arXiv subjects

Eric G. Blackman

Publications and source records attributed to Eric G. Blackman.

At least 181 records · Page 10Linked to original sources

arXiv2000

GRBs from unstable Poynting dominated outflows

Poynting flux driven outflows from magnetized rotators are a plausible explanation for gamma-ray burst engines. We suggest a new possibility for how such outflows might transfer energy into radiating particles. We argue that the Poynting flux drives non-linearly unstable large amplitude electromagnetic waves (LAEMW) which ``break'' at radii $r_t \sim 10^{14} $ cm where the MHD approximation becomes inapplicable. In the ``foaming'' (relativisticly reconnecting) regions formed during the wave breaks the random electric fields stochastically accelerate particles to ultrarelativistic energies which then radiate in turbulent electromagnetic fields. The typical energy of the emitted photons is a fraction of the fundamental Compton energy $ ε\sim f \hbar c/r_e $ with $f \sim 10^{-3}$ plus additional boosting due to the bulk motion of the medium. The emission properties are similar to synchrotron radiation, with a typical cooling time $\sim 10^{-4}$ sec. During the wave break, the plasma is also bulk accelerated in the outward radial direction and at larger radii can produce afterglows due to the interactions with external medium. The near equipartition fields required by afterglow models maybe due to magnetic field regeneration in the outflowing plasma (similarly to the field generation by LAEMW of laser-plasma interactions) and mixing with the upstream plasma.

astro-ph↗

arXiv1999

Constraints on the magnitude of alpha in dynamo theory

We consider the backreaction of the magnetic field on the magnetic dynamo coefficients and the role of boundary conditions in interpreting whether numerical evidence for suppression is dynamical. If a uniform field in a periodic box serves as the initial condition for modeling the backreaction on the turbulent EMF, then the magnitude of the turbulent EMF and thus the dynamo coefficient $\a$, have a stringent upper limit that depends on the magnetic Reynolds number $R_M$ to a power of order -1. This is not a dynamic suppression but results just because of the imposed boundary conditions. In contrast, when mean field gradients are allowed within the simulation region, or non-periodic boundary are used, the upper limit is independent of $R_M$ and takes its kinematic value. Thus only for simulations of the latter types could a measured suppression be the result of a dynamic backreaction. This is fundamental for understanding a long-standing controversy surrounding $α$ suppression. Numerical simulations which do not allow any field gradients and invoke periodic boundary conditions appear to show a strong $α$ suppression (e.g. Cattaneo & Hughes 1996). Simulations of accretion discs which allow field gradients and allow free boundary conditions (Brandenburg & Donner 1997) suggest a dynamo $α$ which is not suppressed by a power of $R_M$. Our results are consistent with both types of simulations.

astro-ph↗

arXiv1999

Coronal activity as a consequence of dynamos in astrophysical rotators

We show that the presence of a steady $\ao$ dynamo in astrophysical rotators likely leads to an outflow of relative magnetic helicity and thus magnetic energy available for particle acceleration in a corona. The connection between energy and magnetic helicity arises because the generation of large scale field is linked to a generation of large scale magnetic helicity. In a steady state, the relative magnetic helicity associated with the large scale field can escape, accompanied by an equal and opposite small scale contribution from the field, since the total magnetic helicity in large magnetic Reynolds number flows is conserved. From the helicity flow, a lower limit on the magnetic energy deposited in the corona can be estimated. Steady coronal activity and the dissipation of magnetic energy is therefore a signature of an internal dynamo. Our theoretical estimate of the power delivered by a mean field dynamo is consistent with that inferred from observations to be delivered to the solar corona, the Galactic corona, and Seyfert I AGN coronae.

