2. Model interstellar medium
An axisymmetric model for the ISM was constructed by Ferrière (1998), based on the best-to-date observational data on the interstellar gas, cosmic rays, and magnetic fields, on the Galactic rotation curve and vertical gravitational acceleration, and on the parameters of the SN distribution. The available observational information, which contains several important gaps (mainly with regard to the hot gas component), was complemented with the requirement that the ISM be in hydrostatic equilibrium and with theoretical considerations on the radial dependence of the hot gas column density and scale height. It was thus fit into a comprehensive picture that represents, at best, the true ISM.
In this picture, the ISM is composed of a molecular medium, a cold neutral medium (CM), a warm neutral medium (WNM), a warm ionized medium (WIM), and a hot ionized medium (HM), respectively denoted by the subscripts and . Hydrogen is completely neutral in the CM and in the WNM, while it is completely ionized in the WIM and in the HM. Helium, which represents 9% of hydrogen by number, is everywhere fully neutral except in the HM where it is doubly ionized.
The space-averaged number density of hydrogen nuclei in the different media is given as a function of Galactic radius, , and height, , by
and kpc being the IAU recommended value of the Galactocentric radius at the Sun.
The space-averaged total interstellar mass density is obtained by summing the partial densities contributed by the different media:
where is the proton rest mass and the factor 1.36 accounts for the 9% by number of helium. The -dependence of is plotted in Fig. 1a at three different Galactic radii: kpc (dotted line), (solid line), and kpc (dashed line). To give a better idea of how the interstellar mass is radially distributed, we also plotted, in Fig. 1b, the R -dependence of the total column density of interstellar hydrogen nuclei through the Galactic disk, .
The space-averaged interstellar thermal pressure can be written as a sum over the four true ISM phases (which do not include the molecular gas):
where is Boltzmann's constant, are the temperatures, assumed to be uniform with the standard values K, K and K, and the numerical factors include the helium abundance and the ionization fractions given above.
The space-averaged interstellar turbulent pressure arising from random bulk motions is
with the one-dimensional turbulent velocities in the molecular and cold neutral media equal to km s-1 and km s-1.
The interstellar CR and magnetic pressures are
where the factor inside the brackets reflects the spatial dependence of the synchrotron emissivity, and the exponents and are given by the implicit equations
in particular, , and .
In Fig. 2, we show the space-averaged total interstellar pressure,
at our three reference radii, and in Fig. 3, we show the average interstellar signal speed defined by
Regarding the Galactic rotation curve, we assume that the rotation velocity, V, increases linearly from the center to kpc, varies quadratically between 3 and 5 kpc, and remains equal to 220 km s beyond 5 kpc. The corresponding rotation rate,
and shear rate,
are displayed in Fig. 4 as a function of .
For the vertical component of the Galactic gravitational acceleration we take
With our adopted rotation law, the last term vanishes and we obtain the vertical profiles of Fig. 5.
The last important ingredient of the model is the SN distribution. Type Ia SNs (hereafter denoted by SNI) arise from old degenerate stars and have a rate per unit volume
Type Ibc and Type II SNs (hereafter denoted by SNII) result from the core collapse of young massive stars. 40% of them are isolated and have a rate per unit volume
leading to a total isolated SN rate per unit volume
The other 60% are clustered and partake to the formation of SBs at a rate per unit volume
where is the molecular scale height, given below Eq. (1). The number, , of SNs contributing to one SB varies between and , with an average of , and is distributed according to
Fig. 6a displays the vertical dependence of the SN and SB rates per unit volume at the three reference Galactic radii, while Fig. 6b gives the radial dependence of the corresponding rates per unit area, , and . The Galactic frequency of isolated SNs, obtained from an integration of Eq. (18) across the Galactic disk, is 1/(101 yr). For comparison, a spatial integration of Eq. (19) yields a SB frequency of 1/(2600 yr), corresponding to a clustered SN frequency of 1/(87 yr). Hence, it appears that isolated SNs are almost as frequent as their clustered counterparts.
© European Southern Observatory (ESO) 1998
Online publication: June 18, 1998