Low mass X-ray binaries as a stellar mass indicator for the host galaxy

Using results of Chandra observations of old stellar systems in eleven nearby galaxies of various morphological types and the census of LMXBs in the Milky Way, we study the population of low mass X-ray binaries and their relation to the mass of the host galaxy. We show that the azimuthally averaged spatial distribution of the number of LMXBs and, in the majority of cases, of their collective luminosity closely follows that of the near-infrared light. Considering galaxies as a whole, we find that in a broad mass range, log(M)~9-11.5, the total number of LMXBs and their combined luminosity are proportional to the stellar mass of the host galaxy. Within the accuracy of the light-to-mass conversion, we cannot rule out the possibility of a weak dependence of the X/M ratio on morphological type. However, the effect of such a dependence, if any, does not exceed a factor of ~1.5-2. The luminosity distributions of LMXBs observed in different galaxies are similar to each other and, with the possible exception of NGC1553, are consistent with the average luminosity function derived from all data. The average XLF of LMXBs in nearby galaxies has a complex shape and is significantly different from that of HMXBs. It follows a power law with a differential slope of ~1 at low luminosities, gradually steepens at log(Lx)>37.0-37.5 and has a rather abrupt cut-off at log(Lx)~39.0-39.5. This value of the cut-off luminosity is significantly, by an order of magnitude, lower than found for high mass X-ray binaries.Comment: Accepted for publication in MNRA

Boundary layer emission in luminous LMXBs

We show that aperiodic and quasiperiodic variability of bright LMXBs - atoll and Z- sources, on ~sec - msec time scales is caused primarily by variations of the boundary layer luminosity. The accretion disk emission is less variable on these time scales and its power density follows 1/f law, contributing to observed flux variation at low frequencies and low energies only. The kHz QPOs have the same origin as variability at lower frequencies - independent of the nature of the "clock", the actual luminosity modulation takes place on the NS surface. The boundary layer spectrum remains nearly constant during luminosity variations and can be represented by the Fourier frequency resolved spectrum. In the range of Mdot~(0.1-1)*Mdot_Edd it depends weakly on the global mass accretion rate and in the limit Mdot~Mdot_Edd is close to Wien spectrum with kT~2.4 keV. Its independence on the Mdot lends support to the suggestion by Inogamov & Sunyaev (1999) that the boundary layer is radiation pressure supported. Based on the knowledge of the boundary layer spectrum we attempt to relate the motion along the Z-track to changes of physically meaningful parameters. Our results suggest that the contribution of the boundary layer to the observed emission decreases along the Z-track from conventional ~50% on the horizontal branch to a rather small number on the normal branch. This decrease can be caused, for example, by obscuration of the boundary layer by the geometrically thickened accretion disk at Mdot~Mdot_Edd. Alternatively, this can indicate significant change of the structure of the accretion flow at Mdot~Mdot_Edd and disappearance of the boundary layer as a distinct region of the significant energy release associated with the NS surface.Comment: Astronomische Nachrichten, 326, No.9, p.812 (2005

Reflection and noise in the low spectral state of GX339-4

We analyze RXTE/PCA observations of GX339-4 in the low spectral state from 1996--1997 and show that the pattern of its spectral and temporal variability is nearly identical to that of Cyg X-1. In particular, a tight correlation exists between the QPO centroid frequency and the spectral parameters. An increase of the QPO centroid frequency is accompanied with an increase of the amplitude of the reflected component and a steepening the slope of the underlying power law. Fourier frequency resolved spectral analysis showed, that the variability of the reflected component at frequencies higher than ~1-10 Hz is suppressed in comparison with that of the primary emission.Comment: 4 pages, 4 figures. Accepted in Astronomy and Astrophysics Main Journa

Frequency resolved spectroscopy of Cyg X-1: fast variability of the reflected emission in the soft state

Using the RXTE/PCA data we study the fast variability of the reflected emission in the soft spectral state of Cyg X-1 by means of Fourier frequency resolved spectroscopy. We find that the rms amplitude of variations of the reflected emission has the same frequency dependence as the primary radiation down to time scales of <30-50 msec. This might indicate that the reflected flux reproduces, with nearly flat response, variations of the primary emission. Such behavior differs notably from the hard spectral state, in which variations of the reflected flux are significantly suppressed in comparison with the primary emission, on time scales shorter than ~0.5-1 sec. If related to the finite light crossing time of the reflector, these results suggest that the characteristic size of the reflector -- presumably an optically thick accretion disk, in the hard spectral state is larger by a factor of >5-10 than in the soft spectral state. Modeling the transfer function of the disk, we estimate the inner radius of the accretion disk R_in~100R_g in the hard and R_in<10R_g in the soft state for a 10M_sun black hole.Comment: submitted to MNRA

Soft state of Cygnus X-1: stable disk and unstable corona

Two component X-ray spectra (soft multicolor black body plus harder power law) are frequently observed from accreting black holes. These components are presumably associated with the different parts of the accretion flow (optically thick and optically thin respectively) in the vicinity of the compact source. Most of the aperiodic variability of the X-ray flux on the short time scales is associated with the harder component. We suggest that drastically different amplitudes of variability of these two components are simply related to the very different viscous time scales in the geometrically thin and geometrically thick parts of the accretion flow. In the geometrically thin disks variations of viscosity or mass accretion rate occurring at large radius from the black hole on the local dynamical or thermal time scales do not cause any significant variations of the mass accretion rate at smaller radii due to a very long diffusion time. Any variations on the time scales shorter than the diffusion time scale are effectively dampened. On the contrary such variations can easily survive in the geometrically thick flows and as a result the mass accretion rate in the innermost region of the flow will reflect modulations of the mass accretion rate added to the flow at any distance from the black hole. Therefore if primary instabilities operate on the short time scales then the stability of the soft component (originating from the geometrically thin and optically thick flow) and variability of the hard component (coming from the geometrically thick and optically thin flow) are naturally explained.Comment: 8 pages; accepted for publication in MNRAS; replaced with accepted versio

Statistical properties of the combined emission of a population of discrete sources: astrophysical implications

We study the statistical properties of the combined emission of a population of discrete sources (e.g. X-ray emission of a galaxy due to its X-ray binaries population). Namely, we consider the dependence of their total luminosity L_tot=SUM(L_k) and of fractional rms_tot of their variability on the number of sources N or, equivalently, on the normalization of the luminosity function. We show that due to small number statistics a regime exists, in which L_tot grows non-linearly with N, in an apparent contradiction with the seemingly obvious prediction =integral(dN/dL*L*dL) ~ N. In this non-linear regime, the rms_tot decreases with N significantly more slowly than expected from the rms ~ 1/sqrt(N) averaging law. For example, for a power law luminosity function with a slope of a=3/2, in the non-linear regime, L_tot ~ N^2 and the rms_tot does not depend at all on the number of sources N. Only in the limit of N>>1 do these quantities behave as intuitively expected, L_tot ~ N and rms_tot ~ 1/sqrt(N). We give exact solutions and derive convenient analytical approximations for L_tot and rms_tot. Using the total X-ray luminosity of a galaxy due to its X-ray binary population as an example, we show that the Lx-SFR and Lx-M* relations predicted from the respective ``universal'' luminosity functions of high and low mass X-ray binaries are in a good agreement with observations. Although caused by small number statistics the non-linear regime in these examples extends as far as SFR<4-5 Msun/yr and log(M*/Msun)<10.0-10.5, respectively.Comment: MNRAS, accepted for publicatio