arXiv subjects

Andrew MacFadyen

Publications and source records attributed to Andrew MacFadyen.

54 records · Page 3Linked to original sources

arXiv2013

GRB Afterglow Blast Wave Encountering Sudden Circumburst Density Change Produces No Flares

Afterglows of gamma-ray bursts are observed to produce light curves with the flux following power law evolution in time. However, recent observations reveal bright flares at times on the order of minutes to days. One proposed explanation for these flares is the interaction of a relativistic blast wave with a circumburst density transition. In this paper, we model this type of interaction computationally in one and two dimensions, using a relativistic hydrodynamics code with adaptive mesh refinement called ram, and analytically in one dimension. We simulate a blast wave traveling in a stellar wind environment that encounters a sudden change in density, followed by a homogeneous medium, and compute the observed radiation using a synchrotron model. We show that flares are not observable for an encounter with a sudden density increase, such as a wind termination shock, nor for an encounter with a sudden density decrease. Furthermore, by extending our analysis to two dimensions, we are able to resolve the spreading, collimation, and edge effects of the blast wave as it encounters the change in circumburst medium. In all cases considered in this paper, we find that a flare will not be observed for any of the density changes studied.

astro-ph.HE↗

arXiv2013

Fitting Afterglows With Multi-Dimensional Simulations

We present preliminary data fit results of synthetic light curves computed from numerical afterglow blast wave simulations. Our technique uses Markov chain Monte Carlo (MCMC) in a new data analysis tool, ScaleFit. Scaling relations in both the hydrodynamics and radiation equations allow light curves to be parameterized by a small set of scale-invariant characteristic quantities. These quantities have been calculated and tabulated from high resolution two-dimensional hydrodynamic simulations. Producing a light curve from the characteristics takes only a millisecond, allowing for the use of MCMC data fitting techniques which can require millions of iterations. ScaleFit is a portable, lightweight, python package which performs this analysis on afterglow light curves. Using the set of Swift-XRT light curves from 2011 & 2012 with known redshifts, we find ScaleFit can measure the jet opening angle, observer angle, and spectral index of most afterglows. Globally we find gamma-ray burst afterglows tend to be observed off axis, at a significant fraction of the jet opening angle.

astro-ph.HE↗

arXiv2013

No flares from Gamma-Ray Burst afterglow blast waves encountering sudden circumburst density change

Afterglows of gamma-ray bursts are observed to produce light curves with the flux following power law evolution in time. However, recent observations reveal bright flares at times on the order of minutes to days. One proposed explanation for these flares is the interaction of a relativistic blast wave with a circumburst density transition. In this paper, we model this type of interaction computationally in one and two dimensions, using a relativistic hydrodynamics code with adaptive mesh refinement called RAM, and analytically in one dimension. We simulate a blast wave traveling in a stellar wind environment that encounters a sudden change in density, followed by a homogeneous medium, and compute the observed radiation using a synchrotron model. We show that flares are not observable for an encounter with a sudden density increase, such as a wind termination shock, nor for an encounter with a sudden density decrease. Furthermore, by extending our analysis to two dimensions, we are able to resolve the spreading, collimation, and edge effects of the blast wave as it encounters the change in circumburst medium. In all cases considered in this paper, we find that a flare will not be observed for any of the density changes studied.

astro-ph.HE↗

arXiv2013

The Transient Gravitational-Wave Sky

Interferometric detectors will very soon give us an unprecedented view of the gravitational-wave sky, and in particular of the explosive and transient Universe. Now is the time to challenge our theoretical understanding of short-duration gravitational-wave signatures from cataclysmic events, their connection to more traditional electromagnetic and particle astrophysics, and the data analysis techniques that will make the observations a reality. This paper summarizes the state of the art, future science opportunities, and current challenges in understanding gravitational-wave transients.

gr-qc↗

arXiv2013

Gamma-ray burst afterglow light curves from a Lorentz-boosted simulation frame and the shape of the jet break

