,\rm{g\,cm}^{-3}$ and
occur on a few days timescale. This is likely what occurred during the
explosions of SN 2020pni and more recently for SN 2023ixf (Zimmerman et al.,
2023), where a rise in temperature was observed during the first few days. In
both cases, breakout occurred from a shell of dense CSM confined to $<2\times
10^{14}$ cm. If the mass of this shell is higher, breakout will occur at the
edge of the shell at densities of $\rho_{bo}\sim 10^{-11}\,\rm{g\,cm}^{-3}$,
resulting in an hours long breakout which will power the optical rise. Since
we do not include breakout in our modelling (assumed to occur before
observations began) the early time light curve will be missed by the fit.
After breakout, the cooling should still evolve according to the predictions
of spherical or planar phase shock cooling, which are insensitive to the exact
shape of the density profile (Sapir et al., 2011; Rabinak & Waxman, 2011;
Sapir & Waxman, 2017). The parameter inference will likely be wrong in this
case, since cooling is measured relatively to the peak of breakout. A delay of
$\delta t_{\rm d}=0.12\frac{\Delta R}{10^{13}\,\rm cm}\frac{v}{10^{9}\,{\rm
cm\,s^{-1}}}^{-1}\rm day$ will result in an increase of $(1+\delta t_{\rm
d})^{1.8}$ in the fit progenitor radius, but will not change the general
conclusion that the radius is large enough to reach such low $\rho_{bo}$. This
scenario is seemingly challenged by the lack of strong association between the
presence of flash ionization features and a large fit radius. However flash
features trace the CSM density profile at $\sim 10^{15}\,\rm cm$ (Yaron et
al., 2017) rather than $R\sim 10^{14}$ cm required for this effect to become
significant. This scenario is consistent with the conclusions of Morozova et
al. (2018), who fit a grid of hydrodynamical models of progenitors surrounded
by dense CSM at $<10^{14}$ cm, and found that they are consistent with the
light curves of observed Type II SNe, with breakout occurring at the edge of
the dense CSM.

Similarly to the heating defining the extended breakout of the II-H category,
an optical rise while the temperature is heating is the unambiguous marker of
an increase in the bolometric luminosity, expected only during breakout
itself. Observing or ruling out such heating during the first day of the
explosion through high-cadence UV-optical observations thus has the potential
to resolve any remaining ambiguity regarding SNe in the II-C- group, since all
three options presented above have different predictions for the breakout
pulse itself:

  1. 1.

The breakout pulse occurs at densities of $\sim 10^{-9}\,\rm{g\,cm}^{-3}$. The
breakout duration is likely dominated by the light travel time, lasting
minutes to an hour. Breakout will likely peak at tens of eV.

  2. 2.

The breakout pulse occurs at densities of $\sim 10^{-9}\,\rm{g\,cm}^{-3}$. The
asymmetric nature of the breakout shell caused a smearing of the breakout to a
timescale of a few hours. Locally, the width of the shock transition is still
similar, so that breakout would still likely peak at tens of eV.

  3. 3.

The breakout pulse occurs at densities of $\lesssim
10^{-11}\,\rm{g\,cm}^{-3}$. The low density causes the intrinsic breakout
timescale to last a few hours, dominating over the light travel time. Locally,
the width of the shock transition is large, so that breakout might be peaking
at $\sim 10$ eV, and could contribute significantly to the optical during the
early rise. No additional short duration pulse can be observed.

####  5.1.2 The intrinsic progenitor radius distribution

To connect the observed parameter distribution to the intrinsic progenitor
radius distribution, we account for the selection effects and biases
introduced by our observation strategy and the dependence of the luminosity on
the breakout radius. We calculate model light curves for the sample of RSG of
Davies et al. (2018). We calculated the radii from the observed effective
temperatures and luminosities, and generate a set of light curves with a
velocity parameter $v_{s*,8.5}$ in the range $0.5-1.5$, with the rest of the
model parameters set to unity and assuming no host or galactic extinction
along the line of sight. We test what fraction of the models is recovered by
our observation strategy as a function of distance, demanding a blue color
($g-r<0\,$mag) at $t=1$ day, and the object brighter than $19.5\,$mag at the
same time, which is the typical brightness limiting our ability to classify
the object as an SN II, a criterion for followup in our program. We repeat
this analysis for an ULTRASAT strategy - demanding an optical brightness above
19.5 mag at peak for spectroscopic classification, and that the light curve is
higher than the limiting magnitude of $22.5\,$mag at 1d (Shvartzvald et al.,
2023).

We find that as the distance increases above $70$ Mpc, we are increasingly
biased towards higher progenitor radii. In panel (a) of Fig. 18, we show the
fraction of RSG explosions recovered as a function of distance with each
strategy, and histogram of the distances of our sample. In panel (b), we show
the mean radius of the recovered sample, as a function of distance. In panel
(c), we show the posterior distribution of the SNe radius above and below a
distance of 70 Mpc. The radius posterior distribution of closer SNe is highly
skewed towards radii below $1000R_{\odot}$, while the distribution of SNe at
larger distances is skewed to values above $1000R_{\odot}$.

We correct the Malmquist bias following the treatment of Rubin et al. (2016).
For each point in the posterior sample, we calculate a weight factor
$w_{i}=\frac{D_{i}^{3}}{\sum_{j}D_{j}^{-3}}$ where
$M_{i}+17=5\log(\frac{D_{i}^{*}}{/10\,\rm pc})$. We show the resulting
corrected posterior distribution in Fig. 18 panel (d), along with the
unweighted distribution and the distribution of RSG radii of Davies et al.
(2018). The error bars are calculated by bootstrapping the posterior
distribution: for every realization, we recalculate the posterior for 33 SNe
randomly sampled from the list of SNe with viable fits, while allowing for
repetition. We repeat this process 500 times and plot the mean and standard
deviation on each bin of the histogram.

