11institutetext:  Department of Physics and Astronomy, University of Turku,
FI-20014 Turku, Finland 22institutetext: Aalto University Metsähovi Radio
Observatory, Metsähovintie 114, 02540 Kylmälä, Finland 33institutetext: Aalto
University Department of Electronics and Nanoengineering, P.O. BOX 15500,
FI-00076 AALTO, Finland 44institutetext: Department of Astronomy, Kyoto
University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
55institutetext: School of Sciences, European University Cyprus, Diogenes
Street, Engomi, 1516, Nicosia, Cyprus 66institutetext: Finnish Centre for
Astronomy with ESO (FINCA), University of Turku, FI-20014, Finland
77institutetext: Okayama Observatory, Kyoto University, 3037-5 Honjo,
Kamogatacho, Asakuchi, Okayama 719-0232, Japan 88institutetext: Hiroshima
Astrophysical Science Center, Hiroshima University, Kagamiyama 1-3-1, Higashi-
Hiroshima , Hiroshima 739-8526, Japan 99institutetext: Department of Physical
Science, Hiroshima University, Kagamiyama 1-3-1, Higashi-Hiroshima 739-8526,
Japan 1010institutetext: Gemini Observatory / NSF’s NOIRLab, Casilla 603, La
Serena, Chile 1111institutetext: Department of Physics and Earth Science,
University of Ferrara, via Saragat 1, I-44122 Ferrara, Italy
1212institutetext: INFN, Sezione di Ferrara, via Saragat 1, I-44122 Ferrara,
Italy 1313institutetext: INAF, Osservatorio Astronomico d’Abruzzo, via Mentore
Maggini snc, 64100 Teramo, Italy 1414institutetext: Department of Astronomy,
University of California, Berkeley, CA 94720-3411, USA 1515institutetext:
Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC,
08860 Castelldefels (Barcelona), Spain 1616institutetext: Institute of Space
Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, E-08193
Barcelona, Spain 1717institutetext: Amanogawa Galaxy Astronomy Research Center
(AGARC), Graduate School of Science and Engineering, Kagoshima University,
1-21-35 Korimoto, Kagoshima, Kagoshima 890-0065, Japan 1818institutetext:
Department of Multi-Disciplinary Sciences, Graduate School of Arts and
Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan

# Evidence for bipolar explosions in Type IIP supernovae

T. Nagao  K. Maeda 112233 S. Mattila 44 H. Kuncarayakti 1155 M. Kawabata 1166
K. Taguchi 77 T. Nakaoka 44 A. Cikota 8899 M. Bulla 1010 S. S. Vasylyev
111112121313 , C. P. Gutiérrez Steven Nelson Graduate Fellow1414 M. Yamanaka
15151616 K. Isogai 1717 K. Uno 771818 M. Ogawa 44 S. Inutsuka 44 M. Tsurumi 44
R. Imazawa 44 99 K. S. Kawabata 8899

(Received ***; accepted ***)

###### Abstract

Aims. Recent observations of core-collapse supernovae (SNe) suggest aspherical
explosions. Globally aspherical structures in SN explosions are regarded as
the key for understanding their explosion mechanism. However, the exact
explosion geometries from the inner cores to the outer envelopes are poorly
understood.

Methods. Here, we present photometric, spectroscopic and polarimetric
observations of the Type IIP SN 2021yja and discuss its explosion geometry, in
comparison to those of other Type IIP SNe that show large-scale aspherical
structures in their hydrogen envelopes (SNe 2012aw, 2013ej and 2017gmr).

Results. During the plateau phase, SNe 2012aw and 2021yja exhibit high
continuum polarization characterized by two components with perpendicular
polarization angles. This behavior can be interpreted to be due to a bipolar
explosion, composed of a polar (energetic) and an equatorial (bulk) components
of the SN ejecta. In such a bipolar explosion, an aspherical axis created by
the polar ejecta would be dominating at early phases, while the perpendicular
axis along the equatorial ejecta would emerge at late phases after the
receding of the photosphere in the polar ejecta. The interpretation of the
bipolar explosions in SNe 2012aw and 2021yja is also supported by other
observational properties, including the time evolution of the line velocities
and the line shapes in the nebular spectra. The polarization of other Type IIP
SNe that show large-scale aspherical structures in the hydrogen envelope (SNe
2013ej and 2017gmr) is also consistent with the bipolar-explosion scenario,
although this is not conclusive.

###### Key Words.:

supernovae: individual: SN 2021yja – supernovae: general – Techniques:
polarimetric

##  1 Introduction

Core-collapse supernovae (SNe) are catastrophic explosions due to the neutrino
heating from a newly-created proto-neutron star after a collapse of the iron
core (the neutrino-driven mechanism; e.g., Janka 2017), characterizing the
deaths of massive stars. For a long time, it has been challenging to conduct
first-principles simulations of SN explosions due to the limitation of the
computational power. There are many complications and difficulties concerning
nuclear and neutrino physics, the three-dimensional progenitor structures, and
numerical challenges in the treatments of the transfer of the radiation and
neutrinos and in general relativistic three-dimensional hydrodynamics
calculations (e.g., Burrows & Vartanyan 2021). Recent advancements in the
computational power and the methodology for the calculations are gradually
allowing successful cases of SN explosions (e.g., Lentz et al. 2015; Melson et
al. 2015; Radice et al. 2017; Vartanyan et al. 2018; Burrows et al. 2020).
However, such successful explosions are limited to a small number of parameter
sets of massive stars, where the majority of massive stars are still difficult
to be exploded as realistic SNe in a computer. Therefore, we are missing some
key elements in our understanding of the SN explosions.

