Maxim Lyutikov

Polarization of Prompt Gamma-Ray Burst Emission: Evidence for Electromagnetically Dominated Outflow

Observations by the RHESSI satellite of the large polarization of the prompt γ-ray emission from γ-ray burst (GRB) 021206 imply that the magnetic field coherence scale is larger than the size of the visible emitting region, ~R/Γ, where R is the radius of the flow and Γ is the associated Lorentz factor. Such fields cannot be generated in a causally disconnected, hydrodynamically dominated outflow. Electromagnetic models of GRBs, in which large-scale, dynamically dominant, magnetic fields are present in the outflow from the very beginning, provide a natural explanation of this large reported linear polarization. We derive the Stokes parameters of the synchrotron emission of a relativistically moving plasma with a given magnetic field configuration and calculate the pulse-averaged polarization fraction of the emission from a relativistically expanding shell carrying a global toroidal magnetic field. For viewing angles larger than 1/Γ, the observed patch of the emitting shell has an almost homogeneous magnetic field, producing a large fractional polarization (56% for a power-law energy distribution of relativistic particles, dn/d -3). The maximum polarization is smaller than the theoretical upper limit for a stationary plasma in a uniform magnetic field because of relativistic kinematic effects.

Explosive reconnection in magnetars

The X-ray activity of anomalous X-ray pulsars and soft γ-ray repeaters may result from the heating of their magnetic corona by direct currents dissipated by magnetic reconnection. We investigate the possibility that X-rayflares and bursts observed from anomalous X-ray pulsars and soft γ-ray repeaters result from magnetospheric reconnection events initiated by development of the tearing mode in magnetically dominated relativistic plasma. We formulate equations of resistive force-free electrodynamics, discuss the relation of the latter to ideal electrodynamics, and give examples of both ideal and resistive equilibria. Resistive force-free current layers are unstable towards the development of small-scale current sheets where resistive effects become important. Thin current sheets are found to be unstable due to the development of the resistive force-free tearing mode. The growth rate of the tearing mode is intermediate between the short Alfven time-scale τ A and a long resistive time-scale τ R : r ∼ 1/(τ R τ A ) 1 / 2 , similar to the case of non-relativistic non-force-free plasma. We propose that growth of the tearing mode is related to the typical rise time of flares, ∼10 ms. Finally, we discuss how reconnection may explain other magnetar phenomena and ways to test the model.

Magnetar giant flares and afterglows as relativistic magnetized explosions

We propose that giant flares on soft γ-ray repeaters produce relativistic, strongly magnetized, weakly baryon-loaded magnetic clouds, somewhat analogous to solar coronal mass ejection (CME) events. The flares are driven by unwinding of the internal non-potential magnetic field which leads to a slow build-up of magnetic energy outside of the neutron star. For large magnetospheric currents, corresponding to a large twist of the external magnetic field, the magnetosphere becomes dynamically unstable on the Alfven crossing time-scale of the inner magnetosphere, t A ∼ R N S/C ∼ 30 μs. The dynamic instability leads to the formation of dissipative current sheets through the development of a tearing mode. The released magnetic energy results in the formation of a strongly magnetized, pair-loaded, quasi-spherically expanding flux rope, topologically connected by the magnetic field to the neutron star during the prompt flare emission. The expansion reaches large Lorentz factors, r ∼ 10-20, at distances r ∼ 1-2 x 10 7 cm, where a leptophotonic load is lost. Beyond this radius plasma is strongly dominated by the magnetic field, though some baryon loading, with M <<E/c 2 , by ablated neutron star material may occur. Magnetic stresses of the tied flux rope lead to a late collimation of the expansion, on time-scales longer than the giant flare duration. Relativistic bulk motion of the expanding magnetic cloud, directed at an angle 0 ∼ 135° to the line of sight (away from the observer), results in a strongly non-spherical forward shock with observed non-relativistic apparent expansion and bulk motion velocities β app ∼ cot 0/2 ∼ 0.4 at times of the first radio observations, approximately one week after the burst. An interaction with a shell of wind-shocked interstellar medium (ISM) and then with the unshocked ISM leads to a deceleration, to non-relativistic velocities approximately one month after the flare.

