arXiv subjects

Paul C. Duffell

Publications and source records attributed to Paul C. Duffell.

At least 37 records · Page 2Linked to original sources

arXiv2021

Moving-mesh radiation-hydrodynamic simulations of wind-reprocessed transients

Motivated by recent theoretical work on tidal disruption events and other peculiar transients, we present moving-mesh radiation-hydrodynamic simulations of radiative luminosity emitted by a central source being reprocessed by a wind-like outflow. We couple the moving-mesh hydrodynamic code JET with our newly-developed radiation module based on mixed-frame grey flux-limited diffusion with implicit timestep update. This allows us to study the self-consistent multi-dimensional radiation-hydrodynamic evolution over more than ten orders of magnitude in both space and time in a single run. We simulate an optically-thick spherical wind with constant or evolving mass-loss rate, which is irradiated by a central isotropic or angularly-dependent radiation source. Our spherically-symmetric simulations confirm previous analytic results by identifying different stages of radiation reprocessing: radiation trapped in the wind, diffusing out through the wind, and reaching constant maximum attenuation. We find that confining the central radiation source in a cone with moderate opening angles decrease up to one order of magnitude the early flux along sightlines oriented away from the direction of radiation injection but that the reprocessed radiation becomes isotropic roughly after one lateral diffusion time through the ejecta. We discuss further applications and guidelines for the use of our novel radiation-hydrodynamics tool in the context of transient modelling.

astro-ph.SR↗

arXiv2021

Orbital Evolution of Equal-mass Eccentric Binaries due to a Gas Disk: Eccentric Inspirals and Circular Outspirals

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 $e_0 \lesssim 0.1$ tend to $e=0$, where the binary semimajor axis expands. All others are attracted to $e \approx 0.4$, where the binary semimajor axis decays. The $e \approx 0.4$ 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 $\dot{a}$ and $\dot{e}$ to steeply change sign at the same critical eccentricity resulting in an attracting solution where $\dot{a} = \dot{e} = 0$. 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 $e_0 \gtrsim 0.1$ evolve toward and then oscillate around $e \approx 0.4$ 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.

astro-ph.HE↗

arXiv2021

Proto-magnetar jets as central engines for broad-lined type Ic supernovae

A subset of type Ic supernovae (SNe Ic), broad-lined SNe Ic (SNe Ic-bl), show unusually high kinetic energies ($\sim 10^{52}$ erg) which cannot be explained by the energy supplied by neutrinos alone. Many SNe Ic-bl have been observed in coincidence with long gamma-ray bursts (GRBs) which suggests a connection between SNe and GRBs. A small fraction of core-collapse supernovae (CCSNe) form a rapidly-rotating and strongly-magnetized protoneutron star (PNS), a proto-magnetar. Jets from such magnetars can provide the high kinetic energies observed in SNe Ic-bl and also provide the connection to GRBs. In this work we use the jetted outflow produced in a 3D CCSN simulation from a consistently formed proto-magnetar as the central engine for full-star explosion simulations. We extract a range of central engine parameters and find that the extracted engine energy is in the range of $6.231 \times 10^{51}-1.725 \times 10^{52}$ erg, the engine time-scale in the range of $0.479-1.159$ s and the engine half-opening angle in the range of $\sim 9-19^{\circ}$. Using these as central engines, we perform 2D special-relativistic (SR) hydrodynamic (HD) and radiation transfer simulations to calculate the corresponding light curves and spectra. We find that these central engine parameters successfully produce SNe Ic-bl which demonstrates that jets from proto-magnetars can be viable engines for SNe Ic-bl. We also find that only the central engines with smaller opening angles ($\sim 10^{\circ}$) form a GRB implying that GRB formation is likely associated with narrower jet outflows and Ic-bl's without GRBs may be associated with wider outflows.

astro-ph.HE↗

arXiv2020

The Effect of Jet-Ejecta Interaction on the Viewing Angle Dependence of Kilonova Light Curves

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 multi-dimensional Monte Carlo radiation transport simulations of the resulting viewing angle-dependent light curves and spectra starting at 1.5h after merger. We find that on this timescale, jet shock heating does not affect the kilonova emission. 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 ($\lesssim 30 °$) 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.

