Comparison between the first and second mass eruptions from progenitors of Type IIn supernovae
AAstronomy & Astrophysics manuscript no. main c (cid:13)
ESO 2020June 12, 2020
The first and second mass eruptions from progenitors of Type IInsupernovae: Is there any difference?
Naoto Kuriyama , and Toshikazu Shigeyama , Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo, Japan Department of Astronomy, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo, JapanReceived XXX / Accepted YYY
ABSTRACT
Context.
Some massive stars experience episodic and intense mass loss phases with fluctuations in the luminosity. Ejected materialforms circumstellar matter around the star, and the subsequent core-collapse results in a type IIn supernova which is characterizedby interaction between supernova ejecta and the circumstellar matter. The energy source which triggers these mass eruptions anddynamics of the outflow have not been clearly explained. Moreover, the mass eruption itself can alter the density structure of theenvelope and a ff ect the dynamics of the subsequent mass eruption if these events repeat. In fact, a large amount of observationalevidence suggests multiple mass eruptions prior to core-collapse. Aims.
We investigate the density structure of the envelope altered by the first mass eruption and the nature of the subsequent secondmass eruption event in comparison with the first one.
Methods.
We deposited an extra energy twice at the bottom of the hydrogen envelope and calculate the time evolution by our radiationhydrodynamical simulation code. We do not deal with the origin of the energy source but focus on the dynamics of repeated masseruptions from a single massive star.
Results.
There are significant di ff erences between the first and second mass eruptions in terms of the luminosity, color, amount ofproduced circumstellar matter. The second eruption leads to a redder burst event with the associated brightening phase lasting longerthan the first one. The amount of ejected matter is di ff erent even with the same deposited energy in the first and second event, but thedi ff erence depends on the density structure of the progenitor star. Conclusions.
Upcoming high cadence and deep transient surveys will provide us a lot of detailed pre-supernova activities, and some ofthem would show multi-peaked light curves. They should be interpreted taking the e ff ect of density structure altered by the precedingoutburst events into consideration. Key words. stars: massive - stars: mass-loss - supernovae: general
1. Introduction
Growing observational evidence suggests that massive starssometimes experience episodic and intense mass loss accompa-nied by temporal brightening. Eta Carinae is one of the mostwell-studied and well-known objects which experienced suchevents (e.g., Davidson & Humphreys 1997). This intense massloss or brightening event has been considered to be related withthe activity of luminous blue variables (LBVs), which were in-troduced by Conti (1984). On the other hand, some recent ob-servations suggest that Wolf-Rayet stars (WR stars) may alsoexperience such events (Foley et al. 2007; Pastorello et al. 2008;Smith et al. 2020).When an intense mass loss takes place, dense circumstellarmatter (CSM) is formed around the star. If a core-collapse su-pernova (SN) takes place in this dense CSM, the expanding SNejecta collide with the CSM. The kinetic energy of the ejecta isdissipated at shocks and becomes the main energy source of ra-diation instead of gamma-ray emission by radio active decays of Ni (e.g., Chugai 1992; Smith 2017). In this case, narrow emis-sion lines due to slowly expanding CSM are seen in the spectrum(e.g., Chugai 1990; Filippenko 1997) and these SNe are classi-fied as Type IIn supernovae (SNe IIn) in case of hydrogen-richCSM (Schlegel 1990) or Type Ibn supernovae (SNe Ibn) in caseof helium-rich CSM (Pastorello et al. 2007). Recent observations reveal that some progenitors of SNe IInactually experienced temporary brightening phase a few or a fewten years before the core-collapse. For example, SN 2018cnf (Pa-storello et al. 2019), SN 2016bdu (Pastorello et al. 2018), SN2013gc (Reguitti et al. 2019), PTF12cxj (Ofek et al. 2014), andSN 2011ht (Fraser et al. 2013) were reported to exhibit suchbrightening. Since the peak luminosity exceeds the Eddingtonluminosity of a massive star, this brightening must lead to aneruptive mass loss. The sparsely observed light curves prior tothese SNe show that the brightening phase typically lasted forseveral years and indicate that the progenitors repeated episodicmass loss events during this period. SN 2009ip (Soker & Kashi2013; Mauerhan et al. 2013; Pastorello et al. 2013; Smith et al.2014; Graham et al. 2017) is one of the most famous SNeIIn whose progenitor