# SN 2013ai: a link between hydrogen-rich and hydrogen-poor core-collapse
supernovae

S. Davis Department of Physics, University of California, 1 Shields Avenue,
Davis, CA 95616-5270, USA  P.J. Pessi Facultad de Ciencias Astronómicas y
Geofísicas (FCAG), Universidad Nacional de La Plata (UNLP), Paseo del bosque
S/N, 1900, Argentina  European Southern Observatory, Alonso de Córdova 3107,
Casilla 19, Santiago, Chile  M. Fraser  School of Physics, O’Brien Centre for
Science North, University College Dublin, Belfield, Dublin 4, Ireland  K.
Ertini  Facultad de Ciencias Astronómicas y Geofísicas (FCAG), Universidad
Nacional de La Plata (UNLP), Paseo del bosque S/N, 1900, Argentina  Instituto
de Astrofísica de La Plata (IALP), CONICET, Paseo del bosque S/N, 1900,
Argentina  L. Martinez Facultad de Ciencias Astronómicas y Geofísicas (FCAG),
Universidad Nacional de La Plata (UNLP), Paseo del bosque S/N, 1900, Argentina
Instituto de Astrofísica de La Plata (IALP), CONICET, Paseo del bosque S/N,
1900, Argentina  P. Hoeflich Department of Physics, Florida State University,
77 Chieftan Way, Tallahassee, FL 32306, USA  E.Y. Hsiao Department of Physics,
Florida State University, 77 Chieftan Way, Tallahassee, FL 32306, USA  G.
Folatelli  Facultad de Ciencias Astronómicas y Geofísicas (FCAG), Universidad
Nacional de La Plata (UNLP), Paseo del bosque S/N, 1900, Argentina  Instituto
de Astrofísica de La Plata (IALP), CONICET, Paseo del bosque S/N, 1900,
Argentina  Kavli Institute for the Physics and Mathematics of the Universe,
Todai Institutes for Advanced Study, University of Tokyo, 5-1-5 Kashiwanoha,
Kashiwa, Chiba 277-8583, Japan  C. Ashall Institute for Astronomy, University
of Hawai’i at Manoa, 2680 Woodlawn Dr. Hawai’i, HI 96822, USA  M. M. Phillips
Carnegie Observatories, Las Campanas Observatory, Casilla 601, La Serena,
Chile  J. P. Anderson European Southern Observatory, Alonso de Córdova 3107,
Casilla 19, Santiago, Chile  M. Bersten  Facultad de Ciencias Astronómicas y
Geofísicas (FCAG), Universidad Nacional de La Plata (UNLP), Paseo del bosque
S/N, 1900, Argentina  Instituto de Astrofísica de La Plata (IALP), CONICET,
Paseo del bosque S/N, 1900, Argentina  Kavli Institute for the Physics and
Mathematics of the Universe, Todai Institutes for Advanced Study, University
of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan  B. Englert
Facultad de Ciencias Astronómicas y Geofísicas (FCAG), Universidad Nacional de
La Plata (UNLP), Paseo del bosque S/N, 1900, Argentina  Agencia Nacional de
Promoción Científica y Tecnológica (ANPCyT), Godoy Cruz 2370, C142FQD, Buenos
Aires, Argentina  A. Fisher  Department of Physics, Florida State University,
77 Chieftan Way, Tallahassee, FL 32306, USA  S. Benetti  1INAF - Osservatorio
Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy  A.
Bunzel  Facultad de Ciencias Astronómicas y Geofísicas (FCAG), Universidad
Nacional de La Plata (UNLP), Paseo del bosque S/N, 1900, Argentina  Instituto
Argentino de Radioastronomía, CC5, 1894 Villa Elisa, Buenos Aires, Argentina
C. Burns Observatories of the Carnegie Institution for Science, 813 Santa
Barbara St., Pasadena, CA 91101, USA  T. W. Chen  The Oskar Klein Centre,
Department of Astronomy, Stockholm University, AlbaNova, SE-10691 Stockholm,
Sweden  C. Contreras Carnegie Observatories, Las Campanas Observatory, Casilla
601, La Serena, Chile  N. Elias-Rosa  INAF Osservatorio Astronomico di Padova,
Vicolo dell’Osservatorio 5, 35122 Padova, Italy  Institute of Space Sciences
(ICE, CSIC), Campus UAB, Carrer de Can Magrans s/n, 08193 Barcelona, Spain  E.
Falco  Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA
L. Galbany Departamento de Física Teórica y del Cosmos, Universidad de
Granada, E-18071 Granada, Spain  R. P. Kirshner Gordon and Betty Moore
Foundation, 1661 Page Mill Road, Palo Alto, CA 94304  Harvard-Smithsonian
Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138  S. Kumar
Department of Physics, Florida State University, 77 Chieftan Way, Tallahassee,
FL 32306, USA  J. Lu Department of Physics, Florida State University, 77
Chieftan Way, Tallahassee, FL 32306, USA  J. D. Lyman  Department of Physics,
University of Warwick, Coventry CV4 7AL, UK  G. H. Marion  University of Texas
at Austin, 1 University Station C1400, Austin, TX, 78712-0259, USA  S. Mattila
Tuorla Observatory, Department of Physics and Astronomy, University of Turku,
FI-20014 Turku, Finland  J. Maund  Department of Physics and Astronomy,
University of Sheffield, F39 Hicks Building, Hounsfield Road, Sheffield, S3
7RH, United Kingdom  N. Morrell Carnegie Observatories, Las Campanas
Observatory, Casilla 601, La Serena, Chile  J. Serón  Cerro Tololo Inter-
American Observatory/NSF’s NOIRLab, Casilla 603, La Serena, Chile  M.
Stritzinger  Department of Physics and Astronomy, Aarhus University, Ny
Munkegade 120, DK-8000 Aarhus C, Denmark  M. Shahbandeh Department of Physics,
Florida State University, 77 Chieftan Way, Tallahassee, FL 32306, USA  M.
Sullivan  School of Physics and Astronomy, University of Southampton,
Southampton, SO17 1BJ, UK  N. B. Suntzeff George P. and Cynthia Woods Mitchell
Institute for Fundamental Physics & Astronomy, Texas A&M University,
Department of Physics, 4242 TAMU, College Station, TX 77843  D. R. Young
Astrophysics Research Centre, School of Mathematics and Physics, Queens
University Belfast, Belfast BT7 1NN, UK Scott Davis<EMAIL_ADDRESS>
(Received XXX; Revised YYY; Accepted ZZZ)

###### Abstract

We present a study of optical and near-infrared (NIR) spectra along with the
light curves of SN 2013ai. These data range from discovery until 380 days
after explosion. SN 2013ai is a fast declining type II supernova (SN II) with
an unusually long rise time; $18.9\pm 2.7$d in $V$-band and a bright $V$-band
peak absolute magnitude of $-18.7\pm 0.06$ mag. The spectra are dominated by
hydrogen features in the optical and NIR. The spectral features of SN 2013ai
are unique in their expansion velocities, which when compared to large samples
of SNe II are more than 1,000 km s-1 faster at 50 days past explosion. In
addition, the long rise time of the light curve more closely resembles SNe IIb
rather than SNe II. If SN 2013ai is coeval with a nearby compact cluster we
infer a progenitor ZAMS mass of $\sim$17 M⊙. After performing light curve
modeling we find that SN 2013ai could be the result of the explosion of a star
with little hydrogen mass, a large amount of synthesized 56Ni, 0.3-0.4 M⊙, and
an explosion energy of $2.5-3.0\times 10^{51}$ ergs. The density structure and
expansion velocities of SN 2013ai are similar to that of the prototypical SN
IIb, SN 1993J. However, SN 2013ai shows no strong helium features in the
optical, likely due to the presence of a dense core that prevents the majority
of $\gamma$-rays from escaping to excite helium. Our analysis suggests that SN
2013ai could be a link between SNe II and stripped envelope SNe.

supernova

††journal: ApJ††facilities: Magellan:Baade, Swope, MAST, GTC, VLT, HST, TAROT,
NTT, CTIO:1.3m††software: PyWiFeS (Childress et al., 2013), IRAF (Tody, 1986),
SNooPy (Burns et al., 2011), Astrodrizzle (Hack et al., 2012), chorizos (Maíz-
Apellániz, 2004)), MESA (Maíz-Apellániz, 2004), HYDRA (Hoeflich, 2003, 2009),
STARS (Eggleton et al., 2011).

##  1 Introduction

Core collapse supernovae (CCSNe) are the result of the explosion of massive
stars ($>8$ M⊙). These explosions are characterized by two main classes: those
that show no hydrogen and those that do, type I (SNe I) and type II supernovae
(SNe II), respectively (Minkowski, 1941).

Type I CCSNe are produced when a massive star is stripped of most of its outer
hydrogen and possibly its helium layers before explosion, thus referred to as
stripped envelope SNe (SESNe, Clocchiatti, & Wheeler, 1997). It is believed
that the outer layers of the SESNe progenitors are primarily removed either
through strong winds (Woosley et al., 1993) or binary interaction (Nomoto et
al., 1995; Podsiadlowski et al., 2004). These SESNe are further divided into
two general spectroscopic groups, SNe Ib that show strong helium lines in
their optical spectra and SNe Ic that do not. SNe Ib and Ic form
spectroscopically homogeneous groups with minimal variation (Modjaz et al.,
2014). The light curves of SNe Ib and Ic are similar and can be characterized
by a slow $\sim 20$ day rise to maximum followed by a post-maximum decline of
$\sim 0.75$ magnitudes per 15 days in the $V$-band (e.g. Drout et al., 2011;
Taddia et al., 2018; Prentice et al., 2019).

