6 The X-ray binary sample

For the X-ray binary sample all classified X-ray binaries given in HP99 have been considered. Three of these X-ray binaries were found to be slightly outside the hardness ratio selection criteria but were also included in the sample. In addition sources were taken into account which were observed in the central 20$\arcmin$ of the detector, which fulfilled the selection criteria for X-ray binaries given in Sect. 2, i.e. sources which were located in the $H\!R1$ - $H\!R2$ plane "above'' the AGN band (cf. Sect. 4). In addition an X-ray spectral fit has been applied to the spectra of these sources and the consistency with an X-ray binary has been checked. Also a time variability study of the source count rate has been performed. There were 30 sources found which were classified as (candidate) X-ray binaries (cf. Table 1). 15 of these sources have more than 50 observed counts and powerlaw photon indices were derived for these sources (excluding HP 914). It is found that the distribution of powerlaw photon indices is consistent with a mean $\Gamma$ of -1.4 and a $\sigma$ of 0.9. But $\Gamma$ strongly depends on the used value of the galactic and LMC absorbing column. For most of the X-ray binaries the total LMC columns have been used in the spectral fit. This assumption need not always be correct and I have taken this fact into account in a few cases where the $N_{\rm H}$ value could be determined in the spectral fit.

If one compares the number of classified AGN and X-ray binaries it is found that a fraction of 80% of the spectrally hard X-ray sources with more than 50 detected counts are AGN and 20% are X-ray binaries.

For the 30 (candidate) X-ray binaries the unabsorbed flux and the luminosity (0.1-2.4) keV have been determined in an X-ray spectral fit. The derived flux and luminosity histograms are given in Fig. 9. It follows that there are 3, 4, 8, 15, and 29 X-ray binaries with luminosities in excess of 10³⁸, 10³⁷, 10³⁶, 10³⁵, and $10^{34}\ {\rm erg}\ {\rm s}^{-1}$ respectively.

These numbers can be compared with the number of X-ray binaries predicted from stellar evolutionary calculations for the LMC (Dalton & Sarazin 1995). According to these calculations there are 1, 5, 18, 125, and 750 X-ray binaries predicted to exist in the LMC with luminosities in excess of 10³⁸, 10³⁷, 10³⁶, 10³⁵, and $10^{34}\ {\rm erg}\ {\rm s}^{-1}$ respectively. Such a comparison will only be valid if the sample of X-ray binaries selected here is complete. There are two factors which have to be taken into account for such a completeness consideration, the sensitivity limit of the LMC X-ray survey and the fraction of the LMC disk covered by the observations.

Figure 9: Distribution of flux and luminosity corrected for absorption (left and right panel respectively) for the 30 (candidate) X-ray binaries in the observed field of the LMC (cf. Table 1). The number of X-ray binaries per flux and luminosity bin is given.

In Paper III it will be shown that our survey is complete in the observed field to a flux of $\sim$ $10^{-12}\ {\rm erg}\ {\rm cm}^{-2}\ {\rm s}^{-1}$ which is equivalent to a luminosity of $3\times 10^{35}\ {\rm erg}\ {\rm s}^{-1}$. Our observations cover 16 square degrees, which is $\sim$24% of the LMC disk. Assuming that X-ray binaries are homogenously distributed across the LMC disk, we extrapolate from the number of 8 observed X-ray binaries with luminosities in excess of $10^{36}\ {\rm erg}\ {\rm s}^{-1}$ that there may be 33 X-ray binaries across the whole LMC disk above this luminosity limit. If one compares this with the number of 18 X-ray binaries predicted from population synthesis calculations then an excess of X-ray binaries appears to exist. But a detailed investigation of the candidate X-ray binaries is required to give reliability to a deviation in these numbers. For a flux in excess of $3\times 10^{-13}\ {\rm erg}\ {\rm cm}^{-2}\ {\rm s}^{-1}$ (which corresponds to a luminosity of $10^{35}\ {\rm erg}\ {\rm s}^{-1}$) 15 X-ray binaries are in our observed sample. Assuming besides the incompleteness due to the covered LMC field the incompleteness due to the given sensitivity (which is about a factor of 1.3, cf. Paper III) we derive an extrapolated population of 81 X-ray binaries. This population would be less than the predicted 125 X-ray binaries but the extrapolated number my have large uncertainties and such a comparison may not be too reliable.

6.1 Comparison with the number of X-ray binaries in the SMC

Two of the newly classified X-ray binaries, RX J0523.2-7004 and RX J0527.1-7005, are located in the optical bar of the LMC (cf. Table 1). Another source newly classified as an X-ray binary, RX J0524.2-6620, lies in the eastern H  I shell of the supergiant shell LMC 4. An additional source which is contained in Table 1 in the section of background AGN, RX J00546.8-6851, but which may be an X-ray binary (see also Paper I and Sasaki et al. 2000) is located in or at least very close to the supergiant shell LMC 2. In total, 9 of the 30 sources classified as X-ray binaries (i.e. 30%) are associated with the supergiant shell LMC 4. This could be a selection effect as the LMC 4 region has been observed during many ROSAT pointings. But also other regions of the LMC, e.g. the 30 Dor area, have been observed during multiple observations and less X-ray binaries have been detected in these areas. Assuming that these sources are high-mass X-ray binary systems which have formed within an evolutionary time scale of $\sim$ $10^{7}\ {\rm years}$ (cf. Popov et al. 1998) may indicate that star formation has taken place in the last 10 million years in the LMC disk (including the H  I boundary of the supergiant shell LMC 4). To find candidate high-mass X-ray binaries in the LMC may be of importance as recent X-ray surveys of the Small Magellanic Cloud (SMC) have revealed a large number of such systems showing X-ray pulsations in this other Magellanic Clouds galaxy (cf. Yokogawa et al. 2000; Finger et al. 2001). One scenario put forward to explain the large number of high-mass X-ray binaries discovered in the SMC is the trigger of star formation during the recent close encounter between the SMC and the LMC $\sim$(0.2-0.4) Gyr ago (cf. Gardiner et al. (1994, hereafter GSF94); Gardiner & Noguchi (1996, hereafter GN96)). In such a scenario it is expected that star formation was also triggered in the LMC (cf. van den Bergh 2000, for a recent update of the star formation rate of the LMC during the last 9 Gyr). Finding new candidate high-mass X-ray binaries in the LMC which are associated with at least two supergiant shells may be consistent with such a scenario.

