Numerically Modeling the First Peak of the Type IIb SN 2016gkg
Anthony L. Piro, Marc Muhleisen, Iair Arcavi, David J. Sand, Leonardo Tartaglia, Stefano Valenti
aa r X i v : . [ a s t r o - ph . H E ] A ug A CCEPTED FOR PUBLICATION IN T HE A STROPHYSICAL J OURNAL
Preprint typeset using L A TEX style emulateapj v. 12/16/11
NUMERICALLY MODELING THE FIRST PEAK OF THE TYPE IIB SN 2016GKG A NTHONY
L. P
IRO , M ARC M UHLEISEN , I AIR A RCAVI , D
AVID
J. S
AND , L EONARDO T ARTAGLIA , AND S TEFANO V ALENTI Accepted for publication in The Astrophysical Journal
ABSTRACTMany Type IIb supernovae (SNe) show a prominent additional early peak in their light curves, which isgenerally thought to be due to the shock cooling of extended hydrogen-rich material surrounding the heliumcore of the exploding star. The recent SN 2016gkg was a nearby Type IIb SN discovered shortly after explosion,which makes it an excellent candidate for studying this first peak. We numerically explode a large grid ofextended envelope models and compare these to SN 2016gkg to investigate what constraints can be derivedfrom its light curve. This includes exploring density profiles for both a convective envelope and an opticallythick steady-state wind, the latter of which has not typically been considered for Type IIb SNe models. We findthat roughly ∼ . M ⊙ of extended material with a radius of ≈ − R ⊙ reproduces the photometric lightcurve data, consistent with pre-explosion imaging. These values are independent of the assumed density profileof this material, although a convective profile provides a somewhat better fit. We infer from our modeling thatthe explosion must have occurred within ≈ − of the first observed data point, demonstrating that thisevent was caught very close to the moment of explosion. Nevertheless, our best-fitting one-dimensional modelsoverpredict the earliest velocity measurements, which suggests that the hydrogen-rich material is not distributedin a spherically symmetric manner. We compare this to the asymmetries seen in the SN IIb remnant Cas A, andwe discuss the implications of this for Type IIb SN progenitors and explosion models. Subject headings: hydrodynamics — radiative transfer — supernovae: general — supernovae: individual: SN2016gkg INTRODUCTIONObservations of supernovae (SNe) during the first few daysprovide valuable information about their progenitors and thecircumstellar environment of the explosion (Piro & Nakar2013, and references therein). Although historically it hasbeen difficult to catch SNe at such early moments, cur-rent and forthcoming wide-field surveys have increased thefocus on early light curves. One of the exciting resultsfrom such observations is the discovery of a subclass ofSNe IIb, SNe showing evidence for both hydrogen and he-lium in early spectroscopic observations (Filippenko 1988,1997), that show a “double-peaked” light curve, wherethe first peak lasts for up to a few days and the secondpeak lasts a couple weeks. Well-observed examples ofdouble-peaked SNe IIb include SN 1993J (Wheeler et al.1993; Richmond et al. 1994), 2011dh (Arcavi et al. 2011;Ergon et al. 2014), 2011fu (Kumar et al. 2013) and 2013df(Morales-Garoffolo et al. 2014; Van Dyk et al. 2014). It isnow generally accepted that the first peak comes fromthe presence of low-mass ( ∼ . − . M ⊙ ), extended( ∼ cm ) material (Woosley et al. 1994; Bersten et al.2012; Nakar & Piro 2014; Piro 2015). This unique struc-ture is consistent with pre-explosion imaging, which has con- The Observatories of the Carnegie Institution for Science, 813 SantaBarbara St., Pasadena, CA 91101, USA; [email protected] California Institute of Technology, 1200 E California Blvd., Pasadena,CA 91125, USA Department of Physics, University of California, Santa Barbara, CA93106, USA Las Cumbres Observatory Global Telescope, 6740 Cortona Dr Ste102, Goleta, CA 93117, USA * Einstein Fellow Texas Tech University, Physics & Astronomy Department, Box 41051,Lubbock, TX 79409-1051, USA Department of Physics, University of California, Davis, CA 95616,USA nected the progenitors to yellow supergiants or at least super-giants that appear much hotter than the typical red supergiantsassociated with hydrogen-rich Type IIP SNe (Aldering et al.1994; Maund et al. 2011; Van Dyk et al. 2014). Such pro-genitors are expected for interacting binary systems (e.g.,Benvenuto et al. 2013; Yoon et al. 2017), although see thework by Kochanek (2017) which argues that Cas A (which isknown to be a Type IIb SN from its light echoes, Krause et al.2008; Rest et al. 2008, 2011; Finn et al. 2016) did not have amassive binary companion at the time of explosion (a fact werevisit later in this work).The recent well-studied Type IIb SN 2016gkg providesan excellent opportunity to test and refine our ideas aboutSNe IIb. It was caught especially early after explosion andshows a prominent double-peaked light curve. It has well-sampled multi-band coverage including ultraviolet wave-lengths, early velocity measurements of the ejecta, andpre-explosion imaging with the
