11institutetext: Instituto de Astrofísica de La Plata (IALP), CCT-CONICET-
UNLP. Paseo del Bosque S/N, B1900FWA, La Plata, Argentina
11email<EMAIL_ADDRESS>22institutetext: Facultad de
Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo
del Bosque S/N, B1900FWA, La Plata, Argentina 33institutetext: Universidad
Nacional de Río Negro. Sede Andina, Mitre 630 (8400) Bariloche, Argentina
44institutetext: Kavli Institute for the Physics and Mathematics of the
Universe (WPI), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba
277-8583, Japan 55institutetext: European Southern Observatory, Alonso de
Córdova 3107, Casilla 19, Santiago, Chile 66institutetext: Vice President and
Head of Mission of AURA-O in Chile, Avda. Presidente Riesco 5335 Suite 507,
Santiago, Chile 77institutetext: Hagler Institute for Advanced Studies, Texas
A&M University, College Station, TX 77843, USA 88institutetext: CENTRA-Centro
de Astrofísica e Gravitaçäo and Departamento de Física, Instituto Superio
Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001 Lisboa,
Portugal 99institutetext: Department of Physics and Astronomy, Aarhus
University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark 1010institutetext:
Carnegie Observatories, Las Campanas Observatory, Casilla 601, La Serena,
Chile 1111institutetext: Finnish Centre for Astronomy with ESO (FINCA),
FI-20014 University of Turku, Finland 1212institutetext: Tuorla Observatory,
Department of Physics and Astronomy, FI-20014 University of Turku, Finland
1313institutetext: Observatories of the Carnegie Institution for Science, 813
Santa Barbara St., Pasadena, CA 91101, USA 1414institutetext: Institute for
Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
1515institutetext: Department of Astronomy, University of California, 501
Campbell Hall, Berkeley, CA 94720-3411, USA. 1616institutetext: Data and
Artificial Intelligence Initiative, Faculty of Physical and Mathematical
Sciences, University of Chile 1717institutetext: Centre for Mathematical
Modelling, Faculty of Physical and Mathematical Sciences, University of Chile
1818institutetext: Millennium Institute of Astrophysics, Chile.
1919institutetext: Department of Astronomy, Faculty of Physical and
Mathematical Sciences, University of Chile 2020institutetext: Institute of
Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, E-08193
Barcelona, Spain. 2121institutetext: Department of Physics, Florida State
University, 77 Chieftan Way, Tallahassee, FL 32306, USA 2222institutetext:
Consejo Nacional de Investigaciones Científicas y Tećnicas (CONICET),
Argentina. 2323institutetext: George P. and Cynthia Woods Mitchell Institute
for Fundamental Physics and Astronomy, Department of Physics and Astronomy,
Texas A&M University, College Station, TX 77843

# Type II supernovae from the Carnegie Supernova Project-I

I. Bolometric light curves of 74 SNe II using $uBgVriYJH$ photometry

L. Martinez 112233 M. C. Bersten 112244 J. P. Anderson 55 M. Hamuy 6677 S.
González-Gaitán 88 M. Stritzinger 99
M. M. Phillips 1010 C. P. Gutiérrez 11111212 C. Burns 1313 C. Contreras 1010
T. de Jaeger 14141515 K. Ertini 1122 G. Folatelli 112244
F. Förster 1616171718181919 L. Galbany 2020 P. Hoeflich 2121 E. Y. Hsiao 2121
N. Morrell 1010 M. Orellana 332222 P. J. Pessi 2255
N. B. Suntzeff 2323

(Received XXX; accepted XXX)

The present study is the first of a series of three papers where we
characterise the type II supernovae (SNe II) from the Carnegie Supernova
Project-I to understand their diversity in terms of progenitor and explosion
properties. In this first paper, we present bolometric light curves of 74 SNe
II. We outline our methodology to calculate the bolometric luminosity, which
consists of the integration of the observed fluxes in numerous photometric
bands ($uBgVriYJH$) and black-body (BB) extrapolations to account for the
unobserved flux at shorter and longer wavelengths. BB fits were performed
using all available broadband data except when line blanketing effects
appeared. Photometric bands bluer than $r$ that are affected by line
blanketing were removed from the fit, which makes near-infrared (NIR)
observations highly important to estimate reliable BB extrapolations to the
infrared. BB fits without NIR data produce notably different bolometric light
curves, and therefore different estimates of SN II progenitor and explosion
properties when data are modelled. We present two methods to address the
absence of NIR observations: (a) colour-colour relationships from which NIR
magnitudes can be estimated using optical colours, and (b) new prescriptions
for bolometric corrections as a function of observed SN II colours. Using our
74 SN II bolometric light curves, we provide a full characterisation of their
properties based on several observed parameters. We measured magnitudes at
different epochs, as well as durations and decline rates of different phases
of the evolution. An analysis of the light-curve parameter distributions was
performed, finding a wide range and a continuous sequence of observed
parameters which is consistent with previous analyses using optical light
curves.

###### Key Words.:

supernovae: general

##  1 Introduction

The Carnegie Supernova Project-I (CSP-I, Hamuy et al. 2006) was a five-year
programme to obtain well-calibrated high-cadence optical and near-infrared
(NIR) light curves (LCs) and optical spectra of every type of supernova (see
e.g. Contreras et al. 2010; Stritzinger et al. 2011; Taddia et al. 2013;
Krisciunas et al. 2017; Stritzinger et al. 2018). The current work is the
first in a series of three papers where the main goal is to analyse a large
sample of type II supernovae (SNe II) observed by the CSP-I in order to
understand SN II diversity in terms of progenitor and explosion properties. In
the present study, we calculate and present the most homogeneous sample of 74
SN II bolometric LCs to date. In the second and third papers in this series,
we fit these bolometric LCs to SN II explosion models. This affords a
characterisation of the progenitor and explosion properties of SNe II
(Martinez et al. 2021b, hereafter Paper II), and an analysis of the underlying
physical parameters defining SN II diversity (Martinez et al. 2021a, hereafter
Paper III).

SNe II are the explosions of massive stars ($\gtrsim$8$-$10 $M_{\odot}$) at
the end of their evolution showing prevalent hydrogen lines in their spectra
(Minkowski 1941). SNe II were initially divided into sub-classes according to
the shape of their LC. SNe II with almost constant luminosity for a few months
are classified as SNe IIP, and those with fast-declining LCs were historically
classified as SNe IIL (Barbon et al. 1979). However, it is now generally
accepted that they belong to a single family as they exhibit a continuous
sequence in their LC decline rates (Anderson et al. 2014b; Sanders et al.
2015; Galbany et al. 2016; Valenti et al. 2016; Rubin & Gal-Yam 2016; de
Jaeger et al. 2019).

Over the years, many subgroups of SNe II have been introduced based on their
spectral and photometric characteristics. SNe IIb show hydrogen lines at early
times that weaken and disappear with time, and seem to be transitional events
between SNe II and SNe Ib (Filippenko et al. 1993, although see Pessi et al.
2019). SNe IIn show narrow emission lines in their spectra and a diversity of
photometric characteristics (e.g. Schlegel 1990; Taddia et al. 2013), possibly
due to an interaction between the ejecta and a dense circumstellar material
(CSM). Meanwhile, the 1987A-like events display typical characteristics of SN
II spectra, but long-rising LCs that resemble that of SN 1987A (e.g. Arnett et
al. 1989; Taddia et al. 2012). The properties of these subgroups are distinct
from the SNe II we focus on in this paper. Therefore, we exclude SNe IIb, IIn,
and 1987A-like from all analyses and use ‘SNe II’ to refer to SNe that would
historically have been classified as SNe IIP or SNe IIL together.

The strong and enduring hydrogen lines in SN II spectra indicate that their
progenitors have retained a significant fraction of their hydrogen-rich
envelope prior to explosion. Indeed, the first models of SNe II (Grassberg et
al. 1971; Falk & Arnett 1977) demonstrate that the LC morphology of slow-
declining SNe II (SNe IIP) can be reproduced assuming a red supergiant (RSG)
progenitor with an extensive hydrogen envelope. More recently, the direct
detections of the progenitor stars of nearby SNe II confirm RSG stars as their
progenitors (e.g. Van Dyk et al. 2003; Smartt 2009).

SNe II are the most common type of SNe in nature (Li et al. 2011; Shivvers et
al. 2017), and their study is closely related to stellar evolution,
nucleosynthesis, and chemical enrichment of the interstellar medium, among
other astrophysical processes. In addition, SNe II have been proposed as
distance indicators (e.g. Kirshner & Kwan 1974; Hamuy & Pinto 2002; Rodríguez
et al. 2014; de Jaeger et al. 2015) and metallicity tracers (Dessart et al.
2014; Anderson et al. 2016; Gutiérrez et al. 2018) which further motivates
their study.

SNe II show a significant diversity in their observed properties. Studies of
large samples have defined several parameters to examine this diversity
finding a continuous sequence within a large range of values for most of the
parameters analysed, including magnitudes, decline rates and durations of
different LC phases (e.g. Anderson et al. 2014b); velocities and pseudo-
equivalent widths of Hα profiles (e.g. Schlegel 1996; Anderson et al. 2014a;
Gutiérrez et al. 2014) in addition to many other spectral lines (e.g.
Gutiérrez et al. 2017a, b); and SN II colours (e.g. de Jaeger et al. 2018, see
also Patat et al. 1994; Hamuy 2003; Faran et al. 2014a, b; González-Gaitán et
al. 2015; Anderson et al. 2016; Gutiérrez et al. 2018; Davis et al. 2019 for
more general studies of SN II diversity).

Efforts have already been made to characterise and analyse the spectral and
photometric properties of the CSP-I SN II sample. Anderson et al. (2014a) and
Gutiérrez et al. (2014) presented a detailed spectroscopic analysis of the Hα
profiles, particularly of the blueshifted emission, velocity, and ratio of
absorption to emission. Moreover, both works searched for correlations between
these spectral parameters and observed parameters of the _V_ -band LCs
(magnitudes, decline rates, and time durations) measured by Anderson et al.
(2014b). A subsequent study was presented in Gutiérrez et al. (2017a, b).
These authors measured expansion velocities and pseudo-equivalent widths for
several spectral lines and analysed correlations between these spectral
properties and the spectral and photometric parameters defined in previous
works. Additionally, de Jaeger et al. (2018) analysed the properties of the
colour curves. These previous works attempted to understand (mostly
qualitatively) observed SN II diversity and correlations through differences
in physical parameters of the explosions. In the present series of papers we
attempt to go a step further and quantitatively derive physical parameters of
SNe II from robustly modelling their data.

This first paper follows a number of previous investigations in the literature
concerning SN II bolometric LCs and their properties (e.g. Bersten & Hamuy
2009; Lyman et al. 2014; Pejcha & Prieto 2015; Lusk & Baron 2017; Faran et al.
2018). In the current study, we present bolometric LCs for 74 SNe II observed
by the CSP-I. Additionally, we outline our bolometric LC creation methodology
and discuss important sources of uncertainty when estimating the bolometric
flux of a SN II. The CSP-I sample comprises high-quality optical ($uBgVri$)
and NIR ($YJH$) photometry homogeneously obtained and processed. The release
of the final CSP-I SN II photometry is presented in Anderson et al. (in
prep.). In the present work, we find that NIR observations are essential for a
reliable calculation of the bolometric luminosity at times later than
$\sim$20$-$30 days after explosion. Therefore, the high-quality LCs and the
considerable amount of NIR data in the CSP-I sample present the opportunity to
calculate the most homogeneous and largest sample of SN II bolometric LCs with
high observational cadence to date. The 74 bolometric LCs from the CSP-I
sample enable new calibrations for bolometric corrections (BCs) as a function
of observed SN II colours from a statistically significant sample. Previous
studies using an approach similar to that used in this paper only employed a
small number of SN II events (Bersten & Hamuy 2009; Lyman et al. 2014).
Furthermore, such a large sample allows a full characterisation of SN II
bolometric LC properties.

The current paper is organised as follows. We give a brief description of the
data sample in Sect. 2. In Sect. 3 we describe the methodology to calculate
bolometric LCs and present them for the entire CSP-I SN II sample. Section 4
presents an analysis of the bolometric LC parameter distributions. New
prescriptions for BCs versus optical colours are presented in Sect. 5.
Finally, some concluding remarks are made in Sect. 6.

##  2 Supernova sample

The data analysed in this study includes 74 SNe II from the CSP-I (Hamuy et
al. 2006, PIs: Phillips and Hamuy; 2004$-$2009). The sample is characterised
by a high cadence and quality of photometric and spectroscopic observations,
and a photometric coverage over a wide wavelength range for most SNe II. The
data set comprises LCs covering optical ($uBgVri$) and NIR ($YJH$) bands, and
optical spectral sequences of nearby SNe II ($z$ $<$ 0.05). A detailed
description of the data reduction and photometric calibration is found in
Hamuy et al. (2006), Contreras et al. (2010), Stritzinger et al. (2011),
Folatelli et al. (2013), and Krisciunas et al. (2017). Release of the final
photometry for the SN II sample is presented in Anderson et al. (in prep.).
Previously, CSP-I SN II  _V-_ band photometry was published by Anderson et al.
(2014b). CSP-I optical spectra were published by Gutiérrez et al. (2017a, b).
LCs, spectra, and colours of these SNe II were already analysed in several
previous papers (Gutiérrez et al. 2014; Anderson et al. 2014a, b, 2016;
Gutiérrez et al. 2017a, b; de Jaeger et al. 2018; Pessi et al. 2019).

The distance of each SN II was taken from Anderson et al. (2014b) except for
SN 2005kh, SN 2009A, and SN 2009aj since these SNe II were not included in
that study. The weighted mean and standard deviation of redshift-independent
distances taken from NED111http://ned.ipac.caltech.edu/ were employed for SN
2005kh and SN 2009A, where only Tully-Fisher estimates are available. In the
case of SN 2009aj, we used the distance from Rodríguez et al. (2020). In
Anderson et al. (2014b) distances were estimated using cosmic-microwave
background corrected recession velocities if this value is higher than 2000 km
s-1, together with an $H_{\rm 0}$ = 73 km s-1 Mpc-1, $\Omega_{m}$ = 0.27, and
$\Omega_{\rm\Lambda}$ = 0.73. Redshift-independent distances taken from NED
were used when recession velocities are lower than 2000 km s-1.

Explosion epochs were taken from Gutiérrez et al. (2017b) with one exception.
In the case of SN 2008bm, the new estimate by Rodríguez et al. (2020) was
used, who include pre-explosion non-detections closer to the SN discovery. It
should be noted that SN 2005gk, SN 2005hd, and SN 2005kh do not allow for
reliable explosion epoch estimates because of the lack of pre-discovery non-
detections and/or spectra. Table LABEL:table:sn_info lists the sample of SNe
II analysed in this work, their distance modulus, explosion epochs, and Milky
Way reddening values.

