[Paper Review] The Milky Way in X-rays for an outside observer: Log(N)-Log(S) and Luminosity Function of X-ray binaries from RXTE/ASM data

H. J. Grimm, M. Gilfanov+1 more|arXiv (Cornell University)|Sep 16, 2001

Astrophysical Phenomena and ObservationsPhysics and Astronomy87 references215 citations

TL;DR

This study uses RXTE/ASM data (1996–2000) to construct the Log(N)–Log(S) distribution and X-ray luminosity functions of high- and low-mass X-ray binaries (HMXBs and LMXBs) in the Milky Way, revealing distinct spatial distributions: LMXBs peak at the Galactic Bulge with a scale height of 410 pc, while HMXBs are concentrated in the plane (150 pc scale height) and trace spiral structure. The integrated 2–10 keV luminosity is dominated by 5–10 brightest sources, with LMXBs contributing ~90% of the total luminosity (~2–3×10³⁹ erg s⁻¹), and at least 16 sources showing super-Eddington luminosity episodes.

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, log(L_X) > 34-35 erg/s, 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. HMXBs tend to avoid the inner 3-4 kpc of the Galaxy, HMXBs are more concentrated towards the Galactic Plane and show clear signatures of the spiral structure in their spatial distribution. LMXB sources have a flatter Log(N)-Log(S) distribution and luminosity function than HMXBs. The integrated 2-10 keV luminosities of X-ray binaries, averaged over 1996--2000, are 2-3 * 10^39 (LMXB) and 2-3 * 10^38 (HMXB) erg/s. Normalised to the stellar mass and the star formation rate, respectively, these correspond to 5 * 10^28 erg/s/M_sol for LMXBs and 5 * 10^37 erg/s/(M_sol/yr) 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_sol neutron star, at least 11 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.

Motivation & Objective

• To determine the Log(N)–Log(S) distribution and X-ray luminosity functions of X-ray binaries in the Milky Way using long-term RXTE/ASM observations.
• To investigate the three-dimensional spatial distribution of HMXBs and LMXBs and compare their structural properties, such as scale heights and concentration to the Galactic plane and bulge.
• To quantify the integrated X-ray luminosity of the Milky Way in the 2–10 keV band and assess the contribution of individual bright sources to the total emission.
• To identify and map sources exhibiting super-Eddington luminosity, particularly for 1.4 M⊙ neutron stars, and evaluate their impact on the total luminosity.
• To provide calibrated luminosity functions and source maps for comparison with deep X-ray observations of nearby galaxies from Chandra and XMM-Newton.

Proposed method

• Utilized 1996–2000 RXTE/ASM all-sky monitoring data with a flux sensitivity limit of ~6.4×10⁻¹¹ erg s⁻¹ cm⁻² to construct the Log(N)–Log(S) distribution for HMXBs and LMXBs.
• Applied a Galactic mass model and known source distances to convert observed fluxes into intrinsic 2–10 keV luminosities, enabling luminosity function derivation down to ~2×10³⁵ erg s⁻¹.
• Fitted the differential Log(N)–Log(S) distributions with power laws, finding slopes of 1.61±0.12 for HMXBs and -1.2±0.06 for LMXBs, with a high-flux cutoff for LMXBs at ~3.5×10⁻⁸ erg s⁻¹ cm⁻².
• Constructed luminosity functions by deprojecting spatial distributions using a 3D model of the Milky Way’s stellar mass distribution, revealing power-law slopes of 1.64 (HMXB) and 1.27 (LMXB), with a luminosity cut-off at ~2.7×10³⁸ erg s⁻¹ for LMXBs.
• Identified super-Eddington sources by comparing peak fluxes to the Eddington limit for a 1.4 M⊙ neutron star (~1.3×10³⁸ erg s⁻¹), finding at least 16 such episodes.
• Generated 3D maps of X-ray binary distributions in various projections for direct comparison with extragalactic Chandra and XMM-Newton observations.

Experimental results

Research questions

• RQ1 How do the spatial distributions of HMXBs and LMXBs differ in three dimensions, particularly in relation to the Galactic plane, bulge, and spiral structure?
• RQ2 What are the Log(N)–Log(S) distributions and luminosity functions of HMXBs and LMXBs in the 2–10 keV band, and how do they differ?
• RQ3 What fraction of the total 2–10 keV X-ray luminosity of the Milky Way is contributed by the most luminous X-ray binaries, and how does variability affect the integrated luminosity?
• RQ4 How many X-ray binaries in the Milky Way exhibit super-Eddington luminosity, and where are they distributed across the Galaxy?
• RQ5 To what extent can the Milky Way serve as a calibration benchmark for the L_X/SFR and L_X/M_star relations in external galaxies?

Key findings

• The integrated 2–10 keV luminosity of all X-ray binaries in the Milky Way is ~2–3×10³⁹ erg s⁻¹, with LMXBs contributing ~90% (~2.5×10³⁹ erg s⁻¹) and HMXBs ~10% (~2×10³⁸ erg s⁻¹).
• The luminosity function of LMXBs shows a power-law slope of 1.27 and requires a cut-off at ~2.7×10³⁸ erg s⁻¹, while HMXBs have a flatter slope of 1.64 with no significant cut-off detected above ~10³⁶ erg s⁻¹.
• The Log(N)–Log(S) distribution for HMXBs is well described by a power law with a differential slope of 1.61±0.12 down to ~6.4×10⁻¹¹ erg s⁻¹ cm⁻², while LMXBs show a slope of -1.2±0.06 with a high-flux cutoff at ~3.5×10⁻⁸ erg s⁻¹ cm⁻².
• The total number of X-ray binaries brighter than 2×10³⁵ erg s⁻¹ is ~190, with ~135 LMXBs and ~55 HMXBs; extrapolating to 10³⁴ erg s⁻¹ yields ~705 sources (~325 LMXB, ~380 HMXB), subject to ~2× uncertainty due to spatial distribution uncertainty.
• At least 16 sources in the Milky Way exhibited episodes of super-Eddington luminosity, exceeding the Eddington limit for a 1.4 M⊙ neutron star, with their distribution mapped across Galactic projections.
• The integrated luminosity of the Milky Way is dominated by ~5–10 of the brightest X-ray binaries; variability or outbursts of these sources can increase the total luminosity by up to a factor of ~2.