It has been suggested that some enhancements of multi-dimensional hydrodynamic
instabilities, such as convective motion, the standing-accretion-shock
instability (Blondin et al. 2003) and/or Rayleigh-Taylor instability, might
play a crucial role because multi-dimensional motions of the gas can increase
the neutrino heating efficiency in the gain region (e.g., Burrows et al.
2020). In fact, using state-of-the-art three-dimensional simulations based on
the neutrino-driven mechanism, Burrows et al. (2024) have demonstrated that
the successful explosions generally have global asymmetric structures and the
asymmetry is correlated with the explosion energy. This is also suggested by
recent observations of core-collapse SNe. Polarimetric observations have
revealed large-scale aspherical structures in the ejecta of hydrogen-rich
(Type II) SNe. Historically, a low level of polarization ($\sim 0.1$%) has
been measured during the plateau phase, followed by a rapid increase of
continuum polarization at the beginning of the tail phase (e.g., Leonard et
al. 2001, 2006; Chornock et al. 2010; Kumar et al. 2016). This polarimetric
feature can be explained by an asymmetric helium core being revealed when the
outer hydrogen envelope becomes optically thin as indicated by the light curve
falling off the plateau. Recently, Nagao et al. (2019) found an
unprecedentedly highly-extended aspherical explosion in Type II SN 2017gmr
indicated by an early rise of polarization even during the plateau phase. This
indicates that asymmetries are present not only in the helium core but also in
a substantial portion of the hydrogen envelope. Furthermore, Nagao et al.
(2024), using a large sample of SNe, discovered a correlation between the
extension of the aspherical structures and the explosion energy, implying that
development of a global aspherical structure might be a key element in the SN
explosions. Such global aspherical structures in core-collapse SNe are also
required by statistical analysis of line shapes in the nebular spectra of
stripped-envelope SNe (e.g., Fang et al. 2024). This study demonstrated that
the spatial distributions of the oxygen-burning ash and the unburnt oxygen
follow the configurations of bipolar explosions. Moreover, they found that the
degree of asphericity, in such bipolar explosions, increased towards
explosions from heavier progenitors.

In this paper, we present photometric, spectroscopic and polarimetric
observations of the Type IIP SN 2021yja and discuss its explosion geometry
together with those of other Type IIP SNe that show large-scale aspherical
structures in the hydrogen envelope (SNe 2012aw, 2013ej and 2017gmr; Nagao et
al. 2024). SN 2021yja was discovered by the Asteroid Terrestrial-impact Last
Alert System (Smith et al. 2020) on 8.55 September 2021 UT (59465.55 MJD;
Tonry et al. 2021). It is located in NGC 1325 (Galaxy Morphology: SA(s)bc;
from NED111NASA/IPAC Extragalactic Database) at $z=0.005307\pm 0.000005$ and
receding with a velocity of $v_{\rm{gal}}=1591\pm 1$ km s-1 (Springob et al.
2005). The object was not detected on 6.48 September 2021 UT (59463.48 MJD;
Tonry et al. 2021). We adopt the explosion date to be MJD 59464.40, estimated
by Hosseinzadeh et al. (2022), which is about the middle point between the
last non-detection and the discovery dates. The object was classified as a
Type II SN about a day after the discovery (59466.60 MJD; Pellegrino et al.
2021), and showed prototypical observational properties for Type IIP SNe
(e.g., Vasylyev et al. 2022; Hosseinzadeh et al. 2022). We adopted the Milky
Way and host galaxy reddening of $E(B-V)_{\rm{MW}}=0.0191$ mag (Schlafly &
Finkbeiner 2011) and $E(B-V)_{\rm{host}}=0.085$ mag derived from the Na I D
absorption lines by Hosseinzadeh et al. (2022), respectively, and thus a total
reddening of $E(B-V)=0.104$ mag. For the extinction correction, we adopt the
extinction law by Fitzpatrick (1999). We adopt the distance and distance
modulus for the SN of $23.4^{+5.4}_{-4.4}$ Mpc and $\mu=31.85\pm 0.45$ mag,
respectively, which were derived by the Tully-Fisher estimate (Tully et al.
2016). In this work, we estimated the timing of the end of the plateau phase
as the mid-point of the luminosity drop from the plateau phase to the tail
phase following Nagao et al. (2024), by fitting the time evolution of the
$g$-band light curve taken from Hosseinzadeh et al. (2022) with an artificial
function (Equation 1 in Nagao et al. 2024): $t=59590.57$ MJD.

##  2 Observations

We performed photometric, spectroscopic and polarimetric observations of the
Type IIP SN 2021yja. The details on the photometric and spectroscopic
observations are described in Appendix B and C. We obtained spectro- and
imaging polarimetry of the Type IIP SN 2021yja, using the FOcal Reducer/low-
dispersion Spectrograph 2 (hereafter FORS2) mounted at the Cassegrain focus of
the Very Large Telescope (VLT) UT1 telescope at the Paranal observatory and
the Alhambra Faint Object Spectrograph and Camera (ALFOSC) mounted on the
2.56-m Nordic Optical Telescope (NOT) at the Roque de los Muchachos
Observatory. The observing logs are shown in Tables 1 and 2. It it noted that
spectropolarimetric observations for SN 2021yja have also been conducted and
reported by Vasylyev et al. (2024). Here, our polarimetric data cover later
epochs.