star had experienced multiple brighteningphases likely associated with episodic mass loss events. The pro-genitor star of SN 2009ip in a brightening phase was first de-tected in 2009, and repeatedly exhibited brightening with shortintervals less than 50 days (Pastorello et al. 2013) in 2011. Even-tually it experienced the most luminous outburst "2012b" in 2012which is thought to be a genuine supernova.The mass loss rates from progenitors of SNe IIn are es-timated at 0 . − . M (cid:12) yr − (Kiewe et al. 2012), 10 − − − M (cid:12) yr − (Taddia et al. 2013) or more than 10 − M (cid:12) (Moriyaet al. 2014). These values are so high that they cannot be recon- Article number, page 1 of 8 a r X i v : . [ a s t r o - ph . S R ] J un & A proofs: manuscript no. main ciled with a steady wind mass loss model like Vink et al. (2001);van Loon et al. (2005); Smith (2014). In addition, some SNe IInshow bumps in their light curves which are thought to be relatedto bumpy density structures of CSM (Reguitti et al. 2019; Ny-holm et al. 2017; Stritzinger et al. 2012). Although they seemto be the rare cases among SNe IIn (Nyholm et al. 2019), thisbumpy CSM structure also implies not steady but episodic massloss events from the progenitor star. Therefore, a dynamical phe-nomenon, which is not included in most of current stellar evo-lution models, would occur during the temporary brighteningphase.Although there is a plenty of observational evidence of in-tense mass loss as described above, the extra energy sourcewhich triggers the intense mass loss has not been fully un-derstood. There are two types of scenarios explaining the ex-tra energy source; energy supplied from nuclear burning and / orcore convection (Woosley et al. 2007; Woosley & Heger 2015;Woosley 2017; Quataert & Shiode 2012; Shiode & Quataert2014; Smith & Arnett 2014; Mocák et al. 2018; Yadav et al.2020; Soker & Gilkis 2017; Moriya 2014) and energy originat-ing from binary interaction (Smith 2011; Mcley & Soker 2014;Danieli & Soker 2019). We focus on the former type and con-sider a single star assuming that the extra energy is supplied fromviolent nuclear burning. The energy generation rate of nuclearburning in a massive star increases with time and reaches at alocal peak about ten years before core-collapse (Fig. 1) depend-ing on the core mass. We assume this local peak is related to anintense mass eruption (Sect. 2).As well as considering an extra energy source, it has beenalso discussed in previous research how the extra energy is trans-ported towards the stellar surface and what kind of observationalfeature emerges. Quataert et al. (2016), Fuller (2017), Fuller &Ro (2018), and Ouchi & Maeda (2019) investigate how the enve-lope responds to an extra energy injected continuously at a super-Eddington rate. Dessart et al. (2010), Owocki et al. (2019), andKuriyama & Shigeyama (2020) consider the dynamical eruptivemass loss event when an extra energy is deposited at the bot-tom of the envelope with a short timescale. In these researches,energy is deposited only once and the corresponding single dy-namical eruption event is discussed. However, intense mass lossevent often repeats in the real situation as discussed above andthis could become a key factor for understanding the mass lossmechanism. Once a dynamical eruption takes place, the expand-ing envelope will keep its altered density profile for the ther-mal time scale. If another eruption event occurs again before thedensity profile relaxes and returns to the hydrostatic state, theproperty of the second eruption may be completely di ff erent be-cause of a di ff erent density profile of the envelope. To deal withthis problem, we study dynamics of eruptive mass loss whichrepeats twice. Of course eruption can repeats more than twice,we focus on a comparison between eruptions from the original(hydrostatic) envelope and the expanding envelope in this work.In this study, we investigate intense and eruptive mass lossfrom progenitors of SNe IIn. We assume that eruptive mass lossis related to the local peak of the energy generation rate of nu-clear burning shown in Figure 1 although the specific mechanismof energy transportation from the burning region to the envelopeis not assumed. We deposit an extra energy at the bottom of thehydrogen envelope twice and investigate the properties of eacheruption and di ff erence between the first and second eruptions.The second energy injection is conducted before the stellar enve-lope relaxes from the first injection. Each extra energy is injectedfor a short period of time and the resulting dynamical eruption isinvestigated by radiation hydrodynamical simulations. In Sect. 2, N u c l ea r l u m i no s i t y l og ( L / L s un ) Time to core-collapse [yr] model RSGmodel BSG
Fig. 1.
