SN 2021foa: Deriving a continuity between SN IIn and SN Ibn
Anjasha Gangopadhyay Naveen Dukiya Takashi J Moriya Masaomi Tanaka Keiichi Maeda D. Andrew Howell Mridweeka Singh Avinash Singh Jesper Sollerman Koji S Kawabata Sean J Brennan Craig Pellegrino Raya Dastidar Kuntal Misra Tatsuya Nakaoka Miho Kawabata Steve Schulze Poonam Chandra Kenta Taguchi Devendra K Sahu Curtis McCully K. Azalee Bostroem Estefania Padilla Gonzalez Megan Newsome Daichi Hiramatsu Yuki Takei Masayuki Yamanaka


firstpage–lastpage
Compression of high-power laser pulse leads to increase of electron acceleration efficiency
    V. Yu. Bychenkov
    September 4, 2024
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§ ABSTRACT 
We present the long-term photometric and spectroscopic monitoring campaign of a transitioning SN IIn/Ibn from -10.8 d to 150.7 d post V-band maximum. SN 2021foa shows prominent He i lines which are comparable in strength to the Hα line around peak luminosity, placing SN 2021foa between the SN IIn and SN Ibn populations. The spectral comparison with SNe IIn and SNe Ibn shows that it resembles the SN IIn population pre-maximum, becomes intermediate between SNe IIn/Ibn and at post-maximum matches with SN IIn 1996al. The photometric evolution shows a precursor at -50 d and a light curve shoulder around 17 d, which matches well with the light curve of the Type IIn SN 2016jbu and some other SNe with interactions. The peak luminosity and color evolution  of SN 2021foa are consistent with those of most SNe IIn and SNe Ibn in our comparison sample. SN 2021foa shows the unique case of a SN IIn where the P-Cygni features in Hα appear at later stages, arising either due to complex geometry of the CSM or an interaction of the ejecta with a CSM shell/disk (similar to SNe 2009ip and 2015bh). Temporal evolution of the Hα profile favours a disk-like CSM geometry (CSM having both H and He) with a narrow (500 – 1200 km s^-1) component, intermediate width (3000 – 8000 km s^-1) and broad component in absorption early on. Hydrodynamical lightcurve modelling can be well-reproduced by a two-component CSM structure with different densities (ρ ∝ r^-2 – ρ ∝ r^-5), mass-loss rates (10^-3 – 10^-1 M_⊙ yr^-1) assuming a wind velocity of 1000 km s^-1 and having a CSM mass of 0.18 M_⊙. The overall lightcurve and spectral 
evolution 
indicates that SN 2021foa most likely originated from a LBV star transitioning to a WR star with the mass-loss rate increasing in the period from 5 to 0.5 years before the explosion or it could be due to a binary interaction. 





spectroscopy, photometry, supernovae (SNe), supernova (SN), SN 2021foa








§ INTRODUCTION



Massive stars that eventually undergo core collapse when surrounded by some dense circumstellar material (CSM) are known as Type IIn/Ibn supernovae (SNe) <cit.>. This is signified in spectra by a bright, blue continuum and narrow emission lines at early times. SNe of Type IIn display H-emission lines with multi-component profiles showing narrow-width lines (NW), Intermediate-width (IW) lines and Broad width lines (BW). Narrow (∼ 100 - 500 km s^-1) components arise mostly in the photo-ionized, slow-moving CSM. Intermediate width emission lines (∼ 1000 km s^-1) arise from either electron scattering of photons in narrower lines or emission from gas shocked by supernova (SN) ejecta. Some events also show very broad emission or absorption features (∼ 10,000 km s^-1) arising from fast ejecta, typically associated with material ejected in the core-collapse explosion. An interesting extension of the Type IIn phenomenon was illustrated by SN 2006jc <cit.>, which exhibited narrow He i lines instead of NW/IW Hydrogen lines as spectral signatures of strong CSM interaction. Spectra of SN 2006jc had intermediate-width lines similar to those of SNe IIn (2000 – 3000 km s^-1), but seen mainly in He i emission lines – there was only a trace amount of Hydrogen in the spectra. It is therefore referred to as a ‘SN Ibn’ event, instead of a SN IIn. It has important implications for understanding the broader class of SNe IIn and Ibn with CSM interaction because it is also one of the few Type Ibn SN that was observed to have a non-terminal LBV-like outburst just 2 years prior to explosion <cit.>. Other than the traditional definition, the existence of transitional events that change type between Type IIn and Type Ibn over time (e.g ) suggests a continuum in the CSM properties of these events and consequently in the mass-loss history of their progenitor stars. We now also have a couple of new candidates of an interesting class of events named SNe Icn, which show narrow narrow emission lines of C and O, but are devoid of H and He <cit.>. <cit.> shows that the appearance of prominent narrow He emission lines in the spectra of SN 2023emq (Icn), around maximum light are typical of a SN Ibn. The family of interacting SNe thus occupy a unique space, but probably linked by a continuum of outer envelopes.

The eruptive mass-loss process expected in these transients has been associated with multiple mechanisms.

The energy deposited in the envelope by waves driven by advanced nuclear burning phases <cit.>, the pulsational pair-instability or late-time instabilities <cit.>, an inflation of the progenitors radius that triggers violent binary interactions like collisions or mergers before the core-collapse event <cit.>, or just the expansion of the envelope pre-collapse in massive stars <cit.>.  
In mass-loss caused by binary interactions, one expects highly asymmetric distributions of CSM (disk-like or bipolar), relevant to the asymmetric line profiles seen in interacting SNe along with high degrees of polarisation <cit.>. 
This brief period of enhanced mass loss likely influences the photometric evolution of the supernova (SN) (having single/double/multiple peaks), including duration and luminosity, along with the spectroscopic appearance of emission/absorption line profiles and their evolution (for example see ). 


The traditional LBV stars as progenitors of Type IIn SNe are generally bright, blue and varying <cit.>. <cit.> introduced the first class of these events SNe 2005la and 2011hw, which as per the interpretation has progenitor star exploded as core-collapse while transitioning from the LBV to WR star phase. Theoretical models show that the event rate of appropriate binary mergers may match the rate of SNe with immediate LBV progenitors; and that the progenitor birthrate is ∼ 1 % of the CCSNe rate <cit.>. Observationally, the LBV/SN IIn connection inferred from properties of the CSM is reinforced by the detection of luminous LBV-like progenitors of three SNe IIn <cit.>. The standard evolution models 
instead suggest that 
massive stars are supposed to undergo only a very brief (10^4 – 10^5 yr) transitional LBV phase, and then spend 0.5-–1 Myr in the core-He burning Wolf-Rayet (WR) phase before exploding as a stripped envelope SN Ib/Ic <cit.>. This discrepancy between observational and theoretical numbers most likely exists due to insufficient mass-loss rate estimates, not considering binary evolution scenario and also not taking into account the criticality of the LBV phase <cit.>. This accounts for the fact that stellar evolution models are missing essential aspects of the end stages of massive stars.

While SNe IIn explosions make up 8–9 percent of all core-collapse SNe in the Lick Observatory Supernova Search sample <cit.>, the Type Ibn events like SN 2006jc represent a substantially smaller fraction. The fraction of SN 2006jc like event in this case constituted only 1 percent of the core-collapse sample which agrees with an independent estimate of the fraction of SN Ibn events by <cit.>. <cit.> updated this fraction for the Zwicky Transient Factory and found that SNe IIn consitute 14.2 percent of H-rich CCSNe while SNe Ibn constitute 9.2 percent of H-poor CCSNe. Given their rare occurrence, additional examples are valuable to demonstrate the diversity of the subclass. Among this whole sample, there are very few members of this peculiar SN class like SNe 2005la and 2011hw which had prominent narrow H and He lines <cit.>.
This motivates us to study another rare case of transitioning Type IIn/Ibn SNe, which belongs to the same category as SNe 2005la and 2011hw. 

SN 2021foa were already investigated by  (hereafter R22).
Here we present further detailed photometric and spectroscopic observations of SN 2021foa, which exhibits both H and He emission features and shows similarities with both Type IIn SNe and Type Ibn SNe at distinct phases of its evolution.
SN 2021foa like SNe show similarities in photometric evolution with both Type IIn and Type Ibn SNe <cit.>, but their diverse spectroscopic behaviour needs to be explored further to understand the division. 