Our analysis shows that even if most ($67^{+9}_{-5}\%$) of the observed SNe
have large ($R>1200\,R_{\odot}$) breakout radii, the breakout radius
distribution would be consistent with the observed RSGs radius distribution
($R<1200\,R_{\odot}$) in $69^{+13}_{-26}\%$ of SNe II explosions. Hinds et al.
(in prep.) will analyze the optical light curves of SNe II in the magnitude-
limited BTS survey, and reaches a similar conclusion. We further note that for
SNe with a CSM breakout such as SN 2020pni or SN 2023ixf, a breakout radius of
$\sim 1500-3000\,R_{\odot}$ is needed to explain the breakout timescale and
would be consistent with the distribution we report here (Zimmerman et al.,
2023). In the case of SN 2023ixf, constraints on the SN progenitor from pre-
explosion data confirms a dusty shell at a similar radius (e.g., Qin et al.,
2023). This supports the the idea that SNe II-C- have large radii due to a
shell of CSM from which shock breakout occurs.

###  5.2 X-ray emission and constraints on extended CSM density

Following SN shock breakout, the accelerated ejecta will expand into the
surrounding optically thin CSM, acting as a piston and creating a shock in the
CSM. For typical CSM densities, this shock is expected to be collisionless,
heat the gas to $\sim 100$ keV temperatures and produce X-ray emission
(Fransson et al., 1996; Katz et al., 2011; Chevalier & Irwin, 2012; Svirski et
al., 2012; Ofek et al., 2014). In $\S$ 3.3, we reported the XRT detections and
upper limits at the SN location, binned over the duration of the Swift
observations (typically $\sim 10,000$ ks). The limits we acquire are several
orders of magnitude deeper than the optical emission, reaching as deep as few
SNe II previously detected by XRT. SN 2005cs (Brown et al., 2007), SN 2006bp
(Brown et al., 2007), SN 2012aw (Immler & Brown, 2012), SN 2013ej (Margutti et
al., 2013), and recently SN 2023ixf (Grefenstette et al., 2023).

In Fig. 19, we show a histogram of the limits ratio of X-ray to UV-optical
emission at the same times (transparent bars), and the 4 detections we report
(vertical red lines with shaded error bars). Our limits range between
$10^{-1}-10^{-4}$ of the optical emission, and the highest detection is $\sim
10^{-2}$. In $\S$ 4.3.2, we derived constraints on the velocity profiles of
the SN ejecta through UV-optical light curve fitting. The photon arrival
weighted time of our detections (as well as those in the literature) typically
correspond to a few days after explosion - probing the forward shock emission
in the extended CSM around the progenitor star at $(0.5-2)\times 10^{15}\,\rm
cm$. We can use these to constrain the CSM density at $\sim 10^{15}$ cm and
subsequently constrain the mass-loss of the progenitor star prior a few years
prior to explosion.

At a time $t$, a constant velocity shock moving through an optically thin CSM
with $v_{s,csm}$ will sweep up a mass:

$\frac{M_{CSM}}{M_{\odot}}=2.7\times 10^{-4}\,v_{s,csm,9}t_{5d}\rho_{o,-16}$
(1)

where
$v_{s,csm,9}=\frac{v_{s,csm}}{10^{9}\,\text{cm\,}\text{s}^{-1}}$,$t_{5d}=\frac{t_{xray}}{5\,\text{d}}$
and $\rho_{o,-16}=\frac{\rho_{o}(r=10^{15}\,\rm
cm)}{10^{-16}\,\text{g\,}\text{cm}^{-3}}$. To find the velocity $v_{s,csm}$ we
assume it is well approximated by the velocity of the piston (the ejected
envelope) at equal mass to the swept of CSM. This is given through the
profiles of Rabinak & Waxman (2011). Following their notation (their equations
3. and 4.) we find:

$\delta_{m,piston}=\frac{M_{csm}}{M_{tot}}=2.7\times
10^{-4}\frac{f_{\rho}v_{s,csm,9}t_{5d}\rho_{o,-16}}{f_{\rho}M_{\odot}}$ (2)
$v_{s,csm}=v_{f}\left(\delta_{m}=\frac{M_{csm}}{M_{tot}}\right)$ (3)

As long as the fraction $\frac{M_{CSM}}{M_{tot}}$ is larger then the mass
fraction in the breakout shell $\delta_{m,bo}$:

$\frac{v_{s,csm}^{\left(1\right)}}{\text{cm\,}\text{s}^{-1}}=1.5\times
10^{9}\left(\frac{f_{v}}{2}v_{s*,8.5}\right)^{0.9}\left(\frac{t_{5d}\rho_{o,-16}}{f_{\rho}M_{\odot}}\right)^{-0.1}$
(4)

Here we took $f_{v}=\frac{v_{f}}{v_{s}}=2$, which is typically the case for
small $\delta_{m}<0.01$ (Matzner & McKee, 1999). This is in agreement with the
the velocity evolution of Chevalier & Fransson (1994) for a steep post-shock
ejecta density profile, as expected here (see e.g., Waxman & Katz, 2017, and
references therin). If $\frac{M_{csm}}{M_{tot}}<\delta_{m,bo}$ we can assume
$v_{f}=f_{v}v_{s,bo}$ which is the maximum velocity at which breakout occurs.
In this case:

$\frac{v_{s,csm}^{\left(2\right)}}{\text{cm\,}\text{s}^{-1}}=2\times
10^{9}\left(\frac{f_{v}}{2}\right)\left(\kappa_{0.34}f_{\rho}M\right)^{0.13}\left(v_{s*,8.5}\right)^{1.13}R_{13}^{-0.26}$
(5)

so that
$v_{s,csm}=min\left(v_{s,csm}^{\left(1\right)},v_{s,csm}^{\left(2\right)}\right)$.

The total luminosity generated by the collisionless shock is given by
$L\left(t\right)=2\pi\rho_{csm}r^{2}v_{s,csm}^{3}$.