Evolution of the energy generation rate by nuclear burning foreach model indicated by labels. The rate becomes higher towards thecore-collapse. There are some local peaks for each model around tenyears , five years , and one year before core-collapse. We adopted thepeaks at 11.2 years before core-collapse (model RSG) and at 7.2 yearsbefore core-collapse (BSG) as initial models for our calculations. Thesepeaks correspond to core neon burning phase. -12 -10 -8 -6 -4 -2
0 2 4 6 8 10 12 14 16 D en s i t y [ g cc - ] Mass Coordinate [M sun ] model RSGmodel BSG
Fig. 2.
Density distribution of each progenitor model. Model RSG has amore extended envelope than model BSG because of higher metallicity(Table 1) and opacity. In addition to that, model RSG has experiencedstronger mass loss due to higher metallicity and thus has a lower totalmass. we introduce the progenitor models which we use as initial mod-els in our simulation and the method of radiation hydrodynam-ical calculation. In Sect.3 we present the results of calculationand find out di ff erences between the first and second eruptions.We clarify implications to observations in Sect. 4 and presentconclusion in Sect. 5.
2. Set up and Methods
Although it has been often considered that eruptive mass loss andSNe IIn are related to activities of LBVs (e.g., Gal-Yam et al.2007; Langer 2012) as described in Sect 1, observations suggestthat red supergiants (RSGs) may also be progenitors of SNe IIn(Smith et al. 2009; Bilinski et al. 2015). Thus, we adopted twotypes of progenitors in this study, namely, blue supergiant model(model BSG) and red supergiant model (model RSG). We madethese progenitor models using a stellar evolution code MESA(Paxton et al. 2011, 2013, 2015, 2018, 2019). We stop the cal-culations of MESA 11.2 yr before core-collapse for model RSG
Article number, page 2 of 8uriyama and Shigeyama: The first and second mass eruption
Table 1.
Properties of two SNe Progenitor models.
Model M ZAMS
Z R T e ff M He core M H env E envelope a Time to CC Burning stageRSG 15 M (cid:12) .
02 696 R (cid:12) . M (cid:12) . M (cid:12) − . × erg 11 . M (cid:12) . R (cid:12) . M (cid:12) . M (cid:12) − . × erg 7 . Notes. a Total energy of H-rich envelope
Table 2.
