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Astron. Astrophys. 318, 111-133 (1997)

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9. Discussion

9.1. The log N([FORMULA] S)-log S relation

We show in Fig. 18 the number count relation for all sources detected in the 'full' area above ML = 8 and ML = 10. From the bending of the log N([FORMULA] S)-log S curve at low count rates we estimate that our total source sample is complete down to about 0.02 and 0.012 cts s-1 for ML = 10 and 8 respectively. We note, however, that the enhanced number of spurious sources (see Sect. 9.3) may complicate the definition of a completeness level at ML = 8. The corresponding source densities are 1.0 deg-2 and 1.7 deg-2 at 0.02 and 0.012 cts s-1 respectively. In order to estimate the slope of the overall relation we used the maximum likelihood technique of Crawford et al. (1970) and Murdoch et al. (1973). For the 67 sources with ML [FORMULA] 10 and count rate [FORMULA] 0.02 cts s-1, we find that:

[EQUATION]

[FIGURE] Fig. 18. The log N([FORMULA] S)-log S function for sources with ML [FORMULA] 10 (lower curves) and ML [FORMULA] 8 (upper curves) in the 'full' area (64.5 square degrees). Above the completeness level of [FORMULA] 0.02 cts s-1 the slope of the distribution is close to -1. The identified stellar component has a slope of -1.48 [FORMULA] 0.23 consistent with the Euclidean value for count rates above our identification completeness level of [FORMULA] 0.03 cts s-1. The dashed line represent the expected extragalactic contribution

The slope and normalisation of the ROSAT survey relation is fully consistent with that reported by Hertz and Grindlay (1984) for the Einstein Galactic Plane Survey. Morley et al. (1996) also report compatible log N([FORMULA] S)-log S relations from deep pointings in the galactic plane. As discussed in the previous section, the extragalactic contribution is probably negligible in our field. At high count rates the relative excess of sources is caused by few objects namely the three white dwarfs and our only identified AGN. In principle the slope of the white dwarf log N([FORMULA] S)-log S function should be close to -1.5. In fact the lack of identified white dwarfs with count rates below 0.11 cts s-1 could reflect the higher completeness flux level for this particular population resulting from the higher X-ray background at low energies. Alternatively we may see the large effects of tenuous interstellar absorption on such soft X-ray spectra.

Our high fraction of identified sources put us in a position to derive the log N([FORMULA] S)-log S relation for stellar sources independently of the overall population. The inflexion of the log N([FORMULA] S)-log S curve for the stellar X-ray sources also shown in Fig. 18 suggests that the identified stellar installment is roughly complete down to [FORMULA] 0.03 cts s-1 in the 'full' area, while the completeness level reaches 0.02 cts s-1 in the 'inner' area (see Sect. 6). Interestingly, we find that the log N([FORMULA] S)-log S function of the optically identified active coronae is steeper than that of the total X-ray population. For the 41 sources with ML [FORMULA] 10 and count rates above our estimated completeness level of identification ([FORMULA] 0.03 cts s-1) we find a slope consistent with the Euclidean value.

[EQUATION]

This indicates that at the flux level of the ROSAT all-sky survey the distribution of the detected stellar population is not severely affected by interstellar absorption. The Euclidean-like distribution is also consistent with the fact that in our low latitude test direction, the maximum distance above the plane ([FORMULA] 30 pc) of the most remote X-ray detections ([FORMULA] 300 pc) is much smaller than the scale height of any known group of late type stars.

9.2. X-ray counts modelling

Optical star count modelling is a very powerful mean to constrain several important parameters describing the various stellar populations of the Galaxy (e.g. Robin & Crézé 1986). Because of the strong dependence of stellar X-ray emission with age, an X-ray view of the sky preferentially reveals the young stellar population. X-ray count modelling such as that developed by Favata et al. (1992) allows in particular the study of the local star forming rate during the last 109  yr, a field of investigation which is usually loosely constrained by optical star count analysis. Looking deep into the galactic plane has specific advantages since it allows to better constrain the youngest most luminous population which is concentrated in the low latitude regions of the galactic plane.