Using the derived $v_{s,csm}$ we find:

$L_{X}=10^{42}\,\rm{erg\,s}^{-1}\times\\\
\begin{cases}2.1\,\rho_{o,-16}^{0.7}v_{s*,8.5}^{2.7}t_{5d}^{-0.3}\left(f_{\rho}M_{\odot}\right)^{0.3}&v_{s,csm}=v_{s,csm}^{\left(1\right)}\\\
0.6\,\rho_{o,-16}\left(\kappa_{0.34}f_{\rho}M_{\odot}\right)^{0.4}\\\
\times\left(v_{s*,8.5}\right)^{3.4}R_{13}^{-0.8}&v_{s,csm}=v_{s,csm}^{\left(2\right)}\end{cases}$
(6)

Using Eq. 6, we convert our constraints on the XRT luminosity to constraints
of the CSM density and mass loss. We assume a Bremsstrahlung spectrum with a
temperature $T=200\mu\,(\frac{v_{s,csm}}{10^{9}\ {\rm cms}^{-1}})^{2}$ keV
(Fransson et al., 1996; Katz et al., 2011), where $\mu$ is the mean particle
weight assumed to be $\mu=0.61$ for an ionized medium with a solar
composition. We then correct the observed XRT luminosity to a bolometric X-ray
luminosity, with correction factors ranging from 2-6 over our sample. We
assume no intrinsic X-ray absorption at the SN site. To estimate the error on
the values, the calculation is repeated for 100 points randomly drawn from the
posterior sample on the shock-cooling light curve fits, and by randomly
drawing points from a Gaussian distribution with a mean and standard deviation
representing the X-ray measurements. We calculate
$\frac{\dot{M}}{M_{\odot}\text{{\rm yr}}^{-1}}=10^{-4}\rho_{o,-16}v_{w,50}$
where $v_{w,50}$ is the CSM velocity in units of $50\,{\rm km\,s}^{-1}$,
assumed to be 1.

We show our constraints in Fig. 20. Here the colored points represent
individual detections, the downward pointing triangles represent upper limits,
and the blue plus stands for the estimate of Grefenstette et al. (2023) for
the mass-loss of SN 2023ixf with a shock velocity arbitrarily chosen to be
$10^{9}\,{\rm cm\,s}^{-1}$, deduced from the absorbing hydrogen column density
between subsequent observations.

There are 2 main systematics involved in our approach. (1) The emission
spectrum of a shock traversing the CSM is highly uncertain, and assuming it
will emit with a temperature equal to the plasma temperature is probably
inaccurate. For example, Grefenstette et al. (2023) found for SN 2023ixf a
temperature of $35^{+22}_{-12}$ keV, which results in a velocity
$v=(0.54^{0.15}_{-0.1})\times 10^{9}\,{\rm cm\,s}^{-1}$ which is lower by at
least a factor of 2 from the observed photospheric velocity of SN 2023ixf
(Zimmerman et al., 2023; Jacobson-Galan et al., 2023). Decreasing the
temperature of the X-ray spectrum from $>120$ keV to $35$ keV would reduce the
bolometric X-ray luminosity by factor $>2$ and subsequently reduce the mass-
loss and density. (2) The intrinsic absorption of the CSM could affect the
emission. In the case of SN 2023ixf, Grefenstette et al. (2023) report an
absorption column density of $2.6\sim 10^{23}$ atoms cm-2 at $t=4$ days, and
$5\sim 10^{22}$ atoms cm-2 at $t=11$ days. Using the NASA Portable,
Interactive Multi-Mission Simulator111111https://heasarc.gsfc.nasa.gov/cgi-
bin/Tools/w3pimms/w3pimms.pl, we estimate our results would change by a factor
of $\times 2$ if $N_{H}=1\times 10^{23}$ cm-2 in the XRT band. Such a value at
the typical photon-weighted XRT observation time would imply a mass loss rate
of $\gtrsim 10^{-4}\,M_{\odot}\,{\rm yr}^{-1}$, indicating this will affect
only a few of the SNe in our sample. Our limits are consistent with the
observed mass-loss of field RSGs (de Jager et al., 1988; Marshall et al.,
2004; van Loon et al., 2005), but lower than inferred through modelling of
narrow “flash-ionization” spectral features, implying mass-loss rates as high
as $10^{-2}M_{\odot}\,{\rm yr}^{-1}$ (Dessart et al., 2017; Boian & Groh,
2019), likely since these methods probe different regions of the CSM density
profile. This is also the case for SN 2023ixf: comparisons of the early time
spectra performed by Jacobson-Galan et al. (2023) and Bostroem et al. (2023a)
to the models of Dessart et al. (2017) indicate a mass-loss rate of
$10^{-3}-10^{-2}\,M_{\odot}\,{\rm yr}^{-1}$, much higher than those inferred
by Grefenstette et al. (2023), probing the extended CSM. The models of Dessart
et al. (2017) introduce a mass-loss rate declining continuously to
$10^{-6}\,M_{\odot}\,{\rm yr}^{-1}$ by $r=10^{15}\ \rm cm$, reflecting a dense
mass-loss region swept up by the shock in the CSM at early times. Thus they
are capable of discriminating between different CSM densities at few
$10^{14}\,$cm.

Since some amount of confined CSM is present in the majority of SNe II (Bruch
et al., 2021) we consider the effect of such dense CSM on our analysis. We
repeat the analysis, but assume that the CSM swept up by the shock at
$t<t_{X}$ has a density profile of $10^{-14}\,{\rm
g\,cm}^{-3}(\frac{r}{10^{15}\,\rm cm})^{-2}$ ($\dot{M}=10^{-3}M_{\odot}\,{\rm
yr}^{-1}$). This weakly decreases $v_{csm}$, and subsequently decreases $L$.
For the majority of the sample, our limits do change by more then $50\%$, and
at most by a factor of 3.

Our results independently support the conclusion that by $\sim 10^{15}$ cm,
the density of the CSM has already declined to typical values observed for RSG
stars, and that regions of dense mass loss are confined to the nearby
environment of the progenitor star, and probing the final year of its
evolution.

