Enhanced mass-loss rate evolution of stars with ≳18 M ⊙ and missing optically-observed type II core-collapse supernovae
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Enhanced mass-loss rate evolution of stars with & M ⊙ and missing optically-observed type II core-collapsesupernovae Roni Anna Gofman, Naomi Gluck, and Noam Soker
1, 3 Department of Physics, Technion, Haifa, 3200003, Israel; [email protected]; [email protected] Department of Physics, Stony Brook University, New York, United States; [email protected] Guangdong Technion Israel Institute of Technology, Shantou 515069, Guangdong Province, China
ABSTRACTWe evolve stellar models with zero-age main sequence (ZAMS) mass of M ZAMS & M ⊙ under theassumption that they experience an enhanced mass-loss rate when crossing the instability strip at highluminosities and conclude that most of them end as type Ibc supernovae (SNe Ibc) or dust-obscuredSNe II. We explore what level of enhanced mass-loss rate during the instability strip would be necessaryto explain the ‘red supergiant (RSG) problem’. This problem refers to the dearth of observed core-collapse supernovae progenitors with M ZAMS & M ⊙ . Namely, we examine what enhanced mass lossrate could make it possible for all these stars actually to explode as CCSNe. We find that the mass-loss rate should increase by a factor of at least about ten. We reach this conclusion by analyzing thehydrogen mass in the stellar envelope and the optical depth of the dusty wind at the explosion, andcrudely estimate that under our assumptions only about a fifth of these stars explode as unobscuredSNe II and SNe IIb. About 10-15 per cent end as obscured SNe II that are infrared-bright but visiblyvery faint, and the rest, about 65-70 per cent, end as SNe Ibc. However, the statistical uncertaintiesare still too significant to decide whether many stars with M ZAMS & M ⊙ do not explode as expectedin the neutrino driven explosion mechanism, or whether all of them explode as CCSNe, as expectedby the jittering jets explosion mechanism. Keywords: supernovae: general — stars: massive — stars: mass-loss — stars: winds, outflows INTRODUCTIONThe two theoretical mechanisms to power core-collapse supernova (CCSN) explosions from the gravita-tional energy that the collapsing core releases are: thedelayed neutrino mechanism (Bethe & Wilson 1985),and the jittering jets explosion mechanism (Soker 2010;or more generally the jet feedback mechanism, e.g.,Soker 2016). Each of these mechanisms in its originally-proposed form encounters some problems that requirethe addition of some ingredients.The extra ingredient that recent numerical simula-tions of the delayed neutrino mechanism introduce toovercome some of the basic problems of the original de-layed neutrino mechanism (for these problems see, e.g.,Papish et al. 2015; Kushnir 2015), is convection abovethe iron core in the pre-collapse core (e.g., Couch & Ott2013, 2015; Mueller & Janka 2015; M¨uller et al. 2017,2019). The flow fluctuations of the convective zone thatease explosion results in large-amplitude stochastic an-gular momentum variations of the mass that the newlyborn neutron star (NS) accretes. These fluctuations seem to lead to the launching of a bipolar outflow withvarying symmetry axis directions, namely, jittering jets(Soker 2019b).Indeed, the jittering jets explosion mechanism is basedon such flow fluctuations in the convective regions ofthe pre-collapse core or envelope (Gilkis & Soker 2014,2015; Quataert et al. 2019). The spiral standing ac-cretion shock instability (SASI) and other instabilitiesbehind the stalled shock at about 100 km from the newlyborn NS amplify these fluctuations (for the physics ofthe spiral SASI see, e.g., Blondin & Mezzacappa 2007;Iwakami et al. 2014; Kuroda et al. 2014; Fern´andez2015; Kazeroni et al. 2017). However, results of nu-merical simulations that find no stochastic accretiondisks around the newly born NS brought to the recog-nition that neutrino heating plays a role in the jitteringjets explosion mechanism (Soker 2018, 2019a). In arecent study, Soker (2019b) analyses three-dimensionalhydrodynamical simulations of CCSNe and concludesthat both neutrino heating and accretion of stochasticangular momentum operate together to launch jitteringjets that explode CCSNe.One of the places where the delayed neutrino mech-anism and the jittering jets explosion mechanism dif-fer from each other is the prediction of the outcomeof stars with zero age main sequence (ZAMS) massof M ZAMS & M ⊙ . According to the delayed neu-trino mechanism for most of the masses in that rangethe core-collapses to form a black hole in a failed su-pernova, i.e., there is no explosion (e.g., Fryer 1999;Horiuchi et al. 2014; Sukhbold et al. 2016; Ertl et al.2016; Sukhbold, & Adams 2019; Ertl et al. 2019), butrather only a faint transient event (Lovegrove & Woosley2013; Nadezhin 1980). According to the jittering jets ex-plosion mechanism, on the contrary, there are no failedCCSNe, and