Hubble Space Telescope (Kilpatrick et al. 2017; Tartaglia et al. 2017; Arcavi et al.2017). Thus far though, most of the work analyzing itsfirst peak has been restricted to analytic and semi-analyticmodels, making use of some combination of the resultsfrom Rabinak & Waxman (2011), Nakar & Piro (2014), Piro(2015), and Sapir & Waxman (2016). Here we extend thiswork by generating a large grid of models representing anextended envelope structure (in total we run 4,800 models),which are then exploded numerically for comparison with SN2016gkg. Although the general properties we find are notqualitatively different from these previous works (we need ∼ . M ⊙ of extended material at a radius of ≈ − R ⊙ ),our calculations provide much better fits to the multi-bandlight curves and give some of the best constraints thus far forany SNe IIb progenitor outer structure.In Section 2, we describe the numerical approach employedin this work. This is followed by the generation of a large F IG . 1.— V -band absolute magnitude light curves for the first peak as K c and R e are varied for a convective outer density profile. In the top panel, wefix R e = 199 . R ⊙ and vary K c = 4 . × , . × , . × , . × , . × , . × , . × , . × , . × .and . × g cm − / from narrow to wide. In the bottom panel, we fix K c = 1 . × g cm − / and vary R e = 79 . , . , . , . , . , . , . , . , . , and . R ⊙ from narrow to wide. grid of models, which are compared to the photometry andvelocity evolution of SN 2016gkg in Section 3. We concludein Section 4 with a summary of our results and a discussionof the implications of our work. EXPLOSION AND LIGHT CURVEIMPLEMENTATIONWe begin by describing our methods for generating stel-lar models, exploding these models, and then calculating theresulting light curves. We start with a helium core that wasgenerated from a M ⊙ zero-age main-sequence star usingthe 1D stellar evolution code MESA (Paxton et al. 2013). Us-ing the overshooting and mixing parameters recommended bySukhbold & Woosley (2014), the star is evolved until a largeentropy jump between the core and envelope was established.The convective envelope is removed to mimic mass loss dur-ing a common envelope phase. The resulting helium core hasa mass of ≈ . M ⊙ .Using this helium core, we next stitch on an extended enve-lope of material to mimic the hydrogen-rich material expectedaround SNe IIb. For this we consider both a convective enve-lope with density profile parameterized as ρ c ( r ) = K c /r / (1)and a steady wind profile parameterized as ρ w ( r ) = K w /r . (2)Here the constant factor is connected to the properties of thewind by K w = ˙ M / πv, (3)where ˙ M is the mass loss rate and v is the wind’s velocity. In each case the density profile extends down until it connectssmoothly with the underlying stellar model, and it extends outto a radius R e where it is abruptly set to zero. The composi-tion is taken to be solar. The convective model would bestrepresent what is typically found in binary evolution modelsthat try to generate SNe IIb progenitors self-consistently (e.g.,Benvenuto et al. 2013; Yoon et al. 2017). As far as we know,a wind profile has not been considered before for SNe IIb pro-genitors. Our motivation for investigating it here is that whena wind is optically thick it might mimic an envelope, and itis plausible that if the SN IIb progenitor is in the midst of amass transfer event as it explodes, then the material aroundthe helium core might be better represented as a wind ratherthan an envelope.These models are then exploded with our open-source nu-merical code SNEC (Morozova et al. 2015). We assume thatthe inner . M ⊙ of the models form a neutron star and excisethis region before the explosion. A Ni mass of . M ⊙ isplaced at the inner edge of the ejecta, with the exact value notbeing critical to our calculation because we only compare thefirst ≈ . of the calculations with the data. The compo-sitional profiles are smoothed using a “boxcar” approach withthe same parameters as in Morozova et al. (2015), and unlikeour previous Type II calculations we do not use an opacityfloor. This is important for having the correct drop of opac-ity as the hydrogen-rich extended material recombines. Weuse a “thermal bomb mechanism” for the explosion, wherea luminosity is provided to the inner region of the ejecta togenerate the explosion. We add an energy of the bomb tothe internal energy in the inner . M ⊙ of the model for aduration of such that the final energy of the explosion is E = 10 E erg . In the work of Morozova et al. (2015,2016, 2017), we explore a range of durations around thistimescale and do not find a considerable differences in thelight curves properties. The equation of state includes con-tributions from ions, electrons and radiation, with the degen-eracy effects taken into account as in Paczy´nski (1983). Wetrace the ionization fractions of hydrogen and helium solvingthe Saha equations in the non-degenerate approximation asproposed in Zaghloul et al. (2000). The numerical grid con-sists of 1000 cells. To ensure convergence, we tested modelsdown to a grid of 400 cells without noticeable changes in thelight curves. Photometric magnitudes are estimated from thesimulations by assuming a blackbody spectrum for the emis-sion and integrating over each of the desired wavebands (asopposed to just taking the model flux at some effective wave-length).Figure 1 highlights how the properties of the early peakchange as the variable K c and R e are varied for a convec-tive density profile. In the top panel, we vary K c and keep R e fixed. This mostly changes the width of the first peak becausethe mass in the convective envelope, which is given by M c = Z R e R ∗ πr ρ c ( r ) dr ≈ π K c R / e , ≈ × − K c, R / M ⊙ , (4)where K c, = K c / g cm − / and R = R e / R ⊙ ,sets the diffusion time of photons through the extended mate-rial. In the bottom panel, we vary R e and keep K c fixed. As R e increases the first peak becomes brighter, consistent withsemi-analytic expectations (Nakar & Piro 2014; Piro 2015).The width also changes because the amount of mass in theextended material also increases as shown by Equation (4).In the case of a wind profile, the width and height of thefirst peak vary with R e and K w in a similar way to the con-vective profile, thus we do not provide actual light curve plotsfor this density profile here. We do investigate the differencesbetween the convective and wind light curves further below.The mass of the optically thick wind has a different depen-dence with the extended radius, given by M w = Z R e R ∗ πr ρ w ( r ) dr ≈ πK w R e , ≈ × − K w, R M ⊙ , (5)where K w, = K w / g cm − . COMPARING SN 2016GKG TO NUMERICALMODELSPhotometric data for SN 2016gkg was mostly taken fromArcavi et al. (2017). This work should be consulted for thefull details, but to quickly summarize, the data is compiledfrom the discovery report by A. Buso and S. Otero, publicly-available early observations taken with the Las Cumbres Ob-servatory (LCO; Brown et al. 2013) global telescope networkand the All-Sky Automated Survey for Supernovae (ASAS-SN; Shappee et al. 2014), publicly-available
Swift
UVOTdata, the Advanced Technology Large Aperture Space Tele-scope (ATLAS; Tonry 2011) early-time detections, and an in-tensive followup campaign with LCO.We adopt a distance of 26.4 Mpc and a distance modu-lus of 32.11 magnitudes to SN 2016gkg, based on Tully-Fisher distance measurements to its host galaxy NGC 613(Nasonova et al. 2011). Extinction corrections are included asthe nominal value found in (Tartaglia et al. 2017). The result-ing multi-band photometric data is later shown in both Figures4 and 6 when we discuss our best fitting numerical models.Of special note are the early photometric points from A.Buso, which are shown with a black circle filled in turquoise.SN2016gkg was discovered by A. Buso on Sep 20.19 UT andreported by A. Buso and S. Otero . The first point, estimatedat 19th magnitude in a clear filter, is extremely important forconstraining the models, and thus we include it in our analysiseven though it is currently only reported in the included linkand not published. Though the band is unfiltered, we modelit as g -band given the early, hot phase of the SN. The exactband is not crucial for the results of our modeling. We triedother bands as well and did not see strong changes in our fitsas long as the assumed band is on the Rayleigh-Jeans side ofthe spectrum. The key is just that this data point is includedbecause it is important for informing us on how quickly thelight curve is rising at these early phases.3.1. Convective Envelope Models