GRB afterglow jets have been notoriously difficult to resolve numerically using 2D hydrodynamical simulations due to high outflow Lorentz factors. By performing simulations in a boosted frame, it is possible to calculate light curves from numerically computed flows in sufficient detail to accurately quantify the shape of the jet break and the post-break steepening of the light curve. We study jet breaks for jets with opening angles of theta_0 = 0.05, 0.1 and 0.2 radians decelerating in a constant density medium, observed at angles (theta_obs) ranging from on-axis to the jet edge. We present a single set of scale-invariant functions describing the time evolution of synchrotron spectral break frequencies and peak flux, depending only on theta_0 and theta_obs, sufficient to reconstruct light curves for arbitrary explosion energy, circumburst density and synchrotron slope p. We compare our light curves to fit functions using sharp breaks and smooth transitions and confirm that the measured jet break time can be delayed due to theta_obs. We find that the difference in temporal indices across the jet break is larger than theoretically anticipated leading to post-break slopes of roughly 0.25 - 1.3 p, sufficiently steep to not easily reconcile with post-break slopes measured for the Swift sample, suggesting that most Swift GRBs do not explode in homogeneous media or that jet breaks are hidden by additional physics such as prolonged energy injection or viewing angle effects. Light curves and spectral break and peak flux evolution functions will be made publicly available on-line at http://cosmo.nyu.edu/afterglowlibrary .

astro-ph.HE↗

arXiv2013

Spectral and Intermittency Properties of Relativistic Turbulence

High-resolution numerical simulations are utilized to examine isotropic turbulence in a compressible fluid when long wavelength velocity fluctuations approach light speed. Spectral analysis reveals an inertial sub-range of relativistic motions with a broadly 5/3 index. The use of generalized Lorentz-covariant structure functions based on the four-velocity is proposed. These structure functions extend the She-Leveque model for intermittency into the relativistic regime.

astro-ph.HE↗

arXiv2011

Numerical Simulations of Driven Supersonic Relativistic MHD Turbulence

Models for GRB outflows invoke turbulence in relativistically hot magnetized fluids. In order to investigate these conditions we have performed high-resolution three-dimensional numerical simulations of relativistic magneto-hydrodynamical (RMHD) turbulence. We find that magnetic energy is amplified to several percent of the total energy density by turbulent twisting and folding of magnetic field lines. Values of epsilon_B near 1% are thus naturally expected. We study the dependence of saturated magnetic field energy fraction as a function of Mach number and relativistic temperature. We then present power spectra of the turbulent kinetic and magnetic energies. We also present solenoidal (curl-like) and dilatational (divergence-like) power spectra of kinetic energy. We propose that relativistic effects introduce novel couplings between these spectral components. The case we explore in most detail is for equal amounts of thermal and rest mass energy, corresponding to conditions after collisions of shells with relative Lorentz factors of several. These conditions are relevant in models for internal shocks, for the late afterglow phase, for cocoon material along the edge of a relativistic jet as it propagates through a star, as well neutron stars merging with each other and with black hole companions. We find that relativistic turbulence decays extremely quickly, on a sound crossing time of an eddy. Models invoking sustained relativistic turbulence to explain variability in GRB prompt emission are thus strongly disfavored unless a persistant driving of the turbulence is maintained for the duration of the prompt emission.

astro-ph.HE↗

arXiv2011

Numerical Simulations of Driven Relativistic MHD Turbulence

A wide variety of astrophysical phenomena involve the flow of turbulent magnetized gas with relativistic velocity or energy density. Examples include gamma-ray bursts, active galactic nuclei, pulsars, magnetars, micro-quasars, merging neutron stars, X-ray binaries, some supernovae, and the early universe. In order to elucidate the basic properties of the relativistic magnetohydrodynamical (RMHD) turbulence present in these systems, we present results from numerical simulations of fully developed driven turbulence in a relativistically warm, weakly magnetized and mildly compressible ideal fluid. We have evolved the RMHD equations for many dynamical times on a uniform grid with 1024^3 zones using a high order Godunov code. We observe the growth of magnetic energy from a seed field through saturation at about 1% of the total fluid energy. We compute the power spectrum of velocity and density-weighted velocity and conclude that the inertial scaling is consistent with a slope of -5/3. We compute the longitudinal and transverse velocity structure functions of order p up to 11, and discuss their possible deviation from the expected scaling for non-relativistic media. We also compute the scale-dependent distortion of coherent velocity structures with respect to the local magnetic field, finding a weaker scale dependence than is expected for incompressible non-relativistic flows with a strong mean field.

