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How Much H and He Is" Hidden" in Sne Ib/C? I.-Low-Mass Objects

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How Much H and He Is Mon. Not. R. Astron. Soc. (2012) (MN LATEX style file v2.2) How much H and He is “hidden” in SNe Ib/c? I. – low-mass objects S. Hachinger1,2, P. A. Mazzali1,2, S. Taubenberger1, W. Hillebrandt1, K. Nomoto3,4, D. N. Sauer5,6 1Max-Planck-Institut f¨ur Astrophysik, Karl-Schwarzschild-Str. 1, D-85748 Garching, Germany 2Istituto Nazionale di Astrofisica-OAPd, vicolo dell’Osservatorio 5, I-35122 Padova, Italy 3Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwanoha 5-1-5, Kashiwa, Chiba 277-8583, Japan 4Department of Astronomy, School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan 5Department of Astronomy, Stockholm University, Alba Nova University Centre, SE-10691 Stockholm, Sweden 6Meteorologisches Institut, Ludwig-Maximilians-Universit¨at M¨unchen, Theresienstr. 37, D-80333 M¨unchen, Germany arXiv v2, 2013 Jan 31. The published version is available at www.blackwell-synergy.com. ABSTRACT H and He features in photospheric spectra have seldom been used to infer quantitatively the properties of Type IIb, Ib and Ic supernovae (SNe IIb, Ib and Ic) and their progenitor stars. Most radiative transfer models ignored NLTE effects, which are extremely strong especially in the He-dominated zones. In this paper, a comprehensive set of model atmospheres for low-mass SNe IIb/Ib/Ic is presented. Long-standing questions such as how much He can be contained in SNe Ic, where He lines are not seen, can thus be addressed. The state of H and He is computed in full NLTE, including the effect of heating by fast electrons. The models are constructed to represent iso-energetic explosions of the same stellar core with differently massive H/He envelopes on top. The synthetic spectra suggest that 0.06–0.14M⊙ of He and even smaller amounts of H suffice for optical lines to be present, unless ejecta asymmetries play a major role. This strongly supports the conjecture that low-mass SNe Ic originate from binaries where progenitor mass loss can be extremely efficient. Key words: supernovae: general – supernovae: individual (SN 2008ax, SN 1994I) – tech- niques: spectroscopic – radiative transfer 1 INTRODUCTION tant role in the SN-gamma-ray-burst (SN-GRB) connection: thick He or even H shells are thought to quench jets (e.g. Mazzali et al. Stripped core-collapse supernovae of types IIb, Ib and Ic (SNe IIb, 2008), from which long GRBs supposedly originate (Woosley Ib and Ic) are increasingly well observed, and long-standing is- 1993; MacFadyen & Woosley 1999; Piran 2005). arXiv:1201.1506v2 [astro-ph.SR] 29 Jan 2013 sues about the explosion physics (Mezzacappa 2005; Janka et al. Spectral modelling of the He-rich layers of SNe has an added 2007) and the progenitor stars (Georgy et al. 2009; Smartt 2009; complication: the calculation of the state of the He-rich plasma. Yoon et al. 2010; Eldridge et al. 2011) are being resolved. How- The excitation/ionisation state of the He component must devi- ever, one possibility for analyses of such SNe has quite seldom been ate significantly from a local thermodynamic equilibrium (LTE) exploited: radiative transfer modelling of the H and He features configuration in order for He I lines to be present in SNe Ib in the spectra (Swartz et al. 1993; Utrobin 1996; James & Baron (Harkness et al. 1987). Processes leading to large departures from 2010; Maurer et al. 2010). Thus, H and He abundances have rarely LTE have to be explicitly included in the simulations. The rele- been quantified. The amount of H and He that can be “hidden” in vant excitation mechanisms were discussed by Chugai (1987b) and Type Ib/c SNe, which do not show clear H or He lines, respectively, Graham (1988). They recognized that He is strongly affected by is still quite uncertain; it also depends somewhat on details of the collisions with fast electrons, which result from Compton processes ejecta configuration like the density and the degree of mixing (cf. with γ-rays from the decay of 56Ni and 56Co. Sauer et al. 2006; Yoon et al. 2010). Lucy (1991) devised a treatment of excitation and ionisation There is ample motivation for studying the H and He layers by nonthermal electrons with typical energies >10 keV and syn- of stripped-envelope SNe. The analysis of abundances and den- thesised pure He I line spectra on a thermal continuum, under en- sities will allow us to validate progenitor models for SNe Ib/Ic velope conditions typical for core-collapse SNe. For modelling the and address the question of envelope stripping. Information on the non-LTE (NLTE) state of He, he devised a treatment of the ex- state of the outer ejecta is also essential to understand early-time citation and ionisation by nonthermal electrons with typical en- light