The Value of Progenitor Radius Measurements for Explosion Modeling of Type II-Plateau Supernovae
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The Value of Progenitor Radius Measurements for Explosion Modeling of Type II-Plateau Supernovae
Jared A. Goldberg and Lars Bildsten
1, 2 Department of Physics, University of California, Santa Barbara, CA 93106, USA Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA
ABSTRACTUsing Modules for Experiments in Stellar Astrophysics (
MESA )+ STELLA , we show that very differentphysical models can adequately reproduce a specific observed Type II-Plateau Supernova (SN). Weconsider SN2004A, SN2004et, SN2009ib, SN2017eaw, and SN2017gmr, Nickel-rich ( M Ni > . M (cid:12) )events with bolometric lightcurves and a well-sampled decline from the plateau. These events alsohave constraints on the progenitor radius, via a progenitor image, or, in the case of SN2017gmr, aradius from fitting shock-cooling models. In general, many explosions spanning the parameter space ofprogenitors can yield excellent lightcurve and Fe line velocity agreement, demonstrating the success ofscaling laws in motivating models which match plateau properties for a given radius and highlightingthe degeneracy between plateau luminosity and velocity in models and observed events, which canspan over 50% in ejecta mass, radius, and explosion energy. This can help explain disagreements inexplosion properties reported for the same event using different model calculations. Our calculationsyield explosion properties when combined with pre-explosion progenitor radius measurements or arobust understanding of the outermost < . M (cid:12) of material that quantifies the progenitor radius fromSN observations a few days after explosion. Keywords: hydrodynamics — radiative transfer — stars: massive — supernovae: general — super-novae: individual (2004A, 2004et, 2009ib, 2017eaw, 2017gmr) INTRODUCTIONMassive stars (
M > ∼ M (cid:12) ) at the end of their evo-lution become red supergiants (RSGs) with radii of ≈ − R (cid:12) , before ending their lives as core-collapse Type IIP supernovae (SNe) with lightcurvesthat plateau over ≈
100 days. The progenitor radius( R ), ejected mass ( M ej ), explosion energy ( E exp ), and Ni mass ( M Ni ) determine these lightcurves (e.g. Popov1993; Sukhbold et al. 2016), and inferring these proper-ties from observations could lend insight into which starsexplode as SNe. Although early work provided scalingrelations attempting to uniquely relate plateau proper-ties and expansion velocities to explosion characteristics(e.g. Litvinova & Nadyozhin 1983; Popov 1993), recentwork highlights the nonuniqueness of lightcurve and ve-locity modeling for a given SN after ≈
20 days (Dessart& Hillier 2019; Goldberg et al. 2019; Martinez & Bersten2019).Building on Goldberg et al. (2019, hereafter GBP19),we verify these degeneracies by comparing explosions ofvery different progenitor models to Nickel-rich ( M Ni > . M (cid:12) ) events with bolometric lightcurves, a well- Corresponding author: J. A. [email protected] sampled decline from the plateau, and constraints onthe progenitor radius. We utilize the open-source 1Dstellar evolution code Modules for Experiments in Stel-lar Astrophysics (
MESA , Paxton et al. 2011, 2013, 2015,2018, 2019) for our evolutionary and explosion mod-els and the multi-group radiation-hydrodynamics instru-ment
STELLA (Blinnikov et al. 1998, 2000, 2006) to pro-duce lightcurves and model expansion velocities. Emis-sion in the first 20 days depends on the radial densitystructure of the outer < . M (cid:12) of matter around a vig-orously convecting RSG progenitor (e.g. Morozova et al.2016). SN emission during this time can be modified bythe uncertain circumstellar environment (e.g.Morozovaet al. 2017), and may reflect the intrinsically 3D struc-ture of these outer layers (see e.g. Chiavassa et al. 2011).Therefore we restrict our analysis to observations afterday ≈
20, when emission comes from the bulk of thestellar envelope. However, we still show our results forearlier times, where the qualitative trends may hold. OBSERVED SUPERNOVAE AND THEIRDEGENERACY CURVESGBP19 showed that Type IIP supernovae with Nimass ( M Ni ≥ . M (cid:12) ), luminosity at day 50 ( L ),and plateau duration ( t p ) can approximately yield theejected mass ( M ≡ M ej / M (cid:12) ) and asymptotic ex-plosion energy ( E ≡ E exp / ergs) as a function of a r X i v : . [ a s t r o - ph . S R ] M a y progenitor radius ( R ≡ R/ R (cid:12) ), via the followingrelations:log( E ) = − .
