Self Similar Adiabatic Strong Explosion in a Medium Gravitationally Free Falling to a Point Mass

We develop a generalisation to the classical Sedov Taylor explosion where the medium free falls to a point mass at the centre of the explosion. To verify our analytic results, we compare them to a suite of numerical simulations. We find that there exists a critical energy below which, instead of propagating outward the shock stalls and collapses under gravity. Furthermore, we find that the value of the critical energy threshold decreases when the adiabatic index increases and material is more evenly distributed within the shocked region. We apply this model to the problem of a shock bounce in core collapse supernova, in which the proto neutron star serves as the point mass. The relation between the threshold energy and the distribution of mass in the shock might help explain how turbulence prevents shock stalling and recession in a core collapse supernova explosion.

Magnetic fields in late-stage proto-neutron stars

ABSTRACT We explore the thermal and magnetic field structure of a late-stage proto-neutron star (proto-NS). We find the dominant contribution to the entropy in different regions of the star, from which we build a simplified equation of state (EOS) for the hot neutron star (NS). With this, we numerically solve the stellar equilibrium equations to find a range of models, including magnetic fields and rotation up to Keplerian velocity. We approximate the EOS as a barotrope, and discuss the validity of this assumption. For fixed magnetic field strength, the induced ellipticity increases with temperature; we give quantitative formulae for this. The Keplerian velocity is considerably lower for hotter stars, which may set a de facto maximum rotation rate for non-recycled NSs well below 1 kHz. Magnetic fields stronger than around 1014 G have qualitatively similar equilibrium states in both hot and cold NSs, with large-scale simple structure and the poloidal field component dominating over the toroidal one; we argue this result may be universal. We show that truncating magnetic field solutions at low multipoles leads to serious inaccuracies, especially for models with rapid rotation or a strong toroidal-field component.

Magnetorotational core collapse of possible GRB progenitors. III. Three-dimensional models

We explore the influence of non-axisymmetric modes on the dynamics of the collapsed core of rotating, magnetized high-mass stars in three-dimensional simulations of a rapidly rotating star with an initial mass of $M_{\rm \small {ZAMS}} = 35 \, M_{\odot }$ endowed with four different pre-collapse configurations of the magnetic field, ranging from moderate to very strong field strength and including the field predicted by the stellar evolution model. The model with the weakest magnetic field achieves shock revival due to neutrino heating in a gain layer characterized by a large-scale, hydrodynamic m = 1 spiral mode. Later on, the growing magnetic field of the proto neutron star launches weak outflows into the early ejecta. Their orientation follows the evolution of the rotational axis of the proto neutron star, which starts to tilt from the original orientation due to the asymmetric accretion flows impinging on its surface. The models with stronger magnetization generate mildly relativistic, magnetically driven polar outflows propagating over a distance of 104 km within a few 100 ms. These jets are stabilized against disruptive non-axisymmetric instabilities by their fast propagation and by the shear of their toroidal magnetic field. Within the simulation times of around 1 s, the explosions reach moderate energies and the growth of the proto neutron star masses ceases at values substantially below the threshold for black hole formation, which, in combination with the high rotational energies, might suggest a possible later proto-magnetar activity.

Developing an end-to-end simulation framework of supernova neutrino detection

Massive stars can explode as supernovae at the end of their life cycle, releasing neutrinos whose total energy reaches 1053erg. Moreover, neutrinos play key roles in supernovae, heating and reviving the shock wave as well as cooling the resulting proto-neutron star. Therefore, neutrino detectors are waiting to observe the next galactic supernova and several theoretical simulations of supernova neutrinos are underway. While these simulation concentrate mainly on only the first one second after the supernova bounce, the only observation of a supernova with neutrinos, SN 1987A, revealed that neutrino emission lasts for more than 10 seconds. For this reason, long-time simulation and analysis tools are needed to compare theories with the next observation. Our study is to develop an integrated supernova analysis framework to prepare an analysis pipeline for treating galactic supernovae observations in the near future. This framework deals with the core-collapse, bounce and proto-neutron star cooling processes, as well as with neutrino detection on earth in a consistent manner. We have developed a new long-time supernova simulation in one dimension that explodes successfully and computes the neutrino emission for up to 20 seconds. Using this model we estimate the resulting neutrino signal in the Super-Kamiokande detector to be about 1,800 events for an explosion at 10 kpc and discuss its implications in this paper. We compare this result with the SN 1987A observation to test its reliability.

A systematic study of proto-neutron star convection in three-dimensional core-collapse supernova simulations

ABSTRACT This paper presents the first systematic study of proto-neutron star (PNS) convection in three dimensions (3D) based on our latest numerical fornax models of core-collapse supernova (CCSN). We confirm that PNS convection commonly occurs, and then quantify the basic physical characteristics of the convection. By virtue of the large number of long-term models, the diversity of PNS convective behaviour emerges. We find that the vigour of PNS convection is not correlated with CCSN dynamics at large radii, but rather with the mass of PNS − heavier masses are associated with stronger PNS convection. We find that PNS convection boosts the luminosities of νμ, ντ, $\bar{\nu }_{\mu }$, and $\bar{\nu }_{\tau }$ neutrinos, while the impact on other species is complex due to a competition of factors. Finally, we assess the consequent impact on CCSN dynamics and the potential for PNS convection to generate pulsar magnetic fields.

Wave heating from proto-neutron star convection and the core-collapse supernova explosion mechanism

ABSTRACT Our understanding of the core-collapse supernova explosion mechanism is incomplete. While the favoured scenario is delayed revival of the stalled shock by neutrino heating, it is difficult to reliably compute explosion outcomes and energies, which depend sensitively on the complex radiation hydrodynamics of the post-shock region. The dynamics of the (non-)explosion depend sensitively on how energy is transported from inside and near the proto-neutron star (PNS) to material just behind the supernova shock. Although most of the PNS energy is lost in the form of neutrinos, hydrodynamic and hydromagnetic waves can also carry energy from the PNS to the shock. We show that gravity waves excited by core PNS convection can couple with outgoing acoustic waves that present an appreciable source of energy and pressure in the post-shock region. Using one-dimensional simulations, we estimate the gravity wave energy flux excited by PNS convection and the fraction of this energy transmitted upwards to the post-shock region as acoustic waves. We find wave energy fluxes near $10^{51}\, \mathrm{erg}\, \mathrm{s}^{-1}\,$ are likely to persist for $\sim \! 1\, \mathrm{s}$ post-bounce. The wave pressure on the shock may exceed $10{{\ \rm per\ cent}}$ of the thermal pressure, potentially contributing to shock revival and, subsequently, a successful and energetic explosion. We also discuss how future simulations can better capture the effects of waves, and more accurately quantify wave heating rates.