curves. At the same time, these layers may play an impor- ergies >10 keV. Then, he simultaneously calculated the radiative c 2012 The Authors. Journal compilation c 2012 RAS 2 Hachinger et al. transfer and solved the NLTE rate equations (equations of statis- stationary, as photon transport through the simulated region is much tical equilibrium). Later, Swartz et al. (1993); Utrobin (1996) and faster than changes in the SN luminosity or in the ejecta radius. Mazzali & Lucy (1998) treated SNe with He with detailed radia- In the course of a MC run, values describing the radiation tive transfer codes, including NLTE calculations. Here, we adopt a field [MC estimators – Mazzali & Lucy (1993); Lucy (1999)] are similar treatment for He and H and present a state-of-the-art code recorded at the midpoints of the shells into which the envelope is module (subsequently called “NLTE solver” or “NLTE module”) discretised2. For the present work, two estimators are particularly that integrates with the radiative transfer / spectral synthesis code relevant. One is the angle-averaged intensity in the blue wing of ˆb ˆ of Mazzali (2000) and Lucy (1999). each line, Jlu [cf. Lucy (1999) – a hat ( ) here denotes an intensity We compute and analyse spectral models for low- to in the co-moving frame, b is for “blue” and lu indicates the tran- moderate-mass SNe IIb/Ib/Ic in the photospheric phase, focussing sition between some lower level l and upper level u]. The second on the question of how much H or He can be hidden in a SN with- one is the frequency-dependent, angle-averaged intensity Jˆν . The out producing spectral lines. First, we use extensive observations of procedure to obtain Jˆν has been newly implemented; some details a SN IIb (SN 2008ax) and a SN Ic (SN 1994I) in order to construct on this are given in Appendix A. In order to reduce the noise on envelope models, respectively, by fitting the observed spectra us- MC estimators, we simulate 500000 radiation packets in each MC ing our radiative transfer code with the NLTE module [abundance run for the present study. tomography – Stehle et al. (2005)]. In a second step, we use the in- ferred abundance and density stratification for the two SNe to set up a sequence of SN IIb/Ib/Ic transition models. The transition models 2.1.2 Determination of the gas state; integration of the NLTE are characterised by decreasing H/He envelope masses until only C module and O remain. We can thus assess the H and He mass required to The MC estimators are used to obtain an improved guess on the identify these elements unambiguously in the observations. state of the gas. In the codes of Mazzali & Lucy (1993) and Mazzali We first outline the spectral synthesis code, the NLTE mod- (2000), the excitation and ionisation state is calculated using a ule (with model atoms), and the integration of the two (Sec. 2). “modified nebular approximation”. A radiation temperature T for We then present the SN IIb and Ic models (Sec. 3) and the transi- R each shell is computed such that the mean frequency of a black- tion sequence, and give limits for the H and He masses (Sec. 4). body at T matches the value ν¯ estimated from the MC run, and We further discuss the results in Sec. 5. Finally, we summarise our R the electron temperature T is approximated as findings and draw conclusions in the context of current progenitor e models for stripped-envelope core-collapse SNe (Sec. 6). Te := 0.9 TR. (1) An equivalent dilution factor W is calculated from 2 SPECTRAL MODELS WITH H AND HE IN NLTE W × B(TR)= J.ˆ (2) We use a Monte-Carlo (MC) radiative transfer code to calculate In the nebular approximation, W, TR and Te completely determine model spectra of SNe for our study. Our code has been presented by the excitation and ionisation. Lucy (1999) and Mazzali (2000) [see also Abbott & Lucy (1985), Numerically, the solution for the excitation and ionisation Mazzali & Lucy (1993)], and includes the possibility to specify a state is obtained by iteration (”plasma state loop“, Fig. 1). The cal- multi-zone chemical composition (Stehle et al. 2005). Apart from culation in the nebular approximation consists of the steps (I), (IIa) the abundances, the input parameters are a density distribution, and and (V) in Fig. 1. The cycles are started with two initial guesses – for each epoch at which we calculate spectra – the emergent lu- ne [initialisation, replacing step (I)], the excitation/ionisation state 1 minosity Lbol and the “photospheric velocity” vph . is calculated, respectively, and a density of electrons ne,free is ob- tained from that state. In general, for both ne guesses, ne,free will differ from the guess. The “real” electron density of the plasma will 2.1 Original code, integration of the NLTE module always be in between an ne guess and the respective ne,free.
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