The electromagnetic model of gamma-ray bursts

The electromagnetic model (EMM) of gamma-ray bursts (GRBs) and a contrast of its main properties and predictions with the hydrodynamic fireball model (FBM) and its magnetohydrodynamical extension are described. The EMM assumes that rotational energy of a relativistic, stellar-mass central source (black hole–accretion disk system or fast rotating neutron star) is converted into magnetic energy through a unipolar dynamo mechanism, propagated to large distances in the form of relativistic, subsonic, Poynting flux-dominated wind and is dissipated directly into emitting particles through current-driven instabilities. Thus, there is no conversion back and forth between internal and bulk energies as in the case of the fireball model. Collimating effects of magnetic hoop stresses lead to strongly non-spherical expansion and formation of jets. Long and short GRBs may develop in a qualitatively similar way, except that in the case of long burst ejecta expansion has a relatively short, non-relativistic, strongly dissipative stage inside the star. EMMs and FBMs (as well as strongly and weakly magnetized fireballs) lead to different early afterglow dynamics, before deceleration time. Finally, the models are discussed in view of latest observational data in the Swift era.

Resonant cyclotron scattering and Comptonization in neutron star magnetospheres

Resonant cyclotron scattering of the surface radiation in the magnetospheres of neutron stars may considerably modify the emergent spectra and impede efforts to constrain neutron star properties. Resonant cyclotron scattering by a non-relativistic warm plasma in an inhomogeneous magnetic field has a number of unusual characteristics. (i) In the limit of high resonant optical depth, the cyclotron resonant layer is half opaque, in sharp contrast to the case of non-resonant scattering. (ii) The transmitted flux is on average Compton up-scattered by ∼1 + 2βT, where βT is the typical thermal velocity in units of the velocity of light; the reflected flux has on average the initial frequency. (iii) For both the transmitted and reflected fluxes, the dispersion of intensity decreases with increasing optical depth. (iv) The emergent spectrum is appreciably non-Planckian while narrow spectral features produced at the surface may be erased. We derive semi-analytically modification of the surface Planckian emission due to multiple scattering between the resonant layers and apply the model to the anomalous X-ray pulsar 1E 1048.1 − 5937. Our simple model fits just as well as the ‘canonical’ magnetar spectra model of a blackbody plus power law.

Tearing instability in relativistic magnetically dominated plasmas

Many astrophysical sources of high-energy emission such as black hole magnetospheres, superstrongly magnetized neutron stars (magnetars) and probably relativistic jets in active galactic nuclei and gamma-ray bursts involve relativistically magnetically dominated plasma. In such plasma the energy density of magnetic field greatly exceeds the thermal and the rest mass energy density of particles. Therefore, the magnetic field is the main reservoir of energy and its dissipation may power the bursting emission from these sources, in close analogy to solar flares. One of the principal dissipative instabilities that may lead to release of magnetic energy is the tearing instability. In this paper we study, both analytically and numerically, the development of tearing instability in relativistically magnetically dominated plasma using the framework of resistive magnetodynamics. We confirm and elucidate the previously obtained result on the growth rate of the tearing mode: the shortest growth time is the same as in the case of classical non-relativistic magnetohydrodynamics (MHD), namely r = √τ a τ d , where τ a is the Alfven crossing time and τ d is the resistive time of a current layer. The reason for this coincidence is the close similarity between the governing equations, especially in the quasi-equilibrium approximation. In particular, the role of the mass density of non-relativistic MHD is played by the mass-energy density of the magnetic field, p = B 2 /8πc 2 .