When a massive star retains most of its hydrogen envelope, it explodes as a SN
II. SNe II were historically divided into groups based on the shape of their
light curves. Those with a slow decline – a plateau – after maximum were
classified as IIP and those with no plateau after maximum were classified as
IIL (Barbon et al., 1979). However, recent studies have shown that there is
likely a continuum in the decline rates and suggest that slow (IIP) and fast
decliners (IIL) are not distinct groups (Anderson et al., 2014a; Sanders et
al., 2015; Galbany et al., 2016; Valenti et al., 2016; Rubin, & Gal-Yam, 2016;
Pessi et al., 2019; de Jaeger et al., 2019). The different decline rates were
proposed to correlate with the amount of hydrogen retained by the progenitor
(e.g. Popov, 1993; Anderson et al., 2014a; Faran et al., 2014; Gutiérrez et
al., 2014; Moriya et al., 2016; Hillier & Dessart, 2019); however, see
(Morozova et al., 2017) for an alternative explanation based on interaction
with dense circumstellar material. On the contrary, the near-infrared (NIR)
shows that there are spectroscopic distinctions between slow and fast
decliners in the 1.06$\mu m$ region, which may be due to progenitor
differences (Davis et al., 2019).

Pre-explosion images of SNe IIP suggest that most of their progenitors are red
supergiants (RSG) (e.g. Smartt et al., 2004; Maund et al., 2005; Smartt et
al., 2009, 2015; Van Dyk, 2017; Van Dyk et al., 2019). However, blue
supergiants can produce SNe II with longer rising light curves called SN
1987A-like after the famous SN 1987A (see Arnett et al. 1989 for a review).
Theory suggests that if a RSG progenitor has most of its hydrogen envelope
stripped pre-explosion, it can give rise to a SN IIb; however, the progenitor
likely plays a role as it may not be that of a normal SN II (see Bersten et
al. 2012). SN IIb show hydrogen at early times and helium in their later
spectra that quickly becomes the dominant feature (Filippenko et al., 1993).
The required strong mass loss is believed to be due to a binary progenitor
(e.g. Podsiadlowski et al., 1993; Aldering et al., 1994).

There is an open question as to whether or not there is a continuum between
fast declining SN II and SN IIb. Arcavi et al. (2012) and Pessi et al. (2019)
suggest that there is a discrete change between SN II and SN IIb. However,
Pessi et al. (2019) discussed a peculiar SN II, SN 2013ai, that presented an
unusually large rise time and was systematically “misclasified” as a SN IIb
when performing clustering analysis. This, along with the spectral
peculiarities discussed later in the current work, encouraged further analysis
of SN 2013ai in order to elucidate if the object is in fact some kind of
transitional event, in which case, it can provide important clues about the
stellar evolutionary pathways leading to CCSNe.

In this paper we present optical and NIR observations and analysis of SN
2013ai. Section 2 outlines the observing techniques and reduction procedures.
In Section 3 we describe the processes used to determine the reddening of SN
2013ai. In Sections 4 and 5 we present the photometric and spectroscopic
properties of SN 2013ai and make comparisons to other CCSNe. The analysis of
the pre-explosion HST images and the possible progenitor scenarios are
described in Section 6. In Section 7 the models and their outcomes are
reviewed. The discussion of results and conclusions are in Sections 8 and 9,
respectively.

##  2 Observations and Data Reduction

SN 2013ai was discovered at RA(2000)$=6^{h}16^{m}18^{s}.35$,
Dec(2000)$=-21^{\circ}22^{\prime}32^{\prime\prime}.90$ with the Zadko 1 meter
telescope at Gingin Observatory, Australia on 2013 March 1 UT at an apparent
$R$-band magnitude of 14.4 mag (Conseil et al., 2013). However, the SN was
previously detected in pre-discovery images as early as 2013 February 26 UT
and not detected in images taken on 2013 February 21 UT, with a limiting
magnitude of $r=20.7$ from the Panoramic Survey Telescope and Rapid Response
System (Pan-STARRS; Chambers et al., 2016). Thus an explosion date of 2013
February 24 UT (56347 MJD) $\pm 2.7$ days is adopted for the remainder of this
work. The error listed on explosion date is a flat distribution without any
obvious bias toward last non-detection or discovery.

The host of SN 2013ai, NGC 2207, is in the process of colliding with another
galaxy, IC 2163, which makes any distance measurement based on galaxian
properties uncertain. The host is a luminous infrared galaxy with a high star
formation rate that produces SNe frequently, e.g. SNe 1975A, 1999ec, 2003H,
2018lab, and AT 2019eez (Kirshner et al., 1976; Jha et al., 1999; Graham et
al., 2003; Sand et al., 2018; Stanek, 2019). At a redshift of 0.009, NGC 2207
is too close for a reliable redshift distance as it is not in the Hubble flow.

NGC 2207 was host to SN 1975A, a SN Ia that provides the only redshift-
independent distance measurement to the galaxy. Using the GELATO
classification tool (Harutyunyan et al., 2008), the best match of the 1975
January 20 spectrum of SN 1975A published by Kirshner et al. (1976) was found
to be SN2003du, which had a $B$-band decline rate of
$\Delta{\rm{m}_{15}}(B)=1.07\pm 0.06$ (Blondin et al., 2012). Pseudo
equivalent width (pEW) measurements of the Si ii $\lambda\lambda$5972 and 6355
lines from this spectrum place SN 1975A in the middle of core-normal SNe in
the Branch diagram (Branch et al., 2006, 2009). In addition, the pEW of the
λ5972 line is consistent with $\Delta{\rm{m}_{15}}(B)\sim$1.1 (see Figure 17b
of Folatelli et al. 2013). Following the procedures of Riess et al. (1998),
and using the reproduced photometry from Kirshner et al. (1976), the SN 1975A
light curves were analyzed using SNooPy (Burns et al., 2011) to estimate a
distance. Fixing the B-band decline rate in the range
$\Delta{\rm{m}_{15}}$(B)$=1.1-1.5$ yielded a 0.1 mag difference in the
distance moduli and a fit error of 0.15 mag from SNooPy. This procedure gives
a final distance modulus of $33.5\pm 0.2$ for NGC 2207, which we adopt in this
paper.

SN 2013ai was classified as a SN II by the Public ESO Spectroscopic Survey of
Transient Objects (PESSTO) (Smartt et al., 2015) due to broad H$\alpha$
emission in its optical spectrum (Klotz et al., 2013). Archival HST-WFPC2
images are available of the field, obtained using the F336W, F439W, F555W, and
F814W filters, which contained the site of SN 2013ai on 1996 May 25 UT.
However, no clear single progenitor could be detected (Milisavljevic et al.,
2013). These data are reanalyzed in Section 6.

Optical photometric follow up commenced soon after SN 2013ai was discovered,
using ESO + EFOSC2, the 1.3 m SMARTS telescope111Operated by the SMARTS
Consortium. \+ ANDICAM, and the 1m Swope telescope + SITe3. Swope + SITe3
images were taken as a part of the Carnegie Supernova Project II (CSP-II)
(Phillips et al., 2019; Hsiao et al., 2019). In the NIR, imaging was obtained
with NTT + SOFI and the 2.5 m du Pont telescope + RetroCam. A Swope $V$-band
image taken at $\sim 10$ days past explosion is shown in Figure 1.

Figure 1: Swope $V$-band image of SN 2013ai in NGC 2207 taken around 10 days
past explosion. The cross hair marks the SN. The compass and size of field are
also noted.

ANDICAM data were reduced with the dedicated pipeline which subtracts the
overscan and bias from each image, followed by flat fielding correction using
dome flats. For EFOSC2 data, the reduction was performed using the PESSTO
pipeline, as described in Smartt et al. (2015), which trims, debiases, and
flat-fields images (using twilight sky flats). In addition, a fringe frame is
used to correct the I-band data. The SN magnitude in each frame was measured
via Point Spread Function (PSF) fitting photometry using the SNOoPy
package222SNOoPy is a package for SN photometry using PSF fitting and/or
template subtraction developed by E. Cappellaro. A package description can be
found at https://sngroup.oapd.inaf.it/snoopy.html, with errors estimated from
artificial star tests. The photometric zero point for each image was
determined from aperture photometry of local sequence stars, which in turn
were calibrated to Landolt fields (Landolt, 1992) observed on multiple
photometric nights. Color terms were applied to the EFOCS2 and ANDICAM
magnitudes using the values listed in Smartt et al. (2013) for the former and
values listed on the SMARTS consortium webpages for the latter. The reduction
of Swope photometry was performed as described in Phillips et al. (2019).
Swope PSF photometry was performed in the same process described for ANDICAM
and EFOSC2 data with standard fields observed on the same nights as the SN
observations when possible. The Swope data have been converted to the standard
system using the process outlined in Phillips et al. (2019). The light curves
are presented without template subtraction as the SN is well separated from
the host. A log of the optical photometry is given in Table 1.

Table 1: Optical Photometry of SN 2013ai.