all of these stars do explode, even if thecollapsing core forms a black hole. According to thejittering jets explosion mechanism when a black holeis formed the outer core material and then the enve-lope gas contains enough stochastic angular momentum(e.g., Gilkis & Soker 2014, 2015; Quataert et al. 2019)to launch jets and set an energetic explosion, up to E exp > erg (Gilkis et al. 2016).These different predictions of the two explosion mech-anisms relate directly to the so-called red supergiant(RSG) problem (Smartt et al. 2009), referring to thefinding that the observed relative number of progenitorsof CCSNe II with ZAMS masses of M ZAMS & M ⊙ ismuch lower than their relative number on the main se-quence (e.g., Jennings et al. 2014; Williams et al. 2014;for a review see, e.g., Smartt 2015). Smartt (2015) ar-gues in his thorough review of the ‘red supergiant prob-lem’ that it is consistent with the claim of the delayedneutrino mechanism that most stars of M ZAMS & M ⊙ collapse to form black holes with no visible supernovae,but possibly a faint transient event. Adams et al. (2017)suggest that the star N6946-BH1 that erupted in 2009(Gerke et al. 2015) was a failed SN event of a progenitorof ≈ M ⊙ . Kashi & Soker (2017) provide an alterna-tive interpretation to that event based on a transientevent (intermediate luminosity optical transient–ILOT)that was obscured by dust in the equatorial plane thathappens to be along our line of sight.We do note that there are claims for massive pro-genitors of some CCSNe, e.g., a progenitor of the typeIIn SN 2010jl of mass M ZAMS & M ⊙ (Smith et al.2011), and a possible SN Ic progenitor with a mass of M ZAMS & M ⊙ (Van Dyk et al. 2018).One possible explanation to the missing massiveprogenitors of CCSNe II might be an obscurationby dust (e.g., Walmswell, & Eldridge 2012), but oneshould properly calculate dust extinction in CCSNe(Kochanek et al. 2012). Jencson et al. (2017) claim that if the two events theystudied in the infrared (IR) are CCSNe, then-currentoptical surveys miss &
18% of nearby CCSNe. In amore systematic study Jencson et al. (2019) find nineIR bright transients, and estimate that 5 of these eventsare dust-obscured CCSNe (probably obscured by dustyclouds in the host galaxy). They further estimate thatoptical surveys miss ≈
40% (the range of 17 − M ZAMS & M ⊙ , implying that these starsalso explode as CCSNe.The obscured CCSNe that Jencson et al. (2019) studyare most likely obscured by dusty clouds in the hostgalaxy, rather by a dust circumstellar matter (CSM).We here raise the following question. What enhancedmass loss rate during the RSG could make the CSMof some RSG with M ZAMS & M ⊙ sufficiently denseto obscure their explosion? We also add the relatedquestion of whether our assumed enhanced mass lossrate might bring some RSG to explode as SNe Ibc ratherthan SNe II or IIb, even if they are not obscured by theirown CSM.Yoon, & Cantiello (2010) already studied the processby which partial ionisation of hydrogen in the envelopecauses RSG stars to strongly pulsate and lose mass ata very high rate (e.g., Heger et al. 1997). They fur-ther discussed the possibility that this enhanced mass-loss rate of stars with M ZAMS & − M ⊙ mightexplain the RSG problem, by both forming an opti-cally thick dusty CSM and by removing most, or evenall, of the hydrogen-rich envelope and forming a SN oftype Ib or Ic (Ibc) progenitor. We continue the ideaof Yoon, & Cantiello (2010) but perform somewhat dif-ferent evolutionary simulations. We assume that thestars have the enhanced mass-loss rate that we requireto explain the RSG problem, when they cross the con-tinuation of the instability strip on the HR diagramwhen they are RSGs. We strengthen the claim ofYoon, & Cantiello (2010) that such an enhanced mass-loss rate might account for RSG problem, allowing allstars to explode as CCSNe. There are other studiesthat include enhanced mass loss rate of stars during theRSG phase, but they do not compare directly to theRSG problem (e.g. Meynet et al. 2015).In Section 2, we describe our numerical setup, andin Section 3 we present the calculation of evolution-ary tracks under the assumption that RSG stars thatcross the instability strip have very high mass-lossrates. In Section 4 we study the enhanced mass lossrate that would be necessary to obscure stars with18 M ⊙ . M ZAMS . M ⊙ , and determine the role ofthis enhanced mass-loss rate in bringing more stars of M ZAMS & M ⊙ to explode as types IIb or Ib CCSNe.We summarise our main conclusions in section 5. NUMERICAL SET UP2.1.
Stellar evolution
We evolve stellar models with ZAMS mass in therange of M ZAMS = 15 − M ⊙ using Modules for Ex-periments in Stellar Astrophysics ( mesa , version 10398Paxton et al. 2011, 2013, 2015, 2018). Each model hasan initial metalicity of Z = 0 .
02, and evolves from thepre-main sequence stage until pre-core-collapse, whichwe take to be the first time the iron core has an inwardvelocity ≥ α MLT = 1 . α sc = 1 . .
