11institutetext: Instituto de Astrofísica de La Plata (IALP), CCT-CONICET-
UNLP. Paseo del Bosque S/N, B1900FWA, La Plata, Argentina
11email<EMAIL_ADDRESS>22institutetext: Universidad Nacional de
Río Negro. Sede Andina, Mitre 630 (8400) Bariloche, Argentina 33institutetext:
Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La
Plata, Paseo del Bosque S/N, B1900FWA, La Plata, 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: Universidad Nacional de Río Negro. Sede Andina, Laboratorio
de Investigación Científica en Astronomía, Anasagasti 1463, Bariloche (8400),
Argentina 66institutetext: Consejo Nacional de Investigaciones Científicas y
Técnicas (CONICET), Argentina

# Circumstellar interaction models for the early bolometric light curve of SN
2023ixf

L. Martinez 1122 M. C. Bersten 331144 G. Folatelli 331144 M. Orellana 5566 K.
Ertini 3311

(Received XXX; accepted XXX)

Type II supernovae (SNe II) show growing evidence of interaction with
circumstellar material (CSM) surrounding their progenitor stars as a
consequence of enhanced mass loss during the last years of the progenitor’s
life, although the exact mechanism is still unknown. We present an analysis of
the progenitor mass-loss history of SN 2023ixf, a nearby SN II showing signs
of interaction. First, we calculate the early-time ($<$ 19 days) bolometric
light curve for SN 2023ixf based on the integration of the observed flux
covering ultraviolet, optical and near-infrared bands, and black-body
extrapolations for the unobserved flux. Our calculations spot the sudden
increase to maximum luminosity and temperature, in addition to the subsequent
fall, displaying an evident peak. This is the first time that this phase can
be precisely estimated for a SN II showing interesting characteristics as: 1)
slope changes during the rise to maximum luminosity; and 2) a very sharp peak
with a maximum luminosity of $\sim$ 3 $\times$ 1045 erg s-1. We use the early-
time bolometric light curve of SN 2023ixf to test the calibrations of
bolometric corrections against colours from the literature. In addition, we
include the observations of SN 2023ixf into some of the available calibrations
to extend their use to earlier epochs. Comparison of the observed bolometric
light curve to SN II explosion models with CSM interaction suggests a
progenitor mass-loss rate of $\dot{M}$ $=$ 3 $\times$ $10^{-3}$ $M_{\odot}$
yr-1confined to 12000 $R_{\odot}$ ($\sim$ 8 $\times$ $10^{14}$ cm) and a wind
acceleration parameter of $\beta$ $=$ 5\. This model reproduces the early
bolometric light curve, expansion velocities, and the epoch of disappearance
of interacting lines in the spectra. This model indicates that the wind was
launched $\sim$ 80 yr before the explosion. If the effect of the wind
acceleration is not taken into account, the enhanced wind must have developed
over the final months to years prior to the SN, which may not be consistent
with the lack of outburst detection in pre-explosion images over the last
$\sim$ 20 yr before explosion.

###### Key Words.:

supernovae: individual (SN 2023ixf) — stars: evolution — stars: massive

##  1 Introduction

Type II supernovae (SNe II111Throughout this paper we use the denomination
‘SNe II’ to refer to hydrogen rich core-collapse supernovae excluding type
IIn, IIb, and SN 1987A-like events.) are the result of the explosion of
massive stars ($\gtrsim$ 9 $M_{\odot}$) that have retained a hydrogen-rich
envelope at the end of their evolution. SNe II are characterised by prominent
hydrogen lines in their spectra (Minkowski 1941; Filippenko 1997) and are the
most common type of core-collapse SNe (Shivvers et al. 2017). Direct
detections of progenitors in pre-explosion images provide strong evidence for
red supergiant (RSG) stars as SN II progenitors (e.g., Van Dyk et al. 2012;
Smartt 2015).

Hydrogen-rich SNe are sub-classified based on their photometric and/or
spectral characteristics. Some of these objects show prevalent narrow emission
lines in their spectra and luminous light curves (Schlegel 1990; Arcavi 2017).
These events are referred to as type IIn SNe. The characteristics of this
subgroup are attributed to the interaction of the SN ejecta with a pre-
existing dense circumstellar material (CSM). This CSM is the result of a high
mass-loss rate during the last stage of the progenitor evolution.

A significant fraction of _normal_ SNe II also show narrow emission features,
disappearing within hours to days after explosion (Bruch et al. 2021), thus
suggesting that the spatial extension of the CSM is small and that the
progenitor experienced enhanced mass loss shortly before core collapse (e.g.,
Yaron et al. 2017). The SN shock wave breaks out from the progenitor surface
emitting high-energy photons that excite and ionise the CSM; moreover, the
continuous interaction between the shock wave and the CSM converts kinetic
energy into radiation that also ionises the material outwards the shock front.
The narrow emission features are a consequence of the recombination of the
slow-expanding ionised CSM (Khazov et al. 2016; Dessart et al. 2017; Smith
2017).

SN 2023ixf is a SN II (Perley et al. 2023) discovered on 2023 May 19
17:27:15.00 UT in the galaxy M101 (Itagaki 2023). The proximity to this object
allowed several detections of the progenitor candidate in pre-explosion images
taken with the Hubble Space Telescope, the Spitzer Space Telescope and ground-
based telescopes. The analysis of these images results in a variable RSG
candidate obscured by dust, whose luminosity is consistent with the evolution
of a star with an initial mass of $M_{\rm ZAMS}$ $=$ 10$-$15 $M_{\odot}$
(Szalai & Dyk 2023; Pledger & Shara 2023; Kilpatrick et al. 2023; Neustadt et
al. 2023; Jencson et al. 2023; Xiang et al. 2023). At the same time, the
analysis of the progenitor variability implies an initially more massive star
of $M_{\rm ZAMS}$ $=$ 20 $\pm$ 4 $M_{\odot}$ (Soraisam et al. 2023).
Additionally, the study of the stellar populations in the vicinity of the site
of explosion of SN 2023ixf infer a progenitor initial mass of $M_{\rm ZAMS}$
$=$ 17$-$19 $M_{\odot}$ (Niu et al. 2023). The progenitor could not be
detected in X-rays and ultraviolet (UV) pre-explosion images (Kong 2023;
Matsunaga et al. 2023; Basu et al. 2023). Pre-explosion observations disfavour
the presence of any outbursts in the last $\sim$20 yr (Neustadt et al. 2023;
Jencson et al. 2023; Dong et al. 2023).

After the discovery, intensive photometric, spectroscopic, and polarimetric
follow up have been carried out (e.g., Hosseinzadeh et al. 2023; Grefenstette
et al. 2023; Singh Teja et al. 2023; Vasylyev et al. 2023). Early-time spectra
show narrow emission features during the first week after discovery, which
indicate the presence of a dense CSM (Sutaria & Ray 2023; Yamanaka et al.
2023; Singh Teja et al. 2023; Jacobson-Galan et al. 2023; Bostroem et al.
2023; Smith et al. 2023).