Amount of injected energy E inj1 , E inj2 and time when a injection begins t inj1 , t inj2 . Two patterns of calculations were conducted for eachmodel (Totally four patterns of calculations). Calculation model Progenitor model t inj1 E inj1 [erg] t inj2 E inj2 [erg]RSG1 RSG 0 s 1 . ×
98 day 1 . × RSG2 0 s 1 . ×
98 day 3 . × BSG1 BSG 0 s 6 . × . × s 6 . × BSG2 0 s 6 . × . × s 9 . × and 7.9 yr before core-collapse for model BSG, respectively andadopted these models as initial models for our hydrodynamicalsimulations presented in Sect. 2.2. These two models have thesame zero-age main sequence mass (15 M (cid:12) ) but di ff erent metal-licities (Table 1). The di ff erence in metallicity causes di ff erentopacities in the stellar envelope and results in the division be-tween RSG and BSG (di ff erent density distributions in Fig. 2,radii, and e ff ective temperatures in Table 2). The time evolutionof the energy generation rate of nuclear burning is also slightlydi ff erent between the two models. The timescale of each nuclearburning stage in model RSG is longer than that in model BSG(Fig. 1) because model RSG has a lower core mass (Fig. 1).Model RSG has experienced more intense steady mass loss be-cause of higher metallicity and thus has a smaller core. We starthydrodynamical calculations at 11.2 yr before core collapse formodels RSG and 7.9 yr for models BSG corresponding to thelocal peaks of nuclear burning luminosity as mentioned in §2.2.Although we can identify other higher peaks within one year be-fore core-collapse, we only focus on these peaks because it couldtake more than one year for the ejected envelope to extending farenough to reproduce the observed typical distance from the pro-genitor star to a CSM (e.g., 160 AU, Smith & McCray 2007).Detailed methods of making the two progenitor models are de-scribed in Appendix A. As described in Sect. 1, the main purpose of this paper is re-vealing di ff erences in the properties between the first and sec-ond mass eruptions from SNe IIn progenitors. To investigate thistopic, we used the same 1-D radiation hydrodynamical simula-tion method as in Kuriyama & Shigeyama (2020). We injectedan extra energy into the bottom of the hydrogen envelope twicewithout specifying from where and how the extra energy is sup-plied (the mechanism for supplying the extra energy has not beenfully understood so far, see Sect. 1). For model BSG, the time-interval between the first and the second energy injection waschosen to reproduce repeated mass eruption events with shortintervals (less than 30 days) observed for SN 2009ip (Pastorelloet al. 2013). This time interval (3 . × s, see Table 1) is justequal to the dynamical timescale of the BSG progenitor modelmade by MESA. To compare with model BSG, the time-intervalbetween two energy injections for model RSG was set to thedynamical timescale of the RSG progenitor model, which corre-sponds to ∼
98 day. According to Table 2, the first energy E inj1 was injected at the time t inj1 and the second energy E inj2 was in-
0 100 200 300 400 500 Lu m i no s i t y [ e r g s - ] Time [day] RSG1RSG2
Fig. 3.
Light curves for models RSG1 and RSG2. The first (the second)eruption, triggered by the injected energy E inj1 ( E inj2 ), produces a peakat day ∼
80 ( ∼ jected at t inj2 . For each of progenitor models RSG and BSG, twopatterns of calculation with di ff erent amounts of the injected en-ergy were conducted (totally four patterns of calculations). Wecall them model RSG1, RSG2, BSG1, and BSG2, respectively(Table 2). E inj1 is roughly set to one third or quarter of | E envelope | ( E envelope represents the total energy of the envelope) for everymodel. This value is enough to expel 10 − − − M (cid:12) material(Kuriyama & Shigeyama 2020) which is a typical amount ofCSM in SNe IIn.
3. Results
Two injections of extra energies at di ff erent epochs cause twodistinct mass eruption events (Table 3) and two distinct peaksof luminosity (Fig 3, 4). About one quarter (model RSG1,2) orone third (BSG1,2) of | E envelope | is injected into the bottom ofthe hydrogen-rich envelope in the first energy injection E inj1 . Arelatively strong shock wave propagates towards the surface andbreaks out with a rapidly rising light curve in all the models.The first energy injection ejects matter with masses of ∼ . M (cid:12) (model RSG1,2) and ∼ . M (cid:12) (model BSG1,2) (Ejected mass inmodel RSG1 and RSG2 (model BSG1 and BSG2) are equal inthe first eruption because the same amount of energy E inj1 is in-jected.). Although the ratio of E inj1 / E envelope for model RSG1,2is similar to that for model BSG1,2, there is an order of mag- Article number, page 3 of 8 & A proofs: manuscript no. main
Table 3.