335 (Brott et al. 2011).We apply wind mass-loss with the mesa ”Dutch”mass-loss scheme for massive stars which combines re-sults from several papers and is based on Glebbeek et al.(2009). For T eff > K and surface hydrogenabundance larger than 0 . . T eff < K mass-loss is treated according tode Jager et al. (1988).We break up the evolution to two parts: inside the in-stability strip and outside it. Figure 1 in Georgy et al.(2013) shows the Hertzsprung Russell (HR) diagramfor non-rotating models with an instability strip in therange of 2 . log ( L/L ⊙ ) . . . log ( T eff [K]) . .
8. From that figure we approximate that the instabil-ity strip to be in the region where64 . log (cid:18) LL ⊙ (cid:19) + 16 . (cid:18) T eff [K] (cid:19) . . (1)We extend the instability strip from Georgy et al. (2013)to higher luminosities, by a linear continuation of thetwo boundaries of the strip on the HR diagram. Laterwe show that for the stars we evolve here, the center ofthe instability strip continuation is at about an effectivetemperature of log( T eff ) ≃ .
6. This is about the samelocation on the HR diagram of the pulsating stars thatYoon, & Cantiello (2010) study. As Yoon, & Cantiello(2010) discuss, the pulsations are driven by partial ioni-sation of hydrogen in the envelope. We further note thatYoon, & Cantiello (2010) assume that these stars havepulsational-driven enhanced mass loss rate. Althoughthey did not show it from first principles, we accept here their assumption, but consider both moderate and largemass loss rate enhancement (see section 2.2).While the star is outside the strip we set the mass-loss scaling factor to f ml = 0 . f ml = 0 .
8. The other 2 cases have enhanced mass-lossinside the instability strip. Once the model enters thestrip from right to left we increase the mass-loss scalingfactor to f ml = 2 in one case and to f ml = 10 in another.As MESA is a numerical simulation code based on agrid (shells) and time steps, we should show that there isa convergence, i.e., no dependence on the grid resolutionfor the value we use (e.g. Farmer et al. 2016). In
MESA there is a parameter “max dq” that sets the maximummass in a shell, expressed as a fraction of total massin the grid. We compared the default value of max dq=0 .
01 that we use in all our cases, to several cases that wesimulated with higher resolution of max dq= 10 − . Wefound no differences in the pre-collapse characteristicswe study in this paper.The timestep control parameter ”delta lg XH cntr min”sets the time step as hydrogen is consumed in the core.Setting small time steps assists in calculating the pas-sage from the ZAMS to the terminal-age main sequence.Similar parameters control the timestep for every sig-nificant evolution stage. We reduce the timesteps atthese phases by setting these parameters to be 10 − forhydrogen and helium (as in, e.g. Farmer et al. 2016),and 10 − for heavier elements.2.2. Enhanced mass loss rate
Our question in this study is as follows.
By what fac-tor should we increase the mass loss rate during the RSGphase to explain the RSG problem?
We examine heretwo mass loss rate enhancement factors (section 2.1).We further assume, as we discussed above, that the en-hanced mass loss rate occurs only when the star crossesthe instability strip from right to left, i.e., when it isvery bright.We emphasise that there is no observational justifica-tions for this enhanced mass loss rate (e.g., Beasor et al.2020). As we mention in section 1, based on theirobservations of dust-enshrouded CCSNe, Jencson et al.(2019) estimate that ≈ −
64% of all CCSNe are dust-enshrouded. In most (or even all) cases the obscuringdust is of ISM origin. Even if in some cases CSM ob-scures the CCSN, it might be that in the enhanced massloss rate of the progenitor was due to binary interaction.We rather raise here a theoretical question: Whatshould the enhanced mass loss rate of single RSG starsbe for single stars to explain the RSG problem? We findbelow (sections 3, 4) that to form a significant numberof enshrouded CCSNe we need to increase the mass lossrate of single stars in the instability strip by a factorof about 10 or somewhat larger (namely, f ml ≃ f ml ≃
10, but we rather claimthat if single stars form some dust-enshrouded CCSNe, then the enhancement factor should be about 10 (herewe take an enhancement factor of 12.5).From the theoretical side, we base our prescription forenhanced mass-loss rate in the instability strip on the re-sults of Yoon, & Cantiello (2010) who argue that RSGstars lose mass at a very high rate when they are insidethe instability strip on the HR diagram. There can betwo basic regimes of the mass loss rate enhancement be-cause of pulsations in the instability strip. In the firstthe effect of the pulsations is linear, like the decreasein gravity and temperature as the envelope expands tomaximum radius in the pulsation cycle. In this case themass loss rate increases by a moderate factor, which wehere take to be 2.5 (for f ml = 2). In the other regimethe effect is non linear. For example, the lower tem-perature together with pulsation-driven shocks in theenvelope lead to substantial extra dust formation (e.g.,Goldman et al. 2017), with a large impact on the massloss rate. Here we take the increase of the mass lossrate in the non-linear regime to be by a factor of 12.5(for f ml = 10). As we discuss below, already in thelinear regime we find a non negligible influence of theenhanced mass loss rate, that becomes quite significantin the non-linear regime.The above discussion shows that from theoretical con-siderations the factor of f ml = 10 is arbitrary, as we haveno derivation of the mass loss rate increase due to theinstability. However, as we explain above, we need thefactor of f ml ≃