MJD | UT Date | Phase |  $u$ ($\sigma$) |  $B$ ($\sigma$) |  $V$ ($\sigma$) |  $g$ ($\sigma$) |  $R$ ($\sigma$) |  $I$ ($\sigma$) | Instrument
---|---|---|---|---|---|---|---|---|---
56344.33 | 2013/02/21 |  $-$2.7 | - | - | - | - |  $>$20.7 | - | GPC1
56349.66 | 2013/02/26 | 2.7 | - | - | - | - | 18.3 | - | TAROT
56351.66 | 2013/02/28 | 4.7 | - | - | - | - | 17.6 | - | TAROT
56352.66 | 2013/03/01 | 5.7 | - | - | - | - | 17.4 | - | TAROT
56354.05 | 2013/03/03 | 7.1 | - | - | - | - | 17.23(03) | - | EFOSC2
56354.25 | 2013/03/03 | 7.2 | 18.43(04) | 18.15(02) | 17.68(02) | 17.80(02) | 17.42(02) | 17.17(02) | SITe3
56355.08 | 2013/03/04 | 8.1 | 18.22(03) | 18.07(02) | 17.58(02) | 17.80(02) | 17.27(03) | 17.06(02) | SITe3
56356.09 | 2013/03/05 | 9.1 | - | 18.22(02) | 17.49(02) | - | 16.94(03) | 16.35(04) | ANDICAM
56357.08 | 2013/03/06 | 10.1 | - | 18.09(01) | 17.45(02) | - | 16.83(01) | 16.21(02) | ANDICAM
56362.15 | 2013/03/11 | 15.2 | - | 18.09(03) | 17.30(02) | - | 16.69(03) | 16.06(03) | ANDICAM
56362.15 | 2013/03/11 | 15.2 | - | - | 17.34(04) | - | - | - | EFOSC2
56364.15 | 2013/03/13 | 17.2 | - | 18.14(03) | 17.29(02) | - | 16.70(03) | 16.05(03) | ANDICAM
56364.15 | 2013/03/13 | 17.2 | - | - | 17.36(03) | - | - | - | EFOSC2
56368.12 | 2013/03/17 | 21.1 | - | 18.21(02) | 17.36(02) | - | 16.65(02) | 15.98(02) | ANDICAM
56368.08 | 2013/03/17 | 21.1 | - | - | 17.37(03) | - | - | - | EFOSC2
56371.13 | 2013/03/20 | 24.1 | - | 18.33(03) | 17.34(04) | - | 16.60(01) | 15.93(04) | ANDICAM
56373.14 | 2013/03/22 | 26.1 | - | 18.36(07) | 17.40(04) | - | 16.59(02) | 15.86(02) | ANDICAM
56374.10 | 2013/03/23 | 27.1 | - | 18.46(04) | 17.40(04) | - | 16.54(04) | 15.96(03) | ANDICAM
56378.05 | 2013/03/27 | 31.1 | - | 18.73(06) | 17.47(04) | - | 16.64(02) | 15.95(03) | ANDICAM
56380.12 | 2013/03/29 | 33.1 | - | 18.73(08) | 17.54(04) | - | 16.69(03) | 16.02(03) | ANDICAM
56385.03 | 2013/04/03 | 38.0 | - | - | 17.75(10) | - | - | - | EFOSC2
56388.07 | 2013/04/06 | 41.1 | - | 19.12(04) | 17.68(03) | - | 16.73(04) | 16.07(02) | ANDICAM
56391.07 | 2013/04/09 | 44.1 | - | 19.25(05) | 17.71(03) | - | 16.79(02) | 16.02(02) | ANDICAM
56394.06 | 2013/04/12 | 47.1 | - | 19.20(42) | 17.81(06) | - | 16.82(04) | 16.06(03) | ANDICAM
56395.00 | 2013/04/13 | 48.0 | - | - | 17.91(03) | - | - | - | EFOSC2
56397.05 | 2013/04/15 | 50.1 | - | 19.54(08) | 17.80(03) | - | 16.82(03) | 16.17(03) | ANDICAM
56400.06 | 2013/04/18 | 53.1 | - | 19.47(36) | 17.92(05) | - | 16.87(06) | 16.09(04) | ANDICAM
56402.02 | 2013/04/20 | 55.0 | - | - | 18.00(04) | - | - | - | EFOSC2
56403.03 | 2013/04/21 | 56.0 | - | 19.57(09) | 17.98(05) | - | 17.02(03) | 16.19(02) | ANDICAM
56411.08 | 2013/04/29 | 64.1 | - | 19.60(60) | - | - | 17.10(03) | - | EFOSC2
56414.51 | 2013/05/02 | 67.5 | - | 19.66(62) | 18.16(17) | - | 17.08(03) | 16.37(03) | ANDICAM
56680.17 | 2014/01/23 | 333.2 | - | - | - | - | - | 21.57(22) | EFOSC2
56695.16 | 2014/02/07 | 348.2 | - | - | 23.75(63) | - | - | 22.33(41) | EFOSC2
56708.15 | 2014/02/20 | 361.2 | - | - | 23.21(31) | - | - | - | EFOSC2
56726.09 | 2014/03/10 | 379.1 | - | - | - | - | - | 21.48(28) | EFOSC2

Note. — The MJD column lists the Modified Julian Date of each observation.
Phase is listed in days since explosion.

The NIR light curves from Dupont + RetroCam were reduced in the standard
manner following Phillips et al. (2019). The NIR NTT + SOFI data were
corrected for crosstalk, flat-fielded (using dome flats), and scattered light,
performed within the PESSTO pipeline. Separate off-target sky frames were
taken as part of the sequence of observations, and these were used to subtract
the sky background from the on-target images. The multiple exposures taken in
each filter were combined to produce a deep image on which photometry was
performed. The log of NIR photometry is given in Table 2. The photometry of SN
2013ai previously published by Valenti et al. (2016) is also included. The
light curves in each band, during the photospheric phase, are presented in
Figure 2.

Table 2: NIR Photometry of SN 2013ai.

MJD | UT Date | Phase |  $Y$ ($\sigma$) |  $J$ ($\sigma$) |  $H$ ($\sigma$) |  $K_{S}$ ($\sigma$) | Instrument
---|---|---|---|---|---|---|---
56354.25 | 2013/03/03 | 7.1 | 15.86(01) | 15.60(01) | 15.24(11) | - | RetroCam
56355.08 | 2013/03/04 | 8.1 | 15.87(01) | 15.47(01) | 15.11(11) | - | RetroCam
56364.10 | 2013/03/13 | 17.1 | - | 14.89(06) | 14.50(03) | 14.18(08) | SOFI

Note. — The MJD column lists the Modified Julian Date of each observation.
Phase is given in days since explosion.

Figure 2: Milky Way corrected optical and NIR light curves of SN 2013ai. Light
curves are presented without host subtractions. Blue and red vertical lines
mark the dates when optical and NIR spectra were taken, respectively. Open
symbols are previously published data from Valenti et al. (2016). The arrow
denotes the magnitude limit of the last non-detection. The inset shows data
taken more than 300 days from $V$-band maximum.

Through the PESSTO collaboration, an optical spectroscopic time-series was
obtained with EFOSC2 on the ESO-NTT (Buzzoni et al., 1984). Complementary,
spectra were taken with the Wide-Field Spectrograph (WiFeS; Dopita et al.,
2010) on the Australian National University (ANU) 2.3m Telescope as part of
the ANU WiFeS Supernova Programme (Childress et al., 2016). The EFOSC2 spectra
were reduced, extracted, and calibrated with the PESSTO pipeline using
standard techniques (Smartt et al., 2015). All spectra were bias-subtracted
and divided by a normalized lamp flat. For the Gr#16 EFOSC2 spectra, flat
fields were taken immediately after the spectrum, and at the same position on
the sky, to allow for the removal of the strong fringing seen at longer
wavelengths. Wavelength calibration was performed with respect to an HeAr arc
lamp. After extracting each spectrum the wavelength of the strong night sky
emission lines were checked, and if necessary, a linear shift was applied to
the dispersion solution. The spectra were flux calibrated using a sensitivity
curve constructed from observations of spectrophotometric standard stars, and
then telluric absorptions were removed using a scaled synthetic model of
atmospheric transmission (Patat et al., 2011). The WiFeS spectra were reduced
using the PyWiFeS software (Childress et al., 2013). The late time spectrum
taken with Gran Telescopio Canarias (GTC) on October 30 2013 was reduced and
extracted using standard IRAF (Tody, 1986) routines and was flux calibrated
using a spectrophotometric standard star observed on the same night. A log of
the spectroscopic observations is presented in Table 3, and the optical
spectra during the photospheric phase are presented in Figure 3.

A NIR spectrum of SN 2013ai was obtained using the Folded-port Infrared
Echellette (FIRE; Simcoe et al., 2013) on the Magellan Baade telescope as part
CSP-II (Phillips et al., 2019; Hsiao et al., 2019). The spectrum was reduced
and telluric corrected following the procedure outlined in Hsiao et al. (2019)
and has been previously published in Davis et al. (2019). All observations
will be made public via WISeREP (Yaron & Gal-Yam, 2012).

Further observations taken with Swift-XRT 25 days after explosion detected an
X-ray source 8′′ from the SN position at a level of $\sim 2\times 10^{-14}$
erg/s/cm2 (Margutti et al., 2013). Radio observations were taken using the
Combined Array for Research in Millimeter-Wave Astronomy (CARMA) 10 and 11
days past explosion at 85 GHz, however, no radio source was detected at either
epoch at a limit of 0.6 mJy (Zauderer et al., 2013).

Table 3: Journal of spectroscopic observations

UT Date | MJD | Instrument | Phase | $t_{max}(V)$
---|---|---|---|---
|  | Optical |  |
2013-03-03 | 56354.1 | NTT + EFOSC2 | 7.1 |  $-$11.3
2013-03-05 | 56356.1 | NTT + EFOSC2 | 9.1 |  $-$9.3
2013-03-08 | 56359.5 | ANU + WiFeS | 12.0 |  $-$5.9
2013-03-11 | 56362.2 | NTT + EFOSC2 | 15.2 |  $-$3.2
2013-03-13 | 56364.2 | NTT + EFOSC2 | 17.2 |  $-$1.2
2013-03-17 | 56368.1 | NTT + EFOSC2 | 21.1 | 2.7
2013-03-25 | 56376.4 | ANU + WiFeS | 29.4 | 11.0
2013-04-03 | 56385.0 | NTT + EFOSC2 | 38.0 | 19.6
2013-04-09 | 56391.4 | ANU + WiFeS | 44.4 | 26.0
2013-04-13 | 56395.0 | NTT + EFOSC2 | 48.0 | 29.6
2013-04-20 | 56402.0 | NTT + EFOSC2 | 55.0 | 36.6
2013-05-26 | 56438.3 | ANU + WiFeS | 91.3 | 72.9
2013-10-30 | 56595.5 | GTC + OSIRIS | 249.5 | 231.1
|  | NIR |  |
2013-03-10 | 56361.5 | Baade + FIRE | 14.5 |  $-$3.9

Note. — The MJD column lists the Modified Julian Date of each observation.
Phase is given as days since explosion. Time relative to $V$ maximum, in days,
is denoted $t_{max}(V)$.

Figure 3: Optical spectra of SN 2013ai. Gaussian smoothed spectra, with a
radius of 30 Å, are plotted (black) over the observed spectra (grey). The UT
date of observation and phase relative to $V$ maximum are labeled for each
spectrum. The gray vertical bands mark the regions of strongest telluric
absorption. The narrow peaks in the H$\alpha$ profile are from the host galaxy
of SN 2013ai.