astro-ph.HE↗

arXiv2011

Slightly Two or Three Dimensional Self-Similar Solutions

Self similarity allows for analytic or semi-analytic solutions to many hydrodynamics problems. Most of these solutions are one dimensional. Using linear perturbation theory, expanded around such a one-dimensional solution, we find self-similar hydrodynamic solutions that are two- or three-dimensional. Since the deviation from a one-dimensional solution is small, we call these slightly two-dimensional and slightly three-dimensional self-similar solutions, respectively. As an example, we treat strong spherical explosions of the second type. A strong explosion propagates into an ideal gas with negligible temperature and density profile of the form rho(r,theta,phi)=r^{-omega}[1+sigma*F(theta,phi)], where omega>3 and sigma << 1. Analytical solutions are obtained by expanding the arbitrary function F(theta,phi) in spherical harmonics. We compare our results with two dimensional numerical simulations, and find good agreement.

astro-ph.HE↗

arXiv2010

Off-Axis Gamma-Ray Burst Afterglow Modeling Based On A Two-Dimensional Axisymmetric Hydrodynamics Simulation

Starting as highly relativistic collimated jets, gamma-ray burst outflows gradually decelerate and become non-relativistic spherical blast waves. Although detailed analytical solutions describing the afterglow emission received by an on-axis observer during both the early and late phases of the outflow evolution exist, a calculation of the received flux during the intermediate phase and for an off-axis observer requires either a more simplified analytical model or direct numerical simulations of the outflow dynamics. In this paper we present light curves for off-axis observers covering the long-term evolution of the blast wave calculated from a high resolution two-dimensional relativistic hydrodynamics simulation using a synchrotron radiation model. We compare our results to earlier analytical work and calculate the consequence of the observer angle with respect to the jet axis both for the detection of orphan afterglows and for jet break fits to the observational data. We find that observable jet breaks can be delayed for up to several weeks for off-axis observers, potentially leading to overestimation of the beaming corrected total energy. When using our off-axis light curves to create synthetic Swift X-ray data, we find that jet breaks are likely to remain hidden in the data. We also confirm earlier results in the literature finding that only a very small number of local Type Ibc supernovae can harbor an orphan afterglow.

astro-ph.HE↗

arXiv2010

Flare-less long Gamma-ray Bursts and the properties of their massive star progenitors

While there is mounting evidence that long Gamma-Ray Bursts (GRBs) are associated with the collapse of massive stars, the detailed structure of their pre-supernova stage is still debatable. Particularly uncertain is the degree of mixing among shells of different composition, and hence the role of magnetic torques and convection in transporting angular momentum. Here we show that early-time afterglow observations with the Swift satellite place constraints on the allowed GRB pre-supernova models. In particular, they argue against pre-supernova models in which different elemental shells are unmixed. These types of models would produce energy injections into the GRB engine on timescales between several hundreds of seconds to a few hours. Flaring activity has {\em not} been observed in a large fraction of well-monitored long GRBs. Therefore, if the progenitors of long GRBs have common properties, then the lack of flares indicates that the massive stars which produce GRBs are mostly well mixed, as expected in low-metallicity, rapidly rotating massive stars.

astro-ph.HE↗

arXiv2009

Hydrodynamical Response of a Circumbinary Gas Disk to Black Hole Recoil and Mass Loss

