ARlogo Annu. Rev. Astron. Astrophys. 2006. 44: 323-366
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The association of luminous X-ray sources (HMXBs, and the less luminous SNRs) with the young stellar population has been known since the dawn of X-ray astronomy (see Giacconi 1974). The presence of X-ray source populations in Local Group and nearby spiral and irregular galaxies was clearly demonstrated by the early Einstein observations (see the 1989 review, Fabbiano 1989; and the Einstein Catalog and Atlas of Galaxies, Fabbiano, Kim & Trinchieri 1992). Luminous HMXBs are expected to dominate the emission of star-forming galaxies (Helfand & Moran 2001). These sources, resulting from the evolution of a massive binary system where the more massive star has undergone a supernova event, are short-lived (~ 106-7 years) and constitute a marker of recent star formation: their number is likely to be related to the galaxy star-formation rate (SFR). This X-ray population-SFR connection was first suggested as a result of the analysis of the sample of normal galaxies observed with Einstein, where a strong correlation was found between global X-ray and FIR emission of late-type star-forming galaxies (Fabbiano & Trinchieri 1985; Fabbiano, Gioia & Trinchieri 1988; David, Forman & Jones 1991; Shapley, Fabbiano & Eskridge 2001; Fabbiano & Shapley 2002), and has been confirmed by analyses of ROSAT observations (Read & Ponman 2001; Lou & Bian 2005).

Though HMXBs are likely to dominate the X-ray emission of galaxies where star formation is most violent, they are also expected to be found in more normal spirals (see the Milky Way population; Section 2), albeit in smaller numbers and mixed with more aged X-ray populations. In bulge-dominated spirals, HMXBs may constitute only a small fraction of the X-ray-emitting population; for example, witness the strong correlation between X-ray and H-band luminosity found in these systems (Shapley, Fabbiano & Eskridge 2001; Fabbiano & Shapley 2002). The study of HMXB populations is then less straightforward than that of LMXBs, because in many cases HMXBs must be culled from the complex X-ray source populations of spiral galaxies.

Below, I first discuss the detection and characterization of populations of X-ray sources in spiral and irregular galaxies with X-ray imaging and photometry (Section 4.1), and then review the work on the XLFs of these star-forming populations (Section 4.2).

4.1. X-Ray Source Populations of Spiral and Irregular Galaxies

Reflecting the complex stellar populations of these galaxies, Chandra and XMM- Newton observations are discovering complex X-ray source populations. Typically, in each observed galaxy, from a few tens to well over hundreds of sources have been detected. Time variability and spectral analysis have been carried out for the most luminous sources, confirming that these sources are accreting binaries; the results are reminiscent of the spectral and temporal-spectral behavior of Galactic XRBs, including soft and hard spectral states [e.g., M31 (NGC 224) - Trudolyubov, Borodzin & Priedhorsky 2001; Trudolyubov et al. 2002a; Kaaret 2002; Kong et al. 2002; Williams et al. 2004; Trudolyubov & Priedhorsky 2004; Pietsch, Freyberg & Haberl 2005; M33 (NGC 598) - Grimm et al. 2005; Pietsch et al. 2004; NGC 1068 - Smith & Wilson 2003; NGC 1637 - Immler et al. 2003; NGC 2403 - Schlegel & Pannuti 2003; M81 (NGC 3031) - Swartz et al. 2003; M108 (NGC 3556) - Wang, Chavez & Irwin 2003; NGC 4449 - Miyawaki et al. 2004; M104 (NGC 4594; Sombrero) - Di Stefano et al. 2003; M51 (NGC 5194/95) - Terashima & Wilson 2004; M83 (NGC 5236) - Soria & Wu 2002; M101 (NGC 5457) - Pence et al. 2001; Jenkins et al. 2004, 2005].

Most detected sources, however, are too faint for detailed analysis; their position relative to the optical image of the galaxy (e.g., bulge, arms, disk, GCs), their X-ray colors, and in some cases optical counterparts have been used to aid in classification. Typically, as demonstrated by Prestwich et al. (2003) who applied this method to five galaxies (Figure 7), color-color diagrams c an discriminate between harder XRB candidates (with relatively harder neutron star HMXBs and softer LMXBs; rare black-hole HMXBs would also belong to this "softer" locus), softer SNR candidates, and very soft sources (SSSs, with emission below 1 keV).

