The finite time, $τ_{\rm dep}$, over which positrons from $β^{+}$ decays of $^{56}$Co deposit energy in type Ia supernovae ejecta lead, in case the positrons are trapped, to a slower decay of the bolometric luminosity compared to an exponential decline. Significant light-curve flattening is obtained when the ejecta density drops below the value for which $τ_{\rm dep}$ equals the $^{56}$Co life-time. We provide a simple method to accurately describe this "delayed deposition" effect, which is straightforward to use for analysis of observed light curves. We find that the ejecta heating is dominated by delayed deposition typically from 600 to 1200~day, and only later by longer lived isotopes $^{57}$Co and $^{55}$Fe decay (assuming solar abundance). For the relatively narrow $^{56}$Ni velocity distributions of commonly studied explosion models, the modification of the light curve depends mainly on the $^{56}$Ni mass-weighted average density, $\langle ρ\rangle t^{3}$. Accurate late-time bolometric light curves, which may be obtained with JWST far-infrared (far-IR) measurements, will thus enable to discriminate between explosion models by determining $\langle ρ\rangle t^3$ (and the $^{57}$Co and $^{55}$Fe abundances). The flattening of light curves inferred from recent observations, which is uncertain due to the lack of far-IR data, is readily explained by delayed deposition in models with $\langle ρ\rangle t^{3} \approx 0.2\,M_{\odot}\,(10^{4}\, \textrm{km}\,\textrm{s}^{-1})^{-3}$, and does not imply supersolar $^{57}$Co and $^{55}$Fe abundances.
The hydrodynamical interaction between freely expanding supernova ejecta and a relativistic wind injected from the central region is studied in analytic and numerical ways. As a result of the collision between the ejecta and the wind, a geometrically thin shell surrounding a hot bubble forms and expands in the ejecta. We use a self-similar solution to describe the early dynamical evolution of the shell and carry out a two-dimensional special relativistic hydrodynamic simulation to follow further evolution. The Rayleigh-Taylor instability inevitably develops at the contact surface separating th…
Investigations of some type Iax supernovae have led to the suggestion that their ejecta must be layered to some degree. Such an ejecta structure has been argued as inconsistent with the well-mixed composition predicted by pure deflagrations. Based on explosion models, we create toy models in which the ejecta are artificially stratified and progressively mixed until a uniform composition is obtained. We find that models that are heavily mixed, containing burned and unburned material at all velocities, produce reasonably good agreement with SN 2012Z, for which a layered structure has been sugges…
We investigate the diversity in the wind density, supernova ejecta energy, and ejecta mass in Type IIn supernovae based on their rise times and peak luminosities. We show that the wind density and supernova ejecta properties can be estimated independently if both the rise time and peak luminosity are observed. The peak luminosity is mostly determined by the supernova properties and the rise time can be used to estimate the wind density. We find that the ejecta energy of Type IIn supernovae needs to vary by factors of 0.2-5 from the average if their ejecta mass is similar. The diversity in the …
We discuss our VLA and VLBI observations of supernova 1986J, which is characterized by a compact radio-bright component within the expanding shell of ejecta. No other supernova (SN) has such a central component at cm wavelengths. The central component therefore provides a unique probe of the propagation of radio signals at cm wavelengths through the ejecta of a young SN. Such a probe is important in the context of Fast Radio Bursts (FRB), which, in many models, are thought to be produced by young magnetars or neutron stars. The FRB signals would therefore have to propagate through the expandin…
The innermost ejecta of core-collapse supernovae are considered to be the sources of some iron-group and heavier nuclei. The ejecta are predominantly driven by neutrino heating, principally due to neutrino capture on free neutrons and protons. Such neutrino interaction plays a crucial role for setting neutron richness in the ejecta. Recent hydrodynamics work with sophisticated neutrino transport indicates that the ejecta are only mildly neutron rich or even proton rich. In such conditions a wide variety of trans-iron isotopes are synthesized, while the neutron richness is insufficient for the …
We conduct three-dimensional hydrodynamical simulations of weak jets that we launch into a core collapse supernovae (CCSNe) ejecta half an hour after the explosion and find that the interaction of the fast jets with the CCSN ejecta creates high pressure zones that induce a backflow that results in mass accretion onto the newly born neutron star. In cases of weak jets, a total power of 10^45-10^46 erg, the backflow mass accretion might power up to an order of magnitude more energetic jets. In total, the jets of the two post-explosion jet-launching episodes have enough energy to influence the mo…
