Time-dependent Hydrodynamic Simulations Research Articles

A physical model of mass ejection in failed supernovae

During the core collapse of massive stars, the formation of the protoneutron star is accompanied by the emission of a significant amount of mass-energy ($\sim 0.3 \, M_{\odot}$) in the form of neutrinos. This mass-energy loss generates an outward-propagating pressure wave that steepens into a shock near the stellar surface, potentially powering a weak transient associated with an otherwise-failed supernova. We analytically investigate this mass-loss-induced wave generation and propagation. Heuristic arguments provide an accurate estimate of the amount of energy contained in the outgoing sound pulse. We then develop a general formalism for analyzing the response of the star to centrally concentrated mass loss in linear perturbation theory. To build intuition, we apply this formalism to polytropic stellar models, finding qualitative and quantitative agreement with simulations and heuristic arguments. We also apply our results to realistic pre-collapse massive star progenitors (both giants and compact stars). Our analytic results for the sound pulse energy, excitation radius, and steepening in the stellar envelope are in good agreement with full time-dependent hydrodynamic simulations. We show that {prior} to the sound pulses arrival at the stellar photosphere, the photosphere has already reached velocities $\sim 20-100 \%$ of the local sound speed, thus likely modestly decreasing the stellar effective temperature prior to the star disappearing. Our results provide important constraints on the physical properties and observational appearance of failed supernovae.

Mass ejection in failed supernovae: variation with stellar progenitor

We study the ejection of mass during stellar core-collapse when the stalled shock does not revive and a black hole forms. Neutrino emission during the protoneutron star phase causes a decrease in the gravitational mass of the core, resulting in an outward going sound pulse that steepens into a shock as it travels out through the star. We explore the properties of this mass ejection mechanism over a range of stellar progenitors using spherically-symmetric, time-dependent hydrodynamic simulations that treat neutrino mass loss parametrically and follow the shock propagation over the entire star. We find that all types of stellar progenitor can eject mass through this mechanism. The ejected mass is a decreasing function of the surface gravity of the star, ranging from several $M_\odot$ for red supergiants to $\sim 0.1M_\odot$ for blue supergiants and $\sim 10^{-3} M_\odot $ for Wolf-Rayet stars. We find that the final shock energy at the surface is a decreasing function of the core-compactness, and is $\lesssim 10^{47}-10^{48}$ erg in all cases. In progenitors with a sufficiently large envelope, high core-compactness, or a combination of both, the sound pulse fails to unbind mass. Successful mass ejection is accompanied by significant fallback accretion that can last from hours to years. We predict the properties of shock breakout and thermal plateau emission produced by the ejection of the outer envelope of blue supergiant and Wolf-Rayet progenitors in otherwise failed supernovae.

Outflows from accretion discs formed in neutron star mergers: effect of black hole spin

The accretion disk that forms after a neutron star merger is a source of neutron-rich ejecta. The ejected material contributes to a radioactively-powered electromagnetic transient, with properties that depend sensitively on the composition of the outflow. Here we investigate how the spin of the black hole remnant influences mass ejection on the thermal and viscous timescales. We carry out two-dimensional, time-dependent hydrodynamic simulations of merger remnant accretion disks including viscous angular momentum transport and approximate neutrino self-irradiation. The gravity of the spinning black hole is included via a pseudo-Newtonian potential. We find that a disk around a spinning black hole ejects more mass, up to a factor of several, relative to the non-spinning case. The enhanced mass loss is due to energy release by accretion occurring deeper in the gravitational potential, raising the disk temperature and hence the rate of viscous heating in regions where neutrino cooling is ineffective. The mean electron fraction of the outflow increases moderately with BH spin due to a highly-irradiated (though not neutrino-driven) wind component. While the bulk of the ejecta is still very neutron-rich, thus generating heavy r-process elements, the leading edge of the wind contains a small amount of Lanthanide-free material. This component can give rise to a ~1 day blue optical `bump' in a kilonova light curve, even in the case of prompt BH formation, which may facilitate its detection.

