6 Total luminosity and diffuse emission

From the first ROSAT PSPC survey of M 31 we had already derived quantities for the total luminosity of M 31 and a possible gaseous component (S97). Because the first survey had to be corrected for several caveats such as the dominant influence of the PSPC support structure, the inhomogeneous exposure, and the rapid decrease of sensitivity from the centre of M 31 to the outer regions, we improved the determination of the total luminosity and diffuse component with the data from the much more homogeneous second survey. One of the big advantages of the second survey is its more or less constant exposure and therefore constant flux limit over the whole $D_{\rm 25}$-area of the galaxy. This allows an improved determination of the background around M 31 and, as a consequence, a more reliable flux determination of components within M 31. Furthermore, it reduces systematical errors in the case of large scale analysis, as discussed in this section. The following description has some overlap with procedures already described in S97, but we decided to briefly summarise them here for completeness.

In this section we will use the term "diffuse component'' to mean the sum of the emission from a truly diffuse (gaseous) emitter and from unresolved point sources. We will refer to "total emission'' as the sum of the diffuse component and the emission from resolved point sources.

As already described in Sect. 3.1, all the data have been cleaned of contamination by solar scattered X-rays and particle background. The resulting photon event files remain contaminated by these components, but only to less than 1% in each pointing. This is up to ten times better than in the worst case of the first PSPC survey. For the analysis in this section, the data were binned into an image with a $30\hbox{$^{\prime\prime}$ }\times 30\hbox{$^{\prime\prime}$ }$ pixel size. For the determination of count rates within the $D_{\rm 25}$-area of M 31, the merged inner regions of the PSPC with $20\hbox {$^\prime $ }$ radius have been used, whereas for the outer area around M 31, a merge of the total photon event files has been used. The resulting images were divided by exposure maps with the same pixel size to obtain count rate images corrected for the effects of the rib structure, vignetting and dead time. These exposure maps were calculated in the following manner: the B-band was divided into 10 energy slices for which EXSAS provides instrument maps for the PSPC detector response. Together with the photon event files, exposure maps for each of these energy slices were created, considering also dead time effects. A weighted addition of these single exposure maps yields the final exposure maps. The pulse height spectra in the 10 energy slices of the photon event files were used as the weighting factors.

From the image of the merged inner PSPC regions we derived count rates for the bulge (1 kpc around the centre) and the M 31 disk region (i.e. outside the bulge up to the $D_{\rm 25}$-ellipse). "Background count rates'' were taken from the image of the merged total PSPC FOV and within an area far outside and around the $D_{\rm 25}$ ellipse of M 31 - explicitly the area between the ellipse with major and minor axes $0.15\hbox{$^\circ$ }$ larger than the $D_{\rm 25}$ ellipse of M 31 and the ellipse $0.30\hbox{$^\circ$ }$ larger. Sources within this area were cut out to a radius of three times the PSF at the source position. With this, we derived count rates for the bulge, disk, and "background'' of $(46.86\pm2.5)$, $(4.278\pm0.04)$, and $(3.311\pm0.038) \mbox{ ct s}^{-1}\mbox{ deg}^{-2}$ respectively, in the broad (0.1-2.0 keV) energy band.

Considering the bulge, a subtraction of the background count rate and a multiplication with the bulge area of $0.026~\mbox{deg}^2$ yields $(1.132\pm0.065)~\mbox{ct~s}^{-1}$. Applying a power law with $\Gamma = -2.0$for the spectral model and a galactic foreground absorption of $N_{\rm H} = 6\times 10^{20}~\mbox{cm}^{-2}$ yields $(2.88\pm0.17)\times 10^{-11} \mbox{ erg~cm}^{-2}~\mbox{s}^{-1}$ for the total flux of the bulge region, which corresponds to a luminosity of $\sim$ $1.6\times 10^{39}~\mbox{erg~s}^{-1}$, assuming a distance of 690 kpc to M 31. A summation over the count rates of all 22 bulge sources detected in the second PSPC survey data in this area initially yields $(2.78\pm0.02)~\mbox{ct~s}^{-1}$. This is much higher than the total emission derived above. The reason is the way the source detection algorithm works. In highly confused regions it tends to overestimate the count rate of each source due to overlapping of the photon extraction circles of neighbouring sources. By determining the individual extraction radii the detection algorithm has used, and the amount of overlapping area under the assumption of a gaussian PSF for the instrumentation, we can globally correct for this effect. With this, we obtain $(0.893\pm0.006)~\mbox{ct~s}^{-1}$ for the resolved emission of the bulge. A comparison with the above derived total emission uncovers an unresolved component of $(0.239\pm0.065)~\mbox{ct~s}^{-1}$. Assuming that this component completely originates from thermal emission of hot gas, and applying a spectral model for an optically-thin thermal plasma (MEKAL) with $kT = 0.35~\mbox{keV}$ (as determined from XMM-Newton observations, e.g. see Shirey et al. 2001) and a galactic foreground absorption of $N_{\rm H} = 6\times 10^{20}~\mbox{cm}^{-2}$, we derive $(3.4\pm0.9)\times 10^{-12}~\mbox{erg~cm}^{-2}~\mbox{s}^{-1}$ for a diffuse X-ray flux. For a distance of 690 kpc to M 31, this corresponds to a luminosity of $(2.0\pm0.5)\times 10^{38}~\mbox{erg~s}^{-1}$ and would indicate a gas mass of $(1.0\pm0.3)\times 10^6 \,{M}_{\odot}$, assuming the gas fills uniformly the bulge region, a sphere with 1 kpc radius (using the power per unit emission integral as a function of temperature for a low density plasma reported by Kato 1976). Because a luminosity function derived from the detected sources in the heavily confused bulge region would be very uncertain, we cannot trust any estimation of the emission from non-detected sources below our detection threshold by extrapolating such a luminosity function. As a consequence, the above derived luminosity (and gas mass) of the diffuse emission must be considered as an upper limit.

