Models of the Interstellar Medium

McKee and Ostriker have tried to put all the wisdom of the ISM at the time (1977) into a coherent picture, coined the three-phase ISM model [39]. One of the most interesting features is the transformation of the "phases" into one another by

Fig. 18.3 Merged image of three XMM-Newton EPIC-pn observations of the Ophiuchus molecular cloud in the 0.5 — 0.9 keV band with IRAS 100 ^m contours overlaid. The cloud casts a shadow onto the X-ray background; the X-ray intensity is anticorrelated with the absorption by the molecular cloud (taken from [18])

Fig. 18.3 Merged image of three XMM-Newton EPIC-pn observations of the Ophiuchus molecular cloud in the 0.5 — 0.9 keV band with IRAS 100 ^m contours overlaid. The cloud casts a shadow onto the X-ray background; the X-ray intensity is anticorrelated with the absorption by the molecular cloud (taken from [18])

different physical processes, such as e.g., radiative cooling, heat conduction, pho-toionization, and evaporation. The underlying assumption of the model is that the ISM is in global pressure equilibrium according to Spitzer's principle [64]. This might be expected with some optimism, if self-regulation is the dominant feature: on the one hand supernova explosions, and to a minor extent stellar winds and HII

regions, inject energy locally. The expansion of remnants and bubbles will distribute it across the disk. A simple estimate shows that practically every point in the ISM within the star-forming Galactic disk will be overrun by a hot bubble within about 107 yrs or less. On the other hand, both radiative and adiabatic cooling will prevent the disk from disruption - a boiling pot needs pressure release valves to prevent explosion. One of these has been ignored in the original three-phase model, viz. the Galactic fountain, proposed by [55] to reconcile observations of the 1/4 keV SXRB with the existence of highly ionized species such as OVI. It is, therefore, not too surprising that the three-phase model in its original form fails, e.g., in the predicted volume filling factors of the diffuse ionized gas (DIG) and especially of the HIM; the latter was predicted at least a factor of 2 too high. The fountain model gained wider attraction, when observations of supershells [26] and superbubbles [10] argued for about half of the supernova explosions to occur in associations (spatially and temporally correlated). This could lead to locally highly overpressured regions, which were hard to confine to the Galactic disk, although strong disk parallel magnetic fields were sometimes invoked to prevent break-out into the halo. These findings are summarized in another analytical model, the so-called "chimney" model [41]. Here break-out and establishment of the fountain flow was accounted for, but the physics of break-out was rather simplistic.

A heavily nonlinear system, such as the ISM, is however very sensitive to changes in the initial conditions, as it is known from deterministic chaos theory. Therefore, the richness of phenomena cannot be covered in an analytical model, and detailed numerical simulations are required. A comparison to the weather forecast might be appropriate. Short term predictions are generally very reliable, but as soon as nonlinear terms in the underlying equations of the system become important, the system undergoes bifurcations and breaks out into chaotic behavior, with e.g., Lorenz attractors being just a very simple representation.

The ISM is a multicomponent (containing gas, dust particles, cosmic rays, magnetic fields), and with respect to the gas, a multiphase (cold neutral medium, warm neutral medium, warm ionized medium, hot ionized medium) system. The fact that at least locally the energy density in the major components, gas (and here separately for kinetic, thermal and turbulent energy density), magnetic field and cosmic rays, amongst others, is comparable and of the order of about 1eVcm-3, suggests that interaction between these components should be strong. As we shall see this is indeed the case. Having stressed this, it is clear that further progress in our understanding of the ISM must rely on numerical simulations, supplemented by the tools of nonlinear dynamics. Earlier work (e.g., [30,51,71,74]) clearly showed the multiphase structure of the ISM and its turbulent nature, but remains exploratory, because of severe restrictions such as e.g., limited grid size, simulation in only two dimensions, too short evolution time scales. Therefore, in the remainder of this section most recent 3D high resolution simulations on large grids, based on adaptive mesh refinement, will be discussed [3,4].

