Astron. Astrophys. 325, 972-986 (1997)

1. Introduction

Assiduous study of spiral galaxies has not yet led to a detailed understanding of their structure, formation and evolution. In particular the physics regulating the formation of stars, and the connection to the global properties of galaxies, is poorly understood. From small scale studies we know that stars form in cold molecular clouds with temperatures below 100 K, but what process is governing the large scale star formation is not clear.

In the last few years several studies have put observational constraints on models of star formation. Kennicutt (1983, 1989) measured the H flux (which is believed to be a measure of the current star formation rate (SFR) of stars with masses in excess of ) for a large sample of spiral galaxies and found a dependence of the SFR on the total gas density that is well described by a power law with index . Recently Ryder & Dopita (1994) obtained photometric CCD imaging data for 34 spiral galaxies. From their I, V and H images, they find a correlation between the surface brightness in the I -band (supposed to measure the surface density of the old, low-mass stars) and the H band. Their conclusion is that the stellar distribution largely controls the SFR and hence the mass distribution.

The theoretical understanding of star formation on large scales and galaxy evolution in general is still in its infancy. The problem is that a wide range of physical processes is involved: gravitational dynamics, hydrodynamics, gas heating and cooling, and stellar evolution. Since all these processes are intimately related, the subject is awfully complicated, and is very hard to tackle analytically. Therefore, at this moment, numerical techniques provide the best possibilities of studying galaxy evolution. Especially the development of N -body codes using a hierarchical tree structure (e.g. Barnes & Hut 1986 , Hernquist 1987 ) is very promising as it does not place any restrictions on spatial resolution or geometry, and the computing time scales only as . The Lagrangian approach of smoothed particle hydrodynamics (SPH; Lucy 1977 , Gingold & Monaghan 1977 ) allows a straightforward inclusion into N -body algorithms. A successful merger of a tree code with an SPH code is TREESPH (Hernquist & Katz 1989 ), which has been used to study the evolution of galaxy mergers (e.g. Barnes & Hernquist 1991 , Mihos & Hernquist 1994 ) and the formation of galaxies (Katz & Gunn 1991 , Katz 1992 ).

The next step is a proper description of star formation in these numerical codes. The inclusion of star formation is difficult for various reasons, both numerical and theoretical. First of all, the physics governing star formation is not well understood. This means that a description of star formation in numerical codes must either be based on simple gravitational instability considerations or must rely on an observational star formation "law" from disk galaxies, where one has to assume that the same law holds in other circumstances.

Second, there is a gap of a factor or so between the size of a galaxy and that of a protostar globule. Since computing time scales as the third power of spatial resolution, this gap will never be bridged. Therefore we must make plausibility arguments for all unresolved processes. Each of the consequent assumptions is a legitimate target for criticism. We try to minimise the damage by choosing star formation criteria that are based on global properties, and thereby maintain a link between the behaviour of the galaxy as a whole and the unresolved small-scale processes. In particular - and we see this as one of our main improvements - our star formation recipe uses a Jeans criterion for the gas as a whole, supplemented with an estimate of the cloud collapse timescale. Thus we forge a connection between the parent galaxy and its small subclouds. In the same vein we calculate cloud heating due to the global radiation field.

Third, there is the computational task of converting gas into stars, which implies many new particles (e.g. Katz 1992 , Navarro & White 1993 ). A sophisticated method has been developed by Mihos & Hernquist (1994), in which gas particles evolve into hybrid gas/star particles and finally into stars, thus keeping the total amount of particles fixed, and yet without constraints on mass conversion from gas to stars. A drawback of their model is that the new star and its parent gas particle are kinematically coupled until the gas is entirely depleted.

An important point of concern is the implementation of radiative heating and cooling processes. Often gas is treated as an isothermal gas. An early attempt to create a truly multi-phase medium is given by Hernquist (1989). Recently, Katz et al. (1996) expanded on previous work and solve for the ionization equilibrium with an ultraviolet radiation background. However in all these models gas is not allowed to cool radiatively below  K (cooling to low temperatures by adiabatic expansion is often allowed), while we know from observations that stars are formed in cold, molecular clouds with temperatures below 100 K.

In order to improve upon this situation, we developed an algorithm in which the gas is heated by the radiation from all stars. The resulting radiation field is position and time dependent, since we follow stellar associations during their evolution. The gas is allowed to have temperatures between 10 and  K, although these high temperatures are never reached (we do not yet include supernovae that could produce them). We use a Jeans instability condition to localize star forming regions, and scale the collapse time for an unstable region directly to the free-fall time. A stellar cluster is formed as soon as the region is unstable longer than the collapse time. In this way we have constructed a self-consistent model where heating and cooling are intimately coupled and direct feedback from star formation is insured. The one major deficiency is that we do not solve the equations of radiative transfer; heating photons are assumed to percolate throughout the galaxy.

In this paper we discuss the importance of a variety of parameters on the outcome of our simulations, and explore some interesting consequences thereof. In Sect. 2we give a detailed description of the star forming algorithm. We explore the parameter space in Sect. 3.2using a model for NGC6503. A detailed analysis of the spatial effects of star formation and the two-phase ISM is given in Sect. 3.3. In Sect. 4we interpret our results as self-regulating star formation and we provide a physical basis for stochastic star formation and galaxy truncation.

© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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