Galactic porosity and a star formation threshold for the escape of ionising radiation from galaxies

The spatial distribution of star formation within galaxies strongly affects the resulting feedback processes. Previous work has considered the case of a single, concentrated nuclear starburst, and also that of distributed single supernovae (SNe). Here, we consider ISM structuring by SNe originating in spatially distributed clusters having a cluster membership spectrum given by the observed HII region luminosity function. We show that in this case, the volume of HI cleared per SN is considerably greater than in either of the two cases considered hitherto. We derive a simple relationship between the ``porosity'' of the ISM and the star formation rate (SFR), and deduce a critical SFR_crit, at which the ISM porosity is unity. This critical value describes the case in which the SN mechanical energy output over a timescale t_e is comparable with the ISM ``thermal'' energy contained in random motions; t_e is the duration of SN mechanical input per superbubble. This condition also defines a critical gas consumption timescale t_exh, which for a Salpeter IMF and random velocities of \simeq 10 km s-1 is roughly 10e10 years. We draw a link between porosity and the escape of ionising radiation from galaxies, arguing that high escape fractions are expected if SFR >~ SFR_crit. The Lyman Break Galaxies, which are presumably subject to infall on a timescale < t_exh, meet this criterion, as is consistent with the significant leakage of ionising photons inferred in these systems. We suggest the utility of this simple parameterisation of escape fraction in terms of SFR for semi-empirical models of galaxy formation and evolution and for modeling mechanical and chemical feedback effects.Comment: Accepted to MNRAS. 11 pages, 1 figure; uses mn2e.cls (included

The Superbubble Size Distribution in the Interstellar Medium of Galaxies

We use the standard, adiabatic shell evolution to predict the size distribution N(R) for populations of OB superbubbles in a uniform ISM. We derive N(R) for simple cases of superbubble creation rate and mechanical luminosity function (MLF). For R < the characteristic radius R_e, N(R) is dominated by stalled objects, while for R>R_e it is dominated by growing objects. We also briefly investigate N(R) resulting from momentum-conserving shell evolution. We predict a peak in N(R) corresponding to individual SNRs. To estimate the MLF, we also examine evolutionary effects on the HII region luminosity function (HII LF), finding that for nebular luminosity fading as a power law in time, there is a minimum observed slope for the HII LFs. Comparison with the largely complete HI hole catalog for the SMC shows surprising agreement in the predicted and observed slope of N(R), suggesting 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 is also encouraging. We present expressions for the ISM porosity parameters, and estimate that they are substantially <1 for all of the galaxies except Holmberg II. Most of these galaxies therefore may not be strongly dominated by a hot interstellar component. However, porosity results for the Galaxy remain inconclusive.Comment: 25 pages, MN latex, 4 figures. MNRAS accepted. Complete abstract and preprint also available at http://ast.cam.ac.uk/~oey/oeypubs.htm

The Bell-Szekeres Solution and Related Solutions of the Einstein-Maxwell Equations

A novel technique for solving some head-on collisions of plane homogeneous light-like signals in Einstein-Maxwell theory is described. The technique is a by-product of a re-examination of the fundamental Bell-Szekeres solution in this field of study. Extensions of the Bell-Szekeres collision problem to include light-like shells and gravitational waves are described and a family of solutions having geometrical and topological properties in common with the Bell-Szekeres solution is derived.Comment: 18 pages, Latex fil

An extension theorem for conformal gauge singularities

We analyse conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem.Comment: 43 pages, no figures, version as published in JMP, small changes, updated reference

Statistical Confirmation of a Stellar Upper Mass Limit

We derive the expectation value for the maximum stellar mass (m_max) in an ensemble of N stars, as a function of the IMF upper-mass cutoff (m_up) and N. We statistically demonstrate that the upper IMF of the local massive star census observed thus far in the Milky Way and Magellanic Clouds clearly exhibits a universal upper mass cutoff around 120 - 200 M_sun for a Salpeter IMF, although the result is more ambiguous for a steeper IMF.Comment: PDF, 5 pages, 4 figures. Accepted to the Astrophysical Journal Letter