All magnitudes were first corrected for Milky Way extinction using the values
from Anderson et al. (2014b) and assuming a standard Galactic extinction law
of 3.1 (Cardelli et al. 1989). While there are a number of methods in the
literature to estimate the host-galaxy reddening, such as the Na i D
equivalent width, the Balmer decrement, the strength of the diffuse
interstellar bands, and the $V-I$ colour excess at the end of the plateau
phase (e.g. Hobbs 1974; Munari & Zwitter 1997; Olivares E. et al. 2010), the
accuracy of these methods is unsatisfactory (Phillips et al. 2013; Galbany et
al. 2016, among others) and any attempt to correct for host-galaxy extinction
is uncertain. Therefore, we did not correct for host-galaxy extinction. In
addition, Faran et al. (2014a), Gutiérrez et al. (2017a), and de Jaeger et al.
(2018) show that several correlations between observed parameters are stronger
when host-galaxy extinction correction is not performed, suggesting that such
corrections are simply adding noise to parameter estimations. Gutiérrez et al.
(2017a) and de Jaeger et al. (2018) also suggest that host-galaxy extinction
is relatively small for most SNe II in the current sample. However, some SNe
II within our sample do show particularly red colours (SNe 2005gk, 2005lw,
2007ab, 2007sq, and 2009ao, de Jaeger et al. 2018) and/or high Na I D
absorption equivalent widths (Anderson et al. 2014b) that may imply
significant host-galaxy extinction in those specific cases. In Paper II, we
derive progenitor and explosion properties of the SNe II in CSP-I sample via
hydrodynamical modelling of their bolometric LCs and expansion velocities.
Given our ignorance on the degree of host-galaxy reddening for each SN II, to
account for such effects we included a scale factor to our fitting procedure
through the definition of our priors. This allows for more luminous bolometric
LCs (through the effects of unaccounted host extinction) during the fitting
(see Paper II, for details). Following the above, it is important that any
future user of our published bolometric LCs considers these issues during
their analysis.

##  3 Bolometric light curves

###  3.1 Light-curve phases

Throughout this article we refer to different phases of SN II LCs, so it is
important to provide a clear definition of each phase and a brief discussion
of the underlying physical processes involved. We do so in this section.

When the core of a massive star collapses, a large amount of energy is
deposited in the inner layers of the progenitor and a powerful shock wave
starts to propagate outwards through the star’s envelope. The shock arrives to
the stellar surface and photons begin to diffuse outwards providing the first
electromagnetic signal of the SN. The shock emergence is referred to as the
‘shock breakout’ and it is characterised by the fast increase of the
bolometric luminosity. Although this increase of the flux is expected in all
photometric bands, it is much more significant at short wavelengths – due to
the high temperature of about 105 K – of the outermost ejecta during the
shock-breakout phase (Grassberg et al. 1971; Bersten et al. 2011). As a
consequence, the shock-breakout signal is expected to be detected more easily
in X-ray or ultraviolet (UV) regimes. The combination between the non-
predictability of the explosion and the short duration of the shock-breakout
phase makes its detection extremely difficult with only few claimed cases
(Campana et al. 2006; Soderberg et al. 2008; Garnavich et al. 2016; Bersten et
al. 2018).

The shock breakout is followed by the fast expansion and rapid cooling of the
outermost layers of the ejecta. At these times the bolometric LC declines
rapidly, which we refer to as the cooling phase. During the cooling phase the
bulk of the emission shifts to longer wavelengths increasing the flux in the
optical bands. The duration of this phase is mostly sensitive to the
progenitor size. The increase of early time data has enabled recent studies to
note that the cooling phase is sometimes larger than model predictions (and
rise times to maximum light of optical LCs are shorter, e.g. González-Gaitán
et al. 2015). The presence of additional material close to the progenitor is a
possible solution to this issue. The interaction between the ejecta and a CSM
lost by the progenitor star shortly before core collapse can boost the
bolometric luminosity through the conversion of kinetic energy into radiation
and produce longer cooling phases and shorter rise times in optical LCs
(Morozova et al. 2018). Additionally, the occurrence of such interaction in
many SNe II is supported by the detection of narrow emission lines in very
early spectra suggesting a confined CSM (e.g. Khazov et al. 2016; Yaron et al.
2017; Bruch et al. 2021).

Once the temperature drops to $\sim$6000 K, the LC settles on a phase commonly
known as the ‘plateau’ although the luminosity may not necessarily be
constant. However, in the current work we decide to continue using this term
because it is frequently used in the literature. During the plateau, hydrogen
recombination occurs at different layers of the ejecta as a recombination wave
moves inwards in mass coordinates (Grassberg et al. 1971; Bersten et al.
2011). Hydrogen recombination reduces the opacity (dominated by electron
scattering during this phase) allowing the radiation to escape. In addition,
the plateau phase is also partially powered by the energy released from the
radioactive decay chain of 56Ni $\rightarrow$ 56Co $\rightarrow$ 56Fe (Kasen &
Woosley 2009). The end of the plateau phase is marked by a sharp decline in
luminosity known as the transitional phase. The combination of the above
mentioned phases is also known as optically-thick phase or photospheric phase.
After the transition from the plateau the luminosity is mostly powered by 56Co
decay. This last phase is commonly referred to in the literature as the
radioactive tail.

###  3.2 Bolometric luminosity calculations

Bolometric LCs are extremely useful to constrain models of SN explosions. One
of the goals of this series of papers is to derive physical properties for SNe
II in the CSP-I sample from the modelling of their bolometric LC and expansion
velocities. Therefore, the first step is to calculate reliable bolometric
luminosities for the entire sample.

Two methodologies are often used in the literature to obtain the bolometric
luminosity of SNe. Either the observed flux is integrated over all available
photometric bands in addition to some corrections for the missing flux at
shorter and longer wavelengths, or BCs are used to convert magnitudes in a
certain photometric band (usually $V$\- or $g$-band magnitudes) into
bolometric magnitudes. Bersten & Hamuy (2009) and Lyman et al. (2014) provide
relations of the BC as a function of optical colours during the photospheric
phase of SNe II (see also Pejcha & Prieto 2015). These allow one to easily
calculate bolometric LCs when only optical magnitudes are available. In our
present study, we have a large set of LCs covering both optical and NIR bands
(from $u$ to $H$). Having such a wide wavelength coverage justifies the
calculation of the bolometric luminosity via full integration. In this
context, SN 1987A has one of the most accurate bolometric LCs calculated to
date (Suntzeff & Bouchet 1990) since it was observed from $U$ to far-infrared
bands. These observations allow the estimation of the fraction of the flux
emitted outside the optical bands during the photospheric and radioactive tail
phases, which were used as bolometric corrections to calculate the bolometric
luminosity for other SNe II (e.g. Schmidt et al. 1993; Clocchiatti et al.
1996).

As a first step, we calculated the pseudo-bolometric flux by direct
integration of the broadband data. The pseudo-bolometric flux represents only
the optical and NIR regime of the spectral energy distribution (SED) of the SN
and does not consider the unobserved flux that falls at redder or bluer
wavelengths. Although the radiation that falls beyond the NIR regime is not
expected to contribute significantly to the bolometric flux (at least during
the photospheric phase), it is necessary to take it into account to avoid a
systematic underestimation. Something similar happens on the UV part of the
SED. This region has its major contribution at early times ($\lesssim$ 20 days
after explosion). However, the UV contribution drops as the SN cools and
expands, and peak emission is set into longer wavelengths. The bolometric flux
is then reached by summing the three flux components of the SN II: UV
extrapolation plus optical–NIR integration plus IR extrapolation. We describe
each method in detail in the following subsections. Some of these techniques
were used in Bersten & Hamuy (2009), Lyman et al. (2014), Lusk & Baron (2017),
and Faran et al. (2018). Finally, the flux was transformed into luminosity
using the distances given in Table LABEL:table:sn_info.

####  3.2.1 Pseudo-bolometric flux estimation

Table 1: Coefficients of the polynomial fits to the intrinsic colour
relations.

Colour |  $g-i$ range | $c_{0}$ | $c_{1}$ | $c_{2}$ | $c_{3}$ | rms
---|---|---|---|---|---|---
$i-Y$ | ($-$0.5, 2.4) | 0.35 | 0.27 |  $-$0.11 | 0.06 | 0.10
$i-J$ | ($-$0.5, 2.4) | 0.52 | 0.44 |  $-$0.22 | 0.12 | 0.13
$i-H$ | ($-$0.5, 2.4) | 0.67 | 0.43 |  $-$0.16 | 0.11 | 0.15
222colour = $\sum_{k=0}^{3}c_{k}(g-i)^{k}$, where colour is chosen from column
1. The coefficients are the median of the marginal distributions.

Figure 1: Optical and NIR LCs of SN 2008ag corrected by Milky Way extinction.
The dots are the observed data and the triangles are the interpolated
magnitudes. Solid lines are the re-sampled LCs via Gaussian processes and the
shaded regions represent the 95% confidence intervals of the interpolation.
The error bars of the observed magnitudes are smaller than the dot size.
Figure 2: Colour-colour diagrams for all objects. All measurements were first
corrected for Milky Way extinction. Blue dots indicate different colour
measurements. The solid orange line shows a polynomial fit to the data. Shaded
regions represent the 95% confidence intervals.

CSP-I photometry was obtained in optical ($uBgVri$) and NIR ($YJH$) bands for
most objects. Although the CSP-I sample is characterised by high-cadence
photometry, not all bands ($u$ to $H$) are always available at a given epoch.
To obtain the full set of magnitudes at each epoch of observation we
interpolated the LCs using Gaussian processes. Gaussian processes were
implemented using the python library scikit-learn (Pedregosa et al. 2011).
Interpolated values are confident when observational gaps are small. A good
representation of the missing part of the LC is easier to achieve when the
observed LC is well sampled. In our sample, the largest gap during the
photospheric phase is of the order of 40 days. Something similar occurs during
the radioactive tail phase. However, such large gaps are not common in the
CSP-I data sample as it is characterised by a high cadence of observations.
The average cadence in optical and NIR bands during the photospheric phase is
4.9 and 8.8 days, respectively. These values increase to 16.2 and 12.8 days
during the radioactive tail phase. Given that during the plateau and
radioactive phases the LC changes smoothly, the interpolation was always
assumed to be robust. The most difficult part for the interpolation is the
transition from the plateau to the radioactive tail. During the transition,
the interpolation resembles the behaviour of the LC if observations exist near
both sides of the transition (e.g. Fig. 1). If such observations were not
available we did not interpolate the LCs during the transition to the
radioactive tail. Extrapolations were only used when the re-sampled LCs were
well-behaved and for times less than two days from the first or last epoch of
observation.

CSP-I built a large sample of 74 SNe II where 47 have optical and NIR LCs with
good temporal coverage, which allows a robust interpolation in all bands.
However, 10 out of the 74 SNe II present well-sampled optical LCs, while NIR
LCs are partially sampled (e.g. the temporal coverage of the NIR data is
around half that of the optical LCs), and 17 have scarce or no NIR data at
all. Thus, despite using interpolation, sometimes it is not possible to obtain
a complete set of magnitudes at each epoch for the last two groups,
particularly due to the scarce NIR band coverage. Therefore, it is desirable
to have a method to complete the NIR LCs of those 27 SNe II where NIR data
availability is limited or non-existent (this is shown to be of significant
importance in Sect. 3.2.2).

To obtain NIR magnitudes for SNe II where no such data exist, we developed a
method based on intrinsic optical colours using our whole sample of SNe II.
Once such relationships are established (see below for details), we are able
to predict NIR photometry for events that lack these data, from their optical
colours. For those limiting cases where NIR LCs are partially sampled, we used
the observed and interpolated magnitudes at all possible epochs and the
predicted NIR magnitudes where these data were missing. We used the $g-i$
colour, and related this to $i-Y$, $i-J$, and $i-H$ colours. These colours
were chosen because: (a) _g-_ and _i-_ band LCs are always well sampled during
the entire evolution of the SNe II in CSP-I sample, which allows the use of
these relations in a wide range of $g-i$ colours; and (b) we produced
polynomial fits for several combinations of colours and found that these sets
have the smallest dispersions. Third-order polynomial fits were found to
produce satisfactory results. While higher-order polynomials might represent
the bluest part better, these polynomials miss the reddest end of the
distribution, where the latter is more important for our aims. As we show in
Sect. 3.2.2, NIR observations are crucial at times later than $\sim$30 days
after explosion when SNe II are intrinsically redder than at earlier times.
Polynomial fits were computed using Markov chain Monte Carlo (MCMC) methods
with the python emcee package (Foreman-Mackey et al. 2013). Intrinsic colours
together with the polynomial fits are shown in Fig. 2. The coefficients of the
polynomial shown correspond to the median of the marginal distributions, and
are presented in Table 1. The relationship between $g-i$ and $i-Y$ colours
presents the lowest dispersion about the polynomial fit with a root mean
square (rms) of 0.10 mag. Dispersions of 0.13 and 0.15 mag are found for $i-J$
and $i-H$, respectively.

The above relations are based on observations that may correspond to different
phases of the SN II evolution. Thus, we also tested the colour calibrations
but separating the colours by different phases of the LC evolution: cooling
phase (t ¡ $t_{\rm trans}$), plateau phase ($t_{\rm trans}$ ¡ t ¡ $t_{\rm
PT}$), and radioactive tail phase (t ¿ $t_{\rm PT}$), where $t_{\rm trans}$
corresponds to the time of the transition between the initial decline and the
decline of the plateau, and $t_{\rm PT}$ is the mid-point of the transition
between the optically-thick phase and the radioactive tail (see Anderson et
al. 2014b, and Sect. 4.1 for details). The values of $t_{\rm trans}$ and
$t_{\rm PT}$ were taken from Anderson et al. (2014b). These calibrations are
shown in Fig. 17. We find that the dispersions of these relations are usually
larger than when all colours are taken together. In addition, the continuous
behaviour between different epochs tend to favour the utilisation of the
combined data set. A large fraction of the observations during the tail phase
($\sim$30%) corresponds to only one SN II (SN 2008bk) which has a peculiar
behaviour in the colour curves during this phase evolving in time to bluer
$g-i$ colours and redder ($i-NIR$ magnitude) colours. This is because the
$i$-band LC declines faster (0.014 mag per day) than the $g$-, $Y$-, $J$-, and
$H$-band LCs ($\sim$0.010 mag per day). We explore whether this behaviour is
intrinsic of low-luminosity SNe II, but we do not have data during the tail
phase for other low-luminosity events to generalise such a tendency. No other
SNe II in the sample display such behaviour. However, we remark that our
observations during the radioactive tail are limited and no strong conclusions
can be drawn. The large amount of observations of SN 2008bk and its peculiar
behaviour during the radioactive tail may bias the colour-colour relations at
this phase. Therefore, we choose not to separate our sample in different
phases until more data are obtained in the radioactive tail phase and we
continue to use the complete colour curves without any separation respect to
their LC evolutionary phases (Fig. 2).

