A Massive Star's Dying Breaths: Pulsating Red Supergiants and Their Resulting Type IIP Supernovae
DDraft version January 24, 2020
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A Massive Star’s Dying Breaths: Pulsating Red Supergiants and Their Resulting Type IIP Supernovae
Jared A. Goldberg, Lars Bildsten,
1, 2 and Bill Paxton Department of Physics, University of California, Santa Barbara, CA 93106, USA Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA
ABSTRACTMassive stars undergo fundamental-mode and first-overtone radial pulsations with periods of 100-1000 days as Red Supergiants (RSGs). At large amplitudes, these pulsations substantially modifythe outer envelope’s density structure encountered by the outgoing shock wave from the eventual corecollapse of these
M > M (cid:12) stars. Using Modules for Experiments in Stellar Astrophysics ( MESA ), wemodel the effects of fundamental-mode and first-overtone pulsations in the RSG envelopes, and theresulting Type IIP supernovae (SNe) using
MESA + STELLA . We find that, in the case of fundamentalmode pulsations, SN plateau observables such as the luminosity at day 50, L , time-integrated shockenergy ET , and plateau duration t p are consistent with radial scalings derived considering explosionsof non-pulsating stars. Namely, most of the effect of the pulsation is consistent with the behaviorexpected for a star of a different size at the time of explosion. However, in the case of overtonepulsations, the Lagrangian displacement is not monotonic. Therefore, in such cases, excessively brightor faint SN emission at different times reflects the underdense or overdense structure of the emittingregion near the SN photosphere. Keywords: hydrodynamics radiative transfer stars: massive stars: oscillations supergiants super-novae: general INTRODUCTIONPeriodic variability is prevalent in Red Supergiant(RSG) stars, and is interpreted as being a result of ra-dial pulsations (Stothers 1969; Stothers & Leung 1971;Guo & Li 2002). The mechanism driving these pulsa-tions is not fully understood, but they are thought tobe driven by a κ mechanism in the hydrogen ionizationzone with some uncertain feedback within the convec-tive envelope (Heger et al. 1997; Yoon & Cantiello 2010).Kiss et al. (2006) and Percy & Khatu (2014) identifiedperiods of a few hundred to a few thousand days withvarying stellar lightcurve morphology for RSGs in theAAVSO International Database. Such pulsations havealso been observed occurring in RSGs within the Smalland Large Magellanic Clouds (Feast et al. 1980; Ita et al.2004; Szczygie(cid:32)l et al. 2010; Yang & Jiang 2011; Yang &Jiang 2012; Yang et al. 2018), M31 and M33 (Soraisamet al. 2018; Ren et al. 2019), M51 (Conroy et al. 2018),M101 (Jurcevic et al. 2000), within HST archival data ofNGC 1326A, NGC 1425, and NGC 4548 (Spetsieri et al.2019), and within the GAIA DR2 RSG sample (Chatyset al. 2019). These works identify these RSG pulsations Corresponding author: J. A. [email protected] as consistent with radial fundamental modes and somefirst radial overtones.More luminous RSGs generally exhibit longer peri-ods and higher pulsation amplitudes, with all RSGs inM31 brighter than M k ≈ −
10 mag (log[
L/L (cid:12) ] > . m R > .
05 mag, with R-band variabil-ity around ∆ m R ≈ . ≈ a r X i v : . [ a s t r o - ph . S R ] J a n monitored are consistent with no variability, with theexception of the progenitor of the Type IIb SN 2011dh(Kochanek et al. 2017), which was variable in R-bandby 0 . ± .