SN 2021foa (a.k.a. ASASSN-21dg, ATLAS21htp, PS21cae) was discovered by the All Sky Automated Survey for SuperNovae (ASAS-SN; ) on 15 March 2021 (MJD=59288.45) at a Sloan g apparent magnitude of 15.9, with the last non-detection 10 days earlier, at g of 17.9 mag <cit.>. The SN was discovered at a RA and Dec of α=13:17:12.29, δ=-17:15:24.19 (J2000) in a barred spiral galaxy IC 863 at a redshift of z=0.008386 <cit.>. The observational and data reduction details of this SN are presented Section <ref>. The spectroscopic classification was done on 09-04-2021 using Nordic Optical Telescope (NOT) <cit.>. The spectroscopic features and the details on the spectral luminosity estimates are provided in Section <ref>. We also show a comparison with other spectra of SNe IIn and SNe Ibn to highlight similarities and dissimilarities in Section <ref>. We discuss the photometric evolution, color, and absolute magnitude of SN 2021foa along with other members of the comparison sample in Section <ref>. The detailed lightcurve and spectral modelling is discussed in Section <ref>. Section <ref> gives an estimate of mass-loss rates in these SNe and relates it with progenitor activity. Section <ref> discusses the overall scenario of SN 2021foa and we summarise our results in Section <ref>.

This work presents an extended analysis on SN 2021foa after R22. In their analysis, R22 showed that SN 2021foa belongs to sub-class of SN IIn which are labelled as SN IId <cit.> and shows prominent narrow Hα early on with ejecta signatures later on. SN 2021foa, however, showed early prominent signatures of He i 5876 Å  than other SNe IIn like 2009ip, 2016jbu. R22 quoted that SN 2021foa may be part of a bridge connecting H-rich SN 2009ip-like and Type Ibn SN events, indicating the possible existence of a continuum in properties, mass-loss history and progenitor types between these two types of peculiar transients. In our paper, we did a more robust modelling of the lightcurve, spectra and derived the physical parameters associated with the explosion. R22 indicated that SNe IId are probably connected to those objects by having similar a progenitor with LBVs transitioning to WR phase, but with a different mass-loss history or observed with a different orientation. We indeed, notice that our estimated mass-loss rates changes at different phases in the evolution of the SN, and spectral modelling shows an asymmetric CSM structure giving rise to Hα and He i at different strengths. Thus, our results are in concordance with what has been predicted by R22 and also an more elaborate description of it.



§ OBSERVATIONS AND DATA REDUCTION




 §.§ Optical Observations

We observed SN 2021foa in UBgVriocRIJHK bands from day -34.3 to ∼150 d post V-band maximum (see section <ref>). The oc-band ATLAS data was reduced and calibrated using the techniques mentioned in <cit.>. The imaging observations were carried out using the 1.5m Kanata telescope (KT; ) of Hiroshima University; Japan, 3.8m Seimei Telescope <cit.> of Kyoto University at Okayama observatory, Japan. Several bias, dark, and twilight flat frames were obtained during the observing runs along with science frames. For the initial pre-processing, several steps, such as bias-subtraction, flat-fielding correction, and cosmic ray removal, were applied to raw images of the SN. We used the standard tasks available in the data reduction software IRAF[IRAF stands for Image Reduction and Analysis Facility distributed by the National Optical Astronomy Observatory, operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation.] for carrying out the pre-processing. Multiple frames were taken on some nights and co-added in respective bands after the geometric alignment of the images to increase the signal-to-noise ratio.  

Given the proximity of SN 2021foa to its host galaxy, host galaxy contamination was removed by performing image subtraction using IRAF. For the templates, we used a set of deep images obtained on 2022 when the SN went beyond the detection limit of the telescope. 
For the optical photometry of KT data, local comparison star magnitudes were calibrated using the photometric standard stars <cit.> observed on the same nights.
The zero point and the color terms were derived from these comparison stars to calibrate the instrumental magnitudes. We also observed SN 2021foa with the Las Cumbres Observatory (LCO) network of telescopes as part of the Global Supernova Project.
The pre-processing of LCO data was conducted using the BANZAI pipeline <cit.>. The photometry was performed using the [<https://github.com/LCOGT/lcogtsnpipe/>] pipeline <cit.>. The template subtraction was performed using PyZOGY library <cit.> implemented within the  pipeline. The UBVgri instrumental magnitudes were obtained from the difference images.
The gri apparent magnitudes of the local comparison stars were taken from the Sloan Digital Sky Survey (SDSS) catalog, and the UBV magnitudes of the local comparison stars were calibrated against standard Landolt fields observed on the same nights as the SN field. Then, instrumental magnitudes of the SN were converted to apparent magnitudes by using the zero point and color terms derived from these comparison stars.
Table <ref> reports the complete photometric lightcurve evolution of SN 2021foa taken from the LCO and the Japan Telescopes.

The near-infrared (NIR) data of SN 2021foa were obtained with the HONIR instrument of KT <cit.>. The sky-background subtraction was done using a template sky image obtained by dithering individual frames at different positions. We performed PSF photometry and calibrated the SN magnitudes using comparison stars in the 2MASS catalog <cit.>. The final NIR magnitudes in the SN field are shown in Table <ref>.


Low-resolution (R ∼ 400-700) optical spectroscopic observations were carried out using the FLOYDS spectrographs mounted on the LCO 2m telescopes. The 1D wavelength and flux calibrated spectra were extracted using the [<https://github.com/LCOGT/floyds_pipeline>] pipeline <cit.>. Spectroscopic observations were also carried out using the KOOLS-IFU <cit.> on the Seimei Telescope. Our spectral coverage spans from -10.8 d to +69.5 d. The spectra with KOOLS-IFU were taken through optical fibers and the VPH-blue grism. The data reduction was performed using the Hydra package in IRAF <cit.> and a reduction software developed for KOOLS-IFU data[<http://www.o.kwasan.kyoto-u.ac.jp/inst/p-kools>]. For each frame, we performed sky subtraction using a sky spectrum created by combining fibers to which the contributions from the object are negligible. Arc lamps of Hg, Ne, and Xe were used for wavelength calibration. Finally, the spectra were corrected for the heliocentric redshift of the host galaxy. The slit loss corrections were done by scaling the spectra with respect to the SN photometry. 
The log of spectroscopic observations is reported in Table <ref>.

Along with that, we also obtained high-resolution spectroscopic data with High Dispersion Spectrograph (HDS) mounted on Subaru Telescope on 2021 April 22 (UT). The echelle setup was chosen to cover the wavelength range of 5700–7100 Å with a spectral resolution of ∼50,000 in the Red Cross Disperser mode. We followed standard procedures to reduce the data. The wavelength calibration was performed using Th–Ar lamps. A heliocentric velocity correction was applied to each spectrum. The sky subtraction was performed using data at an off-target position in the target frames. The spectra were not flux calibrated by a standard star but were scaled to photometric fluxes at similar epochs to account for any flux losses. 



 §.§ Radio Observations
 
The observing campaign of SN 2021foa was carried out using the Giant Meterwave Radio Telescope (GMRT), Pune, India in Bands 4 and 5 (PI: Poonam Chandra). There was no detection of the source on observations dated 11 January 2022 and 31 March 2022. Our rms obtained in Band 5 (1.265 GHz) and Band 4 (0.745 GHz) are 33 and 215 μJy and the 3-sigma limits corresponding to the non-detections are 100 μJy and 645 μJy in the two bands. There was a nearby radio-bright galaxy with extended emission which was contaminating the SN location due to which our Band 4 rms are high. We also checked the Very-Large Array Telescope archive and did not find any detection of this source. The obtained radio luminosities at these phases for Band 5 and Band 4 are 1.455 × 10^26 erg sec^-1 and 9.385 × 10^26 erg sec^-1. Figure 18 of <cit.> shows the radio luminosity of a group of core-collapse SNe which includes SNe IIn. We see that the minimum radio luminosity driving SNe IIn are in between 10^27 - 10^29 erg sec^-1. We do expect a radio emission at a phase of 584 d (1st observation) if it were a SNe IIn. However, given the fast decaying light curve of SN 2021foa, it's expected that the radio power will decrease, and thus, we get only radio upper limits. 