In the present paper, we attempt to estimate the physical properties of the
CSM surrounding the progenitor of SN 2023ixf by modelling the early-time
bolometric light curve and evolution of the expansion velocity. We note that
the characteristics of the wind producing the CSM has to be consistent not
only with the aforementioned observables of SN 2023ixf but also with the epoch
of disappearance of the narrow emission features and the absence of outbursts
—at least— during the last $\sim$20 yr before explosion.

There are only a small number of objects observed as early and intensively as
SN 2023ixf; therefore, it is a great opportunity to calculate and analyse the
early bolometric light curve of a SN II. The early follow-up of SN 2023ixf
allowed to calculate the bolometric light curve before the maximum luminosity,
during the rise to peak. This is of particular interest given that this has
only been observed in a small number of previously discovered SNe II. Given
the exceptional temporal and wavelength coverage of SN 2023ixf observations,
the analysis of this early phase can provide important information about the
shock wave emergence. In addition, the calculation of the early-time
bolometric light curve allows us to estimate bolometric corrections (BCs) and
to extend the calibrations of BC against optical colours previously
established in the literature (Martinez et al. 2022b) to earlier epochs. In a
forthcoming paper, we derive the progenitor and explosion physical properties
of SN 2023ixf by modelling its complete bolometric light curve and
photospheric velocity evolution (Bersten et al. in prep.).

In this work, we adopt a Cepheid-based distance of 6.85 $\pm$ 0.15 Mpc (Riess
et al. 2022). For the explosion epoch, there are various constraints thanks to
the large number of non-detections close to the discovery date. We adopt MJD
60082.75 as the explosion date, following the analysis of Hosseinzadeh et al.
(2023) and the non-detections by Mao et al. (2023). The Milky Way reddening in
the direction of SN 2023ixf is $E(B-V)_{\rm MW}$ $=$ 0.008 mag (Schlafly &
Finkbeiner 2011), while we adopt a host-galaxy reddening of $E(B-V)_{\rm
host}$ $=$ 0.031 mag based on the equivalent widths of Na I lines (Lundquist
et al. 2023, see also Smith et al. 2023). We assume a Galactic extinction law
from Cardelli et al. (1989) with $R_{V}$ $=$ 3.1.

The present paper is organised as follows. Section 2 describes the methodology
to calculate the bolometric light curve of SN 2023ixf. Section 3 inspects the
currently available calibrations for BCs versus optical colours and presents
an extension of the calibrations previously found by Martinez et al. (2022b)
by including SN 2023ixf in the analysis. Section 4 presents the modelling to
the early-time bolometric light curve of SN 2023ixf and the derived physical
properties of the CSM. In Sect. 5, we discuss the scenario that produces the
CSM and compare with the results from the literature. We provide our
concluding remarks in Sect. 6.

##  2 Bolometric light curve

Figure 1: Early bolometric light curve for SN 2023ixf (blue dots). The dashed
line represents the pseudo-bolometric light curve. The inset plot shows the
first week of evolution of the bolometric luminosity. In this plot, the pink
triangles are the bolometric luminosities when observed UV data are not taken
into account in the calculation method. In most cases the error bars are
smaller than the dot size. Figure 2: Evolution in time of black-body fit
parameters for SN 2023ixf: temperature (red dots) and radius (green diamonds).

The main goal of this work is to derive physical properties for the mass-loss
history of the progenitor of SN 2023ixf near core collapse, based on comparing
models with early-time observations (¡ 19 days). The models are computed using
a 1D code that simulates the explosion of the SN and calculates bolometric
luminosities, among other observables (Bersten et al. 2011, see Sect. 4 for
additional details). Therefore, in a first stage, we estimate bolometric
luminosities for SN 2023ixf.

SN 2023ixf has been monitored since shortly after its discovery with an
exceptional cadence and wavelength coverage. In order to estimate a reliable
bolometric light curve, we collect publicly-available multi-band photometric
data from the literature and additional photometry reported through The
Astronomer’s Telegrams222https://www.astronomerstelegram.org/ and TNS
Astronotes333https://www.wis-tns.org/astronotes services. Specifically, we
gathered UV, optical ($UBVu^{\prime}g^{\prime}r^{\prime}i^{\prime}z^{\prime}$
filters) and near-infrared (NIR, $JHK_{s}$ filters) magnitudes from Singh Teja
et al. (2023), and optical photometry ($BVRIg^{\prime}r^{\prime}i^{\prime}$)
from Balam & Kendurkar (2023), D’Avanzo et al. (2023), Fowler et al. (2023),
Kendurkar & Balam (2023), Sgro et al. (2023), and Vannini (2023a, b, c). The
UV data presented in Singh Teja et al. (2023) correspond to $UVW2$, $UVM2$,
and $UVW1$ filters from the Ultraviolet Optical Telescope (Roming et al. 2005)
on board the _Swift_ Observatory (Gehrels et al. 2004). The entire data set
covers from 0.3 to 19 days after explosion, which allow us to analyse the
early SN emission and to estimate the physical properties of the CSM.

The estimation of the bolometric luminosities was performed in the same manner
as in Martinez et al. (2022b). This method consists in the integration of the
observed fluxes, which in the present study represents the spectral energy
distribution (SED) of SN 2023ixf from mid-UV —when available— to NIR
wavelengths. In addition, the calculation method assumes that the SN emits as
a black body at the unobserved wavelengths (see details below).

The early-time photometry of SN 2023ixf is characterised by a high cadence of
observations. However, magnitude values are not always available at a given
epoch for all the observed bands, which are necessary to produce reliable
black-body fits to the observed SED. We obtained a complete set of magnitudes
at each observed epoch performing loess non-parametric regressions using the
ALR code444https://github.com/olrodrig/ALR described in Rodríguez et al.
(2019). Observed $UVW2$ and $UVM2$ light curves have a small number of
observations, therefore, these light curves were not interpolated.
Extrapolations were not allowed for any band.

Having photometric measurements or interpolated magnitudes in all observed
bands at each epoch of observation (with the exception of $UVW2$ and $UVM2$),
we proceeded with the bolometric luminosity estimation method. We transformed
magnitudes into monochromatic fluxes at the mean wavelength of the filter
using the transmission functions provided by the SVO filter service (Rodrigo
et al. 2012; Rodrigo & Solano 2020), taking into account that the collected
data are available in different photometric systems. The monochromatic fluxes
were then integrated using the trapezoidal method and the observed flux was
estimated at each epoch of observation.

To estimate the unobserved flux at shorter and longer wavelengths we assume
that the SN emission in those regimes is well described by a black-body model.
At early times, this assumption is mostly correct. As the SN ejecta expands
and cools, the UV emission starts to depart from a black-body model as a
consequence of the increasing line blanketing produced by iron-group elements.
However, with our collected data set, we note that black-body models are still
consistent with the observed UV emission at least up to $\sim$15 days from
explosion (after this epoch there are no available observations at UV bands).
Therefore, it is not necessary to remove the bluest bands from the black-body
fitting as it is, in general, for later observations (see e.g. Bersten & Hamuy
2009; Faran et al. 2018; Martinez et al. 2022b). Black-body fits were carried
out only for observational epochs with at least four observed/interpolated
bands.

