Observations and Spectral Modelling of the Narrow-Lined Type Ic SN 2017ein
MMNRAS , 1–15 (2021) Preprint 28 January 2021 Compiled using MNRAS L A TEX style file v3.0
Observations and Spectral Modelling of the Narrow–Lined TypeIc SN 2017ein
J. J. Teffs (cid:63) , S. J. Prentice , P. A. Mazzali , C. Ashall Astrophysics Research Institute, Liverpool John Moores University, IC2, Liverpool Science Park, 146 Brownlow Hill,Liverpool L3 5RF, UK School of Physics, Trinity College Dublin, The University of Dublin, Dublin 2, Ireland Institute for Astronomy, University of Hawai’i at Manoa, 2680 Woodlawn Dr.Hawai’i, HI 96822, USA
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
SN 2017ein is a narrow–lined Type Ic SN that was found to share a location witha point–like source in the face on spiral galaxy NGC 3938 in pre–supernova images,making SN 2017ein the first credible detection of a Type Ic progenitor. Results inthe literature suggest this point–like source is likely a massive progenitor of 60–80M (cid:12) , depending on if the source is a binary, a single star, or a compact cluster. Usingnew photometric and spectral data collected for 200 days, including several nebularspectra, we generate a consistent model covering the photospheric and nebular phaseusing a Monte Carlo radiation transport code. Photospheric phase modelling finds anejected mass 1.2–2.0 M (cid:12) with an E k of ∼ (0 . ± . × erg, with approximately 1M (cid:12) of material below 5000 km s − found from the nebular spectra. Both photosphericand nebular phase modelling suggests a Ni mass of 0.08–0.1 M (cid:12) . Modelling the [O i ]emission feature in the nebular spectra suggests the innermost ejecta is asymmetric.The modelling results favour a low mass progenitor of to 16–20 M (cid:12) which is in dis-agreement with the pre–supernova derived high mass progenitor. This contradictionis likely due to the pre–supernova source not representing the actual progenitor. Key words: supernovae: general–radiative transfer–supernovae: individual: SN2017ein
Type Ic SNe are a sub-class of core collapse supernovae inwhich the progenitor star has lost all of its H envelope andall or almost all of its He envelope prior to collapse. Theprocesses needed to strip this material is thought to be pe-riods of significant mass loss driven by winds (e.g. Nomotoet al. (1995); Langer (2012)) or through some binary inter-action mechanism. For high mass single star evolution, theLBV phase may be responsible for the significant mass lossthat could produce H/He-stripped SNe, but this may not beable to reproduce low mass events such as SN1994I (Nomotoet al. 1994; Sauer et al. 2006). However, single star evolu-tionary models are often unable to effectively strip all the Hrequired to produce Type Ib SNe and all the H/He requiredto produce the Type Ic SNe. Mass loss during a common en-velope phase or Roche lobe mass transfer for stars evolvingin a binary can explain stripping but can leave thin shellsof He of low mass above the carbon and oxygen rich (CO)core (Nomoto et al. 1995; Yoon et al. 2010). This may ex- (cid:63)
E-mail:j.j.teff[email protected] plain the sometimes observed weak He i lines in Type Ic SNe(Elmhamdi et al. 2006; Prentice et al. 2018).Several Type II SNe progenitors have been likely iden-tified, summarised in Smartt (2009), and these observationshave given some constraints on the possible progenitor massdistribution for Type II SNe, but no Type Ib/c progenitorshave been definitively observed yet. The Type II identifi-cations have suggested an upper limit for the observed redsupergiants (RSG) to be near ∼
17 M (cid:12) , while the theoreti-cal upper limit was expected to be closer to 20-25 M (cid:12) . Thisdifference between the observed and theoretical upper limitis called the “RSG problem” (Smartt et al. 2009). This gapmay be related to a poor understanding of late time stellarevolution and mass loss rates but is still an open question(Davies & Beasor 2018, 2020). For Type Ib/c SNe, the ejectamass distribution is more varied compared to non-strippedSNe as shown in Prentice et al. (2019) and estimating theprogenitor mass of these SNe from ejecta masses also resultsin a wide range of possible progenitor masses. In addition,the binary and single star channels for Type Ib/c SNe maycontribute to the total number of Type Ib/c SNe at different M ZAMS .SN 2017ein was first detected by Ron Arbour on 2017 © a r X i v : . [ a s t r o - ph . H E ] J a n J. J. Teffs
May 25.97 (Arbour 2017), in the face on spiral galaxy NGC3938. The object was classified soon after detection as anearly Type Ic SN (Xiang et al. 2017). After the detection,Van Dyk et al. (2018); Kilpatrick et al. (2018); Xiang et al.(2019) used archival Hubble images and detected a point-like source at the same location of SN 2017ein, which wouldrepresent the first progenitor detection for a Type Ic SN. Allthree groups used a combination of methods to derive an es-timated progenitor mass based on the observations of thispoint source. One method used is to calculate the colour, de-rived from observations using the two Hubble filters F555Wand F814W, and compare these values to a set of single andbinary star evolutionary tracks. Van Dyk et al. (2018) useda set of evolved rotating massive stars from MIST (Choiet al. 2016) and a set of binary star evolution models fromBPASS V2.1 (Eldridge et al. 2017) and estimated a singlestar M ZAMS of ∼ (cid:12) if the star evolved alone and a M ZAMS of ∼ (cid:12) if the star evolved in a binary, de-pending on the metallicity of the stars. Xiang et al. (2019)used a set of evolved rotating massive stars from Georgyet al. (2012) and estimate a M ZAMS of ∼
60 M (cid:12) . Assumingthe point-like source was instead a compact blue cluster, allthree groups estimate the M ZAMS to within the same massrange of the previous estimates using single or binary starconclusions. Using the nearby environment to constrain theproperties of the star, under the assumption of a single phaseof star formation, they again find a similar progenitor mass.The semi-analytic Arnett fits (Arnett 1982) for Nipowered SNe used in Van Dyk et al. (2018) give an esti-mated M ej of 1-2 M (cid:12) while a similar model in Xiang et al.(2019) finds a M ej of 0.9 ± (cid:12) . Both recognise that theestimated progenitor mass is far more massive than whatthe M ej estimates would suggest. Maund & Ramirez-Ruiz(2016) estimated a M ZAMS for the progenitor of SN 2007gr,using similar methods as above, to be ∼
40 M (cid:12) . This is incontrast to the progenitor mass inferred from the low massejecta modelled from the nebular spectra by Mazzali et al.(2010) of approximately ∼ (cid:12) , which would be analogousto a ∼
15 M (cid:12) progenitor.In this work, we first present and discuss observationsof SN 2017ein and the data reduction methods in Section2, the resulting photometric light curves in Section 3, andthe observed spectra in Section 4. Using this data, we modelboth the photometric and nebular phase of the spectral evo-lution and generate a bolometric light curve in Sections 5.In Section 6, we discuss the synthetic model and its resultswith respect to stellar evolution and possible progenitor pro-prieties.
Observations of SN 2017ein began on 2017 May 28.91 (MJD57901.91) with IO:O on the Liverpool Telescope (LT) (Steeleet al. 2004), based at the Roque de los Muchachos Observa-tory, La Palma, Spain. The first LT spectroscopic observa-tion was made with the SPectrograph for the Rapid Acqui-sition of Transients (SPRAT; Piascik et al. 2014) on 2017May 29.04 (MJD 57902.04). Photometry was performed onsources in the exposures using a custom python pipeline,which called pyraf to run standard iraf routines. The in-strumental magnitudes were then calibrated to Sloan Dig-
Table 1.
Several relevant observational properties of SN 2017ein α δ (J2000) +44:07:26.20Host NGC 3938 µ E ( B − V ) MW E ( B − V ) host †† Van Dyk et al. (2014); Xiang et al. (2019) ital Sky Survey (SDSS; Ahn et al. 2012) standard stars inthe field. SPRAT spectra were automatically reduced andthe wavelength and flux calibration was done via the LTpipeline (Barnsley et al. 2012) and a custom python script.The spectra were then flux calibrated to the photometry.