We build three simple bipolar ejecta models for core collapse supernovae (CCSNe), as expected when the explosion is driven by strong jets, and show that for an observer located in the equatorial plane of the ejecta, the light curve has a rapid luminosity decline, and even an abrupt drop. In calculating the geometrically modified photosphere we assume that the ejecta has an axisymmetrical structure composed of an equatorial ejecta and faster polar ejecta, and has a uniform effective temperature. At early times the photosphere in the polar ejecta grows faster than the equatorial one, leading to …
Fast ejecta expelled in binary neutron star (NS) mergers or energetic supernovae (SNe) should produce late-time synchrotron radio emission as the ejecta shocks into the surrounding ambient medium. Models for such radio flares typically assume the ejecta expands into an unperturbed interstellar medium (ISM). However, it is also well-known that binary NS mergers and broad-lined Ic SNe can harbor relativistic jetted outflows. In this work, we show that such jets shock the ambient ISM ahead of the ejecta, thus evacuating the medium into which the ejecta subsequently collides. Using an idealized sp…
We present a study of 28 Type I superluminous supernovae (SLSNe) in the context of the ejecta mass and photospheric velocity. We combine photometry and spectroscopy to infer ejecta masses via the formalism of radiation diffusion equations. We show an improved method to determine the photospheric velocity by combining spectrum modeling and cross correlation techniques. We find that Type I SLSNe can be divided into two groups by their pre-maximum spectra. Members of the first group have the W-shaped absorption trough in their pre-maximum spectrum, usually identified as due to O II. This feature …
Early light from core-collapse supernovae, now detectable in high-cadence surveys, holds clues to a star and its environment just before it explodes. However, effects that alter the early light have not been fully explored. We highlight the possibility of non-radial flows at the time of shock breakout. These develop in sufficiently non-spherical explosions if the progenitor is not too diffuse. When they do develop, non-radial flows limit ejecta speeds and cause ejecta-ejecta collisions. We explore these phenomena and their observational implications, using global, axisymmetric, non-relativisti…
I study cases where a neutron star (NS; or a black hole) companion to a type Ib or type Ic (stripped-envelope) core collapse supernova (CCSN) accretes mass from the explosion ejecta and launches jets minutes to hours after explosion. The NS orbits at a pre-explosion radius of a=1-5Ro. I find that when the ejecta velocity drops to be <1000-1500km/s the ejecta gas that the NS accretes possesses sufficient specific angular momentum to form an accretion disk around the NS. The NS accretes a fraction of 3e-5 to 3e-4 of the ejecta mass through an accretion disk over a time period of 10min to few hou…
An examination of late-time, optical spectra of type Ia supernovae revealed surprisingly narrow absorption features which only become visible a few months after maximum light. These features, most clearly seen in the late-time spectra of the bright, recent type Ia supernovae ASASSN-14lp and SN 2017bzc, appear as narrow absorptions at ~4840 A, ~5000 A, and as a sharp inflection at ~4760 A on the red side of the prominent late-time 4700 A feature. A survey of on-line archival data revealed similar features present in the spectra of ten other normal and 91T-like SNe Ia, including SN 2011fe. Unlik…
We investigate the explosive nucleosynthesis during two dimensional neutrino-driven explosion of ultra-stripped Type Ic supernovae evolved from 1.45 and 1.5 M$_\odot$ CO stars. These supernovae explode with the explosion energy of $\sim 10^{50}$ erg and release $\sim 0.1$ M$_\odot$ ejecta. The light trans-iron elements Ga-Zr are produced in the neutrino-irradiated ejecta. The abundance distribution of these elements has a large uncertainty because of the uncertainty of the electron fraction of the neutrino-irradiated ejecta. The yield of the elements will be less than 0.01 M$_\odot$. Ultra-str…
We carry out a comprehensive study of supernova ejecta-companion interaction in massive binary systems. We aim to physically understand the kinematics of the interaction and predict observational signatures. To do this we perform simulations over a vast parameter space of binary configurations, varying the masses of the progenitor and companion, structure of the companion, explosion energy, and orbital separation. Our results were not so consistent with classical models by Wheeler et al. 1975, sometimes deviating by an order of magnitude. We construct an alternative simple model which explains…