006 mags per year (Szczygie(cid:32)l et al. 2012).This is not inconsistent with the near ubiquity of RSGpulsations at high luminosities, as most progenitors ob-served before undergoing Type II SNe have been on thelower end of the RSG luminosity spectrum (Smartt 2009,2015), where pulsation amplitudes are likewise gener-ally lower. However, still relatively few such events havebeen monitored, and there is an open theoretical ques-tion about how CCSN lightcurves are influenced by thepresence of progenitor pulsations.Recent work highlights that modeling of lightcurvesand photospheric velocities alone is insufficient to ex-tract progenitor characteristics from observed SNe(Dessart & Hillier 2019; Goldberg et al. 2019; Mar-tinez & Bersten 2019). A progenitor radius can providea crucial constraint, allowing to distinguish between,say, a more compact higher ejecta-mass event with ahigher explosion energy, and an event with a largerprogenitor radius, lower ejecta mass, and lower explo-sion energy. This has been done recently by creatingmatching lightcurve models for SNe with observed pro-genitor radii (e.g. Martinez & Bersten 2019), fixinga mass-radius relationship by fixing stellar evolutionparameters (such as metallicity, mixing length in theH-rich envelope, overshooting, winds) and fitting to alarge set of population synthesis lightcurve models (e.g.Eldridge et al. 2019), and in an ensemble fashion byusing a prior on the radius of RSGs to extract explo-sion energies statistically for an existing sample of IIPlightcurves (Murphy et al. 2019). Because, in reality,the progenitor radius could be affected by RSG pulsa-tions, this could lend itself to additional uncertainty inany explosion parameters recovered from SN observa-tions, especially in the case of directly using an observedprogenitor radius at an unknown phase relative to thetime of explosion.Observed Type IIP SNe are also often reported toshow excess emission before day ≈
30, often attributedto interaction with the extended environment surround-ing the progenitor (e.g. Khazov et al. 2016; Morozovaet al. 2017, 2018; F¨orster et al. 2018; Hosseinzadeh et al.2018). Because models of early emission depend sensi-tively on the progenitor density profile (e.g. Nakar &Sari 2010; Sapir et al. 2011; Katz et al. 2012; Sapir &Waxman 2017; Faran et al. 2019), any modification ofthe outer stellar structure and surrounding environmentcould translate to distinct changes in the early SN emis-sion (see, e.g., Morozova et al. 2016). For example, theeffects of pulsation-driven superwinds (Yoon & Cantiello2010) on early SN-IIP lightcurves have been directlyconsidered by Moriya et al. (2011, 2017). However, 1Dmodeling of the extended atmospheres of massive starsis inherently limited, as 1D codes cannot reproduce thedetailed 3D structure of the outermost envelope (see e.g. Chiavassa et al. 2011; Arroyo-Torres et al. 2015;Kravchenko et al. 2019). Therefore, in this work we pri-marily restrict our discussion to plateau properties afterday ≈
30, at which point the SN emission comes fromthe modified interior of the star and not the outermost ≈ . M (cid:12) .In this work, we consider effects of pulsations on thebulk density structure of the stellar envelope and theimpact these structural differences have on the resultingType IIP SNe. In Section 2 we discuss our approach tocapturing the effects of radial pulsations on the internalstructure of the star using the open-knowledge 1D stellarevolution software instrument Modules for Experimentsin Stellar Astrophysics ( MESA ; Paxton et al. 2011, 2013,2015, 2018, 2019), and compare our pulsating models toexpectations from linear theory. In Section 3 we demon-strate the effects these structural changes have on theresulting SN lightcurves. We show the luminosity atday 50 ( L ), time-integrated shock energy ( ET ), andplateau duration ( t p ) for SNe of progenitors pulsatingin their fundamental mode scale simply with the pro-genitor radius at the moment of explosion as given byPopov (1993); Kasen & Woosley (2009); Nakar et al.(2016); Goldberg et al. (2019) and others. Furthermore,we show that for pulsations where the displacement isnot monotonic, such as the first overtone, SN emissionfrom different regions within the ejecta is influenced bythe differing structure. MODELING RADIAL PULSATIONSWe construct our fiducial model of a CCSN progen-itor with
MESA revision 11701. We choose a nonrotat-ing, solar-metallicity ( Z = 0 .
02) model of 18 M (cid:12) atZAMS, with a convective efficiency of α MLT = 3 . f ov = 0 .
01 and f , ov = 0 . MESA ’s ‘Dutch’ prescription with ef-ficiency η wind = 0 . Cfalls below 10 − , we introduce a maximum timestep of10 − years. This is to ensure that the model remainsnumerically converged, as well as to ensure that we re-solve changes its structure when causing it to pulsate ona timescale of hundreds of days. Other inputs are de-termined following the case of the MESA test suite. At the time of core-collapse,1715 days after the end of core Carbon burning, theunperturbed model has a total mass of M = 16 . M (cid:12) ,a radius of R = 880 R (cid:12) , and a luminosity of L =1 . × L (cid:12) .After evolving the model through the end of corecarbon burning, we use the pulsation instrument GYRE (Townsend & Teitler 2013) to identify the periods andradial displacement eigenfunctions for the first 3 radial( l = 0) modes. We recover a fundamental pulsation pe-riod of 534 days, a first overtone period of 240 days,0 200 400 600 800 r [ R (cid:12) ] − . . . . . . ξ ( r ) FundamentalFirst OvertoneSecond Overtone
Figure 1.