Once we found a black-body model that fits the observed SED, we assume that
the extrapolated flux at longer wavelengths is simply the emission of the
black-body model between the reddest observed band and infinity (known as the
IR correction). At the same time, the extrapolated flux at shorter wavelengths
is the emission of the black-body model between the bluest observed band and
zero wavelength (known as the UV correction). The sum of observed flux and the
extrapolated fluxes from the black-body model equates the bolometric flux.

To take the magnitude uncertainties into account, we calculated the bolometric
flux via a Monte Carlo procedure. For each of the two thousand simulations, we
randomly sampled broadband magnitudes assuming a Gaussian distribution centred
at the magnitude value with a standard deviation equal to the magnitude
uncertainty. Then, the observed flux was integrated, the best-fitting black-
body model was found, and the IR and UV corrections were estimated. The mean
bolometric flux of the two thousand simulations was calculated and taken as
the bolometric flux. We took the standard deviation of the distribution as the
uncertainty of the luminosity. This procedure was repeated at every epoch of
observation. Finally, the bolometric flux was transformed into luminosity
using the distance to the SN. The bolometric light curve was calculated from
1.9 to 18.9 days after explosion.

Figure 1 shows the resulting bolometric light curve for SN 2023ixf. In
addition, Fig. 1 shows the pseudo-bolometric light curve for SN 2023ixf, which
is defined as the integration of the observed flux in the optical and NIR
regimes. At early times, the differences between both light curves are
significant. This behaviour indicates the great contribution of the UV to the
bolometric flux at these epochs. Moreover, the absence of the UV flux erases
the luminosity peak. Therefore, if the photometric coverage is limited to
optical and redder bands, or the unobserved flux in the UV is not taken into
account, the peak in the bolometric light curve is lost. Eventually, the
differences become smaller because the SN ejecta cools and the UV emission
decreases, while the SN emission in the optical increases.

The early bolometric light curve of SN 2023ixf consists of a rapid rise time
of 3.47 days to maximum at $\log$ $L_{\rm bol}$ $=$ 45.5${}^{+0.18}_{-0.30}$
($M_{\rm bol}$ $=$ $-$25.08 $\pm$ 0.54 mag). This is the first time —to our
knowledge— that such a detailed rise to maximum and sharp peak are observed in
bolometric luminosities, having a large wavelength coverage to make reliable
estimations of the bolometric luminosities, and using similar techniques. At
the epoch of maximum luminosity, the black-body model fits observed fluxes in
the following bands: $UVOT$-$B$, $B$, $g$, $UVOT$-$V$, $V$, $r$, $i$, $z$,
$J$, $H$, and $K$; resulting in a black body with a temperature of $\sim$ 1.3
$\times$ 105 K. After peak, the luminosity drops $\sim$2.3 dex in the
following 1.5 days. Then, the luminosity starts a slower decline, at least up
to day 19 post-explosion.

During the luminosity rise, SN 2023ixf shows different slopes to reach the
maximum luminosity (see Fig. 1). First, the luminosity increases almost
linearly up to 2.2 days post-explosion. Then, the luminosity starts a slower
rise up to day 2.9. Finally, the light curve rises up to maximum with a single
slope —much steeper than in earlier times— from day 2.9. This epoch matches
with the last epoch of observation —before maximum— having _Swift_ data in the
UV. Specifically, before maximum luminosity, the $UVW1$-band light curve is
available until 2.9 days post-explosion, while only a single data point in the
$UVM2$ band was obtained.

In order to test the influence of the available UV data on the rise to maximum
luminosity we calculate the early bolometric light curve for SN 2023ixf again,
but this time neglecting the _Swift_ data in the UV regime, both from the
black-body fitting procedure and the integration of the observed SED. This is
shown in the inset plot of Fig. 1 as pink triangles (only the first three days
are shown given that these are the epochs with most UV observations). This
process results in a bolometric light curve without the slope changes
mentioned above, and with lower luminosities before day 2.9 post-explosion.
The lower luminosities are obtained because the _Swift_ data in the UV (mostly
in the $UVW1$ band) are more luminous than the predicted flux from black-body
models at the mean wavelength of the $UVW1$ filter, when the $UVW1$ data are
neglected from the calculation. This means that black-body fits ignoring the
available UV data underestimate the UV extrapolation. Therefore, the observed
$UVW1$ data produce black-body models that peak at shorter wavelengths, i.e.
hotter black-body models, causing larger UV corrections and higher
temperatures during this time interval (see Fig. 2). Although the lack of UV
observations after 2.9 days introduces more uncertainty in the bolometric
luminosities, this lack does not explain the sudden increase in temperature
and luminosity that occurs just after that time. In summary, the bolometric
luminosities before day 2.9 strongly depends on the UV flux, which is very
intense at these epochs. Unfortunately, at the moment there are no more public
data in the UV.

Figure 2 shows the black-body parameters obtained from the fits. Before the
luminosity peak, the temperature shows values between $\log$ T $\sim$
4.3$-$4.4, while the radius increase by a factor of $\sim$2\. Then, the
temperature suddenly increases to a value of $\log$ T $\sim$ 5.1 in less than
0.5 days, coincident with the maximum luminosity. At the same time, the black-
body radius takes smaller values. After the luminosity peak, the black-body
temperature (radius) decreases (increases) almost monotonically.

##  3 Bolometric corrections

In Sect. 2, we estimate bolometric luminosities for SN 2023ixf through direct
integration of the observed flux (covering UV, optical, and NIR bands) and
assuming that the SN emits as a black body at shorter and longer —unobserved—
wavelengths. This is the most accurate method to estimate bolometric
luminosities when extensive wavelength coverage is available. The use of
bolometric corrections to convert broadband magnitudes into bolometric
magnitudes is a more frequent technique when the photometric coverage is
limited only to optical filters. From the work of Bersten & Hamuy (2009),
where the authors developed calibrations between BCs and optical colours,
several other studies have analysed these relations (e.g. Lyman et al. 2014;
Pejcha & Prieto 2015). More recently, Martinez et al. (2022b) presented
updated calibrations of BC against optical colours using the most homogeneous
and largest sample of SN II bolometric light curves.

The unprecedented early-time bolometric light curve of SN 2023ixf,
characterised by a high cadence of observations and the wide wavelength
coverage of the broadband data, allows us to examine the calibrations of
bolometric corrections versus colour found in the literature (Sect. 3.1) and
to extend previous calibrations to bluer colours (i.e. to earlier times, Sect.
3.2).

###  3.1 Testing calibrations of bolometric corrections

Figure 3: Bolometric light curve for SN 2023ixf calculated from the
integration of the observed flux plus black-body extrapolations (thick grey
line, referred to as ‘SED integration’) in comparison with those calculated
from calibrations of bolometric corrections versus colours found in the
literature: Martinez et al. (2022b) (top-left panel), Lyman et al. (2014)
(top-right panel), Bersten & Hamuy (2009), Pejcha & Prieto (2015), and
Pritchard et al. (2014) (bottom-left panel). The bottom-right panel shows
bolometric light curves using the calibrations by Martinez et al. (2022b) when
larger validity ranges of colours are allowed.

