Hydrogenless Superluminous Supernova PTF12dam in the Model of an Explosion inside an Extended Envelope P. V. Baklanov1*, E. I. Sorokina1, 2**, and S. I. Blinnikov1, 2, 3*** 1Institute for Theoretical and Experimental Physics, ul. Bol’shaya Cheremushkinskaya 25, Moscow, 117218 Russia 2Sternberg Astronomical Institute, Moscow State University, Universitetskii pr. 13, Moscow, 119992 Russia 3Kavli IPMU (WPI), the University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan Received November 24, 2014 Abstract—A model of a supernova explosion inside a dense extended hydrogenless envelope is proposed to explain the properties of the light curve for one of the superluminous supernovae PTF12dam. It is argued in the literature that the flux of this supernova rises too fast to be explained by the explosion model due to the instability associated with the electron–positron pair production (pair-instability supernova, PISNe), but it is well described by the models with energy input by a magnetar. We show that the PTF12dam-type supernovae can be explained without a magnetar in a model with a radiative shock in a dense circumstellar envelope that does not require an excessively large explosion energy. DOI: 10.1134/S1063773715040027 Keywords: superluminous supernova, circumstellar envelope. INTRODUCTION an enormous amount of radioactive nickel (several or even tens of solar masses) followed by the envelope’s Rare superluminous supernovae (SLSNe) whose heating from radioactive decays according to the 44 1 luminosity at maximum light can exceed 10 erg s− , 56 56 56 chain Ni ⇒ Co ⇒ Fe; the envelope’s heating which is greater than the typical values for core- through the reprocessing of the rotational energy 42 1 collapse supernovae (CCSNe), ∼10 erg s− , by two released by a spinning-down millisecond magnetar; orders of magnitude, are encountered among the su- and the reprocessing of the kinetic energy of the shock pernovae (SNe). Modern astronomy allows SLSNe into radiation produced when the SN ejecta interact to be observed at redshifts z > 1 (Cooke et al. 2012) with the surrounding extended dense envelope. So owing to their high luminosity, which makes them far there are no convincing arguments for a specific very valuable sources of information at cosmological model. distances. Some of the SLSNe Ic exhibit a slope on the According to the standard classification of SNe, decline of their light curves that is characteristic of SLSNe were divided into two subclasses: with hydrogen lines in the spectrum (SLSNe-II) and radioactive cobalt decay. Such tails of the light curves hydrogen-poor ones (SLSNe-I) (Gal-Yam 2012; can be observed for several hundred days. One of Quimby 2013). In addition, helium lines have never the first such SLSNe Ic was SN 2007bi. The nickel been observed in SLSNe-I; therefore, these SNe are mass capable of providing the observed flux on the more accurately classified as type Ic ones. In this decline of the light curve was determined by modeling paper, we will investigate the latter type of objects. its light curve and spectrum. In the PISN model, M = 3 7 M ; an enormous explosion energy, E = Ni − ? There is no universally accepted model for 53 (0.8−1.3) × 10 erg, must be produced in this case SLSNe-I. Several alternative scenarios are con- (Gal-Yam et al. 2009; Kozyreva et al. 2014). Be- sidered: the explosion of a star with an initial mass low, we will also use the energy unit foe: 1 foe greater than 140 M (PISN) with the production of ≡ ? 1051 erg. Thus, SLSNe Ic with the PISN mechanism *E-mail: [email protected],[email protected] must explode with an energy of ∼100 foe. Moriya **E-mail: [email protected] et al. (2010) showed that the observed light curves *** E-mail: [email protected] were reproduced both in the PISN model with Mej = 95 96 BAKLANOV et al. 121 M and in the CCSN model (core-collapse SNe) spectra of PTF12dam, which allowed it to be clas- ? with a synthesized 56Ni mass near M = 6.1 M , sified as SN Ic. The measured redshift to the host Ni ? but a very large explosion energy was also required, galaxy is z = 0.107. The discovery of this SN is valu- E = 3.6 1052 erg= 36 foe. able in that the fluxes were observed before maximum × light was reached. The fast rise of the light curves Another SLSN Ic, PTF12dam, whose light curve to the peak excludes the PISN models with a large after the peak is very similar to the light curve of amount of 56Ni, which have a long radiative diffusion SN 2007bi, was discovered not so long ago. In con- time scale in the envelope and whose light curves trast to the latter, PTF12dam was discovered at the slowly rise to the peak (Nicholl 2013). Observations rise phase of the light curve; therefore, it