 §.§ Estimation of explosion epoch
 
<cit.> from the ASASSN team report the discovery of SN 2021foa (RA = 13:17:12.290; DEC = -17:15:24.19) on 2021-03-15 10:48:00 
(MJD = 59288.45) at a discovery AB mag of 15.9 using the g filter. A non-detection of the source was reported on 2021-03-05 09:50:24 (MJD = 59278.41) at a limiting magnitude of 17.9 mag (g band). <cit.> report the classification of SN 2021foa from a spectrum taken with ALFOSC mounted on the Nordic Optical Telescope using gr4, which matches with an SN IIn. 

To estimate the explosion epoch, we fitted a parabola function on the rising part of the g-band light curve. The early light curve shape is well-reproduced by a parabola. We performed the fit using 20000 iterations of Markov Chain Monte-Carlo (MCMC) simulations. Using this method, we find the explosion epoch to be MJD = 59284.8 ± 0.2, 3.6 days prior to the first detection. This estimate is consistent with the non-detection of the source, and we adopt it as the explosion epoch.

However, since it is often difficult to estimate the explosion epoch for the comparison SNe in the literature, we adopt the V-band maximum (MJD 59301.8) as the reference epoch. This value is in agreement with the estimate from .



 §.§ Distance & extinction
 Adopting H_0 = 73 km s^-1 Mpc^-1, Ω_m = 0.27 and Ω_Λ = 0.73, we obtain a distance of 34.89 ± 2.44 Mpc (μ = 32.71 ± 0.15) corrected for Virgo, Shapley and GA (corresponding to a redshift z=0.00839 [<https://ned.ipac.caltech.edu/byname?objname=IC0863   hconst=73   omegam=0.27   omegav=0.73   wmap=1   corr_z=2>]) for SN 2021foa. This value is the same as that adopted by . The Milky Way extinction along the line of sight of SN 2021foa is A_V = 0.224 mag <cit.>. We see a conspicuous dip at 5892.5 Å  from Na1D in the spectra of SN 2021foa taken on 2021-03-20, 2021-03-23 and 2021-03-25. For estimating the extinction due to the host galaxy, we estimate equivalent widths of the Na1D line iteratively three times in the combined spectra of these three dates to increase the signal-to-noise ratio. Using the formulation by <cit.>, we estimate host galaxy A_V = 0.40 ± 0.19 mag. We multiply this reddening value by 0.86 to be consistent with the recalibration of Milky Way extinction by <cit.>.
Thus, we adopt a total extinction of  A_V = 0.57 ± 0.16 mag. We use these values of distance and extinction throughout the paper, which is also consistent with the values quoted by .

 



§ SPECTROSCOPIC EVOLUTION



We conducted the spectroscopic follow-up of SN 2021foa from -10.8 d to 58.6 d post V-band maximum. The complete spectral evolution of SN 2021foa, which includes our data and those published in , are shown in Figure <ref>. The early time spectral sequence shows prominent lines of Hα (6563 Å) along with Hβ (4861 Å) and Hγ (4340 Å). From -10.8 d to -3.2 d, the He (5876 Å) line also starts developing but is not very prominent. The Hβ profile initially shows narrow emission, but develops a narrow P-Cygni feature at around -5.8 d in our spectra. The spectra from  show an even earlier appearance of this narrow P-Cygni feature, which can be attributed to the higher resolution of their spectrum. 
The Hα also develops this narrow P-Cygni feature in the -3.2 d spectra. The early spectral sequence till -3.2 d does not show prominent lines of Fe ii (4924, 5018, and 5169 Å), which are characteristic of a typical SN ejecta. 

Post -3.2 d, the He i (5876 Å) line becomes prominent. The other He i (6678, 7065 Å) lines start developing at this phase. The narrow P-Cygni on top of Hα is clearly seen with the blue wing extending up to -1900 km s^-1.  
From 7.2 d to 17.2 d, the Hα and Hβ show very complex profiles. This is also the phase where we see a second shoulder appearing in the light curve of SN 2021foa (c.f.r Section <ref>). 

From 17.2 d, we see that the spectrum transforms significantly. This marks the onset of the phase where we see that the flux of He i 5876 Å  is comparable to Hα. The higher excitation H-lines like Hβ and Hγ no longer show narrow emission lines. However, narrow emission and the corresponding narrow P-Cygni feature are still significant in the Hα line. We also see a red wing developing in the Hα profile, most likely due to He i 6678 Å. The blue part of the spectrum in this phase is also mostly dominated by the He lines, along with the Fe group of elements <cit.>. 

From 26.8 d to 58.6 d, we see that both Hα and He i grow in strength. 
This also marks the phase where we see ejecta signatures in the spectral evolution. The [Ca ii] 7291, 7324 Å  lines emerge at 7300 Å, which could also be blended with He i 7281 Å. This phase also marks the appearance of the broad Ca II NIR triplet. At late times (>60 d), the intermediate to broad-width H-lines develop a slight blueshift in the observed profiles.

Overall, the spectral behaviour shows a striking similarity with an interacting SNe IIn early on, which later on is overtaken by a SN Ibn like behaviour with He lines. The very late spectra shows prominent ejecta signatures of Ca.



 §.§ Line luminosities and line ratios:


 
 
We observed well-developed He i features in the spectra, and the line-luminosity of the He i 5876 Å  line becomes comparable to the Hα line at about 17.2 d. To study the evolution of the He i 5876 Å line in comparison to the Hα line, we estimate the line luminosities of Hα and He i over the evolution of the SN. 

To compare with other well-studied SNe, we selected a group of SNe IIn having diversity in the luminosity distribution and some having precursor detections, similar to SN 2021foa. We also include a set of classical, bright SNe Ibn, along with some that have some residual H-envelope. The sample includes- SNe IIn: 1996al <cit.>, 2009ip <cit.>, 2010mc <cit.>, 2015bh <cit.>, 2016jbu <cit.>, 2018cnf <cit.> and SNe Ibn: 2005la <cit.>, 2006jc <cit.>, 2010al <cit.>, 2011hw <cit.>, 2019uo <cit.>, 2019wep <cit.>.

 

To study whether SN 2021foa belongs to the SNe IIn or the SNe Ibn regime, we compare the evolution of Hα and He i line luminosities with the sample.  The line luminosities are estimated by integrating the continuum-subtracted line regions of the de-reddened spectra. The top panel of the Figure <ref> shows the Hα luminosities of SNe IIn (blue) and SNe Ibn (pink) sample and SN 2021foa marked in black. The Hα luminosities of SNe IIn and SNe Ibn are well separated in luminosity scales. SN 2021foa shows similarity with SN 2011hw in the Hα space, which is an SN Ibn with a significant amount of residual Hydrogen <cit.>. On the contrary, in the He i luminosity scale (middle panel of Figure <ref>), SNe IIn and SNe Ibn do not show a clear distinction. The He i 5876 Å  luminosity of SN 2021foa matches with SN 2006jc <cit.> over the evolution. The lower panel of Figure <ref> shows the luminosity ratios of He i 5876 Å  to Hα. The distinction between these two classes of objects is the most prominent in this plot, however, we want to mention that there might be some residual Hα luminosity from the host galaxy in case of SNe Ibn. 

The line-luminosity ratio of SN 2021foa, from -10.8 d to about 17.2 d, rises from 0.3 to 0.7, placing it in the intermediate region between SNe IIn and SNe Ibn. From 40 d, SN 2021foa shows similarities with SN 1996al, which is a SN showing signs of ejecta signatures and interaction signatures simultaneously for 15 years <cit.>. This also marks the onset of the phase where we see ejecta signatures arising for both SN 1996al and our object SN 2021foa.
To summarize, SN 2021foa shows a complete demarcation and lies intermediate between the SN IIn and SN Ibn population from -20 d to 20 d, which is taken over by its match with SN 1996al at late phases mostly dominated by the appearing ejecta signatures. Also, there is a probability of Hα to He i reaching a straight line for SNe IIn but would be affected by the sample size. 