astro-ph.HE↗

arXiv2020

Circumbinary Disks: Accretion and Torque as a Function of Mass Ratio and Disk Viscosity

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 previous 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 towards 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 $α= 0.03$ to $α= 0.15$, and find that this outward torque is proportional to the viscous torque, simply proportional to viscosity in this range. Dependence of accretion and torque on mass ratio is explored in detail, densely sampling mass ratios between $0.01$ and unity. For mass ratio $q > 0.6$, 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.

astro-ph.SR↗

arXiv2019

How Dense a CSM is Sufficient to Choke a Jet?

The progenitor stars of stripped-envelope high-velocity supernovae (Ic-BL SNe) can explode inside a dense circumstellar medium (CSM) that extends out to many times the progenitor radius. This complicates the question of whether all Ic-BL SNe harbor a jet, which can tunnel through the star and be viewed on-axis as a long-duration gamma-ray burst (GRB). More specifically, a sufficiently dense CSM might "choke" the jet, redistributing its energy quasi-spherically. In this study, we numerically calculate the CSM density necessary for jet-choking. For typical GRBs, we determine the jet is not choked in the CSM unless $ρr^2 > 4 \times 10^{19}$ g/cm; this requires several solar masses of CSM to be situated within $10^{13}$ cm of the progenitor, a much higher density than any CSM observed. We conclude that typical GRB jets are not choked in the CSM. However, in many cases the CSM has sufficient mass to decelerate the jet to a modest Lorentz factor ($Γ\sim 10$), which should lead to a long coasting phase for the jet, observable as a long plateau (potentially up to a few days) in the afterglow light curve. For extreme cases of low-energy GRBs in a high-mass CSM, the jet will decelerate to nonrelativistic velocities, causing it to spread modestly to a larger opening angle ($θ_j \approx 20$ degrees) before breaking out of the CSM. Even in these extreme examples, the jet does not have time to redistribute its energy quasi-spherically in the CSM before breakout.

astro-ph.HE↗

arXiv2019

An empirically-derived formula for the shape of planet-induced gaps in protoplanetary disks

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.

astro-ph.EP↗

arXiv2019

Gas Flows Within Cavities of Circumbinary Discs in Eccentric Binary Protostellar Systems

The structure and evolution of gas flows within the cavity of a circumbinary disk (CBD) surrounding the stellar components in eccentric binaries are examined via two-dimensional hydrodynamical simulations. The degree to which gas fills the cavity between the circumstellar disks (CSDs) and the CBD is found to be greater for highly eccentric systems, in comparison to low-eccentricity systems, reflecting the spatial extent over which mass enters into the cavity throughout the orbit. The pattern of the gas flow in the cavity differs for eccentric binaries from that of binaries in a circular orbit. In particular, the former reveals tightly wound gas streams and figure-eight-like structures for systems characterized by eccentricities, $e \ge 0.4$, whereas the latter only reveal relatively loosely bent streams from the CBD to the CSDs. Hence, the description of the stream structures can be a probe of sufficient non-circularity of the binary orbital motion. Given that the inner edge of the CBD is not very well defined for highly eccentric systems due to the complex gas structures, it is suggested that the area of the cavity for high-sensitivity imaging observations may prove to be a more useful diagnostic for probing the effectiveness of CBD clearing in the future.

astro-ph.SR↗

arXiv2018

Jet Dynamics in Compact Object Mergers: GW170817 Likely had a Successful Jet

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 supplied by the jet to the ejecta and the ability of a jet to escape the homologous ejecta depend on the parameters of the jet engine and the ejecta. For collimated jets 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 absorbing thermal energy, so that 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 GW 170817. We show that for the entire parameter space of jet parameters surveyed here (covering energies $\sim 10^{48}-10^{51}$ ergs and opening angles $θ_j \sim 0.07-0.4$) the thermal energy deposited into the ejecta by the jet propagation is less than that produced by r-process heating on second timescales by a factor of $\gtrsim 10$. Shock heating is thus energetically subdominant in setting the luminosity of thermally powered transients coincident with neutron star mergers (kilonovae). For typical short GRB jet parameters, our conclusion is stronger: there is little thermal energy in the cocoon, much less than what is needed to explain the early blue component of the kilonova in GW 170817.