Figure 19: The ratio of X-ray to UV-optical emission, measured at the same
times and averaged over the duration of the Swift observations. Upper limits
are shown as a transparent histogram, and the 4 detections we report are shown
using vertical red lines with shaded error bars.
Figure 20: X-ray limits on the extended ($\sim 10^{15}$ cm) CSM density, mass
loss and CSM shock velocity. Black triangles represent upper limits, colored
points are detections from this work, and the blue plus represents the X-ray
constraints of SN 2023ixf from Grefenstette et al. (2023). The extended
$10^{15}$ cm mass-loss is consistent with field RSG levels.
Figure 21: Prediction for the breakout flare signal from a sample of SNe II in
the optical and UV. Panel (a) shows a kernel density estimate (KDE) plot of
the ULTRASAT breakout duration and peak magnitude. Grey points correspond to
the prediction of the best fit cooling light curve. The dashed line shows the
limiting magnitude of the survey binned to varying degree. Panel (b) shows the
same for the TESS bandpass, although the prediction for the breakout pulse
spectrum are less certain in the optical, and should be treated as lower
limits. Our results show it is very difficult to rule out the existence of a
breakout pulse in optical wavelengths alone.
Figure 22: (a) Schematic illustration of the proposed alternatives for early
observations of SNe II. The curves represent possible pre-explosion density
profiles of the envelope and CSM, corresponding to the mass-loss history of
the progenitor in the months before explosion. Depending on the exact
parameters of this profile, the breakout shell can be located in 3 possible
locations. The red star represent a breakout radius at the edge of the stellar
envelope. Since the density is steeply declining, the shock transition region
is narrow, and the duration of breakout will be typically dominated by the
light travel time. The blue star corresponds to a breakout at the edge of a
dense shell of CSM. The density profile is declining steeply, and the breakout
pulse duration can be set either by the light travel time or the shock
crossing time, both lasting hours. The green point corresponds to the third
option, occurring for a minority of cases. Here the density profile is
shallow, and increasing the duration of the breakout pulse to the shock
crossing timescale of a few days. The $r\lesssim 3\times 10^{14}$ cm density
will determine the early light curve and spectra, and the $r\gtrsim 3\times
10^{14}$ cm determines the X-ray emission emerging after the first few days.
(b) The breakout radius for a star with a $500R_{\odot}$ and $1M_{\odot}$
stellar envelope surrounded by varying amounts of CSM confined to $1.5\times
10^{14}\rm cm$. The conversion to mass-loss assumed
$v_{w}=50\,\rm{km\,s}^{-1}$. Increasing the mass of the shell of dense CSM
moves the breakout location from the stellar envelope, to the shallow region
of the dense CSM, and onward to the edge of the dense CSM, if a significant
portion of the envelope was ejected.

###  5.3 Observing shock-breakout and shock-cooling with ULTRASAT

ULTRASAT will conduct a high cadence (5 min) UV survey with a 200 $\rm
deg^{2}$ field of view (FOV). It will detect tens of shock breakout signatures
and hundreds of shock cooling light curves in its first 3 years (Shvartzvald
et al., 2023). The high cadence light curves of ULTRASAT will resolve all
phases of the early SN evolution - shock breakout, planar phase and spherical
phase shock cooling. While spherical shock cooling alone provides constraints
on the progenitor parameters, the planar phase, typically lasting hours, can
discriminate between models more finely. Directly observing the breakout pulse
can provide independent constraints on the breakout radius, and the velocity
of the outermost layers of the ejecta. This can resolve the remaining
ambiguity as to the reason for the systematic deviation from the expected
planar phase in large radii fits. Observing the early UV-optical color of SNe
will discriminate between a light curve rise driven by cooling, following a
stellar edge breakout, or by heating of the ejecta, during an extended shock
breakout in a shallow density profile (examples of the latter including SN
2020pni and SN 2023ixf). For SNe with light curves well matched by a stellar
breakout, the velocity and mass of the breakout shell will be constrained by
the breakout pulse itself (Sapir et al., 2011, 2013).

In combination with X-ray followup and spectral modeling, these can be used to
accurately map the CSM density profile, with each tracer probing a different
segment of the density profile. While there have been some candidate shock-
breakout flares in the optical (Garnavich et al., 2016; Bersten et al., 2018),
some claims have been disputed (Rubin & Gal-Yam, 2017), and the sample of TESS
CCSNe of Vallely et al. (2021), binned to 30-min cadence, show no detection of
breakout flares. Breakout flares are expected to peak in the UV or X-ray, but
the non-LTE spectral shape makes prediction in the optical highly uncertain
(Sapir et al., 2013; Sapir & Halbertal, 2014). While initially the number of
photons produced is not enough to reach thermal equilibrium, the planar phase
temperatures are already close to the equilibrium temperature, and the exact
details of this transition can change the optical light curve by orders of
magnitude. The UV peak, closer to the peak frequency of the emission, is much
better understood.

In order to produce a clear prediction for the ULTRASAT survey based on the
observed sample of SNe II, we calculate the breakout signal in the TESS and in
the UVOT $UVM2$ bandpass ($UVM2$ is chosen since it is closest to the ULTRASAT
bandpass). For every SN we fit in $\S$ 4.3, we use breakout properties
$\rho_{bo}$, and $v_{s,bo}$ to calculate the luminosity and spectrum at
breakout according to the models of Sapir et al. (2011); Katz et al. (2012);
Sapir et al. (2013). We integrate the spectrum and and compute the typical
TESS and ULTRASAT brightness during breakout, and the duration of the expected
breakout. We show the distribution of parameters in Fig. 21. Panel (a) shows a
kernel density estimate (KDE) plot of the ULTRASAT breakout landscape, and
panel (b) shows the expected TESS brightness. We highlight the predictions for
SN 2020fqv and SN 2020nvm, observed by TESS. We stress the optical wavelength
predictions are highly uncertain, and should be treated as lower limits. Our
results are consistent with the entirety of the breakout flares predicted by
our modelling being measured by ULTRASAT, and none of the flares being
observed in the optical wavelengths.

##  6 Conclusions and Summary

  * •

In this paper we have presented the UV-optical photometry of 34
spectroscopically regular SNe II detected in the ZTF survey and followed up by
the Swift telescope within 4 days of explosion. In addition to the UV-optical
data, we report four XRT detections and 3 $\sigma$ upper limits for the rest
of the sample.