We developed a method based on intrinsic optical colours in which we use
polynomial relations to obtain $i-Y$, $i-J$, and $i-H$ colour measurements
from $g-i$ colours for the SNe II in our sample with limited (or no) NIR data.
Therefore, we can estimate NIR magnitudes when photometry in these bands is
not available. The errors of each estimate were obtained using the rms of the
residuals. As outlined in the following subsection, NIR data are crucial for
reliable BB fits and estimation of the missing flux at longer wavelengths.
These simple relations (see Table 1) allow one to estimate NIR magnitudes from
optical colours and can be used in future works333The validity of using these
NIR estimations for the use of bolometric LC production is checked in the
analysis in Sect. 3.3..

Armed with photometric measurements or estimations in all $u$ to $H$ bands at
all epochs, pseudo-bolometric LCs were computed. The magnitudes were converted
to monochromatic fluxes at the mean wavelength of the filter using the
transmission functions and zero-points of the photometric system available on
the CSP website444https://csp.obs.carnegiescience.edu/data/filters. The
monochromatic fluxes were then integrated using the trapezoidal method, and
the pseudo-bolometric flux was obtained. The flux bluewards and redwards of
the mean filter wavelength range was set to zero.

####  3.2.2 Extrapolation to redder wavelengths

Figure 3: BB fits for SN 2008if at 72 days after explosion. Different
linestyles and colours correspond to different set of bands used for the
fitting process. The blue solid line is the optimal model since data affected
by line blanketing ($u$, $B$, and $g$ bands) are removed from the fit. The
best-fitting BB temperatures (TBB) are indicated in the legend. An optical
spectrum taken at 70 days after explosion is presented in grey. It shows that
Hα line profile produces an increment of the $r$-band flux above the BB model.
Figure 4: Fraction of the IR correction over the bolometric flux as a function
of time. The black solid line indicates the mean values within each time bin,
while the dashed lines represent the standard deviation. We only include SNe
II with observed $YJH$ photometry. Three SNe II (SNe 2005lw, 2007sq and
2009ao) display unusual values beyond 2$\sigma$ from the mean. This may be due
to a significant uncorrected reddening in the host galaxy (see text).

One of the most frequently used techniques to correct for the missing flux in
the IR is to assume that the SN emission in this region is well described by a
BB function. At early epochs, the BB model provides a good representation of
the SN flux in all optical and NIR bands. As the SN cools and expands, the SN
emission at short wavelengths starts to depart from the BB model because of
the increasing line blanketing produced by iron-group elements. Figure 3 shows
the effect of considering the bands affected by line blanketing in the fitting
process. In this example, we take the fluxes for SN 2008if at 72 days after
explosion. At this time, the $u$, $B$, and $g$ bands are already affected by
line-blanketing effects and are removed for the fitting (blue solid line).
Figure 3 clearly shows that when these bands are taken into account for the
fitting, the BB model tends to peak at redder wavelengths resulting in an
overestimation of the extrapolated IR flux (from $H$ band to longer
wavelengths), and therefore in an overestimation of the bolometric luminosity
(see Sect. 3.3). To solve this issue, we followed a procedure similar to that
of Faran et al. (2018). When the _u-_ band flux dropped 1$\sigma$ below the BB
model, we ran the BB fitting process again but this time excluding the _u_
band from the fitting. The same was done for the $B$, $g$, and $V$ bands. The
SN emission also departs from the BB model at long wavelengths since the flux
past $\sim$2 $\mu$m is dominated by free-free emission (Davis et al. 2019).
However, this should not affect our analysis.

Additionally, during the fitting process, we noted that the $r$-band flux
increases with time with respect to the BB model and is located above the BB
for the vast majority of the SNe II in our sample. This is because Hα
increases in strength over time. Figure 20 from Gutiérrez et al. (2017b) shows
that the equivalent widths of both absorption and emission components of Hα
increase with time. However, the ratio of absorption to emission of the Hα
profile is almost constant at $\sim$0.3 after 40 days from explosion (see
Gutiérrez et al. 2017b, their Fig. 22). This means that the Hα feature becomes
a stronger (positive) contribution to the $r$-band flux with time with respect
to the continuum. In Fig. 3, we include a spectrum taken 70 days after
explosion showing the strength of Hα profile at that time. Thus, when the $r$
band departed 1$\sigma$ from the BB fits, we removed this band in the same way
we did with the bluer bands.

The above indicates that $uBgVr$ bands are omitted from the fitting around the
middle of the photospheric phase. We conclude that NIR data are crucial for
the BB fitting since the $i$ band is the only optical band that is not removed
from the fits. In this context, the method presented in Sect. 3.2.1 is
necessary to obtain NIR magnitudes for SNe II from observed optical colours.

Once we found a BB model for the observed SED (excluding line blanketing and
Hα effects), the missing flux in the IR was estimated by the integral of the
BB emission between the reddest observed band and infinity, and is referred to
as the ‘IR correction’ (see Fig. 4). This procedure was repeated at every
epoch of observation. After the recombination phase the ejecta turns optically
thin and line emission dominates the radiation of the SN II. During this
phase, BB fits are not appropriate to extrapolate the SN radiation in the IR
regime from the physical point of view. However, we used them to estimate IR
corrections given that in Appendix C we showed that they can represent most of
the flux at long wavelengths.

Figure 4 shows the contribution of our IR correction with respect to the total
flux as a function of time, for those SNe II with observed $YJH$ photometry.
As expected, the contribution of the IR at early times is small ($\sim$5% of
the total flux). The IR correction increases with time taking a mean value of
$\sim$10% during the plateau phase, and $\sim$16% in the radioactive tail
phase. We note that three SNe II are notably different during the photospheric
phase: SN 2005lw, SN 2007sq, and SN 2009ao. It is not surprising that these
three SNe II are within the 10% reddest of the sample (de Jaeger et al. 2018),
which may imply significant host-galaxy extinction. If this is the case, a
significant uncorrected reddening in the host galaxy would produce larger
fluxes in the bluest bands with respect to the NIR bands yielding smaller
contributions to the IR, and thus eliminating these objects as outliers.

####  3.2.3 Extrapolation to UV wavelengths

UV flux contributes significantly at early epochs when the SN II emission
peaks in these wavelengths. Bersten & Hamuy (2009) used synthetic SN II
spectra and noted that UV corrections can be as large as $\sim$50$-$80% of the
total flux at early times when the SN II is very blue, but becoming almost
negligible when the plateau phase is settled. This means that the contribution
of the UV regime is significant, at least at very early epochs. Therefore, it
is certainly important to have UV data during the first weeks after explosion
to account for the real UV flux. However, high-cadence observations from UV to
NIR bands for a large sample of SNe II are difficult to obtain. Consequently,
a method is required to estimate the UV contribution for our sample.

In the current work, the UV correction was extrapolated from the _u_ band to
$\lambda$ = 0 using the BB model on all epochs except when the _u_ band was
removed from the fitting process (see Sect. 3.2.2). In the latter cases, the
UV correction was defined as the flux below the straight line from the bluest-
band flux to zero flux at $\lambda$ = 2000 Å, as proposed by Bersten & Hamuy
(2009). These authors chose $\lambda$ = 2000 Å based on synthetic SN II
spectra showing that the flux bluewards of 2000 Å is negligible in comparison
with the bolometric flux. After the transition to the radioactive tail phase,
we did not consider any UV correction since it becomes unimportant at these
epochs (see Bersten & Hamuy 2009, their Fig. 1).

Lyman et al. (2014) utilised _Swift_ -UV data for six stripped-envelope SNe
and two SNe II to test the above-mentioned approaches and found generally good
agreement. The linear extrapolation shows a discrepancy of less than 5% of the
bolometric luminosity for most of the observations, but unfortunately, most of
them correspond to stripped-envelope SNe, with only one SN II being used
(showing good agreement). In Appendix C, we used seven SNe II in the CSP-I
sample with available _Swift_ -UV data to test our extrapolation method to the
UV regime. The details of this test are outlined and these give confidence to
our bolometric calculations for times $\gtrsim$ 20 days from explosion. At the
same time, our results involving bolometric luminosities at times $\lesssim$
20 days should be taken with caution as our calculation method may not predict
the actual UV contribution at those epochs.

####  3.2.4 CSP-I SN II bolometric light curves

Figure 5: Contribution of the UV, optical, and IR fluxes to the bolometric
flux of CSP-I SNe II as a function of time. UV and IR fluxes include
extrapolations. Only SNe II with explosion epoch estimates are shown. Figure
6: Bolometric LCs of the CSP-I SN II sample. LCs are re-sampled via Gaussian
processes for better visualisation, and displayed by black lines. For
comparison, we show in colours three well-studied SNe II: 1999em (Bersten &
Hamuy 2009), 2004et (Martinez et al. 2020), and 2008bk (this work). Only SNe
II with explosion epochs estimates are shown.

The sum of the pseudo-bolometric flux and the missing flux falling at
unobserved wavelengths equates to the bolometric flux. The calculation of each
contribution of the bolometric flux was performed through a simple Monte Carlo
procedure. For each of the thousand Monte Carlo simulations we randomly
sampled the broadband magnitudes within their uncertainties and integrated the
pseudo-bolometric flux, found the best-fitting BB model, and calculated the IR
and UV corrections.

Fig. 5 shows the observed plus extrapolated flux in the UV ($\lambda$ $\leq$
3900 $\AA$), optical (3900 $\leq$ $\lambda$ $\leq$ 9000 $\AA$), and IR
($\lambda$ $\geq$ 9000 $\AA$) with respect to the bolometric flux as a
function of time. In general, optical fluxes dominate the SN emission
representing between 50 and 70% of the bolometric flux for most SNe II in the
sample during the entire evolution. NIR fluxes contribute $\sim$10% of the
total flux at early epochs, increasing with time until values of $\sim$50%.
The UV regime provides a large contribution at early times reaching values of
about 80% for a few SNe II, but after 30 days from explosion its contribution
drops to less than $\sim$10% for most SNe II in the CSP-I sample. We note that
three SNe II (SN 2007sq, SN 2009ao, and SN 2008bp) show markedly lower
(larger) optical (NIR) fractions than the general trend. The first two objects
are within the 10% reddest of the CSP-I SN II sample (de Jaeger et al. 2018),
while SN 2008bp shows particularly red colours and a high pseudo-equivalent
width of Na i D, possibly implying significant uncorrected host-galaxy
extinction (see also Sect. 3.2.2).

The mean bolometric flux of the thousand simulations was calculated and taken
as the final bolometric flux. We took the standard deviation as its error.
This procedure was employed for each epoch of observation. Then, we
transformed flux into luminosity using the distance to each object. The
distance errors were propagated to the final luminosity. In the calculation of
the bolometric luminosity we deal with two major sources of systematic
uncertainties: host-galaxy extinction and distance. Previously, we stated that
we do not correct for host-galaxy extinction, which may produce systematically
dimmer bolometric LCs. Distance is the largest source of uncertainty,
sometimes producing notably different bolometric luminosity LCs for distance
values within error bars. Therefore, we publish bolometric flux LCs instead of
luminosities. In this way, any future user of our bolometric LCs can choose
different distance estimations for their analysis. Bolometric fluxes for the
full sample can be found at the CSP
website555https://csp.obs.carnegiescience.edu/data. Figure 6 shows the
bolometric LCs for our full SN II sample. LCs were re-sampled via Gaussian
processes for better visualisation. Figure 6 shows a large range in
luminosities and LC morphologies, the analysis of which is presented in Sect.
4.1.

###  3.3 Comparison of bolometric light curves from different calculation
methods

Table 2: Physical parameters derived from the hydrodynamic modelling of
bolometric LCs and expansion velocities for three SNe II in our sample when
their bolometric LCs are constructed using different methods.

SN | BLCs | $M_{\rm ZAMS}$ | $M_{\rm ej}$ | $E$ | $M_{\rm Ni}$ |  56Ni mixing
---|---|---|---|---|---|---
|  | ($M_{\odot}$) | ($M_{\odot}$) | (foe) | ($M_{\odot}$) | (%)
2005dn | This work | 10.7${}^{+1.7}_{-0.6}$ | 8.5${}^{+1.2}_{-0.3}$ | 0.94${}^{+0.10}_{-0.12}$ | 0.041${}^{+0.009}_{-0.010}$ | 39${}^{+7}_{-9}$
Method 1 | 11.8${}^{+1.9}_{-1.4}$ | 9.2${}^{+1.8}_{-0.9}$ | 1.12${}^{+0.16}_{-0.15}$ | 0.049${}^{+0.014}_{-0.015}$ | 45${}^{+19}_{-16}$
2007ab | This work | 11.2${}^{+0.3}_{-0.2}$ | 8.8${}^{+0.2}_{-0.2}$ | 1.15${}^{+0.09}_{-0.04}$ | 0.033${}^{+0.003}_{-0.002}$ | 22${}^{+2}_{-1}$
Method 1 | 10.9${}^{+0.5}_{-0.5}$ | 8.6${}^{+0.3}_{-0.2}$ | 1.42${}^{+0.05}_{-0.07}$ | 0.051${}^{+0.006}_{-0.006}$ | 26${}^{+6}_{-4}$
2008if | This work | 10.1${}^{+0.2}_{-0.1}$ | 8.2${}^{+0.1}_{-0.1}$ | 1.00${}^{+0.06}_{-0.06}$ | 0.042${}^{+0.003}_{-0.002}$ | 21${}^{+2}_{-1}$
Method 1 | 10.2${}^{+1.0}_{-0.4}$ | 8.3${}^{+0.5}_{-0.2}$ | 1.33${}^{+0.11}_{-0.13}$ | 0.065${}^{+0.010}_{-0.013}$ | 33${}^{+11}_{-8}$
666BLCs indicates the method used to calculate the bolometric luminosity.
$M_{\rm ZAMS}$, $M_{\rm ej}$, $E$, and $M_{\rm Ni}$ refer to the progenitor
initial mass, ejecta mass, explosion energy, and 56Ni mass, respectively. 56Ni
mixing describes the spatial distribution of 56Ni within the ejecta and is
presented in percentage of the pre-SN mass in mass coordinate. The reader is
referred to Paper II for a full description of our modelling and fitting
procedures.

Figure 7: Comparison of bolometric LCs for SN2005dn (top left), SN 2007ab (top
right), SN 2008ag (bottom left), and SN 2008if (bottom right) using different
methods for their calculation (see text). The relative differences are with
respect to the bolometric luminosities calculated using our method.

In the present study, we construct the largest sample of SN II bolometric LCs
to-date employing a consistent method for all the objects using high-quality
and high-cadence observations characterised by a wide wavelength coverage
including optical and NIR photometry. However, such high-quality data are
often not common in samples of SNe II. SN II LCs evolve for hundreds of days,
which make follow-up observations in several optical and NIR bands time
consuming. For this reason, a large number of SNe II in the literature are
only observed in optical bands, sometimes with very few NIR observations.