 


Figure <ref> aims to show how much the Hα and He i luminosity contributes to the total optical luminosity (V-band; L_v) at peak for a group of SNe IIn and SNe Ibn. To avoid possible biases in the distribution, we added more diverse SNe IIn and SNe Ibn sample for this comparison plot to highlight the position of SN 2021foa in the phase space. The additional SNe IIn used for this comparison plot are : SNe 1998S <cit.>, 2005ip <cit.>, 2006gy <cit.>, 2006tf <cit.>, 2007od <cit.>, 2009kn <cit.>, 2011ht <cit.>, PTF11oxu/2011jc <cit.>, ASASSN-14il <cit.>, 2015da <cit.> and ASASSN-15ua <cit.>. The additional SNe Ibn used for the comparison are : SNe OGLE-2012-SN-006 <cit.>, LSQ12btw <cit.>, LSQ13ccw <cit.>, ASASSN-15ed <cit.>, SNe 2014av <cit.>, 2015U <cit.> and 2015G <cit.>. We added SNe IIn/Ibn of different CSM configurations, long-lived, short-lived, with and without precursor to diversify this plot. Also, we chose only those SNe for which V-band observations around maximum are available with a good signal-to-noise ratio spectrum of min 10. We plot the ratio of Hα to the peak V-band optical luminosity against the ratio of He i to the peak V-band optical luminosity for SN 2021foa and the comparison sample. However, these SNe are in general have asymmetric CSM geometries <cit.> and the peak V-band line luminosities may be slightly affected by our viewing angle. We see that the SNe IIn and SNe Ibn in our sample are well separated in this phase space, with SN 2021foa (black star) lying in between the two sub-classes around peak luminosity. SN 2021foa shares remarkable similarities with SN 2011hw in this space as well. <cit.> have shown that SN 2011hw is also a SN Ibn with significant residual Hα. The distributions of SNe IIn and SNe Ibn also help in deciphering the fact that it is the Hα contributing to the optical luminosity that demarcates the two classes. He i distribution is blended for the SNe IIn and SNe Ibn population. However, we want to remark that a statistically decent sample would help in further verification of this. Nonetheless, SN 2021foa clearly lies at the junction between the two populations at this phase.  



 §.§ Spectral Comparison


In this section, we compare and classify SN 2021foa with a group of SNe IIn and SNe Ibn in the pre-maximum, about 20 d post maximum and around 40 d post-maximum to see the changing trend in the evolution of the SN.

Figure <ref> shows the pre-maximum spectral comparison of SN 2021foa with a group of SNe IIn and SNe Ibn. The pre-maximum spectral profile of SN 2021foa looks very similar to all the SNe IIn in our comparison sample. However, the H-lines are more prominent in the SNe IIn compared to SN 2021foa. In contrast, the SNe Ibn show little to no hydrogen in their spectra.
In SN 2011hw, an SN Ibn with significant residual hydrogen, both H and He lines are visible at this phase, while for SN 2021foa He i lines are not seen. 

Most SNe Ibn at this phase show flash features, which is absent in our observed profile. Overall, at this phase, SN 2021foa behaves more like a SN IIn. 

Figure <ref> shows the spectral comparison at 20 d after the V-maximum. This phase marks the remarkable transition of SN 2021foa, showing prominent lines of Hα and He i simultaneously. We also see narrow P-Cygni of Hα in SN 2021foa at this phase, similar to SNe 1996al and 2016jbu. The strength of Hα remains lower in strength for SN 2021foa than other SNe IIn; however, He i shows similar strength with most SNe Ibn in the sample. This separates SN 2021foa with the SNe IIn and SNe Ibn population, again justifying our case of SN 2021foa having strong Hα and He i emission simultaneously at mid epochs and at similar strengths.

 

We also show the late-time spectral comparison of SN 2021foa in Figure <ref>. 

The spectral evolution of SN 2021foa at this phase matches very well with SNe 2005la and 2011hw, which are SNe Ibn with residual Hydrogen. SNe Ibn at this phase shows very strong He i lines, unlike SN 2021foa. Similarly, the He i lines are more prominent than traditional long-lasting SNe IIn. The Hα and He i line profiles of SN 2021foa also show similarities with SN 1996al at this phase, in addition to the similarities in the line-luminosity ratio, noted earlier.

 

Overall, we conclude that the early time spectral evolution is similar to that of traditional SNe IIn followed by a phase where the spectral evolution is intermediate between those of SNe IIn and SNe Ibn. During late times, the SN shows spectral evolution similar to SNe IIn that show ejecta signatures at late phases or with SNe Ibn having a residual Hydrogen envelope.



§ PHOTOMETRIC EVOLUTION




We present the complete photometric evolution of SN 2021foa from -50 d to about 150 d post maximum, which extends the current published dataset. Our light curve spans about 30 d more than the time evolution presented in , after which the object went behind the sun. The rise and peak of the light curve are well sampled in the V-band, and the adopted value to V-band maximum (MJD 59301.8) is the same as . 
SN 2021foa showed prominent signatures of precursor from -50 d to about -23 d in ATLAS c and o-bands. 

The precursor for SN 2021foa lasted for a shorter duration than SNe 2009ip, 2016jbu and 2018cnf where the precursor event was observed about -90 d to -200 d before maximum. This precursor activity can be mainly attributed to the mass-loss eruptions from the progenitor star that occurred months-years before the explosion (For example, SN 2009ip; <cit.> or SN 2006jc; ). This has been interpreted as LBV stars undergoing eruptions, but, since our CSM is a combination of Hydrogen and Helium, this could be attributed to a LBV star transitioning to a WR phase <cit.>. For SN 2021foa, the non-detection of the precursor before 50 d could be attributed to ATLAS upper limits reaching 20.4 mag (3σ detection), so, there is a chance the precursor activity might have lasted longer than the timescale of detections.  


After the precursor, the lightcurve rose to peak in most of the optical bands in 6 d - 9 d which is consistent with SNe Ibn <cit.> and fast rising sample of SNe IIn <cit.>. From the peak to about 14 d, it did not have much evolution and changed by only 0.3 - 0.5 mag in the optical wavebands. At ∼ 14 d, we see a shoulder in the light curve of SN 2021foa. This also marks the phase where we see the He i features developing and appearance of a narrow P-Cygni on top of Hα (c.f.r Section <ref>). 
The bump or the shoulder in the lightcurve of SN 2021foa is weaker in the redder bands than in the bluer bands. After this phase, the lightcurve drops sharply at a decline rate of about 3 mag in 50 days. 

Post 75 d, the lightcurve shows a flattening lasting from 75 d to 150 d post maximum. The flattening in the light curve of SN 2021foa was also noticed by . The late time flattening in the redder bands have been attributed to the formation of dust <cit.>, but, we do not have any NIR observations to verify this scenario <cit.>. The late time flattening could also be due to interaction with a uniform density CSM as we also see in our lightcurve modelling section (c.f.r Section <ref>). A recent paper by <cit.> shows existence of dust in the spectral evolution of SN 2021foa, justifying the evidence of newly formed dust/old dust in the ejecta-CSM front of SN 2021foa.

The double peak or hump seen in the lightcurve of SN 2021foa can also be reproduced overall by the grid of models by <cit.> which are based on a CSM of mass ∼ 10 M_⊙ assuming a disk-like geometry of the CSM.



Figure <ref> shows the (B-V)_0 color evolution and the absolute magnitude lightcurve of SN 2021foa with other members of the SNe IIn and SNe Ibn subclass. The (B-V)_0 color curve of SN 2021foa increases by ∼ 0.5 mag in colors from -10 d to about 40 d post maximum. In the phase space of color evolution, we see two sectors of events. One set of SNe (1996al, 2006jc, 2016jbu, 2018cnf; Category 1) in our plot, increases from red to blue from -10 d to about maximum and then becomes flatter in the color curve evolution while for the latter, we see a constant rising of red to blue colors upto 30-40 d post maximum (SNe; Category 2) and then drops in the color evolution. Our SN 2021foa follows the latter trend in the evolution. The SNe of Category 1 are the SNe IIn which had a long term precursor activity. Also, for these events the flattening in color evolution is seen after the second peak in the SN light curve <cit.>. This is in contrary to SN 2021foa which shows a short term precursor and becomes red upto 50 d post maximum. Post 50 d, the colorcurve again becomes blue and continues upto 150d. This marks also the phase where we see a change in the mass-loss rates of the evolution (see subsection <ref>). 