  * •

In $\S$ 4.1 we analyze the color evolution in of the sample. We show that
besides SN 2020pni, the rest of our sample had UV-optical colors which are
becoming redder with time across the entire SED, indicating they are cooling.

  * •

We show that the combination of UV, UV-optical and optical colors can be used
as a discriminator between various degree of intrinsic time-dependent
deviations from blackbody and host-galaxy extinction with non-MW extinction
laws. We show there is no preference in UV-optical color for SNe with flash
features, and argue the deviations are consistent with the predictions of
shock cooling models.

  * •

Using the scatter in early time color, we argue our sample has a host
extinction smaller than $E(B-V)=0.2$ mag. Subsequently, we show we can measure
the extinction of highly extinguished SNe to better than $0.2$ mag. The
average early time colors of the SNe in our sample are provided in Table 5.

  * •

In $\S$ 4.2 we fit the SEDs of the SNe in our sample at the times of UVOT
observations to a blackbody, and recover the evolution of their blackbody
radius and temperature. We show that the evolution of these parameters is in
excellent agreement with the predictions of spherical phase shock cooling,
with a statistically significant difference in the average temperature and
radius between object with and without flash features. We also show at least
30% of the objects in our sample are more luminous than expected from an
envelope breakout with $R<10^{14}$ cm- indicating a larger progenitor radius
or a higher shock velocity parameter relative to generic expectations.

  * •

Motivated by the good agreement with the predictions of spherical phase shock-
cooling, we present a method to fit the light curves to latest shock-cooling
models in $\S$ 4.3.1, accounting for deviations from blackbody over a large
range of parameters, and interpolating between the planar and spherical phase
of shock cooling. We demonstrate this method is unbiased when fitting the MG
simulations of M23, although these have correlated residuals. We demonstrate
that we can recover the breakout radius $R_{*}$, the shock velocity parameter
$v_{*,8.5}$ describing the velocity profile in the outer regions of the
ejecta, and the extinction. We show that we cannot recover the envelope mass
$M_{env}$, total mass $M$, or numerical density scaling parameter $f_{\rho}$
using our method.

  * •

Overall we find the early UV-optical light curves of our sample divides into 3
groups. (1) A majority (33/34) of SNe which cool at early times, which we
denote as “II-C”. This group is comprised of (a) SNe that are well fit
throughout their evolution, with radii characteristic of the observed RSG
radius distribution and (b) SNe which are fit by larger radius, more luminous
models and which systematically miss the early ($<$1d) rise. We denote these
as “II-C+” and “II-C-” respectively. (2) The third group is represented by a
single object in our sample (SN 2020pni), which is heating in the first few
days. A similar evolution has been observed for the nearby SN 2023ixf. We
denote these as “II-H”.

  * •

As we have demonstrated that there is no bias in our fitting method, we argue
this reflects a physical difference from an idealized breakout from a
polytropic envelope. We speculate this difference could be related to the
presence of CSM or an asymmetric shock breakout. We assume the inference of
large radii is real, and show that while most of the sample is characterized
by a large radius, this is due to a luminosity bias affecting our sample at
distance $>70$ Mpc. We show the volume corrected probability peaks at radii
similar to those of field RSG. We conclude that while $71^{+7}_{-4}\%$ of
observed SNe II are over luminous, with a large radius, the majority
($66^{+11}_{-22}\%$) of exploding RSG have a typical radius at explosion.
Since some objects in our sample are also consistent with a smaller radius,
this should be treated as a lower limit.

  * •

Using the X-ray limits and the constraints on the velocity profile of the
ejecta from the light curve fitting, we derive limits on the CSM density at
$0.5-2\times 10^{15}$ cm from the progenitor star, which constrains the mass
loss of the progenitors $\sim 3-15$ yrs before the explosion assuming a
$50\,\rm{km\,s}^{-1}$ winds. We show the limits and detection are
systematically lower than the required mass-loss to explain flash ionization
features, supporting the conclusion that these stars undergo increased mass-
loss in the final months before explosion. Uncertainties in the spectral shape
of the X-ray emission, the amount of CSM below $10^{14}$ cm, and absorption in
the CSM will change this result by less than an order of magnitude.

  * •

In $\S$ 5.3 we study the predictions of the fit parameter distribution to the
landscape of shock breakout flares for the ULTRASAT mission and high-cadence
optical missions such as TESS. We argue the non-detections of breakout flares
in the optical surveys is to be expected, and that observations with ULTRASAT
should indeed easily discover the breakout flares from an analogues sample to
ours.

  * •

By combining our constraints on the breakout radius and the extended CSM
density, we propose a scenario that explains all three groups in our sample in
a single framework. By varying the amount of CSM lost in the last year, the
breakout radius, duration and temperature change. If a small amount of mass
($\lesssim 10^{-3}\,M_{\odot}$) is lost, breakout will occur at the stellar
envelope. Its characteristic duration will be minutes to an hour and will peak
in the extreme UV. This scenario can explain most SNe II-C+. If the star loses
most of its envelope ($\gtrsim 0.1\,M_{\odot}$), breakout will occur at the
edge of the dense CSM. The characteristic breakout duration will be hours
long, and can contaminate the early light curves as it will peak in the far
UV. This scenario will explain most II-C-. If the SN loses $\sim
0.01\,M_{\odot}$ during the last year, breakout will occur in the dense CSM.
Such a breakout will be occur over a timescale of a few days, during which a
heating of the breakout region and an increase in luminosity will be observed
as the breakout pulse is released, with an SED peaking in the near UV. This
scenario will account for SNe II-H. This framework is schematically summarized
in Fig. 22.

##  7 Data Availability

All data used in this paper will be made available via
WISeREP121212https://www.wiserep.org (Yaron & Gal-Yam, 2012). We make all
figures of all light curve fits and light curve plots available as online
figures through the journal website upon publication.