MAGNETOSPHERIC ECLIPSES IN THE DOUBLE PULSAR SYSTEM PSR J0737-3039

In the binary radio pulsar system PSR J0737-3039, the faster pulsar, A, is eclipsed once per orbit. A clear modulation of these eclipses at the 2.77 s period of pulsar B has recently been discovered. We construct a simple geometric model that successfully reproduces the eclipse light curves, based on the idea that the radio pulses are attenuated by synchrotron absorption on the closed magnetic field lines of pulsar B. The model explains most of the properties of the eclipse: its asymmetric form, the nearly frequency-independent duration, and the modulation of the brightness of pulsar A at both once and twice the rotation frequency of pulsar B in different parts of the eclipse. This detailed agreement confirms the dipolar structure of the stars poloidal magnetic field. The inferred parameters are the inclination angle between the line of sight and orbital plane normal, ~905; the inclination of pulsar Bs rotation axis to the orbital plane normal, ~60°; and the angle between the rotation axis and the magnetic moment, ~75°. The model makes clear predictions for the degree of linear polarization of the transmitted radiation. The weak frequency dependence of the eclipse duration implies that the absorbing plasma is relativistic, with a density much larger than the corotation charge density. Such hot, dense plasma can be effectively stored in the outer magnetosphere, where cyclotron cooling is slow. The gradual loss of particles inward through the cooling radius is compensated for by an upward flux driven by a fluctuating component of the current and by the pumping of magnetic helicity on the closed field lines. The trapped particles are heated to relativistic energies by the damping of magnetospheric turbulence and, at a slower rate, by the absorption of the radio emission of the companion pulsar. A heating mechanism is outlined that combines electrostatic acceleration along the magnetic field with the emission and absorption of wiggler radiation by charged particle bunches.

On the nature of eclipses in binary pulsar J0737¿3039

We consider the magnetohydrodynamical interaction between the relativistic wind outflowing from pulsar A and the static magnetosphere of pulsar B in the binary pulsar system PSR J0737-3039. We construct a semi-analytical model describing the form of the interface separating the two pulsars. The assumption of vacuum dipole spin-down for pulsar B leads to a duration of the eclipse 10 times longer than observed. We discuss a possible torque modification for pulsar B and magnetic field estimates due to the interaction with the wind from pulsar A. Unless the orbital inclination is ≤ 86°, the duration of eclipses is typically shorter than that implied by the size of the eclipsing region. We propose that eclipses occur as a result of synchrotron absorption by mildly relativistic particles in the shocked wind from pulsar A. The corresponding optical depth may be high enough if the wind density from pulsar A is at the upper allowed limit. We derive jump conditions at oblique, relativistic, magnetohydrodynamical shocks and discuss the structure of the shocked wind from pulsar A. Finally, we speculate on a possible mechanism of orbital modulation of the radio emission from pulsar B.

Did Swift measure gamma-ray burst prompt emission radii?

The Swift X-Ray Telescope often observes a rapidly decaying X-ray emission stretching to as long as t∼ 103 s after a conventional prompt phase. This component is most likely due to a prompt emission viewed at large observer angles θ > 1/Γ, where θ∼ 0.1 is a typical viewing angle of the jet and Γ≥ 100 is the Lorentz factor of the flow during the prompt phase. This can be used to estimate the prompt emission radii, rem≥ 2t c/θ2∼ 6 × 1015 cm. These radii are much larger than is assumed within the framework of a fireball model. Such large emission radii can be reconciled with a fast variability, on time-scales as short as milliseconds, if the emission is beamed in the bulk outflow frame, e.g. because of a random relativistic motion of ‘fundamental emitters’. This may also offer a possible explanation for X-ray flares observed during early afterglows.

Signatures of large-scale magnetic fields in AGN jets: transverse asymmetries

We investigate the emission properties that a large-scale helical magnetic field imprints on AGN jet synchrotron radiation. A cylindrically symmetric relativistic jet and large-scale helical magnetic field produce significant asymmetrical features in transverse profiles of fractional linear polarization, intensity, Faraday rotation, and spectral index. The asymmetrical features of these transverse profiles correlate with one another in ways specified by the handedness of the helical field, the jet viewing angle (theta_ob), and the bulk Lorentz factor of the flow (Gamma). Thus, these correlations may be used to determine the structure of the magnetic field in the jet. In the case of radio galaxies (theta_ob~1 radian) and a subclass of blazars with particularly small viewing angles (theta_ob << 1/Gamma), we find an edge-brightened intensity profile that is similar to that observed in the radio galaxy M87. We present observations of the AGNs 3C 78 and NRAO 140 that display the type of transverse asymmetries that may be produced by large-scale helical magnetic fields.