arXiv subjects

Peter A. Becker

Publications and source records attributed to Peter A. Becker.

At least 55 records · Page 3Linked to original sources

arXiv2009

Particle Acceleration in Advection-Dominated Accretion Disks with Shocks: Green's Function Energy Distribution

The distribution function describing the acceleration of relativistic particles in an advection-dominated accretion disk is analyzed using a transport formalism that includes first-order Fermi acceleration, advection, spatial diffusion, and the escape of particles through the upper and lower surfaces of the disk. When a centrifugally-supported shock is present in the disk, the concentrated particle acceleration occurring in the vicinity of the shock channels a significant fraction of the binding energy of the accreting gas into a population of relativistic particles. These high-energy particles diffuse vertically through the disk and escape, carrying away both energy and entropy and allowing the remaining gas to accrete. The dynamical structure of the disk/shock system is computed self-consistently using a model previously developed by the authors that successfully accounts for the production of the observed relativistic outflows (jets) in M87 and \SgrA. This ensures that the rate at which energy is carried away from the disk by the escaping relativistic particles is equal to the drop in the radial energy flux at the shock location, as required for energy conservation. We investigate the influence of advection, diffusion, and acceleration on the particle distribution by computing the nonthermal Green's function, which displays a relatively flat power-law tail at high energies. We also obtain the energy distribution for the particles escaping from the disk, and we conclude by discussing the spectrum of the observable secondary radiation produced by the escaping particles.

astro-ph.HE↗

arXiv2009

Study of the accreting pulsar 4U 0115+634 with a bulk and thermal Comptonization model

Highly magnetized pulsars accreting matter in a binary system are bright sources in the X-ray band (0.1-100 keV). Despite the early comprehension of the basic emission mechanism, their spectral energy distribution is generally described by phenomenological or simplified models. We propose a study of the spectral emission from the high mass X-ray binary pulsar 4U 0115+634 by means of thermal and bulk Comptonization models based on the physical properties of such objects. For this purpose, we analyze the BeppoSAX data in the energy range 0.7-100 keV of the 1999 giant outburst, 12 days after the maximum. We model the spectral energy distribution of the system using a two-component continuum. At higher energy, above ~7 keV, the emission is due to thermal and bulk Comptonization of the seed photons produced by cyclotron cooling of the accretion column, and at lower energy, the emission is due to thermal Comptonization of a blackbody source in a diffuse halo close to the stellar surface. From the best fit parameters, we argue that the cyclotron emission is produced ~1.7 km above the stellar surface, and escapes from the column near its base, where the absorption features are generated by the interaction with the magnetic field in a surrounding halo. We find that in 4U 0115+634, the observed spectrum is dominated by reprocessed cyclotron radiation, whereas in other bright sources with stronger magnetic fields such as Her X-1, the spectrum is dominated by reprocessed bremsstrahlung.

astro-ph.HE↗

arXiv2008

Hybrid viscosity and the magnetoviscous instability in hot, collisionless accretion disks

We aim to illustrate the role of hot protons in enhancing the magnetorotational instability (MRI) via the ``hybrid'' viscosity, which is due to the redirection of protons interacting with static magnetic field perturbations, and to establish that it is the only relevant mechanism in this situation. It has recently been shown by Balbus \cite{PBM1} and Islam & Balbus \cite{PBM11} using a fluid approach that viscous momentum transport is key to the development of the MRI in accretion disks for a wide range of parameters. However, their results do not apply in hot, advection-dominated disks, which are collisionless. We develop a fluid picture using the hybrid viscosity mechanism, that applies in the collisionless limit. We demonstrate that viscous effects arising from this mechanism can significantly enhance the growth of the MRI as long as the plasma $β\gapprox 80$. Our results facilitate for the first time a direct comparison between the MHD and quasi-kinetic treatments of the magnetoviscous instability in hot, collisionless disks.

astro-ph↗

arXiv2007

Comptonization and the Spectra of Accretion-Powered X-Ray Pulsars

Accretion-powered X-ray pulsars are among the most luminous X-ray sources in the Galaxy. However, despite decades of theoretical and observational work since their discovery, no satisfactory model for the formation of the observed X-ray spectra has emerged. In this paper, we report on a self-consistent calculation of the spectrum emerging from a pulsar accretion column that includes an explicit treatment of the bulk and thermal Comptonization occurring in the radiation-dominated shocks that form in the accretion flows. Using a rigorous eigenfunction expansion method, we obtain a closed-form expression for the Green's function describing the upscattering of monochromatic radiation injected into the column. The Green's function is convolved with bremsstrahlung, cyclotron, and blackbody source terms to calculate the emergent photon spectrum. We show that energization of photons in the shock naturally produces an X-ray spectrum with a relatively flat continuum and a high-energy exponential cutoff. Finally, we demonstrate that our model yields good agreement with the spectra of the bright pulsar Her X-1 and the low luminosity pulsar X Per.