10 to make sure that there is a signifi-cant number of dust-enshrouded CCSNe from single-starevolution.We note that Meynet et al. (2015) conduct RSG evo-lution simulations where they increase the mass lossrates by a factor of 10 and 25 relative to the standardmass-loss rates during the RSG phase. We return tothe study of Meynet et al. (2015) in section 3. Georgy(2012) also enhances the RSG mass loss rate, by a factorof 3 and 10, but for lower masses than what we study, i.e., 12 − M ⊙ . Therefore, our enhanced mass loss ratefactor of up to 12.5 is not an extreme in such studies.Finally, we note the following new results by Beasor et al.(2020). Beasor et al. (2020) study the mass loss rate ofRSGs in two stellar clusters, and conclude that themass loss rates they find are up to a factor of 20 lowerthan what current evolutionary models use. If the re-sults of Beasor et al. (2020) hold by future studies, itwould imply that to reach the desired mass loss ratethat leads to dust-enshrouded CCSNe we would haveto increase the mass loss rate relative to the value thatBeasor et al. (2020) infer by a factor of ≈
100 ratherthan by a factor of ≃
10. Namely, during most of theevolution the mass loss rate is low, as suggested byBeasor et al. (2020), but some progenitors of CCSNesuffers very high mass loss rate just before explosiondue to enhanced mass loss rate, or from binary interac-tion. Specifically, we find below that for single star toexplain the RSG problem, in cases of obscured CCSNethe average mass loss rate hundreds of years before ex-plosion should be ˙ M & × − M ⊙ yr − . There is aclear need for further observations and theoretical studyto explore the full behavior of mass loss from RSG. RESULTSIn this section, we focus mostly on the effect of themass-loss rate inside the instability strip on the pre-collapse state of the stellar models. We evolve over40 stellar models up to the point of core-collapse with16 different values of ZAMS mass for each of the threemass-loss parameters, f ml , that we set in the instabilitystrip.Fig. 1 shows the evolution of some models on theHR diagram, while for others we show only the finalposition. We also present the instability strip, includ-ing our extension to high luminosity. It is evident thatby increasing the mass-loss rate when the star is insidethe instability strip (extension) and crosses from rightto left, the pre-collapse effective temperature of modelsthat leave the strip increases.Moreover, models with M ZAMS & M ⊙ and en-hanced mass-loss rate in the instability strip lose theirentire hydrogen envelope, as we show for in Fig. 2, andbecome hot progenitors of SNe Ib, i.e., Wolf-Rayet (WR)stars. Fig. 2 shows that stars with M ZAMS & M ⊙ and enhanced mass-loss rate do not have hydrogen andhelium in their envelope at explosion; this is becausethese stars loses there entire envelope by that time.These stars will explode as SNe Ib because they havea core helium layer of ≈ M ⊙ . Other models losemost of their hydrogen envelope but still are left with0 . M ⊙ . M H , cc . . − M ⊙ of hydrogen in there Figure 1.
The evolution track of stellar models with ZAMSmasses in the range of 15 − M ⊙ from ZAMS to core-collapseon the HR diagram. The pre-collapse point of each model ismarked by a coloured pentagram for odd masses and a blackmarker for all other masses. The instability strip and itsextension according to equation (1) is marked with two blacklines. The panels have different mass-loss scaling factors, f ml as given in the inset when a star crosses the instability stripfrom right to left in the grey area of the strip. Figure 2.
The final envelope mass of hydrogen (blue circles)and helium (orange triangles) as a function of the ZAMSmass. The three panels are for different mass-loss rate scalingfactor, f ml , inside the instability strip as the star crosses fromright to left in the HR diagram. Although the helium massin the envelope of the most massive three models in the lowertwo panels is zero, there is a helium mass of about 2 M ⊙ inthe core. Therefore, these will explode as SNe Ib. envelope at core-collapse; these become the progenitorsof SNe IIb. We explain the different groups and theirimplications on the RSG problem with more detail insection 4.Now we turn to examine the possibility of obscuredCCSNe. We assume that the dense wind efficientlyforms dust and calculate its optical depth. We con-sider the wind section from an inner radius of R in =0 . − × cm, as we take the supernova to destroydust at inner radii (calculating the exact radius requiresto follow the explosion and its radiation, as well as thecollision of the fastest ejecta with the dust). We alsotake a density of ρ ( r ) = ˙ M / πv w r , where ˙ M is themass-loss rate and v w is the wind velocity. We also takethe opacity in the V-band to be κ V ≈
100 cm g − (e.g.,Kochanek et al. 2012), and derive τ V = R out Z R in κ V ρ d r ≃ ˙ M − M ⊙ yr − ! (cid:18) R in cm (cid:19) − × (cid:18) κ V
100 cm g − (cid:19) (cid:16) v w
10 km s − (cid:17) − , (2)where in the second equality we assume constant mass-loss rate and wind velocity and that R out ≫ R in .To derive a more accurate expression we take themass-loss rate as function of time from our numericalresults. The density, ρ ( r ), at radius r corresponds to amass-loss, ˙ M ( t ), at time t = t cc − r/v w , where t cc is thetime of core-collapse (explosion). We take v w constantwith time according to the following prescription. Wesimply assume that when the mass-loss rate in the stripis higher, the wind velocity is lower even after the starleaves the instability strip. For the default mass-lossrate, f ml = 0 .