728 + 2 .
148 log( L ) − .
280 log( M Ni )+ 2 .
091 log( t p , ) − .
632 log( R ) , log( M ) = − .
947 + 1 .
474 log( L ) − .
518 log( M Ni )+ 3 .
867 log( t p , ) − .
120 log( R ) , (1)where M Ni is in units of M (cid:12) , L = L / erg s − and t p , = t p /
100 d, and log is base 10. Moreover, becauseexpansion velocities inferred from the Fe II 5169˚A lineare determined by line-forming regions near the photo-sphere, velocity data during the plateau period do notbreak this degeneracy ( L ∝∼ v , Hamuy & Pinto 2002;Kasen & Woosley 2009). Rather, SNe with the same L , t p , and M Ni and similar expansion velocities dur-ing the plateau can be realized by a family of explosionswith a range of R , E exp , and M ej obeying the Equa-tion (1) relations.2.1. Measuring Nickel Mass and Plateau Duration ofType IIP SNe
We estimate the plateau duration t p following Valentiet al. (2016), fitting the functional form y ( t ) to thebolometric luminosity ( L bol ) around the fall from theplateau: y ( t ) ≡ log( L bol ) = − A e ( t − t p ) /W + ( P × t ) + M . (2)We use the python routine scipy.optimize.curve fit to fit the lightcurve starting when the luminosity evolu-tion is 75% of the way to its steepest descent, fixing P to be the slope on the Ni tail (GBP19). The fittingparameter t p is the plateau duration. We also extractthe Ni mass from L bol by calculating the cumulativeobservable ET (Nakar et al. 2016), which corresponds tothe total time-weighted energy radiated away in the SNgenerated by the initial shock and not by Ni decay: ET c ( t ) = (cid:90) t t (cid:48) [ L bol ( t (cid:48) ) − Q Ni ( t (cid:48) )] d t (cid:48) , (3)where t is the time in days since the explosion and Q Ni = M Ni M (cid:12) (cid:16) . e − t (cid:48) /t Ni + 1 . e − t (cid:48) /τ Co (cid:17) × erg s − , (4)is the Ni → Co → Fe decay luminosity given byNadyozhin (1994), equivalent to the heating rate of theejecta assuming complete trapping with t Ni = 8 . τ Co = 111 . t → ∞ and all shock en-ergy has radiated away, the slope of the ET c curve onthe Co decay tail should be zero when the estimateof M Ni is correct. This method yields excellent agree-ment between the resulting model lightcurve tails and observed lightcurves, and with the Co decay luminos-ity (Nadyozhin 1994): L ( t → ∞ ) = 1 . × exp (cid:18) − tτ Co (cid:19) M Ni M (cid:12) erg s − . (5)2.2. Supernova Selection
In order to further explore this degeneracy, weapply these scalings to five observed supernovae:
SN2004A , SN2004et , SN2009ib , SN2017eaw , and
SN2017gmr . SN2004A was discovered by K. Itagaki on 9 Jan-uary 2004 in NGC6207 (Hendry et al. 2006). Fol-lowing Pejcha & Prieto (2015) we adopt an explosiondate of MJD 53001.53. Progenitor observations indicatelog( L p /L (cid:12) ) = 4 . ± . T eff = 3890 ±
375 K, im-plying a radius of ≈ R (cid:12) (Smartt 2015). From thePejcha & Prieto (2015) bolometric lightcurve, we getlog( L ) = − .
