Based on Chandra and ASCA observations of nearby starburst galaxies and RXTE/ASM, ASCA and MIR‐KVANT/TTM studies of high‐mass X‐ray binary (HMXB) populations in the Milky Way and Magellanic Clouds, we propose that the number and/or the collective X‐ray luminosity of HMXBs can be used to measure the star formation rate (SFR) of a galaxy. We show that, within the accuracy of the presently available data, a linear relation between HMXB number and star formation rate exists. The relation between SFR and collective luminosity of HMXBs is non‐linear in the low‐SFR regime, LX∝ SFR∼ 1.7, and becomes linear only for a sufficiently high star formation rate, SFR ≳ 4.5 M⊙ yr−1 (for M* > 8 M⊙). The non‐linear LX–SFR dependence in the low‐SFR limit is not related to non‐linear SFR‐dependent effects in the population of HMXB sources. It is rather caused by the fact that we measure the collective luminosity of a population of discrete sources, which might be dominated by the few brightest sources. Although more subtle SFR‐dependent effects are likely to exist, over the entire range of SFRs the data are broadly consistent with the existence of a universal luminosity function of HMXBs that can be roughly described as a power law with a differential slope of ∼1.6, a cut‐off at LX∼ few × 1040 erg s−1 and a normalization proportional to the star formation rate. We apply our results to (spatially unresolved) starburst galaxies observed by Chandra at redshifts up to z∼ 1.2 in the Hubble Deep Field North and show that the calibration of the collective luminosity of HMXBs as an SFR indicator based on the local sample agrees well with the SFR estimates obtained for these distant galaxies with conventional methods.

Abstract. We study the Log(N)-Log(S ) and X-ray luminosity function in the 2-10 keV energy band, and the spatial (3-D) distribution of bright, L X ≥ 10 34 −10 35 erg s −1 , X-ray binaries in the Milky Way. In agreement with theoretical expectations and earlier results we found significant differences between the spatial distributions of low (LMXB) and high (HMXB) mass X-ray binaries. The volume density of LMXB sources peaks strongly at the Galactic Bulge whereas HMXBs tend to avoid the inner ∼3−4 kpc of the Galaxy. In addition HMXBs are more concentrated towards the Galactic Plane (scale heights of ≈150 and ≈410 pc for HMXB and LMXB correspondingly) and show clear signatures of the spiral structure in their spatial distribution. The Log(N)-Log(S ) distributions and the X-ray luminosity functions are also noticeably different. LMXB sources have a flatter Log(N)-Log(S ) distribution and luminosity function. The integrated 2-10 keV luminosities of all X-ray binaries in the Galaxy, averaged over 1996-2000, are ∼2−3 × 10 39 (LMXB) and ∼2−3 × 10 38 (HMXB) erg s −1 . Normalised to the stellar mass and the star formation rate, respectively, these correspond to ∼5 × 10 28 erg s −1 M −1 for LMXBs and ∼5 × 10 37 erg s −1 /(M yr −1 ) for HMXBs. Due to the shallow slopes of the luminosity functions the integrated emission of X-ray binaries is dominated by the ∼5-10 most luminous sources which determine the appearance of the Milky Way in the standard X-ray band for an outside observer. In particular variability of individual sources or an outburst of a bright transient source can increase the integrated luminosity of the Milky Way by as much as a factor of ∼2. Although the average LMXB luminosity function shows a break near the Eddington luminosity for a 1.4 M neutron star, at least 12 sources showed episodes of super-Eddington luminosity during ASM observations. We provide the maps of distribution of X-ray binaries in the Milky Way in various projections, which can be compared to images of nearby galaxies taken by CHANDRA and XMM-Newton.

We compare the results of Grimm, Gilfanov & Sunyaev and Ranalli, Comastri & Seti on the L X -SFR (X-ray luminosity-star formation rate) relation in normal galaxies. Based on the L X -stellar mass dependence for low-mass X-ray binaries (LMXBs), we show that low-SFR ( 1 M yr −1 ) galaxies in the Ranalli et al. sample are contaminated by the X-ray emission from LMXBs, unrelated to the current star formation activity.However, the most important conclusion from our comparison is that, after the data are corrected for the 'LMXB contamination', the two data sets become consistent with each other, despite differences in their content, variability effects, adopted source distances, X-ray fluxes and SFR determinations, and also in the cosmological parameters used in interpreting the Hubble Deep Field North (HDF-N) data. They also agree well, both in the low-and high-SFR regimes, with the predicted L X -SFR dependence derived from the parameters of the 'universal' high-mass X-ray binary (HMXB) luminosity function. This encouraging result emphasizes the potential of the X-ray luminosity as an independent SFR indicator for normal galaxies.

We study the statistical properties of the combined emission of a population of discrete sources (for example, the X‐ray emission of a galaxy due to its population of X‐ray binaries). Namely, we consider the dependence of their total luminosity and of the fractional rmstot of their variability on the number of sources n or, equivalently, on the normalization of the luminosity function. We show that, as a result of small number statistics, a regime exists in which Ltot grows non‐linearly with n, in apparent contradiction with the seemingly obvious prediction . In this non‐linear regime, rmstot decreases with n significantly more slowly than expected from the averaging law. For example, for a power‐law luminosity function with a slope of α= 3/2, in the non‐linear regime, Ltot∝n2 and rmstot does not depend at all on the number of sources n. Only in the limit of n→∞ do these quantities behave as intuitively expected, Ltot∝n and . We give exact solutions and derive convenient analytical approximations for Ltot and rmstot. Using the total X‐ray luminosity of a galaxy due to its X‐ray binary population as an example, we show that the LX–star formation rate and LX–M* relations predicted from the respective ‘universal’ luminosity functions of high‐ and low‐mass X‐ray binaries are in good agreement with observations. Although caused by small number statistics, the non‐linear regime in these examples extends as far as SFR ≲ 4–5 M⊙ yr−1 and log(M*/M⊙) ≲ 10.0–10.5, respectively.

In this paper we present the source list for three Chandra observations of the Local Group galaxy M33. The observations are centered on the nucleus and on the star-forming region NGC 604. We detect a total of 261 sources in an area of $0.2 deg 2 down to a flux limit of 3 ; 10 À16 ergs s À1 cm À2 , which corresponds to a luminosity of $2 ; 10 34 ergs s À1 at a distance of 840 kpc. From the source list we construct the luminosity functions of sources observed in M33. If we take into account background contamination, the luminosity functions are consistent with those of other star-forming galaxies. In addition, the combination of X-ray color analysis and the existence of ''blue'' optical counterparts strongly indicates that the X-ray point-source population in M33 consists of young objects. Above 3 ; 10 35 ergs s À1 there are few X-ray sources in the locus of the X-ray hardness ratio diagram that is generally populated by low-mass X-ray binaries.