Red or blue? A potential kilonova imprint of the delay until black hole formation following a neutron star merger

Mergers of binary neutron stars (NSs) usually result in the formation of a hypermassive neutron star (HMNS). Whether- and when this remnant collapses to a black hole (BH) depends primarily on the equation of state and on angular momentum transport processes, both of which are uncertain. Here we show that the lifetime of the merger remnant may be directly imprinted in the radioactively powered kilonova emission following the merger. We employ axisymmetric, time-dependent hydrodynamic simulations of remnant accretion disks orbiting a HMNS of variable lifetime, and characterize the effect of this delay to BH formation on the disk wind ejecta. When BH formation is relatively prompt (~ 100 ms), outflows from the disk are sufficiently neutron rich to form heavy r-process elements, resulting in ~ week-long emission with a spectral peak in the near-infrared (NIR), similar to that produced by the dynamical ejecta. In contrast, delayed BH formation allows neutrinos from the HMNS to raise the electron fraction in the polar direction to values such that potentially Lanthanide-free outflows are generated. The lower opacity would produce a brighter, bluer, and shorter-lived ~ day-long emission (a `blue bump') prior to the late NIR peak from the dynamical ejecta and equatorial wind. This new diagnostic of BH formation should be useful for events with a signal to noise lower than that required for direct detection of gravitational waveform signatures.

Characterizing SASI- and convection-dominated core-collapse supernova explosions in two dimensions

The success of the neutrino mechanism of core-collapse supernovae relies on the supporting action of two hydrodynamic instabilities: neutrino-driven convection and the Standing Accretion Shock Instability (SASI). Depending on the structure of the stellar progenitor, each of these instabilities can dominate the evolution of the gain region prior to the onset of explosion, with implications for the ensuing asymmetries. Here we examine the flow dynamics in the neighborhood of explosion by means of parametric two-dimensional, time-dependent hydrodynamic simulations for which the linear stability properties are well understood. We find that systems for which the convection parameter is sub-critical (SASI-dominated) develop explosions once large-scale, high-entropy bubbles are able to survive for several SASI oscillation cycles. These long-lived structures are seeded by the SASI during shock expansions. Finite-amplitude initial perturbations do not alter this outcome qualitatively, though they can lead to significant differences in explosion times. Supercritical systems (convection-dominated) also explode by developing large-scale bubbles, though the formation of these structures is due to buoyant activity. Non-exploding systems achieve a quasi-steady state in which the time-averaged flow adjusts itself to be convectively sub-critical. We characterize the turbulent flow using a spherical Fourier-Bessel decomposition, identifying the relevant scalings and connecting temporal and spatial components. Finally, we verify the applicability of these principles on the general relativistic, radiation-hydrodynamic simulations of Mueller, Janka, & Heger (2012), and discuss implications for the three-dimensional case.

HYDRODYNAMICS OF CORE-COLLAPSE SUPERNOVAE AT THE TRANSITION TO EXPLOSION. I. SPHERICAL SYMMETRY

We study the transition to runaway expansion of an initially stalled core-collapse supernova shock. The neutrino luminosity, mass accretion rate, and neutrinospheric radius are all treated as free parameters. In spherical symmetry, this transition is mediated by a global non-adiabatic instability that develops on the advection time and reaches non-linear amplitude. Here we perform high-resolution, time-dependent hydrodynamic simulations of stalled supernova shocks with realistic microphysics to analyze this transition. We find that radial instability is a sufficient condition for runaway expansion if the neutrinospheric parameters do not vary with time and if heating by the accretion luminosity is neglected. For a given unstable mode, transition to runaway occurs when fluid in the gain region reaches positive specific energy. We find approximate instability criteria that accurately describe the behavior of the system over a wide region of parameter space. The threshold neutrino luminosities are in general different than the limiting value for a steady-state solution. We hypothesize that multidimensional explosions arise from the excitation of unstable large-scale modes of the turbulent background flow, at threshold luminosities that are lower than in the laminar case.

