Andrei M. Beloborodov

Plasma Ejection from Magnetic Flares and the X-Ray Spectrum of Cygnus X-1

The hard X-rays in Cyg X-1 and similar black hole sources are possibly produced in an active corona atop an accretion disk. We suggest that the observed weakness of X-ray reflection from the disk is due to bulk motion of the emitting hot plasma away from the reflector. A mildly relativistic motion causes aberration, reducing X-ray emission toward the disk. This in turn reduces the reprocessed radiation from the disk and leads to a hard spectrum of the X-ray source. The resulting spectral index is Γ≈1.9/, where B=γ(1+β) is the aberration factor for a bulk velocity β=v/c. The observed Γ≈1.6 and the amount of reflection (R≈0.3) in Cyg X-1 in the hard state can both be explained assuming a bulk velocity β~0.3. We discuss one possible scenario: the compact magnetic flares are dominated by e± pairs, which are ejected away from the reflector by the pressure of the reflected radiation. We also discuss physical constraints on the disk-corona model and argue that the magnetic flares are related to magnetorotational instabilities in the accretion disk.

Corona of magnetars

We develop a theoretical model that explains the formation of hot coronae around strongly magnetized neutron stars—magnetars. The starquakes of a magnetar shear its external magnetic field, which becomes nonpotential and threaded by an electric current. Once twisted, the magnetosphere cannot untwist immediately because of its self-induction. The self-induction electric field lifts particles from the stellar surface, accelerates them, and initiates avalanches of pair creation in the magnetosphere. The created plasma corona maintains the electric current demanded by ∇ × and regulates the self-induction EMF by screening. This corona persists in dynamic equilibrium: it is continually lost to the stellar surface on the light crossing time ~10-4 s and replenished with new particles. In essence, the twisted magnetosphere acts as an accelerator that converts the toroidal field energy to particle kinetic energy. Using a direct numerical experiment, we show that the corona self-organizes quickly (on a millisecond timescale) into a quasi-steady state, with voltage 108-109 V along the magnetic lines. The voltage is maintained near the threshold for e± discharge. The heating rate of the corona is ~1036 ergs s-1, in agreement with the observed persistent, high-energy output of magnetars. We deduce that a static twist that is suddenly implanted into the magnetosphere will decay on a timescale of 1-10 yr. The particles accelerated in the corona impact the solid crust, knock out protons, and regulate the column density of the hydrostatic atmosphere of the star. The transition layer between the atmosphere and corona may be hot enough to create additional e± pairs. This layer can be the source of the observed 100 keV emission from magnetars. The corona emits curvature radiation and can supply the observed IR-optical luminosity.

Stellar Disk in the Galactic Center: A Remnant of a Dense Accretion Disk?

Observations of the Galactic center revealed a population of young massive stars within 0.4 pc from Sgr A*—the presumed location of a supermassive black hole. The origin of these stars is a puzzle as their formation in situ should be suppressed by the black holes tidal field. We find that out of 13 stars whose three-dimensional velocities have been measured by Genzel et al., 10 lie in a thin disk. The half-opening angle of the disk is consistent with zero within the measurement errors and does not exceed 10°. We propose that a recent burst of star formation has occurred in a dense gaseous disk around Sgr A*. Such a disk is no longer present because, most likely, it has been accreted by the central black hole. The three-dimensional orbit of S2, the young star closest to Sgr A*, has been recently mapped out with high precision. It is inclined to the stellar disk by 75°. We find that the orbit should undergo Lense-Thirring precession with the period of ~(6/a) × 106 yr, where a 0.2(tS2/6 × 106 yr)-1, where tS2 is the age of S2.

Untwisting magnetospheres of neutron stars

Magnetospheres of neutron stars are anchored in the rigid crust and can be twisted by sudden crustal motions (starquakes). The twisted magnetosphere does not remain static and gradually untwists, dissipating magnetic energy and producing radiation. The equation describing this evolution is derived, and its solutions are presented. Two distinct regions coexist in untwisting magnetospheres: a potential region where ∇ × B = 0 (cavity) and a current-carrying bundle of field lines with ∇ × B ≠ 0 (j-bundle). The cavity has a sharp boundary, which expands with time and eventually erases all of the twist. In this process, the electric current of the j-bundle is sucked into the star. Observational appearance of the untwisting process is discussed. A hot spot forms at the footprints of the j-bundle. The spot shrinks with time toward the magnetic dipole axis, and its luminosity and temperature gradually decrease. As the j-bundle shrinks, the amplitude of its twist ψ can grow to the maximum possible value ψmax ~ 1. The strong twist near the dipole axis increases the spindown rate of the star and can generate a broad beam of radio emission. The model explains the puzzling behavior of magnetar XTE J1810–197, a canonical example of magnetospheric evolution following a starquake. We also discuss implications for other magnetars. The untwisting theory suggests that the nonthermal radiation of magnetars is preferentially generated on a bundle of extended closed field lines near the dipole axis.

X-ray spectra of accretion discs with dynamic coronae

We compute the X-ray spectra produced by non-static coronae atop accretion discs around black holes and neutron stars. The hot corona is radiatively coupled to the underlying disc (the reflector) and generates an X-ray spectrum which is sensitive to the bulk velocity of the coronal plasma, β=v/c. We show that an outflowing corona reproduces the hard-state spectrum of Cyg X-1 and similar objects. The dynamic model predicts a correlation between the observed amplitude of reflection R and the X-ray spectrum slope Γ since both strongly depend on β. A similar correlation was observed and its shape was well fitted by the dynamic model. The scattering of soft radiation in an outflowing corona can also account for the observed optical–UV polarization pattern in active galactic nuclei.