Figure 7

Figure 7. Chandra color-color diagram (figure 4 of Prestwich et al. 2003). Energy bands chosen for this diagram are S = 0.3-1 KeV, M = 1-2 KeV, and H = 2-8 KeV. Soft color = (M-S) / (S + M + H), hard color = (H-M) / (S + M + H).

Similarly, XRBs, SNRs, and SSSs are found with XMM-Newton X-ray colors in IC 342, where most sources are near or on the spiral arms, associating them with the young stellar population (Kong 2003). In M33, the Local Group Scd galaxy with a predominantly young stellar population, Chandra and XMM-Newton colors, luminosities, and optical counterparts indicate a prevalence of (more luminous) HMXBs and a population of (fainter) SNRs (Pietsch et al. 2004; Grimm et al. 2005). In M83 (Figure 2, left), the X-ray source population can be divided into three groups, based on their spatial, color, and luminosity distributions (Soria & Wu 2003): fainter SSSs, soft sources (with no detected emission above 2 keV), and more luminous and harder XRBs. The positions of the soft sources are strongly correlated with current star-formation regions, as indicated by Halpha emission in the spiral arms and the starburst nucleus, strongly suggesting that they may be SNRs.

Chandra X-ray colors (or hardness ratios) were also used to study the X-ray source populations of M100 (NGC 4321; Kaaret 2001), M101 (Jenkins et al. 2005), NGC 1637 (Immler et al. 2003), NGC 4449 (Summers et al. 2004), NGC 5494 (the Sombrero galaxy, a Sa, with a predominantly older stellar population; Di Stefano et al. 2003), and the star-forming merging pair NGC 4038/9, the Antennae galaxy (Fabbiano, Zezas & Murray 2001; Fabbiano et al. 2004a), where spectral and flux variability is revealed by color-color and color-luminosity diagrams (Fabbiano et al. 2003a, b; Zezas et al. 2002a, b, 2005). Colbert et al. (2004) employ Chandra color diagrams to classify the X-ray source populations in their survey of 32 nearby galaxies of all morphological types, suggesting that hard accreting X-ray pulsars do not dominate the X-ray populations and favoring softer black-hole binaries.

These spectral, photometric and time-variability studies all point to the prevalence of XRB emission at the higher luminosities in the source population, in agreement with what is known from the X-ray observations of the Milky Way and Local Group galaxies (e.g., Helfand & Moran 2001). Comparison of accurate Chandra source positions with the stellar field in three nearby starburst galaxies shows that some of these sources experience formation kicks, displacing them from their parent star cluster (Kaaret et al. 2004), as observed in the Milky Way. The X-ray luminosity functions, which are discussed below, can then be considered as reflecting the XRB contribution (LMXBs, and HMXBs), with relatively little contribution from the SNRs. This point is confirmed by the direct comparison of HMXB and SNR luminosity functions in M33 (Grimm et al. 2005).

4.2. X-Ray Luminosity Functions - the X-Ray Luminosity Function of the Star-Forming Population

The XLF of LMXB populations (at high luminosity, at least) is well defined by the study of early-type galaxies, which have fairly uniform old stellar populations, and where little if any contamination from a young X-ray source population is expected (Section 3.3). The XLFs of late-type galaxies (spirals and irregulars) are instead the sum of the contributions of different X-ray populations, of different age and metallicity. This complexity was clearly demonstrated by the first detailed studies of nearby galaxies, including a comparison of different stellar fields of M31, with XMM-Newton and Chandra, yielding different XLFs (e.g., Trudolyubov et al. 2002b, Williams et al. 2004, Kong et al. 2003), and the Chandra observations of M81. In this Sab galaxy, the XLF derived from disk sources is flatter than that of the bulge (Tennant et al. 2001; shown in Figure 8, left). In the disk itself, the XLF becomes steeper with increasing distance from the spiral arms. In the arms the XLF is a pure power law with cumulative slope -0.48 ± 0.03 (Swartz et al. 2003), pointing to a larger presence of high luminosity sources in the younger stellar population.

Figure 8

Figure 8. Left: Bulge and disk X-ray luminosity functions (XLFs) of M81 (figure 3 of Tennant et al. 2001). Right: XLF slope versus infrared luminosity for seven galaxies (figure 2 of Kilgard et al. 2002). Younger stellar populations have flatter XLFs.