##  3 Reddening

Milky Way extinction towards SN 2013ai is taken from (Schlafly & Finkbeiner,
2011). In order to estimate the extinction of SN 2013ai the equivalent width
(EW) of the Na I absorption lines at the redshift of the host galaxy NGC 2207
were measured in all available WiFeS spectra as they have the highest
resolution of R$\sim 7000$. Assuming Gaussian profiles for both components, we
obtain an average of $D_{1}=0.68\pm 0.15$ Å, $D_{2}=0.91\pm 0.07$ Å, and
$D_{1}+D_{2}=1.52\pm 0.07$ Å. Using equation (9) from Poznanski et al. (2012)
we obtain an $E(B-V)=0.84\pm 0.64$ mag. However, according to Phillips et al.
(2013) the error associated with this method can be much larger than predicted
by relations derived for typical Milky Way dust and gas. As a check for
consistency, we used the Balmer decrement to determine the dust extinction by
computing the flux ratio of H$\alpha$ and H$\beta$ lines using the same WiFes
spectra. The Balmer decrement was measured using the narrow host galaxy lines
in the spectrum. The obtained color excess was $E(B-V)=0.70\pm 0.34$ mag.
Similar results were obtained using PESSTO low resolution spectra from which
we extracted a region near the SN without subtracting the background. The
Balmer decrement was measured from a flux calibrated MW extinction corrected
spectrum. Errors were determined by a series of Monte Carlo realizations,
assuming the uncertainty is dominated by the photometric errors and therefore
flux calibration. The Balmer decrement was measured for each realization, with
the error taken as the standard deviation. Finally, the diffuse interstellar
band (DIB) at 5780 Å was analyzed. This band appears to be very weak or non
existent in the available spectra. Thus, for this work we adopt a color excess
estimate of $E(B-V)_{host}\sim 0.8\pm 0.5$ mag from the Balmer decrement and
Na ID measurements.

##  4 Photometric Properties

The optical light curves of SN 2013ai have been previously studied by Valenti
et al. (2016) and Pessi et al. (2019). The $V$-band light curve was
characterized by Davis et al. (2019) using the parameters defined by Anderson
et al. (2014a). Here we combine the public data of SN 2013ai along with a
previously unpublished data set to further analyze SN 2013ai.

The new data are in agreement with previous results that positioned SN 2013ai
among typical fast declining SNe II with a decline rate per 100 days, $s_{2}$
(Anderson et al., 2014a), of $\sim 2.0$ (historically SNe IIL, see Barbon et
al., 1979); and an absolute $V$-band maximum of $-18.7\pm 0.06$ mag. The only
photometric difference SN 2013ai displays with respect to normal SNe II is
that it presents an atypically long rise time (e.g. Valenti et al., 2016).
From the Pessi et al. (2019) sample, the typical rise times of SNe II are
$8.3\pm 2.0$ days, $12.8\pm 2.4$ days, and $16.0\pm 3.6$ days in the $B$, $V$,
and $r$ bands, respectively. For SN 2013ai, the rise times are 13.0$\pm$5.3
days, 18.9$\pm$3.7 days, and 24.4$\pm$4.0 days, in the $B$, $V$, and $R$
bands, respectively. On average the rise times of SN 2013ai are 2.4$\sigma$
away from the mean values calculated in Pessi et al. (2019). Note that in
Pessi et al. (2019) the computed rise time average for the SN II sample is
longer than for other higher cadence samples (e.g. González-Gaitán et al.,
2015; Gall et al., 2015; Valenti et al., 2016; Rubin, & Gal-Yam, 2016). Rubin,
& Gal-Yam (2016) studied the $R$-band light curves of 44 SNe II and found an
average rise time of 7.8$\pm$2.8 days with the slowest rising object,
PTF12hsx, taking 16.2 days to reach maximum. SN 2013ai rises significantly
more slowly than any SN in the Rubin, & Gal-Yam (2016) sample. The rise time
of SN 2013ai is significantly longer than that of a typical SNe II.

Late-time photometric data may be used to estimate the 56Ni mass using the
procedure of Hamuy (2003) and the bolometric correction from Bersten & Hamuy
(2009). However, the scarce late-time data do not allow for a decay slope to
be measured, so only a lower limit of the 56Ni mass can be given as the extent
of the $\gamma$-ray trapping can only be estimated. For 100% trapping, we get
$0.14^{+0.06}_{-0.04}$ M⊙ with the error bars including the photometry error
but not the reddening and distance uncertainties. There are large
uncertainties associated with this lower limit as the light curve decay is
highly dependent on the amount of $\gamma$-ray trapping. For the case of SN
1993J (see Hoeflich et al., 1993), which is a good approximation for SN 2013ai
at late times (see Section 7), 79% of $\gamma$-rays had escaped at 350 days
past explosion. However, 56Co decays in two channels, electron capture and
positron capture. Approximately 4% of the decays are positron capture and will
remain trapped, giving a total trapping of $\sim 25$%. This suggests that the
56Ni mass lower limit from observations could be underestimated by up to a
factor of 4, translating to a 56Ni mass of $0.4-0.8$ M⊙. Similarly, assuming
that the light curve is powered by 56Co decay past 50 days from explosion,
i.e. constant slope, the magnitude difference of pure 56Co decay to the
observed light curve gives a similar result.

SN 2013ai may be compared with two other SNe II that were found in the
literature: ASASSN-14kg (Valenti et al., 2016) and SN 2017it (Afsariardchi et
al., 2019). ASASSN-14kg was chosen as it was found to have the most similar
light curve to SN 2013ai. SN 2017it was published as a high 56Ni mass SN II
with a long rise, so despite its slow decline post-maximum, bears comparison
to SN 2013ai. Photometry from Valenti et al. (2016) shows a $V$-band rise time
for ASASSN-14kg of $\sim$18 days while Afsariardchi et al. (2019) report a
$V$-band rise time of $\sim$20 days for SN 2017it. In order to recalculate the
rise times of these objects in a uniform fashion, the explosion epoch of the
comparison SNe is taken as the mid point between the last non-detection and
the first detection while considering the error to be half the difference
between said epochs. The light curves were then interpolated via a Gaussian
process method using the Python library
GPy333https://sheffieldml.github.io/GPy/. Finally, the maximum date was
obtained from the interpolated light curve and the rise times were calculated.
Results are presented in Table 4. It can be seen in Figure 4 that the behavior
of SN 2013ai around peak is similar to ASASSN-14kg. SN 2017it, despite the
long rise, exhibits a post-maximum decline similar to a normal SN II. For
further comparison to the SN IIb subclass, SN 1993J, is added as an example of
a typical SN IIb light curve. The rise time of SN 2013ai is similar to a SN
IIb, however, the post-maximum decline is much slower.

To calculate the bolometric light curve, the Milky Way and NGC 2207 dust
reddening corrected photometry was first converted into AB magnitudes using
the spectral energy distribution of Vega. Monochromatic fluxes for each
available date were numerically integrated in wavelength, obtaining the
pseudo-bolometric flux (Fpbol). For the $UV$ flux (FUV), a linear
extrapolation was used and integrated from the observed flux at the $B$ band
to zero flux at 2000 Å (see Bersten & Hamuy, 2009; Folatelli et al., 2014, for
further details). To estimate the IR flux (FIR) the spectral energy
distribution was fit by a grid of temperatures and angular sizes which define
a black body for each point of the grid. Using the resultant $\chi^{2}$ grid
from each black body, a probability distribution to determine the best
parameters for each epoch is calculated. Afterwards, the flux was integrated
from the effective wavelength of the $I$ filter to 100,000 Å, where the flux
is considered negligible.

The bolometric flux was calculated as $F_{bol}=F_{pbol}+F_{UV}+F_{IR}$. This
bolometric light curve was compared to a subsample of the bolometric light
curves presented by Faran et al. (2018). Their sample includes only objects
with high quality multiband data and rather good time coverage, which makes it
useful for our goal of comparing SN 2013ai to a large sample of bolometric
light curves computed in a uniform manner. Note that the bolometric light
curves of Faran et al. (2018) were computed differently to the SN 2013ai
bolometric light curves as they consider the effects in the bluer and redder
wavelengths, e.g. line blanketing. However, given the uncertainties involved
in calculating bolometric light curves, the comparisons presented would not
significantly change if the bolometrics were recalculated. The subsample was
selected such that only objects that show a clear maximum in the light curve,
meaning there are data points before maximum, are considered. From the 29
objects presented in Faran et al. (2018), only 8 meet this requirement,
although SN 2003hf is much more luminous than the others so it was excluded,
giving 7 comparison objects. The bolometric light curve of SN 1993J (Richmond
et al., 1994) is also presented for comparison. Figure 5 shows that SN 2013ai
is the fastest decliner, except for the SN IIb SN 1993J. Using the explosion
dates published by Faran et al. (2018) we obtain a mean bolometric rise time
of the subsample of 8.6$\pm$2.0 days while the bolometric rise time of SN
2013ai is 14.3$\pm$4.1 days.

Figure 4: $V$-band light curves (dots) and Gaussian interpolations (lines) of
SN 1993J, ASASSN-14kg, SN 2017it, and SN 2013ai normalized to peak magnitude.
Light curves are without host subtractions. SN 1993J is included in order to
compare with the longer rising and faster declining SN IIb class. Table 4:
Explosion epoch for comparison objects.

SN | Last Non-detection | First Detection | Explosion Epoch | Reference |  $V$-band Max Epoch |  $V$-band Rise Time
---|---|---|---|---|---|---
ASASSN-14kg | 56972.4 | 56973.5 | 56972.9$\pm$0.5 | Nicolas et al. (2014) | 56991.1$\pm$2.8 | 18.1$\pm$2.9
SN 2013ai | 56344.3 | 56349.7 | 56347.0$\pm$2.7 | Conseil et al. (2013) | 56365.9$\pm$2.6 | 18.9$\pm$3.7
SN 2017it | 57745.5 | 57746.9 | 57746.2$\pm$0.7 | Afsariardchi et al. (2019) | 57762.8$\pm$4.2 | 16.6$\pm$4.3

Note. — All dates are given in MJD.

Figure 5: Bolometric light curve of SN 2013ai compared to a sub sample of
Faran et al. (2018) objects, normalized by peak luminosity. The Faran et al.
(2018) sample consists of normal SNe II. The shift in luminosity, given in
$10^{42}$ erg s-1, for each object is specified between brackets. The
errorbars are taken from the bolometric corrections and are highly dependent
on the amount of data taken for each epoch. SN 2013ai exhibits the steepest
rise pre-maximum, among this slow rising sample, and quickest drop post-
maximum. The bolometric light curve of SN 1993J is taken from Richmond et al.
(1994) and is shown for comparison with the longer rising and faster declining
SN IIb class.