8, we take the wind velocity to be the es-cape velocity from the star at core-collapse, v esc , cc . Thewind velocity is then v w = v esc , cc (cid:18) f ml . (cid:19) − . (3)Taking r = v w ( t cc − t ) the expression for the opticaldepth is τ V = t in Z t out κ V ˙ M ( t )4 πv ( t cc − t ) d t. (4)We present the wind velocity according to equation(3) for the different models in the top row of Fig. 3.In the second row we present the average mass-loss ratein the last 100 years before explosion, and in the threebottom rows we present the optical depth according toequation (4) for κ V = 100 cm / g, and for three differentvalues of the inner radius R in = 0 . , , × cm. Thedifferences in the optical depth between the three valuesof the inner radius are very small, and in what followswe will refer to the numbers for R in = 10 cm. Wediscuss the implications of the optical depth in section4. Another relevant quantity is the time after the modelexists the instability strip and until explosion, which wepresent in Fig 4.Although Meynet et al. (2015) do not consider theRSG problem, it is beneficiary to compare some of ourresults with theirs. Meynet et al. (2015) enhance themass loss rate by a factor of 10 or 25 when the star is a RSG, which they take to be when the effective tempera-ture is log( T eff /K ) < .
7. Namely, they do not consideran instability strip, but rather they enhance the massloss rate whenever the star has a low effective temper-ature. They chose these factors somewhat arbitrarily.Another difference is that we use an initial metalicity of Z = 0 .
02 while they take Z = 0 . M ⊙ stellar mod-els of Meynet et al. (2015) do not have an effective tem-perature larger than 10 K at explosion. We also findthat our 20 M ⊙ do not reach high temperatures at ex-plosion. Their non-rotating model of 25 M ⊙ reaches atemperature of log( T eff /K ) ≃ . . . M ⊙ .Our 25 M ⊙ model ends with an effective temperatureof log( T eff /K ) ≃ . M & M ⊙ , we obtain dif-ferent results from those of Meynet et al. (2015). Theynote that their prescription forms no WC stars (WC areWR stars with strong carbon and oxygen emission lines).We, on the other hand, account for WR stars, and pos-sibly for WC stars. Our results are compatible with thesuggestion of Shenar et al. (2019) that traditional evo-lution codes might underestimate mass loss rates duringthe RSG phase. Shenar et al. (2019) based their sugges-tion on their claim that, at least in the Small MagellanicCloud, the binary evolution channel does not dominatethe formation of WR stars.Overall, our results and those of Meynet et al. (2015)have some similarities, although they are not identical.This is expected because the enhanced mass loss rateprescription is very different. In any case, the results donot contradict each other. The most important similar-ity is that both studies conclude that with an enhancedmass loss rate a significant fraction of massive stars ex-plode as CCSNe while they are hotter than RSGs. Thisimplies that they might not be SNe II and not even SNeIIb. IMPLICATIONS TO THE RSG PROBLEMIn our search for the mass loss rate that would be nec-essary to explain the RSG problem for single stars, weincreased the mass loss rate in the extension of the in-stability strip. We described the results of stellar evolu-tion simulations in section 3. This introduction of highmass-loss rate in the extension of the instability stripsplits the stars that enter the strip from right to leftto four groups. (1) Stars that explodes while still suf-fering a very high mass-loss rate and are likely to beIR-bright but visibly faint. These stars fulfil our re-quest that the enhanced mass loss rate that we intro-duce forms a CSM that obscures the exploding stars.
Figure 3.
From top row to bottom and in logarithmic scales: The wind velocity according to equation (3), the average mass-loss rate in the last 100 yr before core-collapse, and the optical depth of the dust as given by equation (4) with opacity of κ V = 100 cm g − and for three values of the inner radius, R in = 0 . , , × cm; the dashed black line marks: τ V = 1.We calculate each quantity for the 3 instability strip mass-loss scaling factors f ml = 0 . f ml = 2 (middle column),and f ml = 10 (right column). Figure 4.
The time of explosion after exiting the instabilitystrip as a function of ZAMS mass. (2) Stars that leave the strip and explode as SNe II. (3)Stars that leave the strip and explode with hydrogenmass of 0 . M ⊙ . M H , cc . . − M ⊙ and form SNeIIb. (4) Stars that lose all their hydrogen and explodeas SNe Ib. We infer the mass range of each group fromFigs. 2 and 3.Because of the large uncertainties in mass-loss rates,boundaries of the extension of the instability strip, anda possible influence by weak binary interaction (ourscheme does not treat strong binary interaction), wetake the boundaries between the groups as whole solarmass, beside one case. We basically give the boundariesbetween the above groups for the minimum mass lossrate enhancement that we found to be necessary to ac-count for the RSG problem. Gordon et al. (2016) arguethat 30% −
40% of the yellow supergiants that they studyin the galaxies M31 and M33 are likely in a post-RSGphase. The stars that leave the instability strip in oursimulations (groups 2-4 above) might account in part forthese yellow supergiants.4.1.