We first tried to compare our density of active coronae with the predictions of Favata et al. (1992). In their low galactic latitude model (b = [FORMULA]) the number of X-ray stellar source counts above log([FORMULA] /erg cm-2 s-1) = -12.5 corresponding to a PSPC count rate of [FORMULA] 0.03 cts s-1 is [FORMULA] 0.1 per square degree while our observed density is [FORMULA] 0.6. This rather large discrepancy could be related to the way the youngest stellar populations are treated.

In a second step we designed an age dependent numerical model by folding X-ray luminosity functions (XLFs) with the stellar population model of Robin & Crézé (1986). We used XLFs derived from ROSAT observations of the Pleiades and Hyades young galactic clusters and from Einstein observations of old disc population to handle the steeply varying stellar X-ray activity with age. Binaries are accounted for by using binary corrected luminosity functions. This X-ray model (fully described in Guillout et al. 1996a) allows to predict the distribution in age, spectral type, various colour indices, magnitudes and distance of the stellar content of X-ray flux limited or volume limited surveys. Detailed comparison of model predictions with observations in several low galactic latitude RASS areas will be discussed elsewhere and we only present here a preliminary analysis. Fig. 19 shows the computed log N([FORMULA] S)-log S curves toward the direction of observation (l = [FORMULA], b = [FORMULA]) for the standard model (stellar formation rate constant, slope of the initial mass function below 1 [FORMULA] = 0.7 [FORMULA] 0.2) (Haywood 1995). The most interesting feature in Fig. 19 is the good agreement between observations and the predicted number counts curve. The departure at count rates below 0.02 cts s-1 is probably due to the incompleteness of our optical identifications. This suggests that in this sample region we clearly detect all the active stars expected on the basis of our current knowledge on stellar population and age dependent X-ray coronal activity.

[FIGURE] Fig. 19. Theoretical log N([FORMULA] S)-log S curves for all stellar coronae (thick line), computed for the direction of the test area, assuming a constant stellar formation rate and a slope of the initial mass function below 1 [FORMULA] equal to 0.7 (C07). N is the number of stars per square degree in the direction l,b up to a given PSPC count rate S (0.1 - 2.4 keV band) as a function of the count rate. We also show the log N([FORMULA] S)-log S curves computed separately for A,F,G,K and M type stars (a) - left panel) and various populations of disc stars (b) - right panel). The thin lines on both sides of the sum log N([FORMULA] S)-log S curves represent the possible range resulting from the error due to the binning in age of the X-ray luminosity functions. The observed relation for all identified active coronae (giants excluded) with ML [FORMULA] 10 in the 'full' area is shown with asterisks

Table 8 summarizes the model number of active coronae and the proportion of A, F, G, K, early and late M-type stars for various limiting PSPC count rate (0.1 - 2.4 keV band). For comparison, we list in Table 9 the distribution in spectral types of a completely identified stellar subsample made of the 40 main sequence stars located in the 'inner' area with S [FORMULA] 0.02 cts s-1 together with the predicted distribution at the same flux limit. Considering the small number statistics, the observed distribution is in reasonable agreement with model predictions.


[TABLE]

Table 8. Predicted number of stellar X-ray sources per square degree as a function of PSPC count rate (cts s-1) in the direction of the Cygnus area. Also listed are the relative contributions in percents of various spectral types and age groups



[TABLE]

Table 9. Observed and predicted number of stellar X-ray sources per square degree and distribution in spectral types (percentages) for a limiting count rate of 0.02 cts s-1.


Another important feature shown in Fig. 19 is the outstanding importance of very young stars in the RGPS. For a limiting PSPC count rate S = 0.03 cts s-1 we expect that [FORMULA] 65% of the detected stellar X-ray sources are younger than 0.15 Gyr, this proportion increasing up to [FORMULA] 85% for stars younger than 1 Gyr (see Table 8). These first results indicate that stellar X-ray source counts may indeed be used to derive the basic properties of the young stellar populations and in particular put interesting constraints on the stellar formation rate (e.g. Micela et al. 1993, Guillout et al. 1996b).