Having only optical observations it is possible to estimate a bolometric LC by
means of BCs (Bersten & Hamuy 2009; Lyman et al. 2014; Pejcha & Prieto 2015,
see also Sect. 5), or a pseudo-bolometric LC, that is, through integration of
the flux over the optical range (e.g. Valenti et al. 2016). However, many
studies have estimated bolometric luminosities from BB fits using only optical
data, which may cause large systematic errors. In the current section, we
analyse these issues.

To test these systematics, we calculated the bolometric LCs for the CSP-I SN
II sample again but using only optical data through the following two methods
commonly used in the literature. The first method (‘Method 1’) integrates the
flux from the optical bands and then performs BB fits from optical photometry
without excluding any of the bluest bands affected by line blanketing effects.
UV and IR corrections are estimated by BB extrapolations at each epoch. The
second method (‘Method 2’) finds the best-fitting BB parameters from optical
photometry but excluding the band which includes the Hα line. Then, the
luminosity is calculated from the Stefan–Boltzmann law by means of the
temperature and radius derived from the fits. Additionally, we included
another method (‘Method 3’) to analyse the effect of using the colour-colour
relations presented in Sect. 3.2.1 in the bolometric luminosities (see details
below).

We start by comparing the bolometric LCs resulting from the first two methods
against those resulting from our method (Sect. 3.2). Methods 1 and 2 almost
always produce higher luminosities than our approach, with only a few events
with similar bolometric LCs. In addition, it is generally found that
bolometric LCs from Method 1 are more luminous than those from Method 2.
Figure 7 compares bolometric LCs for the four SNe II with the largest
differences. Additionally, the relative differences are displayed at the
bottom of each subplot with respect to the bolometric luminosity calculated
using our method. SN 2005dn (top-left panel) and SN 2007ab (top-right panel)
show the behaviours discussed above. Bolometric LCs from Methods 1 and 2 are
more luminous than those from our calculation method, with those from Method 1
being the most luminous. In the case of SN 2005dn, the relative differences
are almost constant during the SN II evolution being around 10% and 20% for
Methods 2 and 1, respectively. Something similar happens for SN2007ab. For
Method 2 the differences are between 10$-$15%, except for the first value that
shows a discrepancy of about 60% in luminosity. Method 1 gives a bolometric LC
that is $\sim$25% more luminous during plateau, increasing to $\sim$50$-$60%
at the radioactive tail phase. For SN 2008ag and SN 2008if, the bolometric LCs
from Methods 1 and 2 are similar but both showing large differences compared
to our method.

For the comparison with Method 3, we used the same four SNe II as above. In
this case, we omitted observed NIR magnitudes and instead, we predicted them
using the colour calibrations from which NIR magnitudes can be estimated using
$g-i$ colours. For consistency, we re-calculated the polynomial coefficients
of these relations for each of these four cases, every time removing the
object under analysis. We note excellent agreement between our bolometric LCs
and those calculated with predicted NIR photometry using our colour-colour
relations (Fig. 7). This validates the use of our method to estimate NIR
magnitudes in the absence of such observations. For completeness, in Fig. 7 we
also include the pseudo-bolometric LCs, that is the integration of the
observed fluxes extending from $u$/$B$ to $H$ band. These pseudo-bolometric
LCs are $\sim$20% less luminous than their bolometric counterparts.

In all the examples shown in this section, it is clearly seen that the
bolometric luminosities from Methods 1 and 2 (i.e. BB fits without NIR data)
highly overestimate the luminosity with respect to our more robust
methodology. Figure 3 shows the reason for this discrepancy. Clearly, BB fits
without NIR data (green dashed line and red dash-dot line) are above the
observed NIR photometry. Therefore, the flux redwards of the $i$ band is
overestimated. We conclude that NIR observations are crucial to better
reproduce the behaviour of the BB fits at longer wavelengths, and therefore
for reliable BB extrapolations to the IR. In this sense, we encourage future
works to use the relations presented in Table 1 to estimate NIR magnitudes
from optical colours when NIR observations are not available. Alternatively,
one may use the calibrations of BC against colours (Bersten & Hamuy 2009;
Lyman et al. 2014; Pejcha & Prieto 2015), as we discuss further in Sect. 5.

The bolometric LCs from this study are used to derive SN II progenitor and
explosion properties through hydrodynamical modelling in Paper II. Therefore,
we also quantify the differences in the physical parameters derived via
hydrodynamical modelling that occur when the bolometric LCs are calculated
from different methods. This highlights the need for accurate bolometric LC
construction.

For this test, we used three of the SNe II previously mentioned (SN 2005dn, SN
2007ab, and SN 2008if). The case of SN 2008ag is analysed later. In all cases,
we used our bolometric LCs and those from Method 1, as the latter is the
method producing the greatest differences. SN II physical properties using our
bolometric LCs are presented and analysed in Paper II. Here, we briefly
discuss our modelling procedure and then focus on the analysis of the
discrepancies. The reader is referred to Martinez et al. (2020) and Paper II
for a detailed description. We used the stellar evolution code MESA (Paxton et
al. 2011, 2013, 2015, 2018) to obtain RSG-star models at time of collapse for
initial masses between 9 and 25 $M_{\odot}$ in steps of 1 $M_{\odot}$. For
each progenitor model, we calculated bolometric LC and photospheric velocity
models for a large range of explosion parameters: explosion energy ($E$), 56Ni
mass ($M_{\rm Ni}$), and its spatial distribution within the ejecta, 56Ni
mixing. We used a one-dimensional code (Bersten et al. 2011) that simulates
the explosion of the progenitor star. This grid of hydrodynamical models was
previously presented in Martinez et al. (2020). Finally, we employed MCMC
methods to find the posterior probability of the model parameters of each
observed SN II.

Table 2 compares the progenitor and explosion properties using the bolometric
LCs presented in the current study and the bolometric LCs from Method 1. The
largest differences are found for $E$ and $M_{\rm Ni}$. Discrepancies of the
order of 0.3 foe (1 foe $\equiv$ 1051 erg) are found for the explosion
energies of SN 2007ab and SN 2008if. A smaller difference of $\sim$0.2 foe is
found for the explosion energy of SN 2005dn. Differences in $M_{\rm Ni}$ are
even more notable. The more luminous tail phases derived from Method 1 (Fig.
7) produce significantly larger 56Ni masses, with differences of 0.018 and
0.023 $M_{\odot}$ for SN 2007ab and SN 2008if, respectively. This analysis
shows that for these three SNe II, $M_{\rm Ni}$ estimations using bolometric
LCs from Method 1 might be overestimated between $\sim$20 and 55%. This may
have important implications for the previously analysed distributions of SN II
56Ni masses as compared to stripped-envelope SNe (Kushnir 2015; Anderson
2019). We emphasise that differences are always offset in the same direction,
that is, larger $E$ and $M_{\rm Ni}$ are found for the LCs calculated using
Method 1. This is because the LCs from Method 1 are always more luminous
during plateau and radioactive phases. With respect to progenitor and ejecta
mass estimates, no significant differences are found.

SN 2008ag presents large discrepancies between our bolometric LC and that from
Method 1, with the latter being significantly more luminous. Unfortunately, we
cannot model the LC of SN 2008ag constructed from Method 1 for the following
reason. The grid of explosion models used covers a wide parameter space.
Specifically, $M_{\rm Ni}$ ranges from 0.0001 $M_{\odot}$ to 0.08 $M_{\odot}$
in different intervals (see Martinez et al. 2020, and Paper II). In Paper II,
we derived a 56Ni mass near the upper limit of our range for SN 2008ag,
$M_{\rm Ni}$ = 0.065 $M_{\odot}$. When trying to model the LC from Method 1,
we realised that it requires larger $M_{\rm Ni}$ values than those within our
parameter space. Therefore, we cannot derive all physical parameters
simultaneously for the LC from Method 1. However, due to the large discrepancy
found during the radioactive tail phase it may be enlightening to estimate the
difference in the 56Ni yields between both bolometric LC calculation methods.
Thus, to estimate $M_{\rm Ni}$, the procedure presented in Hamuy (2003) is
followed. We found $M_{\rm Ni}$ $\sim$0.14 $M_{\odot}$, that is, a factor of
2.2 larger than with our method of bolometric luminosity calculation. 56Ni
mass should be the most reliable parameter to determine since it is directly
associated with the luminosity of the tail phase (Hamuy 2003). However, an
inadequate method to construct bolometric LCs can highly overestimate 56Ni
mass yields.

We conclude this analysis emphasising that bolometric luminosities should not
be calculated from BB fits to the SED without NIR observations. Otherwise,
significant discrepancies up to $\sim$30% in the plateau and $\sim$60% in the
radioactive tail are found in the bolometric LCs, and therefore, discrepancies
also appear in the physical properties derived through bolometric LC
modelling. If NIR data are missing, we recommend to use the relations
presented in Table 1 to predict NIR magnitudes from optical colours, or the
prescriptions of BCs against colours (Sect. 5) to estimate bolometric
luminosities.

##  4 SN II properties

In the following sections, we first analyse the distributions of the
bolometric parameters (Sect. 4.1), and then the temperature evolution of the
sample as a function of time (Sect. 4.2).

###  4.1 SN II bolometric parameter distributions

Figure 8: Definition of the bolometric LC parameters measured for each SN. We
use the interpolated bolometric LC of SN 2008M as an example case. Figure 9:
Histograms of the measured bolometric magnitudes. Top panel: magnitudes at the
end of the optically-thick phase ($M_{\rm bol,end}$). Bottom panel: magnitudes
at the radioactive tail phase ($M_{\rm bol,tail}$). In each panel, the number
of SNe II (N) is listed, together with the median and the median absolute
deviation (MAD). Figure 10: Histograms of the three measured decline rates.
Top panel: decline rates of the cooling phase ($s_{\rm 1}$). Middle panel:
plateau decline rates ($s_{\rm 2}$). Bottom panel: decline rates on the
radioactive tail ($s_{\rm 3}$). In this last plot, the dashed line indicates
the expected decline rate for full trapping of 56Co decay. In each panel, the
number of SNe II (N) is listed, together with the median and the median
absolute deviation (MAD). Figure 11: Histograms of the three measured time
durations of SNe II. Top panel: duration of the cooling phase (_Cd_). Middle
panel: duration of the plateau phase (_pd_). Bottom panel: duration of the
optically-thick phase (_optd_). In each panel, the number of SNe II (N) is
listed, together with the median and the median absolute deviation (MAD).

With bolometric LCs in hand, we characterised them by measuring several
parameters. We started by measuring the mid-point of the transition from
plateau to radioactive tail ($t_{\rm PT}$) by fitting the LC around the
transition with the function reported in Eq. (1) from Valenti et al. (2016). A
complementary description of this function is found in Olivares E. et al.
(2010). The fit was computed using MCMC methods via the emcee package
(Foreman-Mackey et al. 2013).

The parameters studied in the present work were already defined by Anderson et
al. (2014b) and Gutiérrez et al. (2017a) for _V-_ band LCs. Figure 8 presents
an example LC indicating the bolometric parameters. The observables are:

  1. 1.

$M_{\rm bol,end}$: defined as the bolometric magnitude measured 30 days before
$t_{\rm PT}$. If $t_{\rm PT}$ cannot be estimated, $M_{\rm bol,end}$
corresponds to the magnitude of the last observation in the optically-thick
phase.

  2. 2.

$M_{\rm bol,tail}$: defined as the bolometric magnitude measured 30 days after
$t_{\rm PT}$. If $t_{\rm PT}$ cannot be estimated but the radioactive tail
phase is clearly observed, $M_{\rm bol,tail}$ is the magnitude at the nearest
point after transition.

  3. 3.

$s_{\rm 1}$: defined as the decline rate in magnitudes per 100 days of the
cooling phase.

  4. 4.

$s_{\rm 2}$: defined as the decline rate in magnitudes per 100 days of the
plateau phase. We reiterate that ‘plateau’ does not necessarily refer to a
phase of constant luminosity.

  5. 5.

$s_{\rm 3}$: defined as the decline rate in magnitudes per 100 days of the
slope in the radioactive tail phase.

  6. 6.

$t_{\rm trans}$: corresponds to the epoch of transition between the cooling
decline ($s_{\rm 1}$) and the plateau decline ($s_{\rm 2}$).

  7. 7.

_optd_ : is the duration of the optically-thick phase and is equal to $t_{\rm
PT}$. If $t_{\rm PT}$ cannot be estimated but it is clear that the SN II has
observations during the transition, we take the time of the last observation
as the _optd_.

  8. 8.

_pd_ : corresponds to the duration of the plateau phase. It is equal to
$t_{\rm PT}$ $-$ $t_{\rm trans}$.

  9. 9.

_Cd_ : corresponds to the duration of the cooling phase, defined between the
explosion epoch and $t_{\rm trans}$.

$M_{\rm bol,end}$ and $M_{\rm bol,tail}$ were interpolated to the chosen
epochs when $t_{\rm PT}$ is defined, and their errors were estimated by
propagation of the uncertainties in the implicated magnitudes. The decline
rates were measured by fitting a straight line to each of the three phases.
$s_{\rm 1}$ and $s_{\rm 2}$ (and $t_{\rm trans}$) were measured in the same
way as in Gutiérrez et al. (2017a, see also  for more details). For $s_{\rm
3}$ we simply fitted a straight line to the radioactive tail with at least
three data points.

Finally, we point out that _pd_ and _optd_ were defined differently than in
Anderson et al. (2014b). For this reason, we named our parameters using
lowercase acronyms (_pd_ , _optd_) instead of $Pd$ and $OPTd$ as in Anderson
et al. (2014b). These authors defined $Pd$ ($OPTd$) as the time between
$t_{\rm trans}$ (explosion epoch) and the end of the plateau, defined as when
the extrapolation of $s_{\rm 2}$ becomes 0.1 mag more luminous than the
$V$-band LC. In the present work, we use $t_{\rm PT}$ as a measure of the
length of the optically-thick phase (_optd_) and, therefore, _pd_ = $t_{\rm
PT}$ $-$ $t_{\rm trans}$. In Table LABEL:table:blc_parameters, we present the
measured bolometric parameters as defined above. Additionally, Figs. 18, 19
and 20 show the bolometric LC for each SN II in the CSP-I sample individually,
together with their measured bolometric parameters.

In Figs. 18 and 20, we note that SN 2004er and SN 2009ao display an unusual
behaviour in their early bolometric LCs. Both SNe II show early rising LCs
until the ‘peak’ is reached. While it is now more common to observe the early
rise of SN II LCs, the peak is observed in optical and NIR bands. This is due
to the shift of the SN spectrum to redder bands as the ejecta cools. An
initial peak in the bolometric luminosity is expected but in this case it is
due to the arrival of the shock wave to the stellar surface. The shock-
breakout detection is extremely difficult to observe due to its short
duration. This situation may change if the SN explodes inside a dense
environment. We further discuss possible explanations for the observed
behaviour.