astro-ph.HE↗

arXiv2018

Interaction of a Supernova with a Circumstellar Disk

Interaction between supernova (SN) ejecta and a dense circumstellar medium (CSM) can power a luminous light curve and create narrow emission lines in the spectra. While theoretical studies of interaction often assume a spherically symmetric CSM, there are observational indications that the gas surrounding some SN has a disk-like geometry. Here, we use moving-mesh hydrodynamics simulations to study the interaction of a SN with a disk and determine how the dynamics and observable signatures may depend on the disk mass, thickness, and radial extent. We find that simple modifications to standard spherically-symmetric scaling laws can be used to describe the propagation and heating rate of the interaction shock. We use the resulting shock heating rates to derive approximate bolometric light curves, and provide analytic formulas that can be used to generate simple synthetic light curves for general supernova-disk interactions. For certain disk parameters and explosion energies, we are able to produce luminosities akin to those seen in super-luminous SN. Because the SN ejecta can flow around and engulf the CSM disk, the interaction region may become embedded and from certain viewing angles the narrow emission lines indicative of interaction may be hidden.

astro-ph.HE↗

arXiv2017

On the Deceleration and Spreading of Relativistic Jets I: Jet Dynamics

Jet breaks in gamma ray burst (GRB) afterglows provide a direct probe of their collimation angle. Modeling a jet break requires an understanding of the "jet spreading" process, whereby the jet transitions from a collimated outflow into the spherical Sedov-Taylor solution at late times. Currently, direct numerical calculations are the most accurate way to capture the deceleration and spreading process, as analytical models have previously given inaccurate descriptions of the dynamics. Here (in paper I) we present a new, semi-analytical model built empirically by performing relativistic numerical jet calculations and measuring the relationship between Lorentz factor and opening angle. We then calculate the Lorentz factor and jet opening angle as a function of shock radius and compare to the numerical solutions. Our analytic model provides an efficient means of computing synthetic GRB afterglow light curves and spectra, which is the focus of paper II.

astro-ph.HE↗

arXiv2017

A GRB and Broad-lined Type Ic Supernova from a Single Central Engine

Unusually high velocities (< ~0.1c) and correspondingly high kinetic energies have been observed in a subset of Type Ic supernovae (so-called "broad-lined Ic" supernovae; SNe Ic-BL), prompting a search for a central engine model capable of generating such energetic explosions. A clue to the explosion mechanism may lie in the fact that all supernovae that accompany long-duration gamma-ray bursts belong to the SN Ic-BL class. Using a combination of two-dimensional relativistic hydrodynamics and radiation transport calculations, we demonstrate that the central engine responsible for long gamma-ray bursts can also trigger a SN Ic-BL. We find that a reasonable gamma-ray burst engine injected into a stripped Wolf-Rayet progenitor produces a relativistic jet with energy ~10^51 ergs, as well as a SN whose synthetic light curves and spectra are fully consistent with observed SNe Ic-BL during the photospheric phase. As a result of the jet's asymmetric energy injection, the SN spectra and light curves depend on viewing angle. The impact of viewing angle on the spectrum is particularly pronounced at early times, while the viewing angle dependence for the light curves (~10% variation in bolometric luminosity) persists throughout the photospheric phase.

astro-ph.HE↗

arXiv2016

DISCO: A 3D Moving-Mesh Magnetohydrodynamics Code Designed for the Study of Astrophysical Disks

This work presents the publicly available moving-mesh magnetohydrodynamics code DISCO. DISCO is efficient and accurate at evolving orbital fluid motion in two and three dimensions, especially at high Mach number. 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 timesteps than a static grid. Magnetohydrodynamics is implemented in DISCO using an HLLD Riemann solver and a novel constrained transport scheme which 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 magnetohydrodynamics tests are performed which demonstrate the accuracy and stability of the new constrained transport approach, including two tests of the magneto-rotational instability (MRI); one testing the linear growth rate and the other following the instability into the fully turbulent regime.