Clumpy structures are a common feature in X-ray images of young Type Ia supernova remnants (SNRs). Although the precise origin of such clumps remains unclear there are three generic possibilities: clumpiness imposed during the explosion, hydrodynamic instabilities that act during the remnant's evolution, and pre-existing structures in the ambient medium. In this article we focus on discriminating between clumping distributions that arise from the explosion and those from the remnant's evolution using existing 3D hydrodynamical simulations. We utilize the genus statistic for this discrimination…
We propose a simple model to explain the velocity of young neutron stars. We attempt to confirm a relationship between the amount of mass ejected in the formation of the neutron star and the `kick' velocity imparted to the compact remnant resulting from the process. We assume the velocity is given by $v_{\rm kick}=α\,(M_{\rm ejecta} / M_{\rm remnant}) + β\,$. To test this simple relationship we use the BPASS (Binary Population and Spectral Synthesis) code to create stellar population models from both single and binary star evolutionary pathways. We then use our Remnant Ejecta and Progenitor Ex…
We study the hydrodynamics and nucleosynthesis in the double-detonation model of Type Ia supernovae (SNe~Ia) and the interaction between the ejecta and a surviving white dwarf (WD) companion in the double-degenerate scenario. We set up a binary star system with $1.0M_\odot$ and $0.6M_\odot$ carbon-oxygen (CO) WDs, where the primary WD consists of a CO core and helium (He) shell with $0.95$ and $0.05M_\odot$, respectively. We follow the evolution of the binary star system from the initiation of a He detonation, ignition and propagation of a CO detonation, and the interaction of SN ejecta with t…
In this paper, we investigate two hydrogen-poor superluminous supernovae (SLSNe) iPTF15esb and iPTF13dcc whose light curves (LCs) show significant deviation from the smooth rise and fall. The LC of iPTF15esb exhibits two peaks and a post-peak plateau, and furthermore the late-time spectrum of iPTF15esb shows a strong, broad H$α$ emission line. The early-time LC of iPTF13dcc shows a long duration bump followed by the second peak. Here we propose an ejecta-circumstellar medium (CSM) interaction model involving multiple shells/winds and use it to explain the LCs of iPTF15esb and iPTF13dcc. We fin…
I review studies of core collapse supernovae (CCSNe) and similar transient events that attribute major roles to jets in powering most CCSNe and in shaping their ejecta. I start with reviewing the jittering jets explosion mechanism that I take to power most CCSN explosions. Neutrino heating does play a role in boosting the jets. I compare the morphologies of some CCSN remnants to planetary nebulae to conclude that jets and instabilities are behind the shaping of their ejecta. I then discuss CCSNe that are descendants of rapidly rotating collapsing cores that result in fixed-axis jets (with smal…
Type Ia supernovae are generally agreed to arise from thermonuclear explosions of carbon-oxygen white dwarfs. The actual path to explosion, however, remains elusive, with numerous plausible parent systems and explosion mechanisms suggested. Observationally, type Ia supernovae have multiple subclasses, distinguished by their lightcurves and spectra. This raises the question whether these reflect that multiple mechanisms occur in nature, or instead that explosions have a large but continuous range of physical properties. We revisit the idea that normal and 91bg-like supernovae can be understood …
We present the results of 3D hydrodynamic simulations of gamma-ray burst (GRB) jet emanating from a massive star with a particular focus on the formation of high-velocity quasi-spherical ejecta and the jet-induced chemical mixing. Recent early-time optical observations of supernovae associated with GRBs (e.g., GRB 171205A/SN 2017iuk) indicate a considerable amount of heavy metals in the high-velocity outer layers of the ejecta. Using our jet simulations, we show that the density and chemical structure of the outer ejecta implied by observations can be naturally reproduced by a powerful jet pen…
The majority of massive stars are formed in binary systems. It is hence reasonable to expect that most core-collapse supernovae (CCSNe) take place in binaries and the existence of a companion star may leave some imprints in observed features. Having this in mind, we have conducted two-dimensional hydrodynamical simulations of the collisions of CCSNe ejecta with the companion star in an almost-equal-mass ($\sim 10M_\odot$) binary to find out possible consequences of such events. In particular we pay attention to the amount of mass removed and its dependence on the binary separation. In contrast…