The distance to the host galaxy, NGC 3938 is highly un-certain, and this has been discussed at length in both VanDyk et al. (2018) and Xiang et al. (2019). The latter adopts µ = 31 . ± . , giving µ = 31 . E ( B − V ) MW = 0 . E ( B − V ) host from the hostNa i D lines in our spectra gives a large range of values from0.1 to 0.5 mag (Poznanski et al. 2012), but these spectra arelow resolution, thus we defer to the value of E ( B − V ) host =0 . Figure 1 shows the ugriz light curves, given in Table 2, ob-tained with the LT over ∼
240 days. SN 2017ein was discov-ered early, as evidenced by the rapid rise in the light curves.Only the rise of u -band is missed. As is typical for SE–SNe,the light curves peak progressively later in the redder bands.The peak of the u -band is 3–5 days before g -band, which islonger than the ∼ z -band evolu-tion, which shows a dramatic decay in luminosity away fromthe linear decline normally seen in these types of events.Further investigation reveals that this is also seen to a lesserextent in r - and i -bands. The drop-off in SN 2017ein is pro-nounced when shown against the evolution of SN 2007gr,which is demonstrated in Fig. 2 for the r - and R -band lightcurves of SN 2017ein, the latter from (Xiang et al. 2019) andthe R -band of SN 2007gr (Hunter et al. 2009). It can be seethat for the first ∼
100 days the three light curves trackeach other but by the time the observations of SN 2017ein NED MNRAS , 1–15 (2021)
N2017ein Rest-frame time since first detection [d] A pp a r e n t m a gn it ud e u +1.5 mag g +0.0 mag r +1 mag i +1.5 mag z +2.5 mag Figure 1.
The LT multi-colour light curves of SN 2017ein. Dashed grey lines represent epochs of LT:SPRAT spectroscopy
Table 2.
A sample of the Liverpool Telescope photometry. The entire table is available online in machine readable format via WISeREP.MJD u g r i z [mag] [mag] [mag] [mag] [mag]57901.91 − . ± .
04 16 . ± .
03 16 . ± .
04 16 . ± . − . ± .
03 16 . ± .
02 16 . ± .
02 15 . ± . − . ± .
03 15 . ± .
02 15 . ± .
04 15 . ± . − . ± .
02 15 . ± .
02 15 . ± .
02 15 . ± . . ± .
04 15 . ± .
03 15 . ± .
04 15 . ± .
03 15 . ± . were resumed there is a clear deviation. As the decline isseen in both SN 2017ein data sets we can conclude that thisis intrinsic to the event and is not a consequence of a datareduction issue. The ugriz photometry allows the construction of a pseudo-bolometric light curve with SEDs covering 3000 – 10000 ˚A.It is constructed using the observed photometry, correctedfor E ( B − V ) tot using the extinction law of Cardelli et al.(1989) and R v = 3 .
1, which is then converted to a flux andthe spectral energy distribution for each data integrated overthe wavelength range. Finally, the bolometric luminosity wascalculated using the luminosity distance derived from the distance modulus. u -band magnitudes were estimated forepochs when no u -band observations were taken by assuminga constant u − g band colour for dates prior to the first obser-vation and after the final u -band observation. The methodis described in more detail in Prentice et al. (2016).The pseudo-bolometric light curve is shown in compar-ison with a sample of SNe Ic in Fig. 3. When looking at thelight curve properties in the photospheric phase, SN 2017einis a typical SN Ic-7 (a narrow lined SN Ic as per Pren-tice & Mazzali 2017). The peak luminosity for the pseudo-bolometric light curve is (2 . ± . × erg s − and istypical for SNe Ic-6/7. The characteristic time-scales, t − / and t +1 / measure the rise from luminosity at half maximumto maximum, and from maximum to half maximum respec- MNRAS000
1, which is then converted to a flux andthe spectral energy distribution for each data integrated overthe wavelength range. Finally, the bolometric luminosity wascalculated using the luminosity distance derived from the distance modulus. u -band magnitudes were estimated forepochs when no u -band observations were taken by assuminga constant u − g band colour for dates prior to the first obser-vation and after the final u -band observation. The methodis described in more detail in Prentice et al. (2016).The pseudo-bolometric light curve is shown in compar-ison with a sample of SNe Ic in Fig. 3. When looking at thelight curve properties in the photospheric phase, SN 2017einis a typical SN Ic-7 (a narrow lined SN Ic as per Pren-tice & Mazzali 2017). The peak luminosity for the pseudo-bolometric light curve is (2 . ± . × erg s − and istypical for SNe Ic-6/7. The characteristic time-scales, t − / and t +1 / measure the rise from luminosity at half maximumto maximum, and from maximum to half maximum respec- MNRAS000 , 1–15 (2021)
J. J. Teffs
Time since max [d] M a gn it ud e + o ff s e t SN 2007gr R bandSN 2017ein r bandXiang SN 2017ein R band Figure 2.
Comparison between our r -band light curve ofSN 2017ein (black circles), the Xiang et al. (2019) R -band lightcurve for the same object (red triangles) and the R -band lightcurve of the spectroscopically similar SN 2007gr (blue squares).The late time light curves of SN 2017ein deviate from SN 2007grafter 100 days. This drop off is seen even more prominently in the i - and z -bands; see Fig 1. A linear fit between the gap in observa-tions is included to guide the eye. It shows that the later declinein SN 2007gr is steeper than at around 100 days, but it is clearlynot as pronounced as in SN 2017ein. Rest-frame time since maximum [d] Å l og ( L ) [ e r g s ] Ic-6/72017ein2007gr
Figure 3.
The pseudo-bolometric light curve of SN 2017ein (redcircles) compared with SN 2007gr (black diamonds) and a sampleof SNe Ic-6/7 (Grey dashed lines) (Prentice et al. 2016). tively. We find t − / = 9 . ± t +1 / = 15 . ± . .These values compare favourably with the SN Ic-6/7 medi-ans of 9 ± ± r -, i -, and z -bands leads to the bolometric light curve deviatingfrom a linear decay line. This is seen in Fig. 3 as the slope ofSN 2017ein light curve gets increasingly steeper with time,exceeding that of the comparison objects. These values agree with those measured from a 4000 − The LT spectra are shown in Fig. 4. The first few spectrashow clear, but narrow absorption features. The Fe ii domi-nated region around 5000 ˚A is clearly blended. Over time theFe ii λλ i D line evolves from a weak absorption at − . t p . O i λ ∼ ii λ t p , the firstclear indication of this line is at − . t p the spectra become more complex in this region, with moreabsorption lines appearing.The SN falls into the Ic-7 He-poor subgroup under theclassification of Prentice & Mazzali (2017) because the meannumber of features at t − / and t p is 7. This group is mainlydefined by the separation of Fe ii λλ >
35 days.
Figure 5 gives the line velocities of SN 2017ein as a func-tion of time for Fe ii λ i D, Si ii λ i λ − . ii and Na i at ∼ − while O i is at v ∼ − . This spectrum is the only one accessibleto this work where the wavelength range covers the Ca ii NIR triplet, for which a velocity of 19000 ± − ismeasured.The line velocities decrease rapidly over the course of aweek, which further hints at the young nature of the tran-sient. Comparison with the mean line velocities for a sampleof Ic-6/7 SNe (Prentice et al. 2019) shows that the veloc-ity curves are typical for a SE-SN of this type. The veloc-ity curve also demonstrates that the line forming regionsfor each element overlaps, suggesting some degree of mixingwithin the ejecta. Some stratification is most noticeable be-tween Si ii λ ∼ − − . Figure 6(a) shows a small sample of Type Ic SNe comparedto SN 2017ein at a epoch of approximately 1 week priorto bolometric peak. While these dates do not always reflectthe epoch with respect to the explosion date, they offer aquick comparative time if the explosion date is not well con-strained. SN 2017ein and SN 2007gr both share narrow fea-tures, with the Fe ii λλ ii features. Figure 6(b) shows the same MNRAS , 1–15 (2021)
N2017ein Rest-frame Wavelength [ Å ] S ca l e d f l ux + c on s t a n t d d d d d d +1.5 d +2.5 d +5.5 d +9.6 d +13.5 d +20.6 d +27.5 d +36.5 d +142.5 d +189.4 d +194.3 d S i II C II F e II N a I O I [O I] [Ca II] Figure 4.
The flux calibrated spectra of SN 2017ein as obtainedby LT:SPRAT. Epochs are since bolometric maximum.
SNe approximately 2 weeks after the time of the bolometricmax, with SN 2007gr and SN 2017ein showing similar spec-tral behaviour over the shared wavelength range. SN 1994Iand SN 2004aw also share similarities with each other, withthe exception of the dominant feature near 5500 ˚A, thoughtto be helium (Filippenko et al. 1995; Sauer et al. 2006). Thenebular epochs in Figure 6(c) show fewer differences betweenthe set of SNe with again, SN 2007gr showing the most sim-ilarity to SN 2017ein.