Normalized radial displacement eigenfunctionsfor our fiducial stellar model at core Carbon depletion. and a second overtone period of 154 days. The ra-dial displacement eigenfunction ξ ( r ) for the fundamentalmode, and the first and second overtones, normalized tomax( ξ ( r )) = 1, are shown in Figure 1.To model the effects of pulsation on the density struc-ture of the envelope, we inject the fundamental eigen-mode as a velocity proportional to the radial displace-ment given by GYRE . For a zone with radial coordinate r , we set v ( r ) = 1 . c s , surf ξ ( r ), where c s , surf is the soundspeed at the surface of the unperturbed model and ξ ( r )is normalized to be 1 at its maximum value. The result-ing pulsation causes significant variation in the radius,from 760 - 1100 R (cid:12) over the course of a few pulsations.This amplitude was chosen to resemble the 0.3-0.4 magamplitudes seen by Soraisam et al. (2018). We do notclaim that the growth in the pulsations is being modeledcorrectly; rather, we are only interested in the effects ofrealistically large pulsations on the SN properties. In or-der to achieve core collapse at different phases of the pul-sation, we inject this velocity eigenfunction starting atincrements of 36.5 days up to 474.5 days after core car-bon depletion and allow the model to ring as it evolvesto core collapse, as shown in Figure 2. For the funda-mental mode, the recovered average peak-to-peak periodis 535 days, and trough-to-trough period is 550 days, asthe pulsation becomes increasingly nonlinear, especiallynear the minimum radius. However, both are close tothe 534 day period expected of a small amplitude pul-sation.The process of causing our models to pulsate withthe first radial harmonic is nearly identical to that de-scribed above. However, since the overtone pulsationperiod of 240 days is approximately half that of thefundamental mode, and there is a node in the radialdisplacement eigenfunction such that the surface dis-placement is only caused by oscillation in the outer en-velope, the radial pulsation amplitude is comparativelysmall for a given injected velocity amplitude. Figure 3 R [ R (cid:12) ] Figure 2.
Stellar radius as a function of time, after injectingthe velocity eigenfunction of the fundamental radial mode.The left-most point on each curve corresponds to the time ofinjection relative to the earliest injection, and the right-mostpoint corresponds to the model at the time of core collapse.The black line shows the negligible variation in the stellarradius of the unperturbed model. shows the overtone pulsation injected with different am-plitudes. A fundamental mode is also shown for compar-ison. The recovered average peak-to-peak and trough-to-trough periods are 236 days and 241 days, respec-tively, taken over the first 4 pulsation cycles. Partic-ularly for larger amplitude pulsations, the fundamen-tal mode grows in the overtone-injected models, causingmodulation on longer timescales than the overtone pe-riod. This effect gets stronger with increasing initialpulsation amplitude, making it very difficult to createa model which rings with a “pure” overtone and has asizeable pulsation amplitude.2.1.
Analytic Expectations in the Linear Regime
For a small perturbation, we can express the radiusof that element as (cid:126)r = (cid:126)r + (cid:126)ξ , where (cid:126)r is the unper-turbed radius and (cid:126)ξ is the Lagrangian displacement. Fora radial oscillation with (cid:126)ξ = ξe iωt ˆ r , where ω is the fre-quency of oscillation, the velocity of that fluid element is (cid:126)v = iω(cid:126)ξ . By continuity, the density of the fluid elementchanges as dρdt + ρ(cid:126) ∇ · (cid:126)v = 0 , (1)where d/dt represents the Lagrangian time derivative d/dt = ∂/∂t + (cid:126)v · (cid:126) ∇ . Equation (1) yields the Lagrangiandensity perturbation ∆ ρ ,∆ ρ = − ρ (cid:126) ∇ · (cid:126)ξ = − ρ r ddr r ξ. (2)In order to check the agreement between our pulsatingmodel and the expectations from linear theory, we save R [ R (cid:12) ] FundamentalFirst Overtone
Figure 3.
Stellar radius as a function of time in our mod-els injected with first overtone velocity eigenfunctions. Theinjected initial velocity amplitudes shown here are A = 0 . v ( r ) = A c s , surf ξ ( r ) where ξ is the displacement eigenfunction for the first overtone. Afundamental mode pulsation is also shown, with its startingpoint chosen to visually resemble the modulation seen in theovertone models. the density profile at the maximum and minimum radiusfor fundamental mode and overtone pulsations. Figure 4shows the agreement between our models and Equation(2). Here we normalize ξ to match the displacement inthe pulsating model at the mass coordinate correspond-ing to 300 R (cid:12) in the unperturbed model, at an overheadmass of 5.7 M (cid:12) . This location was chosen because itcorresponds to roughly half of the envelope mass andhalf of the stellar radius in log-space. The surface ismost severely affected by nonlinearities, and this workprimarily explores effects on the bulk of the material.We also choose to display the overtone profiles at thefirst maximum (1/4 period after injecting the velocityeigenfunction) and the second minimum (7/4 period af-ter injection) of the model with an injected velocity of v ( r ) = 1 . c s , surf ξ ( r ), as these times are most consis-tent with being “pure” overtones. The agreement is verygood in the interior of the star. Deviations from lineartheory occur primarily near the surface, where nonlin-earities due to nearly sonic motion cause a larger impact. EXPLODING PULSATING MODELSAt the time of explosion, the density profiles inthe envelope vary significantly for different pulsationphases. This can be seen in Figure 5, which showsdensity profiles in the envelope at core-collapse forthe fundamental-mode models as a function of radius(left panel). Additionally, Figure 5 shows a compari-son between Lagrangian density profiles of the unper-turbed model, a fundamental mode pulsation near max- f at max f at min1 o at max1 o at min . f , analytic1 o , analytic m [ M (cid:12) ] − . − . . . . ∆ ρ / ρ Figure 4.