Dust enshrouded IR bright CCSNe
From Fig. 3 we see that for f ml = 10 in our mass-lossscheme this group comprises stars with initial masses of M S , IR ≈ . − M ⊙ . We emphasise that the size of theinstability strip in these high luminosities is uncertain,and the range might be somewhat larger. As well, ourscheme refers only to single stars and those that suffera weak binary interaction. Stars with a strong binaryinteraction require different calculations. In any case,this range of stellar mass ( M S , IR ≈ . − M ⊙ ) islarge enough for us to claim that the values of f ml = 10(a factor of 12.5 mass loss rate enhancement) is aboutthe minimum value that is required for the mass lossrate enhancement to possibly explain the RSG problem(or part of it).We assume here and below that about half of the starssuffer only weak or no binary interaction. For an ini-tial mass function (IMF) of dN ∝ M − . dM , we findthis group to account for F S , IR ≈
2% of all CCSNe.With weak binary interactions that enhance mass-lossand somewhat wider instability strip, this group mightbe ≈
5% of all CCSNe. By a weak binary interaction,we refer to a weak to moderate spin-up by a compan-ion or a weak tidal interaction. Our scheme does notinclude strong binary interactions where a companiondetermines the mass-loss rate, e.g., like a massive com-panion that enters a common envelope.In discussing an explosion within a dust shell, wefollow Kochanek et al. (2012) in treating obscuring bydust. They discuss several important processes, such asthe presence of one type of dust, silicate (for massivestars that we study here) or graphitic, and the emissionby the dust shell. Since the dust shell is unresolved, itsemission adds to the luminosity mainly in the IR. Theoptical depth in the visible of wind with constant ve-locity v w and a constant mass-loss rate of ˙ M is givenby equation (2). In the lower row of Fig. 3 we presentthe optical depth in the V-band for a dusty wind thattakes into account the mass-loss rate variation in ourstellar evolution simulations (equation 4 from an innerradius R in = 10 cm), but takes a constant wind veloc-ity (equation 3).Since the shell is not resolved, not all the photonsin the visible that are scattered by dust are lost fromour beam, and the decrease in the visible light is about a factor of few ×
10 for τ V = 5, or more than threemagnitudes in the visible (Kochanek et al. 2012).Shortly after the explosion the SN ejecta collides withthe dense wind, the CSM. The interaction of the ejectawith the CSM converts kinetic energy to radiation. Wescale the efficiency of this process to be ǫ i = 0 . v s = 4000 km s − (e.g., Fox et al. 2013, 2015) L i = ǫ i ˙ M v v w = 5 . × ˙ M − M ⊙ yr − ! × (cid:16) v s − (cid:17) (cid:16) v w
10 km s − (cid:17) − (cid:16) ǫ i . (cid:17) L ⊙ . (5)This corresponds to a bolometric magnitude of about −
12, fainter by several magnitudes relative to typicalCCSNe. In addition, the dust that still resides at largedistances will make the SN redder, and so the visualmagnitude will be lower even relative to typical CCSNe.Such events might be classified at first place as inter-mediate luminosity optical transients (ILOTs), ratherthan CCSNe. But they are fainter in the visible andtherefore will be detected in much lower numbers thanCCSNe that are not enshrouded by a dense dusty wind.We conclude that the dusty wind reduces the lumi-nosity in the visible by several magnitudes. Present ob-servations can still detect such type II CCSNe, but atmuch smaller numbers than their occurrence rate. Aswe write above, these are only for stars in the initialmass range of M S , IR ≈ . − M ⊙ .4.2. Type II CCSNe
This group is of stars that have hydrogen mass at core-collapse of M H , cc & M ⊙ , and that are not enshroudedby optically thick dust. From Fig. 2 we find the uppermass of this group and from Fig. 3 its lower mass. Thesegive for the mass range of this group M S , II ≃ − M ⊙ .This mass range amounts to ≈
2% of all CCSNe, or F S , II ≈
1% of all CCSNe if we take those that do notsuffer strong binary interaction.4.3.
Type IIb CCSNe
SNe IIb are CCSNe that in the first several days havestrong hydrogen lines, but later these lines substantiallyweaken and even disappear. This results from low hy-drogen mass at explosion, about M H , cc ≃ . − . M ⊙ (e.g., Meynet et al. 2015; Yoon et al. 2017), or even upto M H , env ≤ M ⊙ (e.g., Sravan et al. 2018). SNe IIbmake f IIb , H ≃ −
12% of all CCSNe in high metallic-ity stellar populations (e.g., Sravan et al. 2018). FromFig. 2 we find that the relevant mass range for SNe IIbprogenitors in our f ml = 10 case is M S , IIb ≃ − M ⊙ .Meynet et al. (2015) also find that with their scheme ofRSG enhanced mass loss rate many stars end with lowhydrogen mass. For an IMF of dN ∝ M − . dM thisamounts to ≃ .