We first consider fitting envelope models with a convectivedensity profile to SN 2016gkg. We include 20 different radiiwith R e = 12 . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , . , and . R ⊙ , and 15 different density scalings with K c = 4 . × , . × , . × , . × , . × , . × , . × , . × , . × , . × , . × , . × , . × , . × , and . × http://ooruri.kusastro.kyoto-u.ac.jp/mailarchive/vsnet-alert/20188 https://wis-tns.weizmann.ac.il/object/2016gkg F IG . 2.— Contours of σ (red), σ (yellow), σ (green), σ (blue), and σ (purple) for an explosion with E = 1 . and a convective densityprofile. The best fit considered model has R e = 199 . R ⊙ and K c =1 . × g cm − / , which corresponds to M c ≈ . M ⊙ . Lines ofconstant envelope mass (black, dashed lines) are drawn using Equation (4). g cm − / . These are exploded at 8 different energies of E = 0 . , . , . , . , . , . , . , and . . Thus in all weran 2,400 convective envelope explosion models.The models were compared to the data only over the first . so that we focus on just the first peak of the SN.In this way we are not sensitive to the details of the amount,location, or mixing of Ni, which would influence the riseto the second peak. This comparison was evaluated with asimple χ calculation, where we take χ = X i ( M i, observed − M i, model ) / ∆ M i, observed , (6)where M i, observed and M i, model are the observed and modelabsolute magnitudes, respectively, ∆ M i, observed is the ob-served magnitude error, and the index i runs over all datapoints in all photometric bands. In addition, because of theirconstraining nature, we require the model to go through thefirst two data points by A. Buso and S. Otero. For each cal-culated model, we search through various potential explosiontimes using a bisectional algorithm until we find an explosiontime that minimizes χ . This is taken to be the χ for thatparticular model. Once the full grid of models is run, we canidentify the minimum χ for the entire grid. The next stepis how to interpret these values of χ . The issue is thatthe models will never be an exact fit to nature, and in additionthere are systematic uncertainties in both the modeling and thedata, as well as the fact that the grid spacing is not infinitelysmall. Therefore, we should not necessarily find χ = 1 .Our approach to this problem is to consider χ as basicallythe best we can do and therefore effectively treat χ = 1 .From this we can then estimate σ , σ , and σ uncertaintiesas models with χ < χ , χ < χ , and χ < χ ,respectively.The results of applying this procedure are shown for the F IG . 3.— Contours of σ (red), σ (yellow), σ (green), σ (blue), and σ (purple) for an explosion with E = 0 . , . , . , . , . , . , . ,and . (as labeled) and a convective density profile. This demonstrates thatthere are many similarly well-fit models over a range of reasonable energies,although the absolutely best fit model is at E = 1 . , as shown previouslyin Figure 2. Although not labeled here, lines of constant M c run from . , . , and . M ⊙ from left to right in each panel (dashed, black lines). particular explosion energy E = 1 . in Figure 2. There are300 models considered across this panel. The best fit modelcorresponds to the red region with a value R e = 199 . R ⊙ and K c = 1 . × g cm − / , so that M c ≈ . M ⊙ .We note though that given the coarseness of our grid (see thevalues listed above) and uncertainties in the modeling, therestill remains at least a error in these quantities.Also plotted in Figure 2 are lines of constant M c usingEquation (4). From this we see there are two degeneraciesacting in Figure 2. The first is at roughly constant R e . This issimply set by the maximum luminosity of the first peak. Thesecond runs along at roughly constant M c , which is set by thewidth of the first peak. Such degeneracies are expected fromthe scalings described in more detail by Piro (2015), but it isreassuring for our fitting routine here that they naturally ap-pear. This lends some robustness to our derived parametersfor the envelope material even if there are uncertainties in themodeling in detail.In Figure 3, we consider the χ contours across all consid-ered energies. This shows that although the energy we con-sidered in Figure 2 of E = 1 . gives overall the best fit,an energy of E = 1 . can give a similarly good fit witha slight larger radius. One can also see that as the energy isvaried different degeneracies gain or lose strength. At low F IG . 