To derive the XLF of HMXB populations, to a first approximation, one mus t either evaluate the different contributions of older and younger source populations to the XLFs of spiral galaxies, as discussed above in the case of M81, or study galaxies where the star-formation activity is so intense as to produce a predominantly young X-ray source population. Both approaches suggest that the HMXB XLF is overall flatter than that of the LMXBs, with a cumulative power-law slope of -0.6 to -0.4 (to be compared with a cumulative slope of leq -1 for LMXBs, e.g., Kim & Fabbiano 2004); in other words, young HMXB populations contain on average a larger fraction of very luminous sources than the old LMXB populations (see the comparisons of Eracleous et al. 2002; Kilgard et al. 2002; Zezas & Fabbiano 2002; Colbert et al. 2004). These comparisons also show that flatter XLF slopes of about -0.4 to -0.5 (cumulative) are found in intensely star-forming galaxies, such as the merging pair NGC 4838/9 (the Antennae galaxies) and M82 (Zezas & Fabbiano 2002; Kilgard et al. 2002). In particular, Kilgard et al. (2002) find a correlation of the power-law slope with the 60-µm luminosity of the galaxy (shown in Figure 8, right), which suggests that such a flat power law may describe the XLF of the very young HMXB population. A comparison of the XLFs of dwarf starburst galaxies with those of spirals (Hartwell et al. 2004) is consistent with the above picture; cumulative XLF slopes for spirals are -1.0 to -1.4, whereas slopes for starbursts are lower, -0.4 to -0.8. The connection of the slope with the SFR is demonstrated by comparisons with the 60/100-µm ratio, 60-µm luminosity, and FIR/B ratio.

Grimm, Gilfanov & Sunyaev (2003) took these considerations a significant step further by comparing the XLFs of 10 star-forming galaxies (taken from the literature), observed with Chandra and XMM-Newton, with the HMXB luminosity functions of the Small Magellanic Cloud and the Milky Way. They suggest that there is a universal XLF of star-forming populations, stretching over four decades in luminosity (~ 4 × 1036-1040 erg s-1), with a simple power law with cumulative slope -0.6. They reach this conclusion by considering that the XLFs of star-forming galaxies are dominated by young and luminous short-lived HMXBs, whose number would be proportional to the SFR per unit stellar mass; when normalized relative to SFR, the XLFs these authors consider in their study collapse into a single -0.6 power law. Postnov (2003) suggests that this empirically observed slope might result from the mass-luminosity and mass-radius relations in wind-accreting high mass binaries. The possibility of a "universal" HMXB XLF is an interesting result, although there are clear variations in the individual luminosity functions used by Grimm, Gilfanov & Sunyaev (2003), with slopes ranging from ~ -0.4 (the Antennae; Zezas & Fabbiano 2002, where the data were corrected for incompleteness at the low luminosities) to -0.8 (M74-NGC 628; Soria & Kong 2002).

A number of XLFs of spiral galaxies have cumulative slopes close to the -0.6 slope of Grimm, Gilfanov & Sunyaev (2003) (IC 342 - Kong 2003; Bauer, Brandt & Lehmer 2003; NGC 5253 - Summers et al. 2004; NGC 4449 - Summers et al. 2003; NGC 2403 - Schlegel & Pannuti 2003; NGC 6946 - ; NGC 1068 - Smith & Wilson 2003; NGC 2146 - Inui et al. 2005). However, different and more complex XLFs are also observed, pointing to complexity or evolution of the X-ray source populations. In NGC 1637 (Immler et al. 2003), the cumulative XLF is reported to follow a power law of slope -1 for the entire luminosity range covered (~ 6 × 1036 - 1039 erg s-1); though a possible break of the XLF (LX > 1 × 1037 erg s-1) is reported, there is no discussion of completeness correction. In NGC 2403 (Schlegel & Pannuti 2003), the XLF has cumulative slope -0.6, but this galaxy does not follow the XLF slope; FIR correlation of Kilgard et al. (2002) suggesting it may have stopped forming stars, and we may be observing it after the massive stellar population has evolved, but the HMXBs are still emitting. In NGC 6946 (Holt et al. 2003), though the cumulative XLF slope is generally consistent with the Grimm, Gilfanov & Sunyaev (2003) conclusions, differences are seen comparing the XLF of the sources in the spiral arms (slope -0.64) with that of sources within two arcminutes of the starburst central region, which is flatter (-0.5). The XLF of NGC 5194 (M51, Terashima & Wilson 2004) follows an unbroken power law with slope -0.9.