astro-ph↗

arXiv1999

Mean magnetic field generation in sheared rotators

A generalized mean magnetic field induction equation for differential rotators is derived, including a compressibility, and the anisotropy induced on the turbulent quantities from the mean magnetic field itself and a mean velocity shear. Derivations of the mean field equations often do not emphasize that there must be anisotropy and inhomogeneity in the turbulence for mean field growth. The anisotropy from shear is the source of a term involving the product of the mean velocity gradient and the cross-helicity correlation of the isotropic parts of the fluctuating velocity and magnetic field, $\lb{\bfv}\cdot{\bfb}\rb^{(0)}$. The full mean field equations are derived to linear order in mean fields, but it is also shown that the cross-helicity term survives to all orders in the velocity shear. This cross-helicity term can obviate the need for a pre-existing seed mean magnetic field for mean field growth: though a fluctuating seed field is necessary for a non-vanishing cross-helicity, the term can produce linear (in time) mean field growth of the toroidal field from zero mean field. After one vertical diffusion time, the cross-helicity term becomes sub-dominant and dynamo exponential amplification/sustenance of the mean field can subsequently ensue. The cross-helicity term should produce odd symmetry in the mean magnetic field, in contrast to the usually favored even modes of the dynamo amplification in sheared discs. This may be important for the observed mean field geometries of spiral galaxies. The strength of the mean seed field provided by the cross- helicity depends linearly on the magnitude of the cross-helicity.

astro-ph↗

arXiv1999

Reprocessed emission from warped accretion discs with application to X-ray iron line profiles

Flourescent iron line profiles currently provide the best diagnostic for active galactic nuclei (AGN) engine geometries. Here we construct a method for calculating the relativistic iron line profile from an arbitrarily warped accretion disc, illuminated from above and below by hard X-ray sources. This substantially generalises previous calculations of reprocessing by accretion discs by including non-axisymmetric effects. We include a relativistic treatment of shadowing by ray-tracing photon paths along Schwarzchild geodesics. We apply this method to two classes of warped discs, and generate a selection of resulting line profiles. New profile features include the possibility of sharper red, and softer blue fall-offs, a time varying line profile if the warp precesses about the disc, and some differences between `twisted' and `twist-free' warps. We discuss some qualitative implications of the line profiles in the context of Type I and II Seyfert AGN.

astro-ph↗

arXiv1999

Concave Accretion Discs and X-ray Reprocessing

Spectra of Seyfert Is are commonly modelled as emission from an X-ray illuminated flat accretion disc orbiting a central black hole. This provides both a reprocessed and direct component of the X-ray emission as required by observations of individual objects and possibly a fraction of the cosmological X-ray background. There is some observational motivation to at least consider the role that an effectively concave disc surface might play: (1) a reprocessed fraction $\gsim 1/2$ in some Seyferts and possibly in the X-ray background, and (2) the commonality of a sharp iron line peak for Seyferts at 6.4KeV despite a dependence of peak location on inclination angle for flat disc models. Here it is shown that a concave disc may not only provide a larger total fraction of reprocessed photons, but can also reprocess a much larger fraction of photons in its outer regions when compared to a flat disc. This reduces the sensitivity of the 6.4KeV peak location to the inner disc inclination angle because the outer regions are less affected by Doppler and gravitational effects. If the X-ray source is isotropic, the reprocessed fraction is directly determined by the concavity. If the X-ray source is anisotropic, the location of iron line peak can still be determined by concavity but the total reflected fraction need not be as large as for the isotropic emitter case. The geometric calculations herein are applicable to general accretion disc systems illuminated from the center.

astro-ph↗

arXiv1999

Resolution of an ambiguity in dynamo theory and its consequences for back reaction studies

An unsolved problem in turbulent dynamo theory is the ``back reaction'' problem: to what degree does the mean magnetic field suppress the turbulent dynamo coefficients which are needed to drive its growth? The answer will ultimately derive from a combination of numerical and analytical studies. Here we show that analytic approaches to the dynamo and back reaction problems require one to separate turbulent quantities into two components: those influenced by the mean field (which are therefore anisotropic) and those independent of the mean field (and are therefore isotropic), no matter how weak the mean field is. Upon revising the standard formalism to meet this requirement, we find that: (1) The two types of components often appear in the same equation, so that standard treatments, which do not distinguish between them, are ambiguous. (2) The usual first-order smoothing approximation that is necessary to make progress in the standard treatment is unnecessary when the distinction is made. (3) In contrast to previous suggestions, the correction to the dynamo $\a$ coefficient found by Pouquet et al (1976) is actually independent of the mean field, and therefore cannot be interpreted as a quenching.