Comparison of linear theory for the Lagrangiandensity perturbation (black lines) with differences in themodel density profiles from the density profile of the unper-turbed starting model (colored lines) for fundamental modepulsations (solid) and first overtone pulsations (dashed). imum, and a large-amplitude overtone near maximum(right panel). In order to achieve a large-amplitudeovertone pulsations, we inject a velocity profile with v ( r ) = 5 . c s , surf ξ ( r ), where ξ is the displacement forthe first overtone, approximately quarter-period beforecore-collapse, 1533 days after core C depletion, so thatit is approaching its first maximum at the time of ex-plosion. To produce a fundamental mode pulsator withthe same stellar radius and similar phase, we inject avelocity profile v ( r ) = 2 . c s , surf ξ ( r ) approximatelya quarter-period before core-collapse, 1460 days aftercore C depletion. Our models show significant diversityin their density profiles, particularly near the surface.Moreover, the overtone pulsation at maximum phaseis denser in the interior of the star compared to theunperturbed model, but less dense near the surface,whereas the fundamental mode near maximum is lessdense everywhere.We explode our models at different radii. At a cen-tral temperature of log( T c / K) = 9 .
9, we instantaneouslyzero out the velocity profile to “freeze in” the densitystructure of the envelope, since the time to shock break-out ( ≈ M (cid:12) , leading to ejecta masses of M ej =14.54 to
200 400 600 800 1000 r [ R (cid:12) ] − . − . − . − . − . − . l og ( ρ / g c m − ) m [ M (cid:12) ] − . − . − . − . − . − . l og ( ρ / g c m − ) Fundamental, R = 1042 R (cid:12) Overtone, R = 1043 R (cid:12) Unperturbed, R = 880 R (cid:12) Figure 5.
Left: Density profiles in the envelope of our pulsating models just before core collapse, where color corresponds totime the pulsation was injected as in Figure 2. Right: Lagrangian density profiles at core-collapse for large-amplitude pulsationsapproaching maximum displacement, where the velocity eigenfunctions were injected just 1/4 phase before core-collapse topreserve the purity of the modes. In both panels, the dotted black line shows the unperturbed model. M (cid:12) . The unperturbed model has an excised massof 1.73 M (cid:12) . We allow the new inner boundary to infalluntil it reaches an inner radius of 500 km. We then haltthe infall, and inject energy in the innermost 0.1 M (cid:12) of the star for 10 − seconds, until each model reaches atotal energy of 10 ergs.We proceed by modeling the evolution of the shockincluding Duffell RTI (Duffell 2016), and hand off theejecta model at shock breakout to the 1D radiation-hydrodynamics software STELLA (Blinnikov et al. 1998,2000, 2006; Baklanov et al. 2005) as described inMESA IV. The time to shock breakout is 2 days for theunperturbed model, and varies from 1.7 days for oursmallest-radius model to 2.5 days for our largest-radiusmodel. At this explosion energy, there is negligible ad-ditional fallback, which we evaluate using the fallbackscheme described in Appendix A of Goldberg et al.(2019) with an additional velocity cut of 500 km s − athandoff to STELLA . We then rescale the distribution of Ni to match a total mass of 0.06 M (cid:12) , which is typicalof observed events and roughly matches the Ni massesobserved in SNe with L equal to that of the unper-turbed model via the L − M Ni relations from Pejcha& Prieto (2015) and M¨uller et al. (2017). We use 1600spatial zones and 40 frequency bins in STELLA , whichyields convergence in the bolometric lightcurves for thegiven ejecta models (see also Figure 30 of MESA IVand the surrounding discussion). While a significantfraction of SNe II-P have excess emission for the first ∼
20 days (e.g. Morozova et al. 2017), and pulsation-driven outbursts have been proposed as one means ofmass loss at the end of the lives of RSGs (e.g. Yoon& Cantiello 2010), we do not include any extra mate-rial beyond the progenitor photosphere to generate ourmodel lightcurves. In addition, we are focused on the emission from the bulk of the ejecta, that occurs afterday 30. 3.1.