The spectropolarimetric observations and their analysis are similar as
reported in Nagao et al. (2023). We observed SN 2021yja using the low-
resolution G300V grism and a half-wave retarder plate (HWP) with the optimal
set of HWP angles of $0^{\circ}$, $22.5^{\circ}$, $45^{\circ}$ and
$67.5^{\circ}$. The raw data were reduced with IRAF (Tody 1986, 1993) using
standard methods as described, e.g., in Patat & Romaniello (2006). From the
reduced object frames, we extracted the ordinary and extraordinary beams of
the SN with a fixed aperture size of $10$ pixels, and rebinned the extracted
spectra to 50 Angstrom bins to allow a better signal-to-noise ratio. We also
corrected the observations for HWP zeropoint angle chromatism, using tabulated
values for the zero-angle given in the FORS2 user manual
222http://www.eso.org/sci/facilities/paranal/instruments/fors/doc/VLT-MAN-
ESO-13100-1543_P07.pdf. The wavelength scale was corrected to the rest frame
using the host-galaxy redshift. For deriving the continuum polarization from
the spectropolarimetric data, we used the wavelength ranges between 6800 and
7200 Å and between 7820 and 8140 Å, following (Nagao et al. 2024). For the
imaging polarimetry, the same instrumental set-up was adopted, using a narrow-
band filter (FILT_815_13) with the VLT and two broad band filters ($V$ and
$R$) with the NOT instead of the grism in the optical path. We applied bias
subtraction and flat-field correction to all the frames and then performed
aperture photometry on each detected source. For the aperture photometry, we
used an aperture size that is twice as large as the full-width-half-maximum
(FWHM) of the ordinary beam’s point-spread function and a background region
whose inner and outer radii are twice and four times as large as the FWHM,
respectively. Based on these values, we calculated the Stokes parameters, the
linear polarization degree and the polarization angle. When calculating the
polarization degrees, we subtracted the polarization bias, following Wang et
al. (1997). Since the polarization degrees on the H$\alpha$ emission line,
where the intrinsic polarization is supposed to be depolarized and thus the
interstellar polarization (ISP) to be dominant (e.g., Nagao et al. 2023), are
close to zero, we assume that the ISP in SN 2021yja is negligibly small, which
is also adopted by Vasylyev et al. (2024).

##  3 Results and discussion

Figure 1:  Left panel: Polarization degree and angle of SN 2021yja. The filled
black circles connected by a solid line show the continuum polarization
derived from the polarization spectra, while the filled green triangles and
red squares show the values from the $V$\- and $R$-band imaging polarimetry.
The open black circles represent only the second component of the continuum
polarization. The gray crosses trace the $g$-band light curve of SN 2021yja
taken from Hosseinzadeh et al. (2022). Right panel: Time evolution of the
continuum polarization in the q-u plane, compared to that of SN 2012aw. The
first-epochs are indicated with dotted lines. The open black circles are the
same in the left panels, representing only the second component of the
continuum polarization.

Figure 1 shows the continuum polarization of SN 2021yja, derived from
spectropolarimetry and from the narrow/broad-band polarization. As also seen
in Vasylyev et al. (2024), SN 2021yja shows a distinct evolution of the
continuum polarization compared with the majority of other Type IIP SNe. Most
Type IIP SNe show low polarization degrees at early phases and a sudden rise
to $\sim 1$% at a certain point in the plateau phase with a constant
polarization angle (see, e.g., Nagao et al. 2024). In contrast, SN 2021yja
shows a high degree of polarization ($\sim 0.8$%) at early phases and a
decline of the polarization degree with time as well as a gradual change of
the polarization angle. This implies multi-axial structures in the hydrogen
envelope, whose relative contributions to the polarization evolve with time.
The $V$\- and $R$-band data are generally consistent with the continuum
polarization estimated from the polarization spectra, even though they should
be affected by line depolarization/polarization (see the polarization spectra
in Appendix A) and have larger errors. Hereafter, when discussing the
continuum polarization of SN 2021yja, we only use the values derived from the
polarization spectra. It is noted that the polarization angles in the tail
phase estimated from the narrow-band, $V$\- and $R$-band imaging polarimetry
are not stable and thus might indeed be affected by line polarization. In the
tail phase, the line polarization can dominate over the continuum polarization
(see, e.g., the cases of SNe 2017gmr and 2013ej; Nagao et al. 2019, 2021).
Since we do not have spectropolarimetry for the tail phase, we do not further
discuss the polarization in the tail phase in this paper.

We adopt the continuum polarization derived from the first-epoch
spectropolarimetric data as the “first component” ($P=0.78$ %, $\theta=112.1$
degrees). Then, we subtract the first component from the original continuum
polarization. The remaining polarization shows a relatively constant
polarization angle ($\theta\sim 15$ degrees), which we call the “second
component”. This means that the continuum polarization during the plateau
phase can be explained by these two components. It is noted that, if we assume
the polarization degree of the first component with $\theta=112.1$ degrees is
not constant but variable in time, the remaining polarization after the
subtraction of the first component from the original polarization still shows
time-variable polarization angles. Therefore, in order to remove the time
variability of the polarization angle of the remaining polarization, at least
two more additional polarization sources would be required. Consequently, we
need at least three components of the polarization in total as the origin of
the continuum polarization. In addition, any of these components would not
show typical time evolution of the polarization degrees as in other Type IIP
SNe (Nagao et al. 2024). The difference between the polarizatiton angles of
these components is $\sim 95$ degrees. In the q-u plane, the data points of
the second component (open black circles) are clearly located nearly to the
opposite direction relative to the first component (dotted line) towards the
origin of the q-u plane, demonstrating that the axes of the aspherical
structures implied by the first and second components are almost perpendicular
(Figure 1).

In the literature, several other Type II SNe have been reported to clearly
show time-variable polarization angles in their polarization, implying multi-
axis structures in the ejecta (SNe 2012aw, 2013ej and 2023ixf; Nagao et al.
2021, 2024; Vasylyev et al. 2024). SN 2023ixf showed high continuum
polarization with a different polarization angle from that for later phases
only within a few days after the explosion, which coincides with the existence
of highly ionized “flash” features in the spectra (Vasylyev et al. 2022).
Since the flash features are created by highly ionized gas in confined
circumstellar material (CSM) due to high energy photons created in an
interaction between the SN ejecta and the CSM(e.g., Boian & Groh 2020), this
short-lived component of the polarization is interpreted to reflect the
aspherical structure not of the SN ejecta but of the confined CSM (Vasylyev et
al. 2024). In the case of SN 2013ej, the evolution of the polarization angle
happened using the majority part of the plateau phase (Nagao et al. 2021). At
the same time, the SN showed observational signs of a major CSM interaction at
least during first several tens days (e.g., Bose et al. 2015). This evolution
of the polarization is understood as the change in the contributions from two
different aspherical structures originated from both an aspherical CSM
interaction and aspherical SN ejecta. On the contrary, SNe 2012aw and 2021yja
do not show observational features from a strong CSM interaction that could
change the global properties of the SN ejecta, although a weak CSM interaction
is predicted (e.g., Bose et al. 2013; Hosseinzadeh et al. 2022; Vasylyev et
al. 2022). The low degree of the early-phase broad-band polarization in SN
2021yja also disagrees with the scenario of a major spherical CSM interaction
as in the case of SN 2013ej. Furthermore, the change in the polarization angle
between the first and second components in the cases of SNe 2012aw and 2021yja
is close to $\sim 90$ degrees, demonstrating that the axes of these two
components are close to perpendicular, alike in the case of SN 2013ej ($\sim
20$ degrees; Nagao et al. 2021). If the first and second components originate
from an aspherical CSM interaction and aspherical SN ejecta (as in the case of
SN 2013ej), the angle change should be random due to the random orientation
between the CSM structure and the aspherical SN explosion, unless there is
some mechanism to create a common preferential axis for the mass loss and the
SN explosion.