THE SPIRAL MODES OF THE STANDING ACCRETION SHOCK INSTABILITY

A stalled spherical accretion shock, such as that arising in core-collapse supernovae, is unstable to non-spherical perturbations. In three dimensions, this Standing Accretion Shock Instability (SASI) can develop spiral modes that spin-up the protoneutron star. Here we study these non-axisymmetric modes by combining linear stability analysis and three-dimensional, time-dependent hydrodynamic simulations with Zeus-MP, focusing on characterizing their spatial structure and angular momentum content. We do not impose any rotation on the background accretion flow, and use simplified microphysics with no neutrino heating or nuclear dissociation. Spiral modes are examined in isolation by choosing flow parameters such that only the fundamental mode is unstable for a given polar index, leading to good agreement with linear theory. We find that any superposition of sloshing modes with non-zero relative phases survives in the nonlinear regime and leads to angular momentum redistribution. It follows that the range of perturbations required to obtain spin-up is broader than that needed to obtain the limiting case of a phase shift of pi/2. The bulk of the angular momentum redistribution occurs during a phase of exponential growth, and arises from internal torques that are second order in the perturbation amplitude. This redistribution gives rise to at least two counter rotating regions, with the maximum angular momentum of a given sign approaching a significant fraction of the mass accretion rate times the shock radius squared (Mdot * r_shock^2 ~ 1E+47 g/cm^2/s, spin period ~60 ms). Nonlinear mode coupling at saturation causes the angular momentum to fluctuate in all directions with much smaller amplitudes.

THE HYDRODYNAMIC EVOLUTION OF IMPULSIVELY HEATED CORONAL LOOPS: EXPLICIT ANALYTICAL APPROXIMATIONS

We derive simple analytical approximations (in explicit form) for the hydrodynamic evolution of the electron temperature T(s, t) and electron density n(s, t), for one-dimensional coronal loops that are subject to impulsive heating with subsequent cooling. Our analytical approximations are derived from first principles, using (1) the hydrodynamic energy balance equation, (2) the loop scaling laws of Rosner–Tucker–Vaiana and Serio, (3) the Neupert effect, and (4) the Jakimiec relationship. We compare our analytical approximations with 56 numerical cases of time-dependent hydrodynamic simulations from a parametric study of Tsiklauri et al., covering a large parameter space of heating rates, heating timescales, heating scale heights, loop lengths, for both footpoint and apex heating, mostly applicable to flare conditions. The average deviations from the average temperature and density values are typically ≈20% for our analytical expressions. The analytical approximations in explicit form provide an efficient tool to mimic time-dependent hydrodynamic simulations, to model observed soft X-rays and extremeultraviolet light curves of heated and cooling loops in the solar corona and in flares by forward fitting, to model microflares, to infer the coronal heating function from light curves of multi-wavelength observations, and to provide physical models of differential emission measure distributions for solar and stellar flares, coronae, and irradiance.

DYNAMICS OF A SPHERICAL ACCRETION SHOCK WITH NEUTRINO HEATING AND ALPHA-PARTICLE RECOMBINATION

We investigate the effects of neutrino heating and alpha-particle recombination on the hydrodynamics of core-collapse supernovae. Our focus is on the non-linear dynamics of the shock wave that forms in the collapse, and the assembly of positive energy material below it. To this end, we perform time-dependent hydrodynamic simulations with FLASH2.5 in spherical and axial symmetry. These generalize our previous calculations by allowing for bulk neutrino heating and for nuclear statistical equilibrium between n, p and alpha. The heating rate is freely tunable, as is the starting radius of the shock relative to the recombination radius of alpha-particles. An explosion in spherical symmetry involves the excitation of an overstable mode, which may be viewed as the L=0 version of the `Standing Accretion Shock Instability'. In 2D simulations, non-spherical deformations of the shock are driven by plumes of material with positive Bernoulli parameter, which are concentrated well outside the zone of strong neutrino heating. The non-spherical modes of the shock reach a large amplitude only when the heating rate is also high enough to excite convection below the shock. The critical heating rate that causes an explosion depends sensitively on the initial position of the shock relative to the recombination radius. Weaker heating is required to drive an explosion in 2D than in 1D, but the difference also depends on the size of the shock. Forcing the infalling heavy nuclei to break up into n and p below the shock only causes a slight increase in the critical heating rate, except when the shock starts out at a large radius. This shows that heating by neutrinos (or some other mechanism) must play a significant role in pushing the shock far enough out that recombination heating takes over.