4.— Comparison of the multi-band data of SN 2016gkg (Arcavi et al.2017) with our best fit convective envelope model using E = 1 . , R e =199 . R ⊙ , and K c = 1 . × g cm − / , so that M c ≈ . M ⊙ . Earlydata points from A. Buso and S. Otero are emphasized with a black outline. energy, most of the degeneracy is for fixed R e because thesemodels have difficulty matching the width of the first peak.As the energy increases, the width is better matched and adegeneracy at constant M c grows stronger. Nevertheless, in-dependent of these issues, this demonstrates how robustly M c and R e can be constrained from this modeling with values of ∼ . M ⊙ and ≈ − R ⊙ , respectively, where we takethe spread for the value of R e as roughly our σ uncertainties.Distance is an additional uncertainty not included in this esti-mate. Since R e scales proportional to the luminosity at peak,for a distance D the scaling is roughly R e ∝ D .It should be noted that there is also a degeneracy betweenthe explosion energy and the mass of the core, because thelarger the core is, the less energy there is available for theenvelope. Therefore, one should really think about the en-ergy provided by the shock to the envelope, which scales as(Nakar & Piro 2014) E e ≈ × E (cid:18) M core M ⊙ (cid:19) − . (cid:18) M c . M ⊙ (cid:19) . erg . (7)This is an important distinction because the early time evolu-tion and the associated velocities will better reflect E e ratherthan E . For our best fit energy of E = 1 . and M core =3 . M ⊙ (once the neutron star mass is subtracted off), weestimate from Equation (7) that E e ≈ . × erg . Thusa larger or smaller E would be expected for a smaller orlarger M core , respectively, to keep this value of E e roughlyfixed.The overall best fit model is shown in comparison to themulti-band data in Figure 4. In comparison to previous semi-analytic fits to the data, the numerical models do a better jobof following the changes from short to long wavelengths. Inparticular, the model by Piro (2015) predicts a much moresymmetrical peak, which does an okay job of representingthe data at optical wavelength, but does increasingly worse atshorter wavelengths. This is because the accelerating shockvelocity in the decreasing density near the surface of the en-velope causes a stronger temperature evolution than predictedin the one-zone model by Piro (2015), which does not followthis velocity gradient.Furthermore, this comparison demonstrates how crucial theearly data from A. Buso and S. Otero are for constraining therise of the first peak and thus the envelope model. In fact,we infer from our modeling that the explosion must have oc-curred within ≈ − of this first data point! This is veryclose to the moment of explosion; for example, SN 2011fewas also observed very early as well and this was at roughly4 hrs (Bloom et al. 2012). As wide field, transient surveysgrow in the future, this work demonstrates the powerful con-straints we will be able to provide once more early time datais available.Another aspect to note is that the best fit extended massof . M ⊙ is much less than the values around ∼ . M ⊙ that are typically presented by Woosley et al. (1994) andBersten et al. (2012) for SNe IIb. This is because the firstpeak is most sensitive to only the mass near the maximumradius and not the total amount of hydrogen present (see themore detailed discussion in Nakar & Piro 2014, and in par-ticular their Figure 2, which explicitly shows how the massmeasured by the first peak compares with the total hydrogenshell mass). So while the total hydrogen mass can indeed be ∼ . M ⊙ to produce a realistic, hydrostatic model of a con-vective envelope, the first peak itself only can be utilized tomeasure the outer . M ⊙ of material.3.2. Wind Models
