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Astron. Astrophys. 320, 378-394 (1997)

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4. Wind properties

4.1. Analysing the wind

As our aim is to derive spatially resolved plasma parameters (temperature, density, metallicity and absorbing column) it is necessary to assume a geometry for the emission. This will dictate the regions from which spectra are taken and the volumes used in deriving the density of the emitting plasma. Given the lack of symmetry of the diffuse emission (henceforth called the wind, bearing in mind alternative explanations of its origin as wind-shocked ambient material or even a hydrostatic halo as discussed in Sect.  5) apparent in Fig. 1, it is not obvious what geometry to choose. Within the wind paradigm, a conical (e.g. Suchkov et al. 1994) to cylindrical outflow (e.g. Tomisaka & Ikeuchi 1988; Tomisaka & Bregman 1993) along the galaxy's minor axis is expected, and if the emission arises from wind-shocked material a similar geometry would apply.

The azimuthal profile (Fig. 4) of the PSPC data about the centre of the galaxy can be used to explore the geometry of the diffuse emission. A biconical outflow would result in a sharp drop in the azimuthal brightness profile at the angles corresponding to the edges of the cone. If the cone were actually limb brightened (as suggested in some models), then a bimodal structure would be seen in the azimuthal profile of each outflow. In practice, the profile varies quite smoothly with azimuth in both hemispheres, and no suggestion of a limb brightening is apparent. It appears that a conical geometry is a poor representation.

[FIGURE] Fig. 3. The wind regions from which spectra were collected, overlaid onto an X-ray image. Sources (shown as circles and numbered as in Table 2) were removed from the analysis. Contour levels are as in Fig. 1.
[FIGURE] Fig. 4. Azimuthal profile of the emission within [FORMULA] of the nuclear source. Sources other than the nucleus have been masked out. The northern minor axis is at an azimuth of [FORMULA], the southern minor axis at [FORMULA].

Inspection of the surface brightness shows the Northern wind to be reasonably well described as a cylinder of radius [FORMULA]. We therefore adopt a cylindrical geometry for the bulk of our analysis. For consistency, we apply the same geometry to the southern wind, although it is clear from Fig. 3 that this is a poorer approximation, which will overestimate the emitting volume.

A set of spectra along the northern and southern winds were accordingly extracted from a series of rectangular regions of width [FORMULA] and height h along the minor axis (Fig. 3). A compromise must be made between large h (collecting a larger number of photons in the spectrum) and small h (giving good spatial resolution along the wind). A value of [FORMULA] was chosen, giving 9 regions along the wind while still having sufficient photons to give reasonable constraints on the spectra for all but the outermost regions. Corresponding background spectra were formed from the background-model cube for each of the wind region to allow maximum likelihood fitting.

Since it is likely that there will in practice be some degree of divergence of the outflows (though as we will show, the X-ray emission is almost certainly not coming from the wind fluid itself), we have investigated the effects of this by performing an identical analysis using two truncated cones. These truncated cones have a radius in the galactic plane [FORMULA], and an opening angle of [FORMULA]. The height h is again [FORMULA]. The cylindrical and diverging geometries are compared in Fig. 5.

[FIGURE] Fig. 5. Cylindrical and conical geometries assumed for the spectral analysis.

As discussed in Sect.  3.3, several point-sources were detected within or in close proximity to the diffuse wind emission. While it is possible that these represent regions of enhanced diffuse emission rather than truly independent sources, they were masked out of the wind regions to prevent any possible contamination of the wind spectra by foreign flux. The spectra were then corrected for dead-time and exposure corrected.

Raymond & Smith (1977) hot-plasma models were then fitted to the strip spectra using maximum likelihood, initially allowing all parameters to optimise. It was found that the metallicities consistently fitted low, 0.00- [FORMULA]. In view of the present uncertainties in the accuracy of ROSAT metallicities (see Bauer & Bregman 1996), and the expectation that the metallicity should not vary greatly through the wind, we refitted all the spectra with the metal abundance fixed at [FORMULA], which reduced the scatter in the other fit parameters. All results for the wind quoted below are derived from these [FORMULA] fits.