The X-ray count model used here ignores the contribution of giant stars which is expected to be small (Maggio et al. 1990). Another population not taken into account is that of close 'old' binaries. In these systems, the large rotation velocity maintained over the whole stellar life by tidal lock may sometimes yield large X-ray luminosity. However, the large uncertainties on the X-ray luminosity functions, spatial densities, mass ratio distributions of close binaries such as RS CVn systems (e.g. Ottmann & Schmitt 1992, Favata et al. 1995) do not allow to accurately estimate their specific contribution. Using the XLFs in Majer et al. (1986) and Favata et al. (1995), we estimate that more than 3% of the sources brighter than 0.02 cts s-1 could be active close binaries which is close to the observed fraction (4%) in our sample. However, as discussed in Sect. 6, our follow-up observations are not very sensitive to binarity and the actual number of close systems may be somewhat larger.

9.3. Nature of the unidentified sources

Early simulations of survey data have shown that for a typical survey exposure the density of spurious sources was of the order of 0.0145 source per square degree above ML = 10 (Voges 1995). However, the precise number of false sources in a given survey field depends on background intensity and structure mainly determined by diffuse emission in our area. Consequently, the average figure mentioned above may be wrong by a factor of 2 or more in our case. The number of spurious sources per square degree detected above a given M [FORMULA] may be estimated as:

[EQUATION]

This relation implies a formal density of spurious sources of 0.0145, 0.11 and 0.29 deg-2 for M [FORMULA] = 10, 8, and 7 respectively. Therefore, only 20% to 40% of the 0.53 unidentified sources per square degree with ML [FORMULA] 8 may be spurious. The expected extragalactic contribution computed in Sect. 8 is also too weak to explain the remaining number of unidentified sources (see Fig. 18).

We list in Table 10 for two limiting count rates corresponding to the completeness levels for ML = 10 and ML = 8 several characteristic source densities (N([FORMULA] S) deg-2). Minimum and maximum model stellar densities were computed from the error due to binning in age of the XLFs and adding a [FORMULA] 1 [FORMULA] source counting error in the 64.5 deg2 area. In a similar manner we applied a - 1 [FORMULA] counting error to the estimated extragalactic contribution in the test region. The last column of Table 10 lists the maximum possible density range for the optically unidentified sources which are not associated with active coronae nor with extragalactic sources. These figures may be further lowered by the unknown fraction of spurious sources (up to 0.11 deg-2 for ML=8). Using a density of active coronae extrapolated from the fitted log N([FORMULA] S)-log S curve instead of the model prediction does not change the results. Considering the active coronae identified at the 95% confidence level on the basis of positional coincidence may allow to identify another 0.14 sources per square degree above 0.012 cts s-1. We conclude that there is no evidence for a large 'exotic' population in excess of 0.09 deg-2 and 0.29 deg-2 at 0.02 and 0.012 cts s-1 respectively and that stars may well account for most if not all of the unidentified sources.


[TABLE]

Table 10. Density of unidentified sources


9.4. Constraints on X-ray emission from old neutron stars

As many as 109 neutron stars could be born in the Galaxy during the last 1010 yr. After a relatively short lived radio emitting episode, these stellar remnants could reveal themself in the EUV - soft X-ray energy bands if they accrete from the interstellar medium.

First proposed by Ostriker, Rees & Silk (1970) the possibility that such a population could appear in the current X-ray surveys has been recently studied by several authors. Treves & Colpi (1991) have discussed the case of magnetized neutron stars accreting from an homogeneous interstellar medium with particular emphasis put on the ROSAT PSPC instrument. Blaes & Madau (1993) have further studied the observability of old isolated neutron stars in a wide range of energies. They use a slightly different neutron star velocity distribution as Treves & Colpi and consider several typical directions in the Galaxy representing the various distributions of hot tenuous and cool denser phases observed in the nearby interstellar medium. Colpi et al. (1993) have considered in more detail the case of the neutron stars accreting from dense molecular clouds.

