Sudip Bhattacharyya

RELATIVISTIC LINES AND REFLECTION FROM THE INNER ACCRETION DISKS AROUND NEUTRON STARS

A number of neutron star low-mass X-ray binaries (LMXBs) have recently been discovered to show broad, asymmetric Fe K emission lines in their X-ray spectra. These lines are generally thought to be the most prominent part of a reflection spectrum, originating in the inner part of the accretion disk where strong relativistic effects can broaden emission lines. We present a comprehensive, systematic analysis of Suzaku and XMM-Newton spectra of 10 neutron star LMXBs, all of which display broad Fe K emission lines. Of the 10 sources, 4 are Z sources, 4 are atolls, and 2 are accreting millisecond X-ray pulsars (also atolls). The Fe K lines are fit well by a relativistic line model for a Schwarzschild metric, and imply a narrow range of inner disk radii (6-15 GM/c 2) in most cases. This implies that the accretion disk extends close to the neutron star surface over a range of luminosities. Continuum modeling shows that for the majority of observations, a blackbody component (plausibly associated with the boundary layer) dominates the X-ray emission from 8 to 20 keV. Thus it appears likely that this spectral component produces the majority of the ionizing flux that illuminates the accretion disk. Therefore, we also fit the spectra with a blurred reflection model, wherein a blackbody component illuminates the disk. This model fits well in most cases, supporting the idea that the boundary layer illuminates a geometrically thin disk.

Evidence of a Broad Relativistic Iron Line from the Neutron Star Low-Mass X-Ray Binary Serpens X-1

We report on an analysis of XMM-Newton data from the neutron star low-mass X-ray binary (LMXB) Serpens X-1 (Ser X-1). Spectral analysis of EPIC PN data indicates that the previously known broad iron Kα emission line from this source has a significantly skewed structure with a moderately extended red wing. The asymmetric shape of the line is well described with the laor and diskline models in XSPEC and strongly supports an inner accretion disk origin of the line. To our knowledge, this is the first strong evidence of a relativistic line in a neutron star LMXB. This finding suggests that the broad lines seen in other neutron star LMXBs likely originate from the inner disk as well. Detailed study of such lines opens up a new way to probe neutron star parameters and their strong gravitational fields. The red wing of the iron line from Ser X-1 is not as broad as that observed from some black hole systems. This is not unreasonable for a neutron star system, as the accretion disk has to terminate at or before the hard stellar surface. Finally, the inferred source inclination angle in the approximate range 40°-60° is consistent with the lack of dips and eclipses from Ser X-1.

Constraints on Neutron Star Parameters from Burst Oscillation Light Curves of the Accreting Millisecond Pulsar XTE J1814–338

Detailed modeling of the millisecond brightness oscillations during thermonuclear bursts from low-mass X-ray binaries can provide important information about neutron star structure. Until now, the implementation of this idea has not been entirely successful, largely because of the negligible harmonic content in burst oscillation light curves. However, the recent discovery of nonsinusoidal burst oscillation light curves from the accreting millisecond pulsar XTE J1814-338 has changed this situation. We therefore, for the first time, make use of this opportunity to constrain neutron star parameters. In our detailed study of the light curves of 22 bursts, we fit the burst oscillation light curves with fully general relativistic models that include light bending and frame dragging for light curve calculation and numerically compute the structure of neutron stars using realistic equations of state. We find that for our model and parameter grid values, at the 90% confidence level, Rc2/GM > 4.2 for the neutron star in XTE J1814-338. We also find that the photons from the thermonuclear flash come out through the layers of accreted matter under conditions consistent with Thomson scattering and show that the secondary companion is a hydrogen-burning main-sequence star with possible bloating (probably due to X-ray heating).

DETERMINING NEUTRON STAR MASSES AND RADII USING ENERGY-RESOLVED WAVEFORMS OF X-RAY BURST OSCILLATIONS

Simultaneous, precise measurements of the mass M and radius R of neutron stars can yield uniquely valuable information about the still uncertain properties of cold matter at several times the density of nuclear matter. One method that could be used to measure M and R is to analyze the energy-dependent waveforms of the X-ray flux oscillations seen during some thermonuclear bursts from some neutron stars. These oscillations are thought to be produced by X-ray emission from hotter regions on the surface of the star that are rotating at or near the spin frequency of the star. Here we explore how well M and R could be determined by generating and analyzing, using Bayesian techniques, synthetic energy-resolved X-ray data that we produce assuming a future space mission having 2-30 keV energy coverage and an effective area of 10 m2, such as the proposed Large Observatory for X-Ray Timing or Advanced X-Ray Timing Array missions. We find that waveforms from hot spots within 10° of the rotation equator usually constrain both M and R with an uncertainty of about 10%, if there are 106 total counts from the spot, whereas waveforms from spots within 20° of the rotation pole provide no useful constraints. The constraints we report can usually be achieved even if the burst oscillations vary with time and data from multiple bursts must be used to obtain 106 counts from the hot spot. This is therefore a promising method to constrain M and R tightly enough to discriminate strongly between competing models of cold, high-density matter.