The early bolometric LCs for SN 2004er and SN 2009ao resemble the behaviour
seen in some early pseudo-bolometric LCs (see e.g. Fig. 10 from Valenti et al.
2016). Therefore, the problem may arise from the extrapolated UV flux. The
underestimation of the UV correction causes lower luminosities at early times,
when the UV flux contributes significantly. Another possibility is that this
behaviour is produced by significant uncorrected host-galaxy extinction. In
that direction, SN 2004er and SN 2009ao are both within the 20% reddest of the
CSP-I sample (de Jaeger et al. 2018). Re-emission of energy by dust takes
place at longer wavelengths than those observed by the CSP-I and it is not
taken into account in our BB models. Thus, host-galaxy extinction that has
been unaccounted for will increase the flux in the bluest bands producing a
larger contribution in the UV, while the flux in the reddest bands is less
affected. This effect will be larger at early times, when the SN is
intrinsically blue, which means that extinction will affect the bolometric LC
as a function of time, that is, it will change the shape of the bolometric LC.
We tested this hypothesis by correcting the photometry of SN 2004er for
additional extinction. We found that an extra $A_{V}^{\rm host}$ of 0.8 mag
changes the initial rising LC to a typical declining LC at early epochs.
Therefore, the unusual rising behaviour of SN 2004er and SN 2009ao might be
caused by missing UV flux, probably due to uncorrected host-galaxy
reddening777However, the effect of uncorrected host-galaxy extinction on the
shape of bolometric LCs will not affect the overall analysis. This effect
becomes smaller as SNe II evolve to redder colours. For this reason, this is
only significant at early times ($\lesssim$ 30 days) and for large $A_{V}^{\rm
host}$ values. We emphasise that the first 30 days of evolution are removed
from the fitting when determining progenitor and explosion properties of SNe
II (see Paper II, ). Additionally, we note that the presence of dense CSM
surrounding the progenitor star may also explain this behaviour. Recent
photometric and early spectroscopic analyses suggest that such dense CSM may
be present in many SNe II (e.g. González-Gaitán et al. 2015; Yaron et al.
2017; Förster et al. 2018; Morozova et al. 2018; Bruch et al. 2021). Under
this hypothesis, the observed peak in the bolometric LCs of SN 2004er and SN
2009ao may alternatively be caused by the delay of shock breakout due to
ejecta-CSM interaction888Although the actual properties of the CSM are unclear
and beyond the scope of this work. (e.g. Moriya et al. 2018; Haynie & Piro
2020).

Figure 9 shows the distributions of the two measured bolometric magnitudes:
$M_{\rm bol,end}$ and $M_{\rm bol,tail}$. Our sample is characterised by the
following median values and median absolute deviations (MAD): $M_{\rm
bol,end}$ = $-$16.2 mag (MAD = 0.6, 72 SNe II) and $M_{\rm bol,tail}$ =
$-$14.8 mag (MAD = 0.3, 17 SNe II). As expected, the distributions peak at
lower luminosities as time evolves. $M_{\rm bol,end}$ cover a range of
$\sim$2.8 mag from $-$14.7 mag (SN 2008bk) to $-$17.5 mag (SN 2009aj). SN
2008bk is a well-studied SN II (Pignata 2013; Van Dyk et al. 2012a; Van Dyk
2013; Lisakov et al. 2017; Maund 2017; Jerkstrand et al. 2018; Eldridge et al.
2019; Martinez & Bersten 2019; Martinez et al. 2020) that belongs to a class
of sub-luminous SNe II (Spiro et al. 2014). Spiro et al. (2014) proposes that
these faint events represent the lowest-luminosity part of a continuous
distribution of SNe II. This was later verified by a number of studies (e.g.
Anderson et al. 2014b; Sanders et al. 2015; Gutiérrez et al. 2017a). In the
current paper, we find the same continuous distributions in the two measured
bolometric magnitudes. SN 2009aj is found in the upper limit of the $M_{\rm
bol,end}$ distribution. This SN is more luminous than typical SNe II probably
due to CSM interaction (Rodríguez et al. 2020). At the radioactive tail phase,
the sample ranges from $-$12.3 mag (SN 2008bk) to $-$15.2 mag (SN 2007X). SN
2008bk is again the lowest-luminosity event. This is not surprising as low-
luminosity SNe II are characterised, among other properties, by the very-low
luminosity during the radioactive tail which indicates that the mass of 56Ni
ejected during the explosion is considerably low (Pastorello et al. 2004;
Spiro et al. 2014; Lisakov et al. 2018).

Figure 10 presents histograms of the distributions of the decline rates
($s_{\rm 1}$, $s_{\rm 2}$, and $s_{\rm 3}$). The median values of the decline
rates are: $s_{\rm 1}$ = 4.59 mag per 100 days (MAD = 2.84, 42 SNe II),
$s_{\rm 2}$ = 0.81 mag per 100 days (MAD = 0.91, 72 SNe II) and $s_{\rm 3}$ =
1.38 mag per 100 days (MAD = 0.62, 16 SNe II). The bolometric decline rates
show a continuum in their distributions with some minor exceptions: the
$s_{\rm 1}$ distribution shows four SNe II (SNe 2005dk, 2006bl, 2008bu, and
2009A) with rates higher than 10 mag per 100 days. In the case of $s_{\rm 2}$,
the fastest decliner is SN 2009au with a decline rate of 2.78 $\pm$ 0.17 mag
per 100 days, while SN 2009A has the lowest $s_{\rm 2}$ value with a rate of
$-$4.79 $\pm$ 0.47 mag per 100 days, that is, this SN II shows a rising
plateau phase. SN 2009A has a peculiar behaviour as it shows double-peaked
optical and bolometric LCs (Anderson et al. in prep.). However, the lack of
data after 50 days from explosion prevents us to reveal their properties. SN
2008hg has the second lowest $s_{\rm 2}$ with $-$0.96 $\pm$ 0.35 mag per 100
days. In total, eight SNe II have rising plateau phase, but two of them have
insufficient data during the plateau phase for reliable estimates.

Unfortunately, the decline rate of the radioactive tail phase ($s_{\rm 3}$)
can only be measured for 16 objects due to insufficient data during this
phase. A significant number of events (11 of 16) decline quicker than expected
if gamma-ray photons from the radioactive decay of 56Co are fully trapped in
the ejecta (0.98 mag per 100 days; Woosley et al. 1989) implying some gamma-
ray loss. This confirms the results from Anderson et al. (2014b) where _V_
-band data were used999However the fraction showing a steeper decline is
significantly higher here. This is discussed further in Paper III..

In Fig. 11 the distributions of the three measured time durations (_Cd_ , _pd_
, and _optd_) are displayed. A large range of _pd_ and _optd_ values are
observed. _optd_ is characterised by an average of 104 days (MAD = 19, 37 SNe
II). This value is very similar to the historical 100-day _optd_ of SNe IIP
LCs (Barbon et al. 1979). The shortest and longest _optd_ values are 42 $\pm$
2 days (SN 2004dy) and 146 $\pm$ 2 days (SN 2004er) respectively. The average
_pd_ is 75 days (MAD = 26, 22 SNe II) and ranges from 39 $\pm$ 2 days for SN
2008bu to 106 $\pm$ 4 days for SN 2004fc. Only 22 _pd_ values are available
since it is the most difficult time duration – of the three analysed in the
present work – to be measured. Given its definition, _pd_ requires the
estimation of the _optd_ , for which the explosion epoch and the transition to
the radioactive phase is needed, as well as $t_{\rm trans}$. _Cd_ shows a
narrower distribution with a median of 27 days (MAD = 4, 41 SNe II). All
measured time durations display a continuum in their distribution with no
signs of bi-modality indicating the existence of different sub-classes.

###  4.2 Temperature evolution

Table 3: Mean BB temperatures and the standard deviation for our SNe II sample
as a function of time.

Epochaa$a$Days since explosion. (days) | TBB (K)
---|---
5 | 9328 $\pm$ 2164
15 | 8307 $\pm$ 1711
25 | 6766 $\pm$ 1138
35 | 6211 $\pm$ 967
45 | 5948 $\pm$ 882
55 | 5786 $\pm$ 774
65 | 5692 $\pm$ 741
75 | 5673 $\pm$ 881
85 | 5692 $\pm$ 965
95 | 5595 $\pm$ 1211
105 | 5270 $\pm$ 1007
115 | 5342 $\pm$ 1011
125 | 4994 $\pm$ 995
135 | 4379 $\pm$ 657
101010

Figure 12: BB temperature evolution for SNe II in the CSP-I sample with
explosion epochs defined. The red solid line indicates the mean temperature
within each time bin, while the dashed red lines represent the standard
deviation. These values are available in Table 3. SNe II are colour-coded with
the plateau decline rate ($s_{\rm 2}$, top panel) and $M_{\rm bol,end}$
(bottom panel).

The temperature evolution with time for the SNe II in the sample is obtained
from the BB fits and is presented in Fig. 12. This figure also includes the
mean temperature and the standard deviation within each time bin of 10 days.
These values are presented in Table 3.

Shock breakout models predict temperatures of about 105 K or higher (Grassberg
et al. 1971; Kozyreva et al. 2020). Indeed, the modelling of spectra of SN
2013fs taken six hours after explosion revealed a temperature of around 5$-$6
$\times$ 104 K (Yaron et al. 2017). After shock breakout, a rapid cooling of
the outermost layers of the ejecta is expected. During the first ten days, the
mean temperature in our sample is about 9300 K but with a large standard
deviation of 2200 K. The hottest SN II at this stage is SN 2009aj presenting a
temperature of 16300 K. As time progresses, the temperature starts evolving
more slowly compared to earlier phases. Between 30 and 40 days after
explosion, the temperature enters a phase where it remains nearly constant.
This is consistent with hydrogen recombination that occurs when the hydrogen-
rich envelope reaches $\sim$6000 K. At this stage a recombination wave appears
moving inwards in mass coordinate until the entire hydrogen envelope is
recombined and the recombination front arrives to the innermost parts of the
ejecta.

We find six SNe II that enter the plateau phase with temperatures below 5000
K. In particular, SN 2008bp has estimated temperatures around 3500 K. One may
assume that such low temperatures could be obtained if (uncorrected) host-
galaxy extinction is considerably high. However, for low temperature values
(as those of SN 2008bp), the temperature after correcting the photometry by
host-galaxy extinction remains almost the same (see Faran et al. 2018, their
Fig. 6). Therefore, the underlying reason for these low temperatures is
unclear. On the other hand, we find SN 2009A entering the plateau phase with
temperatures of the order of 9000 K. However, this is a very peculiar SN II
given that it shows double-peaked optical LCs (see Anderson et al. in prep.
for details).

Valenti et al. (2016) found that fast-declining SNe II display systematically
lower temperatures at 50 days after explosion and argue that this is to be
expected since fast decliners evolve more quickly and hence are close to the
end of the recombination phase at similar (to slow decliners) epochs. In the
top panel of Fig. 12, the temperature curves are colour-coded with their
$s_{\rm 2}$ values. Six objects present temperatures lower than 5000 K and
only one, SN 2005lw, is a fast decliner with a $s_{\rm 2}$ value of 1.53 $\pm$
0.08 mag per 100 days, while the others (SNe 2004dy, 2007sq, 2008bh, 2008bp,
and 2009ao) have $s_{\rm 2}$ values lower than 1 mag per 100 days. Moreover,
one of the hottest SN II at 50 days, SN 2008bm, has a decline rate $s_{\rm 2}$
= 2.74 $\pm$ 0.12 mag per 100 days. This is in the opposite direction of what
Valenti et al. (2016) found. SN 2008bm belongs to a subgroup of SNe II with
peculiar characteristics: blue colours, low expansion velocities, and more
luminous than ‘normal’ SNe II (Rodríguez et al. 2020). In addition, Rodríguez
et al. (2020) find that these properties can be reproduced by the ejecta-CSM
interaction model, which may also explain the high temperature. The other two
SNe II presented in Rodríguez et al. (2020), SN 2009aj and SN 2009au, also
display high temperatures falling above the standard deviation. Indeed, SN
2009aj is the hottest SNe II in our sample until $\sim$30 days after
explosion. CSM interaction causes a boost in the SN luminosity and greater
photospheric temperatures because of the additional energy source (Hillier &
Dessart 2019). Leaving aside these outliers, we do not find a clear trend of
the temperature with $s_{\rm 2}$ as found by Valenti et al. (2016).

SN II spectra show that some iron-group absorption lines appear earlier in
low-luminosity events, which may be associated with differences in
temperatures and/or metallicity (Gutiérrez et al. 2017b). That is to say, low-
luminosity SN II line forming regions cool faster allowing metal lines to
appear sooner. Therefore, in the bottom panel of Fig. 12, we show the
temperature curves for all SNe II in the CSP-I sample colour-coded according
to $M_{\rm bol,end}$. We find a remarkable trend with low-luminosity (high-)
SNe II displaying low (high) temperatures.

##  5 Bolometric corrections

In Sect. 3.2, we determined bolometric luminosities from the estimation of the
bolometric flux, that is, from the integration of the observed flux in several
photometric bands covering the major part of the SN II emission and the
modelling of the unobserved flux using different techniques for the UV and IR
regimes. This is the most accurate technique in order to calculate bolometric
fluxes, but only in the case where extensive photometric coverage is
available. When this requirement is not fulfilled, the use of BCs might be
more appropriate.

The BC enables a transformation of magnitudes in certain bands into bolometric
magnitudes. By definition,

$\mathrm{BC}_{j}=m_{\rm bol}-m_{j}\,,$ (1)

where $m_{j}$ is the magnitude of the SN in the band $j$ that has been
corrected for extinction, and $m_{\rm bol}$ is the bolometric magnitude. The
BC is independent of the distance since it is defined as a magnitude
difference. Therefore, Eq. 1 can also be defined in absolute magnitudes (BCj =
$M_{\rm bol}-M_{j}$). During the SN evolution, the luminosity changes and the
SED rapidly evolves to redder colours. This means that the BC is not constant
in time, which complicates its calculation and further implementation.