07. Estimates for the Ni mass include M Ni /M (cid:12) = 0 . +0 . − . from points on the bolometric-corrected V-band tail and M Ni /M (cid:12) = 0 . +0 . − . com-paring to the tail of 1987A, which the original authorsaverage to yield M Ni /M (cid:12) = 0 . +0 . − . (Hendry et al.2006). We measure a plateau duration of t p =124 daysand use M Ni = 0 . M (cid:12) . SN2004et was discovered in NGC6946 by S. Morettion 2004 September 27, with a well-constrained explo-sion date of 22.0 September 2004 (MJD 53270.0) (Liet al. 2005). There is some disagreement in the litera-ture about the progenitor (see Smartt 2009 and Davies& Beasor 2018) since follow-up imaging show R- andI-band flux excesses in the location of the inferred pro-genitor in HST pre-imaging (Crockett et al. 2011). Asa result, Martinez & Bersten (2019) report a progeni-tor radius of 350 R (cid:12) − R (cid:12) . We adopt the bolometriclightcurve given by Martinez & Bersten (2019), whichindicates log( L ) = 0 .
27. Estimates for the Ni massinclude M Ni /M (cid:12) = 0 . ± .
01 from the scaled Codecay tail of 1987A to M Ni = 0 . ± .
02 estimated us-ing V-magnitudes from 250-315 days (Sahu et al. 2006).We measure t p = 123 . M Ni = 0 . M (cid:12) . SN2009ib was discovered by the Chilean AutomaticSupernova Search on 6.30 August 2009 in NGC1559,with an estimated explosion date of MJD 55041.3(Tak´ats et al. 2015). HST pre-images indicate eithera yellow source with log( L p /L (cid:12) ) = 5 . ± .
2, or possi-bly a fainter RSG with log( L p /L (cid:12) ) = 5 . ± .
14 and R ≈ R (cid:12) assuming T eff ≈ Co decaytail, falling noticeably off of the M¨uller et al. (2017)relation between L and M Ni . From the Tak´ats et al.(2015) lightcurve, we measure log( L ) = − .
33 and M Ni /M (cid:12) = 0 . t p = 139 . , days. Nakar et al.(2016) also highlighted that this event had a ratio of theintegrated Ni decay chain energy to integrated shockenergy of η Ni = 2 .
6, much larger than typical values of η Ni ≈ . − . η Ni for SN1999em ≈ . SN2017eaw was discovered by P. Wiggins on 14.238May 2017 in NGC6946, with an estimated explosiondate of MJD 57886.0 (Szalai et al. 2019). Pre-explosionimaging suggestslog( L p /L (cid:12) ) = 4 . ± . T eff =3350 +450 − K, corresponding to R ≈ R (cid:12) , obscured bya > × − M (cid:12) dust shell extending out to 4000 R (cid:12) (Kilpatrick & Foley 2018), assuming the distance toNGC6946 to be D = 6 . ± .
15 Mpc (from the tip ofthe red giant branch (TRGB) by Tikhonov 2014). Weadopt the bolometric lightcurve of Szalai et al. (2019)using D = 6 .
85 Mpc, although more recent TRGB mea-surements suggest D = 7 . ± .
78 Mpc (Van Dyk et al.2019). Estimates for the Ni mass assuming D =6 .
85 Mpc range from M Ni /M (cid:12) = 0 . − .
045 (Sza-lai et al. 2019) to M Ni = 0 . M (cid:12) (Tsvetkov et al. 2018).From the Szalai et al. (2019) lightcurve, we measure t p = 117 . M Ni = 0 . M (cid:12) , and log( L ) = 0 . SN2017gmr occurred in NGC988, discovered onMJD 58000.266 during the DLT40 SN search withthe explosion epoch assumed to be MJD 57999.09 at D = 19 . ± R ≈ R (cid:12) . Andrews et al. (2019)find M Ni = 0 . ± . M (cid:12) assuming all late-time lu-minosty comes from Ni decay, although multipeakedemission lines emerging after day 150 suggest asymme-tries present either in the core’s explosion or in late-time interaction with the surrounding environment. Weadopt the Andrews et al. (2019) bolometric lightcurve,and measure log( L ) = 0 . M Ni /M (cid:12) = 0 .