Pulsations and Plateau Properties
As discussed in detail by Arnett (1980), Popov (1993),Kasen & Woosley (2009), Sukhbold et al. (2016), Gold-berg et al. (2019), and others, the plateau luminosity ofa Type IIP SN at day 50, L , depends on the radiusof the progenitor. Popov (1993) gives L ∝ R / atfixed ejecta mass M ej and explosion energy E exp . Froma suite of MESA + STELLA models, Goldberg et al. (2019)recovered a similar scaling, L ∝ R . . Figure 6 showslightcurves for the 13 phases of pulsation shown in Fig-ure 2, as well as for the unperturbed model denotedby the black line in Figure 2. As expected from thescalings, the luminosity at day 50 varies by 0.13 dex,or 0.33 mag, with the brighter explosions correspond-ing to larger radii, with radii ranging from 760-1120 R (cid:12) .The slope on the plateau is somewhat steeper in thebrighter SNe, such that the variation at early time isgreater than closer to the end of the plateau. Addi-tionally, following Goldberg et al. (2019), in the Ni-rich limit M Ni (cid:38) . M (cid:12) , the plateau duration shouldbe approximately independent of the progenitor radius,with some variation for varied distributions of Ni andHydrogen. This can also be seen in our lightcurves inFigure 6, where the recovered plateau durations (usingthe method of Valenti et al. 2016 as in Goldberg et al.2019) ranges from 116.8 to 119.5 days with no correla-tion with progenitor radius. These trends are shown ingreater detail in the upper and lower panel of Figure7, which show good agreement between our models andthe scalings.Figure 5 also shows changes in the outer density pro-files and their slopes as a result of these pulsations.These changes do modify the calculated early lightcurves . . . . . l og ( L b o l / e r g s − ) Figure 6.
Lightcurves for our fundamental mode pulsator atdifferent phases of pulsation. Color corresponds to time thepulsation was injected, as in Figure 2, and tracks pulsationphase. The dotted black line shows the lightcurve of theunperturbed model. shown in Figure 6, causing greater luminoisty excessesat early times in the more extended models. In obser-vations, such apparent excesses are often interpreted asevidence for material beyond the normal stellar photo-sphere. However, because this part of the outer enve-lope is intrinsically uncertain in 1D models, we are notin a position to make strong claims about whether thevariety seen in early lightcurve observations can be ex-plained by pulsations alone.Additionally, the total energy deposited by the shockis reflected in the observable ET (Nakar et al. 2016;Shussman et al. 2016), defined as the total time-weighted energy radiated away in the SN which wasgenerated by the initial shock and not by Ni decay: ET = (cid:90) ∞ t [ L bol ( t ) − Q Ni ( t )] d t, (3)where t is the time in days since the explosion and Q Ni = M Ni M (cid:12) (cid:16) . e − t/ . + 1 . e − t/ (cid:17) × erg s − , (4)is the Ni decay luminosity given in Nadyozhin (1994),which is taken to be equivalent to the instantaneousheating rate of the ejecta assuming complete trapping. ET also scales with the progenitor radius for constant M ej and E exp , given as ET ∝ R by the analytics andmodeling of Nakar et al. (2016); Shussman et al. (2016);Kozyreva et al. (2018), and as ET ∝ R . recoveredfrom MESA + STELLA models by Goldberg et al. (2019).The middle panel of Figure 7 shows the agreement be-tween ET in our model lightcurves and the scalings.Like with L , ET as a function of progenitor radiusexhibits some scatter, which is not surprising given the t p [ d a y s ] . . . . l og ( E T / e r g s ) E T ∝ R . .
90 2 .
95 3 .
00 3 . R/R (cid:12) )42 . . . l og ( L / e r g s − ) L ∝ R . Figure 7.
Lightcurve observables versus progenitor radiusat the time of explosion for our unperturbed model (blackstar) and pulsating models (colored points). The plateauduration (upper panel), ET (middle panel), and L (lowerpanel) are shown along with scalings from Goldberg et al.(2019). Colors match the colors in Figures 2 and 6. significant differences in the density profiles especially inthe models near pulsation minima at core-collapse, butoverall agrees well with the predicted scalings.3.2. Comparing Fundamental and Overtone Pulsations
Although a majority of observed pulsating RSGs aredominated by the fundamental mode, there is evidencefor some pulsating with the first overtone (e.g. Kiss et al.2006; Soraisam et al. 2018; Ren et al. 2019). Becauseof the radial crossing in the overtone, the progenitor ra-dius used in scaling laws may not be sufficient to predict L . Typically, the expansion time characterized by thetime to shock breakout and the mean density of the SNejecta are considered in analytics. However, the localradius and density profile of the progenitor at the masscoordinate of the SN photosphere, which is located nearthe H-recombination front and is defined by the loca-tion where the mean optical depth τ = 2 /
3, must betaken into account. As seen in the left panel of Fig-ure 5, inside the mass coordinate of ≈ . − M (cid:12) ,which is near the zero-crossing in the radial displace-ment (see Figure 4), the overtone progenitor model isdenser than the unperturbed model, and outside thatcoordinate it is less dense. On the other hand, the fun-damental mode pulsation is less dense everywhere whenit is at a positive radial displacement, suggesting that atfixed photospheric mass coordinate in the SN, the starshould appear “larger” and therefore the SN would bebrighter.As shown in the upper panel of Figure 8, the evolu-tion of the mass coordinate of the SN photosphere doesnot change significantly for the pulsating models com-pared to the unperturbed model. At day 50, the SNphotosphere has moved 1 . M (cid:12) into the ejecta for theunperturbed and overtone models, corresponding to astellar mass coordinate of 14 . M (cid:12) , which is near thezero-crossing in the overtone displacement and densityperturbation in the progenitor model. This is reflectedby the lightcurves shown in the lower panel of Figure 8.The evolution of the photospheric radius (middle panelof