We next consider a wind-like density profile for the enve-lope material. Traditionally SN IIb progenitors are thoughtto have extended, convective envelopes due to a recent masstransfer event that stripped the majority of its hydrogen-richenvelope (e.g., Benvenuto et al. 2013; Yoon et al. 2017). Nev-ertheless, if a star is in the midst of a mass transfer event, andthe mass loss rate is great enough, the progenitor could inprinciple look like a yellow supergiant just from the opticallythick wind. This is not traditionally considered for SNe IIb,but we explore such a density profile here in case assumptionsabout the density profile introduce uncertainties in the param-eters estimations.For our grid of wind models we consider the same 20 val-ues for R e and 8 values for E as for the convective mod-els discussed in Section 3.1. For the mass loading factor, weagain consider 15 values with K w = 6 . × , . × , . × , . × , . × , . × , . × , . × , . × , . × , . × , . × , . × , . × , and . × g cm − . This againconstitutes 2,400 different wind models.The comparison of the wind models with the data is sum-marized in Figure 5, plotted in the same way as before inFigure 3. The lines of constant M w use Equation (5), andone can see that the degeneracy in M e (especially at larger E ) follow the slope of these lines. Overall, this he best fitmodel is at E = 1 . , with R e = 251 . R ⊙ and K w =2 . × g cm − , which corresponds to M w ≈ . M ⊙ .This is remarkably close to the result using a convective den-sity profile, especially considering the coarseness of the grid.This demonstrates a strong constraint on these quantities, in-dependent of the density profile.Even though the best fit convective and wind density pro-file models have essentially the same radii and mass associ- F IG . 5.— The same as Figure 3, but now with a wind density profile. Theoverall best fit model is at E = 1 . , with R e = 199 . R ⊙ and K w =4 . × g cm − , which corresponds to M w ≈ . M ⊙ using Equation(5). Lines of constant M w run from . , . , and . M ⊙ from left toright in each panel (dashed, black lines).F IG . 6.— Same as Figure 4, but this time comparing to our best fit windmodel with E = 1 . , R e = 251 . R ⊙ and K w = 2 . × g cm − ,corresponding to M w ≈ . M ⊙ ated with them, the best fit light curve for a wind profile iscompared to the data in Figure 6. This shows that the windprofile gives a noticeably worse fit that the convective pro-file. The decline from the peak is just too steep in compar-ison to the wind profile model, perhaps arguing that such aprofile cannot explain the data. In addition, it is importantto ask whether such a wind model is even physically plausi-ble. Using Equation (3), and an estimated wind velocity of v ≈
100 km s − , the corresponding mass loss rate would be ˙ M ≈ . M ⊙ yr − . This appears very high compared to whatis normally expected for massive stars, although maybe it rep-resents a star in the midst of mass transfer to a close binarycompanion as is expected to take place for the progenitors ofSNe IIb. Furthermore, the length of time implied by the ra-dius of the extended material is ∼ weeks. With such a shorttimescale, it is implausible that the presence of enhanced windgeneration should randomly occur so close to explosion. Ei-ther the two are casually linked, or perhaps the wind modeldoes not really happen in nature. Future work should be doneto better understand whether a wind environment as inferredhere could actually be present in these binary scenarios.3.3. Photospheric Velocities
Besides having early photometry, SN 2016gkg was also ex-ceptional because it had especially early spectra and velocitymeasurements in comparison to other SNe IIb. This providesa unique opportunity to use early velocities as another con-straint on these models.In Figure 7, we plot velocity data for SN 2016gkg fromTartaglia et al. (2017), which were computed by measuringthe positions of the minima of the P-Cygni absorption com-ponents. This is not all the lines that were measured, ratherthis is meant to present a representation of the fastest ( H α ) andslowest ( CaII H&K and