astro-ph↗

arXiv1998

Nonlinear Alpha Effect in Dynamo Theory

We extend the standard two-scale theory of the turbulent dynamo coefficient $α$ to include the nonlinear back reaction of the mean field $\bar B$ on the turbulence. We calculate the turbulent emf as a power series in $\bar B$, assuming that the base state of the turbulence ($\bar B=0$) is isotropic, and, for simplicity, that the magnetic diffusivity equals the kinematic viscosity. The power series converges for all $\bar B$, and for the special case that the spectrum of the turbulence is sharply peaked in $k$, our result is proportional to a tabulated function of the magnetic Reynolds number $R_M$ and the ratio $β$ of $\bar B$ (in velocity units) to the rms turbulent velocity $v_0$. For $β\to 0$ (linear regime) we recover the results of Steenbeck et al. (1966) as modified by Pouquet et al. (1976). For $R_M\gg 1$, the usual astrophysical case, $α$ starts to decrease at $β\sim 1$, dropping like $β^{-2}$ as $β\to \infty$. Hence for large $R_M$, $α$ saturates at $\bar B\sim v_0$, as estimated by Kraichnan (1979), rather than at $\bar B\sim R^{-1/2}_Mv_0$, as inferred by Cattaneo and Hughes (1996) from their numerical simulations at $R_M$=100. We plan to carry out simulations with various values of $R_M$ to investigate the discrepency.

astro-ph↗

arXiv1998

On Proton Energization in Accretion Flows

Two-temperature advection dominated accretion flow (ADAF) or hot ion tori (HIT) models help explain low luminosity stellar and galactic accreting sources and may complement observational support for black holes in nature. But low radiative efficiencies demand that ions receive a fraction $η\gsim 99%$ of energy dissipated in the turbulent accretion. The $η$ depends on the ratio of particle to magnetic pressure. If compressive modes of dissipation, like magnetic mirroring, dominate incompressible modes, then even when the pressure ratio is O(1), the required large $η$ can be attained. However the relative importance of compressive vs. incompressible modes is hard to estimate. The larger up in the turbulent cascade, the more compressible the turbulence. The relevant length scale for particle energization can be determined by equating the dominant eddy turnover time to the time for which an energy equal to that in the turbulence can be drained. Based on the large scales resulting from this estimate, it is suggested that compressive mirroring may be important. Also, regardless of the precise $η$ or dissipation mechanism, non-thermal protons seem natural in two- temperature discs because all dissipation mechanisms, and the use of an isotopic pressure, require wave-particle resonances that operate only on a subset of the particles. Finally, it is briefly mentioned how mirroring may help to generate an ADAF or HIT in the first place.

astro-ph↗

arXiv1998

Variability Associated with Alpha Accretion Disc Theory for Standard and Advection Dominated Discs

The $α$ turbulent viscosity formalism for accretion discs must be interpreted as a mean field theory. The extent to which the disc scale exceeds that of the turbulence determines the precision of the predicted luminosity $L_ν$. The assumption of turbulence and use of $\a$ implies: (1) Field line stretching generates a magnetic pressure $\gsim \a^2/6$ of the total pressure generally, and a 1 to 1 relation between $\a$ and the pressure ratio when shearing instabilities dominate the viscosity. (2) Large eddy sizes and speeds in typical advection dominated accretion flows (ADAFs) lead to a lower precision in $L_ν$ than for thin discs of a given total observation duration and central mass. The allowed variability (relative precision) at a particular frequency increases (decreases) with the size of the contributing region. For X-ray binary type ADAFs, the allowed variability is $\sim 5$% at $R \le 1000$ Schwarzchild radii for averages over $\gsim 1000$sec. But for large galactic nuclei like NGC 4258 and M87, the relative precision error can approach $50-100%$ even at $R \le 100 R_S$ for currently available observation durations. More data are then required to compare with ADAF predictions.