13, and t p =94.5 days.2.3. The Degeneracy Curves
The families of explosion parameters recovered by in-serting each SN’s M Ni , L , and t p into Equations (1)are shown in Figure 1 as a function of R . Also shown isa large suite of RSG progenitor models to demonstratethe potential variety of M ej and R within reasonablestellar evolution assumptions. For each event, M ej and E exp can be inferred from the plot for a given R .The progenitor models were constructed using MESA revision 10398, and evolved to Fe core infall, followingthe example_make_pre_ccsn test case described in de-tail by Paxton et al. (2018, hereafter MESA IV). Wevaried the initial mass ( M ZAMS /M (cid:12) =10.0-15.0 in incre-ments of 0.5 M (cid:12) , and 15.0-25.0 in increments of 1.0 M (cid:12) ),surface rotation ( ω/ω crit = 0 .
0; 0 . α in the H-rich envelope ( α env =2.0; 3.0; 4.0), core over-shooting ( f ov = 0 .
0; 0.01; 0.018), and wind efficiency( η wind = 0 . − .
0, increments of 0.1) using
MESA ’s‘Dutch’ wind scheme. All models had Z = 0 .
02. Onlymodels which reached Fe core infall are shown. Ratherthan one relationship between M ej and R , this set ofmodels suggests a wide range in which RSGs can ex-ist. This diversity reflects the importance of winds in 5101520 M e j [ M (cid:12) ]
400 600 800 1000 1200 R [ R (cid:12) ]0 . . . E e x p [ e r g ] Figure 1.
Degeneracy curves for M ej (top) and E exp (bot-tom) recovered from Equations (1) as a function of R for theobserved SNe considered here. Shaded solid-color regionscorrespond to the ≈
11% RMS deviations between the mod-els of GBP19 and their recovered parameters. Additionalobservational uncertainties are not included. The M ej and R of 2179 progenitor models are also shown in the back-ground, with color ranging from yellow to purple tracking M ZAMS = 10 − M (cid:12) . determining the final masses and radii of stellar models(Renzo et al. 2017), and supports recent work showingdiversity in progenitor masses for comparable positionson the HR diagram (Farrell et al. 2020). EXPLOSION MODELS AND COMPARISON TOOBSERVATIONSWe then select progenitor models to explode in orderto match observations guided by Equations (1) appliedto a SN’s respective L , M Ni , and t p . For SNe 2004A,2004et, SN2017eaw, and 2017gmr, we chose three pro-genitor models each, consistent with the respective de-generacy curves in Figure 1, with ejecta masses near thelarger- M ej , middle- M ej , and smaller- M ej intersections ofthe theoretical curves and the progenitor model suite.For SN2017eaw, we chose three additional models con-sistent with a distance 10% farther away (i.e. increasing L and M Ni by 21%, not shown in Figure 1). Verylow M ej and radii are recovered for SN2009ib, with lit-tle overlap with our progenitor grid, so we exploded onlytwo progenitors, one off the grid ( α = 6). Properties ofthese models at the moment of explosion, input physics,and values for M Ni are shown in Table 1. Also shownare the time to shock breakout ( t sb ) and the mass abovethe photosphere at day 20 ( δm ph , ). Table 1.
