arXiv subjects

Anatoly Spitkovsky

Publications and source records attributed to Anatoly Spitkovsky.

At least 91 records · Page 5Linked to original sources

arXiv2009

Signatures of a Maxwellian Component in Shock-Accelerated Electrons in GRBs

Recent particle-in-cell simulations suggest that a large fraction of the energy dissipated in a relativistic shock is deposited into a Maxwellian distribution of electrons that is connected to the high-energy power-law tail. Here, we explore the observational implications of such a mixed thermal-nonthermal particle distribution for the afterglow and prompt emission of gamma-ray bursts. When the Maxwellian component dominates the energy budget, the afterglow lightcurves show a very steep decline phase followed by a more shallow decay when the characteristic synchrotron frequency crosses the observed band. The steep decay appears in the X-rays at ~100 sec after the burst and is accompanied by a characteristic hard-soft-hard spectral evolution that has been observed in a large number of early afterglows. If internal shocks produce a similar mixed electron distribution, a bump is expected at the synchrotron peak of the nu*f_nu spectrum.

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arXiv2009

Modeling Pulsar Gamma-Ray Light Curves Using Realistic Magnetospheric Geometries

Gamma-ray emission from pulsars is thought to arise from accelerating regions in pulsar's outer magnetosphere. The shape of the light curves is thus sensitive to the details of the magnetic geometry of the magnetosphere. In this work, we show the first calculations of light curves from the more realistic force-free field under the framework of conventional emission models. We compare the properties of gamma-ray emission between the commonly used vacuum dipole magnetic field and the new force-free field. We discuss the role of the polar cap shape and aberration effect on the appearance of the light curves as well as the formation of caustics on the sky map. With the force-free field, the double-peak pulse profile is best reproduced if the emission zone lies in a thin layer just outside the current sheet, and the peaks are mainly contributed from regions near the light cylinder. The conventional two-pole caustic model can produce up to four peaks in general, while the conventional outer-gap model can normally produce only one peak. These results will be useful for interpreting Fermi telescope observations.

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arXiv2009

Magnetohydrodynamic Shallow Water Waves: Linear Analysis

We present a linear analysis of inviscid, incompressible, magnetohydrodynamic (MHD) shallow water systems. In spherical geometry, a generic property of such systems is the existence of five wave modes. Three of them (two magneto-Poincare modes and one magneto-Rossby mode) are previously known. The other two wave modes are strongly influenced by the magnetic field and rotation, and have substantially lower angular frequencies; as such, we term them "magnetostrophic modes". We obtain analytical functions for the velocity, height and magnetic field perturbations in the limit that the magnitude of the MHD analogue of Lamb's parameter is large. On a sphere, the magnetostrophic modes reside near the poles, while the other modes are equatorially confined. Magnetostrophic modes may be an ingredient in explaining the frequency drifts observed in Type I X-ray bursts from neutron stars.

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arXiv2009

Synthetic Spectra from PIC Simulations of Relativistic Collisionless Shocks

We extract synthetic photon spectra from first-principles particle-in-cell simulations of relativistic shocks propagating in unmagnetized pair plasmas. The two basic ingredients for the radiation, namely accelerated particles and magnetic fields, are produced self-consistently as part of the shock evolution. We use the method of Hededal & Nordlund (2005) and compute the photon spectrum via Fourier transform of the electric far-field from a large number of particles, sampled directly from the simulation. We find that the spectrum from relativistic collisionless shocks is entirely consistent with synchrotron radiation in the magnetic fields generated by Weibel instability. We can recover the so-called "jitter'' regime only if we artificially reduce the strength of the electromagnetic fields, such that the wiggler parameter K = qB lambda/mc^2 becomes much smaller than unity ("B" and "lambda" are the strength and scale of the magnetic turbulence, respectively). These findings may place constraints on the origin of non-thermal emission in astrophysics, especially for the interpretation of the hard (harder than synchrotron) low-frequency spectrum of Gamma-Ray Bursts.