We compare the absolute magnitude (r/R-band) lightcurve of SN 2021foa with a group of SNe IIn and SNe Ibn. For the cases where r-band in not available, we use Johnson Cousin R/r-band. The absolute magnitude lightcurve of SN 2021foa behaves similarly with other events having precursor activities. 
The precursor lightcurve (Event A) had an absolute magnitude ∼ -14 mag () similar to SNe 2009ip and 2016jbu. The second peak in the lightcurve (Event B) lies fairly intermediate (M_V = -17.8) among the SNe IIn and SNe Ibn (c.f.r Figure 1 of ). <cit.>, through their studies have found have found that most SNe IIn with precursor events typically rises to second peak around ∼ 17 days. The event B typically rises to a maximum with absolute magnitude ∼ -18 mag ± 0.5 <cit.> followed by a bumpy decline. Our SN 2021foa also reaches a peak mag at around ∼ 20 days, however, SN 2021foa has a low luminosity compared to the sample of <cit.>. Overall, the light curve of SN 2021foa is similar in luminosity to both SNe IIn and SNe Ibn population with L ∼ 10^42 - 10^43 erg sec^-1, but the lightcurve resembles more those of SNe IIn given the heterogeneity. The SNe Ibn in our comparison sample have instead
more short-lived and less bumpy lightcurves, in accordance with the sample presented by <cit.>. Also, interestingly, some events with precursor activity like SNe 2009ip and 2018cnf show a light curve shoulder similar to that of SN 2021foa, 20 d post V-band maximum. This is most likely associated with the change in the mass-loss rate happening years before explosion. This is also affected by the opacity effects influencing the lightcurve behaviour. 

 



§ SPECTRAL AND LIGHTCURVE MODELLING



Figure <ref> shows the zoomed-in spectral evolution of the line profiles of Hα, and He i 5876, 6678, 7065 Å. Hα shows a very complex profile throughout the evolution. Initially, Hα shows a narrow line on the top of a broad component. Around -3.2 d, we see a narrow P-Cygni component appearing on top of a broad Hα profile. Thereafter, the Hα profile is complex and highly asymmetric. Post 14.2 d, the red part of Hα starts developing, possibly due to contamination from He i 6678 Å. The He i 5876 Å  line also shows evolution, with the FWHM varying between 2500 – 4000 km s^-1. The narrow notch on top of the He i profile is mostly due to Na I D. The He i 5876 Å grows in strength and by 7.2 d its luminosity becomes comparable to that of Hα. The He i 7065 Å line develops later, at 14.2 d, and grows in strength thereafter. 

Interestingly, the FWHM of the He i 5876 Å  line is similar to that of the Hα line throughout the evolution, which again may indicate a mixed composition of the CSM. The implications of these line profiles with regards to the geometry of the SN is discussed in Sect. <ref>. 

 

 

To discern the origin of the narrow P-Cygni profile of Hα, we selected the broad emission and absorption components as a continuum and normalize the spectra with respect to it.  
Figure <ref> shows that in the continuum normalized spectra, from -10.8 d to 49.5 d, we still see a narrow emission of FWHM ∼ 500 km s^-1. 
No absorption features are seen in the spectra before -8.3 d. The narrow P-Cygni absorption starts to appear at -5.8 d with its blue edge reaching up to velocities of ∼ -1000 km s^-1. The narrow P-Cygni becomes really prominent at 7.2 d, with the blue edge extending up to -2000 km s^-1. The FWHM of the P-Cygni profile typically varied between 500 km s^-1 to 800 km s^-1.

To compare the origin of the appearance of narrow P-cygni absorption/emission profiles in interacting SNe, we compared the time evolution of the appearance of the P-Cygni profiles for our group of SNe IIn and SNe Ibn (see Figure <ref>). 

For most of the events in our comparison sample (SNe 1996al, 2005la, 2010al, 2016jbu, 2019uo, 2019wep), the narrow P-Cygni lines is present from the beginning of the observed evolution of the SN.
This arises due to the presence of pre-shock CSM present along the line of sight <cit.>. 
However, some objects (SNe 2006jc, 2010mc, 2010al, 2011hw) show only narrow emission profiles. In this case, we are not seeing the ionized pre-shock CSM along the line of sight. 
In addition to that, SN 2015bh shows a delayed onset of a P-Cygni profile similar to what is seen for SN 2021foa <cit.>, and SN 2009ip shows narrow emission early on, followed by narrow P-Cygni at intermediate times and then narrow emission lines again at a later stage of the evolution. <cit.> suggested that in SN 2009ip, narrow P-Cygni initially arose when the star was in the LBV phase. Just after the explosion, it showed narrow emission lines due to interaction with a dense CSM and thereafter from interacting with another shell moving at -2000 km s^-1. <cit.> also associated the origin of the narrow P-Cygni as due to outbursts a few decades prior to a “hyper eruption" or the final core-collapse. For the case of SN 2021foa, we also see that the velocity of the blue edge extends up to -2000 km s^-1 and we see narrow P-Cygni features developing, which indicate the presence of a shell/disk of CSM along the line of sight. A detailed interpretation of this associated with the geometry of the CSM is also described in Sect. <ref>.





 §.§ Hα decomposition


To decipher the origin of the complex Hα structure, we tried to deconvolve the line profiles of this SN. 



 


From the typical explosion circumstances of interacting SNe <cit.>, we expect a narrow component from the unshocked CSM, an intermediate width component either from the e-scattering of the narrow line photons or from the cold, dense shell (CDS), a broad width component from the uninterrupted ejecta which sometimes may show an associated absorption component as well. Therefore, we try to deconstruct Hα profile in terms of these components.
The Hα profile was fitted with combinations of different line profiles in order to reproduce the overall line profile seen in SN 2021foa at different stages of its evolution. We used i) A narrow Gaussian component that is slightly redshifted from the center ii) A Lorentzian/Gaussian intermediate width component that is redshifted from the center, iii) A broad Gaussian component in absorption. At early times, the overall Hα profile is better represented by a Lorentzian intermediate width component as the emission lines are dominated by electron scattering. On top of that, we have a narrow emission mostly arising from pre-shocked CSM. 
During the middle phases, the narrow emission is replaced by a narrow P-Cygni profile, and at late times (>30 d), a Gaussian intermediate width component better reproduces the overall line profile as it evolves into a more complex multi-component structure. The choice of the continuum is very critical for performing these fits. The continuum is selected to be far from the line region by at least 50 Å. The continuum is varied between 50 ± few Å  to check the consistency of the fits. The spectral evolution and the corresponding fits at representative epochs are shown in <ref>. The parameters of the components obtained from the fitting at all epochs are given in <ref>. The errors listed represent only fitting errors, and other uncertainties like resolution matching, subtraction of host-spectra, and imperfections in wavelength calibration have not been included. 

During -10.8 d to -3.2 d, the blue edge of the line profile extends up to -4500 km s^-1 with an estimated FWHM of 3532 km sec^-1. We want to remark that the fitting FWHM from -10.8 to -3.2 generates a limiting FWHM of 3500 km sec^-1 which is our prior in fitting. An increase in prior shifts the absorption center to the redder wavelength, which is unphysical for a P-Cygni profile. Thus, we want to remark that at pre-maximum times, there is a shallow component in absorption mostly due to the freely expanding SN ejecta. Diverse geometry ranging from a disk-like CSM in SN 2012ab <cit.> or a clumpy CSM like in SN 2005ip <cit.> can facilitate direct line of sight to the freely expanding ejecta. In addition to that, we have an intermediate width Lorentzian profile varying in FWHM between 3600 - 4500 km sec^-1 whose wings are mostly dominated by electron scattering and arising due to the ejecta interacting with dense CSM <cit.>. We also see a narrow emission varying in FWHM between 700 - 800 km sec^-1. This indicates that the photosphere lies in the unshocked CSM at this phase. The UV (and bolometric) light curves peak after this phase, which ionizes the unshocked CSM <cit.>. An emission component was fitted in the early spectrum of SN 2021foa at this phase as the P-Cygni was not resolved.