Figure 2:  Schematic presentation of the continuum polarization in SN2021yja
(observer’s view) created by a bipolar explosion. At early phases, the
photosphere is extended vertically due to the energetic ejecta component,
which creates the first vertical polarization component (Phase 1). Then, the
shape of the photosphere is crushed horizontally due to the receding of the
photosphere in the energetic component, which creates the second horizontal
polarization component (Phase 2). This explains the rotation of the observed
polarization angle. The polarization vectors of important individual photons
from the photosphere are indicated with small arrows. The big arrows show the
net polarization vectors of all the photons.

We propose that this is evidence of the presence for two-component ejecta
driven by a bipolar explosion (a collimated energetic component and a
canonical bulk SN component), as implied for the explanation of the
polarization in SN 2012aw by Nagao et al. (2024). We consider a similar
situation with the bipolar ejecta model proposed by Kaplan & Soker (2020). The
schematic picture of this scenario is shown in Figure 2. If an energy
injection is stronger towards the polar directions than to the equatorial
directions, the ejecta in the polar direction (the energetic component) would
create a larger photosphere than that in the equatorial directions (the bulk
component) at early phases (Phase 1). Since the receding of the photosphere
would happen earlier in the polar directions than in the equatorial
directions, the size of the photosphere in the energetic component becomes
smaller than that in the bulk component late in the plateau phase (Phase 2).
This transition from Phase 1 to Phase 2 would create the 90-degree change in
the angle of the axis of the aspherical structures. Such morphology change has
also been predicted by past radiative transfer calculations in a bipolar
explosion (e.g., Maeda et al. 2006; Dessart et al. 2024).

The relative strength of the first and second components and its time
evolution should depend on the ejecta parameters (mass, energy, collimation
degree) for the polar and equatorial directions and on the viewing angle. In
particular, the timing of the transition from Phase 1 to Phase 2 should not
strongly depend on the viewing angle, but on the explosion parameters and the
degree of the collimation of the energetic component. For example, if we
assume that the explosion properties are independent for these perpendicular
directions and that only the inputted specific explosion energy to these
components is different, the timing of the transition from Phase 1 to Phase 2
can be roughly estimated from the relative explosion energy using the scaling
relation in a simple one-zone model of homogeneously expanding gas with
radiative diffusion proposed by Kasen & Woosley (2009): $t_{\rm{sn}}\propto
E^{-1/6}$. In the case that the energetic component has 10 times larger
specific energy than the bulk component, this transition would happen at 70%
of the plateau length of the bulk component, although it should be a
relatively smooth transition in reality. In fact, the timings of this phase
transition in SNe 2012aw and 2021yja are different. There was an earlier
transition in the case of SN 2012aw compared to SN 2021yja. This might imply
that there is diversity in the bipolar structures in Type IIP SNe. It is also
noted that, since the relative strength of the two components depends on the
viewing angle, the different viewing angles might also contribute to the
different timing of the exchange of these two components to some extent.

There may exist other possibilities to create such a bipolar structure before
the explosion, e.g., by some unknown aspherical energy injection just before
the explosion or by extremely rapid rotation. However, SN 2021yja shows low
polarization at very early phases ($\lesssim 0.2$ % at Phase +2.78), which
might suggest that the outermost layer of the ejecta is relatively spherical.
Therefore, this bipolar structure in SN 2021yja might not be due to the
inherent aspherical structure in the progenitor star but a bipolar explosion.
It is noted that the low polarization at early phases might be achieved due to
the high optical depth for electron scattering in the outermost layer (e.g.,
Dessart & Hillier 2011), even if the progenitor originally has an
aspherically-extended envelope. This effect depends on the density
distribution in the extended envelope and should be quantitatively tested.

The other Type IIP SN that show large-scale aspherical structures in the
hydrogen envelope (SN 2017gmr Nagao et al. 2019) did not show the two-
component polarization, which is a strong support for a bipolar explosion, as
in the cases of SNe 2012aw and 2021yja. However, the earliest polarimetric
observation of SN 2017gmr was conducted 45.40 days after the first detection,
and thus the first component might have already been covered by the second
component (see the case of SN 2012aw in Nagao et al. 2024). Alternatively, the
first component might be weak due to the viewing angle. So far, all the Type
IIP SNe that show global aspherical structures in the hydrogen envelope
(energetic Type II SNe Nagao et al. 2024) are consistent with the bipolar-
explosion scenario. It is important to increase the sample size to probe the
diversity in the bipolar explosions.

Figure 3: Time evolution of the H$\alpha$ and Fe II velocities, derived from
the absorption minima of the respective lines. The vertical dotted lines
indicate the timings of the end of the plateau phase.