Model PropertiesSN Name Model name M ZAMS f ov , α env , ω/ω crit , η w M final M c , f M c , He log( L p L (cid:12) ) T eff t sb δm ph , ( M Ni /M (cid:12) ) [ M ej , (cid:12) ][ R (cid:12) ][ E ] [ M (cid:12) ] [ M (cid:12) ] [ M (cid:12) ] [ M (cid:12) ] [K] [days] [ M (cid:12) ]2004A M9.3 R596 E0.4 11.5 0.018, 3.0, 0.0, 0.5 10.87 1.62 3.79 4.86 3900 1.6 0.032(0.042) M10.6 R482 E0.5 12.5 0.01, 4.0, 0.0, 0.2 12.28 1.64 3.89 5.20 5250 1.2 0.061M15.2 R438 E0.8 17.0 0.0, 4.0, 0.0, 0.2 16.66 1.48 5.33 5.23 5610 1.0 0.0962004et M11.8 R945 E0.76 14.0 0.018, 2.0, 0.2, 0.2 13.42 1.59 4.89 5.22 3790 2.2 0.031(0.063) M14.9 R816 E1.0 18.0 0.0, 2.0, 0.0, 0.5 16.53 1.62 5.85 5.44 4640 1.8 0.036M18.3 R791 E1.2 22.0 0.0, 3.0, 0.0, 0.5 19.89 1.55 7.70 5.25 4160 1.7 0.0402009ib M7.86 R375 E0.23 10.0 0.018, 4.0, 0.2, 0.7 9.41 1.55 3.15 5.05 5450 1.1 0.074(0.043) M10.2 R356 E0.3 12.0 0.01, 6.0, 0.2, 0.4 11.65 1.48 3.69 3.99 3040 1.1 0.0822017eaw M10.2 R850 E0.65 13.5 0.01, 2.0, 0.2, 0.8 11.99 1.77 4.24 4.92 3370 2.0 0.032at 6.85Mpc M12.7 R719 E0.84 15.0 0.01, 3.0, 0.0, 0.2 14.53 1.80 5.09 5.04 3910 1.7 0.036(0.048) M17.2 R584 E1.3 20.0 0.0, 4.0, 0.0, 0.4 18.92 1.70 6.79 5.10 4490 1.2 0.0722017eaw, mod. M11.9 R849 E0.9 14.0 0.016, 2.0, 0.0, 0.2 13.64 1.70 4.55 5.08 3690 1.8 0.032at 7.54Mpc M15.7 R800 E1.1 19.0 0.0, 3.0, 0.2, 0.4 17.33 1.66 6.83 5.18 4040 1.7 0.041(0.0581) M19.0 R636 E1.5 22.0 0.0, 4.0, 0.0, 0.2 20.51 1.55 7.74 5.54 5550 1.2 0.0562017gmr M9.5 R907 E1.9 12.0 0.018, 2.0, 0.2, 0.6 11.01 1.48 3.86 5.70 5110 1.1 0.076(0.13) M12.5 R683 E3.0 14.5 0.01, 3.0, 0.0, 0.2 14.09 1.55 4.80 5.46 5120 0.81 0.11M16.5 R533 E4.6 19.0 0.0, 4.0, 0.0, 0.4 18.09 1.57 6.28 5.29 5250 0.55 0.22 We then excised the Fe cores with an entropy cut of4 erg g − K − , and exploded these models using MESA with Duffell RTI (Duffell 2016) and the fallback esti-mation technique described in Appendix A of GBP19,with an additional velocity cut of 500 km s − at handoffto STELLA at shock breakout. All explosions resultedin negligible fallback. At shock breakout, we rescaledthe Ni distribution to match the desired M Ni , and im-ported the ejecta profile into STELLA to model the evo-lution post-shock-breakout. We used 400 spatial zonesand 40 frequency bins in
STELLA , which yields conver-gence in bolometric lightcurves on the plateau (see Fig-ure 30 of MESA IV and the surrounding discussion).For SN2017eaw at 6.85 Mpc, we used 800 spatial zonesin order to more faithfully capture the outermost lay-ers of the ejecta. Because we are focused on matchingplateau emission from the bulk of the ejecta, occurringafter day ≈
20, we do not include any extra material be-yond the progenitor photosphere for most of our modellightcurves.3.1.