10 0 10 20 30 40
Rest-frame time since bolometric maximum [d] V e l o c it y [ k m s ] Fe II 5169Na I 5891Si II 6355 O I 7774
Figure 5.
Velocities as measured from the absorption line minima.Also shown as dashed lines are the median line velocities for aselection of SNe Ic 6/7.
We present the model for SN 2017ein following the abun-dance tomography method (Stehle et al. 2005) used tomodel other SNe such as SN1994I (Sauer et al. 2006) andSN 2004aw (Mazzali et al. 2017). The spectra cover a tem-poral range of − . t p , and three post- t p ,that show the spectral evolution and have a good S/N.We start with an initial density structure based upona 22 M (cid:12) progenitor model. This model is stripped of allH/He to produce a CO core of approximately 3.4 M (cid:12) priorto core collapse. Teffs et al. (2020a) explored this model indetail as part of a parameter study that included four ex-plosion energies of 1, 3, 5, and 8 foe, where 1 foe is definedas 1 × erg. This model had good success in reproducinga set of observed spectra from multiple Type Ic SNe with-out fine tuning any parameters, so we treat the density andabundance structure of the 1 foe model as our base. Giventhe estimated ejecta properties in Van Dyk et al. (2018); Kil-patrick et al. (2018); Xiang et al. (2019) and the results fromour parameter study from Teffs et al. (2020a), the initial COcore model is likely too massive to reproduce both the spec-tra and photometry due to a slower diffusion time post peakand the lack of similarity to SN 1994I shown in Teffs et al.(2020a). To find a better fit for SN 2017ein, we rescale themodel using the method in Hachinger et al. (2009) by usingequations 1 and 2. ρ (cid:48) = ρ (cid:32) E (cid:48) k E k (cid:33) − / (cid:32) M (cid:48) ej M ej (cid:33) / (1) v (cid:48) = v (cid:32) E (cid:48) k E k (cid:33) / (cid:32) M (cid:48) ej M ej (cid:33) − / (2)The primed variables in equations 1 and 2 are the new,rescaled variables and un-primed are the original variables.The model is re–scaled to some initial parameters for E k and M ej , with the initial M Ni derived from the peak luminosity. MNRAS000
We present the model for SN 2017ein following the abun-dance tomography method (Stehle et al. 2005) used tomodel other SNe such as SN1994I (Sauer et al. 2006) andSN 2004aw (Mazzali et al. 2017). The spectra cover a tem-poral range of − . t p , and three post- t p ,that show the spectral evolution and have a good S/N.We start with an initial density structure based upona 22 M (cid:12) progenitor model. This model is stripped of allH/He to produce a CO core of approximately 3.4 M (cid:12) priorto core collapse. Teffs et al. (2020a) explored this model indetail as part of a parameter study that included four ex-plosion energies of 1, 3, 5, and 8 foe, where 1 foe is definedas 1 × erg. This model had good success in reproducinga set of observed spectra from multiple Type Ic SNe with-out fine tuning any parameters, so we treat the density andabundance structure of the 1 foe model as our base. Giventhe estimated ejecta properties in Van Dyk et al. (2018); Kil-patrick et al. (2018); Xiang et al. (2019) and the results fromour parameter study from Teffs et al. (2020a), the initial COcore model is likely too massive to reproduce both the spec-tra and photometry due to a slower diffusion time post peakand the lack of similarity to SN 1994I shown in Teffs et al.(2020a). To find a better fit for SN 2017ein, we rescale themodel using the method in Hachinger et al. (2009) by usingequations 1 and 2. ρ (cid:48) = ρ (cid:32) E (cid:48) k E k (cid:33) − / (cid:32) M (cid:48) ej M ej (cid:33) / (1) v (cid:48) = v (cid:32) E (cid:48) k E k (cid:33) / (cid:32) M (cid:48) ej M ej (cid:33) − / (2)The primed variables in equations 1 and 2 are the new,rescaled variables and un-primed are the original variables.The model is re–scaled to some initial parameters for E k and M ej , with the initial M Ni derived from the peak luminosity. MNRAS000 , 1–15 (2021)
J. J. Teffs (a) t p -2.4 d07gr t p -6.6 d94I t p -6.3 d02ap t p -6 d04aw t p -3.7 d -- O I -- F e II -- N a I -- S i II -- C II (b) -- H e I t p + 13.5 d07gr t p +11.3 d94I t p +10.7 d02ap t p +11.9 d04aw t p +10 d3000 4000 5000 6000 7000 8000 9000 1000054321012 (c) [O I] [Ca II]17ein t p +142.5 d07gr t p +168 d94I t p +145 d02ap t p +151 d04aw t p +251 dRest-Frame Wavelength [Å] N o r m a li z e d F l u x + c o n s t a n t Figure 6.
Selected epochs compared to a small sample of otherType Ic SNe (SN 1994I (Filippenko et al. 1995), SN 2007gr(Valenti et al. 2008), SN 2004aw (Taubenberger et al. 2006),SN 2002ap (Foley et al. 2003)). These SNe are chosen as SN 1994Iand SN 2004aw are both Ic-6 SNe, SN 2002ap is a Type Ic-BL ora Ic-4, and SN 2007gr is a close analogue to SN 2017ein and alsoa Ic-7. The He i is included as SN 1994I is thought to possiblycontain He due to the stronger than normal feature. The scaled density profile is then used in our Monte Carlolight curve code, which tracks the emission and propaga-tion of γ -rays and positrons produced by the decay of Ni,and subsequently Co, in to the homologously expandingejecta as described in detail in Cappellaro et al. (1997). Theoutputted bolometric light curve is then compared to theobserved pseudo-bolometric light curve and the process isrepeated until the calculated light curve reproduces the ob-served light curve with reasonable accuracy.The re–scaled model and its initial abundances are thenused in our spectral synthesis code, described in detail inMazzali & Lucy (1993); Lucy (1999); Mazzali (2000). Thiscode reads in the composition and the density profile of theejecta to produce a stratified model where each layer is de-
Table 3.
Synthetic model properties for SN 2017ein from the neb-ular and photospheric models. The error bounds in the Ni masscomes from the modelling of the nebular and photospheric phases,while the others are estimates from the light curve modelling andthe parameter study of Ashall & Mazzali (2020).Mass M Ni E k E k /M ej [M (cid:12) ] [M (cid:12) ] [10 erg] [10 erg /M (cid:12) ]1.6 ± ± .01 0.9 ± ± .05 fined by an observed spectrum and fitted abundances, pho-tospheric luminosity ( L ph ), and photospheric velocity ( v ph ).These parameters are systematically changed until the syn-thetic spectrum best reflects the observed spectrum and itsbehaviours. By using abundance tomography, this allows usto create a stratified ejecta that gives us both the abundanceand distribution of elements responsible for the formationof the spectral features. For elements that do not producestrong optical features or that produce features beyond theobserved spectral wavelength range of SPRAT ( λ > ii feature near 9000 ˚A, we are unableto constrain the abundance of those elements.Using these methods, we find a model with an M ej of1 . ± . (cid:12) , 0 . ± .