Figure 8) and mass coordinate do not differ tremen-dously on the plateau between the three models, but thelightcurves show a distinct difference. Whereas the pro-genitor radii for the fundamental and overtone are nearlyidentical, the overtone explosion at day 50 is fainter by0.046 dex or 0.115 mags, and in fact much closer in L to the unperturbed progenitor model than to the funda-mental mode. Additionally, the SN from the overtonepulsator is brighter at early times, when the SN emis-sion is coming from what appears to be a more radiallyextended star with a steeper density profile, and fainterat later times, when the emission appears to be comingfrom a more compact star. CONCLUSIONSThere is strong observational evidence for variabilityin large samples of RSGs caused by radial pulsationsin their envelopes, typically with periods between a fewhundred and a few thousand days (Kiss et al. 2006; So-raisam et al. 2018; Chatys et al. 2019). Since the finalstages of burning take place over week-long timescales,much shorter than the pulsation period, the densitystructure of the envelope can reflect any pulsation phaseat the time of explosion. This is significant, as the radiusand density structure of a given Type IIP SN progenitorare important in determining the luminosity evolutionof its resulting SN.We consider the effects of pulsations on the stellarenvelope and SN emission after core-collapse. We showthat SNe of fundamental mode pulsators, which accountfor the majority of observed pulsating RSGs, behave like“normal” Type IIP SNe from progenitors at differentradii. We find that L and ET scale with the progen-itor radius at the time of explosion consistent with thework of Popov (1993); Kasen & Woosley (2009); Nakaret al. (2016); Goldberg et al. (2019) and others, and thatthe plateau duration remains independent of progenitorradius as expected in the Ni − rich regime. The lumi- . . . . M e j − m ph [ M (cid:12) ] r ph [ c m ] . . . . . l og ( L b o l / e r g s − ) Unperturbed, R = 880 R (cid:12) Fundamental, R = 1042 R (cid:12) Overtone, R = 1043 R (cid:12) Figure 8.
Overhead mass coordinate of the SN photosphere(upper panel), photospheric radius (middle panel), andlightcurves (lower panel) for explosions of large-amplitudefundamental mode and overtone pulsations near maximum,compared to the unperturbed model. nosity plateau declines more steeply for brighter eventsbetween days 30 and 80, which in this study correspondto models with positive radial displacement at the timeof core collapse. This is consistent with the observedcorrelation seen in Type II SNe more broadly betweenthe brightness and steeper plateau decline (e.g. Ander-son et al. 2014; Valenti et al. 2016).Additionally, we show that large-amplitude pulsationsin the first overtone yield different lightcurves com-pared to fundamental-mode pulsations at the same ra-dius. This results from the nonmonotonic overtone den-sity perturbation, which, for an explosion near pulsationmaximum, causes the SN to “see” a puffier star at earlytimes, but a more compact star at later times. Thisyields a supernova which is initially brighter than eitherthe fundamental-mode pulsator at equivalent radius orthe unperturbed model at a smaller radius, but fainteronce emission is coming from the denser interior. In allcases, the differing stellar radii and density profiles alsoyield signatures in the calculated early SN emission, butfuture work aided by a more accurate treatment of theprogenitor’s extended atmosphere is necessary to makedefinitive statements and quantitative predictions.Motivated by the observed oscilllations, we only con-sidered the impact of radial pulsations on the result-ing SNe light curves. Non-radial pulsations, if present,would lead to additional phenomena, for example appar-ent asymetries during the plateau phase. Existing spec-tropolarimetric observations (Wang et al. 2001; Leonard& Filippenko 2001; Leonard et al. 2001, 2006; Wang &Wheeler 2008; Kumar et al. 2016; Nagao et al. 2019)sometimes show very low (or undetectable) levels of as-symetries during the plateau, with increasing polariza-tion evident in the late time tail attributed to asymme-tries deep in the helium core.Because a fundamental uncertainty in recovered explo-sion properties from Type IIP SNe stems from the un-known radius at the time of core-collapse, the presence ofa pulsation would translate to an additional uncertaintyin recovering progenitor properties from SN lightcurveseven in conjunction with progenitor detections. There-fore, continued studies of RSG variability will be im-portant in determining the uncertainties within a singleprogenitor radius detection. Future work is also neededto accurately model the winds and surface layers of mas-sive stars, as well as the density profile of any extendedmaterial, all of which are required to effectively modelearly SN emission and could be affected by these pul-sations. Nonetheless, this work highlights the influenceof the complete density profile of the progenitor star on the SN emission on the plateau, beyond the initial shockcooling and early spherical phase.We would like to thank Evan Bauer for formative con-versations and
GYRE insights. We thank Rich Townsendfor discussions about
GYRE . We would also like to thankMatteo Cantiello, Rob Farmer, Josiah Schwab, andFrank Timmes for helpful discussions. It is a plea-sure also to thank Maria Drout, Daichi Hiramatsu,and Christopher Kochanek for discussions and corre-spondences about observations. This research benefitedfrom interactions with Jim Fuller, Adam Jermyn, DavidKhatami, Sterl Phinney, and Eliot Quataert which werefunded by the Gordon and Betty Moore Foundationthrough Grant GBMF5076.J.A.G. is supported by the National Science Founda-tion (NSF) Graduate Research Fellowship under grantnumber 1650114. The
MESA project is supported by theNSF under the Software Infrastructure for Sustained In-novation program grant ACI-1663688. This research wassupported at the KITP by the NSF under grant PHY-1748958.This research made extensive use of the SAO/NASAAstrophysics Data System (ADS).