astro-ph↗

arXiv1998

On Fueling Gamma-Ray Bursts and Their Afterglows with Pulsars

Cosmological gamma-ray bursts (GRBs) and their afterglows seem to result from dissipation of bulk energy in relativistic outflows, but their engine has not been unambiguously identified. The engine could be a young pulsar formed from accretion induced collapse with a dynamo amplified field. Elsewhere, we suggest that such a ``Usov type'' strong field pulsar may help explain the bimodal distribution in GRB durations. Here we discuss possible roles of a pulsar for the afterglow. We derive the expected bolometric luminosity decay. The extracted rotational energy could dissipate by shocks or by large amplitude electromagnetic waves (LAEMW). The simplest LAEMW approach predicts a slower decay in observed afterglow peak frequency and faster decay in flux than the simplest blast-wave model, though more complicated models of both can provide different dependences. LAEMW do not require the rapid magnetic field amplification demanded of the blast-wave approach because the emission originates from a nearly fixed radius. Different time dependent behavior of GRB and post-GRB emission is also predicted. Observational evidence for a pulsar in a GRB would make some GRB engine models, such as neutron star mergers and black holes unlikely. Therefore, the question of whether a pulsar is present is an important one even if it could drive a canonical fireball.

astro-ph↗

arXiv1998

In Situ Origin of Large Scale Galactic Magnetic Fields Without Kinetic Helicity?

The origin and sustenance of large scale galactic magnetic fields has been a long standing and controversial astrophysical problem. Here an alternative to the ``standard'' $\a-Ω$ mean field dynamo and primordial theories is pursued. The steady supply of supernovae induced turbulence exponentiates the total field energy, providing a significant seed mean field that can be linearly stretched by shear. The observed micro-Gauss fields would be produced primarily within one vertical diffusion time since it is only during this time that linear stretching can compete with diffusion. This approach does not invoke exponential mean field dynamo growth from the helicity $\a$-effect but does employ turbulent diffusion, which limits the number of large scale reversals. The approach could be of interest if the helicity effect is suppressed independently of the turbulent diffusion. This is an important but presently unresolved issue.

astro-ph↗

arXiv1997

Importance of an Astrophysical Perspective for Textbook Relativity

The importance of a teaching a clear definition of the ``observer'' in special relativity is highlighted using a simple astrophysical example from the exciting current research area of ``Gamma-Ray Burst'' astrophysics. The example shows that a source moving relativistically toward a single observer at rest exhibits a time ``contraction'' rather than a ``dilation'' because the light travel time between the source and observer decreases with time. Astrophysical applications of special relativity complement idealized examples with real applications and very effectively exemplify the role of a finite light travel time.

physics.ed-ph↗

arXiv1997

An Explanation for the Bimodal Distribution of Gamma-Ray Bursts: Millisecond Pulsars from Accretion-Induced Collapse

Cosmological gamma-ray bursts (GRBs) could be driven by dissipation of pure electromagnetic energy (Poynting flux) extracted from rapidly rotating compact objects with strong magnetic fields. One such possibility is a young millisecond pulsar (MSP) formed from accretion-induced collapse (AIC) of a white dwarf. The combination of an efficient magnetic dynamo, likely operating during the first seconds of the initially hot and turbulent MSP interior, and the subsequent modest beaming of gamma-ray emitting outflows, would easily account for energy constraints. But the remarkable feature of such models is that they may naturally explain the hitherto unexplained bimodal distribution in GRB time durations. The two burst classes could correspond to MSPs that form spinning above and below a gravitationally unstable limit respectively. In the former case, the spin-down time scale is due to gravitational radiation emission ($<1s$) while the spin-down time scale of the latter is due to electromagnetic dipole emission ($\gg 1s$). These two time scales account for the short and long GRB durations, i.e. the observed bimodal GRB duration distribution. A natural prediction is that the short duration GRBs would be accompanied by strong gravitational radiation emission which is absent from the longer class. Both would show millisecond variabilities.