Amount of ejected mass for two distinct mass eruption events corresponding to the first and the second energy injection. model First eruption a Second eruptionRSG1 0 . M (cid:12) . M (cid:12) RSG2 0 . M (cid:12) BSG1 0 . M (cid:12) . M (cid:12) BSG2 2 . M (cid:12) Notes. a RSG1 and RSG2 (BSG1 and BSG2) eject the equal mass in the first eruption because the same amount of energy E inj1 is injected.
0 5 10 15 20 25 30 35 40 45 Lu m i no s i t y [ e r g s - ] Time [day] BSG1BSG2
Fig. 4.
Light curves for model BSG1 and BSG2. The first (the second)eruption, triggered by the injected energy E inj1 ( E inj2 ), produces a peakat day ∼ two ( ∼
0 100 200 300 400 500 T e m pe r a t u r e [ K ] Time [day] RSG1RSG2
Fig. 5.
Evolution of e ff ective temperature for each RSG progenitormodel.
0 5 10 15 20 25 30 35 40 45 T e m pe r a t u r e [ K ] Time [day] BSG1BSG2
Fig. 6.
Evolution of e ff ective temperature for each BSG progenitormodel. RSG1 R ad i u s [ c m ] t = 0 [s]t = 8.4E6 [s]t = 5.0E7 [s]10 RSG2 R ad i u s [ c m ] t = 0 [s]t = 8.4E6 [s]t = 5.0E7 [s]10 BSG1 R ad i u s [ c m ] t = 0 [s]t = 3.0E5 [s]t = 4.0E6 [s]10 R ad i u s [ c m ] Mass Coordinate [M sun ]t = 0 [s]t = 3.0E5 [s]t = 4.0E6 [s]
Fig. 7.
Radii as functions of the enclosed mass for all the models. Thethree lines in each panel represent the profiles before the first energy in-jection (dotted line), between the first and the second energy injections(dashed line), and at the end of the hydrodynamical simulations (solidline). nitude di ff erence in the ejected mass above. This is because theenvelope of model BSG is denser than that of model RSG andtherefore a more energetic shock wave propagates outwards andexpels a considerable amount of the envelope. For both mod-els RSG1,2 and BSG1,2, the hydrogen-rich envelopes remain Article number, page 4 of 8uriyama and Shigeyama: The first and second mass eruption -2x10 RSG1 V e l o c i t y [ c m s - ] t = 8.4E6 [s]t = 2.5E7 [s]t = 5.0E7 [s]-2x10 -1x10 RSG2 V e l o c i t y [ c m s - ] t = 8.4E6 [s]t = 2.5E7 [s]t = 5.0E7 [s]-2x10 -1x10 BSG1 V e l o c i t y [ c m s - ] t = 3.0E5 [s]t = 5.0E5 [s]t = 4.0E6 [s]-2x10 -1x10 V e l o c i t y [ c m s - ] Mass Coordinate [M sun ]t = 3.0E5 [s]t = 5.0E5 [s]t = 4.0E6 [s]
Fig. 8.
Velocity profiles as functions of the enclosed mass for all themodels. The three lines in each panel represent the profiles before thesecond energy injection (dotted line), after the second energy injection(dashed line), and at the end of the hydrodynamical simulations (solidline). inflated after the first eruption as indicated from the significantlyaltered density profiles (Fig. 7 and 9).