01 M (cid:12) of Ni, and an E k of 0 . ± . i λ v > − − , is reduced indensity by expanding the shell. This outer reduction in den-sity may be a result of a low mass He shell not present inthe initial model or some asymmetry. t p − . d, t exp +7 d The epoch shown in Fig. 7(a) is not the earliest availableepoch, but shows good S/N with well defined features com-pared to the earlier spectrum. The best fit synthetic spec-trum has a v ph of 11 000 km s − and an Log ( L ph ) = 42.295erg s − . The v ph and L ph parameters can be modified by of 5-10 % before the fit starts to visibly suffer, and is discussed inmore detail in Ashall & Mazzali (2020). This early observedspectrum has only a few strong features. The re–emissionred of the C ii line at 6500 ˚A is not well reproduced in themodel and the synthetic C ii lines are all slightly too broad.Despite this, the overall flux level and majority of featuresare well reproduced. t p − . d, t exp +11 d The best fit model spectrum in Fig. 7(b) has a v ph of 9300km s − and an Log ( L ph ) = 42.395 erg s − . Most featuresare well reproduced in the synthetic model, but the C ii features at 6500 ˚A is too broad when compared to the ob-served spectrum. In addition, the flux level in the near–UVis slightly under the observed spectrum, but is necessary toreproduce the remaining features. MNRAS , 1–15 (2021)
N2017ein p - 6.2,t exp + 7 d June 1st 2017 -- F e II -- F e II -- F e II -- M g I -- S i II -- C II -- C II -- C II / N a I -- O I -- C a II SN2017einBest Fit Model0123 (b) t p - 2.4,t exp + 11 d June 5th 2017 -- F e II -- F e II -- F e II -- M g I -- N a I -- S i II -- C II -- C II -- O I -- C a II p + 0.4,t exp + 13 d June 7th 2017 -- F e II -- F e II > F e II -- M g I -- N a I -- S i II -- C II -- O I -- C a II p + 2.5,t exp + 15.5 d June 10th 2017 -- F e II -- F e II -- F e II > F e II -- M g I > S c II ? -- N a I -- S i II -- C II -- O I -- C a II p + 9.6,t exp + 23 d June 17th 2017 -- F e II -- F e II -- F e II > F e II -- M g I S c II -- S c II ---- N a I -- S i II -- S i II -- T i II -- T i II -- O I -- C a II p + 2.5,t exp + 27 d June 21st 2017 -- F e II -- F e II -- F e II > F e II -- M g I -- S c II -- S c II -- N a I -- S i II -- S i II -- T i II -- T i II -- T i II -- O I -- C a II Wavelength [Å] F λ [ − e r g c m − s − Å − Figure 7.
The spectral models for best fit model model for a selec-tion of spectral epochs. Line identifications are for strong, domi-nant, or common features observed in SN 2017ein and other TypeIc SNe. The spectral models do contain other weaker lines thatcontribute to the spectral behaviour but are not listed. t p − . d, t exp +13 d The model spectrum in Fig. 7(c) has a v ph of 8800 km s − and an Log ( L ph ) = 42.410 erg s − . The Fe ii lines are verywell reproduced at this epoch, but the flux level is lowerthan the observed in the 5000–6500 ˚A region. Similar tothe previous epoch, more Fe–group material may improvethis at the cost of the Fe ii features. The C ii line at 6200˚A is narrow in the observed spectrum, but too broad in thesynthetic spectrum. There may be a feature near 5600 ˚A butis hard to discern due to noise in the spectrum. This maybe a S i line or an early Sc ii line but is not reproduced inour models. t p +2 . d, t exp +15 . d The model spectrum in Fig. 7(d) has a v ph of 8300 km s − and an Log ( L ph ) = 42.395 erg s − . The region between5200–5800 ˚A is poorly reproduced in this model despitethe remaining features showing strong similarity. The nextepoch shows these may be the beginnings of the Sc ii featuresthat become dominant in the next epoch. By this epoch, theC ii line is blended, too weak, or largely absent and the Na i D line is beginning to become strong. t p +9 . d, t exp +23 d By this epoch, the observed spectrum is relatively low influx, noisy, and has a multitude of weak features in thespectrum. The model spectrum in Fig. 7(e) has a v ph of6000 km s − and an Log ( L ph ) = 42.225 erg s − . The pre-viously tentatively identified Sc ii features are now stronglymatching to the observed spectrum. The abundances of Scand velocity range required to produce these lines are givenin Figure 8. Increasing the velocity range or mass of Sc cancause these lines to dominate in the later spectra. The Fe ii feature is too broad and deep, but is required for the rest ofthe spectrum to match. The region between 6200–7300˚A hascontributions from O i , Fe ii , and Ti ii lines and is difficultto match each one as the features are not strong and thespectrum is noisy.. t p +13 . d, t exp +27 d For the final photospheric epoch modelled in this work, thesynthetic model Fig. 7(f) has a v ph of 4000 km s − and anLog ( L ph ) = 42.10 erg s − . At this phase, the photosphericvelocity becomes harder to define as nebular emission, evi-dent in the Ca ii NIR triplet in the wider wavelength rangespectra given in Van Dyk et al. (2018); Kilpatrick et al.(2018); Xiang et al. (2019), is a non-negligible contributionto the total observed flux. As the spectral synthesis codestrictly treats the photospheric phase, this prevents a harddefinition of the photospheric velocity, so the photosphericvelocity value is the one required by the spectral shape andtotal flux. Beyond that, the rest of the spectrum is well re-produced. The Na i D lines fit could be improved with theaddition of more Fe ii re–emission or a stronger S i contri-bution. MNRAS000
The spectral models for best fit model model for a selec-tion of spectral epochs. Line identifications are for strong, domi-nant, or common features observed in SN 2017ein and other TypeIc SNe. The spectral models do contain other weaker lines thatcontribute to the spectral behaviour but are not listed. t p − . d, t exp +13 d The model spectrum in Fig. 7(c) has a v ph of 8800 km s − and an Log ( L ph ) = 42.410 erg s − . The Fe ii lines are verywell reproduced at this epoch, but the flux level is lowerthan the observed in the 5000–6500 ˚A region. Similar tothe previous epoch, more Fe–group material may improvethis at the cost of the Fe ii features. The C ii line at 6200˚A is narrow in the observed spectrum, but too broad in thesynthetic spectrum. There may be a feature near 5600 ˚A butis hard to discern due to noise in the spectrum. This maybe a S i line or an early Sc ii line but is not reproduced inour models. t p +2 . d, t exp +15 . d The model spectrum in Fig. 7(d) has a v ph of 8300 km s − and an Log ( L ph ) = 42.395 erg s − . The region between5200–5800 ˚A is poorly reproduced in this model despitethe remaining features showing strong similarity. The nextepoch shows these may be the beginnings of the Sc ii featuresthat become dominant in the next epoch. By this epoch, theC ii line is blended, too weak, or largely absent and the Na i D line is beginning to become strong. t p +9 . d, t exp +23 d By this epoch, the observed spectrum is relatively low influx, noisy, and has a multitude of weak features in thespectrum. The model spectrum in Fig. 7(e) has a v ph of6000 km s − and an Log ( L ph ) = 42.225 erg s − . The pre-viously tentatively identified Sc ii features are now stronglymatching to the observed spectrum. The abundances of Scand velocity range required to produce these lines are givenin Figure 8. Increasing the velocity range or mass of Sc cancause these lines to dominate in the later spectra. The Fe ii feature is too broad and deep, but is required for the rest ofthe spectrum to match. The region between 6200–7300˚A hascontributions from O i , Fe ii , and Ti ii lines and is difficultto match each one as the features are not strong and thespectrum is noisy.. t p +13 . d, t exp +27 d For the final photospheric epoch modelled in this work, thesynthetic model Fig. 7(f) has a v ph of 4000 km s − and anLog ( L ph ) = 42.10 erg s − . At this phase, the photosphericvelocity becomes harder to define as nebular emission, evi-dent in the Ca ii NIR triplet in the wider wavelength rangespectra given in Van Dyk et al. (2018); Kilpatrick et al.(2018); Xiang et al. (2019), is a non-negligible contributionto the total observed flux. As the spectral synthesis codestrictly treats the photospheric phase, this prevents a harddefinition of the photospheric velocity, so the photosphericvelocity value is the one required by the spectral shape andtotal flux. Beyond that, the rest of the spectrum is well re-produced. The Na i D lines fit could be improved with theaddition of more Fe ii re–emission or a stronger S i contri-bution. MNRAS000 , 1–15 (2021)
J. J. Teffs M a ss F r a c t i on Log ρ [ g c m − ] Velocity [km s −1 ]CO NeNa MgSi SNi FeCa ρ Figure 8.
Mass fraction of the most abundant elements in the best fit model and the density profile (in black) shown on the right y -axis.The grey lines represent the modelled epochs with the v ph values given in Sections 5.1 to 5.6. S c a l e d F l u x October 28th 2017 Sum of ComponentsCenterRed ShiftedBlue Shifted
Figure 9.