Nuclear Composition of Gamma-Ray Burst Fireballs

We study three processes that shape the nuclear composition of gamma-ray burst (GRB) fireballs: (1) neutronization in the central engine, (2) nucleosynthesis in the fireball as it expands and cools, and (3) spallation of nuclei in subsequent internal shocks. The fireballs are found to have a neutron excess and a marginally successful nucleosynthesis. They are composed of free nucleons, α-particles, and deuterium. A robust result is the survival of a significant neutron component, which has important implications. First, as shown in previous works, neutrons can lead to observable multi-GeV neutrino emission. Second, as we show in an accompanying paper, neutrons impact the explosion dynamics at radii up to 1017 cm and change the mechanism of the GRB afterglow emission.

Gravitational Bending of Light Near Compact Objects

A photon emitted near a compact object at an angle α with respect to the radial direction escapes to infinity at a different angle ψ > α. This bending of light is caused by a strong gravitational field. We show that, in a Schwarzschild metric, the effect is described by 1 - cos α = (1 - cos ψ)(1 - rg/R), where R/rg is the emission radius in Schwarzschild units. The formula is approximate, and it applies at R ≥ 2rg only; however, at these radii it has amazing accuracy, fully sufficient in many applications. As one application, we develop a new formulation for the light-bending effects in pulsars. It reveals the simple character of these effects and gives their quantitative description with practically no loss of accuracy (for the typical radius of a neutron star R = 3rg the error is 1%). The visible fraction of a star surface is shown to be Sv/4πR2 = [2(1 - rg/R)]-1, which is for R = 3rg. The instantaneous flux of a pulsar comes from one or two antipodal polar caps that rotate in the visible zone. The pulse produced by one blackbody cap is found to be sinusoidal (light bending impacts the pulse amplitude but not its shape). When both caps are visible, the pulse shows a plateau: the variable parts of the antipodal emissions precisely cancel each other. The pulsed fraction of blackbody emission with antipodal symmetry has an upper limit Amax = (R - 2rg)/(R + 2rg). Pulsars with A > Amax must be asymmetric.

Collisional mechanism for GRB emission

Nuclear and Coulomb collisions in gamma-ray burst (GRB) jets create a hot e ± plasma. This collisional heating starts when the jet is still opaque, and extends to the transparent region. The e ± plasma radiates its energy. As a result, a large fraction of the jet energy is converted to escaping radiation with a well-defined spectrum. The process is simulated in detail using the known rates of collisions and accurate calculations of radiative transfer in the expanding jet. The result reproduces the spectra of observed GRBs that typically peak near 1 MeV and extend to much higher energies with a photon index β ~ -2.5. This suggests that collisional heating may be the main mechanism for GRB emission.

NuSTAR DISCOVERY OF A 3.76 s TRANSIENT MAGNETAR NEAR SAGITTARIUS A

We report the discovery of 3.76 s pulsations from a new burst source near Sgr A^* observed by the NuSTAR observatory. The strong signal from SGR J1745–29 presents a complex pulse profile modulated with pulsed fraction 27% ± 3% in the 3-10 keV band. Two observations spaced nine days apart yield a spin-down rate of Ṗ =(6.5 ± 1.4) × 10^(–12). This implies a magnetic field B = 1.6 × 10^(14) G, spin-down power Ė =5 × 10^(33) erg s^(–1), and characteristic age P/2Ṗ =9 × 10^3 yr for the rotating dipole model. However, the current Ṗ may be erratic, especially during outburst. The flux and modulation remained steady during the observations and the 3-79 keV spectrum is well fitted by a combined blackbody plus power-law model with temperature kT_(BB) = 0.96 ± 0.02 keV and photon index Γ = 1.5 ± 0.4. The neutral hydrogen column density (N_H ~ 1.4 × 10^(23) cm^(–2)) measured by NuSTAR and Swift suggests that SGR J1745–29 is located at or near the Galactic center. The lack of an X-ray counterpart in the published Chandra survey catalog sets a quiescent 2-8 keV luminosity limit of L_x ≾ 10^(32) erg s^(–1). The bursting, timing, and spectral properties indicate a transient magnetar undergoing an outburst with 2-79 keV luminosity up to 3.5 × 10^(35) erg s^(–1) for a distance of 8 kpc. SGR J1745–29 joins a growing subclass of transient magnetars, indicating that many magnetars in quiescence remain undetected in the X-ray band or have been detected as high-B radio pulsars. The peculiar location of SGR J1745–29 has important implications for the formation and dynamics of neutron stars in the Galactic center region.

GAMMA-RAY BURSTS FROM MAGNETIZED COLLISIONALLY HEATED JETS

Jets producing gamma-ray bursts (GRBs) are likely to carry a neutron component that drifts with respect to the proton component. The neutron-proton collisions strongly heat the jet and generate electron-positron pairs. We investigate radiation produced by this heating using a new numerical code. Our results confirm the recent claim that collisional heating generates the observed Band-type spectrum of GRBs. We extend the model to study the effects of magnetic fields on the emitted spectrum. We find that the spectrum peak remains near 1?MeV for the entire range of the magnetization parameter 0 < ?B < 2 that is explored in our simulations. The low-energy part of the spectrum softens with increasing ?B, and a visible soft excess appears in the keV band. The high-energy part of the spectrum extends well above the GeV range and can contribute to the prompt emission observed by Fermi/LAT. Overall, the radiation spectrum created by the collisional mechanism appears to agree with observations, with no fine tuning of parameters.