We build a toy model where the central object, i.e., a newly born neutron star or a black hole, launches jets at late times and show that these jets might account for peaks in the light curve of some peculiar (i.e., having unusual light curves) core collapse supernovae (CCSNe) when the jets interact with the CCSN ejecta. We assume that the central object accretes fallback material and launches two short-lived opposite jets weeks to months after the explosion. We model each jet-ejecta interaction as a spherically symmetric `mini explosion' that takes place inside the ejecta. We assume that each…
Radiative Transfer Modeling of Stripped-envelope Supernovae II: Neural Network Emulation of Light Curves
Center for Astrophysics | Harvard & Smithsonian（天体物理中心 | 哈佛与史密森尼学会）；The NSF AI Institute for Artificial Intelligence and Fundamental Interactions（美国国家科学基金会人工智能基础相互作用研究所）；David A. Dunlap Department of Astronomy and Astrophysics, University of Toronto（多伦多大学戴维·A·邓普尔天文学与天体物理学系）；Department of Astronomy, The University of Texas at Austin（德克萨斯大学奥斯汀分校天文学系）；Department of Physics and Astronomy, Purdue University（普渡大学物理与天文学系）；Department of Statistics, University of California, Santa Cruz（加州大学圣克鲁兹分校统计学系）
We discuss the possibility of obtaining Fast Radio Bursts (FRBs) from the interior of supernovae, in particular SN 1986J. Young neutron stars are involved in many of the possible scenarios for the origin of FRBs, and it has been suggested that the high dispersion measures observed in FRBs might be produced by the ionized material in the ejecta of associated supernovae. Using VLA and VLBI measurements of the Type IIn SN 1986J, which has a central compact component not so far seen in other supernovae, we can directly observe for the first time radio signals which originate in the interior of a y…
An increase in the number of studied Type Ia supernovae (SNe~Ia) has demonstrated that this class of explosions has a greater diversity in its observables than was previously assumed. The reasons (e.g. the explosion mechanism, progenitor system) for such a diversity remain unknown. Here, we analyse a sample of $r$-band light curves of SNe~Ia, focusing on their behaviour $\sim$ 2-4 weeks after maximum light, i.e. the second maximum. We characterise the second maximum by its timing ($t_{r_2}$) and the integrated flux ($\overline{\mathcal{F}}_{r_2}$). We find that $t_{r_2}$ correlates with the "c…
We present the results of modelling archival observations of type Ib SN 1999dn. In the spectra, two He I absorption features are seen: a slower component with larger opacity, and a more rapid He I component with smaller opacity. Complementary results are obtained from modelling the bolometric light curve of SN 1999dn, where a two-zone model (dense inner region, and less dense outer region) provides a much better fit than a one-zone model. A key result we find is that roughly equal amounts of radioactive material are found in both regions. The two-zone analytical model provides a more realistic…
We use the two-components bipolar toy model of core collapse supernova (CCSN) ejecta to fit the rapid decline from maximum luminosity in the light curve of the type IIb CCSN SN 2018gk (ASASSN-18am). In this toy model we use a template light curve from a different CCSN that is similar to SN 2018gk, but that has no rapid drop in its light curve. The bipolar morphology that we model with a polar ejecta and an equatorial ejecta increases the maximum luminosity and causes a steeper decline for an equatorial observer, relative to a similar spherical explosion. The total energy and mass of our toy mo…
Explaining the observed diversity of supernovae (SNe) and the physics of explosion requires knowledge of their progenitor stars, which can be obtained by constraining the circumstellar medium (CSM). Models of the SN ejecta colliding with CSM are necessary to infer the structure of the CSM and tie it back to a progenitor model. Recent SNe I revealed CSM concentrated at a distance $r\sim10^16$ cm, for which models of SN interaction are extremely limited. In this paper, we assume the concentrated region is a "wall" representing swept-up material, and unswept material lies outside the wall. We sim…
We report the first results from our long-term observational survey aimed at discovering late-time interaction between the ejecta of hydrogen-poor Type I supernovae and the hydrogen-rich envelope expelled from the progenitor star several decades/centuries before explosion. The expelled envelope, moving with a velocity of ~10 -- 100 km s$^{-1}$, is expected to be caught up by the fast-moving SN ejecta several years/decades after explosion depending on the history of the mass-loss process acting in the progenitor star prior to explosion. The collision between the SN ejecta and the circumstellar …