##  8 Acknowledgements

Software: Astropy (Astropy Collaboration et al., 2013, 2018), IPython (Perez &
Granger, 2007), Matpotlib (Hunter, 2007), Numpy (Oliphant, 2006), Scipy
(Virtanen et al., 2020), exctinction (Barbary, 2016), dynesty (Skilling, 2004,
2006; Feroz et al., 2009; Higson et al., 2019; Speagle, 2020) GROWTH marshal
(Kasliwal et al., 2019), Fritz/SkyPortal (van der Walt et al., 2019; Coughlin
et al., 2023), SWarp (Bertin, 2010)

Facilities: Neil Gehrels Swift Observatory, P48, Swift(UVOT, XRT), P60 (RC),
Liverpool telescope (IO:O)

We thank Doron Kushnir, Barak Zackay and Boaz Katz for their insights on the
analysis. We are grateful to the staff at the various observatories where data
were obtained. This work made use of data supplied by the UK Swift Science
Data Centre at the University of Leicester.

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 M. J. Graham). The SED Machine at Palomar
Observatory is based upon work supported by the NSF under grant 1106171. The
Gordon and Betty Moore Foundation, through both the Data-Driven Investigator
Program and a dedicated grant, provided critical funding for SkyPortal.

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 Astrofísica de Canarias with financial support from the UK
Science and Technology Facilities Council. Partly based on observations made
with the Nordic Optical Telescope, operated at the Observatorio del Roque de
los Muchachos.

This research has made use of the Spanish Virtual Observatory
(https://svo.cab.inta-csic.es) project funded by
MCIN/AEI/10.13039/501100011033/ through grant PID2020-112949GB-I00 A.G-Y.’s
research is supported by the EU via ERC grant 725161, the ISF GW excellence
center, an IMOS space infrastructure grant and BSF/Transformative and GIF
grants, as well as the André Deloro Institute for Advanced Research in Space
and Optics, The Helen Kimmel Center for Planetary Science, the
Schwartz/Reisman Collaborative Science Program and the Norman E Alexander
Family Foundation ULTRASAT Data Center Fund, Minerva and Yeda-Sela; A.G.-Y. is
the incumbent of the Arlyn Imberman Professorial Chair. E. Waxman’s research
is partially supported by grants from the ISF, Norman E Alexander Family M
Foundation ULTRASAT Data Center, Nella and Leon Benoziyo Center for
Astrophysics, Schwartz Reisman Institute for Theoretical Physics, and by the
Max Planck Professorial Chair of Quantum Physics.E.O.O. is grateful for the
support of grants from the Benozio center, Willner Family Leadership
Institute, Ilan Gluzman (Secaucus NJ), Madame Olga Klein - Astrachan, Minerva
foundation, Israel Science Foundation, BSF-NSF, Israel Ministry of Science,
Yeda-Sela, and Weizmann-MIT, and the Rosa and Emilio Segre Research Award.