From 7.2 d to 40.2 d, we notice a significant increase in the Lorentzian emission FWHM of Hα, indicating an enhanced interaction between the SN ejecta and the CSM. The FWHM of the emission component typically varied between 5500 km sec^-1 - 7800 km sec^-1. The absorption component at this phase decreases with a reduction in the systematic blueshift. The 26.2 d spectrum marks the onset of the optically thin regime where we no longer see absorption in the Hα profile. Since we have prominent He i emission in the line profiles of SN 2021foa, post 17.2 d, we do not fit the right bump of the profile of Hα which arises possibly due to He i 6678 Å. The beginning of 7.2 d also marks the prominent strength of narrow P-Cygni features appearing in the spectral evolution of SN 2021foa. 

After day 40.2, we see only the intermediate width Lorentzian component in the line profiles of SN 2021foa with FWHM varying between 3900 km sec^-1 - 5200 km sec^-1. However, after 40.2 d, a blueshift can be noticed in the intermediate width component of Hα, which has now centered between ∼ -27 to -377 km s^-1. The late-time blueshift can be explained by dust formation in the post-shock CSM or ejecta (similar to SNe 2005ip, 2010jl, and 2015da; ). The narrow P-Cygni has also now reduced in FWHM between 500 km sec^-1 - 600 km sec^-1.

Figure <ref> shows the deconvolved high resolution Hα region spectrum of SN 2021foa. The narrow component in the spectra of SN 2021foa can be well reproduced by two Lorentzians in absorption and emission with FWHMs of 319 ± 20 km sec^-1 and 782 ± 15 km sec^-1. Along with that, we see an additional IW Hα Lorentzian component of FWHM 900 km sec^-1. We see a very narrow component of FWHM 33 km sec^-1 in the Hα profile which is most likely from the host galaxy contribution. We, thus, see that the narrow component seen in our high resolution spectrum is in concordance with our model fittings validating the narrow emission to narrow P-cygni transition in SN 2021foa. 

The detailed physical interpretation corresponding to the line geometries is explained in Section <ref>. 



 §.§ Radius and Temperature Evolution



 

As the SN ejecta is expanding, the shock breakout from the surface of the progenitor is 
followed by a rapid cooling due to the rapid expansion driven by the shock <cit.>. This would lead to a rapidly increasing photospheric radius and a decrease in the temperature of the SN ejecta within a couple of hours of the explosion. However, this will be affected for extended stars with larger radius. For the case of interacting SNe, this is not always the case as the ejecta is masked by CSM <cit.>. Figure <ref> shows the radius and temperature evolution of SN 2021foa. SN 2021foa first shows a decrease in temperature evolution from 14000 K to about 8000 K. We then see a slight rise in the temperature evolution of SN 2021foa from 7300 K to 8300 K between 17 d and 23 d post maximum, during the shoulder in the lightcurve, and then the temperature evolution becomes flatter. This rise in the temperature indicates an injection of energy in the cooling ejecta, perhaps due to interaction with additional CSM or interaction with regions of enhanced CSM density. This is in turn affected by opacity effects in the CSM ejecta interacting zone. 
 
The black body radius of SN 2021foa increases from 5500 R_⊙ to 15500 R_⊙ at ∼ 10 d past maximum light. From 7 d to ∼ 20 d past max, the radius stays at 16000 R_⊙. The radius evolution then shows a small shoulder similar to the temperature evolution, fluctuating between the values of 16000 R_⊙ to 15000 R_⊙ and then decreases to a value of 2800 R_⊙. The late time radius evolution is flat, as is the temperature evolution and the luminosity as well.

We thus see that the temperature increases at the point in time when we expect an interaction to occur, a few days after maximum light and when the Hα and He i lines start appearing at similar strength in the spectral evolution. A similar flattening behaviour is also noticed in the radius evolution of SN 2021foa at this phase. The radius and temperature evolution are well in synergy with the light-curve evolution.



 §.§ Hydrodynamical Modelling


We conducted light-curve modeling of SN 2021foa using the one-dimensional multi-frequency radiation hydrodynamics code  <cit.>. Because  treats radiation hydrodynamics in multi-frequencies,  can construct pseudo-bolometric light curves that can be directly compared with the observed ones. 

Figure <ref> presents our light-curve models and the initial density structure that can reproduce the overall light-curve properties of SN 2021foa assuming a spherically symmetric configuration. We approximate the SN ejecta by using the double power-law density structure (ρ_ejecta∝ r^-1 inside and ρ_ejecta∝ r^-7 outside, e.g., ). The SN ejecta are assumed to expand homologously. The SN ejecta start to interact with CSM at 10^14 cm. This radius is chosen arbitrarily but it is small enough not to affect the overall light-curve properties. The SN ejecta have an explosion energy of 3× 10^51 erg and a mass of 5 M_⊙. We want to remark here that there is a degeneracy in the ejecta mass and energy, and thus the particular set taken here (5 M_⊙) is an assumption.

We found that the CSM with two power-law density components can reproduce the overall light-curve properties of SN 2021foa. The wind velocity is assumed to be 1000 km s^-1. The inner CSM component has ρ_CSM∝ r^-2. The CSM with 10^-1 M_⊙ yr^-1 can account for the early-time luminosity around the light-curve peak. After around 30 days, the luminosity decline becomes faster than expected from interaction with a CSM with ρ_CSM∝ r^-2. We found that the fast luminosity decline can be reproduced when the CSM density structure follows ρ_CSM∝ r^-5 from 3× 10^15 cm. This CSM component has mass of 0.18 M_⊙.

The pseudo-bolometric light-curve of SN 2021foa flattens from around 80 days. In order to reproduce the luminosity flattening, an extended CSM component that is flatter than ρ_CSM∝ r^-5 is required. We found that if the extended CSM with ρ_CSM∝ r^-2 is attached above 1.5× 10^15 cm, we can reproduce the flat phase in the light curve when 10^-3 M_⊙ yr^-1 is assumed. Assuming a wind velocity of v_wind=1000 km s^-1, this kind of the CSM structure can be achieved if the mass-loss rate of the progenitor gradually increase from 10^-3 M_⊙ yr^-1 to 10^-1 M_⊙ yr^-1 from about 5 years to 1 year before the explosion, and the mass-loss rate is kept at 10^-1 M_⊙ yr^-1 in the final year before the explosion.

Also, we want to mention that the model is stable around the peak time, however, the latter part of the lightcurve is not well-established due to numerical limitations of . Hence, a two zone CSM for SN 2021foa well-reproduces the lightcurve until 80 d.

 



§ MASS-LOSS RATES


The mass-loss rates are governed by the ejecta-CSM interaction in SNe IIn/Ibn and can be estimated from spectral profiles as well <cit.>. Assuming that the luminosity of the ejecta-CSM interaction is fed by energy at the shock front, the progenitor mass-loss rate Ṁ can be calculated using the relation of <cit.>: 


    Ṁ=2L/ϵv_w/v_SN^3


where ϵ (<1) is the efficiency of conversion of the shock's kinetic energy into optical radiation (an uncertain quantity), v_w is the velocity of the pre-explosion stellar wind, v_SN is the velocity of the post-shock shell, and L is the bolometric luminosity of the SN. The above equation is derived assuming a spherical symmetry and assuming M_ej ≥ ≥ M_csm. We see changes in the spectral line profile for SN 2021foa around maximum light, so we estimate the mass-loss rates at both -5.8 d and at 7.2 d post maximum.

Since we see narrow emission lines of both Hα and He i at different stages of the evolution, we assume a typical unshocked wind velocity as observed for LBV winds of v_w∼100 km s^-1 and v_w∼1000 km s^-1 for the WR stars. The shock velocity is inferred from the intermediate width component. We want to remark, however, that the first phase might be affected by electron scattering, and there may be contamination by the ejecta signatures at these epochs. We take the shock velocities to be 3612 km sec^-1 and 7843 km sec^-1 at -5.8 d and 7.2 d. Using the bolometric luminosity at day -5.8 (L = 3.77 × 10^42 erg sec^-1), wind speeds of 100 (and 1000) km sec^-1 and assuming 50% conversion efficiency (ϵ=0.5), the estimated mass-loss rate is found to be  0.05 (and 0.5) M_⊙ yr^-1. The estimated mass-loss rate at 7.2 d when the narrow P-Cygni line profile becomes prominent in the spectra are estimated similarly for the wind speed of 100 (and 1000) km sec^-1 and assuming L=5.48 × 10^42 erg sec^-1 gives 0.007 (and 0.07) M_⊙ yr^-1. 