astro-ph↗

arXiv2006

Thermal and Bulk Comptonization in Accretion-Powered X-Ray Pulsars

We develop a new theoretical model for the spectral formation process in accretion-powered X-ray pulsars based on a detailed treatment of the bulk and thermal Comptonization occurring in the accreting, shocked gas. A rigorous eigenfunction expansion method is employed to obtain the analytical solution for the Green's function describing the scattering of radiation injected into the column from a monochromatic source located at an arbitrary height above the stellar surface. The emergent spectrum is calculated by convolving the Green's function with source terms corresponding to bremsstrahlung, cyclotron, and blackbody emission. The energization of the photons in the shock, combined with cyclotron absorption, naturally produces an X-ray spectrum with a relatively flat continuum shape and a high-energy quasi-exponential cutoff. We demonstrate that the new theory successfully reproduces the phase-averaged spectra of the bright pulsars Her X-1, LMC X-4, and Cen X-3. In these luminous sources, it is shown that the emergent spectra are dominated by Comptonized bremsstrahlung emission.

astro-ph↗

arXiv2006

Further constraints on electron acceleration in solar noise storms

We reexamine the energetics of nonthermal electron acceleration in solar noise storms. A new result is obtained for the minimum nonthermal electron number density required to produce a Langmuir wave population of sufficient intensity to power the noise storm emission. We combine this constraint with the stochastic electron acceleration formalism developed by Subramanian & Becker (2005) to derive a rigorous estimate for the efficiency of the overall noise storm emission process, beginning with nonthermal electron acceleration and culminating in the observed radiation. We also calculate separate efficiencies for the electron acceleration -- Langmuir wave generation stage and the Langmuir wave -- noise storm production stage. In addition, we obtain a new theoretical estimate for the energy density of the Langmuir waves in noise storm continuum sources.

astro-ph↗

arXiv2005

Using transport coefficients of cosmic rays in turbulent magnetic fields to determine hybrid viscosity in hot accretion disks around AGN

The nature of the viscosity operative in hot, two-temperature accretion disks around AGN has been a long-standing, unsolved problem. It has been previously suggested that protons, in conjunction with the turbulent magnetic field that is likely to exist in the accretion disk, might be crucial in providing this viscosity. Several authors have recently determined diffusion coefficients for charged particles (cosmic rays) propagating in turbulent magnetic fields by means of extensive Monte Carlo simulations. We use the diffusion coefficients for protons determined by these simulations to find the effective mean free path for protons in hot accretion disks. This in turn yields good estimates of the viscosity due to energetic protons embedded in the turbulent magnetic field of a hot, two-temperature accretion disk. We combine this with a simple two-temperature accretion disk model to determine the Shakura-Sunyaev $α$ viscosity parameter arising out of this mechanism. We find that protons diffusing in the turbulent magentic field embedded in a hot accretion d isk provide a physically reasonable source of viscosity in hot accretion disks around AGN.

astro-ph↗

arXiv2005

Particle Acceleration and the Production of Relativistic Outflows in Advection-Dominated Accretion Disks with Shocks

Relativistic outflows (jets) of matter are commonly observed from systems containing black holes. The strongest outflows occur in the radio-loud systems, in which the accretion disk is likely to have an advection-dominated structure. In these systems, it is clear that the binding energy of the accreting gas is emitted primarily in the form of particles rather than radiation. However, no comprehensive model for the disk structure and the associated outflows has yet been produced. In particular, none of the existing models establishes a direct physical connection between the presence of the outflows and the action of a microphysical acceleration mechanism operating in the disk. In this paper we explore the possibility that the relativistic protons powering the jet are accelerated at a standing, centrifugally-supported shock in the underlying accretion disk via the first-order Fermi mechanism. The theoretical analysis employed here parallels the early studies of cosmic-ray acceleration in supernova shock waves, and the particle acceleration and disk structure are treated in a coupled, self-consistent manner based on a rigorous mathematical approach. We find that first-order Fermi acceleration at standing shocks in advection-dominated disks proves to be a very efficient means for accelerating the jet particles. Using physical parameters appropriate for M87 and SgrA*, we verify that the jet kinetic luminosities computed using our model agree with estimates based on observations of the sources.