Comparison to Observed SNe
Despite intrinsic scatter amounting to ≈
11% RMS de-viations between model parameters and M ej and E exp For all models except 2017eaw at 6.85 Mpc,
MESA revision10925 was used, as in GBP19. Because we consider excessemission in the early lightcurve of 2017eaw at 6.85 Mpc, revi-sion 11701 was used with a dense mesh near the surface set by‘ split merge amr logtau zoning=.true. ’ in inlist controls toensure that the outer region is adequately resolved. recovered from Equations (1) applied to model radiiand lightcurves (GBP19), computations approximatelyobeying Equations (1) produce bolometric lightcurveswhich match the observations. Figure 2 shows the re-sults for SN2004A (top two panels) and SN2004et (bot-tom two panels). Both SN2004A and SN2004et exhibitgood agreement between models, lightcurves, and ve-locity evolution on the plateau, with no model beingthe “best-fit” for either event. Photospheric velocitiesat very early times ( < ∼
20 days) do differ between dif-ferent models, with more compact, higher- E exp modelsyielding faster early-time velocities. However, velocitymeasurements before day 20 are rare, and at these timesvelocities might be modified by the circumstellar envi-ronment (e.g. Moriya et al. 2018). The early observedlightcurve ( < ∼
30 days) of SN2004et also exhibits a clearluminosity excess compared to the lightcurve models.Such excess is often attributed to interaction with an ex-tended envelope or wind, or with pre-SN outbursts(e.g.Morozova et al. 2017, 2020).All three models for SN2004et are consistent with thereported R = 350 − R (cid:12) . For SN2004A, only thelow-mass/low-energy model M9.3 R596 E0.4 is consis-tent with the progenitor observations, and we concludefor that SN that M ej < ∼ M (cid:12) and E exp < ∼ . × erg.3.2. SN2017eaw at Two Distances
To show the impact of changing the assumed distanceon our modeling, we model SN2017eaw at two differ-ent distances: 6.85 Mpc, using the fiducial Szalai et al.(2019) lightcurve, and at 7.54 Mpc, with the same t p but41 . . l og ( L b o l / e r g s − ) SN2004A
SN2004A observationsM9.3 R596 E0.4M10.6 R482 E0.5M15.2 R438 E0.8 v [ k m s − ] v Fe , τ Sob = 1 v ph , τ = 2 / . . . . l og ( L b o l / e r g s − ) SN2004et
SN2004et observationsM11.8 R945 E0.76M14.9 R816 E1.0M18.3 R791 E1.2 v [ k m s − ] v Fe , τ Sob = 1 v ph , τ = 2 / Figure 2.
Lightcurves and Fe line velocities for SN2004A(top two panels) and SN2004et (bottom two panels). Greymarkers correspond to the observations, and colored linescorrespond to explosion models, ordered in ascending M ej and E exp , and descending R . with 21% brighter L bol and M Ni = 0 . M (cid:12) . Modelswere selected to match Equations (1) with the appro-priate L , t p , and M Ni for each distance. Figure 3compares models to observations. The top two panelscorrespond to D = 6 .
85 Mpc, and the bottom two pan-els to D = 7 .
54 Mpc. Like SN2004A and SN2004et,models agree well with the data, and agreement in L also yields agreement in the velocity of the models afterday ≈
20. Agreement between models and both velocityand luminosity data is better for D = 7 .
54 Mpc. For D = 6 .
85 Mpc, two of our models, M10.2 R850 E0.65 The farther distance was motivated by the fact that velocitiesof models matching L and t p of the fiducial distance are ≈ L ∝ D ∝∼ v , (Hamuy & Pinto 2002; Kasen & Woosley 2009; GBP19), an intrin-sically brighter SN at a distance ≈
10% farther produces modelswhich better match the velocity data. This distance is also consis-tent with a recent TRGB estimate of 7 . ± .
78 Mpc (Van Dyket al. 2019). . . . l og ( L b o l / e r g s − ) SN2017eaw at 6.85Mpc
SN2017eaw observationsM10.2 R850 E0.65M12.7 R719 E0.84M17.2 R584 E1.3 0.4 M (cid:12) wind0.4 M (cid:12) wind0.4 M (cid:12) wind v [ k m s − ] v Fe , τ Sob = 1 v ph , τ = 2 / v Fe , model+wind v ph , model+wind . . . l og ( L b o l / e r g s − ) SN2017eaw at 7.54Mpc
SN2017eaw, modified distanceM11.9 R849 E0.9M15.7 R800 E1.1M19.0 R636 E1.5 v [ k m s − ] v Fe , τ Sob = 1 v ph , τ = 2 / Figure 3.
