Polarization properties of X-ray millisecond pulsars

Radiation of X-ray bursts and of accretion shocks in weakly magnetized neutron stars in low-mass X-ray binaries is produced in plane-parallel atmospheres dominated by electron scattering. We first discuss polarization produced by single (non-magnetic) Compton scattering, in particular the depolarizing effect of high electron temperature, and then the polarization due to multiply electron scattering in a slab. We further predict the X-ray pulse profiles and polarization properties of nuclear- and accretion-powered millisecond pulsars. We introduce a relativistic rotation vector model, which includes the effect of rotation of polarization plane due to the rapid motion of the hot spot as well as the light bending. Future observations of the X-ray polarization will provide a valuable tool to test the geometry of the emission region in pulsars and its physical characteristics.Comment: 8 pages, 6 figures, to appear in "X-ray Polarimetry: A New Window in Astrophysics", edited by R. Bellazzini, E. Costa, G. Matt and G. Tagliaferri (Cambridge University Press

Time Lags in Compact Objects: Constraints on the Emission Models

Accreting black holes and neutron stars in their hard (low) state show not only very similar X/gamma-ray spectra but also that the behaviour of their light curves is quite similar which can be quantified as having similar power-density spectra and Fourier-frequency-dependent time/phase lags. Taken together this argues for a common mechanism of the X/gamma-ray production in these objects. This mechanism is probably a property of the accretion flow only since it does not depend on the nature of the compact object. In this paper, I review the observational data paying most attention to the properties of the temporal variability such as the time/phase lags that hopefully can help us to discriminate between different theoretical models. I also discuss the models developed to account for the basic observational facts. Particularly, I show that the commonly used Compton cloud models with constant temperature cannot explain variable sources without violating the energy conservation law. Alternative models where time lags are related to the spectral evolution during X-ray flares are discussed and compared with observations. Compton reflection from the outer edge of the accretion disc is shown to markedly affect the time lag Fourier spectrum.Comment: 16 pages; invited talk at the meeting "X-ray Astronomy 1999: Stellar Endpoints, AGN and the Diffuse Background", held in Bologna, Italy, September 199

On the Nature of the X-ray Emission from the Accreting Millisecond Pulsar SAX J1808.4-3658

The pulse profiles of the accreting X-ray millisecond pulsar SAX J1808.4-3658 at different energies are studied. The two main emission component, the black body and the Comptonized tail that are clearly identified in the time-averaged spectrum, show strong variability with the first component lagging the second one. The observed variability can be explained if the emission is produced by Comptonization in a hot slab (radiative shock) of Thomson optical depth ~0.3-1 at the neutron star surface. The emission patterns of the black body and the Comptonized radiation are different: a "knife"- and a "fan"-like, respectively. We construct a detailed model of the X-ray production accounting for the Doppler boosting, relativistic aberration and gravitational light bending in the Schwarzschild spacetime. We present also accurate analytical formulae for computations of the light curves from rapidly rotating neutron stars using formalism recently developed by Beloborodov (2002). Our model reproduces well the pulse profiles at different energies simultaneously, corresponding phase lags, as well as the time-averaged spectrum. We constrain the compact star mass to be bounded between 1.2 and 1.6 solar masses. By fitting the observed profiles, we determine the radius of the compact object to be R~11 km if M=1.6 M_sun, while for M=1.2 M_sun the best-fitting radius is ~6.5 km, indicating that the compact object in SAX J1808.4-3658 can be a strange star. We obtain a lower limit on the inclination of the system of 65 degrees.Comment: 11 pages, 7 figures, submitted to MNRA

Spectra of the spreading layers on the neutron star surface and constraints on the neutron star equation of state

Spectra of the spreading layers on the neutron star surface are calculated on the basis of the Inogamov-Sunyaev model taking into account general relativity correction to the surface gravity and considering various chemical composition of the accreting matter. Local (at a given latitude) spectra are similar to the X-ray burst spectra and are described by a diluted black body. Total spreading layer spectra are integrated accounting for the light bending, gravitational redshift, and the relativistic Doppler effect and aberration. They depend slightly on the inclination angle and on the luminosity. These spectra also can be fitted by a diluted black body with the color temperature depending mainly on a neutron star compactness. Owing to the fact that the flux from the spreading layer is close to the critical Eddington, we can put constraints on a neutron star radius without the need to know precisely the emitting region area or the distance to the source. The boundary layer spectra observed in the luminous low-mass X-ray binaries, and described by a black body of color temperature Tc=2.4+-0.1 keV, restrict the neutron star radii to R=14.8+- 1.5 km (for a 1.4-Msun star and solar composition of the accreting matter), which corresponds to the hard equation of state.Comment: 13 pages, 13 figures, MNRAS, in pres

Gamma-ray burst spectra from continuously accelerated electrons

We discuss here constraints on the particle acceleration models from the observed gamma-ray bursts spectra. The standard synchrotron shock model assumes that some fraction of available energy is given instantaneously to the electrons which are injected at high Lorentz factor. The emitted spectrum in that case corresponds to the spectrum of cooling electrons, F_\nu ~ \nu^{-1/2}, is much too soft to account for the majority of the observed spectral slopes. We show that continuous heating of electrons over the life-time of a source is needed to produce hard observed spectra. In this model, a prominent peak develops in the electron distribution at energy which is a strong function of Thomson optical depth \tau_T of heated electrons (pairs). At \tau_T>1, a typical electron Lorentz factor \gamma ~ 1-2 and quasi-thermal Comptonization operates. It produces spectrum peaking at a too high energy. Optical depths below 10^{-4} would be difficult to imagine in any physical scenario. At \tau_T =10^{-4}-10^{-2}, \gamma ~ 30-100 and synchrotron self-Compton radiation is the main emission mechanism. The synchrotron peak should be observed at 10--100 eV, while the self-absorbed low-energy tail with F_\nu ~ \nu^2 can produce the prompt optical emission (like in the case of GRB 990123). The first Compton scattering radiation by nearly monoenergetic electrons peaks in the BATSE energy band and can be as hard as F_\nu ~ \nu^1 reproducing the hardness of most of the observed GRB spectra. The second Compton peak should be observed in the high-energy gamma-ray band, possibly being responsible for the 10-100 MeV emission detected in GRB 941017. A significant electron-positron pair production reduces the available energy per particle, moving spectral peaks to lower energies as the burst progresses.Comment: 4 pages, 1 figure, Il nuovo cimento C, in press. Proceedings of the 4th Workshop Gamma-Ray Bursts in the Afterglow Era, Rome, 18-22 October 200