Software:
Python from python.org, py mesa reader (Wolf & Schwab 2017), ipython/jupyter (P´erez &Granger 2007; Kluyver et al. 2016),
SciPy (Jones et al.2001–),
NumPy (van der Walt et al. 2011), and matplotlib (Hunter 2007).REFERENCES
Anderson, J. P., Gonz´alez-Gait´an, S., Hamuy, M., et al.2014, ApJ, 786, 67Arnett, W. D. 1980, ApJ, 237, 541Arroyo-Torres, B., Wittkowski, M., Chiavassa, A., et al.2015, A&A, 575, A50Baklanov, P. V., Blinnikov, S. I., & Pavlyuk, N. N. 2005,Astronomy Letters, 31, 429Blinnikov, S., Lundqvist, P., Bartunov, O., Nomoto, K., &Iwamoto, K. 2000, ApJ, 532, 1132Blinnikov, S. I., Eastman, R., Bartunov, O. S., Popolitov,V. A., & Woosley, S. E. 1998, ApJ, 496, 454Blinnikov, S. I., R¨opke, F. K., Sorokina, E. I., et al. 2006,A&A, 453, 229Chatys, F. W., Bedding, T. R., Murphy, S. J., et al. 2019,MNRAS, 487, 4832Chiavassa, A., Freytag, B., Masseron, T., & Plez, B. 2011,A&A, 535, A22Conroy, C., Strader, J., van Dokkum, P., et al. 2018, ApJ,864, 111Dessart, L., & Hillier, D. J. 2019, A&A, 625, A9Duffell, P. C. 2016, ApJ, 821, 76 Eldridge, J. J., Guo, N. Y., Rodrigues, N., Stanway, E. R.,& Xiao, L. 2019, arXiv e-prints, arXiv:1908.07762Faran, T., Goldfriend, T., Nakar, E., & Sari, R. 2019, ApJ,879, 20Feast, M. W., Catchpole, R. M., Carter, B. S., & Roberts,G. 1980, MNRAS, 193, 377F¨orster, F., Moriya, T. J., Maureira, J. C., et al. 2018,Nature Astronomy, 2, 808Glebbeek, E., Gaburov, E., de Mink, S. E., Pols, O. R., &Portegies Zwart, S. F. 2009, A&A, 497, 255Goldberg, J. A., Bildsten, L., & Paxton, B. 2019, ApJ, 879,3Guo, J. H., & Li, Y. 2002, ApJ, 565, 559Heger, A., Jeannin, L., Langer, N., & Baraffe, I. 1997,A&A, 327, 224Hosseinzadeh, G., Valenti, S., McCully, C., et al. 2018,ApJ, 861, 63Hunter, J. D. 2007, Computing In Science &Engineering, 9, 90Ita, Y., Tanab´e, T., Matsunaga, N., et al. 2004, MNRAS,347, 720
Johnson, S. A., Kochanek, C. S., & Adams, S. M. 2018,MNRAS, 480, 1696Jones, E., Oliphant, T., Peterson, P., et al. 2001–, SciPy:Open source scientific tools for PythonJurcevic, J. S., Pierce, M. J., & Jacoby, G. H. 2000,MNRAS, 313, 868Kasen, D., & Woosley, S. E. 2009, ApJ, 703, 2205Katz, B., Sapir, N., & Waxman, E. 2012, ApJ, 747, 147Khazov, D., Yaron, O., Gal-Yam, A., et al. 2016, ApJ, 818,3Kiss, L. L., Szab, G. M., & Bedding, T. R. 2006, MNRAS,372, 1721Kluyver, T., Ragan-Kelley, B., P´erez, F., et al. 2016, inPositioning and Power in Academic Publishing: Players,Agents and Agendas: Proceedings of the 20thInternational Conference on Electronic Publishing, IOSPress, 87Kochanek, C. S., Beacom, J. F., Kistler, M. D., et al. 2008,ApJ, 684, 1336Kochanek, C. S., Fraser, M., Adams, S. M., et al. 2017,MNRAS, 467, 3347Kozyreva, A., Nakar, E., & Waldman, R. 2018, MNRAS,483, 1211Kravchenko, K., Chiavassa, A., Van Eck, S., et al. 2019,arXiv e-prints, arXiv:1910.04657Kumar, B., Pandey, S. B., Eswaraiah, C., & Kawabata,K. S. 2016, MNRAS, 456, 3157Leonard, D. C., & Filippenko, A. V. 2001, PASP, 113, 920Leonard, D. C., Filippenko, A. V., Ardila, D. R., &Brotherton, M. S. 2001, ApJ, 553, 861Leonard, D. C., Filippenko, A. V., Ganeshalingam, M.,et al. 2006, Nature, 440, 505Martinez, L., & Bersten, M. C. 2019, A&A, 629, A124Moriya, T., Tominaga, N., Blinnikov, S. I., Baklanov, P. V.,& Sorokina, E. I. 2011, MNRAS, 415, 199Moriya, T. J., Yoon, S.