##  5 Spectral Properties

The optical and NIR spectra of SN 2013ai were analyzed quantitatively by
measuring expansion velocities and pEWs for every feature present. These
techniques have been implemented succesfully before to study large samples of
SNe II and their diversity (e.g. Gutiérrez et al., 2017; Davis et al., 2019;
de Jaeger et al., 2019).

###  5.1 Time Evolution

Figure 3 shows the optical spectra of SN 2013ai. In the optical, at all
epochs, we see narrow optical emission in H$\alpha$, H$\beta$, [O ii]
$\lambda$3727, [O iii] $\lambda$5007 and [S ii] $\lambda\lambda$6717, 6731 at
the redshift of NGC 2207. The earliest spectra, taken $11$ days before $V$
maximum, show only a broad H$\alpha$ P Cygni profile with narrow Na I D
$\lambda\lambda$5890 and 5896 likely from the interstellar medium (ISM).
H$\beta$ is not present until later times, first seen around $3.2$ days before
$V$ maximum. A montage of the optical spectra is presented in Figure 3.

Starting with the spectrum taken $3$ days after $V$ maximum, the H$\alpha$
absorption becomes split, likely due to Si ii $\lambda$6355 at these early
times (Gutiérrez et al., 2017). Fe-group lines are also present during this
epoch, primarily Fe ii $\lambda\lambda$5169, 5267, and 5363. We also see the
emergence of the Ca ii NIR triplet as a broad and blended P Cygni line around
8500 Å.

From $11-20$ days after maximum, SN 2013ai became even redder, as more flux is
lost to absorption by Cr, Sc, Ba and Fe in the blue. The usual Fe-group lines
seen in SNe II are present between 3500-5500 Å; however, these lines are
weaker than what are seen in a normal SN II (see Gutiérrez et al. 2017; de
Jaeger et al. 2019). H$\alpha$ has a strong absorption component in its P
Cygni profile, with a minimum at a velocity of 11,000 km s-1, while the second
absorption, which was tentatively associated with Si ii, is still present as a
“notch” in the feature. There is a lack of absorption from Sc ii and Ba ii on
the blue side of the H$\alpha$ absorption line.

By $30$ days after maximum, the notch in H$\alpha$ is no longer present in the
spectrum of SN 2013ai, suggesting that the notch was not due to high velocity
(HV) H i (see Gutiérrez et al. 2017 for more information on this feature). The
spectrum shows relatively little evolution over the following period, from
$30$ to $73$ days post explosion, the continuum continues to become redder,
while the most notable change in the lines is an increase in the strength of
the Na I D absorption.

The late time optical spectrum obtained $230$ days after $V$ maximum with
GTC+OSIRIS is shown in Figure 6. This spectrum was taken 250 days from the
estimated explosion epoch and is shown in comparison to the SN IIP SNe 1999em
and the SN IIb SN 1993J at similar times. The spectrum of SN 2013ai contains
very little flux from the SN. Nonetheless, several lines characteristic of
core-collapse SNe in their nebular phase are detected, namely broad H$\alpha$
emission, [Ca ii] $\lambda$7291, and possibly [O i] $\lambda$6300\. The
reddening corrected [Ca ii] to [O i] line ratio appears approximately similar
to that in SN 2004et (see Jerkstrand et al., 2012), suggesting that the core
mass of the star which exploded was probably quite similar and not
exceptionally massive. However, the weakness of these lines makes it difficult
to accurately measure a flux ratio and suggest that the SN is not sufficiently
nebular for an accurate progenitor to be assumed using the method of
Jerkstrand et al. (2012). The H$\alpha$ profile at this epoch is dominated by
emission and shows a profile with a wide base and narrow top with no
absorption. Together with the early X-ray observations, as noted in Section 2,
this suggests interaction with circumstellar material (CSM).

Figure 6: The late time nebular spectrum of SN 2013ai taken with GTC+OSIRIS on
2013 October 30 (black), compared to spectra of the Type IIP SN 1999em and the
Type IIb SN 1993J at a comparable epoch (from Elmhamdi et al. 2003 and
Matheson et al. 2000 respectively). The spectrum has contamination from the
host seen primarily around 5000 Å in emission. The features present in the
spectrum of SN 2013ai are identified, while the regions of strong telluric
absorption are indicated with a $\oplus$ symbol. The H$\alpha$ profile is two-
tiered and has no absorption at this phase, suggesting interaction with CSM.

The NIR spectrum of SN 2013ai is shown in Figure 7 and exhibits mostly
hydrogen and helium features, such as $P_{\delta}$ and $B_{\gamma}$ and the He
i/$P_{\gamma}$ blend. In the NIR, SN 2013ai does not exhibit any lack of
features like the absence Sc ii and Ba ii in the optical.

Figure 7: NIR spectra comparison of SN 2013ai with other SNe II around the
same epoch. Prominent H and He line absorptions are marked with dashed
vertical lines to emphasis the fast velocities of SN 2013ai. The phase from
explosion is listed for each spectrum along with the SN subtype. The gray
vertical bands mark the regions of strongest telluric absorption. SN 2011dh
has little data taken within the telluric bands and it is not plotted in these
regions. SN 2013ai shows no sign of being a weak SN II (Davis et al., 2019).
The spectra of SNe 2012aw and 2013hj are from Davis et al. (2019). The
spectrum of SN 2011dh is from Ergon et al. (2014).

###  5.2 Comparison to Other Core-Collapse SNe

Figure 8 shows optical spectra of SN 2013ai compared to other SNe at similar
phases. Included are examples of well-studied SNe IIP, IIL, and IIb. This
comparison highlights the uniqueness of SN 2013ai in the features seen, their
strengths, and expansion velocities. As previously noted, there is a lack of
features on the blue side of H$\alpha$ and the Na/He absorption around 5990 Å
is significantly shallower than that seen in a normal SN II/IIb.

Figure 7 shows the 14.5 day NIR spectrum of SN 2013ai compared to other SNe II
at similar epochs. The SN does not show any signs of being a NIR _weak_ SN II
(Davis et al., 2019); however, at such early times it is not always possible
to determine a NIR spectroscopic subclass. The He i $1.083\,\mu m$ line is
stronger than that of SN 2013hj at a similar phase. Both SNe show a boxy
$P_{\beta}$ emission profile. Overall, the NIR features of SN 2013ai are much
more normal than in the optical. However, similar to the optical, the features
in the NIR have much higher velocities than other SNe IIP/L at similar times.

Figure 8: Optical spectra comparison of SN 2013ai with other SNe II during the
photospheric phase. Prominent H line absorptions are marked with dashed
vertical lines to emphasise the fast velocities of SN 2013ai. The phase from
explosion is listed for each spectrum along with the SN subtype. The gray
vertical bands mark the regions of strongest telluric absorption. Data from
SNe 2012aw, 2013ej, and 1993J are from Dall’Ora et al. (2014), Childress et
al. (2016), and Barbon et al. (1995), respectively.

The top row of Figure 9 compares the pEW of all optical features present in
the spectra of SN 2013ai with the mean from Gutiérrez et al. (2017) and all
data from the de Jaeger et al. (2019) and Liu et al. (2016) samples. The metal
lines, from 4500-5500 Å, of SN 2013ai evolve like those of a typical SN II.
The 5990 Å He/Na blend is particularly interesting due to its weakness at
later times. The pEWs of all features seen in the optical lie amongst normal
SNe II values. Similarly, the top row of Figure 10 compares the pEW of all NIR
spectral features of SN 2013ai with the sample from Davis et al. (2019). The
NIR pEWs, like the optical, lie within the large comparative samples.

Figure 9: Comparison of SN 2013ai optical absorption pEWs and velocities over
time to the mean values from Gutiérrez et al. (2017) and all data from Liu et
al. (2016) and de Jaeger et al. (2019). The samples of Gutiérrez et al. (2017)
and de Jaeger et al. (2019) are made up of SNe II. Included is data from Liu
et al. (2016) in order to compare to SESNe. Data from Liu et al. (2016) was
published relative to maximum, thus for this comparison we determine the
explosion date for each SN in the Liu et al. (2016) sample from the last non-
detection method described in Section 2. SN 2013ai matches more closely to the
velocities of a SESN than a SN II. The velocities of all features of SN 2013ai
start much higher ($\sim 2\sigma$) and stay high while decreasing at a similar
rate to normal SNe II. The pEWs of SN 2013ai match within 1 sigma of the mean.
No SN in either SN II sample sustains velocities as high as SN 2013ai. Figure
10: SN 2013ai (large red dots) compared to the sample of normal SNe II from
Davis et al. (2019) (blue triangles) in NIR pEWs and velocities. SN 2013ai is
at significantly higher velocities than any SN in the Davis et al. (2019)
sample. However, much like the optical, SN 2013ai has normal pEWs when
compared with SNe II.

The bottom row of Figure 9 shows the absorption velocities of SN 2013ai
compared to the samples of Liu et al. (2016), Gutiérrez et al. (2017), and de
Jaeger et al. (2019). SN 2013ai exhibits high velocities in all features
observed, for a SN II. The 5990 Å He/Na blend is particularly interesting due
to its high velocities if assumed to be Na i $\lambda 5993$, giving velocities
over 13,000 km s-1 at early times. While the Fe ii velocities are closer to
normal SN II values, they are still noticeably higher than the comparative SN
II samples, with the velocities more similar to SESNe. Despite the high
velocities, the evolution is decreasing with time, as that of a normal SN II.
Figure 10 shows the NIR absorption velocities of SN 2013ai compared to that of
the data from Davis et al. (2019). Much like the optical, the velocities are
significantly higher than the sample, $\sim 2\sigma$, with the P$\beta$ and
P$\delta$ features around 12,000-13,000 km s-1 and He i $\lambda 1.083\,\mu m$
around 11,500 km s-1at 22 days past maximum. The offset of velocities from
typical SN II values are similar in the optical and NIR. The normal pEWs and
high velocities of SN 2013ai suggest that the features are not broad, but are
fast, like those of a SN IIb. However, the spectral features present are
typical of a SN II.