,

## References

  * Arcavi et al. (2011) Arcavi, I., Gal-Yam, A., Yaron, O., et al. 2011, ApJ, 742, L18
  * 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
  * Barbary (2016) Barbary, K. 2016, extinction v0.3.0, doi:10.5281/zenodo.804967
  * Baron et al. (2000) Baron, E., Branch, D., Hauschildt, P. H., et al. 2000, The Astrophysical Journal, 545, 444
  * Bellm et al. (2019) Bellm, E. C., Kulkarni, S. R., Graham, M. J., et al. 2019, Publications of the Astronomical Society of the Pacific, 131, 018002
  * Ben-Ami et al. (2014) Ben-Ami, S., Gal-Yam, A., Mazzali, P. A., et al. 2014, The Astrophysical Journal, 785, 37
  * Bersten et al. (2018) Bersten, M. C., Folatelli, G., García, F., et al. 2018, Nature, 554, 497
  * Bertin (2010) Bertin, E. 2010, SWarp: Resampling and Co-adding FITS Images Together, Astrophysics Source Code Library, record ascl:1010.068, ascl:1010.068
  * Blagorodnova et al. (2018) Blagorodnova, N., Neill, J. D., Walters, R., et al. 2018, Publications of the Astronomical Society of the Pacific, 130, 035003
  * Blinnikov et al. (2000) Blinnikov, S., Lundqvist, P., Bartunov, O., Nomoto, K., & Iwamoto, K. 2000, The Astrophysical Journal, 532, 1132
  * Boian & Groh (2019) Boian, I., & Groh, J. H. 2019, A&A, 621, A109
  * Bostroem et al. (2023a) Bostroem, K. A., Pearson, J., Shrestha, M., et al. 2023a, arXiv e-prints, arXiv:2306.10119
  * Bostroem et al. (2023b) Bostroem, K. A., Dessart, L., Hillier, D. J., et al. 2023b, arXiv e-prints, arXiv:2305.01654
  * Breeveld et al. (2011) Breeveld, A. A., Landsman, W., Holland, S. T., et al. 2011, in American Institute of Physics Conference Series, Vol. 1358, Gamma Ray Bursts 2010, ed. J. E. McEnery, J. L. Racusin, & N. Gehrels, 373–376
  * Brown et al. (2007) Brown, P. J., Dessart, L., Holland, S. T., et al. 2007, ApJ, 659, 1488
  * Bruch et al. (2021) Bruch, R. J., Gal-Yam, A., Schulze, S., et al. 2021, ApJ, 912, 46
  * Bruch et al. (2023) Bruch, R. J., Gal-Yam, A., Yaron, O., et al. 2023, ApJ, 952, 119
  * Burrows et al. (2005) Burrows, D. N., Hill, J. E., Nousek, J. A., et al. 2005, Space Sci. Rev., 120, 165
  * Calzetti et al. (2000) Calzetti, D., Armus, L., Bohlin, R. C., et al. 2000, ApJ, 533, 682
  * Cardelli et al. (1989) Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245
  * Cenko et al. (2006) Cenko, S. B., Fox, D. B., Moon, D.-S., et al. 2006, PASP, 118, 1396
  * Chambers et al. (2016) Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, arXiv:1612.05560
  * Chevalier (1992) Chevalier, R. A. 1992, ApJ, 394, 599
  * Chevalier & Fransson (1994) Chevalier, R. A., & Fransson, C. 1994, ApJ, 420, 268
  * Chevalier & Irwin (2011) Chevalier, R. A., & Irwin, C. M. 2011, ApJ, 729, L6
  * Chevalier & Irwin (2012) Chevalier, R. A., & Irwin, C. M. 2012, The Astrophysical Journal Letters, 747, L17
  * Coughlin et al. (2023) Coughlin, M. W., Bloom, J. S., Nir, G., et al. 2023, The Astrophysical Journal Supplement Series, 267, 31
  * Dahiwale & Fremling (2020a) Dahiwale, A., & Fremling, C. 2020a, Transient Name Server Classification Report, 2020-2576, 1
  * Dahiwale & Fremling (2020b) —. 2020b, Transient Name Server Classification Report, 2020-3837, 1
  * Davies et al. (2018) Davies, B., Crowther, P. A., & Beasor, E. R. 2018, Monthly Notices of the Royal Astronomical Society, 478, 3138
  * Davies et al. (2013) Davies, B., Kudritzki, R.-P., Plez, B., et al. 2013, ApJ, 767, 3
  * de Jager et al. (1988) de Jager, C., Nieuwenhuijzen, H., & van der Hucht, K. A. 1988, A&AS, 72, 259
  * Deckers et al. (2021) Deckers, M., Prentice, S., Maguire, K., et al. 2021, Transient Name Server Classification Report, 2021-1376, 1
  * Dekany et al. (2020) Dekany, R., Smith, R. M., Riddle, R., et al. 2020, PASP, 132, 038001
  * Delgado et al. (2021) Delgado, M., Galbany, L., Gonzalez, R., Munoz, S., & Zimmerman, E. 2021, Transient Name Server Classification Report, 2021-202, 1
  * Dessart & Hillier (2019) Dessart, L., & Hillier, D. J. 2019, A&A, 625, A9
  * Dessart et al. (2017) Dessart, L., Hillier, D. J., & Audit, E. 2017, A&A, 605, A83
  * Efron & Tibshirani (1993) Efron, B., & Tibshirani, R. J. 1993, An Introduction to the Bootstrap, Monographs on Statistics and Applied Probability No. 57 (Boca Raton, Florida, USA: Chapman & Hall/CRC)
  * Evans et al. (2007) Evans, P. A., Beardmore, A. P., Page, K. L., et al. 2007, A&A, 469, 379
  * Evans et al. (2009) —. 2009, MNRAS, 397, 1177
  * Faran et al. (2017) Faran, T., Nakar, E., & Poznanski, D. 2017, Monthly Notices of the Royal Astronomical Society, 473, 513
  * Feroz et al. (2009) Feroz, F., Hobson, M. P., & Bridges, M. 2009, MNRAS, 398, 1601
  * Fransson et al. (1996) Fransson, C., Lundqvist, P., & Chevalier, R. A. 1996, ApJ, 461, 993
  * Fremling et al. (2016) Fremling, C., Sollerman, J., Taddia, F., et al. 2016, A&A, 593, A68
  * Fremling et al. (2020) Fremling, C., Miller, A. A., Sharma, Y., et al. 2020, ApJ, 895, 32
  * Förster et al. (2018) Förster, F., Moriya, T. J., Maureira, J. C., et al. 2018, Nature Astronomy, 2, 808, number: 10 Publisher: Nature Publishing Group
  * Gal-Yam (2017) Gal-Yam, A. 2017, in Handbook of Supernovae, ed. A. W. Alsabti & P. Murdin (Springer International Publishing AG), 195
  * Gal-Yam et al. (2007) Gal-Yam, A., Leonard, D. C., Fox, D. B., et al. 2007, ApJ, 656, 372
  * Gal-Yam et al. (2011) Gal-Yam, A., Kasliwal, M. M., Arcavi, I., et al. 2011, ApJ, 736, 159
  * Gal-Yam et al. (2014) Gal-Yam, A., Arcavi, I., Ofek, E. O., et al. 2014, Nature, 509, 471
  * Gal-Yam et al. (2022) Gal-Yam, A., Bruch, R., Schulze, S., et al. 2022, Nature, 601, 201