Bersten & Hamuy (2009) calculated BCs for three well-observed SNe II (SNe
1987A, 1999em, and 2003hn) and derived calibrations of BCs against optical
colours. This is an easy and quick technique to implement as it allows the
calculation of bolometric luminosities using only two optical Johnson-Cousins
filters. The same procedure was implemented in Lyman et al. (2014). In the
latter study, the authors analysed a larger sample of six SNe II, three of
which being those previously studied in Bersten & Hamuy (2009), and three
others: SN 2004et, SN 2005cs, and SN 2012A. In addition, Lyman et al. (2014)
also presented calibrations for BCs from optical colours in Sloan bands.
However, Lyman et al. (2014) obtained Sloan magnitudes through the
interpolation of the SED constructed using Johnson filters. Although they
corrected their magnitudes for the mean offset found by means of the
comparison with synthetic magnitudes from spectra, this technique might add
systematic errors to the BC calibrations against colours. For this reason,
Lyman et al. (2014) point to a re-evaluation of their calibrations once an
appreciable data set of SNe II observed directly in Sloan bands with good NIR
coverage exists, which is what we present in the current study. More recently,
Pejcha & Prieto (2015) utilised 26 well-observed SNe II and a model that
disentangles the observed multi-band LCs and expansion velocities into radius
and temperature changes by simultaneously fitting the entire set of
observations. With this model, Pejcha & Prieto (2015) were able to provide
polynomial fits to the BCs as a function of every colour defined within the
large set of filters used. The latter study includes observations in the
_Swift_ -UV bands which is the main difference with the previous works.

All the previously mentioned studies (Bersten & Hamuy 2009; Lyman et al. 2014;
Pejcha & Prieto 2015) constructed calibrations for the BC as a function of
colours. Maguire et al. (2010) presented BCs against time for four SNe II and
found a large scatter in the BC relative to the $V$ band, although the BC to
the $R$ band is more homogeneous but only after 50 days since explosion. This
may indicate that colour is a better indicator of the BC than time for SNe II.

###  5.1 Calibrations of bolometric corrections versus colours

Table 4: Coefficients of the polynomial fits to the BC versus different
colours.

Colour | Phase | Range | $c_{0}$ | $c_{1}$ | $c_{2}$ | $c_{3}$ | $c_{4}$ | $\sigma$
---|---|---|---|---|---|---|---|---
$B-V$ | Cooling | ($-$0.10, 1.16) |  $-$0.740 | 4.472 |  $-$9.637 | 9.075 |  $-$3.290 | 0.12
Plateau | (0.07, 1.98) |  $-$0.384 | 1.692 |  $-$2.370 | 1.524 |  $-$0.476 | 0.19
Tail | (0.46, 1.78) |  $-$2.696 | 11.532 |  $-$18.805 | 13.040 |  $-$3.315 | 0.21
$g-r$ | Cooling | ($-$0.26, 1.09) |  $-$0.352 | 1.753 |  $-$4.078 | 1.961 | — | 0.11
Plateau | (0.01, 2.17) |  $-$0.219 | 0.813 |  $-$2.194 | 1.205 |  $-$0.305 | 0.14
Tail | (0.78, 2.07) |  $-$9.994 | 21.507 |  $-$15.343 | 3.273 | — | 0.22
$g-i$ | Cooling | ($-$0.50, 1.15) |  $-$0.214 | 0.789 |  $-$2.357 | 1.097 | — | 0.11
Plateau | ($-$0.10, 2.79) |  $-$0.140 | 0.292 |  $-$1.224 | 0.522 |  $-$0.090 | 0.07
Tail | (0.86, 2.43) |  $-$0.263 |  $-$0.154 |  $-$0.256 | — | — | 0.08
111111BC = $\sum_{k=0}^{n}c_{k}(colour)^{k}$, where colour is taken from
Column 1. $\sigma$ is the standard deviation about the fit.

Figure 13: Bolometric corrections to the $V$ band as a function of $B-V$
colour (top panel), and to the $g$ band as a function of $g-r$ colour (middle
panel) and $g-i$ colour (bottom panel) for all SNe II in the sample. The data
and fits are separated into three epochs: cooling phase (blue triangles,
dashed line), plateau phase (green dots, solid line), and radioactive tail
phase (red squared, dotted line). The bottom panel also shows the effect of
reddening in this plot by re-analysing SN 2008ag with $A_{V}^{\rm host}$ = 0.6
mag. Both curves for SN 2008ag are offset from the data for visualisation
purposes.

In this section, we calculate BCs for our entire sample of 74 SNe II. We first
converted the bolometric luminosities (Sect. 3.2) into bolometric magnitudes
using

$M_{\rm bol}=M_{\odot,\rm bol}-2.5\,\mathrm{log}_{10}\,\left(\frac{L_{\rm
bol}}{L_{\odot,\rm bol}}\right)\,,$ (2)

where $L_{\odot,\rm bol}$ = 3.845 $\times$ 1033 erg s-1 and $M_{\odot,\rm
bol}$ = 4.74 are the luminosity and the absolute bolometric magnitude of the
Sun (Drilling & Landolt 2000), and then we calculated the BC from Eq. 1.

We then looked for correlations between the BC and three colour indices.
Figure 13 shows the BC relative to the $V$ band (BCV) as a function of $B-V$
colour (top panel), and the BC relative to the $g$ band (BCg) as a function of
$g-r$ and $g-i$ colours (middle and bottom panels, respectively). For all
cases, we find strong relations. Particularly, BCg versus $g-r$ and $g-i$
present the tightest correlations. In Fig. 13, we also include polynomial fits
to the data. The order of the polynomials has been chosen to give the smallest
dispersions. For each colour, we decide to separate the data into three groups
determined by the phase of evolution in which the SN II is: cooling phase
(i.e. at times earlier than $t_{\rm trans}$), plateau phase (for times between
$t_{\rm trans}$ and the end of the plateau), and radioactive tail phase. The
coefficients of the polynomial fits are shown in Table 4. The cooling phase
needs a separate examination for the following reason. The lack of near-UV
data forces an extrapolation of the flux bluewards of the $u$ band. As already
pointed out in Sect. 3.2.3, the UV correction utilised in the present study
may not predict the actual flux in the UV at times earlier than $\sim$20 days
from explosion epoch, when the flux at wavelengths shorter than the $u$ band
contains a significant fraction of the bolometric flux. Therefore, at early
times, the BC can also be underestimated. For this reason, we produced fits to
early data (i.e. during the cooling phase) separately. However, care has to be
taken when using our fits to predict early BCs, as these may be
underestimated. At early times, it may be more appropriate to use the
calibrations from Pejcha & Prieto (2015) as they include _Swift_ observations
(see also Pritchard et al. 2014).

The scatter of the BCV against $B-V$ is relatively large during the plateau
and radioactive tail phases (Fig. 13, top panel). In fact, the rms dispersion
between the BC and the fits is 0.19 mag and 0.21 mag respectively, which is
about a factor of two larger than previous works. We also calculated the BC
relative to the $B$ band for comparison, but similar scatter is found. BCg
versus Sloan optical colours display smaller dispersions. The calibration
using $g-r$ colours displays a dispersion of 0.14 mag in the plateau phase.
While this value is smaller than what we found for $B-V$, it is still a factor
of three larger than previous calibrations (Lyman et al. 2014). We note a
tight relation at blue colours ($g-r$ $\lesssim$ 0.5 mag), however the scatter
increases at redder colours (later times). The increase in strength over time
of the Hα profile, which falls in the $r$ band at low redshifts like those
from the CSP-I SN II sample, and the diversity in the equivalent widths of the
absorption and emission components of Hα (Gutiérrez et al. 2017b) may explain
such behaviour. The calibration of BCg versus $g-i$ colours exhibits the
tightest relation of the three. The scatter is 0.07 mag during the plateau
phase, and 0.08 mag during the tail phase. For this reason, we suggest future
works to use our BCg versus $g-i$ calibration to construct bolometric LCs when
NIR data are not sufficient for reliable BB fits.

The bottom panel of Fig. 13 also illustrates the effect of extinction in the
BCg versus $g-i$ colour diagram. For this purpose, we re-analysed SN 2008ag
but with a simulated host-galaxy extinction of 0.6 mag (yellow solid line).
The original curve for SN 2008ag (filled cyan diamonds) and that with extra
host-galaxy extinction are offset from the data for better visualisation.
Additional extinction makes the SN intrinsically bluer, while the BCg takes
larger values. Thus, both contributions move the SNe II in the same direction
as the fits. This means that host-galaxy extinction uncertainties do not
significantly affect the BC calibration producing the low dispersion found
(see also Lyman et al. 2014, for discussion).

###  5.2 Comparison to previous calibrations

Table 5: Average difference and standard deviation between our bolometric LCs
and those calculated using different BC calibrations from the literature.

Colour | Average difference (dex) | BC calibration
---|---|---
$B-V$ | 0.05 $\pm$ 0.04 | This work
$B-V$ | 0.08 $\pm$ 0.05 | Bersten & Hamuy (2009)
$B-V$ | 0.08 $\pm$ 0.04 | Lyman et al. (2014)
$B-V$ | 0.07 $\pm$ 0.04 | Pejcha & Prieto (2015)
$g-r$ | 0.05 $\pm$ 0.04 | This work
$g-r$ | 0.05 $\pm$ 0.02 | Lyman et al. (2014)
$g-r$ | 0.05 $\pm$ 0.03 | Pejcha & Prieto (2015)
$g-i$ | 0.03 $\pm$ 0.01 | This work
$g-i$ | 0.04 $\pm$ 0.01 | Pejcha & Prieto (2015)

Figure 14: Comparison of the bolometric corrections estimated in this study
with other calibrations found in the literature. Left panel: BCV as a function
of $B-V$ colour. Middle panel: BCg as a function of $g-r$ colour. Right panel:
BCg as a function of $g-i$ colour. The BC calibrations from the literature
extend bluer, possibly because those studies correct for host-galaxy
reddening.

Figure 15: Bolometric LCs for SN 2005dz (left panel), SN 2004ej (middle
panel), and SN 2005dw (right panel) in comparison with those calculated from
calibrations of BC versus colour found in the literature. BH09, L14, and PP15
refer to Bersten & Hamuy (2009), Lyman et al. (2014), and Pejcha & Prieto
(2015), respectively.

Figure 16: Bolometric LCs for SN 2005dz (left panel), SN 2004ej (middle
panel), and SN 2005dw (right panel) in comparison with those calculated from
the calibrations of BC versus colour presented in the current study.

In this section, we compare our results with the calibrations of the BC versus
colour found in the literature. We begin by comparing the calibrations
directly, and then we compare our bolometric LCs (Sect. 3.2.4) with those
calculated using the different calibrations in the literature for the same
sample of 74 SNe II, whenever possible.

The left panel of Fig. 14 shows our fits to the BCV against $B-V$. We also
include the results from Bersten & Hamuy (2009) and Pejcha & Prieto (2015). We
do not include the fits by Lyman et al. (2014) as they calculate the BC
relative to the $B$ band and a direct comparison is not possible. We find a
very good agreement with the BCs of Bersten & Hamuy (2009). The difference
between the latter and that from Pejcha & Prieto (2015) may be due to a
difference in the zero point (Pejcha & Prieto 2015). Fits to the BCg versus
$g-r$ and $g-i$ are shown in the middle and right panels of Fig. 14,
respectively. In these cases, we can only compare with the study of Lyman et
al. (2014) since Pejcha & Prieto (2015) present BCs relative to the $r$ band
for $g-r$ colour and relative to the $i$ band for $g-i$, and Bersten & Hamuy
(2009) uses photometry in Johnson filters. In both cases, we find good
agreements with the BCs of Lyman et al. (2014). We are not able to compare
with the BCs of Pritchard et al. (2014), as they use colours from _Swift_
-UVOT bands.

In the three cases analysed above we note that the BC calibrations from the
literature extend bluer than ours. The calibration of Bersten & Hamuy (2009)
results in lower BC values than our fits at blue colours (early times),
probably because Bersten & Hamuy (2009) used spectral models to extrapolate
the missing UV flux at these early times which suggest larger UV corrections
than observations. Moreover, the analysis of the BCg versus $g-r$ and $g-i$
shows that our fits yield lower BCs for $g-r$ ¡ 0.5 mag and $g-i$ ¡ 0.2 mag,
respectively. The bottom panel of Fig. 13 shows the effect of additional
extinction in the BC$-$colour plane, finding that the BCs are larger and the
SN moves to bluer colours (see also Lyman et al. 2014, their Fig. 8).
Therefore, the differences found with previous calibrations may point to
uncorrected host-galaxy extinction in our sample. However, while the data from
Bersten & Hamuy (2009), Lyman et al. (2014), and Pejcha & Prieto (2015) are
corrected for host-galaxy extinction, the reader should again note the issues
present in the calculation of these values (Sect. 2). Another important point
to mention is with respect to the different ranges of validity of the
calibrations. Our calibrations of BCV and BCg can be used for a larger range
of colours which means that a larger number of bolometric LCs of SNe II can be
predicted and to later times, as the SN evolves to redder colours.

We also estimated the bolometric luminosity for the 74 SNe II in the CSP-I
sample by means of the BC calibrations reported in the literature and those
presented in the current work, and compare them with our bolometric LCs
presented in Sect. 3.2.4. The calibrations of BC versus colour used in this
analysis are shown in Table 5. It also shows the average of the differences
for the entire sample and the standard deviation. We find major agreements for
most BC calibrations. However, we note some peculiarities that are important
to mention. First, we compare the bolometric LCs presented in this study with
those calculated using the BC calibrations from the literature (Fig. 15) and
then with those using the new calibrations from the current study (Fig. 16).

The bolometric LCs presented in Fig. 15 represent the behaviour of the vast
majority of the SNe II in the sample. The left panel of Fig. 15 shows that all
the bolometric LCs using previous BC calibrations are similar to each other,
although they are dimmer than our bolometric LC. This behaviour is also seen
for a number of other CSP-I SNe II. In several cases, there is a significant
offset between the bolometric LCs from previous BC calibrations and our
bolometric LCs. This is shown in the middle panel of Fig. 15 taking SN 2004ej
as an example. The difference is obvious and tends to increase with time,
being even more significant in the radioactive tail. For this SN, the $g-r$
calibration from Lyman et al. (2014) is the only one showing good agreement in
the photospheric phase. The large differences found during the tail phase are
seen for almost all the SNe II in the sample. Sometimes the discrepancy is
even larger than that for SN 2004ej, which can significantly bias the 56Ni
mass estimates (see Sect. 3.3). This may be due to the constant BC adopted by
Bersten & Hamuy (2009) and Pejcha & Prieto (2015) during the exponential decay
phase. Although the BC at late times may be constant for individual SNe II, it
does not mean that the same value should be adopted for all SNe II. In Fig. 13
it is clearly shown that the BC during the radioactive phase is not constant
when considering all SNe II together. Lyman et al. (2014) do not present BC
calibrations during the radioactive phase.