In this section, we compare the bolometric light curve of SN 2023ixf estimated
in Sect. 2 with those constructed employing the calibrations of bolometric
corrections from the literature. Specifically, we compare with the
calibrations from Bersten & Hamuy (2009), Lyman et al. (2014), Pritchard et
al. (2014), Pejcha & Prieto (2015), and Martinez et al. (2022b). Figure 3
shows the results of the analysis. Each panel also shows the colour curves
used for the calculation. The details of the comparison are found below.

Martinez et al. (2022b) presented calibrations of BCs versus $(B-V)$, $(g-r)$,
and $(g-i)$ colours, with the latter two colour indices showing the smallest
dispersions. These BC calibrations are distinguished according to the phase in
which the SN is found. For the comparison, we utilised the calibrations that
corresponds to the ‘cooling phase’, since these are the most appropriate for
our data set. In addition, these calibrations were performed with photometric
data points in the natural system of the Swope telescope at Las Campanas
Observatory (Contreras et al. 2010). Therefore, the first step is to convert
our data into the corresponding photometric system. Vega magnitudes were
transformed into AB system using the conversion values published in Blanton &
Roweis (2007). We then used the magnitude offsets from Krisciunas et al.
(2017) to convert AB magnitudes into the natural system of the Swope
telescope. At that moment, the calibrations of BCs were applied.

We find good agreements between the bolometric light curve calculated in Sect.
2 (referred to as ‘SED integration’ in Fig. 3), and those calculated using the
BC calibrations from Martinez et al. (2022b) (Fig. 3, top-left panel). The
bolometric light curve constructed with the BC calibration against $(g-r)$
produces the most similar light curve to that observed. At the same time, the
predicted bolometric luminosities using the calibration versus $(g-i)$ are
slightly brighter than those estimated using the $(g-r)$ colour index. The
bolometric light curve using the BC calibration against $(B-V)$ agrees well
between days 6 and 10. After day 10 the predicted bolometric luminosities
overestimate the observations. We note that earlier estimations are not
possible because the colour values are bluer than the validity ranges of the
calibrations (see below for predicted bolometric luminosities if the validity
colour ranges are not considered).

The top-right panel of Fig. 3 compares our bolometric light curve and those
predicted using the BC calibrations for the cooling phase from Lyman et al.
(2014). These authors constructed calibrations for several colour indices.
However, we show comparisons only to calibrations using $(B-V)$, $(g-r)$, and
$(g-i)$ given that the other colour indices present a small number of data
points. The bolometric light curve computed using BC calibrations versus
$(B-V)$ shows good agreement with our, with the exception of the data points
between 7 and 10 days post-explosion. At those epochs, the predicted
luminosities underestimate our estimation by $\sim$0.1 dex. The predicted
bolometric light curves using $(g-r)$ and $(g-i)$ colours show similar
behaviours. In both cases, the luminosity is underestimated, especially during
the first 5 days post-explosion. For the $(g-i)$ colour, the rise to maximum
is much smoother than the calculated with our procedure, similar to the
behaviour of the pseudo-bolometric light curve (see Fig. 1).

The bottom-left panel of Fig. 3 shows a comparison with several other
calibrations found in the literature. We chose to compare with the BC
calibrations versus $(B-V)$ from Bersten & Hamuy (2009) and Pejcha & Prieto
(2015). The other BC calibrations from these latter two papers cannot be well
compared due to the small number of data points for the colours involved
[($B-I$) and ($V-I$) in the case of Bersten & Hamuy (2009) and ($B-R$) and
($B-I$) for Pejcha & Prieto (2015)]. The bolometric light curve calculated
with the BC calibration from Bersten & Hamuy (2009) present two data points
—around days 6.5 and 10.5 post-explosion— much brighter than those using the
SED integration method. With the exception of these values, the luminosity
agree well with our estimate. The BC calibration from Pejcha & Prieto (2015)
agrees well with our bolometric light curve at some epochs. However, other
epochs show a variable behaviour. This behaviour can possibly be explained due
to the irregular conduct of the $(B-V)$ colour curve, which could also explain
the over-luminous data points in the comparison with the BC calibration from
Bersten & Hamuy (2009). Additionally, we compare to the BC calibrations from
Pritchard et al. (2014). These calibrations were performed for ($U-B$) and
($B-V$) colours using _Swift_ +UVOT filters; therefore, we use the available
_Swift_ +UVOT photometry for this comparison. For both BC calibrations, the
resulting bolometric light curves are much dimmer than that estimated via SED
integration.

Finally, we used the BC calibrations from Martinez et al. (2022b) again, but
this time without considering the validity ranges of colours. This means that
we extrapolated the calibrations to bluer colours. The predicted bolometric
light curves using the extrapolated BC calibrations versus $(g-r)$ and $(g-i)$
shows remarkable good agreement at these early epochs, with the exception of
the value around day 6. However, we note the large error bars in the $(g-r)$
and $(g-i)$ colour curves at that epoch, arising predominantly from the
$g$-band magnitude. Surprisingly, the BC calibration versus $(B-V)$ predicts
the behaviour of the rise to maximum luminosity and the subsequent drop,
although the following data points clearly overestimate the luminosity from
the SED integration method. However, as stated before, we note the variable
behaviour of the $(B-V)$ colour curve. This analysis shows that the BC
calibrations from Martinez et al. (2022b) are a satisfactory method to
estimate bolometric luminosities, particularly the calibrations versus $(g-r)$
and $(g-i)$ colours.

###  3.2 Calibrations of bolometric corrections including SN 2023ixf

Table 1: Coefficients of the polynomial fits to the bolometric corrections
versus optical colours.

Colour | Range | $c_{0}$ | $c_{1}$ | $c_{2}$ | $c_{3}$ | $c_{4}$ | $\sigma$
---|---|---|---|---|---|---|---
($g-r$) | ($-$0.43, 1.09) |  $-$0.353 | 1.643 |  $-$3.574 | 1.474 | — | 0.133
($g-i$) | ($-$0.60, 1.15) |  $-$0.220 | 0.738 |  $-$2.137 | 0.913 | — | 0.125
($B-V$) | ($-$0.35, 1.16) |  $-$0.704 | 4.013 |  $-$7.985 | 6.904 |  $-$2.357 | 0.206

555BC = $\sum_{k=0}^{n}c_{k}(colour)^{k}$, where colour is taken from the
first column. The last column ($\sigma$) represents the standard deviation
about the fit.

Figure 4: Bolometric corrections relative to the $g$ band as a function of
($g-r$) colour (top panel) and ($g-i$) colour (middle panel), and relative to
the $V$ band as a function of $(B-V)$ colour (bottom panel). SN 2023ixf is
presented as blue dots, while pink dots represent the cooling phase of the SNe
II in the CSP-I sample (see Martinez et al. 2022b). The dashed lines shows the
fit to the data. The errors in the CSP-I SN II data are not plotted for better
visualisation.