Bondi accretion heavily depends on the relative velocity of the neutron star with respect to the interstellar medium and only the low velocity tail of the neutron star velocity distribution is expected to be detectable in X-rays. Another important parameter is the strength of the magnetic field which channels the accreted matter towards the poles and increases the effective temperature of the X-ray photons emerging from the polar cap.

The sensitivity of the ROSAT all-sky survey offers for the first time the possibility to sample this hypothetical population up to rather large distances over the whole sky. Treves & Colpi (1991) find that [FORMULA] 5000 old neutron stars spread almost isotropically over the sky should be present above a PSPC count rate of 0.015 cts s-1 which is the assumed sensitivity limit of the all-sky survey. Assuming a total number of [FORMULA] = 109 neutron stars in the Galaxy, Blaes and Madau (1993) argue that at this level of X-ray flux, the number of detectable X-ray emitting members could be in the range from [FORMULA] 2,000 to 10,000 depending on the accretion mode (polar or isotropic) with a marked concentration in the galactic plane.

We show in Fig. 20 and 21 the log N([FORMULA] S)-log S function for our unidentified source fraction together with the various theoretical predictions.

[FIGURE] Fig. 20. The log N([FORMULA] S)-log S relation for all unidentified sources with ML [FORMULA] 8 and ML [FORMULA] 10 (thick lines) in the 64.5 square degrees area. Over-plot are the predictions of Treves & Colpi (1991) for an interstellar density of n = 0.07 cm-3 (dotted line) and n = 1 cm-3 (dashed line)
[FIGURE] Fig. 21. The log N([FORMULA] S)-log S relation for all unidentified sources with ML [FORMULA] 8 and ML [FORMULA] 10 (thick lines) in the 64.5 square degrees area. Over-plot are the predictions of Blaes & Madau (1993); Case 1 polar (dotted line), Case 1 isotropic (dotted dashed line) and Case 4 polar (dashed line)

Our observed log N([FORMULA] S)-log S relation for unidentified sources and the upper limits listed in Table 10 clearly rule out the n = 1 cm-3 density case of Treves & Colpi and are marginally compatible with the n = 0.07 cm-3 density case. More stringent constraints may be put on the model of Blaes & Madau (1993) ([FORMULA] = 109) since we can exclude their case 1 thought to be representative of the galactic plane whatever is the accretion mode polar or isotropic.

The enhanced density of the interstellar medium in molecular clouds favours the detection of accreting neutron stars in their direction. Colpi, Campana & Treves (1993) estimated that the CYG OB7 cloud which is the dominant CO feature in our area could harbour as many as 1000 lonely accreting neutron stars. Fig. 4 shows that we cover a very large fraction of this molecular cloud, especially the densest parts. These authors estimate that [FORMULA] 70 neutron stars with accretion luminosity of the order of 1032 erg s-1 could be detected above 0.02 cts s-1. Our detection at similar count rates of X-ray emission from two bright OB stars probable members of CYG OB7 shows that we are indeed sensitive to accreting neutron stars located in this molecular cloud. Our observations seem to be at variance with predictions since at the level of 0.02 cts s-1, we only have 8 unidentified sources over the whole field (see Table 3) instead of the expected 72 for the entire cloud or 36 for a half cloud. We show in Fig. 22 the position of the unidentified sources overlayed on the CO map (Dame et al. 1987). The absence of correlation between the location of unidentified sources and CO intensity seems indeed incompatible with the idea that the majority of these sources are old neutron stars accreting from the dense interstellar medium. However, we cannot completely rule out a conspiracy resulting from the correlation between high X-ray luminosities and photoelectric absorption. In a recent paper, Zane et al. (1995) perform a more accurate analysis of the distribution of old neutron star. Assuming the most favourable cases of polar cap accretion, they predict that [FORMULA] 9 to 17 such sources may be detected in the entire CYG OB7 above 0.02 cts s-1. This reduced number is now compatible with our observations.