The interpretation of the bipolar explosions in SNe 2012aw and 2021yja are
also supported by other observational properties. The general photometric and
spectroscopic properties of SNe 2012aw and 2021yja are relatively similar
(e.g., plateau luminosity, plateau length, the velocity evolution of the
H$\alpha$ line; see Appendix B and C), implying that the basic parameters of
the SN ejecta are relatively similar. However, they show a different feature
in the velocity evolution of the Fe II $\lambda$5169 line, which is often used
as a tracer of the velocity of the photosphere. At early phases, both SNe show
similar velocity evolution for the Fe II line as for the H$\alpha$ line, while
SN 2021yja shows slower velocities than SN 2012aw at later plateau phase alike
in the H$\alpha$ line (Figure 3). This observational property might be
explained with different viewing angles towards relatively similar bipolar
explosions. The viewing angle of SN 2021yja is closer to the polar direction
compared to that of SN 2012aw. Thus, the slowdown of the Fe II velocity, i.e.,
the photospheric velocity, might be related to the receding of the photosphere
in the energetic component of the ejecta, i.e., the transition from Phase 1 to
Phase 2. This might also be the reason why the relative strength of the first
polarization component compared to the second component in SN 2021yja is
larger than that in SN 2012aw.

Figure 4:  ALFOSC/NOT spectrum of SN 2021yja at 352.82 days after the
explosion, compared to the spectrum of SN 2012aw obtained with the same
instrument and telescope (ALFOSC/NOT) at +369 days after the explosion
(Jerkstrand et al. 2014). Wavelengths of prominent lines are indicated with
vertical dashed lines.

Nebular spectroscopy is also a powerful tool to study the geometry of the SN
ejecta, especially for the inner parts (e.g., Maeda et al. 2008; Taubenberger
et al. 2009; Fang et al. 2024), while polarimetry during the plateau phase
provides information on the structure of the hydrogen envelope as discussed
above. Figure 4 shows a part of the nebular spectra of SNe 2021yja and 2012aw,
taken with the ALFOSC/NOT (see Appendix C for details). SN 2021yja shows
broader [Fe II] $\lambda$ 7155 line than that observed in SN 2012aw, although
the Fe II velocity during the plateau phase in SN 2021yja was slower than that
seen in SN 2012aw. In addition, the [Ca II] $\lambda\lambda$ 7291,7323 lines
are wider than those seen in SN 2012aw, while their [O I] $\lambda\lambda$
6300,6363 lines are similar. These properties might also be explained by a
scenario with the viewing angle effects of a bipolar explosion: The viewing
angle of SN 2021yja is closer to the polar direction compared to that of SN
2012aw. Since the energetic ejecta component creates more burning ash (Fe and
Ca) than the bulk component, the relative line widths of the iron and calcium
lines to the oxygen line can be larger, if the viewing angle is closer to the
polar direction. This interpretation is consistent with the properties of the
polarization and the line velocities. This also suggests that the aspherical
structure of the hydrogen envelope extends into the inner core, maintaining
its shape. This provides strong evidence in favour of the bipolar explosion
scenario, disfavouring the possibility of the CSM interaction scenario.

###### Acknowledgements.

This work is partly based on observations collected at the European
Organisation for Astronomical Research in the Southern Hemisphere (ESO) under
programmes 108.228k.001 and 108.228k.002. This work is partly based on
observations made under program IDs P63-016, P64-023 and P65-005 with the
Nordic Optical Telescope, owned in collaboration by the University of Turku
and Aarhus University, and operated jointly by Aarhus University, the
University of Turku and the University of Oslo, representing Denmark, Finland
and Norway, the University of Iceland and Stockholm University at the
Observatorio del Roque de los Muchachos, La Palma, Spain, of the Instituto de
Astrofisica de Canarias. The data from the Seimei and Kanata telescopes were
taken under the KASTOR (Kanata And Seimei Transient Observation Regime)
project (Seimei program IDs: 21B-N-CT09, 21B-K-0004, 21B-K-0011, 22A-K-0004,
22A-O-0003, 22B-N-CT10, 22B-K-0003). The Seimei telescope at the Okayama
Observatory is jointly operated by Kyoto University and the Astronomical
Observatory of Japan (NAOJ), with assistance provided by the Optical and Near-
Infrared Astronomy Inter-University Cooperation Program. This research was
made possible through the use of the AAVSO Photometric All-Sky Survey (APASS),
funded by the Robert Martin Ayers Sciences Fund and NSF AST-1412587. TN
acknowledges support from the Research Council of Finland projects 324504,
328898 and 353019. KM acknowledges support from the Japan Society for the
Promotion of Science (JSPS) KAKENHI grant (JP20H00174 and JP24H01810) and by
the JSPS Open Partnership Bilateral Joint Research Project between Japan and
Finland (JPJSBP120229923). SM was funded by the Research Council of Finland
project 350458. HK was funded by the Research Council of Finland projects
324504, 328898, and 353019. CPG acknowledges financial support from the
Secretary of Universities and Research (Government of Catalonia) and by the
Horizon 2020 Research and Innovation Programme of the European Union under the
Marie Skłodowska-Curie and the Beatriu de Pinós 2021 BP 00168 programme, from
the Spanish Ministerio de Ciencia e Innovación (MCIN) and the Agencia Estatal
de Investigación (AEI) 10.13039/501100011033 under the PID2020-115253GA-I00
HOSTFLOWS project, and the program Unidad de Excelencia María de Maeztu
CEX2020-001058-M. This work was supported by JST, the establishment of
university fellowships towards the creation of science technology innovation,
Grant Number JPMJFS2129.

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##  Appendix A Polarimetry

The observing logs for the spectro- and imaging polarimetry of SN 2021yja are
presented in Tables 1 and 2. The full polarization spectra are shown in Figure
5 and 6.

Table 1: Log and measurements of the spectropolarimetric observations of SN
2021yja.

