Annu. Rev. Astron. Astrophys. 1984. 22: 37-74 Copyright © 1984 by Annual Reviews. All rights reserved

4.3 SSPSF: A Possible Model

Much work has been done on the theory of density-wave-induced star formation in spiral galaxies, but it is only recently that the first major theory of global star formation processes applicable to Irrs was developed. The stochastic self-propagating star formation (SSPSF) model is one in which star formation is continued through the energy dumped back into the interstellar medium by evolving massive stars through HII region expansions, stellar winds, and supernovae (for a review, see 316). Theoretical models of galaxian evolution with this mechanism were first computed by Mueller & Arnett (252) and have been developed extensively by Gerola, Seiden, and collaborators (130, 131, 315) as well as others (64, 116).

In the SSPSF models of Gerola & Seiden, a two-dimensional galaxy is divided into cells that represent the average size of distinct star-forming complexes; Comins (64) has extended this approach to three dimensions. The probability that a cell will form stars is greatly incraesed if an adjacent region formed stars in a previous time step, i.e. star formation stimulates further star formation as suggested by Opik (256). Once a cell has formed stars, it is initially unable to produce any further stars, and the probability of further star formation thereafter increases as a function of time corresponding to the replenishment of cool gas supplies.

Models of low-mass galaxies with little or no differential rotation (64, 108, 131) produce systems with chaotic morphologies and properties (metallicity, stellar content, etc.) that depend primarily on the ratio of galaxy size to the size of star-forming cells. A smaller galaxy has a low average star formation rate, but the rate fluctuates widely between bursts and quiescent levels as cells individually and in small groups experience star formation. Larger systems exhibit a more constant and higher mean star formation rate and display more morphological structure as sites of current star formation activity move around the disk. Because of their higher mean star formation rates, the larger galaxies will be more evolved and hence have higher metallicities and lower fractional gas masses. Even in larger galaxies, however, collective effects can lead to significant nonrandom time variations in total stellar birthrates (317), which could explain the existence of luminous systems in apparent burst states.

Quantitative comparisons between the SSPSF models and observations are not easy. Measurements of the sizes of H complexes in nearby (< 10 Mpc) high surface brightness Irrs indicate that the concept of an average ``cell'' size may not be entirely arbitrary (169, 188, 203, 204, 297). Therefore, the models predict that for a fixed cell size the gas fraction and average metallicity should correlate with galaxy size. In fact, no clean relationships are seen, although very small galaxies do tend to be the most metal poor and gas rich (189, 190, 238). Similarities between the mean colors of galaxies covering a considerable range in optical size also present a problem for basic SSPSF models. Morphologically the models reproduce reasonable Irrs. Star formation in many Irrs is not observed to be purely random, and any successful model must account for this fact. But SSPSF is not a unique answer. Ultimately the local gas characteristics, such as density, will determine when and where the star formation occurs. The origin of these density fluctuations could be associated with a variety of other mechanisms, such as the global velocity field, gas infall, magnetic field structures, etc., which could also act to organize star formation.

Direct evidence for propagation of star formation from one cloud complex or cell to a neighboring cell is lacking. The simplest version of SSPSF, in which star-forming events directly stimulate preexisting analogues to interstellar clouds, therefore may not apply to real galaxies. Sequential star formation within a cloud complex has been observed in the Galaxy (cf. 217), which could be interpreted as star-induced star formation, but again this is within a cell rather than between cells. Measurements of the energetics of HII regions show that considerable amounts of energy from massive stars are being dumped back into the interstellar medium (cf. 188). And we can see in nearby galaxies that the process of star formation does have a large effect on the interstellar medium; HI holes centered on NGC 206 in the M31 spiral (40) and the LMC's Constellation III (243, 383), as well as the supershells in our Galaxy (152), are examples. However, we still do not know what ultimate effects star formation may have on interstellar gas and whether these are sufficient to allow star formation to propagate on galactic scales. Until this problem is overcome, SSPSF will not be on a physically sound basis, although it should be emphasized that this theory provides a very general framework (316, 324, 325) in which the role of feedback (either positive or negative) in star formation processes can be readily examined.