Finding electromagnetic (EM) counterparts of future gravitational wave (GW) sources would bring rich scientific benefits. A promising possibility, in the case of the coalescence of a super-massive black hole binary (SMBHB), is that prompt emission from merger-induced disturbances in a supersonic circumbinary disk may be detectable. We follow the post-merger evolution of a thin, zero-viscosity circumbinary gas disk with two-dimensional simulations, using the hydrodynamic code FLASH. We analyze perturbations arising from the 530 km/s recoil of a 10^6 M_sun binary, oriented in the plane of the disk, assuming either an adiabatic or a pseudo-isothermal equation of state for the gas. We find that a single-armed spiral shock wave forms and propagates outward, sweeping up about 20% of the mass of the disk. The morphology and evolution of the perturbations agrees well with those of caustics predicted to occur in a collisionless disk. Assuming that the disk radiates nearly instantaneously to maintain a constant temperature, we estimate the amount of dissipation and corresponding post-merger light-curve. The luminosity rises steadily on the time-scale of months, and reaches few times 10^{43} erg/s, corresponding to about 10% of the Eddington luminosity of the central SMBHB. We also analyze the case in which gravitational wave emission results in a 5% mass loss in the merger remnant. The mass-loss reduces the shock overdensities and the overall luminosity of the disk by 15-20%, without any other major effects on the spiral shock pattern.

astro-ph.HE↗

arXiv2009

The Dynamics and Afterglow Radiation of Gamma-Ray Bursts. I. Constant Density Medium

Direct multi-dimensional numerical simulation is the most reliable approach for calculating the fluid dynamics and observational signatures of relativistic jets in gamma-ray bursts (GRBs). We present a two-dimensional relativistic hydrodynamic simulation of a GRB outflow during the afterglow phase, which uses the fifth-order weighted essentially non-oscillatory scheme and adaptive mesh refinement. Initially, the jet has a Lorentz factor of 20. We have followed its evolution up to 150 years. Using the hydrodynamic data, we calculate synchrotron radiation based upon standard afterglow models and compare our results with previous analytic work. We find that the sideways expansion of a relativistic GRB jet is a very slow process and previous analytic works have overestimated its rate. In our computed lightcurves, a very sharp jet break is seen and the post-break lightcurves are steeper than analytic predictions. We find that the jet break in GRB afterglow lightcurves is mainly caused by the missing flux when the edge of the jet is observed. The outflow becomes nonrelativistic at the end of the Blandford-McKee phase. But it is still highly nonspherical, and it takes a rather long time for it to become a spherical Sedov-von Neumann-Taylor blast wave. We find that the late-time afterglows become increasingly flatter over time. But we disagree with the common notion that there is a sudden flattening in lightcurves due to the transition into the Sedov-von Neumann-Taylor solution. We have also found that there is a bump in lightcurves at very late times ($\sim 1000$ days) due to radiation from the counter jet. We speculate that such a counter jet bump might have already been observed in GRB 980703.

astro-ph.HE↗

arXiv2009

Three-Dimensional Relativistic MHD Simulations of the Kelvin-Helmholtz Instability: Magnetic Field Amplification by a Turbulent Dynamo

Magnetic field strengths inferred for relativistic outflows including gamma-ray bursts (GRB) and active galactic nuclei (AGN) are larger than naively expected by orders of magnitude. We present three-dimensional relativistic magnetohydrodynamics (MHD) simulations demonstrating amplification and saturation of magnetic field by a macroscopic turbulent dynamo triggered by the Kelvin-Helmholtz shear instability. We find rapid growth of electromagnetic energy due to the stretching and folding of field lines in the turbulent velocity field resulting from non-linear development of the instability. Using conditions relevant for GRB internal shocks and late phases of GRB afterglow, we obtain amplification of the electromagnetic energy fraction to $ε_B \sim 5 \times 10^{-3}$. This value decays slowly after the shear is dissipated and appears to be largely independent of the initial field strength. The conditions required for operation of the dynamo are the presence of velocity shear and some seed magnetization both of which are expected to be commonplace. We also find that the turbulent kinetic energy spectrum for the case studied obeys Kolmogorov's 5/3 law and that the electromagnetic energy spectrum is essentially flat with the bulk of the electromagnetic energy at small scales.