$\begin{array}[]{lccccccc}\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr\rm{Date}&\rm{MJD}&\rm{Phase}^{a}&\rm{Days\;from\;explosion}^{b}&\rm{Exp.\;time}&\rm{Pol.\;degree}^{c}&\rm{Pol.\;angle}^{c}&\rm{Telescope}\\\
(\rm{UT})&(\rm{days})&(\rm{days})&(\rm{days})&(\rm{seconds})&(\%)&(\rm{degrees})&\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\hline\cr\vskip 3.0pt plus
1.0pt minus 1.0pt\cr 2021-10-02.24&59489.24&-101.33&+24.84&4\times
300&0.78(0.00)\pm 0.03&112.1(-)\pm 1.4&\rm{VLT}\\\ \vskip 3.0pt plus 1.0pt
minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
2021-11-11.26&59529.26&-61.31&+64.86&4\times 300&0.74(0.05)\pm
0.03&112.9(11.1)\pm 3.7&\rm{VLT}\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
2021-12-03.09&59551.09&-39.48&+86.69&4\times 300&0.51(0.29)\pm
0.03&116.5(14.3)\pm 3.0&\rm{VLT}\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
2022-01-06.10&59585.10&-5.47&+120.70&4\times 300&0.46(0.69)\pm
0.04&142.5(4.2)\pm 4.4&\rm{VLT}\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\end{array}$ Notes. aRelative to $t_{0}=59590.57$ (MJD),
which is the estimated time of the end of the plateau phase. bRelative to
$t=59464.40$ (MJD), which is the estimated explosion time. cContinuum
polarization degree and angle. The values in brackets for the polarization
degree and angle refer to the continuum polarization after subtraction of the
first component. The errors of the polarization degrees and angles represent
the photon shot noise.

Table 2: Log and measurements of the imaging-polarimetric observations of SN
2021yja.

$\begin{array}[]{lcccccccc}\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr\rm{Date}&\rm{MJD}&\rm{Phase}&\rm{Days\;from\;explosion}&\rm{Exp.\;time}&\rm{Pol.\;degree}&\rm{Pol.\;angle}&\rm{Filter}&\rm{Telescope}\\\
(\rm{UT})&(\rm{days})&(\rm{days})&(\rm{days})&(\rm{seconds})&(\%)&(\rm{degrees})&&\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\hline\cr\vskip 3.0pt plus
1.0pt minus 1.0pt\cr\hbox{\multirowsetup 2021-09-10.18}&\hbox{\multirowsetup
59467.18}&\hbox{\multirowsetup-123.39}&\hbox{\multirowsetup+2.78}&4\times
40&0.08\pm 0.07&110.8\pm 23.5&V&\hbox{\multirowsetup\rm{NOT}}\\\ &&&&4\times
40&0.17\pm 0.07&125.0\pm 11.2&R&\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hbox{\multirowsetup
2021-09-16.22}&\hbox{\multirowsetup
59473.22}&\hbox{\multirowsetup-117.35}&\hbox{\multirowsetup+8.82}&4\times
30&0.22\pm 0.08&163.6\pm 9.9&V&\hbox{\multirowsetup\rm{NOT}}\\\ &&&&4\times
30&0.73\pm 0.26&124.0\pm 10.2&R&\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hbox{\multirowsetup
2021-09-26.16}&\hbox{\multirowsetup
59483.16}&\hbox{\multirowsetup-107.41}&\hbox{\multirowsetup+18.76}&4\times
30&1.21\pm 0.10&125.9\pm 2.4&V&\hbox{\multirowsetup\rm{NOT}}\\\ &&&&4\times
30&0.78\pm 0.08&101.2\pm 3.0&R&\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hbox{\multirowsetup
2021-11-13.01}&\hbox{\multirowsetup
59531.01}&\hbox{\multirowsetup-59.56}&\hbox{\multirowsetup+66.61}&4\times
30&0.68\pm 0.11&104.6\pm 4.6&V&\hbox{\multirowsetup\rm{NOT}}\\\ &&&&4\times
30&0.60\pm 0.09&108.1\pm 4.1&R&\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hbox{\multirowsetup
2021-12-23.96}&\hbox{\multirowsetup
59571.96}&\hbox{\multirowsetup-18.61}&\hbox{\multirowsetup+107.56}&4\times
40&0.39\pm 0.09&119.1\pm 6.4&V&\hbox{\multirowsetup\rm{NOT}}\\\ &&&&4\times
30&0.60\pm 0.07&135.6\pm 3.5&R&\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hbox{\multirowsetup
2022-02-07.83}&\hbox{\multirowsetup
59617.83}&\hbox{\multirowsetup+27.26}&\hbox{\multirowsetup+153.43}&4\times
100&0.39\pm 0.29&75.1\pm 21.2&V&\hbox{\multirowsetup\rm{NOT}}\\\ &&&&4\times
80&0.69\pm 0.16&105.4\pm 6.6&R&\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
2022-03-27.01&59665.01&+74.44&+200.61&4\times 300&0.85\pm 0.26&57.4\pm
8.9&\rm{FILT\\_815\\_13}&\rm{VLT}\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\end{array}$

Figure 5: Polarization degree (left) and angle (right) of SN 2021yja. The red
hatching shows the adopted wavelength range for the estimation of continuum
polarization. The grey lines in the background of each plot are the unbinned
flux spectra at the corresponding epochs.

Figure 6: Spectropolarimetric data in the q-u plane. The estimated continuum
polarization and its angle are shown with black points and lines,
respectively.

##  Appendix B Photometry

We obtained $B$-, $V-$, $R$\- and $I$-band photometry of SN 2021yja using the
Hiroshima One-shot Wide-field Polarimeter (HOWPol; Kawabata et al. 2008)
mounted on the 1.5-m Kanata telescope at the Higashi-Hiroshima Observatory in
Japan. We performed the point spread function (PSF) photometry using the
DAOPHOT package (Stetson 1987) as a part of IRAF. Since the host galaxy at the
SN position is faint, we did not subtract the template images for the
photometry. The magnitudes of the local comparison stars were obtained from
the AAVSO Photometric All-Sky Survey (APASS; Henden et al. 2012). We estimated
the $R$\- and $I$-band magnitudes of the comparison stars from the Sloan
magnitudes using the relations in Jester et al. (2005). The results of
photometry are provided in Table 3 and Figures 7 and 8.

Table 3: Log of the photometric observations of SN 2021yja and photometric
measurements (Vega magnitudes).