Considering the disk, a subtraction of the background count rate and a multiplication with the disk area of $2.6~\mbox{deg}^2$ yields $(1.68\pm0.14) \mbox{ct~s}^{-1}$. A summation of the count rates of all the sources detected in the disk within the second PSPC survey data yields $(2.06\pm0.31)~\mbox{ct~s}^{-1}$. Here no correction had to be applied, as no important source confusion exists. This value is slightly higher than the one derived from the total emission. It may indicate a possible diffuse absorption of background photons by M 31. Although both derived count rates are comparable within their $1\sigma$ errors, this is an effect of the integral consideration of the whole disk. A division into several annular regions indicates an absorption at the $1\sigma$ significance level in some of these regions. A more detailed report will be the subject of a future paper. In the following discussion, we neglect a possible (slight) absorption in the M 31 disk.

As already mentioned in Sect. 4.2, a fair number of the detected sources do not belong to M 31, but are foreground sources or background sources shining through the galaxy. Therefore, the derived flux of all the resolved disk sources mentioned above (or the sum of the flux in the disk area) cannot be used for a determination of the total X-ray luminosity of the disk of M 31. Following the procedure described in S97 we use the there derived logN-logS distribution for sources truly belonging to M 31 (from a statistical point of view). We come up with $(1.26\pm0.20)~\mbox{ct~s}^{-1}$ for the resulting count rate, or a total flux of $(1.7\pm0.3)\times 10^{-11}~\mbox{erg~cm}^{-2}~\mbox{s}^{-1}$ for the disk of M 31 (using the above spectral model). This corresponds to a total luminosity of $(1.8\pm0.3) \times 10^{39} \mbox{ erg s}^{-1}$.

All together, applying a power law spectral model with photon index $\Gamma = -2.0$ and a galactic foreground absorption of $N_{\rm H} = 6\times 10^{20}~\mbox{cm}^{-2}$, we obtain for the total (0.1-2.0 keV) luminosity of M 31, $(3.4\pm0.3)\times 10^{39}~\mbox{erg~s}^{-1}$, approximately equally distributed between the bulge and disk.

6.1 Comparison with earlier results

A comparison with the results derived from the first ROSAT PSPC survey of M 31 (S97) uncovered a difference in the bulge luminosities. For the total emission as well as for the sum of the resolved flux of detected sources we determined slightly higher values from the second PSPC survey data. Although the difference in significance for the total emission is less than $1.5\sigma$, we decided to take the new value from the second survey as the better one due to the above mentioned reasons. Because the flux of the resolved emission increased approximately by the same (small) amount we would obtain nearly the same value for a possible gaseous component in the bulge of M 31 as previously derived from the first survey data when applying the same spectral model as used in S97 (now $(4.4\pm1.2)\times 10^{-12}~\mbox{erg~cm}^{-2}~\mbox{s}^{-1}$, compared to $(4.6\pm1.1)\times 10^{-12}~\mbox{erg~cm}^{-2}~\mbox{s}^{-1}$ in S97). It shows, that the change of the here newly given value ( $(3.4\pm0.9)\times 10^{-12}~\mbox{erg~cm}^{-2}~\mbox{s}^{-1}$) is mainly due to the new spectral model used (optically-thin thermal plasma with $kT = 0.35~\mbox{keV}$), which we adopted from recent results of XMM-Newton observations (Shirey et al. 2001). With this, the ROSAT derived diffuse luminosity within $5\hbox{$^\prime$ }$ of the nucleus of M 31 is comparable to the luminosity found for the same bulge area with the Chandra (Garcia et al. 2000) and the XMM-Newton observation (Shirey et al. 2001). It is commonly assumed that the hot component of the interstellar medium (ISM) is created by winds from massive young stars and supernova explosions in star-forming regions. The diffuse emission from the hot ISM in M 31 is less pronounced than that detected from the inner spiral arms in the neighboring Local Group galaxy M 33. For this galaxy ROSAT HRI (Shulman & Bregman 1994) and PSPC observations (Long et al. 1996) show diffuse emission with a luminosity of about $10^{39} \mbox{ erg s}^{-1}$ that traces the spiral arms within $15\hbox{$^\prime$ }$ of the nucleus and has a temperature of $kT = 0.4 \mbox{ keV}$. Galaxies with high star-forming activity may be even brighter in diffuse X-rays by factors of more than 10 (see e.g. Read et al. 1997; Vogler & Pietsch 1999a). The low diffuse X-ray luminosity in M 31 therefore supports the view that the galaxy is in a phase of low star-forming activity.