Measurement of neutron star parameters: a review of methods for low-mass X-ray binaries

Measurement of at least three independent parameters, for example, mass, radius and spin frequency, of a neutron star is probably the only way to understand the nature of its supranuclear core matter. Such a measurement is extremely difficult because of various systematic uncertainties. The lack of knowledge of several system parameter values gives rise to such systematics. Low mass X-ray binaries, which contain neutron stars, provide a number of methods to constrain the stellar parameters. Joint application of these methods has a great potential to significantly reduce the systematic uncertainties, and hence to measure three independent neutron star parameters accurately. Here, we review the methods based on: (1) thermonuclear X-ray bursts; (2) accretion-powered millisecond-period pulsations; (3) kilohertz quasi-periodic oscillations; (4) broad relativistic iron lines; (5) quiescent emissions; and (6) binary orbital motions.

Temperature Profiles of Accretion Disks around Rapidly Rotating Neutron Stars in General Relativity and the Implications for Cygnus X-2

We calculate the temperature profiles of (thin) accretion disks around rapidly rotating neutron stars (with low surface magnetic fields), taking into account the full effects of general relativity. We then consider a model for the spectrum of the X-ray emission from the disk that is parameterized by the mass accretion rate, the color temperature, and the rotation rate of the neutron star. We derive constraints on these parameters for the X-ray source Cygnus X-2 using the estimates of the maximum temperature in the disk along with the disk and boundary layer luminosities, using the spectrum inferred from the EXOSAT data. Our calculations suggest that the neutron star in Cygnus X-2 rotates close to the centrifugal mass-shed limit. Possible constraints on the neutron star equation of state are also discussed.

THE SHAPES OF ATOMIC LINES FROM THE SURFACES OF WEAKLY MAGNETIC ROTATING NEUTRON STARS AND THEIR IMPLICATIONS

Motivated by the report by Cottam et al. of iron resonance scattering lines in the spectra of thermonuclear bursts from EXO 0748-676, we have investigated the information about neutron star structure and the geometry of the emission region that can be obtained by analyzing the profiles of atomic lines formed at the surface of the star. We have calculated the detailed profiles of such lines, taking into account the stars spin and the full effects of special and general relativity, including light bending and frame dragging. We discuss the line shapes produced by rotational Doppler broadening and magnetic splitting of atomic lines for the spin rates and magnetic fields expected in neutron stars in low-mass X-ray binary systems. We show that narrow lines are possible even for rapidly spinning stars if the emission region or the line of sight are close to the spin axis. For most neutron stars in low-mass systems, magnetic splitting is too small to obscure the effects of special and general relativity. We show that the ratio of the stars mass to its equatorial radius can be determined to within 5% using atomic line profiles, even if the lines are broad and skewed. This is the precision required to constrain strongly the equation of state of neutron star matter. We show further that if the radius and latitude of emission are known to ~5%-10% accuracy, then frame dragging has a potentially detectable effect on the profiles of atomic lines formed at the stellar surface.

A Non-PRE Double-peaked Burst from 4U 1636–536: Evidence of Burning Front Propagation

We analyze Rossi X-Ray Timing Explorer (RXTE) Proportional Counter Array (PCA) data of a double-peaked burst from the low-mass X-ray binary (LMXB) 4U 1636-536 that shows no evidence of photospheric radius expansion (PRE). We find that the X-ray-emitting area on the star increases with time as the burst progresses, even though the photosphere does not expand. We argue that this is a strong indication of thermonuclear flame spreading on the stellar surface during such bursts. We propose a model for such double-peaked bursts, based on thermonuclear flame spreading, that can qualitatively explain their essential features as well as the rarity of these bursts.

General Relativistic Spectra of Accretion Disks around Rotating Neutron Stars

General relativistic spectra from accretion disks around rotating neutron stars in the appropriate spacetime geometry for several different equations of state, spin rates, and masses of the compact object have been computed. The analysis involves the computation of the relativistically corrected radial temperature profiles and the effect of Doppler and gravitational redshifts on the spectra. Light-bending effects have been omitted for simplicity. The relativistic spectrum is compared with the Newtonian one, and it is shown that the difference between the two is primarily a result of the different radial temperature profiles for the relativistic and Newtonian disk solutions. To facilitate direct comparison with observations, a simple empirical function has been presented which describes the numerically computed relativistic spectra well. This empirical function (which has three parameters including normalization) also describes the Newtonian spectrum adequately. Thus, the function can in principle be used to distinguish between the two. In particular, the best-fit value of one of the parameters

Temperature profiles of accretion discs around rapidly rotating strange stars in general relativity: A comparison with neutron stars

(\beta-parameter)