Fits to the [O i ] λλ i ] Asymmetry in the Nebular Spectra The [O i ] λλ i ] components, each comprising of two Gaussian featuresthat form a simplified [O i ] λλ i ] pro-file is shown for the three nebular spectra in Figure 4. Whencompared to a set of other Type Ic in Figure 6, SN 2007grand the others do not show a similar [O i ] profile. The sec-ondary bump near 6400 ˚A and the approximately equal fluxvalues of the two doublet peaks suggested two blobs of oxy-gen shifted by ±
30 ˚A. Driven by this, we use three Gaus-sians comprised of a red and blue shifted blob and a centralblended feature. We find a redshifted blob at a velocity shiftof − − and a blueshifted blob at a velocity shift of2000 km s − . From Taubenberger et al. (2009), a combina-tion of these three components best reflects an asymmetricejecta. In order to establish the properties of the inner M ej , Ni mass and distribution in particular, we modelled thenebular-epoch spectra of SN 2017ein. Three spectra areavailable, at rest-frame epochs of 160, 207 and 212 days fromthe putative time of explosion. They all show emission linesof the elements that are typically seen in SNe Ib/c. Unfor-tunately, the signal-to-noise ratio of the spectra is not al-ways very high, especially in the blue. The region short of5000 ˚A is extremely noisy, which makes it very difficult touse the strength of the [Fe ii ] lines as a test for the mass of Ni. Although this somewhat limits our models, we still usethe overall flux to estimate the Fe flux. The strongest linesthat are seen are [O i ] λλ ii ] λλ i ] λ ii ] lines, but it isaffected by noise.A particularly interesting aspect of the spectra is themulti-peaked structure of the [O i ] λλ MNRAS , 1–15 (2021)
N2017ein Figure 10.
The nebular model for the observed spectrum, in black,at day 160, where the blue line represents the flux from a smallmass of blueshifted oxygen, the pink from a more massive centralmass of oxygen, and the green is the combined flux from bothcontributions separated peaks or an abnormally narrow [O i ] line suggesta highly aspherical explosion. These are typically seen in en-ergetic events like GRB/SNe (Mazzali et al. 2001, 2005), butthese events are quite rare. More often narrowly separatedpeaks are seen (e.g., Maeda et al. 2008; Taubenberger et al.2009), or composite profiles (e.g., Mazzali et al. 2017). Thesemay be interpreted as asymmetries that affect only the in-nermost ejecta, which may carry the signature of an asym-metric or aspherical behaviour in the collapse/explosion,which was however not strong enough to affect the entireprogenitor and then the SN ejecta as a whole. The rate ofoccurrence of this type of profiles is quite high, suggestingthat most SNe Ib/c are affected to some degree by inner as-phericity (Maeda et al. 2008).In the particular case of SN 2017ein, however, the pro-file analysis above suggests the presence of components atdifferent bulk velocities. This makes it interesting to modelthe spectra using a multi-component scenario as done forthe peculiar SN Ia 2007on (Mazzali et al. 2018). For themodelling, we used our SN non-local thermodynamic equi-librium (NLTE) nebular spectral synthesis code. The codehas been discussed and used in several papers, dealing withboth SNe Ib/c (e.g., Mazzali et al. 2007, 2017) and Ia (e.g.,Mazzali et al. 2008, 2020). Given a density and composi-tion, the code first computes the emission of gamma-raysand positrons from the decay chain Ni → Co → Fe.This can be done in both a 1-zone or a stratified approach,where density and abundances change with radius in aone-dimensional setup. The propagation and deposition ofthe gamma-rays and positrons is then computed using aMonte Carlo method. Typical opacities that are used are κ γ = 0 .
027 cm g − and κ e + = 7 cm g − .The deposited energy heats and ionizes the gas and, fol-lowing Axelrod (1980), ionization is assumed to be caused by impact with the high-energy particles produced in thedeposition of gamma-ray and positron energy, while pho-toionization is assumed to be negligible (Kozma & Fransson1998). Ionization balance is obtained matching impact ion-ization and the rate of recombination for each ion, whichdepends mostly on density. Level population is computed inNLTE, balancing the thermal heating rate with cooling vialine emission. This takes place mostly via forbidden lines,but some permitted transitions that can be strong in emis-sion and contribute therefore to cooling are also included,e.g. Ca ii IR triplet and H&K. The nebula is assumed tobe optically thin, therefore radiation transport is not per-formed. This is a reasonable approximation at late times.Line emission then tracks the distribution of the emittingelements and that of Ni.Given the profile of the [O i ] line, it is clear that a sin-gle, spherically symmetric emission component would notbe able to reproduce the observations in detail. Thereforewe take a different approach. Using the abundance distribu-tion derived from the early-time spectra, we model the broadcomponent of the emission, completing the mapping of thedensity and abundances at low velocities as required to opti-mise the fit. We then add a narrow, blue-shifted componentto reproduce the narrow peaks in the observed [O i ] line. Fi-nally, we test our results by evolving the model to differentepochs and comparing to the observations. We note a dis-continuity in the light curve when one compares points near150 days and 200 days (Fig. 1). This poses a problem forboth nebular and light curve modelling, which are based onthe same treatment of gamma-ray and positron deposition.As a first step, we determine the width of the [O i ] λλ v = 5000 km s − is found to be appropriate at all epochs,when line blending is accounted for. This confirms that most Ni, as well as a significant fraction of oxygen, must be lo-cated inside this velocity. The broad emission profile is rea-sonably symmetric, suggesting that a 1D approach is suffi-cient for the bulk of the inner ejecta. Using the model above,which has M ej ≈ (cid:12) and E k ≈ . × erg s − , we findthat a Ni mass of ≈ .
078 M (cid:12) , combined with an oxygenmass of ≈ .
86 M (cid:12) yields a good fit to the broad feature atday 160.When including the other elements at low velocity, weneed to remember that we have no direct handle on impor-tant elements such as silicon and sulphur, whose strongestemission lines are predominantly in the near-infrared (NIR).Depending on the amount of these elements that is includedin the model, the overall mass can change significantly (e.g.,Mazzali et al. 2019). Here we chose to keep the total mass asdefined by the early-time modelling, which limits the mass ofSi to ≈ .
60 M (cid:12) and that of S to ≈ .
07 M (cid:12) , most of whichis at velocities between 3000 and 7000 km s − . Calcium isresponsible for the second strongest observed emission line,Ca ii ] 7291,7324. The strength of this semi-forbidden tran-sition allows us to determine the local density, which weachieve by setting some degree of clumping in the ejecta.We use a volume filling factor of 0.1 for the inner ejecta,which is in line with previous results for SNe Ib/c (e.g., Maz-zali et al. 2010), and a total Ca mass of ≈ .
014 M (cid:12) . Thesynthetic spectrum obtained for day 160 is shown in Fig. 10.A narrow-line emission spectrum is then computed asa 1-zone model, and added to the broad-lined spectrum. A
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MNRAS000 , 1–15 (2021) J. J. Teffs i ] emis-sion has a velocity width of ≈ − , which meansthat the two components are individually observed. The factthat they are in a ratio of about 2/3 implies that the localdensity is quite high, so again we need to use a volume fillingfactor of 0.1 for this clump of material. We assume that thisclump is mostly composed of oxygen and heated by Ni de-cay. This is obviously an over-simplification, as given its lowblueshift the clump is likely to be residing inside the bulkof the ejecta and therefore to be exposed to radioactivityfrom the rest of the Ni. In any case, under the approxima-tion we used, it is sufficient to place 0.10 M (cid:12) of oxygen in aclump heated by 0 .
023 M (cid:12) of Ni to reproduce the observednarrow emission. When added to the broad component, areasonable fit is obtained for the whole profile (Fig. 10).The profile decomposition performed above suggestedthe need for three components, but we do not need that whenwe compute our synthetic models: the two main narrowpeaks correspond to [O i ] 6300 and 6363, respectively, notto a blue-and red-shifted narrow component. A 3-componentmodel may explain the small ledge near 6400 ˚A as red-shifted[O i ] 6363, but it fails to explain the corresponding ledgenear 6200 ˚A. It is actually more likely that these two ledges,if they are indeed real and not just due to noise, are fea-tures of the overall density/abundance distribution, as theyare rather symmetric with respect to [O i ] 6300, at veloc-ities of ∼ − . The narrow-lined spectrum showsemission also in [O i ] 5577, which is a tracer of recombina-tion, and which may correspond to an observed feature. Italso shows several [Fe ii ] lines, but these are too weak to bedistinguished in the noisy observed spectra.If we evolve the model to later epochs, we can only ob-tain a good fit to the observations if we apply multiplicativecorrection factors of 1.3 for the spectrum on day 207 and 1.6for that on day 212. Such rapid changes in the luminosityare unlikely unless we invoke improbable sudden changes inthe gamma-ray or positron opacities. We discuss this issuein further detail in Section 6.4.In conclusion, the nebular models largely confirm that Ni is concentrated to low velocities, as is expected ina low-energy explosion. The mass of Ni that is derived, ∼ .
