The Superbubble Size Distribution in the Interstellar Medium
of Galaxies
M.S. Oey & C.J. Clarke
We use the standard, adiabatic shell evolution to predict the
differential size distribution N(R) for populations of OB
superbubbles in a uniform ISM. Assuming that shell growth stalls upon
pressure equilibrium with the ambient ISM, and that all shells have
the same lifetime t_e, we derive N(R) for simple cases of
superbubble creation rate and mechanical luminosity function (MLF).
For constant creation and an MLF \phi(L) \propto L^{\beta},
we find that N(R) \propto R^{12\beta} for R < R_e, and
N(R) \propto R^{45\beta} for R > R_e, where the
characteristic radius R_e ~ 1300 pc is the stall radius
associated with t_e. For R < R_e, N(R) is dominated by
stalled objects, while for R > R_e it is dominated by growing
objects. The relation N(R) \propto R^{12\beta}
appears to be quite robust, and also results from the
momentumconserving shell evolution. We predict a peak in
N(R) corresponding to individual SNRs, and suggest that the
contribution of Type Ia SNRs should be apparent in the observed form
of N(R). We present expressions for the porosity parameters,
Q_{2D} and Q_{3D},
derived from our analysis. Q_{2D} is dominated by the largest
superbubbles for \beta < 2 and individual SNRs for \beta > 2,
whereas Q_{3D} is normally dominated by the few largest shells.
We examine evolutionary effects on the HII region luminosity
function (HII LF), in order to estimate \beta. If the
nebular luminosity {\Lha} fades too quickly,
the observed slope a of the HII LF will be steepened, since bright
objects are quickly diminished. We find that for a nebular fading
{\Lha} \propto t^{\eta}, there is a minimum observed slope
a_{min} for the HII LFs, describing the relative importance of
this effect. Empirical measurements all show a > a_{min}, therefore
implying that usually we may take \beta = a.
We also find that if nebular luminosity is instantaneously
extinguished at some given age, rather than continuously fading, no
a_{min} will be observed.
Comparison with the largely complete HI hole catalog for the SMC
shows surprising agreement in the predicted and observed slope of N(R).
This suggests that no other fundamental process is
needed to explain the size distribution of shells in the SMC.
Further comparison with largely incomplete HI data for M31, M33,
and Holmberg II also shows agreement in the slopes, but perhaps
hinting at systematic differences between spiral and Im galaxies.
We estimate porosities that are substantially < 1 for all
of the galaxies except Holmberg II, for which we obtain values
>~ 1. Most of these galaxies therefore may not be strongly
dominated by a hot interstellar component. However, porosity results
for the Galaxy remain inconclusive with the available data.
1997 MNRAS, 289, 570
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