Before the expanding envelope shrinks and returns to a hy-drostatic state, the second energy injection is conducted. Theamount of injected energy is the same as in the first injection formodel RSG1 ad BSG1. On the other hand, for models RSG2 andBSG2, twice (model RSG2) or 1.5 times (model BSG2) moreenergies are injected. These second energy injections trigger thesecond mass eruption events accompanied with the second peaksin luminosity. The matter ejected by the second energy injec- -16 -14 -12 -10 -8 -6 -4 RSG1 D en s i t y [ g cc - ] t = 0 [s]t = 8.4E6 [s]t = 5.0E7 [s]10 -16 -14 -12 -10 -8 -6 -4 RSG2 D en s i t y [ g cc - ] t = 0 [s]t = 8.4E6 [s]t = 5.0E7 [s]10 -18 -16 -14 -12 -10 -8 -6 -4 -2 BSG1 D en s i t y [ g cc - ] t = 0 [s]t = 3.0E5 [s]t = 4.0E6 [s]10 -18 -16 -14 -12 -10 -8 -6 -4 -2 D en s i t y [ g cc - ] Mass Coordinate [M sun ]t = 0 [s]t = 3.0E5 [s]t = 4.0E6 [s]
Fig. 9.
Same as figure 7 but for the density profiles. tion collides and interacts with the expanding envelope or matterejected by the first energy injection.There are three key di ff erences between the first and secondmass eruptions. First, the brightening phase associated with thesecond mass eruption lasts more than ten times longer than thatin the first mass eruption (Fig. 3 and 4). The luminosity graduallyincreases because photons can easily di ff use out from the shockwave in the inflated low-density envelope. After the peak, theluminosity slowly declines and the brightening phase lasts ∼ ∼ ten days in model BSG1,2.Second, there is a significant di ff erence in the color betweenthe first and second mass eruption events (Fig. 5 and 6). For ev-ery model, when the first mass eruption takes place, its e ff ectivetemperature rises by a factor of ∼ ten. On the other hand, in thesecond mass eruption, the e ff ective temperature rises but doesnot reach 10,000 K. The temperature at the local maximum inthe second mass eruption is even lower than the e ff ective tem-perature of the original state before the first energy injection(namely the output value from MESA). Thus a progenitor star Article number, page 5 of 8 & A proofs: manuscript no. main -20 -19 -18 -17 -16 -15 -14 -13 -12 D en s i t y [ g cc - ] Velocity [cm s -1 ]RSG1, 1st eruptionRSG2, 1st eruptionBSG1, 1st eruptionBSG2, 1st eruption RSG1, 2nd eruptionRSG2, 2nd eruptionBSG1, 2nd eruptionBSG2, 2nd eruption Fig. 10.
Density profiles of CSM as functions of velocity at the corecollapse. Broken lines (Solid lines) correspond to the CSM erupted bythe first injection (second injection). Grey line represents the relation ρ ∝ v − . which we adopt as a fiducial slope in case of the eruptive massloss (Kuriyama & Shigeyama 2020; Tsuna et al. 2020). observed a few years before the supernova does not necessarilyfollow the standard core mass luminosity relation constructedby the standard stellar evolution models which assume quasi-hydrostatic evolution.Third, the amount of ejected mass is di ff erent between thefirst and second mass eruption even with the same injected en-ergy ( E inj1 = E inj2 for RSG1 and BSG1). Interestingly, RSG1and BSG1 show the opposite results. While the second energyinjection ejects ∼ . ff ects,which are the weakly bound envelope after the first eruption (thise ff ect enhances eruption) and shock wave attenuation due to dif-fusion of photons (this e ff ect weakens eruption). While the lattere ff ect works in model RSG1, the former one works stronger inmodel BSG1.In model RSG2, the second energy injection ejects ∼ × times larger mass than that in model RSG1 even though the dif-ference of E inj2 between them is only a factor of two. This resultimplies that, although there are wide diversity of observed SNeIIn or II-P in terms of the presence or the amount of CSM, theremay be smaller di ff erence in the late phase progenitor evolutionand extra energy supply between them than it has been thought.Each ejected fluid element which has a positive total en-ergy (summation of thermal, gravitational, and kinetic energy)keeps expanding at an almost constant velocity until core col-lapse of the star and SN ejecta-CSM interaction. Erupted mate-rial reaches ∼ × cm (RSG1,2) or ∼ × cm (BSG1,2)from the progenitor when the star undergoes core collapse. Theirvelocities are several 10 cm s − (RSG1,2) or several 10 cm s − (BSG1,2) (Fig. 10). These values do not contradict with obser-vations (e.g., Kiewe et al. 2012). When we express the velocity-density relation in Fig. 10 as ρ ∝ v − s , the CSM formed by thefirst eruption (broken line) have larger s values compared withthat by the second ejection (solid line), which roughly follow aline with s ∼ .