[FIGURE] Fig. 22. Position of the unidentified X-ray sources (maximum likelihood [FORMULA] 8, all count rates) overlayed on the CO map from Dame et al. (1987) where we also sketch the area investigated in X-rays. The absence of a correlation between the distribution of the unidentified population and the CO structures seems to rule out the possibility that these sources consist of a majority of extragalactic sources or of lonely neutron stars accreting from the dense interstellar medium. The log N([FORMULA] S)-log S function and the spatial repartition rather suggest that most unidentified sources are active coronae

Considering the various ingredients entering these models the lack of a large population of unidentified, old neutron star candidate X-ray sources may have one or several different interpretations.

The first important parameter is the density of the interstellar medium in the direction surveyed here. Because of the very low density of the local cavity ([FORMULA] 0.015 cm-3) in which the Sun seems presently embedded and which extends at least up to 50 pc in most directions (Paresce 1984, Welsh et al. 1994), we do not expect the presence of nearby X-ray luminous lonely neutron stars (Blaes & Madau 1993). At larger distances from the Sun, the mean density of the interstellar medium reaches more typical values for the Galaxy ([FORMULA] 1.0 cm-3, Blaes & Madau 1993). Although there exists some general agreement on the main structure of the local bubble, namely a large extent toward galactic longitudes l = [FORMULA], the details of the boundary are poorly known. However, Welsh et al. (1994) claim that the bubble radius could be as narrow as 25 pc toward l = [FORMULA] and Paresce (1984) find consistent results although with a lower spatial resolution (see also Zane et al. (1996) for a recent discussion of the local interstellar medium). The maps of interstellar extinction from Neckel & Klare (1980) show that in most directions concerned here [FORMULA] smoothly increases to [FORMULA] 1 at 1 kpc and that in the innermost regions of the plane the interstellar absorption already reaches [FORMULA] [FORMULA] 2.5 at 500 pc. This indicates a mean hydrogen density in the range of 0.6-3.0 cm-3 up to a few hundreds of parsecs. We conclude that in the direction surveyed here in X-rays the interstellar medium has a density and a radial distribution typical of the mid-plane conditions as defined by Blaes & Madau (1993) and that the correct models to compare with are those of case 1 (see Fig. 21).

Following Madau & Blaes (1994) we argue that the second crucial parameter is the velocity distribution of the old neutron stars since the most powerful X-ray sources will be those few with very low velocities relative to the interstellar medium. If the mechanism increasing the velocity dispersion of old stars (Wielen 1977) is also at work for old neutron stars, the number of low velocity neutron stars may be severely overestimated. Finally, the overall number of neutron stars assumed to be born in the Galaxy may also be overestimated.

Madau & Blaes (1994) demonstrated that a model taking into account the dynamical heating of the old neutron star population would indeed drastically decrease the detectability of these objects in the RASS. Following their computations, our limit on the density of non-coronal non-extragalactic sources could imply an overall number of old neutron stars of only ([FORMULA] [FORMULA] 108) if accretion always occurs on polar caps. Alternatively, a large number of fossil neutron stars ([FORMULA] = 109) would only be acceptable if accretion occurs isotropically and if the dynamical heating mechanism is at work. Based on results from the EUVE and WFC all-sky surveys and using an early report on a parallel optical identification program of RASS sources carried out by our group in the Taurus constellation (Guillout et al. 1996b), Madau & Blaes (1994) concluded that the presently available observations may already hint at a much less numerous old neutron star population than previously thought. The present constraints, however, do not preclude the discovery of few relatively close ([FORMULA] 100 pc) isolated neutron stars (e.g. Walter et al. 1996).


[TABLE]

Table 11. Optical identifications for sources with ML [FORMULA] 8. Entries are sorted by decreasing count rates. For the sake of completeness, we also list the proposed counterparts having a probability of identification in the range 95% - 98%. These more uncertain cases are marked by a '?' as first letter of the identification name and the class acronym is followed by a '?'



[TABLE]

Table 11. (continued)



[TABLE]

Table 12. Optical identifications for sources with 7 [FORMULA] ML [FORMULA] 8. Entries are sorted by decreasing count rates. For the sake of completeness, we also list the proposed counterparts having a probability of identification in the range 95% - 98%. These more uncertain cases are marked by a '?' as first letter of the identification name and the class acronym is followed by a '?'


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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998
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