Can this scenario account for the observed number of candidate high-mass X-ray binaries in the LMC and SMC. In the previous section we estimated an extrapolated number of 33 X-ray binaries with luminosities in excess of $10^{36}\ {\rm erg}\ {\rm s}^{-1}$ in the LMC field. A comparable number for the population of high-mass X-ray binaries in the SMC has been set up by Haberl & Sasaki (2000) who recently increased the number of detected Be-type X-ray binaries in the SMC to $\sim$50. Assuming that at least 40% of these X-ray binaries have outburst luminosities in excess of $10^{36}\ {\rm erg}\ {\rm s}^{-1}$ would give a ratio of LMC to SMC high-mass X-ray binaries of $\sim$(0.7-1.7). An additional uncertainty in these numbers may be due to the fact that not all Be-type X-ray binaries have so far been detected in the LMC and the SMC (either in quiescence or in outburst). A value for the number ratio of $\sim$(0.7-1.7) is not in agreement with the mass ratio of both galaxies of $\sim$10 (the mass of the LMC and the SMC is $\sim$ $2\times 10^{10}\ M_{\odot}$ and $\sim$ $2\times 10^{9}\ M_{\odot}$ respectively, cf. GSF94). It would be more consistent with the ratio of the gas mass of both galaxies of $\sim$(1.2-1.8) (the H  I mass of the LMC and SMC is $\sim$ $5.2\times 10^{8}\ M_{\odot}$ (Kim et al. 1998) and $\sim$ $4.2\times 10^{8}\ M_{\odot}$ (Stanimirovic et al. 1999) respectively, and for the LMC the gas mass may be larger than the H  I mass by $\sim$40% due to the contribution of molecular hydrogen). Assuming that the star formation rate is proportional to the gas mass of a galaxy, the comparable gas mass of the SMC and the LMC may give an explanation for the comparable number of high-mass X-ray binaries found in both galaxies.

Star formation may have been triggered during an encounter of these two galaxies. Assuming that during the encounter turbulence was introduced into the gaseous phase of the galaxy disk, from the condition of conservation of angular momentum constraints can be derived for the ratio of star formation rates SFR induced in both galaxies. Making use of the formalism for the star formation rate given by Kennicutt (1998) in which the star formation rate scales with the gas density and the orbital time scale and which has been found to give a good fit for a large sample of normal and starburst galaxies, then one finds that this ratio can be expressed as

$$\frac{SFR_{\rm LMC}}{SFR_{\rm SMC}} \approx \left(\frac{R_{\rm SMC}}{R_{\rm LMC}}\right)^2$$ (3)

with R the radius of the gaseous disk of a galaxy. If one uses for the LMC $R_{\rm LMC}=3.7$ kpc (Kim et al. 1998) and for the SMC $R_{\rm SMC}=2.3$ kpc (e.g. Stanimirovic et al. 1999), then one obtains $\frac{SFR_{\rm LMC}}{SFR_{\rm SMC}}\approx 0.4$.

If one assumes that the starburst was efficient enough to significantly increase the star formation rate preferentially in the SMC and that the number of high-mass X-ray binaries scales with the star formation rate of a galaxy at an epoch of $\sim$10⁷ years ago (which may be somewhat earlier if a delay for the onset of star formation is taken into account) then one can directly compare the ratio of the star formation rates of two galaxies during this epoch with the ratio of presently observed numbers of high-mass X-ray binaries in these galaxies. The ratio of high-mass X-ray binaries in the LMC to those in the SMC is derived from the observed numbers to be $\sim$(0.7-1.7). There appear to be many more X-ray binaries in the LMC than predicted from Eq. (3). One explanation may be that the formation of high-mass X-ray binaries in the LMC is less affected by the starburst than in the SMC, i.e. in the LMC we observe the constant star formation with a minor contribution from a starburst.

From the OGLE survey of 93 star clusters in a field in the central $2.4\ {\rm deg}^{2}$ of the SMC Pietrzynski & Udalski (1999) derived that most of these star clusters are younger than $\sim$ $20\times 10^{7}\ {\rm years}$. This finding could mean that the formation of star clusters during the last $(20 {-} 30)\times 10^{7}\ {\rm years}$ was enhanced at least in the central field of the LMC. Alternatively it may be explained by an efficient process of disintegration of clusters older than $(20 {-} 30)\times 10^{7}\ {\rm years}$. Both effects may be explained by a tidal interaction of the SMC with the LMC which may have resulted in a burst of cluster formation and/or in the disruption of pre-existing stellar clusters.