5. This is because a part of photons di ff using outfrom the shock wave formed by the second ejection can be ab-sorbed and accelerate the inner part of the CSM formed by thefirst eruption. This "steepening" of s value from ∼ . ff ect the light-curve of SNe powered by CSMinteraction modeled by Chevalier (1982).
4. Discussion
Our results show unambiguous di ff erences between the firstand second mass eruption in terms of light curves, colors, andamounts of erupted unbound mass. Therefore when we discussthe observation of pre-CCSN mass eruption events and comparethem with some physical models or simulations, we may have totake the e ff ect of repeated mass eruptions seen in our simulationsand the altered density profile of the envelope into consideration.Here we present some implications for the interpretation of re-cently observed transient events.The motivation of this work is interpreting the nature of mul-tiple mass eruption events accompanied by rapid and repeatedluminosity variance like erratic pre-CCSN phase of SN 2009ipduring 2011 March-November. The photometric observationsshow magnitude oscillation with an amplitude of ∼ three magwithin the range of R (cid:39) −
20 (Pastorello et al. 2013). Theperiod of this luminosity oscillation is less than 50 days and thisphase lasts about 10 months. The peak magnitudes in R-bandand the time interval of each local peak are almost constant dur-ing this erratic phase. On the other hand, in our work, once thefirst mass eruption occurs, the density structure of the envelopeis altered. Thus the local peak luminosity and color are signifi-cantly di ff erent between the first and second mass eruption(Fig.3, 4, 5 and 6) although the same amount of energy is depositedon the same time scale (model RSG1 and BSG1). In addition,our models failed to reproduce the fast declining of the luminos-ity after the second local peak because of the extended envelope.From these view points, our results suggest that the nature ofmass eruption from SN 2009ip in 2011 cannot be explained bythe spherically symmetric eruption of a single star triggered byextra energy supply into the envelope, although there is a roomthat asymmetric eruption in 2D or 3D simulation or binary inter-actions can explain it.Observations have revealed the diversity of SNe IIn (Taddiaet al. 2013; Smith 2017) in the amount, composition, positionand morphology of CSM. Especially, there is a wide range of va-riety in the amount of CSM. While some progenitors hold morethan 20 M (cid:12) (SN 2016aps; Nicholl et al. (2020)) or 30 − M (cid:12) (SN 2010jl; Zhang et al. (2012)) or 20 M (cid:12) (SN 2006gy; Smithet al. (2010)) of CSM, others hold only 0 . M (cid:12) (SN 1998S;Fassia et al. (2001)) or less than 0 . M (cid:12) (SN 2005gl; Gal-Yam& Leonard (2009)). This variety could originate from di ff erentmechanisms of eruption to form CSM and of course from di ff er-ent progenitor mass. As introduced in Sect. 1, there are a widevariety of scenarios that may explain extra energy supply andresulting mass loss and CSM formation. On the other hand ourresults show that only a factor of two di ff erence in the amountof deposited energy results in a di ff erence of ejected mass bymore than two orders of magnitude (the second mass eruption inRSG1 and RSG2, Table 3). Thus a wide range of the amount ofCSM might also reflect small di ff erence in the amount of extraenergy supplied and the number of eruption events.When we compare the results of model RSG and BSG, wefind that model BSG requires more than ten times larger amountof energy than model RSG to eject the same mass (both of modelRSG2 and BSG1 expel ∼ . M (cid:12) throughout double eruptionevents). From this aspect, model RSG (i.e., stars in a relativelymetal rich environment) is preferred as progenitors of SNe IIn ifwe focus on only the envelope density stratification and ignorethe metallicity dependence of the physics involved in the extraenergy injection. At a glance, our results seem to be consistentwith Graham (2019), which suggests that SNe IIn prefer rela-tively higher metallicity environment compared with the other Article number, page 6 of 8uriyama and Shigeyama: The first and second mass eruption subtypes of SNe II based on a database analysis work. How-ever, there should be various physical factors which are corre-lated with metallicity and a ff ect the classification of a (sub-)typeof an SN. Therefore our result that metal rich star seems to eas-ily su ff er from mass eruption is just one of the possible factorswhich determine the environment to whom SNe IIn prefer.