In Sect. 3.1, we show that the BC calibrations from Martinez et al. (2022b)
adequately reproduce the bolometric light curve of SN 2023ixf. In addition, SN
2023ixf has an unique early-time bolometric light curve, due to the high
observational cadence that resolves the rise to maximum luminosity, and the
extensive wavelength coverage —from UV to NIR— that allows us to estimate
precise bolometric luminosities. This motivates us to incorporate the early-
time data of SN 2023ixf to the BC calibrations from Martinez et al. (2022b) in
order to extend the calibrations (corresponding to the ‘cooling phase’) to
bluer colours (i.e. to earlier times).

The BC calibrations from Martinez et al. (2022b) were performed using a sample
of 74 SNe II observed by the Carnegie Supernova Project-I (Hamuy et al. 2006)
using the facilities of the Las Campanas Observatory. Therefore, we used the
same data, in addition to those from SN 2023ixf, to construct new BC
calibrations.

First, we converted the bolometric luminosities of SN 2023ixf into bolometric
magnitudes. By definition

$M_{\rm bol}=M_{\odot,\rm bol}-2.5\,\mathrm{log}_{10}\,\left(\frac{L_{\rm
bol}}{L_{\odot,\rm bol}}\right)\,,$ (1)

where $L_{\odot,\rm bol}$ = 3.845 $\times$ 1033 erg s-1 and $M_{\odot,\rm
bol}$ = 4.74 mag are the luminosity and the absolute bolometric magnitude of
the Sun (Drilling & Landolt 2000). We then calculated the bolometric
corrections for SN 2023ixf employing the definition, BCj = $m_{\rm
bol}-m_{j}$, where $m_{j}$ is the extinction-corrected magnitude in the band
$j$ of the SN, and $m_{\rm bol}$ is its the bolometric magnitude. Finally, we
looked for calibrations between the bolometric corrections and the same three
colour indices.

Figure 4 displays the bolometric correction relative to the $g$ band (BCg) as
a function of $(g-r)$ and $(g-i)$ colours (top and middle panels,
respectively). Figure 4 also includes polynomial fits to the data computed via
Markov chain Monte Carlo (MCMC) methods using the python package emcee
(Foreman-Mackey et al. 2013). We used third order polynomial fits for the
calibrations comprising $(g-r)$ and $(g-i)$ colours. We find good agreement
between the polynomial fits and the data, except for the lowest BCg value in
both plots (BCg $=$ $-$2.40 mag). This value corresponds to the epoch when the
luminosity peak is taking place.

We also searched for calibrations between the bolometric correction relative
to the $V$ band (BCV) as a function of $(B-V)$. This is shown in the bottom
panel of Fig. 4. For this case, we utilised a fourth order polynomial to fit
the early-time data of SN 2023ixf. We did not find any improvement in the BC
calibration versus $(B-V)$ colour with respect to that obtained using the
CSP-I SN II data, i.e. towards $(B-V)$ values lower than $-$0.10 mag. The
lowest two BCV values (BCV $=$ $-$5.04 and $-$4.10 mag) corresponds to the
peak time. However, we note that these calibrations should be considered more
uncertain for the bluest colours for the following reasons: 1) we are using
only one SN II at these colour ranges; and 2) the steep dependence of the BC
with colour, which implies that an uncertainty in the colour measurement could
produce a considerable error in the estimation of the BC. The coefficients of
the polynomial fits and the standard deviation around the fits are presented
in Table 1.

##  4 Modelling

Table 2: Summary of the initial conditions of the models presented in this
work.

Model | $\dot{M}$ | $R_{\rm CSM}$ | $R_{\rm CSM}$ | $\beta$ | $M_{\rm CSM}$ | $t_{\rm dis}$
---|---|---|---|---|---|---
| [$M_{\odot}$ yr-1] | [$R_{\odot}$] | [cm] |  | [$M_{\odot}$] | [days]
m15_w0.3_r2500 | 0.3 | 2500 | 1.7 $\times$ 1014 | 0 | 0.08 | 1.4
m15_w0.5_r2500 | 0.5 | 2500 | 1.7 $\times$ 1014 | 0 | 0.14 | 1.5
m15_w1.0_r2500 | 1.0 | 2500 | 1.7 $\times$ 1014 | 0 | 0.28 | 1.1
m15_w1.0_r3000 | 1.0 | 3000 | 2.1 $\times$ 1014 | 0 | 0.37 | 0.7
m15_w1.2m2_r8000 | 1.2 $\times$ 10-2 | 8000 | 5.6 $\times$ 1014 | 0 | 0.02 | 6.7
m15_w3m2_r8000 | 3 $\times$ $10^{-2}$ | 8000 | 5.6 $\times$ 1014 | 0 | 0.04 | 8.5
m15_w1.2m2_r5000 | 1.2 $\times$ $10^{-2}$ | 5000 | 3.5 $\times$ 1014 | 0 | 9 $\times$ 10-3 | 3.9
m15_w3m3_r12000_beta5 | 3 $\times$ 10-3 | 12000 | 8.4 $\times$ 1014 | 5 | 0.23 | 6.5
m15_w3m3_r7000_beta5 | 3 $\times$ 10-3 | 7000 | 4.9 $\times$ 1014 | 5 | 0.23 | 4.8
m15_w1m2_r12000_beta5 | 1 $\times$ 10-2 | 12000 | 8.4 $\times$ 1014 | 5 | 0.76 | 10.0
m15_w3m3_r12000_beta2 | 3 $\times$ 10-3 | 12000 | 8.4 $\times$ 1014 | 2 | 0.05 | 5.0
666$\dot{M}$ is the progenitor mass-loss rate, $R_{\rm CSM}$ is the extension
of the wind material, $\beta$ is the wind acceleration parameter ($\beta$ $=$
0 corresponds to steady-state winds), $M_{\rm CSM}$ is the CSM mass, and
$t_{\rm dis}$ is the theoretical epoch of disappearance of interacting lines.

The early-time bolometric light curve of SN 2023ixf allows us to constrain its
progenitor mass-loss history by comparing models with observations.
Theoretical light curves are calculated using a code that solves the
hydrodynamical equations assuming spherical symmetry coupled to the radiation
transfer equations in the diffusion approximation (Bersten et al. 2011). The
explosion is simulated by injecting energy near the centre of the progenitor
star, producing a powerful shock wave that propagates out.

In addition to bolometric light curves, our code calculates expansion
velocities at different layers. Therefore, we also compare the expansion
velocity at the photospheric layer to the Fe II $\lambda$5169 line velocity,
given that this line gives a good estimation of the photospheric velocity
(Dessart & Hillier 2005). The omission of the expansion velocities in the
fitting procedure can result in solutions that are not consistent with the SN
expansion rate (see Martinez et al. 2020). If this is the case, the solution
found is spurious. In order to measure expansion velocities of SN 2023ixf, we
used public spectra from the WISeREP777https://www.wiserep.org/ archive (Yaron
& Gal-Yam 2012) in those epochs where Fe II $\lambda$5169 profiles started
appearing (approximately at 25 days after explosion). We used three spectra
uploaded to WISeREP from the Dark Energy Spectroscopic Instrument (DESI; Levi
et al. 2019) at the 4m Mayall Telescope at Kitt Peak National Observatory and
one spectrum uploaded by TNS, without information about the telescope and
instrument listed. We measured the expansion velocities of Fe II $\lambda$5169
in the spectra by fitting a Gaussian to the minimum of the absorption
profiles. Additionally, we utilised the relation by Faran et al. (2014) that
predicts the photospheric velocity at 50 days post-explosion from Fe ii
velocity measurements.