In the right panel of Fig. 15, the bolometric LCs for SN 2005dw are shown as
an example. The bolometric LCs constructed using the calibration of BC versus
$B-V$ from Bersten & Hamuy (2009) and Lyman et al. (2014) (orange and green
lines, respectively) systematically underestimate the luminosity of our LC,
while the opposite is found for the BC calibration against $g-r$ colours from
Lyman et al. (2014) (red line). However, we are most interested in how the
distinct validity ranges of the BC calibrations affect the luminosity
estimation during the SN II evolution. In Fig. 14, we already indicated that
the BC calibrations from Lyman et al. (2014) are valid over shorter ranges of
colours than the colours from our SN II sample. This means that the bolometric
luminosity cannot be estimated when the SN II colours fall outside the
validity range. We found that for most SNe II in our sample, the luminosity
estimates using some of the calibrations from the literature do not cover the
entire evolution in the photospheric phase. Figure 15 (right panel) shows that
the bolometric LC using the BC calibration versus $g-r$ colours from Lyman et
al. (2014) only covers 90 days of evolution of SN 2005dw. This is even worse
when using the BC calibrations from Pejcha & Prieto (2015) since these
calibrations are valid over a much shorter range of colours. The bolometric
LCs using the BC calibrations from Pejcha & Prieto (2015) only cover the first
55 days of evolution. This behaviour occurs for the majority of the SNe II in
our sample. While the bolometric LCs using the relations from Pejcha & Prieto
(2015) show small differences with our LCs (see Table 5), we note that most of
the times the BC calibrations from Pejcha & Prieto (2015) estimate the
luminosity only up to phases around the middle of the plateau phase. In
principle, this issue could be connected with the fact that we do not correct
for host-galaxy extinction, resulting in redder SN II events that fall outside
the validity ranges. We tested this by randomly sampling 74 host-galaxy
extinction values from an uniform distribution with values between 0 and 0.6
mag. CSP-I photometry was then corrected for host-galaxy extinction (i.e. one
value for each SN II) and we constructed the bolometric LCs using the BC
calibrations from the literature. Some of the bolometric LCs now cover the
plateau phase up to later epochs, but only for $\sim$10 additional days. The
luminosity estimates still do not cover the entire photospheric phase of the
SNe II.

Finally, Fig. 16 compares the bolometric LCs for the same three SNe II (SNe
2004ej, 2005dw, 2005dz) calculated using the method presented in Sect. 3.2
with those constructed from the BC calibrations provided in the current work
(Fig. 13). We find excellent agreement between both methods, except for the
radioactive tail of SN 2004ej which is systematically dimmer when the BC
calibration against $B-V$ is used. We note that the calibration of BCg against
$g-i$ colours presents the smallest differences when all the bolometric LCs
from CSP-I SN II sample are used (Table 4). Such behaviour is expected since
that calibration shows the lowest dispersion.

In summary, we have constructed BC calibrations against optical colours from
74 SNe II that are valid over a wide range of colours. Therefore, we are
confident that our BC calibrations are an appropriate method to estimate
bolometric luminosities, particularly the calibration of BCg versus $g-i$ as
it shows the tightest correlation.

##  6 Summary and conclusions

In this paper, we have presented bolometric LCs for 74 SNe II using
$uBgVriYJH$ photometry from the CSP-I. Our calculation method is based on the
integration of the observed SED and extrapolations for the flux that falls
bluewards and redwards of the wavelength range. The contribution of the IR
regime was derived from BB fits. At early times, the UV flux was assumed to be
that of a BB. Once the observed SED departs from a BB model a linear
extrapolation was used to estimate the flux in the UV. Thus, we have built the
most homogeneous sample of SN II bolometric LCs so far in the literature.

Several studies calculate bolometric LCs from BB fits to optical data only. We
compared the latter calculation method with ours and found that a BB fitted
only with optical data systematically overestimate the SN luminosity for the
vast majority of the SNe II in our sample. These differences cause variations
in the SN II physical parameters derived from LC modelling. Specifically, we
found significant discrepancies in the explosion energy and 56Ni mass
estimates. This argues that NIR observations are crucial to obtain reliable BB
fits, and therefore, accurate bolometric luminosities. For this reason, we
recommend the following options to calculate bolometric luminosities when NIR
data is missing: (a) using CSP-I SN II NIR photometry as a template. In Table
1, we provide relationships between the $g-i$ colour and colours involving the
$i$ magnitude and a NIR magnitude ($YJH$). Using these relationships, NIR
magnitudes can be estimated using optical colours; (b) the bolometric
luminosity can be determined by means of BCs. In Sect. 5, we present
calibrations of BC against three optical colours (Table 4) using the 74 SNe II
in the CSP-I sample. Specifically, the calibration of BCg versus $g-i$ colour
presents the tightest relation. Previous BC calibrations from the literature
agree quite well with those from the current study. However, the previous
calibrations are often valid only over a small range of colours and most of
the times the luminosity estimates do not cover the entire optically-thick
phase of the SN II. Our calibrations were constructed from 74 SNe II which
cover a larger range of colours.

A full characterisation of the bolometric LCs based on several observed
parameters was provided. Magnitudes were measured at different epochs, as well
as durations and decline rates of different phases of the evolution. The
analyses of the parameter distributions give a continuous sequence of observed
LC properties which is consistent with previous analyses using optical LCs.
Bolometric LCs cover a wide range of observed parameters in terms of their
luminosities and decline rates. During the radioactive phase, most of the SNe
II decline more quickly than expected if full trapping of gamma-ray photons is
assumed. This is further discussed in Paper III. The _optd_ distribution shows
a continuous sequence between 42 days and 146 days.

The bolometric LCs from this work are used in Paper II to determine the
progenitor and explosion properties of SNe II through the hydrodynamical
modelling of LCs and expansion velocities. In Paper III, the physical
parameters are correlated with the observed LC properties measured in the
current paper and several other spectroscopic properties to understand the
observed SN II diversity from the variety of progenitor systems and explosion
properties.

Finally, we remind the reader that our bolometric fluxes are available for
widespread use. Such data will be useful for independent modelling to test the
consistency between different approaches and further refine how SN II
observations can be understood in terms of massive star explosions.

###### Acknowledgements.

The work of the Carnegie Supernova Project was supported by the National
Science Foundation under grants AST-0306969, AST-0607438, AST-1008343,
AST-1613426, AST-1613472, and AST-1613455. L.M. acknowledges support from a
CONICET fellowship. L.M. and M.O. acknowledge support from UNRN PI2018 40B885
grant. M.H. acknowledges support from the Hagler Institute of Advanced Study
at Texas A&M University. S.G.G. acknowledges support by FCT under Project
CRISP PTDC/FIS-AST-31546/2017 and Project No. UIDB/00099/2020. M.S. is
supported by grants from the VILLUM FONDEN (grant number 28021) and the
Independent Research Fund Denmark (IRFD; 8021-00170B). F.F. acknowledges
support from the National Agency for Research and Development (ANID) grants:
BASAL Center of Mathematical Modelling AFB-170001, Ministry of Economy,
Development, and Tourism’s Millennium Science Initiative through grant
IC12009, awarded to the Millennium Institute of Astrophysics, and FONDECYT
Regular #1200710. L.G. acknowledges financial support from the Spanish
Ministry of Science, Innovation and Universities (MICIU) under the 2019 Ramón
y Cajal program RYC2019-027683 and from the Spanish MICIU project
PID2020-115253GA-I00. P.H. acknowledges the support by National Science
Foundation (NSF) grant AST-1715133.
Software: NumPy (Oliphant 2006; Van Der Walt et al. 2011), matplotlib (Hunter
2007), scikit-learn (Pedregosa et al. 2011), SciPy (Virtanen et al. 2020),
emcee (Foreman-Mackey et al. 2013), Pandas (McKinney 2010), ipython/jupyter
(Perez & Granger 2007).

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##  Appendix A SN II sample

1]

Table 6: SN II sample. SN | Host galaxy | Distance modulus | Explosion epoch | $E(B-V)_{\rm MW}$
---|---|---|---|---
|  | (mag) | (MJD) | (mag)
2004dy | IC 5090 | 35.46(0.07) | 53240.5(2) | 0.045
2004ej | NGC 3095 | 33.10(0.21) | 53223.9(9) | 0.061
2004er | MCG -01-7-24 | 33.79(0.16) | 53271.8(2) | 0.023
2004fb | ESO 340-G7 | 34.54(0.11) | 53258.6(7) | 0.056
2004fc | IC 701 | 31.68(0.31) | 53293.5(1) | 0.023
2004fx | MCG -02-14-3 | 32.82(0.24) | 53303.5(4) | 0.090
2005J | NGC 4012 | 33.96(0.14) | 53379.8(7) | 0.025
2005K | NGC 2923 | 35.33(0.08) | 53369.8(8) | 0.035
2005Z | NGC 3363 | 34.61(0.11) | 53396.7(6) | 0.025
2005af | NGC 4945 | 27.75(0.36) | 53320.8(17) | 0.156
2005an | ESO 506-G11 | 33.43(0.18) | 53431.8(6) | 0.083
2005dk | IC 4882 | 34.01(0.14) | 53601.5(6) | 0.043
2005dn | NGC 6861 | 32.83(0.24) | 53602.6(6) | 0.048
2005dt | MCG -03-59-6 | 35.02(0.09) | 53605.6(9) | 0.025
2005dw | MCG -05-52-49 | 34.17(0.13) | 53603.6(9) | 0.020
2005dx | MCG -03-11-9 | 35.18(0.08) | 53611.8(7) | 0.021
2005dz | UGC 12717 | 34.32(0.12) | 53619.5(4) | 0.072
2005es | MCG +01-59-79 | 35.87(0.06) | 53638.7(5) | 0.076
2005gk | 2MASX J03081572 | 35.36(0.08) | — | 0.050
2005hd | anon | 35.38(0.08) | — | 0.054
2005kh | NGC 3094 | 32.94(0.04) | — | 0.025
2005lw | IC 672 | 35.22(0.08) | 53713.8(7) | 0.043
2005me | ESO 244-31 | 34.76(0.10) | 53717.9(10) | 0.022
2006Y | anon | 35.73(0.06) | 53766.5(4) | 0.115
2006ai | ESO 005- G009 | 34.01(0.14) | 53781.6(5) | 0.113
2006bc | NGC 2397 | 31.97(0.26) | 53815.5(4) | 0.181
2006be | IC 4582 | 32.44(0.29) | 53802.8(9) | 0.026
2006bl | MCG +02-40-9 | 35.65(0.07) | 53822.7(10) | 0.045
2006ee | NGC 774 | 33.87(0.15) | 53961.9(4) | 0.054
2006it | NGC 6956 | 33.88(0.15) | 54006.5(3) | 0.087
2006iw | 2MASX J23211915 | 35.42(0.07) | 54010.7(1) | 0.044
2006ms | NGC 6935 | 33.90(0.15) | 54028.5(6) | 0.031
2006qr | MCG -02-22-023 | 34.02(0.14) | 54062.8(7) | 0.040
2007P | ESO 566-G36 | 36.18(0.05) | 54118.7(5) | 0.036
2007U | ESO 552-65 | 35.14(0.08) | 54133.6(6) | 0.046
2007W | NGC 5105 | 33.22(0.20) | 54130.8(7) | 0.045
2007X | ESO 385-G32 | 33.11(0.21) | 54143.5(5) | 0.060
2007aa | NGC 4030 | 31.95(0.27) | 54126.7(8) | 0.023
2007ab | MCG -01-43-2 | 34.94(0.09) | 54123.9(10) | 0.235
2007av | NGC 3279 | 32.56(0.22) | 54173.8(5) | 0.032
2007hm | SDSS J205755.65 | 34.98(0.09) | 54336.6(6) | 0.059
2007il | IC 1704 | 34.63(0.11) | 54349.8(4) | 0.042
2007it | NGC 5530 | 30.34(0.50) | 54348.5(1) | 0.103
2007ld | anon | 35.00(0.09) | 54376.5(8) | 0.081
2007oc | NGC 7418 | 31.29(0.15) | 54388.5(3) | 0.014
2007od | UGC 12846 | 31.91(0.80) | 54400.6(5) | 0.032
2007sq | MCG -02-23-5 | 34.12(0.13) | 54422.8(6) | 0.183
2008F | MCG -01-8-15 | 34.31(0.12) | 54469.6(6) | 0.044
2008K | ESO 504-G5 | 35.29(0.08) | 54475.5(6) | 0.035
2008M | ESO 121-26 | 32.55(0.28) | 54471.7(9) | 0.040
2008W | MCG -03-22-7 | 34.59(0.11) | 54483.8(8) | 0.086
2008ag | IC 4729 | 33.91(0.15) | 54477.9(8) | 0.074
2008aw | NGC 4939 | 33.36(0.19) | 54517.8(10) | 0.036
2008bh | NGC 2642 | 34.02(0.14) | 54543.5(5) | 0.020
2008bk | NGC 7793 | 27.68(0.05) | 54540.9(8) | 0.017
2008bm | CGCG 071-101 | 35.66(0.07) | 54486.5(10) | 0.023
2008bp | NGC 3095 | 33.10(0.21) | 54551.7(6) | 0.061
2008br | IC 2522 | 33.30(0.20) | 54555.7(9) | 0.083
2008bu | ESO 586-G2 | 34.81(0.10) | 54566.8(7) | 0.376
2008ga | LCSB L0250N | 33.99(0.14) | 54711.5(7) | 0.582
2008gi | CGCG 415-004 | 34.94(0.09) | 54742.7(9) | 0.060
2008gr | IC 1579 | 34.76(0.10) | 54769.6(6) | 0.012
2008hg | IC 1720 | 34.36(0.12) | 54779.8(5) | 0.016
2008ho | NGC 922 | 32.98(0.23) | 54792.7(5) | 0.017
2008if | MCG -01-24-10 | 33.56(0.17) | 54807.8(5) | 0.029
2008il | ESO 355-G4 | 34.61(0.11) | 54825.6(3) | 0.015
2008in | NGC 4303 | 30.38(0.47) | 54825.4(2) | 0.020
2009A | KUG 0150-036B | 34.40(0.03) | 54823.0(10) | 0.025
2009N | NGC 4487 | 31.49(0.40) | 54846.8(5) | 0.019
2009aj | ESO 221-G018 | 33.89(0.20) | 54880.5(7) | 0.130
2009ao | NGC 2939 | 33.33(0.20) | 54890.7(4) | 0.034
2009au | ESO 443-21 | 33.16(0.21) | 54897.5(4) | 0.081
2009bu | NGC 7408 | 33.32(0.19) | 54901.9(8) | 0.022
2009bz | UGC 9814 | 33.34(0.19) | 54915.8(4) | 0.035
Table 6: continued. 121212Columns 1 and 2 list the SN name and its host-
galaxy, respectively. In Column 3 the distance modulus is presented, followed
by explosion epochs in Column 4, and Milky-Way reddening values in Column 5.
Errors are indicated in parenthesis.