Such a low metallicity, whilst surprising, is supported by the results of recent ASCA observations (Ptak et al. 1996; Tsuru 1996). ASCA has the spectral resolution to clearly distinguish the iron L complex, which is the strongest metallicity indicator for plasmas of this temperature, and the implied iron abundances in the soft spectral component is 0.04-0.05 [FORMULA] (with a typical error of [FORMULA]), in good agreement with our results.

Since emission lines are so strong in the ROSAT energy band for [FORMULA] plasma, metallicity trades off against emission measure in fitted spectra. This can be clearly seen in Fig. 6, which shows the error ellipses for 68% confidence for two interesting parameters (optimising temperature and absorbing column) for all of the regions used in the analysis. Hence any error in our assumed metallicity will lead to a corresponding error in derived emission measure, and hence in inferred gas density. As can be seen, from Fig. 6, the error envelopes generally fall below [FORMULA]. Hence, taking [FORMULA] as the highest plausible value for metallicity (though this falls well outside the ASCA errors), our emission measures would be overestimated by a factor [FORMULA], and hence the densities would be a factor [FORMULA] too high. Such an error is quite modest compared to those introduced by the unknown filling factor and uncertain geometry of the emitting material.

[FIGURE] Fig. 6. Error ellipses for metallicity against emission measure at 68% confidence for two interesting parameters, for all the wind regions. Regions n7 and n8 are clearly peculiar as discussed in Sect. 4.5. Region n5 is poorly constrained.

As previous X-ray observations of M 82 have been unable to determine whether a hot plasma or a power law gives a better fit, we also fitted power law spectra to the data. These were found to give significantly poorer fits than the hot plasma fits (see e.g. Fig. 7) for all but the outer regions, where the statistics were too poor to tell. Although maximum likelihood gives no absolute goodness of fit measure, the relative likelihood between two fits to the same data can be derived from the Cash C-statistic. From Cash (1979), the relative probabilities [FORMULA], where [FORMULA] is the change in Cash statistic between the two fits. For the inner wind, contamination-corrected Raymond & Smith fits are clearly superior, e.g. for region n2, the hot plasma fit is [FORMULA] times more probable than the best-fit power law.

[FIGURE] Fig. 7. Spectral fits to two for two of the wind regions, n2 (left) and n6 (right), representative of the range in quality of the spectra obtained. Normalised background-subtracted spectra are shown overlaid with power law (dashed line) and contamination corrected Raymond & Smith (solid line) best fits. For the inner regions (such as n2) the power law is clearly a poorer fit than the Raymond & Smith model.

4.2. Nuclear contamination of the wind

Given the presence of an extremely luminous hard point source (nearly a third of all counts detected from M 82 with the PSPC are within a PSF sized region of [FORMULA]) at the centre of M 82, and the increasing size of the PSPC PSF at higher energies, one expects some contamination of the wind emission in the inner strips by photons from the nuclear source.

We can roughly assess the level of contamination by asking what fraction of the flux within the two innermost wind regions (n1 and s1) is due to scattered nuclear flux. If we assume all the flux within a [FORMULA] region centred on the nuclear source were due to a point source, then the fraction of this flux scattered into wind region n1 is 15% of the total flux observed in n1. For the innermost southern region, s1, the value is 12%. These are overestimates, as only [FORMULA] of the flux within [FORMULA] is due to the point source.

We allow for nuclear contamination by using two-component models for the wind regions: a soft Raymond & Smith plasma for the wind, and a harder bremsstrahlung component for the nuclear contamination. The bremsstrahlung component in each strip was fixed: the absorbing column and temperature taking the values derived from the nuclear fit discussed in Sect.  3.4, and the contaminating flux being estimated from the (energy dependent) PSPC point spread function.