Supernova remnants (SNRs) are diffuse extended sources characterized by a complex morphology and a non-uniform distribution of ejecta. Such a morphology reflects pristine structures and features of the progenitor supernova (SN) and the early interaction of the SN blast wave with the inhomogeneous circumstellar medium (CSM). Deciphering the observations of SNRs might open the possibility to investigate the physical properties of both the interacting ejecta and the shocked CSM. This requires accurate numerical models which describe the evolution from the SN explosion to the remnant development a…
The shape of the light curve peak of radioactive--powered core--collapse "stripped--envelope" supernovae constrains the ejecta mass, nickel mass, and kinetic energy by the brightness and diffusion time for a given opacity and observed expansion velocity. Late--time light curves give constraints on the ejecta mass and energy, given the gamma--ray opacity. Previous work has shown that the principal light curve peaks for SN~IIb with small amounts of hydrogen and for hydrogen/helium--deficient SN~Ib/c are often rather similar near maximum light, suggesting similar ejecta masses and kinetic energie…
We present a photometric study of 17 Type Ia supernovae (SNe) based on multi-color (Bessell BVRI) data taken at Piszkesteto mountain station of Konkoly Observatory, Hungary between 2016 and 2018. We analyze the light curves (LCs) using the publicly available LC-fitter SNooPy2 to derive distance and reddening information. The bolometric LCs are fit with a radiation-diffusion Arnett-model to get constraints on the physical parameters of the ejecta: the optical opacity, the ejected mass and the expansion velocity in particular. We also study the pre-maximum (B-V) color evolution by comparing our …
Ground-based optical spectra and Hubble Space Telescope images of ten core-collapse supernovae (CCSNe) obtained several years to decades after outburst are analyzed with the aim of understanding the general properties of their late-time emissions. New observations of SN 1957D, 1970G, 1980K, and 1993J are included as part of the study. Blueshifted line emissions in oxygen and/or hydrogen with conspicuous line substructure are a common and long-lasting phenomenon in the late-time spectra. Followed through multiple epochs, changes in the relative strengths and velocity widths of the emission line…
SN 2007bi and SN 1999as are among the first superluminous supernovae discovered. SN 2007bi was suggested to be powered by the radioactive decay of a large amount (5 - 10 Msun) of 56Ni. SN 1999as has a similar spectrum to SN 2007bi. One suggested way to synthesize such a large amount of 56Ni is through energetic core-collapse supernovae from very massive progenitors. Although the synthetic light curves of extremely energetic core-collapse supernovae have been shown to be consistent with SN 2007bi, no synthetic spectra have been reported. Here, we present synthetic spectra of extremely energetic…
A Monte Carlo code (ARTIS) for modelling time-dependent three-dimensional spectral synthesis in chemically inhomogeneous models of Type Ia supernova ejecta is presented. Following the propagation of gamma-ray photons, emitted by the radioactive decay of the nucleosynthesis products, energy is deposited in the supernova ejecta and the radiative transfer problem is solved self-consistently, enforcing the constraint of energy conservation in the co-moving frame. Assuming a photoionisation dominated plasma, the equations of ionisation equilibrium are solved together with the thermal balance equati…
Very massive 140-260 Msun stars can die as highly-energetic pair-instability supernovae (PI SNe) with energies of up to 100 times those of core-collapse SNe that can completely destroy the star, leaving no compact remnant behind. These explosions can synthesize $0.1-30$ Msun of radioactive Ni56, which can cause them to rebrighten at later times when photons due to Ni56 decay diffuse out of the ejecta. However, heat from the decay of such large masses of Ni56 could also drive important dynamical effects deep in the ejecta that are capable of mixing elements and affecting the observational signa…
We present POSSIS, a time-dependent three-dimensional Monte Carlo code for modelling radiation transport in supernovae and kilonovae. The code incorporates wavelength- and time-dependent opacities and predicts viewing-angle dependent spectra, light curves and polarization for both idealized and hydrodynamical explosion models. We apply the code to a kilonova model with two distinct ejecta components, one including lanthanide elements with relatively high opacities and the other devoid of lanthanides and characterized by lower opacities. We find that a model with total ejecta mass $M_\mathrm{ej…