08 M (cid:12) , is consistent with that obtained from the lightcurve. An interesting question is the origin of the oxygen-richblue-shifted clump. We do not see evidence of a counter-clump at some red-shift. It is possible, but unlikely giventhe symmetric profiles of the broad emission features, thatsuch a clump might exist but its emission is absorbed bythe bulk of the ejecta. The innermost layers of the ejectamay be characterised by some degree of asphericity, whichmay have been imprinted upon them at the time of the ex-plosion. The mass of the clump is however quite small, andit would be even smaller if we actually embedded it in the Ni-dominated inner ejecta. It does not seem too likely,given the small amount of material comprising the clump,that the asphericity is caused by jets, but if that is indeedthe case the jet(s) were weak and easily choked inside thedense deep CO core of the star. Such events may indeed bequite common in SNe Ib/c (Piran et al. 2019), and possiblyin all core-collapse SNe (Nakar & Piran 2017; Gottlieb et al.2021) L o g L ( e r g / s ) Best Fit ModelModel + Nebular Inner17ein ugriz flux17ein ugriz + NIR fluxSpectral Synthesis
Figure 11.
Bolometric light curves for both SN 2017ein, two syn-thetic models, and the integrated flux from the spectral models
We compute a synthetic light curve using a Monte Carlocode discussed in detail in Cappellaro et al. (1997) and Maz-zali (2000). The code requires a choice of density structureand elemental abundances including Ni. The code tracksthe emission and propagation of γ -rays and positrons pro-duced by the decay of Ni, and subsequently Co, into theexpanding ejecta. The gamma ray and positron opacities aregiven by κ γ = 0 .
027 cm g − and κ e + = 7 cm g − (Axelrod1980). The deposited energy from the decay is recycled intooptical photons and the resulting propagation is followedusing a similar Monte Carlo scheme. The optical opacity isboth time and metallicity dependent, which aims to repro-duce the dominance of line opacity in the ejecta (Ashall et al.2019; Mazzali 2000). This code is used initially to producean approximate model for the model inputs in the spectralsynthesis code. After the photospheric and nebular spectraare fit, any changes to the model in density or abundancesare used to produce a final light curve shown in Fig. 11.The mass of Ni required to match the flux level ofthe nebular spectra is approximately 0.08 M (cid:12) comparedto the 0.1 M (cid:12) of Ni required to match the pseudo-bolometric light curve in Figure 3. Photometric observationsfor SN 2017ein cover only the ugriz bands which cover awavelength range of 3000 – 10000 ˚A, with no UV or IR con-tributions. Sauer et al. (2006) used the NIR/IR flux fromSN2002ap, scaled to SN1994I to calculate an estimated NIR( λ >
JHK band (10000 – 25000 ˚A ) coverage forboth near peak and late time epochs. We follow the samemethod described in Sauer et al. (2006) to generate a mod-ified bolometric light curve.While the explosion models match the observed ugriz +NIR light curve, the bolometric light curve from oursynthetic spectral modelling is too luminous by 5-10%. Thismismatch is likely the missing UV flux not taken into ac-count in addition to the standard errors inherent to the ob-servations and the modelling process that is discussed later.
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N2017ein The modified inner density and Ni distribution requiredto match the nebular spectra is used to generate a secondmodel. The modified model has a bolometric light curve thatreproduces both early phase and late time phases fairly well.As only the innermost ejecta is modified, the spectra in Fig.7 are unchanged.
The initial model in this work is based upon the CO core ofa 22 M (cid:12) progenitor model evolved at solar metallicity, withno binary, then stripped of all helium and exploded at 1 foe.The initial model with no modifications failed to reproducethe spectra and the light curve as did the higher E k modelsin Teffs et al. (2020a) using the same initial progenitor. Thisrequired us to modify the CO core model in order to bestfit the observed spectra and light curve to get the results inSection 5.Based upon the estimates given in Van Dyk et al.(2018); Kilpatrick et al. (2018); Xiang et al. (2019) and thesimilarity to SN 2007gr in Fig. 6, we re–scaled the massof the model to get a M ej of 1.6 M (cid:12) and the energy tomatch the relatively low velocity lines. We do note that re–scaling a model in either or both E k and M ej may not re-flect the properties of an evolved CO core of the re–scaledmass. Based upon only the photospheric modelling, we sug-gest that the M ej of SN 2017ein is within the range of 1.2–2.0M (cid:12) , using the error estimates from Ashall & Mazzali (2020).The E k was modelled to be ∼ E k /M ej ratio to be ∼ (cid:12) for the best fit model.Comparing these ratios to those found in Prentice & Maz-zali (2017), the E k /M ej ratio for our model is on the low end.Both SN 1994I and SN 2004aw have E k /M ej ratios near 1foe/M (cid:12) , but show broader spectral features than SN 2017einor SN 2007gr. Using the classification system from Prentice& Mazzali (2017), both SN 1994I and SN 2004aw are definedas Type Ic-6 due to the blending of two of the three primaryFe ii lines while SN 2017ein is a Type Ic-7. For modelledSNe, as the classification increases from very blended TypeIc-3 to narrow lined Type Ic-7, the E k /M ej ratio decreases.Based on this, the low E k /M ej ratio found for SN 2017ein,which is the first SN Ic-7 to undergo this kind of analysis,fits in with the previous trend. The modelling of the nebularphase spectra also matches the model from the photosphericphase. From day 15 and onward, the region near 5500˚A containstwo features between the strong Fe ii and Na i lines. A sim-ilar pair of lines were seen in SN 2007gr and Valenti et al.(2008) suggested these are Sc ii lines but no abundance to-mography model has been done for that event. Sc ii lineshave been in observed in Type II SNe, such as SN 1987a(Mazzali et al. 1992) and the line velocities of the 5527 and6245 ˚A Sc ii lines were measured in the Type II SNe 2012A,1999em, 2005cs and 2009bw, summarised in Tomasella et al.(2013) Millard et al. (1999) tentatively identified Sc ii in sev-eral spectra of SN1994I as well but Sauer et al. (2006) were unable to reproduce the identified Sc ii line without produc-ing other unwanted spectral lines.For the models in Fig. 7, a small mass of Sc is locatedbetween 8300 – 11000 km s − . These two features are bestfit in the June 17th or June 21st spectra, (Fig. 7(e-f)). Theaddition of Sc ii produces a set of lines between 6000–7000˚A, but this is also combined with Fe ii , Si ii , and variousother weaker features. The June 10th spectrum shows whatmay be the beginnings of the Sc ii lines, but the syntheticmodel has a weaker flux in this region. Increasing the Fe ii mass can cause re–emission of flux into this area, improv-ing the flux level but can produce unwanted behaviour inother regions of the spectrum or for later spectra. The ear-lier spectra do not show strong evidence for Sc ii and theflux at the later epochs is fairly low. Increasing the mass ofSc ii at a higher velocity can reproduce both the two linesand re-emits flux towards the Na i D region, reducing thedepth of that feature but producing much stronger featuresin this epoch and later epochs between 6000–7000 ˚A that arenot observed. Sulphur can also produce the redder feature,but given the constraints on S/Si ratio from explosive nucle-osynthesis (1/3 – 1/5), increasing the amount of sulphur toproduce this line requires too much Si in the outer region.One can also use Cr to reproduce part of the bluer line, butthe mass and location of the material needed in the modelproduces too many unobserved lines if the feature is solelyformed from Cr, in addition to the lack of a physical originfor such high amounts of Cr.