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arXiv2009

Magnetic field evolution in relativistic unmagnetized collisionless shocks

We study relativistic unmagnetized collisionless shocks using unprecedentedly large particle-in-cell simulations of two-dimensional pair plasma. High energy particles accelerated by the shock are found to drive magnetic field evolution on a timescale >10^4 plasma times. Progressively stronger magnetic fields are generated on larger scales in a growing region around the shock. Shock-generated magnetic fields and accelerated particles carry >1% and >10% of the downstream energy flux, respectively. Our results suggest limits on the magnetization of relativistic astrophysical flows.

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arXiv2009

Extreme Astrophysics with Neutron Stars

We highlight recent theoretical and observational progress in several areas of neutron star astrophysics, and discuss the prospect for advances in the next decade.

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arXiv2009

Particle Acceleration in Relativistic Magnetized Collisionless Pair Shocks: Dependence of Shock Acceleration on Magnetic Obliquity

We investigate shock structure and particle acceleration in relativistic magnetized collisionless pair shocks by means of 2.5D and 3D particle-in-cell simulations. We explore a range of inclination angles between the pre-shock magnetic field and the shock normal. We find that only magnetic inclinations corresponding to "subluminal" shocks, where relativistic particles following the magnetic field can escape ahead of the shock, lead to particle acceleration. The downstream spectrum in such shocks consists of a relativistic Maxwellian and a high-energy power-law tail with exponential cutoff. For increasing magnetic inclination in the subluminal range, the high-energy tail accounts for an increasing fraction of particles (from ~1% to ~2%) and energy (from ~4% to ~12%). The spectral index of the power law increases with angle from -2.8+-0.1 to -2.3+-0.1. Particle energization is driven by the Diffusive Shock Acceleration process for nearly parallel shocks, and switches to Shock-Drift Acceleration for larger subluminal inclinations. For "superluminal" shocks, the downstream particle spectrum does not show any significant suprathermal tail. As seen from the upstream frame, efficient acceleration in relativistic (Lorentz factor gamma0 > 5) magnetized (sigma > 0.03) flows exists only for a very small range of magnetic inclination angles (< 34/gamma0 degrees), so relativistic astrophysical pair shocks have to be either nearly parallel or weakly magnetized to generate nonthermal particles. These findings place constraints on the models of AGN jets, Pulsar Wind Nebulae and Gamma Ray Bursts that invoke particle acceleration in relativistic magnetized shocks. (Abridged)

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arXiv2008

Non-linear Study of Bell's Cosmic Ray Current-driven Instability

The cosmic ray current-driven (CRCD) instability, predicted by Bell (2004), consists of non-resonant, growing plasma waves driven by the electric current of cosmic rays (CRs) that stream along the magnetic field ahead of both relativistic and non-relativistic shocks. Combining an analytic, kinetic model with one-, two-, and three-dimensional particle-in-cell simulations, we confirm the existence of this instability in the kinetic regime and determine its saturation mechanisms. In the linear regime, we show that, if the background plasma is well magnetized, the CRCD waves grow exponentially at the rates and wavelengths predicted by the analytic dispersion relation. The magnetization condition implies that the growth rate of the instability is much smaller than the ion cyclotron frequency. As the instability becomes non-linear, significant turbulence forms in the plasma. This turbulence reduces the growth rate of the field and damps the shortest wavelength modes, making the dominant wavelength, λ_d, grow proportional to the square of the field. At constant CR current, we find that plasma acceleration along the motion of CRs saturates the instability at the magnetic field level such that v_A ~ v_{d,cr}, where v_A is the Alfven velocity in the amplified field, and v_{d,cr} is the drift velocity of CRs. The instability can also saturate earlier if CRs get strongly deflected by the amplified field, which happens when their Larmor radii get close to λ_d. We apply these results to the case of CRs in the upstream medium of supernova remnants. Considering only the most energetic CRs that escape from the shock, we obtain that the field amplification factor of ~10 can be reached. This confirms the CRCD instability as a potentially important component of magnetic amplification process in astrophysical shocks.

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arXiv2008

Radiative cooling in relativistic collisionless shocks. Can simulations and experiments probe relevant GRB physics?