The estimated value of mass-loss rate are consistent with the typical LBV winds <cit.> and are consistent with most SNe IIn, which are of the order of 0.1 M_⊙ yr^-1 as observed in some giant eruptions of LBVs <cit.>. These values are higher than those of normal-luminosity SNe IIn like SN 2005ip (2-4×10^-4 M_⊙ yr^-1; ). It is also much larger than the typical values of RSG and yellow hypergiants (10^-4-10^-3 M_⊙ yr^-1; ), and quiescent winds of LBV (10^-5-10^-4 M_⊙ yr^-1, ). The obtained mass-loss rate in SN 2021foa indicates the probable progenitor to be an LBV star transitioning to a WR star that underwent an eruptive phase and transitioning mass-loss rates. The CSM may be the result of interaction with a binary companion as well, which would explain the asymmetry we see in the line profiles of SN 2021foa. 

In between the forward shock and the reverse shock, there is a contact discontinuity between the shocked CSM and shocked ejecta where material cools, mixes via Rayleigh-Taylor instabilities, and piles up. This is often
called the cold, dense shell (CDS), and we define the velocity at this front as v_CDS. If we look at the narrow component of the Hα evolution, it did not change significantly over the evolution of the SN however, V_CDS changed at this boundary of 7.2 d in the Hα evolution. Considering these two epochs of time at -5.8 d and 7.2 d, estimating the time periods preceding the explosion when the progenitor showed some activity is calculated by t = t_obs x (v_w/v_CDS). Assuming v_w from the narrow component of Hα at these two phases indicates that the progenitor had undergone a change in the eruptive activity at two stages corresponding to 0.5 – 1 year before exploding as an SN. This is much lower than the traditional SNe IIn and super luminous SNe IIn like 2006gy, 2010jl and 2017hcc <cit.> which showed eruptive activity 6-12 years before the explosion. On the contrary, this is quite similar to SN 2019uo <cit.>, resulting in a shorter-lived light curve as SNe Ibn. This has also been observed previously for the case of SN 2020oi which is a SN Ic showing radio interaction signatures and showed progenitor activity/ expelled shells 1 yr before the explosion <cit.>.



§ DISCUSSION:



We have presented the photometric and spectroscopic analysis of SN 2021foa, and hereafter, we discuss the major properties of the SN and summarise our results. 

In this paper, we present the unique case of SN 2021foa, where we see line luminosity ratios intermediate between SNe IIn and SNe Ibn. We also come to the conclusion that it is Hα line luminosity that better separates the two populations, while the two classes can not be segregated based on He i 5876 Å line luminosities. SN 2021foa exhibits the classic evolution of line profile shapes that is common in strongly interacting SNe IIn, which transition from symmetric Lorentzian profiles at early times (before and during peak), to irregular, broader, and asymmetric shapes at late times well after peak. The phenomena is understood as a shift from narrow CSM lines broadened by electron scattering to emission lines formed in the post-shock cold dense shell CDS <cit.>. In addition, for SN 2021foa, we also see asymmetric He i lines which broaden over time from 2000 km sec^-1 to 5000 km sec^-1 and show line luminosities comparable to Hα around the lightcurve peak. 

The spectral evolution also shows narrow and intermediate-width H lines at pre-maximum times. Around -3.8 d, we see narrow P-Cygni appearing in Hα. The narrow P-Cygni in Hα appears later than the narrow P-Cygni in Hβ.  Additionally, a recent study by <cit.> explores the relations between the line shapes and CSM structure by Monte Carlo radiative transfer codes. They find that a narrow line exhibits a P-Cygni profile only when an eruptive mass-loss event forms the CSM. The CSM structure from a steady mass loss will have a negative velocity gradient after the SN event due to radiative acceleration. Therefore, an Hα photon emitted at the deeper CSM layers, traveling outwards, will never be able to undergo another Hα transition. However, if there is an eruptive mass-loss that comes into play after a steady wind scenario, then a positive velocity gradient would give rise to narrow P-Cygni lines formed along the line of sight. We see from subsection <ref> and Section <ref>, the mass-loss rates typically varies from 10^-3  - 10^-1 M_⊙ yr^-1 during this phase. Also, the light curve modelling helps us to infer that the density-radius variation occurs from ρ ∝ r^-2 to ρ ∝ r^-5. This validates our scenario that probably the change in this mass-loss rates and possible eruption would have given rise to this P-Cygni arising along the line of sight. The changing mass-loss rates and the eruptive activity seen at 0.5 – 5 years before the explosion typically also govern the dual peaked light curve and appearance of P-Cygni seen in the light curve and spectral evolution of SN 2021foa. <cit.> checked the pre-cursor activities of SN 2021foa and have detected it only upto -50 days pre-explosion. This implies that even though there is an activity in the progenitor driving the peak luminosities at 0 and 17 d post maximum, it was not significant enough to be detected as a precursor in the light curve a year before the explosion. <cit.> have explained the origin of double-peak due to the interaction with a shell at a later point in time, which can also be a possible case of SN 2021foa. But, we find that a disk-like geometry better explains our overall line profiles, and we discuss below in detail the physical scenario (see subsection <ref>) governing the CSM and the explosion geometry.



 §.§ Physical scenario and asymmetry: 


Figure <ref> describes a physical scenario for SN 2021foa, although not unique <cit.>, which explains all the observable of SN 2021foa through various stages of its evolution. In this scenario, the ejecta of the SN interacts with a disk-like CSM structure. The viewing angle of the observer is located at an angle from the horizontal plane of the disk. 

 

Figure <ref>(a) describes a scenario where the photosphere lies in the pre-shock CSM surrounding the interaction region. The early profiles ≤ -4 d are characterised by a narrow line emission. These early profiles have broad wings that follow a symmetric Lorentzian shape, which is most likely due to incoherent electron scattering of narrow emission from pre-shock gas <cit.>. At these particular epochs, pre-SN mass-loss speeds are mostly determined from the width of the line profiles while the line wings are caused by thermal broadening and not reflecting the expansion velocities. So, as shown in Panel (a) of our cartoon diagram, at ≤ -4 d the continuum photosphere is in the CSM ahead of the shock, which will hide the emission from the SN ejecta and the CDS. However, we mentioned in Section <ref> that we do see ejecta signatures as well, in the form of broad absorption at FWHM ∼ 3500 km sec^-1. This indicates the geometry of the CSM is asymmetric and the viewing angle is not inclined to a plane but rather at an angle. This is also the phase where we see Lorentzian profiles in the spectral evolution along with absorption components, which further indicates an asymmetric CSM configuration. So, up to -3.2 d, a disk-like CSM configuration with the observer placed at a viewing angle which also justifies our case where we see the freely expanding ejecta, narrow emission lines from pre-shocked material and intermediate width components due to interaction of the SN ejecta with the disk-like CSM.

Figure <ref>(b) marks the onset of narrow P-Cygni features along with IW Lorentzian profiles as seen in the spectral profiles. As the photosphere recedes, the interaction zone of the photosphere and the disk comes along our line of sight, giving rise to a narrow P-Cygni profile. This phase also marks the onset of the phase where we see strong IW/BW interaction signatures with FWHM ∼ 3000 – 5000 km s^-1, which most likely arises from the combination of both post-shock gas in the CDS and freely expanding ejecta. The absorption component in Hα vanishes at ∼ 26 d. The transition occurs for a phase where the ejecta becomes optically thin and the essential properties of this transition are reproduced in the radiative transfer simulation of <cit.>. These simulations also indicate that the early time data is driven by electron scattering in the CSM and the late time data is driven by emission from post-shock gas at later times. An interesting aspect of the broad component that we see is given by the fact that even though we see it in the absorption profiles of spectral evolution, we cannot separate the contribution of CDS or ejecta in the emission profiles. Seeing strong emission lines for ejecta in SNe IIn are not common as continuum optical depths often hide emission from underlying ejecta or the IW component due to interaction with a dense CSM dominates the line profiles. Previous examples of SN 2010jl <cit.> and SN 2006tf <cit.> have only showed IW Hα emission and weak He i absorption at fast blueshifts. We also see the case of SN 2017hcc where we see freely expanding SN ejecta in emission which mostly arises due to viewing angle from polar regions <cit.>. Thus, similar explosion/CSM geometry have been proposed for SNe 2010jl, 2006tf, 2015da, and 2017hcc <cit.> but with different viewing angles. <cit.> have generated the lightcurves of SNe IIn using a grid of CSM masses, different viewing angles and assuming a disk-like geometry. We see that disk-like geometry fairly reproduces the double-peaked lightcurve (seen for SN 2021foa) with a CSM mass of 10 M_⊙ and a viewing angle between 30 – 60 degrees. 