Similar to other Type Ic SNe, SN 2017ein has been suggestedto have some amount of He in the outer atmosphere. Thesynthetic model in Fig. 7 contains no He, and only Na isrequired to produce the feature at 5875˚A with good successthroughout all the synthetic spectra. The two weaker opticalHe i lines at 6678 and 7065 ˚A are not present or easily iden-tifiable in any of the spectra and we have no NIR spectrato cover the stronger 10830 and 20581 ˚A lines. Due to thesefactors, we would have to solely rely on the He i λ i D line islocated, this is difficult. Hachinger et al. (2012) and Teffset al. (2020b) found that up to 0.06–0.14 M (cid:12) of He could bepresent before the optical and NIR He i lines are strong andeasily identifiable, with a much lower amount of “hideable”He if only NIR lines are considered.Figure 12 shows the four earliest epochs with a total M He ∼ (cid:12) above a v ph > − . The additionof He to this model (blue line in Fig. 12) reproduces the pri-mary optical He i line at 5875 ˚A to an adequate degree, butthe lack of the weaker He i lines at 6678 and 7065 ˚A makes asingle line fit hard to interpret as the model without He alsomatches the features adequately. Increasing the amount ofHe beyond the ∼ (cid:12) can drastically strengthen the opti-cal features beyond what is seen in the observed spectra. ForSN 1994I, in which the 5875 ˚A region shows a stronger fea-ture than in other Type Ic SNe, the possible signature of He i is relatively weak and short lived. Models for SN 1994I withand without He can often reproduce the bulk behaviour,suggesting that if He is present in SN 1994I, and by rela-tion SN 2017ein, the contribution from He would be mini- MNRAS000
Similar to other Type Ic SNe, SN 2017ein has been suggestedto have some amount of He in the outer atmosphere. Thesynthetic model in Fig. 7 contains no He, and only Na isrequired to produce the feature at 5875˚A with good successthroughout all the synthetic spectra. The two weaker opticalHe i lines at 6678 and 7065 ˚A are not present or easily iden-tifiable in any of the spectra and we have no NIR spectrato cover the stronger 10830 and 20581 ˚A lines. Due to thesefactors, we would have to solely rely on the He i λ i D line islocated, this is difficult. Hachinger et al. (2012) and Teffset al. (2020b) found that up to 0.06–0.14 M (cid:12) of He could bepresent before the optical and NIR He i lines are strong andeasily identifiable, with a much lower amount of “hideable”He if only NIR lines are considered.Figure 12 shows the four earliest epochs with a total M He ∼ (cid:12) above a v ph > − . The additionof He to this model (blue line in Fig. 12) reproduces the pri-mary optical He i line at 5875 ˚A to an adequate degree, butthe lack of the weaker He i lines at 6678 and 7065 ˚A makes asingle line fit hard to interpret as the model without He alsomatches the features adequately. Increasing the amount ofHe beyond the ∼ (cid:12) can drastically strengthen the opti-cal features beyond what is seen in the observed spectra. ForSN 1994I, in which the 5875 ˚A region shows a stronger fea-ture than in other Type Ic SNe, the possible signature of He i is relatively weak and short lived. Models for SN 1994I withand without He can often reproduce the bulk behaviour,suggesting that if He is present in SN 1994I, and by rela-tion SN 2017ein, the contribution from He would be mini- MNRAS000 , 1–15 (2021) J. J. Teffs p - 6.2,t exp + 7 d June 1st 2017 -- H e I -- H e I -- H e I SN2017einBest Fit+HeBest Fit0.40.60.81.01.2 (b) t p - 2.4,t exp + 11 d June 5th 2017 -- H e I -- H e I -- H e I p + 0.4,t exp + 13 d June 7th 2017 -- H e I -- H e I -- H e I p + 2.5,t exp + 15.5 d June 10th 2017 -- H e I Wavelength [Å] F λ [ − e r g c m − s − Å − ] Figure 12.
The best fit model with Na and no He and an alternatemodel with He and no Na for the first four epochs. The spectralrange is constrained to 5000–7500 ˚A in order to cover the threeoptical He i lines at 5875, 6678, and 7065 ˚A. mal, especially compared to He dominated features in TypeIb SNe. As concluded in Hachinger et al. (2012) and Teffset al. (2020b), a combination of optical and NIR He i linesare needed to determine how much He is present in Type IcSNe. The modelled values for the ejecta mass, explosion energy,and Ni mass in this work are similar to the approximate fitsfrom either the pseudo-bolometric light curve or the multi-band photometry, in Van Dyk et al. (2018). However, theestimated M ej from the progenitor masses found in Van Dyket al. (2018); Kilpatrick et al. (2018); Xiang et al. (2019)show a significant disparity. The ejecta masses from both thesingle star or binary star masses are in the range of 4-8 M (cid:12) .Figure 13, derived from spectral models and summarised inmore detail in Mazzali et al. (2017), shows that a correlationexists between M ej and E k . Placing a SN with 4-8 M ej and E k < ∼ × erg in this plane would result in a significantoutlier compared with other modelled SN Ic. Taking thatsame E k and the ∼ (cid:12) ejecta mass found in this work,gives a point that does align with other objects.The modelling of SN 2017ein in this work uses the abun- Figure 13.
A sample of modelled results from a variety of SN typesthat show the explosion energy and M ej . See Mazzali et al. (2017)for individual SN references dance tomography method that has been used often for awide variety of SE-SNe. This is a multi-variable approachto modelling SNe, and combined with photometric and neb-ular fits can produce a consistent model that reproducesboth the photometry and the early and late time spectrawithin the limitations of the modelling framework. Recentwork by Ashall & Mazzali (2020) focused on how changes inthe model parameters, such as v ph , L ph , and M ej can alter afitted synthetic spectrum and found that modelling both thephotospheric and nebular phase spectra results in approx-imately 5–10% error bars for both the E k and M ej . Theyalso suggested that a well fitted spectrum seems to prefera single combination of L ph and v ph with a synthetic spec-trum deviating from the fit with a 5-10% change in eitheror both the L ph and v ph .Using the modelled ejecta mass of 1.5 ± (cid:12) , we canfirst consider the low mass (i.e. M ZAMS ≤
22 M (cid:12) ) modelsfrom Woosley et al. (1993, 1995); Woosley & Weaver (1995).The M ZAMS models that best reproduce a 1.2–2.1 M (cid:12)
COcore are those in the 16–20 M (cid:12) range. These models are alla result of single star evolution. For the same model set, a M ZAMS >
35 M (cid:12)
Wolf–Rayet stage star has mass loss thatproduces CO cores with a narrow final mass range of ∼ (cid:12) . Pols & Dewi (2002) find a much higher CO core massfor the same mass range, as the resulting CO core masses arehighly dependent on the Wolf–Rayet stage mass loss ratesused (Yoon 2017).If we consider that the progenitor is a He star that hasevolved in a binary, such as those generated by Woosley(2019) and exploded in Ertl et al. (2020), we can find masscases where its possible that the resulting He envelope canbe lost. In particular, He stars of masses 3-5 M (cid:12) , reflectinga M ZAMS of 15-20 M (cid:12) , were found to have either a rapid Heenvelope expansion that could transfer mass or depending onthe choice of mass loss rates, could lose their He envelopesthrough stellar winds. The CO core masses for this range(1.3-2.7 M (cid:12) ) also matches the model derived in this work.