-C., Gr¨afener, G., & Blinnikov, S. I.2017, MNRAS, 469, L108Morozova, V., Piro, A. L., Renzo, M., & Ott, C. D. 2016,ApJ, 829, 109Morozova, V., Piro, A. L., & Valenti, S. 2017, ApJ, 838, 28—. 2018, ApJ, 858, 15M¨uller, T., Prieto, J. L., Pejcha, O., & Clocchiatti, A. 2017,ApJ, 841, 127Murphy, J. W., Mabanta, Q., & Dolence, J. C. 2019,MNRAS, 489, 641Nadyozhin, D. K. 1994, ApJS, 92, 527Nagao, T., Cikota, A., Patat, F., et al. 2019, MNRAS, 489,L69Nakar, E., Poznanski, D., & Katz, B. 2016, ApJ, 823, 127Nakar, E., & Sari, R. 2010, ApJ, 725, 904 Nugis, T., & Lamers, H. J. G. L. M. 2000, A&A, 360, 227Paxton, B., Bildsten, L., Dotter, A., et al. 2011, ApJS, 192,3Paxton, B., Cantiello, M., Arras, P., et al. 2013, ApJS, 208,4Paxton, B., Marchant, P., Schwab, J., et al. 2015, ApJS,220, 15Paxton, B., Schwab, J., Bauer, E. B., et al. 2018, ApJS,234, 34Paxton, B., Smolec, R., Schwab, J., et al. 2019, ApJS, 243,10Pejcha, O., & Prieto, J. L. 2015, ApJ, 799, 215Percy, J. R., & Khatu, V. C. 2014, Journal of the AmericanAssociation of Variable Star Observers (JAAVSO), 42, 1P´erez, F., & Granger, B. E. 2007, Computing in Science &Engineering, 9, 21Popov, D. V. 1993, ApJ, 414, 712Ren, Y., Jiang, B.-W., Yang, M., & Gao, J. 2019, ApJS,241, 35Sapir, N., Katz, B., & Waxman, E. 2011, ApJ, 742, 36Sapir, N., & Waxman, E. 2017, ApJ, 838, 130Shussman, T., Nakar, E., Waldman, R., & Katz, B. 2016,arXiv e-prints, arXiv:1602.02774Smartt, S. J. 2009, ARA&A, 47, 63—. 2015, Publications of the Astronomical Society ofAustralia, 32, e016Soraisam, M. D., Bildsten, L., Drout, M. R., et al. 2018,ApJ, 859, 73Spetsieri, Z. T., Bonanos, A. Z., Yang, M., Kourniotis, M.,& Hatzidimitriou, D. 2019, A&A, 629, A3Stothers, R. 1969, ApJ, 156, 541Stothers, R., & Leung, K. C. 1971, A&A, 10, 290Sukhbold, T., Ertl, T., Woosley, S. E., Brown, J. M., &Janka, H.-T. 2016, ApJ, 821, 38Szczygie(cid:32)l, D. M., Gerke, J. R., Kochanek, C. S., & Stanek,K. Z. 2012, ApJ, 747, 23Szczygie(cid:32)l, D. M., Stanek, K. Z., Bonanos, A. Z., et al. 2010,AJ, 140, 14Townsend, R. H. D., & Teitler, S. A. 2013, MNRAS, 435,3406Valenti, S., Howell, D. A., Stritzinger, M. D., et al. 2016,MNRAS, 459, 3939van der Walt, S., Colbert, S. C., & Varoquaux, G. 2011,Computing in Science Engineering, 13, 22Vink, J. S., de Koter, A., & Lamers, H. J. G. L. M. 2001,A&A, 369, 574Wang, L., Howell, D. A., H¨oflich, P., & Wheeler, J. C. 2001,ApJ, 550, 1030Wang, L., & Wheeler, J. C. 2008, ARA&A, 46, 4330