We address the question of whether numerical particle-in-cell (PIC) simulations and laboratory laser-plasma experiments can (or will be able to, in the near future) model realistic gamma-ray burst (GRB) shocks. For this, we compare the radiative cooling time, t_cool, of relativistic electrons in the shock magnetic fields to the microscopic dynamical time of collisionless relativistic shocks -- the inverse plasma frequency of protons, omega_pp^{-1}. We obtain that for t_cool*omega_pp^{-1}\lesssim ~few hundred, the electrons cool efficiently at or near the shock jump and are capable of emitiing away a large fraction of the shock energy. Such shocks are well-resolved in existing PIC simulations; therefore, the microscopic structure can be studied in detail. Since most of the emission in such shocks would be coming from the vicinity of the shock, the spectral power of the emitted radiation can be directly obtained from finite-length simulations and compared with observational data. Such radiative shocks correspond to the internal baryon-dominated GRB shocks for the conventional range of ejecta parameters. Fermi acceleration of electrons in such shocks is limited by electron cooling, hence the emitted spectrum should be lacking a non-thermal tail, whereas its peak likely falls in the multi-MeV range. Incidentally, the conditions in internal shocks are almost identical to those in laser-produced plasmas; thus, such GRB-like plasmas can be created and studied in laboratory experiments using the presently available Petawatt-scale laser facilities. An analysis of the external shocks shows that only the highly relativistic shocks, corresponding to the extremely early afterglow phase, can have efficient electron cooling in the shock transition. We emphasize the importance of radiative PIC simulations for further studies.

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arXiv2008

Particle acceleration in relativistic collisionless shocks: Fermi process at last?

We present evidence that relativistic shocks propagating in unmagnetized plasmas can self-consistently accelerate particles. We use long-term two-dimensional particle-in-cell simulations to study the well-developed shock structure in unmagnetized pair plasma. The particle spectrum downstream of such a shock consists of two components: a relativistic Maxwellian, with characteristic temperature set by the upstream kinetic energy of the flow, and a high-energy tail, extending to energies >100 times that of the thermal peak. This tail is best fitted as a power law in energy with index -2.4+-0.1, modified by an exponential cutoff. The cutoff moves to higher energies with time of the simulation, leaving a larger power law range. The number of particles in the tail is ~1% of the downstream population, and they carry ~10% of the kinetic energy in the downstream. Upon investigation of the trajectories of particles in the tail, we find that the energy gains occur as particles bounce between the upstream and downstream regions in the magnetic fields generated by the Weibel instability. We compare this mechanism to the first order Fermi acceleration, and set a lower limit on the efficiency of shock acceleration process.

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arXiv2008

Long Term Evolution of Magnetic Turbulence in Relativistic Collisionless Shocks

We study the long term evolution of magnetic fields generated by an initially unmagnetized collisionless relativistic $e^+e^-$ shock. Our 2D particle-in-cell numerical simulations show that downstream of such a Weibel-mediated shock, particle distributions are approximately isotropic, relativistic Maxwellians, and the magnetic turbulence is highly intermittent spatially, nonpropagating, and decaying. Using linear kinetic theory, we find a simple analytic form for these damping rates. Our theory predicts that overall magnetic energy decays like $(ω_p t)^{-q}$ with $q \sim 1$, which compares favorably with simulations, but predicts overly rapid damping of short wavelength modes. Magnetic trapping of particles within the magnetic structures may be the origin of this discrepancy. We conclude that initially unmagnetized relativistic shocks in electron-positron plasmas are unable to form persistent downstream magnetic fields. These results put interesting constraints on synchrotron models for the prompt and afterglow emission from GRBs.

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arXiv2007

On the structure of relativistic collisionless shocks in electron-ion plasmas

Relativistic collisionless shocks in electron-ion plasma are thought to occur in the afterglow phase of Gamma-Ray Bursts (GRBs), and in other environments where relativistic flows interact with the interstellar medium. A particular regime of shocks in an unmagnetized plasma has generated much interest for GRB applications. In this paper we present ab-initio particle-in-cell simulations of unmagnetized relativistic electron-ion shocks. Using long-term 2.5-dimensional simulations with ion-electron mass ratios from 16 to 1000 we resolve the shock formation and reach a steady-state shock structure beyond the initial transient. We find that even at high ion-electron mass ratios initially unmagnetized shocks can be effectively mediated by the ion Weibel instability with a typical shock thickness of ~50 ion skin-depths. Upstream of the shock the interaction with merging ion current filaments heats the electron component, so that the postshock flow achieves near equipartition between the ions and electrons, with electron temperature reaching 50% of the ion temperature. This energy exchange helps to explain the large electron energy fraction inferred from GRB afterglow observations.