is well known reveal a considerable broadening of spectral lines cor- how its flux rose to the peak. This imposes additional 4 1 constraints on the possible explosion models. Nicholl responding to characteristic velocities ≈10 km s− et al. (2013) showed that the PISN mechanism led during the entire period of observations of this SLSN. to an excessively long rise time of the light curve for High velocities at the peak luminosity are generally a characteristic feature of all SLSNe Ic, but they are PTF12dam and proposed instead a model with energy 3 1 input by a magnetar that did not require extremely an order of magnitude lower, ∼10 km s− , in most high energies. It should be emphasized that Nicholl cases. et al. (2013) did not construct a self-consistent model with allowance made for the interaction of the magne- MODELING tar’s radiation with the ejecta and did not consider the transfer of photons in the inner and outer SN layers. General Properties of the Models The model proposed by them is basically a roughly The presupernova models were constructed by a evaluative one and shows that the rise time and the nonevolutionary method described previously (Bak- peak luminosity could be explained at a sufficiently lanov et al. 2005; Blinnikov and Sorokina 2010). A large initial angular momentum of a magnetar with quasi-polytrope in hydrostatic equilibrium was con- a high magnetic field. structed in the inner regions. The temperature in this 0.31 In this paper, we propose not an evaluative but region is related to the density as T ∝ ρ . After an a detailed radiation-hydrodynamics model of this artificial explosion at the center, we call this region interesting object without invoking the energetics of “ejecta.” Its mass and radius are Mej and Rej, respec- a magnetar. Based on our numerical calculations of tively. the radiative transfer in the entire SN volume, we We surround the ejecta by a dense expanding en- show that very powerful and long SLSNе Ic like velope whose origin is of no great importance for our PTF12dam can be explained in terms of the model modeling. The envelope could be formed, for example, of a supernova explosion inside an extended envelope by a previous explosion (or several explosions) in (Grasberg and Nadyozhin 1986; Chugai et al. 2004; the model with pulsational pair instability (Woosley Woosley et al. 2007; Moriya et al. 2013; Baklanov et al. 2007), an intense outflow of the presupernova et al. 2013). The possibility of the formation of within several months or years before its explosion, such envelopes is justified, for example, in Woosley single or multiple mergers of stars. The velocity et al. (2007) and Moriya and Langer (2014). An profile in the envelope is chosen to be similar to that extended envelope efficiently reprocesses the kinetic obtained in the evolution calculations by Woosley energy of the radiative shock propagating through et al. (2007); more specifically, the velocity in the it into radiation from several months to ∼1 year. bulk of the envelope is considerably lower than that of The rise time of the light curve to the peak depends the ejecta and can increase considerably in the outer on the chemical composition and structure of the layers (see the model profiles in Fig. 5). A shock envelope. We find a model for which the rise time is produced at the interface between the ejecta and and the decline rate of the light curve for PTF12dam the circumstellar envelope, where the kinetic energy correspond to the observations. In this case, we are of the ejecta is efficiently converted into the thermal able to reproduce not only the bolometric luminosity motion of particles and into radiation. but also the fluxes in the main filters and the behavior The density distribution in an extended envelope is of the color temperature. p specified by a power-law profile ρ ∝ r− . An example of the density profile is shown in Fig. 1. We chose p = OBSERVATIONS OF SN PTF12dam 1.8 for our model, following one of the most suitable models from Sorokina et al. (2015). The mass and ra- SN PTF12dam was discovered on May 23, 2012, dius of the envelope are designated as Menv and Renv. at the Palomar Transient Factory (Quimby 2012). The elemental abundances in the entire model were There were no signatures of H and He lines in the homogeneous. We used a carbon–oxygen model HYDROGENLESS SUPERLUMINOUS SUPERNOVA PTF12dam 97 0 M53He48e40 –5 ρ g o l –10 10 12 14 16 logR 0 M53He48e40 –5 ρ g o l –10 0 20 40 Mr/M? Fig. 1. Radial density profile. The upper panel: the logarithm of radius in centimeters is along the horizontal axis. The lower panel: density versus Mr, the mass within radius r, i.e., versus Lagrangian mass coordinate.