General Relativistic Spectra of Accretion Disks around Rotating Neutron Stars

Abstract

A B S T R A C T We present computed spectra, as seen by a distant observer, from the accretion disc around a rapidly rotating neutron star. Our calculations are carried out in a fully general relativistic framework, with an exact treatment of rotation. We take into account the Doppler shift, gravitational redshift and light-bending effects in order to compute the observed spectrum. We find that light bending significantly modifies the high-energy part of the spectrum. Computed spectra for slowly rotating neutron stars are also presented. These results would be important for modelling the observed X-ray spectra of low-mass X-ray binaries containing fast-spinning neutron stars. The central accretors in a large number of low-mass X-ray binaries (LMXBs) are believed to be neutron stars, rotating rapidly due to accretion-induced angular momentum transfer. LMXBs are thought to be the progenitors of millisecond (ms) radio pulsars (Bhattacharya & van den Heuvel 1991) like PSR 1937121 with P , 1:56 ms (Backer et al. 1982). The recent discovery of millisecond ðP , 2:49 msÞ X-ray pulsations in XTE J18082369 (Wijnands & van der Klis 1998) has strengthened this hypothesis. Kilohertz quasi-periodic oscillations (kHz QPOs) seen in a number of LMXBs are another indicator of the rapid rotation of the accreting neutron star. For example, in beat-frequency models of kHz QPOs, the difference (,300–500 HzÞ in the frequencies of two simultaneously observed kHz QPO peaks is interpreted as the rotational frequency of the neutron star (e.g. van der Klis 2000). Fast rotation makes the neutron star considerably oblate and also modifies both the interior and the exterior space – time geometry. These, in turn, modify the size and the temperature profile of the accretion disc and hence the corresponding spectrum (Bhatta-charyya et al. 2000; Bhattacharyya, Misra & Thampan 2001). General relativity also plays an important role in shaping the spectrum. As neutron stars are very compact objects, the effect of general relativity is very significant, particularly near the surface of the star. For luminous LMXBs, the observed X-ray spectrum can be well fitted by the sum of a multicolour blackbody spectrum (presumably from the accretion disc) and a single-temperature blackbody spectrum (presumably from the boundary layer) (see Mitsuda et al. 1984). The multicolour spectrum can be calculated if the temperature profile in the accretion disc is known. Recently Bhattacharyya et al. (2000) have calculated the disc temperature profile as a function of the spin rate (V) and the mass (M) of the neutron star for different equations of state (EOS), including the effects of rotation and general relativity. In this paper, we calculate the observed spectrum from the accretion disc, using the temperature profiles. While doing so, we take into account the effects of gravitational redshift, Doppler broadening and the light-bending effect in the gravitational field of the accreting star. For non-rotating neutron stars, an attempt has been made by Ebisawa, Mitsuda & Hanawa (1991) to compute the disc spectrum including the effects mentioned above. Sun & Malkan (1989) included relativistic effects of disc inclination, including Doppler boosting, gravitational focusing, and gravitational redshift, on the observed disc spectra for both Kerr and Schwarzschild black holes (in the context of supermassive black holes). They find (as we also do) that the higher energy part of the spectrum gets significantly modified due to the general relativisitic effects. A computation similar to that of Ebisawa et al. (1991), for Galactic black hole candidates, has been done by Asaoka (1989) using the Kerr metric. However, our work incorporating both the full general relativistic effects of rapid rotation, and the realistic EOS describing interiors of neutron stars, using an appropriate metric, is the first calculation for rotating neutron stars. In the present work we ignore the effects of the stellar magnetic field, so our results are applicable to weakly magnetized neutron stars. The structure of the paper is as follows. In Section 2, we describe