Forum Springer Astron. Astrophys.
Forum Whats New Search Orders

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

Previous Section Next Section Title Page Table of Contents

5. Comparison with wind models

Given previous claims that the X-ray emission from M 82 is consistent with that expected from the adiabatic expansion of a free flowing wind (Fabbiano 1988; Bregman et al. 1995), in particular that the density derived from the surface brightness falls off as [FORMULA], it is worth investigating whether our spectral results are consistent with this idea.

5.1. Chevalier & Clegg's adiabatic wind

The simplest useful model of a galactic wind is that of Chevalier & Clegg (1985). This is just a spherically-symmetric outflow from a region of constant mass and energy injection (the starburst) ignoring the effects of gravity, radiative cooling and the presence of any ambient medium. The hot gas smoothly passes through a sonic transition at the radius of the starburst region, and then becomes a supersonic outflow which cools adiabatically. Provided the kinetic energy supplied by the numerous SN and stellar winds within the starburst is efficiently thermalised, the temperature of the hot gas within the starburst region will be [FORMULA] for reasonable mass and energy injection rates, making the neglect of the effects of gravity and radiative cooling valid. For regions well outside the starburst region, [FORMULA], the wind density [FORMULA], wind temperature [FORMULA] and thermal pressure [FORMULA]. McCarthy et al. (1987) compared variation of pressure with radius in the optical filamentation with the Chevalier & Clegg (CC) model, under the assumption that the thermal pressure in the filaments would equal the total (thermal plus ram) pressure in the wind, achieving a good match within a kiloparsec of the nucleus. Fabbiano (1988) reported in a reanalysis of the Einstein IPC data, that the radial distribution of the X-ray emission was consistent with [FORMULA], i.e. a free-flowing wind.

The Chevalier & Clegg model assumes a spherical outflow, in contrast to the cylindrical geometry we have adopted. What would we expect to see from a free wind in a more generalised outflow geometry, e.g. a bubble that has broken out of the disk of the galaxy and now allows free escape of the wind material? Assuming a constant mass loss rate, [FORMULA], where [FORMULA] and [FORMULA] are the cross-sectional area and the velocity of the flow, and [FORMULA] of the form [FORMULA], together with a constant outflow velocity, it follows that [FORMULA]. For a cylinder, [FORMULA], hence [FORMULA] is constant. For a sphere or a cone of constant opening angle, [FORMULA]. The density for a cone is just a constant ratio higher ([FORMULA], where [FORMULA] is the opening angle in steradians) than that for a spherical wind for a constant [FORMULA]. Obviously we can produce any [FORMULA] and retain the concept of the emission as arising from a free wind, by choosing the appropriate geometry. However, for isentropic gas, the temperature [FORMULA], where [FORMULA] in the present case. In the absence of cooling (a good approximation given that the outflow timescale is [FORMULA] while the cooling timescales are [FORMULA]) a free wind would expand adiabatically. Hence we expect a [FORMULA] graph to have a slope of [FORMULA] for any free wind irrespective of geometry. Inspection of Table 8 shows that although the northern emission is consistent with this, the southern emission is inconsistent at greater than the 95% confidence level, in the sense that the temperature drops too slowly relative to the density - i.e. the entropy rises outwards.

Note that if the absorbing columns in the northern outer regions are overestimated, then the real temperatures for these regions will be higher, reducing the temperature gradient. This would make the north less isentropic and reduce the difference between north and south. However the fits clearly require a higher column than Stark for these regions.

As discussed in Sect.  4.6, our use of a cylindrical geometry will lead us to underestimate the slope of the density profile if the emission comes from a conical outflow, whilst our temperature estimate is quite robust. This means that the inconsistency of the southern wind with an adiabatic outflow can only be accentuated if the flow diverges. The slopes for the re-analysis with a truncated conical geometry confirm this, the southern emission being less isentropic than for the cylindrical analysis.