astro-ph↗

arXiv1997

A Vorticity-Magnetic Field Dynamo Instability

We generalize the mean field magnetic dynamo to include local evolution of the mean vorticity in addition to the mean magnetic field. The coupled equations exhibit a general mean field dynamo instability that enables the transfer of turbulent energy to the magnetic field and vorticity on larger scales. The growth of the vorticity and magnetic field both require helical turbulence which can be supplied by an underlying global rotation. The dynamo coefficients are derived including the backreaction from the mean magnetic field to lowest order. We find that a mean vorticity field can actually seed exponential growth of mean magnetic field from only a small scale seed magnetic field, without the need for a seed mean magnetic field. The equations decouple when the fluctuating velocity and magnetic field cross-correlations vanish, resulting in the separate mean field magnetic and mean field vorticity dynamo equations.

astro-ph↗

arXiv1997

Formation of Millisecond Pulsars from Accretion Induced Collapse and Constraints on Pulsar Gamma Ray Burst Models

We study accretion induced collapse of magnetized white dwarfs as an origin of millisecond pulsars. We apply magnetized accretion disk models to the pre-collapse accreting magnetic white dwarfs and calculate the white dwarf spin evolution. If the pulsar magnetic field results solely from the flux-frozen fossil white dwarf field, a typical millisecond pulsar is born with a field strength $\sim 10^{11}-10^{12}G$. The uncertainty in the field strength is mainly due to the uncertain physical parameters of the magnetized accretion disk models. A simple correlation between the pulsar spin $Ω_*$ and the magnetic field $B_*$, $(Ω_*/10^4s^{-1})\sim (B_{*}/10^{11}G)^{-4/5}$, is derived for a typical accretion rate $\sim 5\times 10^{-8}M_{\sun}/yr$. This correlation remains valid for a wide pre-collapse physical conditions unless the white dwarf spin and the binary orbit are synchronized prior to accretion induced collapse. We critically examine the possibility of spin-orbit synchronization in close binary systems. Using idealized homogeneous ellipsoid models, we compute the electromagnetic and gravitational wave emission from the millisecond pulsars and find that electromagnetic dipole emission remains nearly constant while millisecond pulsars may spin up rather than spin down as a result of gravitational wave emission. We also derive the physical conditions under which electromagnetic emission from millisecond pulsars formed by accretion induced collapse can be a source of cosmological gamma-ray bursts. We find that relativistic beaming of gamma-ray emission and precession of gamma-ray emitting jets are required unless the dipole magnetic field strengths are $>10^{15}$G; such strong dipole fields are in excess of those allowed from the accretion induced collapse formation process except in spin-orbit synchronization.

astro-ph↗

arXiv1997

Distinguishing Solar Flare Types by Differences in Reconnection Regions

Observations show that magnetic reconnection and its slow shocks occur in solar flares. The basic magnetic structures are similar for long duration event (LDE) flares and faster compact impulsive (CI) flares, but the former require less non-thermal electrons than the latter. Slow shocks can produce the required non-thermal electron spectrum for CI flares by Fermi acceleration if electrons are injected with large enough energies to resonate with scattering waves. The dissipation region may provide the injection electrons, so the overall number of non-thermal electrons reaching the footpoints would depend on the size of the dissipation region and its distance from the chromosphere. In this picture, the LDE flares have converging inflows toward a dissipation region that spans a smaller overall length fraction than for CI flares. Bright loop-top X-ray spots in some CI flares can be attributed to particle trapping at fast shocks in the downstream flow, the presence of which is determined by the angle of the inflow field and velocity to the slow shocks.

astro-ph↗

arXiv1996

Relativistic Precessing Jets and Cosmological Gamma Ray Bursts

We discuss the possibility that gamma-ray bursts may result from cosmological relativistic blob emitting neutron star jets that precess past the line of sight. Beaming reduces the energy requirements, so that the jet emission can last longer than the observed burst duration. One precession mode maintains a short duration time scale, while a second keeps the beam from returning to the line of sight, consistent with the paucity of repeaters. The long life of these objects reduces the number required for production as compared to short lived jets. Blobs can account for the time structure of the bursts. Here we focus largely on kinematic and time scale considerations of beaming, precession, and blobs--issues which are reasonably independent of the acceleration and jet collimation mechanisms. We do suggest that large amplitude electro-magnetic waves could be a source of blob acceleration.

astro-ph↗