astro-ph↗

arXiv2002

Luminosity and Variability of Collimated Gamma-ray Bursts

Within the framework of the internal shock model, we study the luminosity and the variability in gamma-ray bursts from collimated fireballs. In particular we pay attention to the role of the photosphere due to $e^\pm$ pairs produced by internal shock synchrotron photons. It is shown that the observed Cepheid-like relationship between the luminosity and the variability can be interpreted as a correlation between the opening angle of the fireball jet and the mass included at the explosion with a standard energy output. We also show that such a correlation can be a natural consequence of the collapsar model. Using a multiple-shell model, we numerically calculate the temporal profiles of gamma-ray bursts. Collimated jets, in which the typical Lorentz factors are higher than in wide jets, can produce more variable temporal profiles due to smaller angular spreading time scales at the photosphere radius. Our simulations quantitatively reproduce the observed correlation.

astro-ph↗

arXiv2000

Collapsars

A variety of stellar explosions powered by black hole accretion are discussed. All involve the failure of neutrino energy deposition to launch a strong supernova explosion. A key quantity which determines the type of high energy transient produced is the ratio of the engine operation time, $\rm t_{engine}$, to the time for the explosion to break out of the stellar surface, $\rm t_{bo}$. Stars with sufficient angular momentum produce collapsars -- black holes accreting rapidly through a disk -- in their centers. Collapsars can occur in stars with a wide range of radii depending on the amount of pre-collapse mass loss. The stellar radius and jet properties determine the degree of beaming of the explosion. In some cases the stellar envelope serves to focus the explosion to narrow beaming angles. The baryon loading of various models for classical GRBs formed in massive stars is examined and the consequences are explored. For $\rm t_{engine} > t_{bo}$, highly relativistic outflow is possible and classical GRBs accompanied by supernovae can be produced. In other cases hyper-energetic, asymmetric supernovae are produced. Longer GRBs ($t \gtaprx 100 \s$) can be produced by fallback following a weak neutrino-driven supernova explosion.

astro-ph↗

arXiv2000

Relativistic Jets from Collapsars

Using a collapsar progenitor model of MacFadyen & Woosley we have simulated the propagation of an axisymmetric jet through a collapsing rotating massive star with the GENESIS multi-dimensional relativistic hydrodynamic code. The jet forms as a consequence of an assumed (constant or variable) energy deposition in the range $10^{50}$ erg s$^{-1}$ to $10^{51}$ erg s$^{-1}$ within a $30^{\circ}$ cone around the rotation axis. The jet flow is strongly beamed ($\la$ few degrees), spatially inhomogeneous, and time dependent. The jet reaches the surface of the stellar progenitor ($R_{\ast} = 2.98 \times 10^{10} $cm) intact. At breakout the maximum Lorentz factor of the jet flow is 33. After breakout the jet accelerates into the circumstellar medium, whose density is assumed to decrease exponentially and then being constant $ρ_{\rm ext} = 10^{-5}$ gcm$^{-3}$. Outside the star the flow begins to expand also laterally ($v \sim c$), but the beam remains very well collimated. At a distance of $2.54 R_{\ast}$, where the simulation ends, the Lorentz factor has increased to 44.

astro-ph↗

arXiv1999

Relativistic Jets from Collapsars

We have studied the relativistic beamed outflow proposed to occur in the collapsar model of gamma-ray bursts. A jet forms as a consequence of an assumed energy deposition of $\sim 10^{50}- 10^{51}$ erg/s within a $30^{\circ}$ cone around the rotation axis of the progenitor star. The generated jet flow is strongly beamed ($\la$ few degrees) and reaches the surface of the stellar progenitor (r $\approx 3 10^{10} $cm) intact. At break-out the maximum Lorentz factor of the jet flow is about 33. Simulations have been performed with the GENESIS multi-dimensional relativistic hydrodynamic code.

astro-ph↗