The optical absorption velocities at 50 days past explosion, the middle of the
plateau for a normal SN II, were also compared to the Gutiérrez et al. (2017)
and de Jaeger et al. (2019) samples in order to see if any other SNe II have
been found with velocities as high as SN 2013ai. No SNe with velocities as
high as SN 2013ai were found, except for SN 2007ld from the Gutiérrez et al.
(2017) sample, which has a 50 day H$\alpha$ velocity over 11,000 km s-1. SN
2007ld has a normal photometric and spectroscopic evolution; however, it shows
some contamination in the H$\alpha$ emission profile which could be due to He
i, a common sign of a SN IIb. Unfortunately, SN 2007ld has no spectra towards
the end of its plateau, when a SN IIb can be easily identified. SN 2007ld does
not exhibit a long rising light curve or a quick decline after maximum. Super-
luminous SNe (e.g. SN 2013fc, SN 2016gsd Kangas et al., 2016; Reynolds et al.,
2020) are not included for comparison as SN 2013ai is not super-luminous.
However, see SN 2016gsd (Reynolds et al., 2020) for a super-luminous SNe II
that exhibits high velocities similar to SN 2013ai.

The spectra of SNe with similar rise times to SN 2013ai (see Section 4) were
also examined. The classification spectrum of ASASSN-14kg is plotted with the
earliest spectrum of SN 2013ai in Figure 11. The spectra look similar at these
early times. There are no later spectra taken of ASASSN-14kg. ASASSN-14kg has
a well defined explosion date, $59672.9\pm 0.5$ MJD (Nicolas et al., 2014).
Given the similarity of the light curves and early spectra of ASASSN-14g and
SN 2013ai, it is likely that SN 2013ai is around the same phase from explosion
in the spectra seen in Figure 11. Afsariardchi et al. (2019) presented the
H$\alpha$ velocity of SN 2017it at 93 days past explosion, which is higher
than that of a normal SNe II. However, it is still $\sim$1000 km s-1 slower
than SN 2013ai. We were unable to find any SN II with expansion velocities
comparable to SN 2013ai during the photospheric phase. However, the similarity
of the early-time spectra and light curves of ASASSN-14kg and SN 2013ai
suggests that they could be alike.

Figure 11: Comparison of the early spectrum SN 2013ai to ASASSN-14kg. The
spectra are dereddened. Both SNe show high velocities and have similar spectra
at these early phases. The rest wavelength of each hydrogen and helium line
possibly present are labeled. Regions of strong telluric absorption are
outlined in gray. ASASSN14-kg is the only SN found to be similar to SN 2013ai
in both spectral features and velocities.

##  6 Progenitor

###  6.1 Pre-explosion Observations

Pre-explosion HST observations were available for SN 2013ai, consisting of
HST+Wide-Field and Planetary Camera 2 (WFPC2) images taken on 1996 May 25, see
Figure 12. The SN location lies on the WF2 chip, which has a pixel scale of
0.1″/pixel. Four exposures, consisting of two cr-split pairs, were taken in
each of the F336W, F439W, F555W, and F814W filters, with total exposure times
of 2000s, 2000s, 660s, and 720s, respectively. The pipeline reduced _c0f files
were downloaded from the Mikulski Archive for Space Telescopes
(MAST)444http://archive.stsci.edu/. The images were first masked with their
associated _c1f files, and the cr-split pairs were combined to reject cosmic
rays using the crmask task within IRAF. Finally, the dithered images in each
filter were aligned and coadded.

Figure 12: Pre- and post-explosion images of SN 2013ai from HST+WFPC2 and
VLT+NaCo. (a) VLT Ks image of SN 2013ai. (b) Section of HST WFPC2 F814W pre-
explosion image, with the same orientation and scale as in panel (a). The
dashed box is shown in more detail in panel (c). (c) Region indicated with the
dashed box in panel (b). The transformed SN pixel coordinates are indicated
with cross hairs, while the bad column discussed in the text is also
indicated.

Unfortunately, the SN position lies very close to the charge transfer trap
2-337 on the WF2 chip in all images (Whitmore & Wiggs, 1995), which gives rise
to a bad column artefact. While it is possible to attempt to reconstruct the
flux lost due to the trap, as dithered exposures were available, we instead
ensured that the bad column was masked in both cr-split pairs for each filter
before coadding. As the cr-split pairs in each filter were offset by $\sim$3
pixels in the x direction, the defect (when masked) does not contribute to the
final image when they are shifted and combined.

We also attempted to use the drizzle algorithm (Fruchter & Hook, 1997) as
implemented in astrodrizzle within the drizzlepac package to improve the
spatial resolution of the F814W image. Before drizzling, the bad column close
to the position of SN 2013ai was flagged in the data quality image. A series
of drizzled images were produced, to test the effect of varying the output
pixel scale and the size of the drop. However, in all cases a faint artefact
was still visible at the position of SN 2013ai in the final image. It is
likely that the artefact in the output image results from the interpolation
over the masked bad column. Thus the drizzled images were not considered any
further.

To identify the position of SN 2013ai in our pre-explosion images, we obtained
Ks filter imaging of SN 2013ai with the Nasmyth Adaptive Optics System and
Near-Infrared Imager and Spectrograph (NAOS-CONICA; NaCo) on the Very Large
Telescope UT4 over 2013 March 3-4. SN 2013ai itself was used as a guide star
for NAOS, while the S54 camera was employed on CONICA, yielding a pixel scale
of 0.0543″/ pixel, over a field of view of 56″$\times$56″. Daytime calibration
data consisting of flat fields and long and short exposure darks were reduced
with the NaCo pipeline (version 4.3.1), to give a master flat field and a map
of aberrant pixels on the detector. Using these, the individual science frames
were masked and flat-fielded. All images of SN 2013ai were dithered on-source,
facilitating the subtraction of the sky background using the IRAF xdimsum
package. After sky-subtraction, the individual frames were aligned and
combined to yield a single, deep image with a total exposure time of 5040s.

The NaCo post-explosion image was aligned to the pre-explosion WFPC2 F814W
image using a geometric transformation derived from the pixel coordinates of
sources common to both images. Two separate sets of sources were used for the
alignment: a “good” set of 21 sources which were clearly point-like, detected
with good S/N, and which appear to lie within NGC 2207, and a larger superset
of 31 sources which we term the “complete” set, where the signal to noise
(S/N) of sources were lower, and which also included foreground and slightly
extended objects. For both the “good” and “complete” sets, the pixel
coordinates of each source were measured in the WFPC2 and NaCo frames, and
three separate geometric transformations were then derived using the lists of
matched coordinates, one allowing for translation, rotation, and scaling in x
and y, and two which also included second and third order polynomial terms,
respectively.

The pixel coordinates of SN 2013ai were measured in the NaCo image using three
different algorithms (centroid, gauss and ofilter within IRAF), which had a
standard deviation of only 0.05 pixels, or 3 mas. The average of the three
algorithms was taken as the position of SN 2013ai in the NaCo image. This
position was then transformed to the pixel coordinates of the pre-explosion
image using each of the transformations derived using both the “good” and
“complete” sources. The standard deviation of the transformed positions was 16
mas, and we take this to be indicative of the uncertainty in SN position
depending on the geometry or sources used for the alignment. We add this in
quadrature with the uncertainty in the SN position in the NaCo observation (3
mas), and the average of the RMS error found when fitting each transformation
(58 mas), to obtain the total uncertainty of 60 mas on the location of SN
2013ai in the WFPC2 image.

###  6.2 Progenitor Age Estimate

The SN falls close to, but is not coincident, with a source in the WFPC2
image, which we designate “Source A”. The centre of Source A (see Fig. 12), as
measured using three centering algorithms within IRAF phot, lies 193 mas (1.93
pixels) from the transformed SN position. This offset is a factor $\sim$3
greater than the uncertainty in the transformed position of SN 2013ai (60 mas)
and so we discount the possibility that this is a single stellar progenitor of
SN 2013ai.

By eye, Source A appears to be somewhat extended. To test this, 14 isolated,
point-like sources were fit with Moffat profiles to determine their full-width
at half maximum (FWHM). The average FWHM of these sources was 1.6$\pm$0.2
pixels. Source A is significantly broader, with a FWHM of 2.5 pixels. On these
grounds, it appears that the source may be an unresolved cluster or complex
(2.5 WF pixels corresponds to a physical scale of 46 pc at the distance of NGC
2207).

While the position of SN 2013ai lies outside the FWHM of Source A, it still
appears to fall within the wings of the PSF. To quantify the degree to which
SN 2013ai lies within the position of Source A, the latter was fit with a
Moffat profile. Then, we integrated under this profile to determine the flux
within an aperture with a radius corresponding to the distance from Source A
to SN 2013ai. Assuming that SN 2013ai is associated with a cluster, it was
found that 97${}^{+2}_{-6}$ percent of the flux of Source A is in the position
of SN 2013ai. In the remainder of this section, we consider the implications
for the progenitor of SN 2013ai both if it was associated with Source A, and
if it was unrelated.

Photometry was performed on Source A using hstphot, (Dolphin, 2000a) a stand-
alone photometry package for use with WFPC2 data. hstphot includes corrections
for charge transfer efficiency (CTE) losses, aperture corrections, and
zeropoints appropriate to WFPC2 (Dolphin, 2000b). While Source A is somewhat
broader than most point sources in the field, it is still relatively well fit
by a PSF. We measure PSF-fitted magnitudes for Source A in the HST flight
system (Holtzman et al., 1995), with updated zeropoints as per Andrew
Dolphin’s webpages555http://americano.dolphinsim.com/wfpc2_calib/ of
F336W=22.68$\pm$0.12 mag, F439W=23.90$\pm$0.15 mag, F555W=23.40$\pm$0.12 mag,
F814W=22.60$\pm$0.13 mag. Transforming to the standard UBVRI system, these
correspond to U=22.68$\pm$0.12 mag, B=23.89$\pm$0.15 mag, V=23.38$\pm$0.12
mag, I=22.56$\pm$0.13 mag. As a test of the PSF-fitting results, aperture
photometry was also performed using a small (2 WF pixel) aperture. For all
four filters, the difference between PSF-fitting and aperture photometry was
$<$0.1 mag, i.e. less than the photometric error.