$\begin{array}[]{cccccc}\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr\rm{MJD}&\rm{Days\;from\;explosion}&B&V&R&I\\\
(\rm{days})&(\rm{days})&(\rm{mag})&(\rm{mag})&(\rm{mag})&(\rm{mag})\\\ \vskip
3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 59488.75&+24.35&15.11\pm 0.03&14.70\pm 0.03&14.37\pm 0.03&14.27\pm
0.02\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt
minus 1.0pt\cr 59489.72&+25.32&15.18\pm 0.02&14.66\pm 0.02&14.34\pm
0.02&14.23\pm 0.02\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip
3.0pt plus 1.0pt minus 1.0pt\cr 59490.78&+26.38&15.26\pm 0.02&14.67\pm
0.03&14.38\pm 0.02&14.25\pm 0.03\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
59492.75&+28.35&15.29\pm 0.02&14.69\pm 0.02&14.36\pm 0.02&14.21\pm 0.02\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 59494.71&+30.31&15.35\pm 0.02&14.72\pm 0.02&14.35\pm 0.02&14.22\pm
0.02\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt
minus 1.0pt\cr 59495.79&+31.39&15.46\pm 0.02&14.79\pm 0.03&14.42\pm
0.02&14.24\pm 0.03\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip
3.0pt plus 1.0pt minus 1.0pt\cr 59496.68&+32.28&15.38\pm 0.02&14.73\pm
0.02&14.36\pm 0.02&14.23\pm 0.03\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
59501.77&+37.37&15.62\pm 0.02&14.82\pm 0.02&14.44\pm 0.02&14.27\pm 0.02\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 59512.74&+48.34&15.88\pm 0.02&14.90\pm 0.03&14.48\pm 0.02&14.31\pm
0.02\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt
minus 1.0pt\cr 59536.62&+72.22&16.06\pm 0.03&14.98\pm 0.02&14.49\pm
0.02&14.27\pm 0.02\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip
3.0pt plus 1.0pt minus 1.0pt\cr 59545.65&+81.25&16.09\pm 0.02&15.00\pm
0.02&14.49\pm 0.02&14.28\pm 0.02\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
59561.55&+97.15&16.36\pm 0.02&15.20\pm 0.02&14.59\pm 0.02&14.40\pm 0.02\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 59562.65&+98.25&16.23\pm 0.03&15.15\pm 0.03&14.58\pm 0.02&14.42\pm
0.02\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt
minus 1.0pt\cr 59567.56&+103.16&16.48\pm 0.11&15.33\pm 0.05&14.70\pm
0.04&14.46\pm 0.02\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip
3.0pt plus 1.0pt minus 1.0pt\cr 59571.60&+107.20&16.62\pm 0.03&15.34\pm
0.02&14.71\pm 0.03&14.50\pm 0.02\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
59581.58&+117.18&17.05\pm 0.02&15.67\pm 0.02&14.94\pm 0.02&14.70\pm 0.03\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 59583.48&+119.08&17.10\pm 0.02&15.79\pm 0.02&15.01\pm 0.02&14.77\pm
0.02\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt
minus 1.0pt\cr 59585.56&+121.16&17.28\pm 0.02&15.87\pm 0.03&15.09\pm
0.03&14.86\pm 0.02\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip
3.0pt plus 1.0pt minus 1.0pt\cr 59587.53&+123.13&17.38\pm 0.02&15.98\pm
0.02&15.14\pm 0.02&14.89\pm 0.02\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
59590.41&+126.01&17.44\pm 0.07&16.04\pm 0.05&15.19\pm 0.02&14.98\pm 0.02\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 59591.55&+127.15&17.62\pm 0.03&16.14\pm 0.02&15.33\pm 0.02&15.05\pm
0.02\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt
minus 1.0pt\cr 59594.52&+130.12&17.80\pm 0.03&16.34\pm 0.02&15.43\pm
0.02&15.18\pm 0.02\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip
3.0pt plus 1.0pt minus 1.0pt\cr 59596.52&+132.12&17.71\pm 0.06&16.44\pm
0.04&15.44\pm 0.02&15.24\pm 0.03\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
59606.47&+142.07&18.35\pm 0.03&16.85\pm 0.02&15.82\pm 0.02&15.57\pm 0.02\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 59607.46&+143.06&18.15\pm 0.04&16.82\pm 0.02&15.82\pm 0.02&15.58\pm
0.02\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt
minus 1.0pt\cr 59609.46&+145.06&18.27\pm 0.16&-&15.90\pm 0.02&15.62\pm 0.03\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 59612.48&+148.08&18.33\pm 0.05&16.94\pm 0.03&15.87\pm 0.02&15.65\pm
0.02\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt
minus 1.0pt\cr 59626.49&+162.09&-&-&-&15.78\pm 0.02\\\ \vskip 3.0pt plus 1.0pt
minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
59628.44&+164.04&18.37\pm 0.11&17.16\pm 0.03&15.97\pm 0.02&15.85\pm 0.03\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 59641.44&+177.04&18.32\pm 0.21&17.26\pm 0.03&16.05\pm 0.02&15.90\pm
0.02\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt
minus 1.0pt\cr 59788.80&+324.40&-&19.01\pm 0.11&17.52\pm 0.02&-\\\ \vskip
3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
59792.79&+328.39&-&18.91\pm 0.04&17.54\pm 0.02&17.52\pm 0.02\\\ \vskip 3.0pt
plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
59819.82&+355.42&-&-&17.87\pm 0.02&-\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
59820.78&+356.38&-&19.19\pm 0.11&-&-\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
59851.71&+387.31&-&19.51\pm 0.04&18.34\pm 0.02&18.22\pm 0.02\\\ \vskip 3.0pt
plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
59865.72&+401.32&20.77\pm 0.39&19.65\pm 0.07&18.68\pm 0.05&18.52\pm 0.08\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 59877.74&+413.34&-&-&18.75\pm 0.02&18.62\pm 0.04\\\ \vskip 3.0pt plus
1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
59885.58&+421.18&20.99\pm 0.48&19.94\pm 0.09&18.91\pm 0.04&18.73\pm 0.03\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 59904.58&+440.18&-&20.05\pm 0.06&19.19\pm 0.03&19.03\pm 0.03\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 59928.57&+464.17&-&20.18\pm 0.13&19.57\pm 0.03&19.47\pm 0.05\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\end{array}$

Figure 7: Light curves of SN 2021yja in the optical ($BVRI$) bands. The
magnitudes have been corrected for a reddening of $E(B-V)=0.104$ Figure 8:
Time evolution of the $V$-band absolute magnitudes of SNe 2021yja and 2012aw.
The data of SN 2012aw were taken from Munari et al. (2013); Bose et al.
(2013); Dall’Ora et al. (2014); Brown et al. (2014). The $V$-band extinction
for SN 2012aw is assumed to be $A_{V}=0.23$ mag (Bose et al. 2013).