  * Gall et al. (2015) Gall, E. E. E., Polshaw, J., Kotak, R., et al. 2015, A&A, 582, A3
  * Ganot et al. (2022) Ganot, N., Ofek, E. O., Gal-Yam, A., et al. 2022, The Astrophysical Journal, 931, 71
  * Garnavich et al. (2016) Garnavich, P. M., Tucker, B. E., Rest, A., et al. 2016, The Astrophysical Journal, 820, 23
  * Gehrels et al. (2004) Gehrels, N., Chincarini, G., Giommi, P., et al. 2004, ApJ, 611, 1005
  * Goldberg et al. (2019) Goldberg, J. A., Bildsten, L., & Paxton, B. 2019, The Astrophysical Journal, 879, 3
  * Goldberg et al. (2022a) Goldberg, J. A., Jiang, Y.-F., & Bildsten, L. 2022a, The Astrophysical Journal, 929, 156
  * Goldberg et al. (2022b) —. 2022b, The Astrophysical Journal, 933, 164
  * González-Gaitán et al. (2015) González-Gaitán, S., Tominaga, N., Molina, J., et al. 2015, Monthly Notices of the Royal Astronomical Society, 451, 2212
  * Graham et al. (2019) Graham, M. J., Kulkarni, S. R., Bellm, E. C., et al. 2019, PASP, 131, 078001
  * Grefenstette et al. (2023) Grefenstette, B. W., Brightman, M., Earnshaw, H. P., Harrison, F. A., & Margutti, R. 2023, ApJ, 952, L3
  * Hachinger et al. (2009) Hachinger, S., Mazzali, P. A., Taubenberger, S., Pakmor, R., & Hillebrandt, W. 2009, MNRAS, 399, 1238
  * HI4PI Collaboration et al. (2016) HI4PI Collaboration, Ben Bekhti, N., Flöer, L., et al. 2016, A&A, 594, A116
  * Higson et al. (2019) Higson, E., Handley, W., Hobson, M., & Lasenby, A. 2019, Statistics and Computing, 29, 891
  * Hillier & Dessart (2019) Hillier, D. J., & Dessart, L. 2019, A&A, 631, A8
  * Hiramatsu et al. (2020) Hiramatsu, D., Arcavi, I., Zimmerman, E., et al. 2020, Transient Name Server Classification Report, 2020-1922, 1
  * Hiramatsu et al. (2023) Hiramatsu, D., Tsuna, D., Berger, E., et al. 2023, arXiv e-prints, arXiv:2307.03165
  * Ho et al. (2019) Ho, A. Y. Q., Goldstein, D. A., Schulze, S., et al. 2019, ApJ, 887, 169
  * Hosseinzadeh et al. (2018) Hosseinzadeh, G., Valenti, S., McCully, C., et al. 2018, The Astrophysical Journal, 861, 63
  * Hosseinzadeh et al. (2022) Hosseinzadeh, G., Kilpatrick, C. D., Dong, Y., et al. 2022, ApJ, 935, 31
  * Hosseinzadeh et al. (2023) Hosseinzadeh, G., Farah, J., Shrestha, M., et al. 2023, ApJ, 953, L16
  * Hunter (2007) Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90
  * Immler & Brown (2012) Immler, S., & Brown, P. J. 2012, The Astronomer’s Telegram, 3995, 1
  * Itagaki (2023) Itagaki, K. 2023, Transient Name Server Discovery Report, 2023-1158, 1
  * Jacobson-Galán et al. (2022) Jacobson-Galán, W. V., Dessart, L., Jones, D. O., et al. 2022, ApJ, 924, 15
  * Jacobson-Galan et al. (2023) Jacobson-Galan, W. V., Dessart, L., Margutti, R., et al. 2023, arXiv e-prints, arXiv:2306.04721
  * Jones et al. (2021) Jones, D. O., Foley, R. J., Narayan, G., et al. 2021, ApJ, 908, 143
  * Kasliwal et al. (2019) Kasliwal, M. M., Cannella, C., Bagdasaryan, A., et al. 2019, PASP, 131, 038003
  * Katz et al. (2013) Katz, B., Kushnir, D., & Dong, S. 2013, arXiv:1301.6766
  * Katz et al. (2011) Katz, B., Sapir, N., & Waxman, E. 2011, arXiv e-prints, arXiv:1106.1898
  * Katz et al. (2012) —. 2012, ApJ, 747, 147
  * Khazov et al. (2016) Khazov, D., Yaron, O., Gal-Yam, A., et al. 2016, ApJ, 818, 3
  * Kulkarni (2013) Kulkarni, S. R. 2013, The Astronomer’s Telegram, 4807, 1
  * Law et al. (2009) Law, N. M., Kulkarni, S. R., Dekany, R. G., et al. 2009, Publications of the Astronomical Society of the Pacific, 121, 1395
  * Margutti et al. (2013) Margutti, R., Chakraborti, S., Brown, P. J., & Sokolovsky, K. 2013, The Astronomer’s Telegram, 5243, 1
  * Marshall et al. (2004) Marshall, J. R., van Loon, J. T., Matsuura, M., et al. 2004, MNRAS, 355, 1348
  * Masci et al. (2019) Masci, F. J., Laher, R. R., Rusholme, B., et al. 2019, Publications of the Astronomical Society of the Pacific, 131, 018003
  * Matzner & McKee (1999) Matzner, C. D., & McKee, C. F. 1999, The Astrophysical Journal, 510, 379
  * Modjaz et al. (2019) Modjaz, M., Gutiérrez, C. P., & Arcavi, I. 2019, Nature Astronomy, 3, 717
  * Morag et al. (2023) Morag, J., Irani, I., Sapir, N., & Waxman, E. 2023, arXiv e-prints, arXiv:2307.05598
  * Morag et al. (2022) Morag, J., Sapir, N., & Waxman, E. 2022, arXiv e-prints, arXiv:2207.06179
  * Morozova et al. (2018) Morozova, V., Piro, A. L., & Valenti, S. 2018, The Astrophysical Journal, 858, 15
  * Mould et al. (2000) Mould, J. R., Huchra, J. P., Freedman, W. L., et al. 2000, ApJ, 529, 786
  * Nakar & Sari (2010) Nakar, E., & Sari, R. 2010, ApJ, 725, 904
  * Nugent et al. (2011) Nugent, P. E., Sullivan, M., Cenko, S. B., et al. 2011, Nature, 480, 344
  * Ofek et al. (2010) Ofek, E. O., Rabinak, I., Neill, J. D., et al. 2010, ApJ, 724, 1396
  * Ofek et al. (2014) Ofek, E. O., Zoglauer, A., Boggs, S. E., et al. 2014, ApJ, 781, 42
  * Oliphant (2006) Oliphant, T. 2006, Guide to NumPy
  * Perez & Granger (2007) Perez, F., & Granger, B. E. 2007, Computing in Science and Engineering, 9, 21
  * Perley (2019) Perley, D. 2019, Transient Name Server Classification Report, 2019-2715, 1
  * Perley et al. (2020) Perley, D. A., Taggart, K., Dahiwale, A., & Fremling, C. 2020, Transient Name Server Classification Report, 2020-2086, 1
  * Perley et al. (2020) Perley, D. A., et al. 2020, Astrophys. J., 904, 35
  * Perley et al. (2022) Perley, D. A., Sollerman, J., Schulze, S., et al. 2022, ApJ, 927, 180
  * Pessi et al. (2020) Pessi, P., Anderson, J., Gutierrez, C., & Irani, I. 2020, Transient Name Server Classification Report, 2020-3798, 1
  * Phillips et al. (1999) Phillips, M. M., Lira, P., Suntzeff, N. B., et al. 1999, AJ, 118, 1766
  * Piro (2015) Piro, A. L. 2015, ApJ, 808, L51