2]

Table 7: SN II bolometric light$-$curve parameters. SN | $M_{\rm bol,end}$ | $M_{\rm bol,tail}$ | $s_{\rm 1}$ | $s_{\rm 2}$ | $s_{\rm 3}$ | $Cd$ | $pd$ | $optd$
---|---|---|---|---|---|---|---|---
| (mag) | (mag) | (mag 100 day-1) | (mag 100 day-1) | (mag 100 day-1) | (days) | (days) | (days)
2004dy |  $-$16.4(0.1) | — | — | 1.01(2.68) | — | — | — | 42.0(2.0)
2004ej |  $-$16.4(0.2) |  $-$13.9(0.2) | — | 0.65(0.12) | 1.48(0.04) | — | — | 116.4(9.0)
2004er |  $-$16.3(0.2) |  $-$14.9(0.2) | 0.84(0.70) | 0.35(0.09) | 0.68(0.03) | 45.5(10.8) | 100.9(8.8) | 146.4(2.0)
2004fb |  $-$15.8(0.1) | — | — | 0.79(0.22) | — | — | — | —
2004fc |  $-$15.8(0.4) | — | 2.83(0.37) | 0.27(0.13) | — | 29.4(5.3) | 106.2(4.3) | 135.6(1.0)
2004fx |  $-$15.3(0.3) |  $-$13.0(0.2) | — | 0.18(0.13) | 0.94(0.01) | — | — | 103.3(4.0)
2005J |  $-$16.4(0.2) | — | 5.23(0.36) | 0.78(0.06) | — | 29.2(8.5) | 82.5(1.5) | 111.7(7.0)
2005K |  $-$16.0(0.1) | — | — | 1.33(0.20) | — | — | — | —
2005Z |  $-$16.3(0.1) | — | — | 1.32(0.03) | — | — | — | —
2005af |  $-$15.6(0.4) |  $-$14.6(0.4) | — |  $-$0.08(0.68) | 1.28(0.02) | — | — | 117.1(17.0)
2005an |  $-$16.2(0.2) | — | 3.97(0.59) | 1.99(0.47) | — | 27.8(11.9) | 53.1(5.9) | 80.9(6.0)
2005dk |  $-$16.7(0.1) | — | 10.68(0.87) | 1.31(0.05) | — | 26.2(6.7) | 73.1(0.7) | 99.3(6.0)
2005dn |  $-$16.6(0.2) | — | — | 1.12(0.04) | — | — | — | 95.8(6.0)
2005dt |  $-$16.0(0.1) | — | — | 0.25(0.14) | — | — | — | 123.0(9.0)
2005dw |  $-$15.9(0.1) | — | 1.72(0.74) | 0.68(0.13) | — | 35.3(16.5) | 75.4(7.5) | 110.7(9.0)
2005dx |  $-$15.4(0.1) | — | 4.08(1.16) | 0.70(0.25) | — | 27.4(12.2) | 74.5(5.2) | 101.9(7.0)
2005dz |  $-$15.9(0.1) | — | 4.34(0.27) | 0.43(0.08) | — | 28.6(6.1) | 85.5(2.1) | 114.1(4.0)
2005es |  $-$16.5(0.1) | — | 8.23(4.81) | 0.66(0.49) | — | 20.7(20.6) | — | —
2005gk |  $-$16.2(0.1) | — | — | 0.83(0.17) | — | — | — | —
2005hd |  $-$17.0(0.1) |  $-$15.2(0.1) | — | 1.02(0.17) | 1.80(0.04) | — | — | —
2005kh | — |  $-$13.7(0.1) | — | — | 0.85(0.01) | — | — | —
2005lw |  $-$15.5(0.1) | — | — | 1.53(0.08) | — | — | — | —
2005me |  $-$15.7(0.1) | — | — | 1.69(0.11) | — | — | — | —
2006Y |  $-$17.1(0.1) |  $-$15.0(0.1) | 8.02(0.54) | 0.80(0.41) | 2.11(0.17) | 23.9(5.7) | 39.6(1.7) | 63.6(4.0)
2006ai |  $-$17.0(0.2) |  $-$14.9(0.2) | 6.25(0.30) | 1.61(0.18) | 1.66(0.14) | 25.7(6.5) | 48.2(1.5) | 73.8(5.0)
2006bc |  $-$15.2(0.3) | — | 5.09(0.66) |  $-$0.95(0.30) | — | 21.8(5.5) | — | —
2006be |  $-$16.2(0.3) | — | 2.03(5.06) | 0.44(0.11) | — | 26.9(20.3) | 62.0(11.3) | 88.9(9.0)
2006bl |  $-$16.7(0.1) | — | 11.93(2.75) | 2.27(0.22) | — | 15.1(11.7) | — | —
2006ee |  $-$16.0(0.2) | — | — | 0.08(0.07) | — | — | — | 116.0(4.0)
2006it |  $-$16.0(0.2) | — | 2.11(0.79) | 0.07(0.81) | — | 29.4(8.3) | — | —
2006iw |  $-$16.3(0.1) | — | 4.27(0.41) | 0.65(0.14) | — | 28.6(4.1) | — | —
2006ms |  $-$15.8(0.2) | — | 4.33(4.11) | 0.04(0.50) | — | 25.5(13.1) | — | —
2006qr |  $-$15.1(0.2) | — | 3.91(0.88) | 0.99(0.07) | — | 19.6(11.8) | 100.3(4.8) | 119.9(7.0)
2007P |  $-$16.8(0.1) | — | 7.65(0.60) | 1.44(0.37) | — | 28.7(7.3) | — | —
2007U |  $-$16.9(0.1) | — | 5.63(1.18) | 1.74(0.26) | — | 22.7(13.1) | — | —
2007W |  $-$15.4(0.2) | — | 6.07(18.98) | 0.20(0.16) | — | 20.5(17.2) | 105.3(10.2) | 125.8(7.0)
2007X |  $-$16.9(0.2) |  $-$15.2(0.2) | 2.74(0.15) | 0.91(0.05) | 1.51(0.01) | 33.2(7.9) | 86.5(2.9) | 119.7(5.0)
2007aa |  $-$16.2(0.3) | — | — |  $-$0.10(0.07) | — | — | — | 103.1(8.0)
2007ab |  $-$16.9(0.1) |  $-$14.6(0.1) | — | 2.37(0.14) | 1.79(0.21) | — | — | 80.2(10.0)
2007av |  $-$15.8(0.2) | — | — | 0.86(0.04) | — | — | — | —
2007hm |  $-$15.6(0.1) | — | — | 1.34(0.10) | — | — | — | —
2007il |  $-$16.6(0.1) | — | 3.25(1.21) | 0.15(0.10) | — | 30.7(9.1) | 95.1(5.1) | 125.7(4.0)
2007it | — |  $-$15.0(0.5) | 5.51(0.38) | — | 1.08(0.01) | — | — | 116.7(1.0)
2007ld |  $-$16.5(0.1) | — | 8.08(0.60) | 1.10(0.14) | — | 18.6(9.1) | — | —
2007oc |  $-$16.0(0.2) | — | 2.61(0.86) | 1.55(0.09) | — | 29.6(12.3) | 52.4(9.3) | 82.0(3.0)
2007od |  $-$16.9(0.8) | — | 6.98(0.48) | 1.36(0.05) | — | 19.2(6.1) | — | —
2007sq |  $-$15.9(0.1) | — | — | 0.72(0.07) | — | — | — | 104.8(6.0)
2008F |  $-$15.7(0.1) | — | — | 0.14(0.13) | — | — | — | —
2008K |  $-$16.3(0.1) |  $-$13.9(0.1) | 2.25(0.33) | 1.70(0.31) | — | 42.4(21.0) | 56.1(15.0) | 98.4(6.0)
2008M |  $-$16.1(0.3) |  $-$13.7(0.3) | 7.66(0.52) | 0.91(0.08) | 1.80(0.01) | 24.4(10.1) | 61.4(1.1) | 85.8(9.0)
2008W |  $-$16.2(0.1) | — | — | 0.72(0.11) | — | — | — | 104.3(8.0)
2008ag |  $-$16.7(0.2) |  $-$15.1(0.2) | — | 0.15(0.04) | 0.41(0.05) | — | — | 129.4(8.0)
2008aw |  $-$16.4(0.2) |  $-$15.1(0.2) | 3.84(1.23) | 1.82(0.11) | 2.11(0.03) | 34.4(15.0) | — | —
2008bh |  $-$15.7(0.2) | — | — | 0.95(0.15) | — | — | — | —
2008bk |  $-$14.7(0.1) |  $-$12.3(0.1) | — | 0.08(0.08) | 1.13(0.02) | — | — | —
2008bm |  $-$17.3(0.1) | — | — | 2.74(0.12) | — | — | — | 93.7(10.0)
2008bp |  $-$15.3(0.2) | — | — |  $-$0.22(0.41) | — | — | — | —
2008br |  $-$14.9(0.2) | — | — | 0.19(0.12) | — | — | — | —
2008bu |  $-$16.8(0.1) | — | 10.92(6.38) | 2.21(0.19) | — | 12.7(8.8) | 39.2(1.8) | 51.9(7.0)
2008ga |  $-$16.3(0.2) | — | — | 0.82(0.26) | — | — | — | 91.2(7.0)
2008gi |  $-$16.2(0.1) | — | 2.22(1.42) | 1.56(0.38) | — | 32.3(33.1) | — | —
2008gr |  $-$16.6(0.1) | — | 5.43(0.36) | 1.86(0.11) | — | 14.7(7.4) | — | —
2008hg |  $-$15.7(0.1) | — | 1.68(0.46) |  $-$0.96(0.35) | — | 26.2(8.8) | — | —
2008ho |  $-$15.0(0.2) | — | — | 1.11(0.25) | — | — | — | —
2008if |  $-$16.7(0.2) |  $-$14.8(0.2) | 6.84(0.25) | 1.89(0.08) | 0.88(0.19) | 28.3(6.1) | 58.5(1.1) | 86.8(5.0)
2008il |  $-$16.1(0.1) | — | 4.84(3.24) | 0.00(3.23) | — | 19.7(17.2) | — | —
2008in |  $-$14.8(0.5) | — | 2.19(2.05) | 0.51(0.45) | — | 26.4(24.5) | 79.8(22.5) | 106.3(2.0)
2009A |  $-$16.7(0.0) | — | 12.60(0.68) |  $-$4.79(0.47) | — | 27.35(10.7) | — | —
2009N |  $-$15.3(0.4) | — | 2.74(1.62) |  $-$0.14(0.07) | — | 21.4(9.1) | 90.3(4.1) | 111.8(5.0)
2009aj |  $-$17.5(0.2) | — | 8.46(0.14) | 1.46(0.05) | — | 29.8(8.0) | — | —
2009ao |  $-$16.0(0.2) | — | — | 0.83(0.21) | — | — | — | —
2009au |  $-$14.9(0.2) | — | 5.91(0.77) | 2.78(0.17) | — | 27.4(7.5) | — | —
2009bu |  $-$16.2(0.2) | — | — |  $-$0.05(0.08) | — | — | — | —
2009bz |  $-$16.2(0.2) | — | 3.51(0.74) | 0.48(0.14) | — | 26.6(8.0) | — | —
Table 7: continued. 131313Column 1 lists the SN names. Columns 2 and 3 show
the absolute bolometric magnitudes of $M_{\rm bol,end}$ and and $M_{\rm
bol,tail}$. In columns 4, 5, and 6, we list the decline rates $s_{\rm 1}$,
$s_{\rm 2}$, and $s_{\rm 3}$, respectively. Columns 7, 8, and 9 present the
_Cd_ , _pd_ , and _optd_ , respectively. Errors are indicated in parenthesis.

SNe II from the CSP-I sample are presented in Table LABEL:table:sn_info,
together with their host galaxies, distance moduli, explosion epochs, and
Milky Way reddenings. Table LABEL:table:blc_parameters presents the measured
bolometric LC parameters as defined in Sect. 4.1.

##  Appendix B Additional plots

###  B.1 Colour-colour diagrams

Additional plots of $g-i$ against $i-Y$, $i-J$, and $i-H$ colours are
presented in Fig. 17. Here, the data were separated into three epochs: cooling
phase (blue triangles), plateau phase (green dots), and radioactive tail phase
(red squares). Additionally, polynomial fits are presented to each phase of SN
evolution.

Figure 17: Colour-colour diagrams when separating the sample into three
epochs: cooling (blue triangles), plateau (green dots), and radioactive tail
phase (red squares). All measurements were first corrected for Milky Way
extinction. The solid line indicates the polynomial fit to the plateau phase
data, while dashed and dotted lines to the cooling and radioactive tail
phases, respectively.

###  B.2 Light-curve parameters

Figures 18, 19, and 20 present absolute bolometric magnitude LCs for the 74
SNe II within the CSP-I sample, together with their measured parameters listed
in Table LABEL:table:blc_parameters.

Figure 18: Absolute bolometric LCs of SNe II in our sample. The panels present
SNe in order of their discovery dates, from SN 2004dy to SN 2006Y. Bolometric
luminosities are presented as blue dots. The errors are not plotted for better
visualisation, but in general they are small. Measured bolometric LC
parameters are also presented: $M_{\rm bol,end}$ as magenta triangles, $M_{\rm
bol,tail}$ as magenta diamonds, $s_{\rm 1}$ as solid orange lines, $s_{\rm 2}$
as dashed red lines, $s_{\rm 3}$ as dotted green lines, $t_{\rm PT}$ as thick
vertical black lines, and $t_{\rm trans}$ as dashed vertical black lines. Thin
vertical black lines show the explosion epoch and its uncertainty. SNe 2005gk,
2005hd, and 2005kh do not show this line because they have no explosion epoch
estimation.

Figure 19: Same as in Fig. 18, but from SN 2006ai to SN 2009A. Figure 20: Same
as in Fig. 18, but from SN 2009N to SN 2009bz.

##  Appendix C IR and UV corrections

In Sect. 3.2.2, we mentioned that BB fits are not suitable to extrapolate IR
fluxes during the radioactive tail phase since at these times the SN radiation
is dominated by line emission. However, Fig. 4 shows that the IR correction
takes a value of about $\sim$15% by the end of the photospheric phase, meaning
that it is certainly important to correct for the missing flux in the IR
during the radioactive tail phase or the bolometric luminosities will be
considerably underestimated. In the following, we tested if BB extrapolations
can account for the flux beyond the $H$ band during the tail phase, while
keeping in mind the strong caveat that BB fits are not physically justified at
these epochs. We took two SNe II with mid-infrared (MIR) observations in the
literature: SN 1987A and SN 2004et. SN 1987A presents extensive NIR and MIR
observations, while SN 2004et has five observations in the MIR (four of them
at nebular times). It is not expected that the flux longwards of 5 microns
significantly contributes to the total flux. For SN 1987A, we took optical and
IR ($JHKLM$ bands) data from Hamuy & Suntzeff (1990) and Bouchet et al.
(1989), respectively. Optical and NIR data for SN 2004et was taken from
Maguire et al. (2010), and MIR data from Kotak et al. (2009). The latter
observations were obtained in the 3.6 $\mu$m and 4.5 $\mu$m bands (I1 and I2,
respectively) using the InfraRed Array Camera (IRAC) on the _Spitzer_ Space
Telescope.

The goal of this test is to compare the observed flux between the $H$ and $M$
($I2$) bands for SN 1987A (SN 2004et) with the flux from BB extrapolations in