Progenitor models at the time of core collapse are needed to initialise the
explosion. In this context, we used the public stellar evolution code
MESA888http://mesa.sourceforge.net/ version 22.6.1 (Paxton et al. 2011, 2013,
2015, 2018, 2019; Jermyn et al. 2023) to obtain a non-rotating RSG pre-SN
model at solar metallicity (Z⊙ $=$ 0.0142; Asplund et al. 2009) for a star of
15 $M_{\odot}$ on the main sequence. The choice of this initial mass value was
carried out to agree with the progenitor luminosity observed in pre-explosion
images (Jencson et al. 2023; Neustadt et al. 2023; Van Dyk et al. 2023; Xiang
et al. 2023). The stellar models were evolved from the main sequence to core
collapse, defined as the time when any location inside the iron core reaches
an infall velocity of 1000 km s-1. During massive-star evolution, mass loss
was treated using the ‘Dutch’ wind scheme defined in MESA (Vink et al. 2001;
de Jager et al. 1988). Convection was modelled using the mixing-length theory
(Böhm-Vitense 1958) adopting a mixing-length parameter $\alpha_{\rm mlt}$ $=$
2.0. The convective regions were determined using the Ledoux criterion.
Semiconvenction was implemented as a diffusive process adopting an efficiency
of $\alpha_{\rm sc}$ $=$ 1.0 (Langer et al. 1983). Convective-core
overshooting is treated in the step formalism during hydrogen- and helium-core
burning adopting overshooting parameters of $\alpha_{\rm os}$ $=$ 0.15
(Martins & Palacios 2013) and 0.03 (Li et al. 2019) pressure scale heights,
respectively. For later core-burning stages, we adopted the decreasing
exponential approach implemented in MESA to account for convective
overshooting with a parameter $f$ $=$ 0.003 (Farmer et al. 2016; Jones et al.
2017). The evolution of the initially 15$M_{\odot}$ star with the above
evolutionary parameters results in a progenitor model with a final mass of
12.7 $M_{\odot}$, hydrogen-rich envelope of 8.0 $M_{\odot}$, and radius of 918
$R_{\odot}$.

The observation of narrow emission lines in early-time SN spectra result from
the presence of a dense and confined CSM surrounding the progenitor star. The
CSM formation is thought as a consequence of a high mass-loss rate occurred
during the last years to decades before core collapse, although the exact
mechanism is unclear. As the SN ejecta interacts with the CSM, kinetic energy
of the ejecta is converted to radiation that can ionise the CSM and boost the
SN early-time luminosity. Given that the progenitor models computed with MESA
do not consider the mass loss producing the CSM we are interested in, we
artificially attached a CSM profile to the outer layers of the pre-SN model as
usually done in the literature (e.g., Moriya et al. 2011; Morozova et al.
2018; Englert Urrutia et al. 2020).

Before attaching any CSM profile, we computed several models with different
explosion energies ($E_{\rm exp}$) and compared them to our observations.
Particularly, we look for agreement to the observed expansion velocities of SN
2023ixf, since these observables are strongly influenced by the energy of the
explosion (for a fixed pre-SN model). We choose an explosion energy of $E_{\rm
exp}$ $=$ 1.25 $\times$ 1051 erg for each of our simulations with CSM
interaction999We note that the inclusion of CSM can alter the photospheric
velocities of a SN due to the conversion of kinetic energy into radiation at
the shock front. This depends on the adopted physical parameters for the CSM..
We note that the ejecta mass and the explosion energy are rough estimates
because in the present paper we are focused on the properties of the CSM. In a
forthcoming paper we analyse the complete evolution of the bolometric light
curve and estimate the physical properties of the progenitor and explosion
(Bersten et al. in prep.).

In the following we aim to reproduce the early-time bolometric light curve of
SN 2023ixf by considering two different scenarios to simulate the CSM
formation: steady-state (Sect. 4.1) and accelerated (Sect. 4.2) winds. The
nomenclature is based on naming each model according to its initial mass, wind
mass-loss rate, radial CSM extension, and velocity law for the wind velocity.
For example, m15_w3m3_r12000_beta5 corresponds to a initial mass of $M_{\rm
ZAMS}$ $=$ 15 $M_{\odot}$, a mass-loss rate of $\dot{M}$ $=$ 3 $\times$ 10-3
$M_{\odot}$ yr-1, $R_{\rm CSM}$ $=$ 12000 $R_{\odot}$, and velocity law
$\beta$ $=$ 5\. A summary of the presented models is found in Table 2. We note
that none of the models presented in this section can reproduce the change in
the slope during the rise to maximum, observed in the bolometric light curve
before day 2.9 post-explosion (see Sect. 2).

We note that the explosion epoch of SN 2023ixf is based on the first detection
and last non-detection, while in our models the explosion epoch is defined as
the moment when the energy is deposited near the centre of the progenitor
star. Given the difference in the definition of ‘explosion epoch’ and that it
takes a few days for the shock wave to break out from the CSM, we shifted our
models to match the time of maximum luminosity. These shifts were always less
than 1 day for the best-fitting models.

###  4.1 Steady-state winds

Figure 5: Comparison between the bolometric light curve of SN 2023ixf (dots)
with models varying the CSM properties (lines), assuming steady-state mass
loss. The upper panel involves models with higher mass-loss rates and more
confined CSMs than the models shown in the bottom panel. The inset plot
compares the photospheric velocities of SN 2023ixf to the same models
previously mentioned. For the model nomenclature, see Sect. 4.

The first scenario to survey involves steady-state winds. In this scenario,
the CSM density ($\rho_{\rm CSM}$) is represented as $\rho_{\rm CSM}(r)$ $=$
$\dot{M}$/(4$\pi v_{\rm wind}r^{2}$), where $r$ is the radial coordinate,
$\dot{M}$ is the wind mass-loss rate and $v_{\rm wind}$ is the velocity of the
wind. Throughout the present work, we assume a terminal wind velocity of
$v_{\rm wind}$ $=$ 115 km s-1, as measured by Smith et al. (2023).

The top panel of Fig. 5 compares explosion models including CSM-ejecta
interaction to observations of SN 2023ixf. In this case, we choose CSM models
characterised for their confined radial extent between 2500 and 3000
$R_{\odot}$ ($\sim$1.7$-$2.1 $\times$ 1014 cm) and high mass-loss rates in the
range of 0.3$-$1.0 $M_{\odot}$ yr-1. While all of these models reproduce the
width of the luminosity peak, model m15_w0.3_r2500 does it better. However,
this model underestimates the luminosity after day 6 after explosion. Higher
mass-loss rates (models m15_w0.5_r2500 and m15_w1.0_r2500) result in higher
peak luminosities. However, these models achieve more luminous light curves
after peak than observed, and underestimate the observed luminosities after
day 10. A more extended CSM produce higher luminosities after peak,
inconsistent with observations.