For the determination of the disk luminosity we adopted the procedure from our previous calculations used in the first survey. Hence, we obtained the same results. Also the considerations concerning the normalized luminosity distribution of the discrete X-ray sources in the disk of M 31 are still valid (see S97). A comparison with the luminosity distributions (normalized to bulge luminosity) of other nearby spiral galaxies like M 33, M 51, M 83, M 100, M 101, NGC 253, NGC 1566, NGC 4258, NGC 4559, NGC 4565, and NGC 4631 (see Vogler & Pietsch 1999b) shows no significant differencies in shape and reveals the distribution of M 31 as being typical for this class of galaxy. However, we do not find super-luminous sources (SLS) above several times $10^{38}~\mbox{erg~s}^{-1}$, as is also the case in M 33 and NGC 253, but not for the other (star-forming) galaxies mentioned above. Although NGC 253 is a (bulge) star-forming galaxy it shows no SLSs in its disk population. Therefore it is difficult to interpret the absence of SLSs in M 31, but it perhaps tends to show that M 31 is not in a star-forming phase.

The discussion of the comparison of our results with those obtained from the Einstein observatory and reported by TF also changes slightly under the transition from the first to the second PSPC survey. For the total luminosity of M 31, TF found a value of $\sim$ $3\times 10^{39}~\mbox{erg~s}^{-1}$. To compare with our values, one has to take into account the different spectral models, energy ranges, and especially the different fields of M 31 investigated. TF derived the luminosities from the Einstein data by applying a thermal bremsstrahlung spectrum in the energy band 0.2 keV-4.0 keV with $kT = 5 \mbox{ keV}$ and $N_{\rm H} = 7\times 10^{20}~\mbox{cm}^{-2}$. They integrated the count rates within an ellipse of $\sim$ $2.5\hbox{$^\circ$ }\times 1.0\hbox{$^\circ$ }$ which is a bit smaller than the $D_{\rm 25}$ellipse we used for our calculations. A conversion of our results to the spectral model and reduced area of TF yields for the total luminosity $(3.3\pm0.3)\times 10^{39}~\mbox{erg~s}^{-1}$. The $1\sigma$ agreement with the value reported by TF, however, is somewhat coincidental: while our observations covered the whole galaxy, those of TF did not. On the other hand, TF did not correct for background sources.

Comparing the total luminosity of the bulge region, TF reported $\sim$ $1.5\times 10^{39}~\mbox{erg~s}^{-1}$, which is in agreement with our value of $1.6\times 10^{39}~\mbox{erg~s}^{-1}$ (in this case the effect of the different assumed spectral models is below the errors and therefore negligible). In contrast, for the disk alone we found a somewhat higher luminosity ( $(1.8\pm0.3)\times 10^{39}~\mbox{erg~s}^{-1}$) than TF ($\sim$ $1.5\times 10^{39}~\mbox{erg~s}^{-1}$), though there is still a $1\sigma$agreement. Considering the fact that TF did not describe the errors and furthermore did not explicitly quote the values for the bulge and disk emission, but simply mentioned that "the emission is roughly equally divided between the bulge and the disk'', as well as their neglecting to compensate for background/foreground sources, we desist from a more quantitative comparison, noting that the agreement is surprisingly good. Our results tend to show that TF determined the disk luminosity too low and with it, the total luminosity of M 31. With the improved capabilities of ROSAT, the complete coverage of the total galaxy, and our considerations of statistical errors, we were able to clarify the luminosities in M 31 at a more reliable level.

As already mentioned, the second survey data did not (significantly) change the results concerning a possible diffuse emission component in the bulge region (from $(2.6\pm0.6)\times 10^{38}~\mbox{erg~s}^{-1}$ to $(2.5\pm0.7)\times 10^{38}~\mbox{erg~s}^{-1}$, when using the spectral model of S97). The exhaustive discussion of the comparison with the value reported by TF ($\sim$ $3.8\times 10^{38}~\mbox{erg~s}^{-1}$) and the reasons for the difference have already been undertaken in S97, and are still valid.