STABILITY OF A SPHERICAL ACCRETION SHOCK WITH NUCLEAR DISSOCIATION

We examine the stability of a standing shock wave within a spherical accretion flow onto a gravitating star, in the context of core-collapse supernova explosions. Our focus is on the effect of nuclear dissociation below the shock on the linear growth, and non-linear saturation, of non-radial oscillations of the shocked fluid. We combine two-dimensional, time-dependent hydrodynamic simulations using FLASH2.5 with a solution to the linear eigenvalue problem, and demonstrate the consistency of the two approaches. Previous studies of this `Standing Accretion Shock Instability' (SASI) have focused either on zero-energy accretion flows without nuclear dissociation, or made use of a detailed finite-temperature nuclear equation of state and included strong neutrino heating. Our main goal in this and subsequent papers is to introduce equations of state of increasing complexity, in order to isolate the various competing effects. In this work we employ an ideal gas equation of state with a constant rate of nuclear dissociation below the shock, and do not include neutrino heating. We find that a negative Bernoulli parameter below the shock significantly lowers the real frequency, growth rate, and saturation amplitude of the SASI. A decrease in the adiabatic index has similar effects. The non-linear development of the instability is characterized by an expansion of the shock driven by turbulent kinetic energy at nearly constant internal energy. Our results also provide further insight into the instability mechanism: the rate of growth of a particular mode is fastest when the radial advection time from the shock to the accretor overlaps with the period of a standing lateral sound wave. The fastest-growing mode can therefore be modified by nuclear dissociation.

Nonequilibrium of Ionization and the Detection of Hot Plasma in Nanoflare‐heated Coronal Loops

Impulsive nanoflares are expected to transiently heat the plasma confined in coronal loops to temperatures of the order of 10 MK. Such hot plasma is hardly detected in quiet and active regions, outside flares. During rapid and short heat pulses in rarefied loops, the plasma can be highly out of equilibrium in ionization. Here we investigate the effects of the nonequilibrium of ionization (NEI) on the detection of hot plasma in coronal loops. Time-dependent loop hydrodynamic simulations are specifically devoted to this task, including saturated thermal conduction, and coupled to the detailed solution of the equations of the ionization rate for several abundant elements. In our simulations, initially cool and rarefied magnetic flux tubes are heated to 10 MK by nanoflares deposited either at the footpoints or at the loop apex. We test for different pulse durations and find that, due to NEI effects, the loop plasma may never be detected at temperatures above ~5 MK for heat pulses shorter than about 1 minute. We discuss some implications in the framework of multistranded nanoflare-heated coronal loops.

Multithread Hydrodynamic Modeling of a Solar Flare

Past hydrodynamic simulations have been able to reproduce the high temperatures and densities characteristic of solar flares. These simulations, however, have not been able to account for the slow decay of the observed flare emission or the absence of blueshifts in high spectral resolution line profiles. Recent work has suggested that modeling a flare as a sequence of independently heated threads instead of as a single loop may resolve the discrepancies between the simulations and observations. In this paper, we present a method for computing multithread, time-dependent hydrodynamic simulations of solar flares and apply it to observations of the Masuda flare of 1992 January 13. We show that it is possible to reproduce the temporal evolution of high temperature thermal flare plasma observed with the instruments on the GOES and Yohkoh satellites. The results from these simulations suggest that the heating timescale for a individual thread is on the order of 200 s. Significantly shorter heating timescales (20 s) lead to very high temperatures and are inconsistent with the emission observed by Yohkoh.

On Magnetohydrodynamic Jet Production in the Collapsing and Rotating Envelope

We present results from axisymmetric, time-dependent hydrodynamic (HD) and magnetohydrodynamic (MHD) simulations of a gaseous envelope collapsing onto a black hole (BH). We consider gas with such small angular momentum that, after an initial transient, the flow in the HD case accretes directly onto a BH without forming a rotationally supported torus. However, in the MHD case, even with a very weak initial magnetic field, the flow settles into a configuration with four components: (1) an equatorial inflow, (2) a bipolar outflow, (3) polar funnel outflow, and (4) polar funnel inflow. We focus our analysis on the second flow component of the MHD flow, which represents a simple yet robust example of a well-organized inflow/outflow solution to the problem of MHD jet formation. The jet is heavy, highly magnetized, and driven by magnetic and centrifugal forces. A significant fraction of the total energy in the jet is carried out by a large-scale magnetic field. We review previous simulations, in which specific angular momentum was higher than that assumed here, and conclude that our bipolar outflow develops for a wide range of the properties of the flow near the equator and near the poles. Future work on such a simple inflow/outflow solution will help to pinpoint the key elements of real jets/outflows as well as help to interpret much more complex simulations aimed at studying jet formation and the collapse of magnetized envelopes.