MNRAS , 1–15 (2021)
N2017ein The explosion properties of these models in Ertl et al. (2020)are within the range of our modelled E k and synthesised M Ni as well, but their E k and M Ni relation is not well constraineddue to approximations taken in the production of Ni. Inaddition, “off the shelf” SNe models often do not replicatethe spectra and photometry of observed SNe, so additionalcare should be taken.As mentioned previously, the progenitor properties de-termined by Van Dyk et al. (2018); Kilpatrick et al. (2018);Xiang et al. (2019) suggests a massive star with an M ZAMS ∼ (cid:12) , that with reasonable assumptions results in a4-8 M (cid:12) ejecta mass. This is at odds with the approximatemodelling methods used in those works that find an M ej closer to 1-2 M (cid:12) . In addition, our modelling also favours alow M ej of 1.6 ± (cid:12) as well. This is not the first timea contradiction between an estimated progenitor mass de-rived from pre–supernova imaging and modelling as arisen.The nebular phase of SN 2007gr was modelled by Mazzaliet al. (2009) to have ∼ (cid:12) of ejecta below 5000 km s − withan estimated explosion energy of 1 foe. Other estimates forSN 2007gr give an M ej of 2–3.5 M (cid:12) by Valenti et al. (2008)and ∼ (cid:12) from Drout et al. (2011), both with a sim-ilar energy range of ∼ (cid:12) as well. Maund& Ramirez-Ruiz (2016) estimates a much higher progenitormass of 40 M (cid:12) by associating the progenitor with nearbystellar populations although with SN 2007gr, no object wasdetected in the pre–supernova images.The pre–supernova imaging is limited to two Hubbleimages and Kilpatrick et al. (2018) and Xiang et al. (2019)show a slight offset in the position of the compact sourceand the supernova. While this offset is well within the errorbounds in the methods used, a combination of this and thecontradictory modelling results may suggest that the pro-genitor is instead a faint star within the line of sight of thecompact source. Follow up Hubble imaging by other groupsis planned and would determine if the compact source re-mains after SN 2017ein dims.An alternative explanation is to assume that the pro-genitor star is a massive star or in a massive binary thatmatches the pre–supernova imaging and is stripped of allH/He resulting in 4–8 M (cid:12) of ejecta at the point of collapse.At collapse, a significant fraction of this material forms amassive remnant with the explosion still ejecting 1-2 M (cid:12) ofmaterial. This would allow both the modelling in this workand the pre–supernova imaging to be correct. The resultingremnant mass would be in the range of 2–6 M (cid:12) , which isin the range of observed black hole x-ray transients (Wik-torowicz et al. 2014) and within some theoretical ranges formassive stars, depending on mass loss and binary/single starevolution (Fryer et al. 2012). Van Dyk et al. (2018); Kil-patrick et al. (2018); Xiang et al. (2019) all consider bothbinary/single star evolution as a possible candidate. Thisexplanation is partially fine tuned, as it arbitrarily requiresa particular black hole mass to form at collapse for bothresults to work together. Ni Mass
Approximately ∼ (cid:12) of Ni was required in the photo-spheric models with 0.08 M (cid:12) required in the nebular model.Given the estimated error in both the observational data and the modelling, a difference of 0.02 M (cid:12) is reasonable. OtherSNe modelled using a combination of both photospheric andspectral methods show a soft correlation between Ni massand E k with lower Ni masses favouring lower ejecta masses(Mazzali et al. 2017). Ni masses found from photometricmethods typically find similar results (Drout et al. 2011;Lyman et al. 2016; Prentice et al. 2019). The most notableof these is SN 1994I, discussed previously, which is estimatedto have a similar M ej of 1-2 M (cid:12) , an E k of ∼ Nimass of ∼ (cid:12) , with some dependence on the reddeningassumed.If we compare the photometry and spectra of SN 2007grto that of SN 2017ein, we find similarities at both early andlate epochs, excluding the latetime drop in the r -band. Maz-zali et al. (2009) used the nebular phase spectra of SN 2007grand estimated a total M ej of 1–1.5 M (cid:12) . Several other esti-mates for SN 2007gr are summarised in Van Dyk et al. (2018)but Drout et al. (2011) uses a multiband fit and gets a similarmass and an E k < E k /M ej ratio lessthan 1, similar to what we have found for SN 2017ein, whichexplains the similarity in spectra. This similarity allows us toapproximate the NIR contribution of SN 2017ein in the totalobserved flux. The addition of this flux increases the peakluminosity by approximately 10–20%. This requires a slightincrease in Ni mass in the explosion model, from 0.08 to0.1 M (cid:12) , slightly different from the nebular model. The lightcurve from the synthetic model was still too bright, but fallswithin the observational error estimates and the 5-10% miss-ing UV flux not considered in the other light curves.
We note in Section 3 and in Fig 2 that the late time photom-etry at ∼
200 days after t exp shows a larger magnitude dropin the r -, i -, and z -bands post 150 days, than in the g -band.This additional drop results in the bolometric light curvenot following a linear decay as seen in other Ni poweredSNe (Fig. 3).As mentioned in Section 5.8, the first nebular spectrummodel can be powered by a similar mass of Ni to that ofthe early light curve, but the next two phases show a dropin flux that is inconsistent with the initial model unless amultiplicative factor is included to the total flux. In the nextfew subsections we discuss possible explanations to explainthis drop.
The reduction of overall flux seen in the nebular model canbe explained by removing mass from the model between thefirst and final nebular phase epochs. This reduction in massresults in less material being heated and therefore less overallflux for the entire wavelength range. Using accretion as a pri-mary energy source is often used to explain super luminousevents with broad early light curves, of which SN 2017ein hasneither. If we consider the semi–analytic model for accretionpowered SNe found in Dexter & Kasen (2013), we can assign Note, it is currently suspected that the use of ‘Arnett’s rule’ forSE-SNe may lead to a ∼
50% overestimate in M Ni (e.g., Woosleyet al. 2020).MNRAS000
50% overestimate in M Ni (e.g., Woosleyet al. 2020).MNRAS000 , 1–15 (2021) J. J. Teffs the luminosity from accretion to only an arbitrary fractionof the total luminosity, with the majority of the luminosityfrom a Ni decay model. A fit in this manner would see anyfallback that occurs soon after the explosion be of low mass,low accretion rate, or have a very low efficiency of energytransfer; all of which would only be needed to add to thetotal luminosity 100 days after peak. Given the 100 days ofmissing data, a fit of this nature is arbitrary and fine tuned.The other alternative is that the fallback only occurs atsome late time (t >
50 days). This may be induced throughlate time CSM interaction which produces a strong enoughreverse shock to cause the innermost material to fallback tothe remnant (Dexter & Kasen 2013) or some other denseenough material. If this did occur, the material would havehad to been ejected many years prior to the collapse for itto be at such a distance from the star. However, there is noevidence of any CSM interaction in the spectra nor the lightcurve, unless it occurred in the 100 days when the event wasbehind the sun, but this would be an unlikely convenience.
As mentioned in Section 6.4.1, late time CSM interactioncould generate fallback and is thought to be a common en-ergy source for superluminous SNe or those with long lastinglight curves. The typical conditions used to suggest CSMinteraction are not found in either the light curve or thespectra. Given the drop in bolometric flux at day 150, theinteraction phase would need to occur and stop during the100 days the SN was not observed, and the drop we see isthe fall of the light curve towards a Ni decay curve.A magnetar as a primary or secondary energy sourceis invoked when the Ni mass required is too high or thelight curve is broad and long lasting. Both our light curvecode and semi-analytic models for Ni decay as a primaryenergy source reproduce the early phase quite well withoutrequiring significant amounts of synthesised Ni. Given thatonly the late time ( t >
140 d) shows deviation from atypical Ni decay model, a magnetar model would have toonly show evidence in this late phase, or have a turnoff pointclose to day 140 which is difficult to explain.
Allowing for a time dependant γ –ray opacity can reduce thetotal flux of the later two epochs that matches the multi-plicative factor. This would also alter the bolometric lightcurve as less flux is trapped. However, we know of no mech-anism that can arbitrarily change the γ –ray opacity over thetime span of a month. In this work, we model the light curve and the photosphericand nebular phase spectra to find a self consistent model forSN 2017ein. This model has an M ej of 1.6 ± (cid:12) , an E k of 0.9 ± M Ni of 0.09 ± (cid:12) .These param-eters are required to reproduce the narrow lined spectra andcompare favourably to a progenitor mass of 16–20 M (cid:12) . Thedrop in the late time photometry and nebular flux is unex-plained using our models, but the lack of spectroscopic data at λ > (cid:12) range,depending on a single or binary star evolution or a compactcluster. Under reasonable assumptions for mass loss and evo-lution, this M ZAMS results in an M ej of 4–8 M (cid:12) . This is astrong contradiction between the modelled results and theobserved estimations.The evidence from the SN itself favours the model prop-erties found in this work. As the progenitor and ejecta massincrease, the required binding energy that results in a suc-cessful explosion typically increases. The narrow lines andmeasured line velocities do not favour high energy models.High mass events also typically have broader light curves,which SN 2017ein also does not show. Similarly, as the E k and M ej increases, the Ni mass synthesised typically in-creases. The Ni mass in this work does not match that ofhigh energy and mass events. These results are all contra-dictory if one assumes a massive progenitor and a resultinglarge M ej .The pre–supernova observations show a slight offset inthe supernova position and that of the point source. This off-set is not significant, but combined with the contradictoryresults regarding explosion properties suggests the likelychance that the progenitor is not associated with the pointlike source and is a faint object within the line of sight. Ex-otic situations, such as a massive remnant with a low massejecta could link the two results, but is a fine tuned mecha-nism with weak explanation. Further Hubble imaging afterthe SN 2017ein fades will hopefully solve this problem. ACKNOWLEDGEMENTS
JT is funded by an STFC grant. CA is supported byNASA grant 80NSSC19K1717 and NSF grants AST-1920392and AST-1911074. SJP is supported by H2020 ERC grantno. 758638. The Liverpool Telescope is operated on the is-land of La Palma by Liverpool John Moores University inthe Spanish Observatorio del Roque de los Muchachos of theInstituto de Astrofisica de Canarias with financial supportfrom the UK Science and Technology Facilities Council.
DATA AVAILABILITY
Data will be made available on the Weizmann In-teractive Supernova Data Repository (WISeREP) athttps://wiserep.weizmann.ac.il/.
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