Bearing in mind the geometry issue, we can attempt a more quantitative comparison between the observed temperatures and densities and the CC model, using the forms for [FORMULA] and T from CC, and the scaling relationships for the mass and energy injection given by Heckman et al. (1993). These use the predicted deposition of mass, kinetic energy and momentum from a starburst calculated by Leitherer et al. (1992). For a constant star formation rate over a period of [FORMULA], solar metallicity and a normal Salpeter IMF extending up to [FORMULA], the various injection rates are related to the starburst bolometric luminosity by:


where [FORMULA] is the bolometric luminosity in units of [FORMULA]. For most starbursts [FORMULA], is the dominant contributor to [FORMULA] so it is a reasonable approximation to equate [FORMULA] with [FORMULA]. How valid are these scaling relations for M 82? Visual inspection of Leitherer et al. 's figures show that for all but the lowest metallicities the injection rates are approximately constant after [FORMULA], similar to the age of M 82's starburst (Rieke et al. , 1993).

Applying the above scaling relations to Chevalier & Clegg's model we obtain, for radii large compared to the starburst radius [FORMULA]:


where [FORMULA] is the electron number density number density, T the temperature and [FORMULA] the total solid angle through which the wind flows out.

Note that the temperature is independent of [FORMULA], being a ratio of the energy and mass injection rates. For a bolometric luminosity of [FORMULA] (Rieke et al. 1993) and a characteristic radius, [FORMULA], for the starburst of [FORMULA], we can predict [FORMULA] and T at radii corresponding to the regions in Fig. 3.2 - see Table 9. Even for the innermost regions (n1 and s1) the CC model underestimates the density by an order of magnitude. Although the predicted temperature is almost equal to that observed near the galactic centre, the adiabatically expanding wind cools too quickly to match the PSPC data, dropping to [FORMULA] in the outermost regions, whereas the observed temperature along the minor axis is almost constant at [FORMULA] and even rises in regions [FORMULA] and [FORMULA] to [FORMULA].


Table 9. Predicted parameters of the X-ray emitting gas using the simple models discussed in Sect. 5. The shocked cloud temperatures are calculated using the derived electron densities from the northern wind for unit filling factor. Predicted cloud temperatures for the south are similar. Values assume spherical outflow for the wind. For a conical outflow of total solid angle [FORMULA], the shocked cloud temperature [FORMULA] and the CC wind density are [FORMULA], and the CC temperature [FORMULA].

In summary, the densities and temperatures derived under our assumed cylindrical geometry differ greatly from those predicted under a spherical geometry by the CC model. Given an arbitrary outflow geometry, it is in principle possible for the adiabatic wind model to reproduce the observed shallower trend in density, however the departure of the southern wind from constant entropy is a robust result which is incompatible with the basic assumptions of the CC model. We conclude, therefore, that the observed X-ray emission cannot arise from a single phase, expanding wind. The fact that the entropy actually rises with z in the south, means that the CC model cannot be saved by supposing that additional material is entrained into the flow as it proceeds. Although this might raise the density, it would cause the entropy to decline with z, accentuating the disagreement with our results.

5.2. A hydrostatic halo

It has been suggested (W. Pietsch, private communication) that the extended X-ray emission around NGC 253 may be due not to a wind or shocked cloud emission, but to a static halo. For M 82 the optical emission line velocity data and spectral index variations in the radio halo (McKeith et al. 1995; Seaquist & Odegard 1991) demonstrate conclusively the presence of a galactic wind. Since the synchrotron emission is very similar to the X-ray in extent, so it is difficult to argue that the X-ray emission is not associated with a wind.

Can we rule out a hydrostatic halo on the basis of the observed X-ray properties? From the observed density and temperature the mass within some radius r for a hydrostatic halo, assuming spherical symmetry, is:


where the observed temperature [FORMULA] and density [FORMULA]. For regions n3 and s3 the predicted mass within [FORMULA] are [FORMULA] and [FORMULA] respectively. From Götz et al. (1990) the mass within this radius, based on velocities measured in HI , is [FORMULA], an order of magnitude lower.

Hence we can rule out any possibility that the X-ray emitting gas is bound to M 82 as a static halo.