The comparison from the top panel of Fig. 5 shows that some parts of the early
light curve of SN 2023ixf can be reproduced with the adopted CSM parameters.
Potentially, a more detailed study around these parameters could result in
better agreements. However, all of these models are inconsistent with the
epoch of disappearance of the narrow emission lines in observed spectra.
Following Dessart et al. (2017), the narrow lines last as long as the shock is
placed within a slow-moving optically-thick material (i.e., until the shock
goes through the SN photosphere). We checked this epoch in each of our
simulations and found values around $\sim$0.7$-$1.5 days after explosion,
while the observations of SN 2023ixf show interacting lines until 6$-$7 days
post-explosion (Bostroem et al. 2023).

In the following we look for a model that reproduces the epoch when the
interaction lines have faded, while matching the bolometric light curve and
photospheric expansion velocities. The thick blue solid line in the bottom
panel of Fig. 5 shows a CSM interaction model for $\dot{M}$ $=$ 1.2 $\times$
10-2 $M_{\odot}$ yr-1 and $R_{\rm CSM}$ $=$ 8000 $R_{\odot}$ ($\sim$5.5
$\times$ 1014 cm). This model is able to reproduce the width of the luminosity
peak, post-peak luminosities, photospheric velocities, and the epoch of
disappearance of the narrow emission features. However, this model fails to
reproduce the peak luminosity. Higher mass-loss rates produce wider peaks and
more luminous post-maximum light curves (bottom panel of Fig. 5, dashed line).
The opposite effect is expected for lower mass-loss rates. Alternatively, a
more confined CSM produce a higher peak luminosity, but lower luminosities
post-maximum (bottom panel of Fig. 5, dotted line).

###  4.2 Accelerated winds

Figure 6: Comparison between the bolometric light curve of SN 2023ixf (dots)
with models varying CSM properties (lines) assuming wind acceleration. The
inset plot compares the photospheric velocities of SN 2023ixf to the same
models previously mentioned. For the model nomenclature, see Sect. 4.

In this section we model SN explosions within a CSM but considering the wind
acceleration mechanism previously presented in Moriya et al. (2018). In this
scenario, the mass-loss rate is set constant and the CSM density follows the
same expression as in Sect. 4.1; however, the wind velocity is no longer
constant. As in Moriya et al. (2018), the wind velocity takes the form of a
$\beta$ velocity law given below:

$v_{\rm
wind}(r)=v_{0}+(v_{\infty}-v_{0})\left(1-\frac{R_{0}}{r}\right)^{\beta},$ (2)

where $v_{0}$ is the initial wind velocity (0.1 km s-1), $v_{\infty}$ is the
terminal velocity of the wind (115 km s-1, Smith et al. 2023), $R_{0}$ is the
radial coordinate where the CSM is attached, and $\beta$ is the wind
acceleration parameter (see also Lamers & Cassinelli 1999).

We compare the early-time bolometric light curve and photospheric velocity
evolution of SN 2023ixf with explosion models assuming different CSM
parameters ($\dot{M}$, $R_{\rm CSM}$, and $\beta$). Figure 6 shows some of
these models. The thick solid line in Fig. 6 represents the model
m15_w3m3_r12000_beta5, i.e., with $\dot{M}$ $=$ 3 $\times$ 10-3 $M_{\odot}$
yr-1, $R_{\rm CSM}$ $=$ 12000 $R_{\odot}$, and $\beta$ $=$ 5\. From all the
models we computed, this is the one that best reproduces the observations,
even better than those models assuming steady mass loss (see Sect. 4.1). In
addition, model m15_w3m3_r12000_beta5 predicts that the narrow emission
features should disappear at day 6.5, which is consistent with the observed
date (Bostroem et al. 2023).

Figure 6 also shows models computed with varying CSM properties to notice the
sensitivity of the early bolometric light curve with these parameters. Higher
mass-loss rates (e.g., model m15_w1m2_r12000_beta5) produce wider peaks and
more luminous post-peak light curves, while more confined CSMs (e.g., model
m15_w3m3_r7000_beta5) underestimate the post-peak luminosity. Alternatively, a
smaller wind acceleration parameter (e.g., model m15_w3m3_r12000_beta2)
results in narrower and less luminous peak, while at the same time, less
luminous light curves after maximum. This behaviour is due to the different
amount of CSM mass near the progenitor surface for varying wind acceleration
parameters. A larger $\beta$ involves more mass near the progenitor surface,
and therefore, a larger boost to the luminosity due to conversion of kinetic
energy into radiation. We note that the models presented cannot reach the
observed maximum luminosity.

##  5 Discussion

The first wind mass-loss scenario explored assumes a steady flow from the
progenitor. With the assumed wind velocity ($v_{\rm wind}$ $=$ 115 km s-1;
Smith et al. 2023), the size of the progenitor, and the extent of the CSM
presented in Sect. 4, we looked for an estimate of the time before explosion
in which this enhanced mass loss must have started. For the CSM extents
between 2500 and 3000 $R_{\odot}$ ($\sim$1.7$-$2.1 $\times$ 1014 cm) first
analysed, we found an enhanced wind that developed over the last 0.3$-$0.4 yr
before explosion101010We note again that these CSM parameters do not reproduce
the fading time of the narrow emission lines.. In addition, for a CSM
extension of 8000 $R_{\odot}$ ($\sim$5.5 $\times$ 1014 cm), the enhanced wind
should have started $\sim$1.3 yr before explosion. Adopting a commonly-used
wind velocity for a ‘superwind’ (50 km s-1), the enhanced mass loss would have
developed over the last $\sim$3 yr. The inferred timescales and mass-loss
rates are similar to some values found in the literature for SN 2023ixf (e.g.,
Jacobson-Galan et al. 2023; Hiramatsu et al. 2023). However, these timescales
appear to be inconsistent with pre-explosion observations.

Mid-IR Spitzer data in the preceding $\sim$20 yr before the explosion show
variability similar to those pulsating RSGs, but does not show any indication
of eruptive mass-loss processes (Szalai & Dyk 2023; Jencson et al. 2023;
Kilpatrick et al. 2023; Soraisam et al. 2023). Neustadt et al. (2023) found no
evidence of outbursts in optical data taken with the Large Binocular Telescope
between $\sim$1 and 15 yr before the SN. The analysis of pre-explosion optical
data from the Zwicky Transient Facility (Bellm et al. 2019; Graham et al.
2019), Asteroid Terrestrial-impact Last Alert System (Tonry et al. 2018; Smith
et al. 2020), Distance Less Than 40 Mpc, and All-Sky Automated Survey for
Supernovae (Kochanek et al. 2017) surveys during the last 8 yr up to 0.3 days
before explosion also found no evidence of precursor activity in the optical
(Hiramatsu et al. 2023; Dong et al. 2023; Panjkov et al. 2023). In addition,
UV observations from the Galaxy Evolution Explorer and Swift space telescopes
did not find pre-explosion outbursts $\sim$20 yr prior to explosion (Flinner
et al. 2023; Panjkov et al. 2023). Therefore, pre-explosion observations
indicate a quiescent progenitor in the last $\sim$20 yr, with no indication of
any pre-SN outbursts or large magnitude changes —except for the IR variability
similar to pulsating RSGs (Soraisam et al. 2023). The assumption of steady-
state winds results in enhanced mass loss shortly before explosion, which does
not seem consistent with a quiescent progenitor.