045 of all CCSNe. However, if about halfof these stars suffer strong binary interaction that ourscheme does not consider, the single-star and weak bi-nary interaction channels that we study here for SNe IIbcorrespond to F S , IIb ≈
2% of all CCSNe. We note thatNaiman et al. (2019) crudely suggest that the single-starchannel for SNe IIb accounts for ≈ −
4% of all CCSNe(about 20 −
40% of all SNe IIb).4.4.
Type Ib CCSNe
In the mass range we calculate here this group comesfrom stars with an initial mass of M S , Ib & −
25, aswe see from Fig. 2. Meynet et al. (2015) simulated en-hanced mass loss rate from stars up to M ZAMS = 25 M ⊙ and find that all of them maintain hydrogen. We findthis limit at M ZAMS = 24 M ⊙ . Consider that we do notuse the same mass loss rate enhancement scheme as theydo, this is not a large difference. This range amounts to ≃
20% of all CCSNe if we take the upper mass limitto be M ZAMS = 100 M ⊙ . If we consider that about halfsuffer strong binary interaction (e.g., Sana et al. 2012),the single star evolution (including weak binary interac-tions) that we study here amounts to F S , Ib ≈
10% of allCCSNe. Some of them might lose also all their heliumand lead to SNe Ic. Our finding that most, ≃ /
3, of thestars with M S , Ib &
18 form SNe Ib and possibly SNe Ic,is compatible with the finding of Smartt (2015). Theclaim of Stritzinger et al. (2020) that the progenitor ofthe SN Ib LSQ13abf had an initial mass of & M ⊙ (or & − M ⊙ in an alternative model) supports ourclaim.This group of stars adds to the role of the mass lossrate enhancement in accounting for the RSG problem.Namely, the research question of this study, which isabout the enhanced mass loss rate that is necessary toexplain the RSG problem, refers both to obscured CC-SNe and to transforming some RSG stars to progenitorsof SNe Ibc (section 1).The finding above has implications to the rate offormation of WR stars in the single-star channel.Many WR stars are observed to be single, but tra-ditional stellar evolution calculations are short in ac-counting for these WR stars as well as other proper-ties (e.g., Shenar et al. 2020). For that, some (e.g.,Schootemeijer, & Langer 2018) claim that the compan-ion in many of these systems is a low mass star thatobservations did not reveal yet. However, other stud-ies (e.g., Shenar et al. 2016) suggest that, at least inthe Small Magellanic Cloud, the binary evolution chan-nel does not dominate WR formation. Shenar et al. (2019) study WR stars and their formation in the bi-nary and single-stellar channels, and suggest that it ispossible that traditional evolution codes underestimatemass loss (mainly) during the red supergiant phase (foran earlier similar claim see Vanbeveren et al. 1998a,b.Our assumption of an enhanced mass loss rate in theupper instability strip, and the results of high fractionof SNe Ibc progenitors, are compatible with the claimof Shenar et al. (2019) of a higher mass loss rate thanwhat traditional evolution code give. SUMMARYWe are motivated by the theoretical disagreement onthe fate of star with ZAMS mass of M ZAMS & M ⊙ (section 1). For that, we examined the question of whatenhanced mass loss rate during the RSG would be neces-sary to explain the RSG problem. We noted that there isno support from observations for such a large enhancedmass loss rate factor. Therefore, we raised a theoreticalquestion. We found that we need to increase the massloss rate by at least a factor of about ten (we used afactor of 12.5 in this study) in the instability strip ofthe RSG to explain the RSG problem (or part of it).Using the numerical stellar evolution code mesa wehave simulated the evolution of 48 stellar models tothe point of core-collapse and explored the effect of anenhanced mass-loss inside the instability strip as theevolved stars cross from right to left at very high lu-minosities. Based on Yoon, & Cantiello (2010) we as-sumed an enhanced mass-loss rate as the star crossesthe instability strip from right to left at high luminosi-ties (grey area of the instability strip on Fig. 1). Ourmass-loss prescription is for single star evolution andpossibly weak binary interaction. We do not includestrong binary interaction.We concentrated on two pre-core-collapse stellar prop-erties, the stellar hydrogen mass (Fig. 2), and the opti-cal depth of the dusty wind (Fig. 3). From these prop-erties we divide the stars that enter or cross the upper(extension) instability strip to four groups with very un-certain mass boundaries between them. (1) Stars thatexplode as SNe II while they are in the strip and there-fore are enshrouded by dust (section 4.1). These haveinitial mass in the range of M S , IR ≃ . − M ⊙ . (2)Stars that leave the instability strip from the left and ex-plode as SNe II. They have M S , II ≃ − M ⊙ (section4.2). (3) Stars that leave the strip and at core-collapsehave a hydrogen mass of M H , cc . . − M ⊙ . They ex-plode as SNe IIb and have M S , IIb ≃ − M ⊙ (section4.3). (4) Stars that leave the strip and explode as SNe Iband possibly as SNe Ic. These have M S , Ib &