5.3. Shocked clouds in a wind

An alternative to emission from a free wind is emission from shocked material embedded in such a wind. Any clouds of denser material overrun by the wind, be they fragmented remnants of the dense shell swept up by the wind in its "snow-plough" phase or clouds in the ISM, will be shock-heated. The [FORMULA] filamentation seen along the minor axis has line ratios indicative of material shocked to [FORMULA]. Less dense material would be heated to even higher temperatures, and could be the source of the soft X-rays seen, rather than the emission being due to the wind itself.

The temperature to which these clouds will be heated depends on the speed of the shock driven into them by the wind. This depends on the relative densities of the cloud and the wind, and the wind velocity. In the case of strong shocks (Mach number M [FORMULA] 1) we can ignore the thermal pressure of both the wind and the cloud, and equate momentum flux across the shock. Given the mass and energy injection rates, one expects a wind velocity [FORMULA], whereas the sound speed in the X-ray emitting gas is [FORMULA]. Clouds will be accelerated by the wind to varying extents depending on their column density and individual histories, but only to velocities of order hundreds of [FORMULA], as seen in the [FORMULA] filaments. Hence the strong shock approximation is not unreasonable. The shock driven into the cloud will then have a velocity [FORMULA]. The eventual temperature of the cloud will be proportional to [FORMULA].

For a constant velocity, spherical or conical wind flowing into solid angle [FORMULA], with constant mass injection rate [FORMULA], the wind density [FORMULA], and the shocked cloud temperature


where [FORMULA] is the wind velocity in units of [FORMULA], and [FORMULA] in units of [FORMULA]. We assume the postshock cloud density is four times the preshock density, and that ionization, dissociation, magnetic fields and radiative losses are negligible. Relaxing the previous four assumptions would result in lower shocked cloud temperatures.

Given [FORMULA], the number densities derived above, a wind velocity of [FORMULA] and [FORMULA] from Eq. (2) we can predict the temperature we expect assuming unit filling factor and [FORMULA] (Table 9). From Fig. 1 one can estimate the solid angle the wind flows into as [FORMULA] steradians, raising [FORMULA] by a factor [FORMULA]. In the context of clouds in a wind, the filling factor should be substantially less than unity. The [FORMULA] filaments have [FORMULA] (McCarthy et al. 1987) in the inner kiloparsec, so it would not be unreasonable to expect cloud filling factors of order [FORMULA] at larger distances from the nucleus. This would reduce [FORMULA] by a factor [FORMULA] -10. The net effect is that the predicted temperatures are rather lower than those observed, but considering the large uncertainties involved, this simple model must be regarded as giving results consistent with observation.

Assuming that [FORMULA] and the filling factor do not vary with distance along the wind, the predicted temperatures (Table 9) drop off too quickly to match the observed trend of T with z. The steepness of the predicted temperature profile could be due to the assumed geometry. As discussed in Sect.  4.6the inner densities may be higher than calculated. Higher inner cloud densities would lead to lower postshock cloud temperatures and hence flatten the trend.

So, in summary, predicted postshock temperatures for a simple model where the wind shock heats clouds are consistent with, if slightly lower than, those observed, given the observed emission measure (density).

5.4. Numerical models

Tomisaka & Ikeuchi (1988) were the first to explicitly model the wind in M 82 using 2D hydrodynamical simulations. They found a roughly cylindrical bipolar wind formed naturally for a constant mass and energy input rate in the nucleus of 0.1 SN [FORMULA]. However, they modelled the ISM as a cold rotationally supported disk in which the angular velocity was independent of the distance from the plane of the disk. This physically unrealistic configuration creates a strong funnel along the z -axis which strongly collimates the wind. Tomisaka & Bregman (1993) allowed the rotational velocity to decrease exponentially away from the cold disk, into a hot low density halo. This distribution still provides a strong cylindrical funnel for the expansion of the wind at low z. Suchkov et al. (1994, hereafter SBHL) provide a more realistic ISM for their modelling of M 82: a two component cold rotating dense disk and non-rotating hot tenuous halo, and a starburst history incorporating the milder mass and energy input from stellar winds before the more energetic supernovae dominated stages. They find bipolar outflows form easily over a wide range in different halo and disk conditions. Shocked halo gas at temperatures [FORMULA] provides the majority of the X-ray emission in their "soft" band ([FORMULA]).

