Probing ISM Models with H observations

Turbulent Models of the ISM

Massive stars are probably the most important energy sources for the ISM. They inject power both in radiative (with ionizing photons creating HII regions) and mechanical (supernova explosions) form. The rate of kinetic energy density deposited via photoionization is
 
the analogous quantity for a supernova explosion is
 
where is the total (both Type I and II) supernova rate and is the volume of the Galaxy (McKee 1990, Ricotti et al. 1997). Assuming an efficiency of kinetic energy conversion into the ISM and (Spitzer 1978) for radiative and mechanical input, respectively, we find the total rate per unit volume at which energy available for motions in the ISM is produced:  ergs  cm s. Kinetic energy is mostly dissipated by cloud collisions at a rate
 
where and are the typical cloud density, relative velocity and the mean time interval between collisions, respectively. Thus, there is clearly enough energy production to support the observed motions in the ISM.

These bulk motions have a strong impact on the structure of the Galactic ISM. For example, they are shown to largely regulate and reproduce the vertical distribution of the HI in the gravitational potential of the Galaxy (Lockman & Gehman 1991), once the effect of radiation pressure on dust grains embedded in clouds (the so-called ``photolevitation'', Ferrara 1993) is properly taken into account. In addition, turbulence may be the most important form of energy storage in the ISM, as can be appreciated from Fig. 1: the thermal pressure contributed by all known gaseous ISM phases, , appears to be at most 13% of the total pressure, , as derived by imposing gas hydrostatic equilibrium in the galactic gravitational field. Such a large ratio of the turbulent to thermal pressure implies a large porosity factor, Q, of the hot gas. McKee (1990) estimates that , implying Q=0.92 from the above estimates if the non-thermal energy is predominantly in turbulent form; this corresponds to a hot gas filling factor .

Given these arguments it seems necessary to revise the current ISM models to include turbulence. A first attempt in this direction has been carried out by Norman & Ferrara (1996). The authors calculate the detailed grand source function (shown in Fig. 2) for the conventional sources of turbulence from supernovae, superbubbles, stellar winds and HII regions. As seen from Fig. 2, superbubbles are the main contributors to interstellar turbulence. In addition, from the study of the general properties of the turbulent spectrum using an approach based on a spectral transfer equation derived from the hydrodynamic Kovasznay approximation, they conclude that the turbulent pressure calculated from the grand source function is . Also, given the scale dependent energy dissipation from a turbulent cascade, the multi-phase medium concept has to be generalized to a more natural continuum description where density and temperature are functions of scale.

  
Figure 2: Normalized turbulent source functions for supernovae, superbubbles, winds and HII regions. Solid lines show the sum of primary and secondary shock contributions for each source; dashed lines show secondary shocks only (see Norman & Ferrara 1996). The thick line is the total grand source function.

As recalled above, cloud collisions represent the most efficient dissipation mechanism of large scale turbulence. The simple estimate for given above, assumes that all the kinetic energy of the clouds is radiated away by the post-shock gas, i.e. an inelastic collision. This hypothesis is correct only in a restricted region of the collision parameters (velocity and mass ratio of the colliding clouds, magnetic field strength, gas metallicity). Ricotti etal. 1997 have studied the dependence of the elasticity (defined as the ratio of the final to the initial kinetic energy of the clouds) on such parameters (recently extended to include pre-interaction with the intercloud medium by Miniati etal. 1997). They find that (i) the collision elasticity is maximum for a cloud relative velocity km s; (ii) the elasticity is , where Z is the metallicity and is the cloud size: the larger is , the more dissipative (inelastic) the collision will be. During the collision the warm post-shock gas will radiate a substantial fraction of its internal energy in the H line depending on and . Fig. 3 shows the H luminosity for a collision occurring  kpc away from us for different values of and . Thus, H observations can be used in principle as a powerful indicator of large scale turbulent motion dissipation.

  
Figure 3: H luminosity evolution from cloud collisions at a distance of 1 kpc as a function of time in units of collision time (). The upper (lower) group of lines refer to a cloud size  pc ( pc) for different values of the relative velocity of the collision:  km  (solid),  km  (long-dashed),  km  (short-dashed ),  km  (dotted)

© Copyright Astronomical Society of Australia 1997