FeII 5169 ) features observed duringthese early phases. Nominally, one would expect that thesevelocities represent an upper limit to the photospheric veloc-ity, where the photospheric velocity roughly corresponds towhere the continuum emission is mostly being generated.We also plot in Figure 7 the photospheric velocities inferredfrom our explosion modeling. These are defined as the veloc-ity at the radius where the optical depth satisfies τ = Z ∞ r κρdr = 2 / , (8)where κ is the specific opacity. Each color line in Figure 7represents a best fit model to the photometry for a given valueof E . The specific value of E = 1 . is represented with athicker line to highlight that this was our best fit model over-all. The numerical models generically show a large gradientin velocity as the photosphere transitions from the low den-sity extended material into the higher density helium core. Acomparison between the numerical results and the data showthat none of the calculations are consistent with the observa-tions. Even the lowest energy explosion we consider overpre-dicts the velocities at the earliest times. The best fit explosionenergy does even worse. We make a similar comparison inFigure 8 for our wind models to emphasize that this problemcannot be reconciled by using a different density profile. Atthe earliest times, high velocities can cause the the lines tobecome diluted. This can cause the velocity measurements tobe more difficult to make, but it does not appear to explain thediscrepancy we find here.How can these differences between the theory and obser- F IG . 7.— Velocity data from Tartaglia et al. (2017) for a representativerange of spectral lines (as labeled) in comparison to the best fit convectivedensity model for each considered energy. The best fit model with E = 1 . is highlighted with a thicker line.F IG . 8.— The same as Figure 7, but in this case comparing to the best fitwind models at each energy. vations be reconciled when the photometric fits seem reason-able? One resolution would be if the hydrogen-rich mate-rial of this SN is not distributed spherically symmetrically. Insuch a case, the material we are modeling to produce the firstpeak is indeed moving faster and is hotter than the materialrepresented by the H α absorption, but the two componentshave different angular distributions. This is interesting be-cause it might provide an important clue about the nature ofhydrogen-rich material surrounding the helium core, which isrelated to the progenitor scenarios. For example, one couldexpect for a wind or strong mass transfer event that the mate-rial would be denser (and thus able to sustain the shock gener-ated by the SN) in some regions rather than others dependingon the binary configuration.Alternatively, the asymmetries we are inferring here maypoint to the generation of deeper asymmetries from the explo-sion itself. Light echoes from the SN that generated the CasA remnant show that it was a SN IIb as is being studied here(Krause et al. 2008; Rest et al. 2008, 2011; Finn et al. 2016).Detailed studies of the distribution of material and kinemat-ics in the remnant show that the explosion must have beenvery asymmetric with some indication that it could have evenhad a jet-like component (Milisavljevic & Fesen 2013, 2015;Fesen & Milisavljevic 2016).Cas A is additionally interesting because the region withinits remnant does not show evidence for a massive ( & M ⊙ )companion at the moment of explosion (Kochanek 2017).This is surprising both because models of SN IIb progenitorstypically invoke a binary origin (e.g., Benvenuto et al. 2013;Yoon et al. 2017), but also because the great majority of mas-sive stars are in binaries (Sana et al. 2012). One way to rec-oncile this is if Cas A was instead the result of a merger (asolution also suggested by Kochanek 2017), so that there wasa companion, but it was lost before the SN. A merger mightalso explain the asymmetries that we infer for SN 2016gkgas well as those seen in the remnant of Cas A. In the future,it will be important to continue looking for companions tonearby SNe IIb to get better statistics on how many were inbinaries and how many may be due to mergers.Finally, we note that Folatelli et al. (2014) also point outthat some SNe IIb have strangely low velocities and discusswhether this can be produced by asymmetries. In that casethough the features in question are HeI 5876 and