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arXiv2006

Pulsar electrodynamics: a time-dependent view

Pulsar spindown forms a reliable yet enigmatic prototype for the energy loss processes in many astrophysical objects including accretion disks and back holes. In this paper we review the physics of pulsar magnetospheres, concentrating on recent developments in force-free modeling of the magnetospheric structure. In particular, we discuss a new method for solving the equations of time-dependent force-free relativistic MHD in application to pulsars. This method allows to dynamically study the formation of the magnetosphere and its response to perturbations, opening a qualitatively new window on pulsar phenomena. Applications of the method to other magnetized rotators, such as magnetars and accretion disks, are also discussed.

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arXiv2006

Simulations of relativistic collisionless shocks: shock structure and particle acceleration

We discuss 3D simulations of relativistic collisionless shocks in electron-positron pair plasmas using the particle-in-cell (PIC) method. The shock structure is mainly controlled by the shock's magnetization ("sigma" parameter). We demonstrate how the structure of the shock varies as a function of sigma for perpendicular shocks. At low magnetizations the shock is mediated mainly by the Weibel instability which generates transient magnetic fields that can exceed the initial field. At larger magnetizations the shock is dominated by magnetic reflections. We demonstrate where the transition occurs and argue that it is impossible to have very low magnetization collisionless shocks in nature (in more than one spatial dimension). We further discuss the acceleration properties of these shocks, and show that higher magnetization perpendicular shocks do not efficiently accelerate nonthermal particles in 3D. Among other astrophysical applications, this may pose a restriction on the structure and composition of gamma-ray bursts and pulsar wind outflows.

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arXiv2006

Time-dependent force-free pulsar magnetospheres: axisymmetric and oblique rotators

Magnetospheres of many astrophysical objects can be accurately described by the low-inertia (or "force-free") limit of MHD. We present a new numerical method for solution of equations of force-free relativistic MHD based on the finite-difference time-domain (FDTD) approach with a prescription for handling spontaneous formation of current sheets. We use this method to study the time-dependent evolution of pulsar magnetospheres in both aligned and oblique magnetic geometries. For the aligned rotator we confirm the general properties of the time-independent solution of Contopoulos et al. (1999). For the oblique rotator we present the 3D structure of the magnetosphere and compute, for the first time, the spindown power of pulsars as a function of inclination of the magnetic axis. We find the pulsar spindown luminosity to be L = (mu^2 Omega^4/c^3) (1+ sin^2(alpha)) for a star with the dipole moment "mu", rotation frequency "Omega", and magnetic inclination angle "alpha". We also discuss the effects of current sheet resistivity and reconnection on the structure and evolution of the magnetosphere.

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arXiv2005

Revised Pulsar Spindown

We address the issue of electromagnetic pulsar spindown by combining our experience from the two limiting idealized cases which have been studied in great extent in the past: that of an aligned rotator where ideal MHD conditions apply, and that of a misaligned rotator in vacuum. We construct a spindown formula that takes into account the misalignment of the magnetic and rotation axes, and the magnetospheric particle acceleration gaps. We show that near the death line aligned rotators spin down much slower than orthogonal ones. In order to test this approach, we use a simple Monte Carlo method to simulate the evolution of pulsars and find a good fit to the observed pulsar distribution in the P-Pdot diagram without invoking magnetic field decay. Our model may also account for individual pulsars spinning down with braking index n < 3, by allowing the corotating part of the magnetosphere to end inside the light cylinder. We discuss the role of magnetic reconnection in determining the pulsar braking index. We show, however, that n ~ 3 remains a good approximation for the pulsar population as a whole. Moreover, we predict that pulsars near the death line have braking index values n > 3, and that the older pulsar population has preferentially smaller magnetic inclination angles. We discuss possible signatures of such alignment in the existing pulsar data.