Steady winds assume that the mass-loss rate and wind velocity are constant
through the wind. However, the wind is gradually accelerated at the stellar
surface until the terminal velocity is reached. This produces an increment of
the timescales for the wind development to reach a particular extension. The
bolometric light-curve modelling including CSM interaction that takes the wind
acceleration into account infer that the enhanced mass loss was launched
$\sim$80 yr prior to the SN. These timescales are related to the final stages
of massive-star evolution, although the details of the connection are unknown.
Some mechanisms propose mass loss driven by gravity waves excited in the
convective core (Quataert & Shiode 2012; Shiode & Quataert 2014; Fuller 2017),
local radiation-driven instabilities in the outer layers (Suárez-Madrigal et
al. 2013), and hydrodynamic and turbulence at pre-SN stage driven by turbulent
convection (Smith & Arnett 2014).

Singh Teja et al. (2023) compared the $g$-band light curve of SN 2023ixf with
a grid of models of SN II explosions interacting with an accelerated RSG wind
(Moriya et al. 2023). The CSM parameters found in our study are within the
ranges of values constrained by Singh Teja et al. (2023), with the exception
of the wind-acceleration parameter for which we infer a larger value. However,
Singh Teja et al. (2023) infer higher explosion energies (2$-$5 $\times$ 1051
erg), much larger than typical SNe II (e.g., Morozova et al. 2018; Martinez et
al. 2020, 2022a) and the predictions from 1D neutrino-powered explosions
(Sukhbold et al. 2016). These high values could be because Singh Teja et al.
(2023) did not use velocity measurements in their fitting. If expansion
velocities are not taken into account in the fitting procedure, it could lead
to incorrect determination of the explosion energy (Martinez et al. 2020).

Davies et al. (2022) carried out an analysis where they predict the
characteristics of the RSGs at core collapse based on two enhanced mass-loss
scenarios: a short outburst lasting a few months and a ‘superwind’ arising
from a very high mass-loss rate during the last decades prior to explosion.
These authors considered an accelerated wind for the latter scenario. Davies
et al. (2022) found that the outburst scenario produces redder colours in a
short timescale after the outburst, which would not be consistent with the
steady IR variability of the progenitor of SN 2023ixf (e.g., Jencson et al.
2023). Alternatively, the scenario that involves the acceleration of the RSG
winds causes redder colours decades prior the SN explosion. Jencson et al.
(2023) found that the IR colours of the progenitor of SN 2023ixf are well
reproduced by one of the ‘superwind’ models from Davies et al. (2022), which
assumes the same wind acceleration mechanism than the one analysed in our
work. The discussion provided in this section would imply that the enhanced
mass loss started decades before core collapse, supporting the wind
acceleration scenario.

Regarding the modelling of the bolometric light curve peak, we note that none
of our models can reproduce the maximum luminosity of $L_{\rm bol}$ $=$ 3
$\times$ 1045 erg s-1. While the assumption of steady-state winds produces
closer values than the accelerated winds, the former is in contradiction with
the epoch of disappearance of the interacting lines as described in Sect. 4.1.
This indicates that we still need to improve our knowledge of the conditions
under which the CSM was formed. It is also important to mention that some
physics are not included in our code, as non-local thermodynamic equilibrium
or multi-dimensional effects (see Bersten et al. 2011, for detailes).

##  6 Summary and conclusions

SN 2023ixf is among the closest SN II in the last decades, which allowed
intensive multi-wavelength and high-cadence observations. We used publicly
available data to calculate the early ($<$19 days post-explosion) bolometric
light curve based on the integration of the observed SED (from UV to NIR
bands) and black-body extrapolations for the unobserved flux at shorter and
longer wavelengths. Thanks to the early monitoring and high cadence of
observations, we capture the sudden rise to maximum and the successive fall of
the bolometric light curve. This is the first time that this behaviour is
observed in bolometric luminosities given the lack of early-time multi-
wavelength observations for most SNe II.

The fact that there are a small number of SNe II with detailed calculations of
their early bolometric light curve (see e.g., Yaron et al. 2017 and Jacobson-
Galán et al. 2022 for bolometric light curves after maximum for SN 2013fs and
SN 2020tlf, respectively), allowed us to test the currently available
calibrations of BC against colours. This analysis provides good agreements for
most of these calibrations. Additionally, we included the observations of SN
2023ixf to the recently-published calibrations of BC from Martinez et al.
(2022b). These calibrations include data of 74 SNe II, but none with
observations as early as SN 2023ixf. Therefore, the incorporation of SN
2023ixf to the previously-mentioned calibrations allows to extend them to
bluer optical colours, and therefore, to earlier epochs. It would be necessary
to include all SNe II with early detections and good photometric coverage in
order to analyse the bluest part of these calibrations in detail, and to study
a possible general behaviour.

Armed with the bolometric light curve for SN 2023ixf, we have studied the
mass-loss history of the progenitor of SN 2023ixf through comparison with
hydrodynamical simulations of SN II explosions with CSM interaction. We found
that a CSM interaction model that takes the wind acceleration into account
with $\dot{M}$ $=$ 3 $\times$ 10-3 $M_{\odot}$ yr-1, $R_{\rm CSM}$ $=$ 12000
$R_{\odot}$, and $\beta$ $=$ 5 reproduces the width of the luminosity peak,
the post-peak luminosity, and the epoch of disappearance of the interaction
lines in the spectra. Our findings indicate an enhanced wind that developed
continuously over the last $\sim$80 yr of the progenitor evolution. This may
be consistent with the quiescent of SN 2023ixf in the last 20 yr prior to
explosion, favouring the accelerated wind scenario —in connection with the
results of Jencson et al. (2023). In a forthcoming paper, we analyse the
complete bolometric light curve and photospheric velocity evolution of SN
2023ixf and derive the physical properties of the progenitor and explosion,
which allow us to have a full description of the nature of SN 2023ixf (Bersten
et al. in prep.).

###### Acknowledgements.

L.M. acknowledges support from a CONICET fellowship. L.M. and M.O.
acknowledges support from UNRN PI2022 40B1039 grant. This research has made
use of the Spanish Virtual Observatory (https://svo.cab.inta-csic.es) project
funded by MCIN/AEI/10.13039/501100011033/ through grant PID2020-112949GB-I00.
This work has made use of WISeREP (https://www.wiserep.org).
Software: NumPy (Oliphant 2006; Van Der Walt et al. 2011), matplotlib (Hunter
2007), Astropy (Astropy Collaboration et al. 2013, 2018, 2022), SciPy
(Virtanen et al. 2020), emcee (Foreman-Mackey et al. 2013), Pandas (McKinney
2010), ipython/jupyter (Perez & Granger 2007), extinction
(https://github.com/kbarbary/extinction).

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