It was recently shown that the bolometric light curves of type II supernovae (SNe) allow an accurate and robust measurement of the product of the radiation energy in the ejecta, $E_r$, and the time since the explosion, $t$, at early phases ($t\lesssim 10d$) of the homologous expansion. This observable, denoted here $ET \equiv E_rt$ is constant during that time and depends only on the progenitor structure and explosion energy. We use a 1D hydrodynamic code to find $ET$ of simulated explosions of 145 red supergiant progenitors obtained using the stellar evolution code MESA, and relate this obser…
The dense wind environment (or circumstellar medium) may be ubiquitous for the regular Type II supernovae (SNe) before the explosion, the interaction of which with the SN ejecta could result in a wind breakout event. The shock generated by the interaction of the SN ejecta and the wind can accelerate the protons and subsequently the high-energy gamma-rays and neutrinos could arise from the inelastic pp collisions. In this work, we present the detailed calculations of gamma-ray and neutrino production for the regular Type II SNe. The calculation is executed by applying time-dependent evolutions …
We construct a numerical light curve model for interaction-powered supernovae that arise from an interaction between the ejecta and the circumstellar matter (CSM). In order to resolve the shocked region of an interaction-powered supernova, we solve the fluid equations and radiative transfer equation assuming the steady states in the rest frames of the reverse and forward shocks at each time step. Then we numerically solve the radiative transfer equation and the energy equation in the CSM with the thus obtained radiative flux from the forward shock as a radiation source. We also compare results…
Type Ia supernovae (SNe Ia) are likely the thermonuclear explosions of carbon-oxygen white-dwarf stars, but their progenitor systems remain elusive. A few theoretical scenarios for the progenitor systems have been suggested, which have been shown to agree with some observational properties of SNe Ia. However, several computational challenges prohibit a robust comparison to the observations. We focus on the observed $t_0-M_\text{Ni56}$ relation, where $t_0$ (the $γ$-rays' escape time from the ejecta) is positively correlated with $M_\text{Ni56}$ (the synthesized $^{56}$Ni mass). Comparing to th…
We present an analytic model for bolometric light curves which are powered by the interaction between supernova ejecta and a dense circumstellar medium. This model is aimed at modeling Type IIn supernovae to determine the properties of their supernova ejecta and circumstellar medium. Our model is not restricted to the case of steady mass loss and can be applied broadly. We only consider the case in which the optical depth of the unshocked circumstellar medium is not high enough to affect the light curves. We derive the luminosity evolution based on an analytic solution for the evolution of a d…
[Abridged] Superluminous Supernovae (SN2006gy, SN2005gj, SN2005ap, SN2008fz, SN2003ma) have been a challenge to explain by standard models. We present an alternative scenario involving a quark-nova (QN), an explosive transition of the newly born neutron star to a quark star in which a second explosion (delayed) occurs inside the already expanding ejecta of a normal SN. The reheated SN ejecta can radiate at higher levels for longer periods of time primarily due to reduced adiabatic expansion losses, unlike the standard SN case. Our model is successfully applied to SN2006gy, SN2005gj, SN2005ap, …
(Abridged) The explosion mechanism of electron-capture supernovae (ECSNe) remains equivocal. We attempt to constrain the explosion mechanism (neutron-star-forming implosion or thermonuclear explosion) and the frequency of occurrence of ECSNe using nucleosynthesis simulations of the latter scenario, population synthesis, the solar abundance distribution, pre-solar meteoritic oxide grain isotopic ratio measurements and the white dwarf mass-radius relation. Tracer particles from 3d hydrodynamic simulations were post-processed with a large nuclear reaction network in order to determine the complet…
Plasma Instabilities Dominate Radioactive Transients Magnetic Fields: The self-confinement of leptons in Type Ia and Core-Collapse Supernovae, and Kilonovae
We present the nucleosynthesis of magneto-rotational supernovae (MR-SNe) including neutrino-driven and magneto-rotational-driven ejecta based, for the first time, on 2D simulations with accurate neutrino transport. The models analysed here have different rotation and magnetic fields, allowing us to explore the impact of these two key ingredients. The accurate neutrino transport of the simulations is critical to analyse the slightly neutron-rich and proton-rich ejecta that are similar to the, also neutrino-driven, ejecta in standard supernovae. In the model with strong magnetic field, the r-pro…