HeI 7065 ,and they are being measured well after the first peak and closeto the second peak. Thus that work is probing different mate-rial than the very shallow material we are focusing on here. Atlarger depths, the low velocities are more natural, and may po-tentially be attributed to the high ionization energy of helium(Piro & Morozova 2014), but further work should be done toprobe how deep asymmetries may be present in SN IIb ejecta. CONCLUSIONS AND DISCUSSIONWe have investigated the constraints placed by the well-resolved first light curve peak of SN 2016gkg by comparingthese observations to a large grid of numerical envelope mod-els. We considered both convective and wind density profilesto test whether the specific profile assumed leads to any biasin the inferred properties. We find that the first peak is well-described by extended material with a mass of ≈ . M ⊙ and radius ≈ − R ⊙ . Although these values are inde-pendent of the density distribution, we find that the convectiveprofile gives a somewhat better fit to the data in comparisonto the wind profile.As mentioned in Section 3.1, this mass is just refers to theextended material, so that in a realistic stellar model the to-tal hydrogen mass could be larger. This radius is consistentwith pre-explosion imaging with the Hubble Space Telescope by Kilpatrick et al. (2017), who constrained the radius to be ∼ − R ⊙ . It is somewhat larger than the early tempera-ture modeling by Tartaglia et al. (2017), who use the analyticwork of Rabinak & Waxman (2011) to find ∼ − R ⊙ .The numerical models provide a much more detailed fit to thedata (see Figure 4), even for different density profiles, whichhelps strengthen the argument for the radius we find. Themeasured explosion energy is E = 1 . , but this is degener-ate with the mass of the helium core, as described by Equation(7). We infer from our modeling that the explosion must haveoccurred within ≈ − of the first observed data point,demonstrating that this event was caught very close to the mo-ment of explosion.SN 2016gkg also has some of the earliest velocity mea-surements of any SN IIb, potentially providing a unique lookinto the details of the hydrogen-rich outer material. Compar-ing our predicted photospheric velocity evolution to these ob-served velocities show that the models nearly always predicttoo high of velocities. We suggest that this may be due toasymmetries in the hydrogen-rich outer material, or even theexplosion itself. We also discuss our results in light of theremnant asymmetries and the lack of a companion for Cas A,which may point to a merger origin (Kochanek 2017).Asymmetry is, of course, a limitation of the one-dimensional modeling performed in this study. Therefore,our modeling may really only represent the densest, opticallythick regions of the hydrogen-rich ejecta, with the envelopemass we infer actually being an upper limit if this material isnot distributed the same in all directions. It is an open ques-tion how the SN shock would propagate in such a geometrybecause it is possible that the helium-core ejecta may flowmore readily to less dense regions, impacting how well thehydrogen-rich material can be thermalized by the explosion.Early spectropolarimetry data would be helpful for measur-ing the strength of these asymmetries as well as following howlong they last. This would provide some idea about how farthe asymmetries extend into the exploding star. Already, us-ing data at radio and X-ray wavelengths as well as late-timespectra, there are indications of a diversity of circumstellarenvironments around SNe IIb (e.g., Chevalier & Soderberg2010; Maeda et al. 2015; Kamble et al. 2016). These probemuch larger radii and less dense material than the work pre-sented here. Nevertheless, looking for correlations betweenthese studies and the mismatch between theoretical and obser-vational velocities as found here may be one way of teasingout the origin of these different populations.We thank Maria Drout, Chris Kochanek, and Ben Shappeefor feedback on a previous draft, and Saurabh Jha for helpfuldiscussions. We thank the Summer Undergraduate ResearchFellowship (SURF) program at Caltech, which supported theinternship of M.E.M. at the Carnegie Observatories. We alsothank Drew Clausen for generating the M ⊙ model and as-sociated helium core with MESA that was used in this work.Support for I.A. was provided by NASA through the EinsteinFellowship Program, grant PF6-170148. D.J.S acknowledgessupport from NSF grant AST-1517649. The computationswere performed on the MIES cluster of the Carnegie Obser-vatories, which was made possible by a grant from the Ah-manson Foundation.