The eventual wind geometry depends on the initial gas distribution and the mass and energy input history. For those models with "mild" early winds (models A1 and A2 in SBHL) biconical outflows of opening angle [FORMULA] with dense disk material entrained along the surface do occur naturally. Initially the mild wind creates a cavity in the disk to the halo for the wind to escape, without substantially damaging the disk. The wind then propagates outward in the halo, sweeping it up and shocking it. In the later SN-driven stage of the starburst, the more vigorous wind does manage to disrupt some of the disk, dragging it out to form a cone within a much larger bubble. This provides a natural explanation for the difference in distribution between the outflow cone seen in H [FORMULA] and the more extended X-ray emission. Without an early mild wind (models B1 and B2), the disk is disrupted before the wind has easy access to the halo, and so no obvious cone in the X-ray is visible. Even when present, the conical wind does not provide appreciable soft X-ray flux compared to the shocked halo (see Figs. 4, 10 and 14 in SBHL), so we would not expect to see such structures in the ROSAT data. The radial extent of the soft X-ray emitting material is much greater than that of the cones, the emission appearing more like a figure-of-eight (Fig. 4 in SBHL) or a cylinder (Fig. 10 in SBHL). None of the models SBHL present would be seen as more conical than cylindrical when projected along the line of sight and observed by a real X-ray instrument. As SBHL did not provide projected surface brightness plots, it is difficult to assess how limb-brightened the emission would be, but given the brightness of the shocked halo material it should be a detectable effect.

The luminosity varies greatly between the different models, and is not simply proportional to the mass and energy input in the starburst. Model A1 has a time averaged mass and energy input an order of magnitude less than model B1, but has a soft ([FORMULA]) luminosity of [FORMULA] at [FORMULA] Myr (when the starburst luminosity is [FORMULA], very close to M 82's bolometric luminosity), well above the [FORMULA] wind luminosity of [FORMULA] derived above for M 82. Model B1 has a corresponding X-ray luminosity of only [FORMULA], despite having a similar initial gas distribution to model A1. Given the wide range of predicted wind luminosity it would require a deeper investigation of the available parameter space to use M 82's luminosity to constrain the allowable models.

SBHL provide "effective" temperatures for the gas in their "soft" band which corresponds well to the ROSAT band, by comparing fluxes in two energy bands of [FORMULA] and [FORMULA], as well as the temperature range for the gas that provides the majority of the soft emission. In all cases the emission is very soft, typically [FORMULA]. The hottest model (B1) has a characteristic temperature of only [FORMULA]. This is still cooler than M 82's wind, where the temperature varies between [FORMULA]. SBHL stress the lack of appreciable amounts of gas hotter than [FORMULA]. The wind itself is much hotter, but provides very little emission, [FORMULA]. The lower temperatures predicted by SBHL do correspond with observations of some galaxies for which soft X-ray emission can be detected. NGC 891 has a halo with [FORMULA] (Bregman & Pildis, 1994), and Wang et al. (1995) detect soft [FORMULA] X-ray emission out to more than [FORMULA] from the plane of NGC 4631. A survey of ROSAT PSPC observation of nearby normal and starburst galaxies by Read et al. (1996) shows that many starbursts have diffuse gas with temperatures [FORMULA], more in line with our results.

The density of the gas responsible for the emission in SBHL's models is typically [FORMULA]. This is not inconsistent with our results of [FORMULA]. The filling factor of the emitting gas in their models we can roughly estimate as [FORMULA], which bring their densities close to ours. The gas mass providing the bulk of the soft emission depends strongly on the model used, but model B1 which has a soft X-ray luminosity similar to that observed for M 82's wind has a gas mass of [FORMULA], comparable with the total mass derived from the PSPC of [FORMULA] for reasonable values of the filling factor.

Previous Section Next Section Title Page Table of Contents

© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998