physics.comp-ph↗

arXiv2016

A One-Dimensional Model for Rayleigh-Taylor Instability in Supernova Remnants

This study presents a method for approximating the multidimensional effects of Rayleigh-Taylor instability as a modification of the one-dimensional hydro equations. This modification is similar to the Shakura-Sunyaev α 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 Rayleigh-Taylor unstable flows. A complete description of the model is presented, along with a handful of test problems that demonstrate the extent to which the one-dimensional model is able to reproduce multidimensional effects.

astro-ph.HE↗

arXiv2015

Eccentric Jupiters via Disk-Planet Interactions

Numerical hydrodynamics calculations are performed to determine 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 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 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 ($\sim$$0.04$) is not much smaller than the final eccentricity to which orbits grow ($\sim$$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 $\lesssim 0.1$ exhibited by many giant planets (including Jupiter and Saturn), especially those without planetary or stellar companions.

astro-ph.EP↗

arXiv2015

A Narrow Short-Duration GRB Jet from a Wide Central Engine

We use two-dimensional relativistic hydrodynamic numerical calculations to show that highly collimated relativistic jets can be produced in neutron star merger models of short-duration gamma ray bursts without the need for a highly directed engine or a large net magnetic flux. Even a hydrodynamic engine generating a very wide sustained outflow on small scales can in principle produce a highly collimated relativistic jet, facilitated by a dense surrounding medium which provides a cocoon surrounding the jet core. An oblate geometry to the surrounding gas significantly enhances the collimation process. Previous numerical simulations have shown that the merger of two neutron stars produces an oblate, expanding cloud of dynamical ejecta. We show that this gas can efficiently collimate the central engine power much as the surrounding star does in long-duration GRB models. For typical short-duration GRB central engine parameters, we find jets with opening angles of order 10 degrees in which a large fraction of the total outflow power of the central engine resides in highly relativistic material. These results predict large differences in the opening angles of outflows from binary neutron star mergers versus neutron star-black hole mergers.

astro-ph.HE↗

arXiv2015

A Simple Analytical Model for Gaps in Protoplanetary Disks

An analytical model is presented for calculating the surface density as a function of radius $Σ(r)$ in protoplanetary disks in which a planet has opened a gap. This model is also applicable to circumbinary disks with extreme binary mass ratios. The gap profile can be solved for algebraically, without performing any numerical integrals. In contrast with previous one-dimensional gap models, this model correctly predicts that low-mass (sub-Jupiter) planets can open gaps in sufficiently low-viscosity disks, and it correctly recovers the power-law dependence of gap depth on planet-to-star mass ratio $q$, disk aspect ratio $h/r$, and dimensionless viscosity $α$ found in previous numerical studies. Analytical gap profiles are compared with numerical calculations over a range of parameter space in $q$, $h/r$, and $α$, demonstrating accurate reproduction of the "partial gap" regime, and general agreement over a wide range of parameter space.

astro-ph.EP↗

arXiv2015

Halting Migration: Numerical Calculations of Corotation Torques in the Weakly Nonlinear Regime

Planets in their formative years can migrate due to the influence of gravitational torques in the protoplanetary disk they inhabit. For low-mass planets in an isothermal disk, it is known that there is a strong negative torque on the planet due to its linear perturbation to the disk, causing fast inward migration. The current investigation demonstrates that in these same isothermal disks, for intermediate-mass planets, there is a strong positive nonlinear corotation torque due to the effects of gas being pulled through a gap on horseshoe orbits. For intermediate-mass planets, this positive torque can partially or completely cancel the linear (Type I) torque, leading to slower or outward migration, even in an isothermal disk. The effect is most significant for Super-Earth and Sub-Jovian planets, during the transition from a low-mass linear perturber to a non-linear gap-opening planet, when the planet has opened a so-called 'partial gap'. In this study, numerical calculations of planet-disk interactions calculate these torques explicitly, and scalings are empirically constructed for migration rates in this weakly nonlinear regime. These results find outward migration is possible for planets with masses in the 20 - 100 Earth Mass range.

astro-ph.EP↗