The Hα profile of SN 2021foa shows a deficit in the flux in the red side of the wing and a systematic blueshift in the line centers from -27 km s^-1 to 377 km s^-1. This deficit is visible as an overall blueshift of the line after day 40 and this increases with time.

Blueshifts can arise due to various reasons in a SN IIn/Ibn. Radiative acceleration, asymmetric CSM or lop-sided ejecta, and obscuration of the receding material by the continuum photosphere can all give rise to 
asymmetric CSM. Blueshifted line profiles that become more prominent with time can also arise from the formation or re-growth of dust grains in either the post-shock zone of the CDS or in the unshocked SN ejecta. Both ejecta and CSM components have a differing relative contribution to the total dust at different times in the evolution of SNe IIn/Ibn. The optical to IR analysis of SN 2010jl at early and late times demonstrated dust formation in the post-shock CDS and continual grain growth in the SN ejecta <cit.>.

To investigate the case of SN 2021foa, we see that the blueshift increases with time. In the case of a blueshift caused by the radiative acceleration of the CSM, the blueshift should decrease as the luminosity drops, and we expect no significant wavelength dependence for this case. Additionally, in the case of a blueshift caused by the radiative acceleration scenario, the original narrow line photon source should be blueshifted as well which is not true for SN 2021foa  <cit.>. For obscuration by the continuum photosphere, the blueshift should be strongest in early times and decrease later on as continuum optical depth drops. For a lopsided CSM structure as well, blueshift should be present from early times which is not consistent with observations of SN 2021foa. So, we propose that the arising blueshift is most-likely arising due to newly formed dust grains in the ejecta or post-shock CSM. We do see a late-time flattening in the optical light curves of SN 2021foa. However, we should remark that other signatures of dust formation which involves increase in NIR flux is not seen in the case of SN 2021foa due to lack of observations and also because it went behind the sun. Nonetheless, dust formation is very common in SNe IIn/Ibn 2006tf <cit.>, 2006jc <cit.>, 2010jl <cit.> and should be the most-likely case happening for SN 2021foa as shown in the recent paper by <cit.>.

<cit.> investigated the case of SN 2014C, a SN Ib, which showed narrow emission lines of Hydrogen about 127 d post-explosion. They proposed a torus-like geometry which is also consistent with <cit.>. Our proposed disk-like scenario also supports a case similar to SN 2014C as well. While some asymmetries may be produced by single stars, they proposed a binary evolution <cit.> that led to a common envelope phase that was responsible for the formation of the Hydrogen-rich CSM. The likely distribution of matter in a system that has undergone binary evolution with the ejection of a common envelope is that the Hydrogen-rich envelope material substantially will be confined to the equatorial plane with a He-rich star as the progenitor. SN 2021foa could also be in such a scenario where the progenitor would be a star that stripped both H and He in the CSM and blew a fast wind that interacted with the main-sequence secondary that facilitated the past expulsion of the progenitor’s outer H, and He layers in a common envelope interaction. The secondary blows a slower Hydrogen-rich wind that would be entrained by the fast Hydrogen + Helium wind of the primary, thus forming a torous/disk-like structure in the equatorial plane.

An interesting point and open question to the behaviour of the SN is if the intermediate/narrow lines are from the CSM, what is going on behind the SNe IIn to SNe Ibn transition is indeed hard to explain. If this would simply reflect the CSM composition, it requires that the fraction of He in the mass-loss wind/ejecta is decreasing toward the SN, the opposite from the standard picture. At the same time, it might be difficult to explain this transition in terms of ionization, as the SN luminosity decreases. So, even though the claims of a single star exploding while transitioning from a LBV to WR phase is explained in past studies, the He envelope in the CSM could be due to a star in binary composition giving rise to narrow emission lines. A detailed theoretical interpretation is essential to describe the plausible scenario giving rise to these kind of SNe. 



§ SUMMARY:



    
  * SN 2021foa is a unique member in the transitional SN IIn to SN Ibn subclass with Hα to He i line ratios intermediate between those of SNe IIn and SNe Ibn around maximum light. 
    
  * Early time spectral comparison shows that SN 2021foa is similar to SNe in the Type IIn class while the mid and late-time spectral evolution indicates its similarity with SNe Ibn. At ∼ 7 – 14 d, we also see that the He i line luminosity is of comparable strength to the Hα luminosity, justifying the transitional nature of the SN. 
    
  * SN 2021foa shows a dramatic lightcurve evolution with a precursor activity (M_ v ∼ -14 mag) and reaching a secondary maximum at -17.8 mag, a shoulder at about ∼ 17 d and a late-time flattening. The SN lies in the middle of the luminosity distribution of SNe IIn and SNe Ibn. Even though the light curve shows a short-duration precursor, the colors are more similar to SNe without precursor activity.
    
  * The Hα evolution is complex having a NW (500 – 1000 km s^-1), IW component in emission (2000 – 4000 km s^-1) and a BW component in absorption at ∼ 3500 km s^-1. We see a narrow P-Cygni profile in the Hα line arising after the line is seen in emission, which could be due to either precursor activity, viewing angle and geometrical effects of the CSM, or interaction with another shell of CSM. 
    
  * We propose that the shoulder in the lightcurve arises due to the geometry of the CSM and the late-time flattening is most-likely arising due to either formation of new dust or pre-existing dust as seen from the systematic blueshift in the Hα profile at late phases which is confirmed by the presence of thermal dust by <cit.>. 
    
  * Hydrodynamical lightcurve modelling using  indicates that the lightcurve until 80 d can be reproduced by a two-component CSM with ρ_CSM∝ r^-2 – ρ_CSM∝ r^-5 starting from 3× 10^15 cm, with a CSM mass of 0.18 M_⊙ and mass-loss rate of 10^-1 M_⊙. If the extended CSM with ρ_CSM∝ r^-2 is attached above 1.5× 10^15 cm, then we can also reproduce the late time flattening of the lightcurve.   
    
  * Combining spectral and lightcurve modelling, the mass-loss rates would have increased from 10^-3 M_⊙ yr^-1 to 10^-1 M_⊙ yr^-1 from 5 years to 1 year before the explosion, and also varied between 0.05 – 0.5 M_⊙ yr^-1 with mass expelled at both 0.5 year to 1 year before the explosion assuming a wind velocity of 1000 km sec^-1. This changing mass-loss rate is most probably an indicator of the precursor activity and also explains the shoulder appearing in the light curve of SN 2021foa. 
    
  * We see that a disk-like geometry like SN 2009ip best reproduces our observed profiles but the composition of CSM is most likely mixed composition with both Hα and He i.
    
  * The composition of the CSM, the line ratios, spectral and temporal evolution, mass-loss rates all points towards a scenario where  SN 2021foa most-likely arose from the explosion of an LBV star which was transitioning to its WR phase. However, we cannot completely rule out the possibility of a binary scenario as proposed for the case of SN 2014C <cit.>.










































§ ACKNOWLEDGEMENTS

This work makes used of data from the Las Cumbres Observatory global telescope network.  The LCO group is supported by NSF grants AST-1911151 and AST-1911225. C.P. acknowledges support from ADAP program grant No. 80NSSC24K0180 and from NSF grant AST-2206657.





§ DATA AVAILABILITY


 








mnras
 



















§ PHOTOMETRY





          