The magnetohydrodynamical (MHD) equations are solved on a Cartesian grid of 0 < (x, y) < 1 kpc size in the Galactic plane and extending -10 < z < 10kpc into the halo. This will ensure the full tracking of the Galactic fountain flow. The grid is centered on a typical ISM patch on the orbit of the Sun around the Galactic center, with a finest adaptive mesh refinement resolution of 1.25 pc in the layer -1 < z < 1 kpc. Following the observations, basic physical ingredients of the model are: (i) massive star formation in regions of converging flows (V • v < 0, where v is the gas velocity) where density and temperature are n > 10 cm-3 and T <100K, respectively; (ii) the distribution of masses and individual life times of stars are derived from a Galactic initial mass function; (iii) supernova explosions occur at a Galactic rate and with a canonical energy of 1051 erg (including the scale height distributions of types Ia, Ib, and II); (iv) the gas is immersed in a gravitational field provided by the stellar disk following [31]; (v) radiative cooling, assuming an optically thin gas in collisional ionization equilibrium, with a temperature cut off at 10 K, and uniform heating due to starlight varying with z [77] *; (vi) an initially disk parallel magnetic field composed of random (Br) and uniform (Bu) components, with total field strength of 4.5|G (Bu = 3.1 and Br = 3.3|G). The establishment of the fountain flow up to heights of 5 - 10 kpc in the vertical direction takes about 100 - 200 Myr, so that a simulation time of 400 Myr seems adequate to recover the main features. Boundary conditions are periodic on the side walls of the computational box and outflow on its top and bottom.

The results are quite remarkable. Figure 18.4 shows the vertical distribution of the magnetic field (left panel) and the corresponding density (right panel) after 330Myr of evolution. The former shows a detailed loop structure of the field, with large scale outflow in between. Therefore, an important result is that break-out of the disk cannot be inhibited, but only delayed. Once holes have been punched into the thick disk, the flow is channelled through them and out into the halo. The density distribution in z-direction exhibits a thin dense gas disk, with clouds ascending into and descending from the halo, i.e., the disk-halo-disk circulation is in full swing. Inspection of corresponding cuts parallel to the disk (see Fig. 18.5) reveals a filamentary structure of the magnetic field (left panel). Most interesting is the temperature distribution (right panel). First, hot bubbles with temperatures in excess of 106 K are clearly visible, and in case they are more evolved, i.e., larger in size, they are also elongated. This must be an effect of the magnetic field. Suppose the initial field was parallel to the disk. Then, as the bubble radius increases magnetic tension forces become stronger, and expansion along the field will prevail. It may even be possible that toward the end of expansion, provided that the bubble is not disrupted by nearby explosions, Maxwell stresses will cause the bubble to shrink again. Second, the cold medium exhibits a filamentary structure with lots of small-scale wiggles arising from turbulent motions.

Gas associated with bubbles should be clearly visible in soft X-rays, namely in Ovii, whereas the ubiquitous Ovi absorption line mainly traces gas in old remnants. Our long term simulations show that the volume filling factors in the disk are quite different from the three-phase model, in particular for the hot gas. Irrespective of the presence of a magnetic field, it is always less than 25%, in agreement with the disk

* It has been pointed out that the plasma is out of ionization equilibrium in many regions [6,7]; the implementation of non-equilibrium ionization (NEI) simulations is underway.