##  Appendix C Spectroscopy

In addition to the spectra obtained from the spectropolarimetric observations
with the FORS2/VLT (see Section 2), we obtained optical spectra of SN 2021yja
using the Kyoto Okayama Optical Low-dispersion Spectrograph with optical-fiber
Integral Field Unit (KOOLS-IFU; Matsubayashi et al. 2019) mounted on the
Seimei telescope (Kurita et al. 2020) at the Okayama Observatory of Kyoto
University and the Alhambra Faint Object Spectrograph and Camera
(ALFOSC)333https://www.not.iac.es/instruments/alfosc/ mounted on the 2.56-m
Nordic Optical Telescope (NOT)444https://www.not.iac.es/ at the Roque de los
Muchachos Observatory. The log of spectroscopic observations are provided in
Table 4.

For the KOOLS-IFU/Seimei, we used the VPH-blue grism, giving a wavelength
coverage of 4100–8900 Å and a spectral resolution of
$R=\lambda/\Delta\lambda\sim 500$. The data reduction was performed following
the standard procedures that are developed for KOOLS-IFU
data555http://www.o.kwasan.kyoto-u.ac.jp/inst/p-kools/reduction-201806/index.html,
using the IRAF. For the ALFOSC/NOT, we used Grism 4, giving a wavelength
coverage of 3200–9600 Å and a spectral resolution of $\sim 360$. The spectrum
was reduced with the alfoscgui pipeline666FOSCGUI is a graphical user
interface aimed at extracting SN spectroscopy and photometry obtained with
FOSC-like instruments. It was developed by E. Cappellaro. A package
description can be found at https://sngroup.oapd.inaf.it/foscgui.html. The
procedures include overscan, bias, and flat-field corrections, as well as
removing cosmic-ray artefacts. Extraction of a one-dimensional spectrum and
sky subtraction were performed. Wavelength calibration was performed by
comparison with arc lamps. The spectra were flux-calibrated against a
sensitivity function derived from a standard star observed on the same night.
The reduced spectra are shown in Figures 9 and 10.

Table 4: Log of the spectroscopic observations of SN 2021yja.

$\begin{array}[]{lccccc}\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr\rm{Date}&\rm{MJD}&\rm{Phase}&\rm{Days\;from\;explosion}&\rm{Exp.\;time}&\rm{Instrument/Telescope}\\\
(\rm{UT})&(\rm{days})&(\rm{days})&(\rm{days})&(\rm{seconds})&\\\ \vskip 3.0pt
plus 1.0pt minus 1.0pt\cr\hline\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 2021-09-09.75&59466.75&-123.82&+2.35&300\times 3&\rm{KOOLS-
IFU/Seimei}\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt
plus 1.0pt minus 1.0pt\cr 2021-09-15.79&59472.79&-117.78&+8.39&600\times
3&\rm{KOOLS-IFU/Seimei}\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
2021-09-18.76&59475.76&-114.81&+11.36&300\times 3&\rm{KOOLS-IFU/Seimei}\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 2021-09-19.76&59476.76&-113.81&+12.36&600\times 3&\rm{KOOLS-
IFU/Seimei}\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt
plus 1.0pt minus 1.0pt\cr 2021-09-29.78&59486.78&-103.79&+22.38&900\times
3&\rm{KOOLS-IFU/Seimei}\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
2021-10-02.24&59489.24&-101.33&+24.84&300\times 4&\rm{FORS2/VLT}\\\ \vskip
3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
2021-10-05.78&59492.78&-97.79&+28.38&300\times 3&\rm{KOOLS-IFU/Seimei}\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 2021-11-11.26&59529.26&-61.31&+64.86&300\times 4&\rm{FORS2/VLT}\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 2021-11-14.60&59532.60&-59.97&+68.20&600\times 3&\rm{KOOLS-
IFU/Seimei}\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt
plus 1.0pt minus 1.0pt\cr 2021-12-03.09&59551.09&-39.48&+86.69&300\times
4&\rm{FORS2/VLT}\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip
3.0pt plus 1.0pt minus 1.0pt\cr
2021-12-30.51&59578.51&-12.06&+114.11&1200\times 2&\rm{KOOLS-IFU/Seimei}\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 2022-01-06.10&59585.10&-5.47&+120.70&300\times 4&\rm{FORS2/VLT}\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 2022-01-10.47&59589.47&-1.1&+125.07&1200\times 1&\rm{KOOLS-
IFU/Seimei}\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt
plus 1.0pt minus 1.0pt\cr 2022-02-10.39&59620.39&+29.82&+155.99&600\times
2&\rm{KOOLS-IFU/Seimei}\\\ \vskip 3.0pt plus 1.0pt minus
1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
2022-08-26.22&59817.22&+226.65&+352.82&1800\times 1&\rm{ALFOSC/NOT}\\\ \vskip
3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus 1.0pt\cr
2022-09-21.74&59842.74&+252.17&+378.34&900\times 1&\rm{KOOLS-IFU/Seimei}\\\
\vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\vskip 3.0pt plus 1.0pt minus
1.0pt\cr 2022-10-18.67&59870.67&+280.10&+406.27&900\times 3&\rm{KOOLS-
IFU/Seimei}\\\ \vskip 3.0pt plus 1.0pt minus 1.0pt\cr\hline\cr\end{array}$

Figure 9: Spectral evolution of SN 2021yja. The numbers show days from the
explosion.  Figure 10: Same as Figure 4, but for the full wavelength range.