Lightcurves and Fe-line velocities for observa-tions and models of SN2017eaw at D =6.85 Mpc (top twopanels) and D =7.54 Mpc (bottom two panels). Grey mark-ers correspond to observations, and colored lines correspondto explosion models. Colored dotted lines in the upper pan-els correspond to models with an additional 0.4 M (cid:12) wind( v wind = 8 km s − , ˙ M wind = 0 . M (cid:12) /year). and M12.7 R719 E0.84, match the progenitor proper-ties within the uncertainties. At a 10% farther distance,assuming 21% brighter L p and the same T eff , only ourM11.9 R849 E0.9 model is consistent with the updatedprogenitor properties. Assuming the measured progeni-tor radius of 845 R (cid:12) , we chose models with R ≈ R (cid:12) for both distances. The 10% greater distance leadsto ≈
17% increase in M ej , from 10 . M (cid:12) to 11 . M (cid:12) and ≈
40% increase in E exp , from 0.65 × ergs to0.9 × ergs.For D = 6 .
85 Mpc, we also show lightcurves withand without a dense wind to reproduce the early ex-cess emission (top two panels of Figure 3). We af-fix a wind density profile with total mass M wind and ρ wind ( r ) = ˙ M wind / πr v wind , where ˙ M wind is a constant,and v wind is the wind velocity. We varied ˙ M wind =(0 . , . , . , . M (cid:12) / yr and v wind = (3 , , ,
12) km / swith M wind from 0 . − . M (cid:12) . In the top of Figure 3 we 41 . . . . l og ( L b o l / e r g s − ) SN2009ib
SN2009ib observationsM7.86 R375 E0.23M10.2 R356 E0.3 v [ k m s − ] v Fe , τ Sob = 1 v ph , τ = 2 / . . . . l og ( L b o l / e r g s − ) SN2017gmr
SN2017gmr observationsM9.5 R907 E1.9M12.5 R683 E3.0M16.5 R533 E4.6 v [ k m s − ] v Fe , τ Sob = 1 v ph , τ = 2 / Figure 4.
Lightcurves and Fe line velocities for SN2009ib(top two panels) and SN2017gmr (bottom two panels). Greymarkers correspond to observations, and colored lines corre-spond to explosion models. show values of v wind = 8 km s − , ˙ M wind = 0 . M (cid:12) /year,and M wind = 0 . M (cid:12) . We find that the same wind pa-rameters produce comparable early excesses when addedto the three degenerate lightcurves, suggesting that theexcess is set by properties of the wind itself and the un-derlying lightcurve, rather than, e.g. E exp . This windalso modifies the early velocity evolution. We do notclaim that this is the only way to reproduce the early ex-cess, as a variety of other outer density profiles can giverise to similar early excesses without affecting plateauproperties (e.g. Morozova et al. 2020).3.3. Modeling Challenges
For two events, SN2009IB and SN2017gmr, we seegeneral agreement between models and bulk propertiesof the lightcurves ( L and t p ), with distinct differencesshown in Figure 4. Specifically, these models differ be-yond an early luminosity excess which might be ex-plained by pulsations, a wind, varied structure of theextended stellar atmosphere, or other early interaction.In SN2009ib (top two panels of Figure 4), the rel-atively low luminosity and high Ni heating yield lightcurve models which rise significantly between days20 −
80. The narrow overlap between Equations (1)and our model grid suggests low M ej and small R .For a reasonable range of R , explosion energies recov-ered are also low ( E ≈ . − . L bol is underestimated in some way (see thediscussion in section 3.2). However, we found thatadditional models consistent with the velocity dataand a brighter lightcurve of the same t p still exhibita similar, slightly shallower positive plateau slope. Itis also possible that the estimated explosion epochis too early. Moreover, neither explosion is consis-tent with a RSG of R ≈ R (cid:12) (derived assuming T eff = 3400K), as R = 1000 R (cid:12) implies exceedinglylow M ej ≈ M (cid:12) and E exp ≈ × erg. However,model M7.86 R375 E.023 is able to reproduce the ob-served log( L p /L (cid:12) ) = 5 . ± . T eff ≈ Co-decay tail. Ob-served velocities are taken from the reported Fe-line ra-dius evolution, and are only shown before day 120, afterwhich point the evolution is not photospheric. The slightdisagreement between modeled and observed velocitiessuggests that perhaps the distance is