ABSTRACT This study presents a method for approximating the multidimensional effects of Rayleigh-Taylor (RT) instability as a modification of the one-dimensional (1D) hydro equations. This ...modification is similar to the Shakura-Sunyaev prescription for modeling the coarse-grained effects of turbulence in astrophysical disks. The model introduces several dimensionless tunable parameters that are calibrated by comparing with high-resolution two-dimensional axisymmetric numerical calculations of RT unstable flows. A complete description of the model is presented, along with a handful of test problems that demonstrate the extent to which the 1D model is able to reproduce multidimensional effects.
ABSTRACT This work presents the publicly available moving-mesh magnetohydrodynamics (MHD) code DISCO. DISCO is efficient and accurate at evolving orbital fluid motion in two and three dimensions, ...especially at high Mach numbers. DISCO employs a moving-mesh approach utilizing a dynamic cylindrical mesh that can shear azimuthally to follow the orbital motion of the gas. The moving mesh removes diffusive advection errors and allows for longer time-steps than a static grid. MHD is implemented in DISCO using an HLLD Riemann solver and a novel constrained transport (CT) scheme that is compatible with the mesh motion. DISCO is tested against a wide variety of problems, which are designed to test its stability, accuracy, and scalability. In addition, several MHD tests are performed which demonstrate the accuracy and stability of the new CT approach, including two tests of the magneto-rotational instability, one testing the linear growth rate and the other following the instability into the fully turbulent regime.
This study uses numerical hydrodynamics calculations and a novel method for densely sampling parameter space to measure the precise shape of a gap opened by a planet in a gaseous disk, as a function ...of planet-to-star mass ratio, disk Mach number, and disk viscosity. Formulas for gap depth and width are determined, which are combined to form a complete formula for surface density as a function of radius in the disk. This new analytical formula is compared with numerically derived gaps opened by planets ranging from very low masses up to a few times Jupiter's mass, and excellent agreement is found over a wide range of parameter space relevant to planet-disk interactions. A simple-to-use code is presented to rapidly generate synthetic disk profiles.
ABSTRACT Numerical hydrodynamics calculations are performed to determine the conditions under which giant planet eccentricities can be excited by parent gas disks. Unlike in other studies, ...Jupiter-mass planets are found to have their eccentricities amplified-provided their orbits start off as eccentric. We disentangle the web of co-rotation, co-orbital, and external resonances to show that this finite-amplitude instability is consistent with that predicted analytically. Ellipticities can grow until they reach of order of the disk's aspect ratio, beyond which the external Lindblad resonances that excite eccentricity are weakened by the planet's increasingly supersonic epicyclic motion. Forcing the planet to still larger eccentricities causes catastrophic eccentricity damping as the planet collides into gap walls. For standard parameters, the range of eccentricities for instability is modest; the threshold eccentricity for growth (∼0.04) is not much smaller than the final eccentricity to which orbits grow (∼0.07). If this threshold eccentricity can be lowered (perhaps by non-barotropic effects), and if the eccentricity driving documented here survives in 3D, it may robustly explain the low-to-moderate eccentricities 0.1 exhibited by many giant planets (including Jupiter and Saturn), especially those without planetary or stellar companions.
Using numerical hydrodynamics calculations and a novel method for densely sampling parameter space, we measure the accretion and torque on a binary system from a circumbinary disk. In agreement with ...some earlier studies, we find that the net torque on the binary is positive for mass ratios close to unity, and that accretion always drives the binary toward equal mass. Accretion variability depends sensitively on the numerical sink prescription, but the torque and relative accretion onto each component do not depend on the sink timescale. Positive torque and highly variable accretion occurs only for mass ratios greater than around 0.05. This means that for mass ratios below 0.05, the binary would migrate inward until the secondary accreted sufficient mass, after which it would execute a U-turn and migrate outward. We explore a range of viscosities, from = 0.03 to = 0.15, and find that this outward torque is proportional to the viscous torque, so that torque per unit accreted mass is independent of . Dependence of accretion and torque on mass ratio is explored in detail, densely sampling mass ratios between 0.01 and unity. For mass ratio q > 0.2, accretion variability is found to exhibit a distinct sawtooth pattern, typically with a five-orbit cycle that provides a smoking gun prediction for variable quasars observed over long periods, as a potential means to confirm the presence of a binary.
We use relativistic hydrodynamic numerical calculations to study the interaction between a jet and a homologous outflow produced dynamically during binary neutron star mergers. We quantify how the ...thermal energy imparted by the jet and the ability of the jet to escape the ejecta depend on the parameters of the jet engine and the ejecta. Under our assumptions, a collimated jet initiated at early times compared to the engine duration, we show that successful breakout of the forward cocoon shock necessitates a jet that successfully escapes the ejecta. This is because the ejecta is expanding, and the forward shock from a failed jet stalls before it reaches the edge of the ejecta. This conclusion can be circumvented only for very energetic wide angle jets, with parameters that are uncomfortable given short-duration GRB observations. For successful jets, we find two regimes of jet breakout from the ejecta: early breakout on timescales shorter than the engine duration, and late breakout well after the engine shuts off. A late breakout can explain the observed delay between gravitational waves and gamma rays in GW170817. We show that for the entire parameter space of jet parameters surveyed here (covering energies ∼1048-1051 erg and opening angles θj ∼ 0.07-0.4) the thermal energy deposited by the jet is less than that produced by r-process heating on second timescales by at least an order of magnitude. Shock heating is thus energetically subdominant in setting the luminosity of thermally powered transients coincident with neutron star mergers (kilonovae).