5. Conclusions
We have carried out radiation hydrodynamical simulations to in-vestigate the properties of the repeated dynamical mass erup-tion events from a single massive star prior to the core-collapse,in the context of the formation of circumstellar matter (CSM)around SNe IIn. The key point of this work is that we causedmass eruption events not only once but twice by depositing en-ergy two times. The dynamical properties of single mass erup-tion event have been already studied by (Kuriyama & Shigeyama2020; Owocki et al. 2019; Dessart et al. 2010). However, recentobservations of SN IIn progenitors indicate that mass eruptionphase often occurs more than once just before core-collapse. Amass eruption event can alter the density structure of the enve-lope and therefore the subsequent mass eruption event can showcompletely di ff erent observational feature. From this view point,we deposited the extra energy into the bottom of the progenitorenvelope twice and simulated the time evolution of both erup-tion events. The progenitor models were made by MESA. Wedid not deal with the origin of extra energy which has not beencompletely understood so far, although it should be studied inour future work.Results show nonnegligible di ff erences between the firstand second mass eruption events. After the first eruption eventoccurs, the envelope is inflated temporarily on the Kelvin-Helmholtz timescale. Thus, when the second mass eruption takesplace consecutively in the inflated envelope, it shows fainter,redder, and long-term eruption. This result conflicts with obser-vations for SN 2009ip during the outburst phase in 2011 and,therefore the symmetric mass eruption model from a single starmust be ruled out for this event. Erupted material from the sec-ond eruption collides with the prior CSM from the first eruptionand alter the density profile of the prior CSM as described inSect.3.2. This interaction can a ff ect the light-curve of the sub-sequent CSM interacting SN. Another suggestion of our workis that only a few factors of di ff erence in extra energy makeslarger (by a few orders of magnitude) di ff erence in the amountof erupted mass. In other words, a little di ff erence in the pro-genitor stellar evolution can be amplified and emerges as a sig-nificant di ff erence in the observational features during the pre-CCSN phase and SN-itself. From this view point, the di ff erenceof the progenitor star evolution between SNe IIn and normal SNeII could be smaller than we think. Higher cadence and deepertransient survey in the future will provide us a larger amountof detailed pre-SN activity data and some objects would showmulti-peaked luminosity fluctuations. Interpreting them wouldrequire to include the e ff ect of multiple eruptions and the corre-sponding altered density structure discussed here. References
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Appendix A: Detailed methods of making the twoprogenitor models using MESA
The two progenitor models, RSG and BSG, which were used inour simulation as the initial models, were made by using a stellarevolution code MESA release 10398 (Paxton et al. 2011, 2013,2015, 2018, 2019).According to Table 1, initial mass and metallicity were setto the following values and we started to make these modelsevolved. initial_mass = 15.0d0initial_z = 0.02d0 (for model RSG)Zbase = 0.02d0 (for model RSG)initial_z = 0.0002 d0 (for model BSG)Zbase = 0.0002 d0 (for model RSG)
After the termination of main sequence, we set the followingoptions which designate the method of opacity and mass loss. use_Type2_opacities = .true.cool_wind_RGB_scheme = ’Dutch ’cool_wind_AGB_scheme = ’Dutch ’RGB_to_AGB_wind_switch = 1d-4Dutch_scaling_factor = 0.8