Reconciling Hydrodynamic Simulations with Spectroscopic Observations of Solar Flares

Chromospheric evaporation is a central element of current models of solar flares. The high-velocity upflows that should accompany evaporation, however, are rarely observed in high-resolution solar flare spectra. Thus the absence of blueshifted line profiles represents a significant discrepancy between the theory and observations of this phenomenon. In this Letter we present an algorithm for computing multiple-loop time-dependent hydrodynamic simulations of solar flares using a minimum of assumptions. We show that these simulations can accurately reproduce the Ca XIX and S XV line profiles observed with the Bragg Crystal Spectrometer on Yohkoh during the earliest stages of a flare. Since our model represents the flare as a succession of independently heated threads, the strongly blueshifted emission evident during the initial heating of a thread is largely masked by emission from threads that have been heated previously and do not show bulk motions.

Density and Temperature Measurements in a Solar Active Region

We present electron density and temperature measurements from an active region observed above the limb with the Solar Ultraviolet Measurements of Emitted Radiation spectrometer on the Solar and Heliospheric Observatory. Density-sensitive line ratios from Si VIII and S X indicate densities greater than 108 cm-3 as high as 200'' (or 145 Mm) above the limb. At these heights, static, uniformly heated loop models predict densities close to 107 cm-3. Differential emission measure analysis shows that the observed plasma is nearly isothermal with a mean temperature of about 1.5 MK and a dispersion of about 0.2 MK. Both the differential emission measure and the Si XI/Si VIII line ratios indicate only small variations in the temperature at the heights observed. These measurements confirm recent observations from the Transition Region and Coronal Explorer of overdense plasma at temperatures near 1 MK in solar active regions. Time-dependent hydrodynamic simulations suggest that impulsive heating models can account for the large densities, but they have a difficult time reproducing the narrow range of observed temperatures. The observations of overdense, nearly isothermal plasma in the solar corona provide a significant challenge to theories of coronal heating.

Hydrodynamic Modeling of Active Region Loops

Recent observations with the Transition Region and Coronal Explorer (TRACE) have shown that many apparently cool (Te ~ 1-1.5 MK) active region loops are much brighter and have flatter temperature profiles than static loop models predict. Observations also indicate that these loops can persist much longer than a characteristic cooling time. Using time-dependent hydrodynamic simulations, we explore the possibility that these active region loops are actually a collection of small-scale filaments that have been impulsively heated and are cooling through the TRACE 171 A (Fe IX/X) and 195 A (Fe XII) bandpasses. We find that an ensemble of independently heated filaments can be significantly brighter than a static uniformly heated loop and would have a flat filter ratio temperature when observed with TRACE.

Semiempirical limits on the thermal conductivity of intracluster gas

A semiempirical method for establishing lower limits on the thermal conductivity of hot gas in clusters of galaxies is described. The method is based on the observation that the X-ray imaging data (e.g., Einstein IPC) for clusters are well described by the hydrostatic-isothermal beta model, even for cooling flow clusters beyond about one core radius. In addition, there are strong indications that noncooling flow clusters (like the Coma Cluster) have a large central region (up to several core radii) of nearly constant gas temperature. This suggests that thermal conduction is an effective means of transporting and redistributing the thermal energy of the gas. This in turn has implications for the extent to which magnetic fields in the cluster are effective in reducing the thermal conductivity of the gas. Time-dependent hydrodynamic simulations for the gas in the Coma Cluster under two separate evolutionary scenarios are presented. One scenario assumes that the cluster potential is static and that the gas has an initial adiabatic distribution. The second scenario uses an evolving cluster potential. These models along with analytic results show that the thermal conductivity of the gas in the Coma Cluster cannot be less than 0.1 of full Spitzer conductivity. These models also show that high gas conductivity assists rather than hinders the development of radiative cooling in the central regions of clusters.