In a detailed Chandra study of M83, a grand design spiral with a nuclear starburst, Soria & Wu (2003) find that the XLFs of different groups of sources identified by their X-ray colors differ. SSSs (see Section 5), which are found in regions with little or no Halpha emission, have steep XLFs, typical of old populations; soft SNR candidates, which tend to be associated with the spiral arms, also have fairly steep XLFs, although they extend to luminosities higher than that of the SSSs; the hard XRB candidates dominate the overall X-ray emission, and therefore the overall XLF. For these sources differences in the XLF are also found, which can be related to stellar age. The XLF of the actively star-forming central region is a power law with cumulative slope -0.7; the XLF of the outer disk has a break at LX ~ 8 × 1037 erg s-1, follows a power law with slope -0.6 below the break, and gets considerably steeper at higher luminosities (-1.6). This type of broken power law has also been found in the disk of M31 (Williams et al. 2004, Shirey et al. 2001). In M83, a dip is seen in the XLF at ~ 3 × 1037 erg s-1, corresponding to 100-300 detected source counts (well above source detection threshold), for sources in the disk and spiral arms where confusion is not a concern. The XLF rises again (toward lower luminosities) after the ~ 3 × 1037 erg s-1 dip, so incompleteness effects are not likely here. Soria & Wu (2003) speculate that this complex XLF (shown in Figure 9) may result from an older population of disk sources mixing with a younger (but aging) population of spiral arm sources.

Figure 9

Figure 9. X-ray luminosity functions of inner regions (red, d < 60" from galactic center) and outer disk (green) of M83 (figure 11 of Soria & Wu 2003).

The highest reaches of a star-forming XLF are found in the Cartwheel galaxy (Wolter & Trinchieri 2004), whose detected XRB population is dominated entirely by ULXs. This XLF has a slope consistent with that of Grimm, Gilfanov & Sunyaev (2003) and a large normalization, which suggests a SFR of ~ 20-25 Modot yr-1.

Grimm et al. (2005) and Shtykovskiy & Gilfanov (2005) explore the lowest luminosity reaches of the HMXB XLF with the Chandra survey of M33 (reaching ~ 1034 erg s-1) and with the XMM-Newton observations of the Large Magellanic Cloud (reaching ~ 3 × 1033 erg s-1), respectively. In both galaxies, a large number of the detected sources are background AGNs. In M33, the XLF, corrected for interlopers and incompleteness, is consistent with the HMXB XLF of the Milky Way (Grimm, Gilfanov & Sunyaev 2002). In the Large Magellanic Cloud, the corrected XLF, with spurious sources removed and rescaled for the SFR, globally fits the HMXB XLF of Grimm, Gilfanov & Sunyaev (2003) at the high luminosities (~ 1037 erg s-1). The dearth of low-luminosity sources in this XLF leads Shtykovskiy & Gilfanov to suggest a propeller effect (i.e., the magnetic field stopping the accretion flow away from the pulsar surface of the pulsar for relatively low accretion rates). Observing regions of intense local star formation (as indicated by Halpha and FIR maxima), where no HMXBs are found, these researchers also suggest an age effect: these star-forming regions could be too young for HMXBs to have evolved, as HMXBs take on the order of 10 Myr to emerge after the star-formation event. Tyler et al. (2004) advanced a similar suggestion in their comparison of Halpha, mid-IR, and Chandra images of 12 nearby spiral galaxies.

In conclusion, the XLFs of sources in a given galaxy reflect the formation, evolution, and physical properties of the X-ray source populations. These differences are evident, for example, in different regions of M81 and M83 (see Figures 8 and 9), by comparing elliptical and spiral galaxies and by comparing star-forming galaxies with different SFRs. These differences may be related to the aging of the X-ray source population, which will be gradually depleted of luminous young (and short-lived) sources associated with more massive, faster-evolving donor stars, and also to metallicity effects (Wu 2001; Belczynski et al. 2004). In the future, these X-ray population studies will constitute the baseline against which to compare models of X-ray population synthesis. An early effort toward this end can be found in Belczynski et al. (2004).

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