To estimate an age for Source A, the chorizos SED-fitting package was used
(Maíz-Apellániz, 2004). A grid of Starburst99 models was fit (Leitherer et
al., 1999) to the measured WFPC2 photometry of the source, constraining the
reddening-law parameter R5495 to be 3.1, and the metallicity to the solar
value, while allowing the cluster age and extinction to vary. The results of
the fitting procedure are shown in Figure 13. The best fitting model (shown in
the left panel) has an age of 7.9 Myr and a relatively low extinction of
E(4405-5495)=0.12 mag. Comparing to the STARS
models666https://people.ast.cam.ac.uk/ stars/ (Eggleton et al., 2011), such a
cluster age would imply a progenitor mass of $\sim$21 M⊙; however, we note
that there are also reasonable fits for 11.2 Myr, giving a lower progenitor
mass of $\sim$17 M⊙ and higher extinction. The low mass best fit of $\sim 17$
M⊙ is at the high end of SN II progenitor masses (Smartt et al., 2009;
Sukhbold & Adams, 2020).

Figure 13: chorizos fits to host cluster of SN 2013ai. (a) STARBURST99 model
fitted to the photometry of the probable host cluster of SN 2013ai. (b) Chi-
squared plane of the fit.

The extinction towards the cluster inferred by the fit is considerably lower
than that seen towards SN 2013ai itself. There is a tail of solutions in the
$\chi^{2}$ plane which accommodates a reddening of E(4405-5495)=0.7 mag, which
is consistent with that seen towards the SN. However, these solutions require
the cluster to be younger than $\sim$3 Myr, which would in turn lead to a
progenitor which is extremely massive, and probably inconsistent with the
maximum mass of a star that can maintain its H envelope to the point of core-
collapse.

Further analysis was done using the Bayesian fitting technique of Maund
(2018), which addresses cluster mass, distances, and filter transformations.
Both the WFPC2 photometry and WFPC2 photometry converted to Johnson-Cousins
photometry were included as seperate runs. Given the luminosity of the
cluster, the mass is constrained to lie in the range
$\log(M)=10^{4.5}-10^{5.5}M_{\odot}$. At such masses, individual, luminous
stars may have a disproportionate influence on the colour of the cluster that
might cause deviations from the expected colour-sequence predicted by
STARBURST99 (for much more massive clusters of $10^{6}M_{\odot}$).

The progenitor of SN 2013ai could be a single, isolated red supergiant as
found for other Type II SNe. The relatively bright cluster nearby makes the
identification of such a progenitor difficult, as the flux in the wings of the
cluster may mask that of a fainter progenitor close by. The most convincing
demonstration of such a progenitor would rely on image subtraction, where a
flux deficit in new HST images taken after SN 2013ai has faded would indicate
the absence of progenitor flux which was present in pre-explosion images. As
demonstrated by Maund et al. (2014) and Folatelli et al. (2015), difference
imaging using late-time data can substantially improve the precision and
sensitivity of limits placed on SN progenitors. While such a test will have to
wait for new observational data, it is still possible to estimate the
sensitivity of pre-explosion data to a single red supergiant progenitor. From
photometry of point sources close to the SN position, we estimate a $5\sigma$
limiting magnitude of F814W $\gtrsim$ 24.5 mag for the WFPC2 images. At the
distance of NGC 2207, this would imply an absolute magnitude for the
progenitor of F814W$>$-9 mag, which unfortunately only allows us to constrain
the luminosity of the progenitor to log L/L⊙$<$5.5. For single star models,
this luminosity corresponds to a progenitor zero age main sequence mass of
$<$24 M⊙ (Eldridge & Tout, 2004).

##  7 Modeling

###  7.1 Modeling Background

Determining the properties of CCSNe poses a challenge due to the wide range of
parameters, e.g. progenitor mass, mass loss pre-explosion, explosion
mechanism, mixing, and possible interaction, which affect the observational
features. However, using a combination of empirical measurements and modeling
we attempt to reconstruct these properties for SN 2013ai and motivate the use
of a SN 1993J inspired model.

The chemical and density structures of the outer layers of the progenitor are
revealed by the spectral evolution. In general, at early epochs, the spectral
features are formed at or above the electron scattering photosphere in the
H-rich layers. During this time, the photosphere can be traced with
measurements of weak lines that form near the photosphere, e.g. Fe ii. The
inner edge of the H-rich layers is determined by the point in time when the
Doppler shifts of the Balmer lines becomes constant, around 40 days past
explosion in SN 2013ai, whereas Fe ii still receeds. At the photosphere, the
ejecta density profile of a SN II can be approximated by a power law, much
like that of a stellar atmosphere, $\rho=r^{-n}$, with $n$ the density slope
and $r$ the radius at a point in the ejecta (Hoeflich, 1990). Before the
recombination phase of H, the differential Doppler shift between Balmer series
H-lines can be used to reconstruct the density structure by integration of the
density and slope (see Hoeflich, 1988, 1990, for applications to SNe II). The
result of applying this technique to SN 2013ai gives a density slope, n,
ranging from $\sim$12-25. A typical SN II has a density slope of $\sim$10 at
early times (Hoeflich, 1990), significantly flatter than that of SN 2013ai.
The steep density profile, H line profiles, and Doppler shifts are more
similar to SN 1993J than the other SNe compared to (see Figures 8 and 10) with
both SNe having photospheric velocities of $\sim$12,500 km s-1 at the time of
the transition between the H- and He-rich layers, suggesting a similar
specific energy in the H-rich layers.

Around a week after maximum, Fe ii is used to trace the photosphere. This is
around the same time that a sharp drop in the Fe ii $\lambda 5169$ velocity is
observed, as seen in Figure 9. The drop in velocity is likely caused by the
photosphere receding quickly through the He layers into the carbon/oxygen
(C/O) core. He i has a high ionization potential and requires high energy
nonthermal photons to be observed (Graham, 1988). We see little evidence of He
i in the optical which supports the notion that the jump in Fe ii velocity is
caused by the photosphere quickly passing through the He layer. In the NIR, He
i $\lambda 1.083\,\mu m$ is seen, however, this He feature is the basis for
many other He transitions. Thus, even an object with little He should show NIR
He i $\lambda 1.083\,\mu m$ given its high population.

The light curves are powered by the energy deposition due to the propagating
shock wave, the radioactive decay of
${}^{56}Ni\rightarrow$${}^{56}Co\rightarrow$${}^{56}Fe$, and the recombination
energy. The rise time is dominated by the diffusion time scales in the
optically thick inner layers, and the light curve tail is governed by
radioactive decay and, possibly, interaction with the CSM and ISM. The rise
time of SN 2013ai is typical of a SN IIb and in particular similar to that of
the prototypical SN IIb SN 1993J, which, together with the spectroscopic
similarities highlighted above, motivate us to use SN1993J as a starting point
to model SN 2013ai. SN 1993J was extensively modeled by Hoeflich et al. (1993)
and was found to have a layered He-C/O core of $\sim 10$ M⊙ with an outer
H-rich layer mass of $\sim$ 3 M⊙ originating from a progenitor with a main
sequence mass ($M_{MS}$) of $\sim$ 25 M⊙. Note that the final H, He, and C/O
core masses depend on the phase of stellar evolution during which mass-loss
occurs.

###  7.2 Modeling Results

For the progenitor evolution of SN 2013ai, we use the stellar evolution code
MESA (Paxton et al., 2011). To trigger the explosion, the explosion energy
($E_{exp}$) is put in the inner region as a thermal bomb which causes the
ejection of the envelope leaving behind a neutron star or a black hole. For
computational efficiency and to cover a sufficiently wide range of parameters,
we first used the code developed by Bersten et al. (2011) to model SN 2013ai.
To verify and further constrain these models, we then modeled SN 2013ai with
the non-LTE hydrodynamical-radiation code HYDRA (Hoeflich, 2003, 2009). A wide
range of $M_{MS}$, $E_{exp}$, and mixing, including pure C/O cores, were
evaluated. We will omit the “failed” attempts.

The comparison between a frequency independent model from the code of Bersten
et al. (2011) with the photometry is shown in Figure 14 using depth dependent
mean opacities based on SN 1993J and originating from a 20 M⊙ star. The
resulting models have 0.55 M⊙ of 56Ni. Such a high 56Ni mass is problematic
for the explosion of a massive star both from observations and theory (see
Thielemann et al. 2018 for a review). The bolometric light curve, in
principle, is a sensitive measure of the physical parameters (e.g. Suntzeff et
al., 1992; Bersten et al., 2011). Despite the advantage of the bolometric
light curve, three problem zones may be identified: 1) the reconstruction of
the bolometric light curve, 2) distance uncertainties, and 3) asymmetries.
Moreover, using the bolometric light curve reduces the information for finding
model parameters. Due to these uncertainties, we use monochromatic light
curves based on detailed non-LTE models.

In Figures 15 and 16, we show the results of HYDRA starting with the
progenitor of SN 1993J but modifying the explosion energy, the mass of the
H-rich layers, the explosion energy, and the 56Ni mass. The H-rich layer mass
was adjusted to 0.2 M⊙, and the 56Ni mass to 0.3 M⊙. These models are based on
the results from the previously mentioned models, hereafter referred to as “LC
models”. The results between best fit models of our simulations, presented as
(LC, HYDRA), give consistent results within the uncertainties:
$M_{MS}=(20,30)$ M⊙, $E_{exp}=(3.0,2.5)$ foe7771 foe = $10^{51}$ ergs, and
$M_{Ni}=(0.55,0.3)$ M⊙.