4.3. X-ray morphology

It is clear from Fig. 1 that the diffuse emission is not symmetric around the plane of the galaxy. The surface brightness in a strip of width [FORMULA] parallel to the minor axis (Fig. 8) is initially higher to the south, but then drops more rapidly than to the north. Beyond [FORMULA] ([FORMULA]) from the nucleus the northern wind is consistently brighter. This asymmetry is also seen in the radio data of Seaquist & Odegard (1991). Within [FORMULA] of the nucleus, the brightness profile at [FORMULA] is brighter towards the south, while beyond [FORMULA] the north is brighter.

[FIGURE] Fig. 8. Surface brightness along the minor axis in a slice [FORMULA] wide. Diamonds represent the emission to the south, crosses the northern data. In each case the line represents the data with sources (other than the nuclear source) excluded. The south is brighter than the north within [FORMULA] in both the X-ray and the radio (Seaquist & Odegard 1991). Diffuse emission extends out to [FORMULA]. The emission seen in the north at [FORMULA] is a point source (number 5 in Fig. 3).

Emission can be traced out to [FORMULA] ([FORMULA]) from the nucleus along the minor axis, before dropping into the noise. The Einstein IPC estimate of emission extending to [FORMULA] from the nucleus was due to the inclusion of a point source (source 5 in Table 2) in the diffuse emission (see Fig. 3 in Fabbiano 1988).

4.4. Comparison with HI distribution

As can be seen in Fig. 9, the X-ray emission appears to anti-correlate with the large scale distribution of HI surrounding M 82. To the north-east, the X-ray emission appears to be bounded by the northern tidal streamer. Yun et al. (1993) claim this to be M 82's tidally disrupted outer HI disk. To the north-west, another streamer of HI intrudes onto the X-ray distribution on the eastern edge of regions n4 and n5. This northern HI has a velocity consistent with being on the far side of M 82, as is the northern wind. The southern wind appears confined between the clump of hydrogen to the south-east and the beginnings of the southern tidal streamer to the south-west. The south-eastern HI clump shows a broad blueshifted line wing which Yun et al. (1993) note may be due to the impact of a wind. The HI in the tidal streamers could provide a natural obstacle for the wind, constraining its expansion. The northern and southern streamers each contain [FORMULA], similar to the mass of material we infer below for the soft X-ray emitting material in the wind; so the HI could potentially form a significant barrier for the wind.

[FIGURE] Fig. 9. Comparison between X-ray and HI distributions. A greyscale X-ray image (lowest tone corresponding a flux of [FORMULA] arcmin-2), overlaid with contours of HI column density (adapted from Yun et al. (1993)). The contours correspond to [FORMULA] times 1, 2, 3, 4, 6, 10, 15 and 25.

In the inner regions, Fig. 9, shows significant amounts of HI in the region occupied by the optical filamentation and inner wind. The inner HI displays a velocity gradient along the minor axis in the same sense as the [FORMULA] emission, hence the HI probably consists of material swept out of the disk by the wind. As is discussed below, the X-ray spectra show signs of excess absorption.

4.5. Wind parameters

The results of the spectral fitting to the wind regions are given in Table 6. Contamination of the spectral properties of the wind by the nuclear point source has been allowed for as discussed in Sect.  4.2. As can be seen from Fig. 3 there is little wind emission beyond regions n8 and s6, and no useful spectral parameters could be derived for these outermost strips.


Table 6. Spectral fits to the wind regions. The Stark column is [FORMULA]. The metallicity is frozen at [FORMULA].

The absorbing column is found to decrease as the distance from the plane of the galaxy increases. Only in the south does the column drop to the Stark (1992) value of [FORMULA]. It can be seen from Fig. 9 that, on the basis of the HI distribution, excess [FORMULA] would be expected to extend only to [FORMULA], and the magnitude of the observed excess for the north ([FORMULA]) is larger than expected, except in the nuclear region. Absorption in the ROSAT band arises predominantly from He, C, N, and O rather than HI, hence, if the absorbing gas has a low metallicity such as is inferred for the hot X-ray emitting gas, the absorbing masses required at large heights above the plane are several [FORMULA] to several [FORMULA].

