The Supernova Progenitor Mass Distributions of M31 and M33: Further Evidence for an Upper Mass Limit

Using Hubble Space Telescope (HST) photometry to measure star formation histories, we age-date the stellar populations surrounding supernova remnants (SNRs) in M31 and M33. We then apply stellar evolution models to the ages to infer the corresponding masses for their supernova progenitor stars. We analyze 33 M33 SNR progenitors and 29 M31 SNR progenitors in this work. We then combine these measurements with 53 previously published M31 SNR progenitor measurements to bring our total number of progenitor mass estimates to 115. To quantify the mass distributions, we fit power laws of the form $dN/dM propto M^{-alpha}$. Our new, larger sample of M31 progenitors follows a distribution with $alpha = 4.4pm 0.4$, and the M33 sample follows a distribution with $alpha = 3.8^{+0.4}_{-0.5}$. Thus both samples are consistent within the uncertainties, and the full sample across both galaxies gives $alpha = 4.2pm 0.3$. Both the individual and full distributions display a paucity of massive stars when compared to a Salpeter initial mass function (IMF), which we would expect to observe if all massive stars exploded as SN that leave behind observable SNR. If we instead fix $alpha = 2.35$ and treat the maximum mass as a free parameter, we find $M_{max} sim 35-45M_{sun}$, indicative of a potential maximum cutoff mass for SN production. Our results suggest that either SNR surveys are biased against finding objects in the youngest (<10 Myr old) regions, or the highest mass stars do not produce SNe.

Supernova Remnant Progenitor Masses in M31

Using HST photometry, we age-date 59 supernova remnants (SNRs) in the spiral galaxy M31 and use these ages to estimate zero-age main sequence masses (MZAMS) for their progenitors. To accomplish this, we create color-magnitude diagrams (CMDs) and use CMD fitting to measure the recent star formation history (SFH) of the regions surrounding cataloged SNR sites. We identify any young coeval population that likely produced the progenitor star and assign an age and uncertainty to that population. Application of stellar evolution models allows us to infer the MZAMS from this age. Because our technique is not contingent on precise location of the progenitor star, it can be applied to the location of any known SNR. We identify significant young SF around 53 of the 59 SNRs and assign progenitor masses to these, representing a factor of 2 increase over currently measured progenitor masses. We consider the remaining 6 SNRs as either probable Type Ia candidates or the result of core-collapse progenitors that have escaped their birth sites. The distribution of recovered progenitor masses is bottom heavy, showing a paucity of the most massive stars. If we assume a single power law distribution, dN/dM proportional to M^alpha, we find a distribution that is steeper than a Salpeter IMF (alpha=-2.35). In particular, we find values of alpha outside the range -2.7 to -4.4 inconsistent with our measured distribution at 95% confidence. If instead we assume a distribution that follows a Salpeter IMF up to some maximum mass, we find that values of M_max greater than 26 Msun are inconsistent with the measured distribution at 95% confidence. In either scenario, the data suggest that some fraction of massive stars may not explode. The result is preliminary and requires more SNRs and further analysis. In addition, we use our distribution to estimate a minimum mass for core collapse between 7.0 and 7.8 Msun.

A Global Turbulence Model for Neutrino-Driven Convection in Core-Collapse Supernovae

Simulations of core-collapse supernovae (CCSNe) result in successful explosions once the neutrino luminosity exceeds a critical curve, and recent simulations indicate that turbulence further enables explosion by reducing this critical neutrino luminosity. We propose a theoretical framework to derive this result and take the first steps by deriving the governing mean-field equations. Using Reynolds decomposition, we decompose flow variables into background and turbulent flows and derive self-consistent averaged equations for their evolution. As basic requirements for the CCSN problem, these equations naturally incorporate steady-state accretion, neutrino heating and cooling, non-zero entropy gradients, and turbulence terms associated with buoyant driving, redistribution, and dissipation. Furthermore, analysis of two-dimensional (2D) CCSN simulations validate these Reynolds-averaged equations, and we show that the physics of turbulence entirely accounts for the differences between 1D and 2D CCSN simulations. As a prelude to deriving the reduction in the critical luminosity, we identify the turbulent terms that most influence the conditions for explosion. Generically, turbulence equations require closure models, but these closure models depend upon the macroscopic properties of the flow. To derive a closure model that is appropriate for CCSNe, we cull the literature for relevant closure models and compare each with 2D simulations. These models employ local closure approximations and fail to reproduce the global properties of neutrino-driven turbulence. Motivated by the generic failure of these local models, we propose an original model for turbulence which incorporates global properties of the flow. This global model accurately reproduces the turbulence profiles and evolution of 2D CCSN simulations.

Criteria for Core-Collapse Supernova Explosions by the Neutrino Mechanism

We investigate the criteria for successful core-collapse supernova explosions by the neutrino mechanism. We find that a critical-luminosity/mass-accretion-rate condition distinguishes non-exploding from exploding models in hydrodynamic one-dimensional (1D) and two-dimensional (2D) simulations. We present 95 such simulations that parametrically explore the dependence on neutrino luminosity, mass accretion rate, resolution, and dimensionality. While radial oscillations mediate the transition between 1D accretion (non-exploding) and exploding simulations, the non-radial standing accretion shock instability characterizes 2D simulations. We find that it is useful to compare the average dwell time of matter in the gain region with the corresponding heating timescale, but that tracking the residence time distribution function of tracer particles better describes the complex flows in multi-dimensional simulations. Integral quantities such as the net heating rate, heating efficiency, and mass in the gain region decrease with time in non-exploding models, but for 2D exploding models, increase before, during, and after explosion. At the onset of explosion in 2D, the heating efficiency is $sim$2% to $sim$5% and the mass in the gain region is $sim$0.005 M$_{sun}$ to $sim$0.01 M$_{sun}$. Importantly, we find that the critical luminosity for explosions in 2D is $sim$70% of the critical luminosity required in 1D. This result is not sensitive to resolution or whether the 2D computational domain is a quadrant or the full 180$^{circ}$. We suggest that the relaxation of the explosion condition in going from 1D to 2D (and to, perhaps, 3D) is of a general character and is not limited by the parametric nature of this study.

BETHE-Hydro: An Arbitrary Lagrangian-Eulerian Multi-dimensional Hydrodynamics Code for Astrophysical Simulations

In this paper, we describe a new hydrodynamics code for 1D and 2D astrophysical simulations, BETHE-hydro, that uses time-dependent, arbitrary, unstructured grids. The core of the hydrodynamics algorithm is an arbitrary Lagrangian-Eulerian (ALE) approach, in which the gradient and divergence operators are made compatible using the support-operator method. We present 1D and 2D gravity solvers that are finite differenced using the support-operator technique, and the resulting system of linear equations are solved using the tridiagonal method for 1D simulations and an iterative multigrid-preconditioned conjugate-gradient method for 2D simulations. Rotational terms are included for 2D calculations using cylindrical coordinates. We document an incompatibility between a subcell pressure algorithm to suppress hourglass motions and the subcell remapping algorithm and present a modified subcell pressure scheme that avoids this problem. Strengths of this code include a straightforward structure, enabling simple inclusion of additional physics packages, the ability to use a general equation of state, and most importantly, the ability to solve self-gravitating hydrodynamic flows on time-dependent, arbitrary grids. In what follows, we describe in detail the numerical techniques employed and, with a large suite of tests, demonstrate that BETHE-hydro finds accurate solutions with 2$^{nd}$-order convergence.