astro-ph↗

arXiv2005

A Strong X-Ray Burst from the Low Mass X-Ray Binary EXO0748-676

We have observed an unusually strong X-ray burst as a part of our regular eclipse timing observations of the low mass binary system EXO0748-676. The burst peak flux was 5.2x10^-8 ergs cm^-2 s^-1, approximately five times the normal peak X-ray burst flux observed from this source by RXTE. Spectral fits to the data strongly suggest that photospheric radius expansion occurred during the burst. In this Letter we examine the properties of this X-ray burst, which is the first example of a radius expansion burst from EXO0748-676 observed by RXTE. We find no evidence for coherent burst oscillations. Assuming that the peak burst luminosity is the Eddington luminosity for a 1.4 solar mass neutron star we derive a distance to EXO0748-676 of 7.7 kpc for a helium-dominated burst photosphere and 5.9 kpc for a hydrogen-dominated burst photosphere.

astro-ph↗

arXiv2005

Exact Solution for the Hypergeometric Green's Function Describing Spectral Formation in X-Ray Pulsars

An eigenfunction expansion method involving hypergeometric functions is used to solve the partial differential equation governing the transport of radiation in an X-ray pulsar accretion column containing a radiative shock. The procedure yields the exact solution for the Green's function, which describes the scattering of monochromatic radiation injected into the column from a source located near the surface of the star. Collisions between the injected photons and the infalling electrons cause the radiation to gain energy as it diffuses through the gas and gradually escapes by passing through the walls of the column. The presence of the shock enhances the energization of the radiation and creates a power-law spectrum at high energies, which is typical for a Fermi process. The analytical solution for the Green's function provides important physical insight into the spectral formation process in X-ray pulsars, and it also has direct relevance for the interpretation of spectral data for these sources. Additional interesting mathematical aspects of the problem include the establishment of a closed-form expression for the quadratic normalization integrals of the orthogonal eigenfunctions, and the derivation of a new summation formula involving products of hypergeometric functions. By taking various limits of the general expressions, we also develop new linear and bilinear generating functions for the Jacobi polynomials.

math-ph↗

arXiv2005

Spectral Formation in X-Ray Pulsars: Bulk Comptonization in the Accretion Shock

Accretion-powered X-ray pulsars are among the most luminous X-ray sources in the Galaxy. However, despite decades of theoretical and observational work since their discovery, no satisfactory model for the formation of the observed X-ray spectra has emerged. In particular, the previously available theories are unable to reproduce the power-law variation observed at high energies in many sources. In this paper, we present the first self-consistent calculation of the spectrum emerging from a pulsar accretion column that includes an explicit treatment of the energization occurring in the shock. Using a rigorous eigenfunction expansion method based on the exact dynamical solution for the velocity profile in the column, we obtain a closed-form expression for the Green's function describing the upscattering of radiation injected into the column from a monochromatic source located at the top of the thermal mound, near the base of the flow. The Green's function is convolved with a Planck distribution to calculate the radiation spectrum resulting from the reprocessing of blackbody photons emitted by the thermal mound. We demonstrate that the energization of the photons in the shock naturally produces an X-ray spectrum with a power-law shape at high energies and a blackbody shape at low energies, in agreement with many observations of accreting X-ray pulsars.

astro-ph↗

arXiv2005

Spectral Formation in X-Ray Pulsar Accretion Columns

We present the first self-consistent model for the dynamics and the radiative transfer occurring in bright X-ray pulsar accretion columns, with a special focus on the role of the shock in energizing the emerging X-rays. The pressure inside the accretion column of a luminous X-ray pulsar is dominated by the photons, and consequently the equations describing the coupled radiative-dynamical structure must be solved simultaneously. Spectral formation in these sources is therefore a complex, nonlinear phenomenon. We obtain the analytical solution for the Green's function describing the upscattering of monochromatic radiation injected into the column from the thermal mound located near the base of the flow. The Green's function is convolved with a Planck distribution to model the X-ray spectrum resulting from the reprocessing of blackbody photons produced in the thermal mound. These photons diffuse through the infalling gas and eventually escape out the walls of the column, forming the observed X-ray spectrum. We show that the resulting column-integrated, phase-averaged spectrum has a power-law shape at high energies and a blackbody shape at low energies, in agreement with the observational data for many X-ray pulsars.

astro-ph↗

arXiv2004

A Self-Consistent Model for the Formation of Relativistic Outflows in Advection-Dominated Accretion Disks with Shocks

In this Letter, we suggest that the relativistic protons powering the outflows emanating from radio-loud systems containing black holes are accelerated at standing, centrifugally-supported shocks in hot, advection-dominated accretion disks. Such disks are ideal sites for first-order Fermi acceleration at shocks because the gas is tenuous, and consequently the mean free path for particle-particle collisions generally exceeds the thickness of the disk. The accelerated particles are therefore able to avoid thermalization, and as a result a small fraction of them achieve very high energies and escape from the disk. In our approach the hydrodynamics and the particle acceleration are coupled and the solutions are obtained self-consistently based on a rigorous mathematical treatment. The theoretical analysis of the particle transport parallels the early studies of cosmic-ray acceleration in supernova shock waves. We find that particle acceleration in the vicinity of the shock can extract enough energy to power a relativistic jet. Using physical parameters appropriate for M87 and Sgr A*, we confirm that the jet kinetic luminosities predicted by the theory agree with the observational estimates.