Given the model best fits, the effect of uncertainties on the $M_{Ni}$,
$E_{exp}$, C/O core mass, and distance modulus must be discussed. Linear
polarizations give evidence for a symmetry axis and bipolar explosions with
$P\approx 1\%$ indicating axis ratios; a measure of how non-spherical an
object is, of 1/2-1/4 (Wang et al., 1998; Maund et al., 2007a, b; Stevance et
al., 2016; Reilly et al., 2017). To estimate the uncertainty for the light
curves, we use SN 1998bw/GRB980425 as a proxy for the explosion of a massive
stripped envelope SN (Hoeflich et al., 1999). Detailed analysis of
polarization spectra resulted in an axis ratio of 0.7 for SN 1998bw seen from
an angle of $30^{o}$ (Hoeflich, 1995) but with significant uncertainties as
discussed in Stevance et al. (2020). The possible effect of asymmetry on the
$V$-band light curve of SN 2013ai is shown in Figure 17. Asymmetry may change
the shape of the light curve by varying the maximum brightness up to $\pm 1$
mag, placing SN 2013ai near superluminous SNe (see Figure 17), and can shift
the rise time by about 10 days.

Even for the same model, the light curve rises more slowly and shows a lower
maximum brightness that directly translates into uncertainties in $E_{exp}$,
and the C/O core mass. The error for the asymmetry and the shape may be
regarded as an upper limit because even for purely jet-driven explosions of
CCSNe, an extended outer envelope tends to become more spherical with time
(Khokhlov et al., 1999; Hoeflich et al., 2004; Couch et al., 2009). The colors
are found to be less sensitive as they are a measure of the physical
conditions at the photosphere, namely the flux density rather than the total
flux. In either case, the tail of the light curve is less effected by
polarization because the luminosity becomes isotropic within $\sim 0.2$ mag
1-2 months after the explosion, which translates directly into an error for
$M_{Ni}$. For the 56Ni mass, both 0.3 and 0.55 M⊙ fit the data; however, as
previously mentioned $0.3-0.55$ M⊙ of 56Ni is higher than expected for a
massive star explosion.

Though beyond the physics included in our simulations, note that the
theoretical $V$-band light curve at 250 days is fainter by $\sim$ 1 mag than
observed. This may indicate a significant contribution by interaction between
the SN-ejecta and the ISM or a pre-explosion stellar wind. This theory would
also be consistent with the multi-tiered H$\alpha$ emission profile seen in
the nebular spectrum of SN 2013ai, which indicates interaction.

##  8 Discussion

Given the similar early time light curve timing, expansion velocities, and
density structure to SESNe, we suggest that the core of SN 2013ai is closer in
physical properties to a SESNe than a normal SN II. This would give SN 2013ai
a dense $\sim$ 10 M⊙ C/O core and little hydrogen ($0.2$ M⊙ from models) in
its outer layers, consistent with the quick decline post-maximum. In addition,
the explosion energies of SNe 2013ai and 1993J are comparable, 2.5 foe and 2.0
foe, respectively. In this scenario, the progenitor of SN 2013ai would have
most of its hydrogen envelope stripped before explosion, much like a SN IIb.

This brings us to the differences between SN 2013ai and SESNe. The first
difference is seen in the shape of the early time, $\sim$2 weeks pre-maximum,
light curve. SN 1993J, for example, shows an initial maximum and subsequent
decline in the light curve lasting about one week (see Figure 4) that is
powered by the energy deposited by the shock in the very outer layers. This
structure of the SN 2013ai theoretical LC is very similar to that observed in
SN 1993J but this phase has not been observed in SN 2013ai. In the SN 2013ai
HYDRA models, the early peak is much less pronounced because the lower H-shell
mass and the longer diffusion times with limited mixing, as predicted by
Bersten et al. (2012). Secondly, the 56Ni mass is significantly larger in SN
2013ai than in SN 1993J, which could affect the lack of strong He i seen in
the optical. However, in SN 2013ai, the much stronger He i line in the NIR
$\lambda 1.083\,\mu m$ is present and shows the presence of a He layer. To
boost the optical He i lines in SN 1993J, models with 56Ni mixed into the
outer layers of the ejecta were needed. This is also consistent with the rapid
drop in velocity seen at about 1 week after maximum because the continuum
opacity is low. Finally, SN 2013ai shows a much slower post-maximum decline
rate over 30 days ($\sim$0.5 mag) compared to the rapid decline in SN1993J,
($\sim$2 mag). The difference can be attributed to strong 56Ni mixing in SN
1993J that results in a steeply increasing $\gamma$-ray escape, whereas SN
2013ai has almost full trapping. While the models based on Bersten et al.
(2011) show general agreement with the observations, the strong mixing needed
is not consistent with little He i seen in the optical.

From observations, SN 2013ai seems to be rather unusual but, overall, it fits
well within the picture of an energetic explosion of a massive star which lost
most (but not all) of its hydrogen envelope, which puts it at the edge of
becoming a SN Ib or SN Ic, physically. However, using the observational
classification scheme of SNe, SN 2013ai lies between a SN II and a SN IIb as
its spectra are that of a SN II and its light curve more similar to SESNe.
Explosions of massive stars may appear either as SNe II, IIb, Ib, or Ic
depending on the details of the mass loss and the amount of mixing. The open
question remains whether the mass loss in SN 2013ai is line driven or the
result of a binary evolution. However, given its similarities to a SN IIb we
cannot rule out that mass loss pre-explosion occurred in a binary system for
SN 2013ai. As such, the current classification scheme may mask diversity and
similarity as SN 2013ai has the spectra of a SN II but after analysis of
spectra and light curves SN 2013ai lies between SNe II and SNe IIb.

##  9 Conclusions

SN 2013ai is a rare SN that exhibits a long light curve rise, sustained high
expansion velocities, and a light curve decline similar to a SN IIL. Only one
SN II was found to have comparable light curves and spectra, ASASSN-14kg.
However, the lack of ASASSN-14kg data prevents a more detailed comparison
between the two SNe. Some similarities were seen in light curve shape and
expansion velocities when comparing SN 2013ai with SNe IIb. The data presented
provide a link between different classes of SNe. In the current classification
scheme, SN 2013ai lies between SNe II and SESNe with possible signs of
interaction seen in the late-time H$\alpha$ profile and early X-ray
observations. The mass loss during the stellar evolution may be a decisive
factor. However, similar data sets for a large number of SNe II are needed to
better describe details of the explosion physics and to search for the
diversity and address the question of the origin of this mass loss. We
demonstrated the importance of the combination of optical and NIR spectra with
light curves but, in lack of spectropolarimetry, we had to rely on similarity
arguments and were unable to constrain some errors present in the early light
curve data due to asymmetry.

Figure 14: Our preferred light curves and velocities of SN 2013ai using the
procedure and codes of Bersten et al. (2011). The observed photosphere
velocties are from the Fe ii $\lambda$5169 absorption feature. The bolometric
model shows good agreement with observations. The free parameters were thus
constrained to give an explosion energy of 3.0 foe, a 56Ni mass of 0.55 M⊙,
and a progenitor mass of 20 M⊙. Also shown is a lower 56Ni mass model to
demonstrate that the light curve shape is robust to changes in 56Ni mass. Note
that the early maximum in the model light curves are from shock breakout.
Figure 15: Spherical model calculations for the $B$ and $V$ light curves with
the same progenitor model used for SN 1993J, made using non-LTE code with
full-radiation transport (Hoeflich, 2003, 2009). Early $R$-band data is
included as a proxy for $V$. Free parameters were $E_{exp}=2.0$ foe, the mass
of the H-shell $M_{H}=0.2$ M⊙, $M_{Ni}=0.3$ M⊙, and Rayleigh-Tailor mixing of
the stellar core that gave $v_{RT}=2500$ km s-1after the explosion. Note that
the early peak in these models is not due to a UV flash, but arises from
energy stored in the H-rich shell at early times, similar to what was seen in
observations of SN 1993J. Figure 16: Photospheric radius as a function of time
for the non-LTE explosion model shown in Figures 15 and 17 using the Rossland-
averaged opacities in V. The observed velocties are from the Fe ii
$\lambda$5169 absorption feature. The rapid drop seen in the velocity marks
the transition from the H-rich to He-rich layers. Figure 17: Potential
influence of asymmetry on the $V$-band light curve of SN 2013ai if seen from
the pole, $30^{o}$, and the equator (top to bottom) and for both the
observations (dots) and model (lines) (see Fig. 15). Both the rise time and
magnitude are highly dependent on viewing angle at early times, however, the
light curve becomes more robust to asymmetry at later times. For the
asymmetry, we use the redistribution function of jet-driven explosion models
with a difference of a factor of two in the directional dependent explosion
which has been used for SN 1998bw, an extreme example (Hoeflich et al., 1999).

We thank the staff at the different observatories for performing the
observations. Some of the data presented in this paper were obtained from the
Mikulski Archive for Space Telescopes (MAST). STScI is operated by the
Association of Universities for Research in Astronomy, Inc., under NASA
contract NAS5-26555. Based on observations made with the 6.5 meter Magellan
Telescopes at Las Campanas Observatory, Chile. Based on observations made with
the Gran Telescopio Canarias (GTC), installed at the Spanish Observatorio del
Roque de los Muchachos of the Instituto de Astrofísica de Canarias, in the
island of La Palma. Based on observations collected at the European
Organisation for Astronomical Research in the Southern Hemisphere, Chile as
part of PESSTO, (the Public ESO Spectroscopic Survey for Transient Objects
Survey) ESO program ID 188.D-3003. Based on observations made with the the
Very Large Telescope (VLT) and Nasmyth Adaptive Optics System (NAOS) Near-
Infrared Imager and Spectrograph (CONICA) program ID 090.D-0329. The work of
the CSP-II has been generously supported by the National Science Foundation
under grants AST-1008343, AST-1613426, AST-1613455, and AST1613472. The CSP-II
was also supported in part by the Danish Agency for Science and Technology and
Innovation through a Sapere Aude Level 2 grant. MF is supported by a Royal
Society - Science Foundation Ireland University Reseach Fellowship. P.H.
acknowledges support by grants of the NSF AST-1008962 and Nasa’s ATP-1909476.
L.G. was funded by the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie grant agreement No. 839090. This
work has been partially supported by the Spanish grant PGC2018-095317-B-C21
within the European Funds for Regional Development (FEDER). T.W.C.
acknowledges the EU Funding under Marie Skłodowska-Curie grant agreement No
842471. M.S. is supported by generous grants from Villum FONDEN (13261, 28021)
and by a project grant (8021-00170B) awarded by the Independent Research Fund
Denmark.

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