AMR Level 2 Image 130.00 M

AMR Level 2 Image 130.00 m

AMR Level 2 Image 130.00 M

AMR Level 2 Image 130.00 m

Fig. 18.4 Large scale numerical hydro- and magnetohydrodynamic simulations of a supernova driven ISM performed on parallel computers with typically 1 million hours of CPU time per run. The vertical distribution (perpendicular to the midplane) of the magnetic field (left panel) and the density (right panel) are shown at time t = 330 Myr for a mean field of 3 ||G. The disk stretches horizontally from z = 0 (midplane), and the extension into the halo reaches z = ±10kpc (abscissa range 1 kpc, ordinate range ±10kpc). The color coding is red/blue for low/high field (logarithmically 10—2 — 101 |G) and density (logarithmically 10—3 — 101 cm-3), respectively. The break-out of superbubbles through the disk, and the generation of magnetic loops in the lower halo is striking

coverage of supershells in our and in external galaxies. The main reason for these low values is the pressure release in the disk because of the set-up of the fountain flow. It should be stressed at this point that numerical simulations can be rather arbitrary if they are resolution dependent. Therefore, it is reassuring that the filling factors shown in Table 18.1 do not change when the resolutions is increased by a factor of 2 (i.e., to 0.625 pc).

Another result that could not be derived from the analytical model is the large amount of turbulence in the ISM. This is not completely unexpected in a supernova

Fig. 18.5 The distribution of magnetic field (left panel) and the temperature (right panel) in the Galactic disk at time t = 358 Myr for a mean field of 3 ||G. The color coding is the same as in Fig. 18.4. Note the elongated bubbles in the disk, and the filamentary structure of the cold (~100 K) gas (from [4])

Fig. 18.5 The distribution of magnetic field (left panel) and the temperature (right panel) in the Galactic disk at time t = 358 Myr for a mean field of 3 ||G. The color coding is the same as in Fig. 18.4. Note the elongated bubbles in the disk, and the filamentary structure of the cold (~100 K) gas (from [4])

Table 18.1 Summary of the average values of volume filling factors, mass fractions, and root mean square velocities of the disk gas at the different thermal regimes for pure hydrodynamical (HD) and MHD runs, taken from Avillez and Breitschwerdt (2005)

[K]

<fv;

)a [%]

<fM)

b [%]

<vrms Y

HD

MHD

HD

MHD

HD

MHD

<200 K

5

6

44.2

39.9

7

10

200 -1039

46

29

49.0

43.7

15

15

1039 -104 2

10

11

4.4

8.5

25

21

104'2 -1055

22

33

2.0

7.4

39

28

>1055

17

21

0.3

0.5

70

55

a Occupation fraction (volume filling factor) b Mass fraction c Root mean square velocity in units of km s_1

driven ISM, since expanding bubbles and colliding streams of gas generate lots of shear and vorticity. As the simulations show, turbulent mixing between hot and cold gas is fairly efficient, and there seems to be no need for heat conduction to promote phase transitions as in the three-phase model. A rather surprising result of these simulations, obtained by massively parallel computing is the amount of gas in classical thermally unstable regimes. Most of the disk mass is found in the T < 1039 K gas, with the cold (T < 200 K) and thermally unstable gases (200 < T < 1039 K) harboring on average 80 and 90% of the disk mass in the MHD and HD runs. About 55-60% of the thermally unstable gas (200 < T < 103 9 K) has 500 < T <5000 K in both runs, consistent with recent observations of the warm neutral medium [27].

An explanation for such an unexpected behavior, contradicting all analytical models, in particular the failure of the [14] criterion, may be found in the role turbulence (both supersonic and superalfvenic) plays. Turbulence can have a stabilizing effect thereby inhibiting local condensation modes. The situation is reminiscent of the existence of the solar chromosphere, consisting of gas at around 105 K in the thermally unstable regime. Here, heat conduction can prevent thermal runaway on small scales. In other words, diffusion processes may have a stabilizing effect. In our case, it is turbulent diffusion that replaces the role of conduction, again, most efficient for large wavenumbers. The turbulent viscosity vturb — Re vmoi can be orders of magnitude larger than the molecular viscosity, vmol; here Re is the Reynolds number of the highly turbulent flow. Therefore, with increasing eddy wavenumber, the eddy crossing time becomes shorter than the cooling time.

These new and exciting findings have provided new insight into the complex behavior of the ISM, and have opened up new paths to follow. However, it is fair to state that both on the observational and theoretical side, there are still more questions open than have been solved.

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