Abstract
The astrophysical environments capable of triggering heavy-element synthesis via rapid neutron capture (the
r
-process) remain uncertain. While binary neutron star mergers (NSMs) are known ...to forge
r
-process elements, certain rare supernovae (SNe) have been theorized to supplement—or even dominate—
r
-production by NSMs. However, the most direct evidence for such SNe, unusual reddening of the emission caused by the high opacities of
r
-process elements, has not been observed. Recent work identified the distribution of
r
-process material within the SN ejecta as a key predictor of the ease with which signals associated with
r
-process enrichment could be discerned. Though this distribution results from hydrodynamic processes at play during the SN explosion, thus far it has been treated only in a parameterized way. We use hydrodynamic simulations to model how disk winds—the alleged locus of
r
-production in rare SNe—mix with initially
r
-process-free ejecta. We study mixing as a function of the wind mass, wind duration, and the initial SN explosion energy, and find that it increases with the first two of these and decreases with the third. This suggests that SNe accompanying the longest long-duration gamma-ray bursts are promising places to search for signs of
r
-process enrichment. We use semianalytic radiation transport to connect hydrodynamics to electromagnetic observables, allowing us to assess the mixing level at which the presence of
r
-process material can be diagnosed from SN light curves. Analytic arguments constructed atop this foundation imply that a wind-driven
r
-process-enriched SN model is unlikely to explain standard energetic SNe.
Abstract
We present the publicly available moving-mesh hydrodynamics code
Sprout
.
Sprout
solves the equations of ideal hydrodynamics on an expanding Cartesian mesh. The expanding mesh can follow ...fluid outflows for several orders of magnitude with very little numerical diffusion, thereby capturing shocks and fine structures accurately. Following the bulk flow accurately also allows for longer time steps in general. This makes
Sprout
particularly suitable for studying expanding outflows such as supernova remnants and active galactic nuclei. Relative to other moving-mesh codes, the simple mesh structure in
Sprout
is also convenient for implementing additional physics or algorithms. Many code tests are performed to test the accuracy and performance of the numerical scheme.
Abstract
We solve the equations of two-dimensional hydrodynamics describing a circumbinary disk accreting onto an eccentric, equal-mass binary. We compute the time rate of change of the binary ...semimajor axis
a
and eccentricity
e
over a continuous range of eccentricities spanning
e
= 0 to
e
= 0.9. We find that binaries with initial eccentricities
e
0
≲ 0.1 tend to
e
= 0, where the binary semimajor axis expands. All others are attracted to
e
≈ 0.4, where the binary semimajor axis decays. The
e
≈ 0.4 attractor is caused by a rapid change in the disk response from a nearly origin-symmetric state to a precessing asymmetric state. The state change causes the time rates of change
a
̇
and
e
̇
to steeply change sign at the same critical eccentricity resulting in an attracting solution where
a
̇
=
e
̇
=
0
. This does not, however, result in a stalled, eccentric binary. The finite transition time between disk states causes the binary eccentricity to evolve beyond the attracting eccentricity in both directions resulting in oscillating orbital parameters and a drift of the semimajor axis. For the chosen disk parameters, binaries with
e
0
≳ 0.1 evolve toward and then oscillate around
e
≈ 0.4 where they shrink in semimajor axis. Because unequal mass binaries grow toward equal mass through preferential accretion, our results are applicable to a wide range of initial binary mass ratios. Hence, these findings merit further investigations of this disk transition; understanding its dependence on disk parameters is vital for determining the fate of binaries undergoing orbital evolution with a circumbinary disk.
ABSTRACT
The merger of two neutron stars produces an outflow of radioactive heavy nuclei. Within a second of merger, the central remnant is expected to also launch a relativistic jet, which ...shock-heats and disrupts a portion of the radioactive ejecta. Within a few hours, emission from the radioactive material gives rise to an ultraviolet, optical, and infrared transient (a kilonova). We use the endstates of a suite of 2D relativistic hydrodynamic simulations of jet–ejecta interaction as initial conditions for multidimensional Monte Carlo radiation transport simulations of the resulting viewing angle-dependent light curves and spectra starting at $1.5\, \mathrm{h}$ after merger. We find that on this time-scale, jet shock heating does not affect the kilonova emission for the jet parameters we survey. However, the jet disruption to the density structure of the ejecta does change the light curves. The jet carves a channel into the otherwise spheroidal ejecta, revealing the hot, inner regions. As seen from near (≲30°) the jet axis, the kilonova is brighter by a factor of a few and bluer. The strength of this effect depends on the jet parameters, since the light curves of more heavily disrupted ejecta are more strongly affected. The light curves and spectra are also more heavily modified in the ultraviolet than in the optical.
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