24 (section4.4).0In short, we have found that an enhanced mass lossrate in the instability strip (Fig. 1) by a factor of aboutten or more, helps solving the RSG problem by causingsome CCSN to be obscured by dust (group 1 above) andby causing other stars to explode as SNe Ibc (group 4above).Because the mass boundaries of the four groups arehighly uncertain, so are the fraction F S of each groupis highly uncertain. For the minimum mass loss rateenhancement that would be necessary to solve the RSGproblem, our estimated fractions of CCSNe in each ofthese four groups are F S , IR ≈ F S , II ≈ F S , IIb ≈ F S , Ib ≈ dN ∝ M − . dM witha maximum mass of 100 M ⊙ and assumed that abouthalf of the stars suffer strong binary interaction thatwe do not consider here. Therefore, our assumption ofenhanced mass-loss while in the instability strip impliesthat single star evolution brings only a fraction of η S , II ≡ F S , II + F S , IIb F S , IR + F S , II + F S , IIb + F S , Ib ≈
20% (6)of stars with M ZAMS & . M ⊙ to end as SNe II orSNe IIb that are not heavily enshrouded by dusty CSM. Smartt (2015) lists 30 progenitors of SN type II or IIbwhich all have a ZAMS mass of M ZAMS . M ⊙ . Fromthat he argues that the IMF implies that if all thesesstars explode there should be ≈
13 CCSNe of types IIand IIb with a progenitor of M ZAMS & M ⊙ . Accord-ing to our analysis (equation 6) we expect that out ofthese 13 SNe with progenitor mass M ZAMS & M ⊙ ,only ≈ − .Our main conclusion is that the statistical uncertain-ties are too large to decide whether many stars with M ZAMS & M ⊙ do not explode as expected in the neu-trino driven explosion mechanism, or whether most ofthem form SNe Ibc and obscured SNe II that are IR-bright, as expected by the jittering jets explosion mech-anism. ACKNOWLEDGEMENTSWe thank an anonymous referee for detailed and usefulcomments. This research was supported by a grant fromthe Israel Science Foundation. N.S. research is partiallysupported by the Charles Wolfson Academic Chair.REFERENCES Adams, S. M., Kochanek, C. S., Gerke, J. R., Stanek K. Z.,Dai X., 2017, MNRAS, 468, 4968Beasor, E. R., Davies, B., Smith, N., van Loon, J. T.,Gehrz, R. D., & Figer D. F. 2020, arXiv:2001.07222Bethe, H. A., & Wilson, J. R. 1985, ApJ, 295, 14Blondin, J. M., & Mezzacappa, A. 2007, Nature, 445, 58Brott, I., de Mink, S. E., Cantiello, M., et al. 2011,Astronomy and Astrophysics, 530, A115Couch, S. M., & Ott, C. D. 2013, ApJL, 778, L7Couch, S. M., & Ott, C. D. 2015, ApJ, 799, 5de Jager, C., Nieuwenhuijzen, H., van der Hucht, K. A.1988, A&AS, 72, 259Ertl T., Janka, H.-T., Woosley S. E., Sukhbold, T., UglianoM., 2016, ApJ, 818, 124Ertl T., Woosley ,S. E., Sukhbold, T., Janka, H.-T., 2019,arXiv:1910.01641 At the Symposium ”The Deaths and After-lives of Stars” (Space Telescope Science Institute,April 22-24, 2019) Smartt updated the observed num-ber of progenitors with M ZAMS . M ⊙ to 35 (https://cloudproject.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=d6217958-cb9c-4825-8005-aa3700f5dfb0).In this case 15 progenitors with a mass of M ZAMS & M ⊙ areexpected. By our analysis, only 3 of them should be type II orIIb CCSNe. Farmer R., Fields C. E., Petermann I., Dessart L., CantielloM., Paxton B., Timmes F. X., 2016, ApJS, 227, 22Fern´andez, R. 2015, MNRAS, 452, 2071Fox O. D., Filippenko A. V., Skrutskie M. F., SilvermanJ. M., Ganeshalingam M., Cenko S. B., Clubb K. I.,2013, AJ, 146, 2Fox, O. D., Smith, N., Ammons, S. M., et al. 2015,MNRAS, 454, 4366Fryer, C. L. 1999, ApJ, 522, 413Gerke, J. R., Kochanek, C. S., & Stanek, K. Z. 2015,MNRAS, 450, 3289Georgy, C. 2012, A&A, 538, L8Georgy, C., Ekstr¨om, S., Eggenberger, P., et al. 2013, A&A,558, A103Gilkis, A., & Soker, N. 2014, MNRAS, 439, 4011Gilkis, A., & Soker, N. 2015, ApJ, 806, 28Gilkis, A., Soker, N., & Papish, O. 2016, ApJ, 826, 178Glebbeek, E., Gaburov, E., de Mink, S. E., et al. 2009,A&A, 497, 255Goldman, S. R., van Loon, J. T., Zijlstra, A. A., et al. 2017,MNRAS, 465, 403Gordon, M. S., Humphreys, R. M., & Jones, T. J. 2016,ApJ, 825, 501