Fig. 10 shows 68% confidence error ellipses for column and temperature. Excess absorption is required to the north, although the column for the south drops to close to the Stark value. The temperatures are well constrained, and do not depend strongly on the fitted column. The origin of the excess absorption to the north remains to be determined.

[FIGURE] Fig. 10. Error ellipses for column against temperature at 68% confidence in two interesting parameters for the wind regions. Regions n7 and n8 are peculiar, as discussed in Sect. 4.5. The dotted line shows the Stark column. For the northern regions (n1-n6) it is clear that: a (upper figure) altering the temperature will not remove the need for excess absorption, and b (lower figure) the temperatures for the innermost regions are well determined.

Temperature and density both decrease with increasing distance along the minor axis z, although the temperature drop is small (Figs.  1213). The density is initially higher to the south, but then drops below the density to the north beyond [FORMULA], as indicated by the surface brightness profiles (Fig. 8).

[FIGURE] Fig. 11. Absorbing column against minor axis distance for Northern (crosses) and Southern (diamonds) winds. The column is in units of [FORMULA]. The Stark (1992) column is [FORMULA] in these units. As the northern side of M 82 is inclined away from us, the initially higher column to the north is entirely natural.

[FIGURE] Fig. 12. Temperature against minor axis distance for Northern (data: crosses, regression line: dashed) and Southern(data: diamonds, regression line: solid) winds. Only the first six points (n1 - n6 and s1 - s6) are used in the regressions.

[FIGURE] Fig. 13. Derived density against minor axis distance for Northern (data: crosses, regression line: dashed) and Southern (data: diamonds, regression line: solid) winds. Only the first six points (n1 - n6 and s1 - s6) are used in the regressions.

Under our assumed cylindrical geometry, it is possible to derive further useful gas parameters (see Table 7). We assume a distance of [FORMULA] to M 82 throughout. The volume V is derived from the geometry, of which the emitting gas is assumed to occupy some fraction [FORMULA] (the filling factor of the hot gas). The fitted emission measure then equals [FORMULA], and (assuming an ionised hydrogen plasma for simplicity) the mean electron density, total gas mass [FORMULA], thermal energy [FORMULA], bulk kinetic energy [FORMULA], cooling timescale [FORMULA], mass deposition rate [FORMULA], and sound speed [FORMULA], can then be calculated. The intrinsic (i.e. corrected for both galactic and intrinsic absorption) X-ray luminosity [FORMULA] in the ROSAT band is also given.


Table 7. Derived gas parameters for the wind, assuming a distance of [FORMULA] to M 82. [FORMULA] is the volume filling factor of the gas. All parameters have been derived assuming [FORMULA]. Conversion factors to arbitrary [FORMULA] are given. [FORMULA] is the outflow velocity of the X-ray emitting gas in units of [FORMULA], which may not be the same as the wind velocity.

In order to quantify the trends in the data, particularly in the behaviour of the temperature and density with increasing distance along the wind, we perform weighted least-squares fits to the data for north and south separately. We also regress temperature against density using weighted orthogonal regression (Feigelson & Babu 1992), allowing for the significant errors on both axes, using the package ODRPACK (Boggs et al. 1992).

Table 8 gives the fitted slopes, while the data and fitted lines are plotted in Figs. 12-14. The fits used data for regions n1-n6 and s1-s6 only; regions n7 & n8 were excluded as they clearly deviate from the general trend in the North.


Table 8. Results of the linear regression applied separately to the data from both north and south winds as described in the text. z is the distance along the minor axis. Results are given for both the contamination "corrected" and uncorrected data to demonstrate the effect the contamination has. To assess the effect of the chosen geometry, results for a truncated conical geometry with radius on the major axis [FORMULA] and an opening angle of [FORMULA] are also shown.