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arXiv2005

Steady-State Electrostatic Layers from Weibel Instability in Relativistic Collisionless Shocks

It is generally accepted that magnetic fields generated in the nonlinear development of the transverse Weibel instability provide effective collisionality in unmagnetized collisionless shocks. Recently, extensive two and three dimensional simulations improved our understanding of the growth and saturation of the instability in colliding plasma shells. However, the steady-state structure of the shock wave transition layers remains poorly understood. We use basic physical considerations and order-of-magnitude arguments to study the steady state structure in relativistic unmagnetized collisionless shocks in pair plasmas. The shock contains an electrostatic layer resulting from the formation of stationary, magnetically-focused current filaments. The filaments form where the cold upstream plasma and the counterstreaming thermal plasma interpenetrate. The filaments are not entirely neutral and strong electrostatic fields are present. Most of the downstream particles cannot cross this layer into the upstream because they are trapped by the electrostatic field. We identify the critical location in the shock transition layer where the electromagnetic field ceases to be static. At this location, the degree of charge separation in the filaments reaches a maximum value, the current inside the filaments comes close to the Alfvén limit, and the phase space distribution function starts to isotropize. We argue that the radius of the current filaments upstream of the critical location is about twice the upstream plasma skin depth. Finally, we show that some downstream particles cross the electrostatic layer and run ahead of the shock into the preshock medium without causing instability. These particles may play an important role in particle acceleration.

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arXiv2004

Orbital Modulation of the Apparent Dispersion Measure Towards PSR J0737-3039A

This paper has been withdrawn from astro-ph and from the submission process to ApJ Letters since the variations "observed" are not real. As pointed out to me first by Willem van Straten and shortly thereafter by Matthew Bailes and Dick Manchester, the "Orbital Modulation of the Apparent Dispersion Measure Towards PSR J0737-3039A" is, in fact, an artifact of the data reduction. The problem occurs only for observations using very wide bandwidths of fast-moving and compact-orbit binary pulsars when reduced in a "traditional" manner (for folding of data, this means using a single set of polycos to fold the full bandwidth of data -- as was done for this paper). To quote Dick Manchester: "I believe I know the reason for the apparent DM variation in your data. We saw a similar effect as soon as we started taking the dual-freq [i.e. simultaneous 10cm/50cm data from Parkes] data. I showed that the effect was due to calling the polyco for folding the data with an incorrect RF frequency. The differential delay due to the dispersion moves the apparent orbital phase by a significant amount for these very short-period binaries. This leads to a sinusoidal modulation at the orbital period in the residuals, the amplitude (and sign) of which is a function of the difference between the prediction frequency and the observed frequency." and Willem Van Straten: "We were using a polyco created with a constant centre frequency [...] to fold data observed at all other frequencies. The canonical thinking behind this was to leave the relative dispersion delays in the data, so that tempo could later fit for DM. However, because the position of PSR J0737-3039A changes significantly during the dispersion delay time, the binary phase predicted at the [...] barycentric proper time [for the observing frequency used for the polycos] is significantly different to that at the proper time of other frequencies. For most pulsars, this doesn't matter much. But v/c for PSR J0737-3039A is about 10^-3. Another way to describe the problem is that, although the dispersion time delay does not evolve with binary phase, the corresponding pulsar _phase_ varies strongly as a function of dispersion delay (and therefore frequency)." Matthew Bailes pointed out that if this Doppler-like effect is not accounted for, than for any binary pulsar, an orbital variation in DM will occur of amplitude: dDM = V_orb/c * DM. This implies that for binaries where this effect is significant, an orbital phase dependent de-dispersion methodology is required. For pulsar folding, that can be accomplished by using a different set of polycos for _each_ frequency channel (or subband) in your data. I have confirmed that the DM variations do in fact go away when the data is processed correctly. Hopefully this mistake on my part did not cause too many people to waste significant amounts of time trying to explain the "effect"! Sincerely, Scott Ransom

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