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Register a new userMatching the Observed Star Formation Intensity Distribution with Empirical Laws
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Authors
Rodger I. Thompson
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This letter matches the shape of the star formation intensity distribution function to empirical laws such as the Schmidt law. The shape of the distribution at a redshift of one is reproduced from the empirical Schmidt law with a critical density, a Schechter distribution of galaxy masses and the assumption that star formation occurs mainly in exponential disks. The shape of the distribution depends primarily on two values, the characteristic mass m* in the Schechter mass distribution and the characteristic radius re in the exponential disk. As these characteristic values evolve they will affect the shape of the distribution function. The expected direction of evolution of the parameters partially cancels each other leaving the distribution shape relatively invariant.
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We investigate the consequences of applying different star formation laws in the galaxy formation model GALFORM. Three broad star formation laws are implemented: the empirical relations of Kennicutt and Schmidt and Blitz & Rosolowsky and the theoretical model of Krumholz, McKee & Tumlinson. These laws have no free parameters once calibrated against observations of the star formation rate (SFR) and gas surface density in nearby galaxies. We start from published models, and investigate which observables are sensitive to a change in the star formation law, without altering any other model parameters. We show that changing the star formation law (i) does not significantly affect either the star formation history of the universe or the galaxy luminosity functions in the optical and near-IR, due to an effective balance between the quiescent and burst star formation modes; (ii) greatly affects the cold gas contents of galaxies; (iii) changes the location of galaxies in the SFR versus stellar mass plane, so that a second sequence of passive galaxies arises, in addition to the known active sequence. We show that this plane can be used to discriminate between the star formation laws.
Recently, Lanzetta et al. (2002) have measured the distribution of star formation rate intensity in galaxies at various redshifts. This data set has a number of advantages relative to galaxy luminosity functions; the effect of surface-brightness dimming on the selection function is simpler to understand, and this data set also probes the size distribution of galactic disks. We predict this function using semi-analytic models of hierarchical galaxy formation in a LCDM cosmology. We show that the basic trends found in the data follow naturally from the redshift evolution of dark matter halos. The data are consistent with a constant efficiency of turning gas into stars in galaxies, with a best-fit value of 2%, where dust obscuration is neglected; equivalently, the data are consistent with a cosmic star formation rate which is constant to within a factor of two at all redshifts above two. However, the practical ability to use this kind of distribution to measure the total cosmic star formation rate is limited by the predicted shape of an approximate power law with a smoothly varying power, without a sharp break.
The observational study of star-formation laws is paramount to disentangling the physical processes at work on local and global scales in galaxies. To this aim we have expanded the sample of extreme starbursts, represented by local LIRGs and ULIRGs, with high-quality data obtained in the 1-0 line of HCN. The analysis of the new data shows that the star-formation efficiency of the dense molecular gas, derived from the FIR/HCN luminosity ratio, is a factor 3-4 higher in extreme starbursts compared to normal galaxies. We find a duality in the Kennicutt-Schmidt laws that is enhanced if we account for the different conversion factor for HCN (alpha_HCN) in extreme starbursts and correct for the unobscured star-formation rate in normal galaxies. We find that it is possible to fit the observed differences in the FIR/HCN ratios between normal galaxies and LIRGs/ULIRGs with a common constant star-formation rate per free-fall time (SFR_ff) if we assume that HCN densities are ~1-2 orders of magnitude higher in LIRGs/ULIRGs, and provided that SFR_ ff~0.005-0.01 and/or if alpha_HCN is a factor of a few lower than our favored values.
We have updated the Munich galaxy formation model to the Planck first-year cosmology, while modifying the treatment of baryonic processes to reproduce recent data on the abundance and passive fractions of galaxies from z= 3 down to z=0. Matching these more extensive and more precise observational results requires us to delay the reincorporation of wind ejecta, to lower the surface density threshold for turning cold gas into stars, to eliminate ram-pressure stripping in haloes less massive than ~10^14 Msun, and to modify our model for radio mode feedback. These changes cure the most obvious failings of our previous models, namely the overly early formation of low-mass galaxies and the overly large fraction of them that are passive at late times. The new model is calibrated to reproduce the observed evolution both of the stellar mass function and of the distribution of star formation rate at each stellar mass. Massive galaxies (M>10^11 [Msun]) assemble most of their mass before z=1 and are predominantly old and passive at z=0, while lower mass galaxies assemble later and, for M<10^9.5 (Msun), are still predominantly blue and star forming at z=0. This phenomenological but physically based model allows the observations to be interpreted in terms of the efficiency of the various processes that control the formation and evolution of galaxies as a function of their stellar mass, gas content, environment and time.
Recent observational results indicate that the functional shape of the spatially-resolved star formation-molecular gas density relation depends on the spatial scale considered. These results may indicate a fundamental role of sampling effects on scales that are typically only a few times larger than those of the largest molecular clouds. To investigate the impact of this effect, we construct simple models for the distribution of molecular clouds in a typical star-forming spiral galaxy, and, assuming a power-law relation between SFR and cloud mass, explore a range of input parameters. We confirm that the slope and the scatter of the simulated SFR-molecular gas surface density relation depend on the size of the sub-galactic region considered, due to stochastic sampling of the molecular cloud mass function, and the effect is larger for steeper relations between SFR and molecular gas. There is a general trend for all slope values to tend to ~unity for region sizes larger than 1-2 kpc, irrespective of the input SFR-cloud relation. The region size of 1-2 kpc corresponds to the area where the cloud mass function becomes fully sampled. We quantify the effects of selection biases in data tracing the SFR, either as thresholds (i.e., clouds smaller than a given mass value do not form stars) or backgrounds (e.g., diffuse emission unrelated to current star formation is counted towards the SFR). Apparently discordant observational results are brought into agreement via this simple model, and the comparison of our simulations with data for a few galaxies supports a steep (>1) power law index between SFR and molecular gas.
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