[FIGURE] Fig. 14. Temperature against density for Northern (data: crosses, regression line: dashed) and Southern (data: diamonds, regression line: solid) winds. For an adiabatically expanding gas the slope of the [FORMULA] regression line would be [FORMULA].

The elevated temperatures of n7 and n8 are difficult to explain. We have checked that the two point sources which fall in the vicinity have been effectively excluded from the data. One obvious possibility is that the temperature rise is due to a shock, however, in this case the density would also be expected to rise, whereas it appears lower than expected from the trend of the inner six northern regions. A hardness map shows a lack of soft flux at the edges of the wind in regions n7 and n8, with no corresponding lack of hard flux, but the regions of reduced soft flux do not seem to correspond to areas of excess HI and hence higher absorption. We have investigated the possibility of the excess hard flux being due to the energy dependent scattering from inner regions of the wind, but such contamination from one region into the next is at too low a level, decreases in importance with z, and is not strongly energy dependent. Also, it should be noted that there is no corresponding temperature rise in the south.

A systematic error in the background subtraction could possibly mimic a real trend with increasing distance along the wind due to the increasing importance of the background as the surface brightness of the emission decreases. To check the effects of this, the analysis was repeated for backgrounds 5% over and undersubtracted with respect to the ideal background described above. The fitted parameters were within [FORMULA] of those from the standard background in all cases. Hence over or undersubtraction is not a serious problem.

4.6. The effect of the assumed geometry

As discussed in Sect.  4.1, M 82's X-ray emission is not obviously well approximated by either a conical or a cylindrical outflow. In addition, the asymmetry between north and south makes the choice of a consistent geometry difficult. The inclination of the galactic plane to our line of sight will also blur any results, by superposition of physically differing regions, even if the plasma's properties do vary only with z. It is not unreasonable to expect variation perpendicular to the minor axis, leading to further superposition of different components along the line of sight. We checked for this by performing spectral fits for regions n3, n4, s3 & s4, binning the emission into eastern, central and western spectra. The resulting temperatures across the wind fell within [FORMULA] of each other, indicating that cross-wind variations are not a major effect.

Let us suppose that the plasma properties vary not with z, but with radius from the galactic centre, as in a spherical or conical outflow. Our derived spectral properties, using a cylindrical geometry, will then differ from the true properties. For a conical distribution, the degree to which the fitted parameters deviate from the true parameters depends on the opening angle of the cone. The fitted parameters will be some flux-weighted average of the various components of different r that fall within a slice at constant z. The effect will be worst for the inner regions, and for large cone opening angle, but will be small at large z. For a parameter F that decreases with r, the fitted parameter F at some z will always be lower than the true value for [FORMULA], due to the incorporation of flux from regions of greater r and hence lower F. This will have the effect of flattening the slope of any real trend in the data as the discrepancy between true and fitted values is less at large r.

In the present case, given the flatness of the temperature profile, the true temperature will not vary much from the fitted values. The emission measure will not be too far out either, given that the higher surface brightness emission along the minor axis dominates the fitted emission measure (i.e. the inclusion of the lower surface brightness emission further from the minor axis in our cylindrical geometry has rather little effect). The major source of bias is the volume, which we would overestimate at small r, and underestimate at large r. However, it should be borne in mind that the derived gas density depends only on the inverse square root of the assumed volume, [FORMULA].

In conclusion, if the soft X-ray emission does have a rather more divergent geometry than we have assumed, then the true temperatures will be similar to those obtained, while the density will drop off faster than our result, the inner densities being higher and the outer densities lower than those we have derived.

In order to test the magnitude of these effects, the standard analysis above was repeated treating the emission as arising from two inverted truncated cones of radius [FORMULA] on the galactic major axis and semi-opening angle [FORMULA], chosen by eye to give an reasonable approximation to the observed emission in the North (see Fig. 5). The results of this on the derived trends in n and T, can be seen in Table 8. The slope of the [FORMULA] relation is essentially unchanged, whilst the [FORMULA] trend becomes steeper, as expected. The implications of this will be discussed below.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998