overestimated, butmodeling to match a fainter bolometric lightcurve pro-vides no change in the apparent late-time excess.Although this event has no progenitor pre-image, if R at the time of explosion is consistent with ≈ R (cid:12) re-covered from fitting shock-cooling models to the photo-metric bands (Andrews et al. 2019), Equations (1) implyan enormous E exp ≈ × ergs! Our 533 R (cid:12) progen-itor model indeed matches L and t p when explodedwith 4 . × ergs, shown in green in the lower twopanels of Figure 4.Our modeling procedure only considers matching L and t p . To compare directly to the day 1 results in An-drews et al. (2019) Figure 9, we re-ran the SN2017gmrmodels with a surface resolution adequate to resolveemission at day 1 ( δm ph ∼ − − − M (cid:12) ). Allthree of our models yield luminosities at 1 day post-shock-breakout ( L ) a factor of ≈ L ofSN2017gmr recovered by their Sapir & Waxman (2017)shock-cooling model fits. Of our models, the day 1photospheric temperature ( T ) of M16.5 R533 E4.6does come closest to the reported shock-cooling T =25 , T ≈ , L and t p ob-servations. CONCLUSIONSThe capability of
MESA + STELLA to model observedSNe was introduced in MESA IV and demonstratedthere and by Ricks & Dwarkadas (2019) to model afew Type IIP SNe. GBP19 introduced scaling relations(Equations 1) fit from a suite of
MESA + STELLA models inorder to guide explosion modeling efforts for an observedSN lightcurve with a given L , t p , and M Ni . In the ab-sence of understanding in models of the first 20 days, ourapplication of these relations to the observed SNe 2004A,2004et, 2009ib, 2017eaw, and 2017gmr shows families ofexplosion models that match the data for a wide rangeof M ej , R , and E exp . These degeneracies will not beeasily lifted without an observed progenitor radius (andunderstanding the progenitor’s variability; see Goldberget al. 2020) or other constraints. However, when com-bined with a radius given by progenitor pre-imaging orfitting the shock-cooling phase, we show that explosionmodels can be constrained following E exp ∝ R − . and M ej ∝ R − . .If there was confidence in stellar evolutionary inputconstraining a R − M ej relation at the time of explo-sion, then these degeneracies could be broken, as as-sumed in the population synthesis/lightcurve modelingof Eldridge et al. (2019). However, when varying rota-tion, winds, core overshooting, and mixing length within a reasonable range of values, we find no single ejecta-mass − radius relation.It remains possible that detailed spectral modelingwill lend insights which might aid in uniquely determin-ing explosion properties from plateau observations. Ad-ditionally, velocity observations before day ≈
20 or pho-tospheric radii derived from shock-cooling models witha secure density structure in the outer < . M (cid:12) remainother promising paths forward to breaking the remain-ing degeneracies exhibited here.We thank Bill Paxton for continued support and ad-vancement of MESA ’s capabilities, and Josiah Schwaband Benny Tsang for conversations and guidance. Wethank the referees for helpful comments that signifi-cantly improved our presentation. We thank J´ozsefVink´o and Tam´as Szalai for providing bolometric datafor SN2017eaw. It is a pleasure also to thank K. AzaleeBoestrom, Daichi Hiramatsu, D. Andrew Howell, andStefano Valenti for correspondences about observations.J.A.G. is supported by the National Science Founda-tion (NSF) GRFP grant No. 1650114. The
MESA projectis supported by the NSF under the Software Infras-tructure for Sustained Innovation program grant ACI-1663688. This research was supported in part by theGordon and Betty Moore Foundation through GrantGBMF5076 and at the KITP by the NSF under grantPHY-1748958. We acknowledge the use of computa-tional facilities through the Center for Scientific Com-puting at the CNSI, MRL: an NSF MRSEC (DMR-1720256) and NSF CNS-1725797.This research made extensive use of the SAO/NASAAstrophysics Data System (ADS).
Software:
MESA , STELLA , py mesa reader (Wolf &Schwab 2017), SciPy (Jones et al. 2001–), matplotlib (Hunter 2007).REFERENCES