astro-ph↗

arXiv2004

Restrictions on the Physical Prescription for the Viscosity in Advection-Dominated Accretion Disks

It has recently been demonstrated that the Shakura-Sunyaev prescription for the kinematic viscosity in an advection-dominated accretion disk yields physically reasonable solutions for the structure of the inflow close to the event horizon. In particular, no violations of relativistic causality occur at the horizon. This is somewhat surprising considering the diffusive nature of the angular momentum transport in the Shakura-Sunyaev scenario, and it is therefore natural to ask whether one can also obtain acceptable solutions for the disk structure based on the various alternative models for the viscosity that have been proposed, including the "deterministic" forms. In this paper we perform a rigorous asymptotic analysis of the structure of an advection-dominated accretion disk close to the event horizon of a nonrotating black hole based on three of the alternative prescriptions for the viscosity that have been suggested in the literature. We constrain the physical disk model by stipulating that the stress must vanish at the horizon, which is the fundamental inner boundary condition imposed by general relativity. Surprisingly, we find that none of the three alternative viscosity prescriptions yield physically acceptable disk structures close to the horizon when the zero-torque condition is applied, whether the flow is in vertical hydrostatic equilibrium or free-fall. Hence we conclude that the original Shakura-Sunyaev prescription is the only one proposed so far that is physically consistent close to the event horizon.

astro-ph↗

arXiv2004

Angular momentum transport in accretion disks

We reexamine arguments advanced by Hayashi & Matsuda (2001), who claim that several simple, physically motivated derivations based on mean free path theory for calculating the viscous torque in a quasi-Keplerian accretion disk yield results that are inconsistent with the generally accepted model. If correct, the ideas proposed by Hayashi & Matsuda would radically alter our understanding of the nature of the angular momentum transport in the disk, which is a central feature of accretion disk theory. However, in this paper we point out several fallacies in their arguments and show that there indeed exists a simple derivation based on mean free path theory that yields an expression for the viscous torque that is proportional to the radial derivative of the angular velocity in the accretion disk, as expected. The derivation is based on the analysis of the epicyclic motion of gas parcels in adjacent eddies in the disk.

astro-ph↗

arXiv2004

Noise storm continua: power estimates for electron acceleration

We use a generic stochastic acceleration formalism to examine the power $L_{\rm in}$ (${\rm erg s^{-1}}$) input to nonthermal electrons that cause noise storm continuum emission. The analytical approach includes the derivation of the Green's function for a general second-order Fermi process, and its application to obtain the particular solution for the nonthermal electron distribution resulting from the acceleration of a Maxwellian source in the corona. We compare $L_{\rm in}$ with the power $L_{\rm out}$ observed in noise storm radiation. Using typical values for the various parameters, we find that $L_{\rm in} \sim 10^{23-26}$ ${\rm erg s^{-1}}$, yielding an efficiency estimate $η\equiv L_{\rm out}/L_{\rm in}$ in the range $10^{-10} \lsim η\lsim 10^{-6}$ for this nonthermal acceleration/radiation process. These results reflect the efficiency of the overall process, starting from electron acceleration and culminating in the observed noise storm emission.

astro-ph↗

arXiv2003

On the integration of products of Whittaker functions with respect to the second index

Several new formulas are developed that enable the evaluation of a family of definite integrals containing the product of two Whittaker W-functions. The integration is performed with respect to the second index, and the first index is permitted to have any complex value, within certain restrictions required for convergence. The method utilizes complex contour integration along with various symmetry relations satisfied by the Whittaker functions. The new results derived in this paper are complementary to the previously known integrals of products of Whittaker functions, which generally treat integration with respect to either the first index or the primary argument. A physical application involving radiative transport is discussed.

math-ph↗

arXiv2003

Broad redshifted line as a signature of outflow

We formulate and solve the diffusion problem of line photon propagation in a bulk outflow from a compact object (black hole or neutron star) using a generic assumption regarding the distribution of line photons within the outflow. Thomson scattering of the line photons within the expanding flow leads to a decrease of their energy which is of first order in v/c, where v is the outflow velocity and c is the speed of light. We demonstrate that the emergent line profile is closely related to the time distribution of photons diffusing through the flow (the light curve) and consists of a broad redshifted feature. We analyzed the line profiles for the general case of outflow density distribution. We emphasize that the redshifted lines are intrinsic properties of the powerful outflow that are supposed to be in many compact objects.

astro-ph↗