We introduce a simple model to explore the star formation histories of disk galaxies. We assume that the disk origins and grows by continuous gas infall. The gas infall rate is parametrized by the Gaussian formula with one free parameter: infall-peak
time $t_p$. The Kennicutt star formation law is adopted to describe how much cold gas turns into stars. The gas outflow process is also considered in our model. We find that, at given galactic stellar mass $M_*$, model adopting late infall-peak time $t_p$ results in blue colors, low metallicity, high specific star formation rate and high gas fraction, while gas outflow rate mainly influences the gas-phase metallicity and star formation efficiency mainly influences the gas fraction. Motivated by the local observed scaling relations, we construct a mass-dependent model by assuming low mass galaxy has later infall-peak time $t_p$ and larger gas outflow rate than massive systems. It is shown that this model can be in agreement with not only the local observations, but also the observed correlations between specific star formation rate and galactic stellar mass $SFR/M_* sim M_*$ at intermediate redshift $z<1$. Comparison between the Gaussian-infall model and exponential-infall model is also presented. It shows that the exponential-infall model predicts higher star formation rate at early stage and lower star formation rate later than that of Gaussian-infall. Our results suggest that the Gaussian infall rate may be more reasonable to describe the gas cooling process than the exponential infall rate, especially for low-mass systems.
We investigate the radial color gradients of galactic disks using a sample of about 20,000 face-on spiral galaxies selected from the fourth data release of the Sloan Digital Sky Survey (SDSS-DR4). We combine galaxies with similar concentration, size
and luminosity to construct composite galaxies, and then measure their color profiles by stacking the azimuthally averaged radial color profiles of all the member galaxies. Except for the smallest galaxies (R_{50}<3 kpc), almost all galaxies show negative disk color gradients with mean g-r gradient G_{gr}=-0.006 mag kpc^{-1} and r-z gradient G_{rz}=-0.018 mag kpc^{-1}. The disk color gradients are independent of the morphological types of galaxies and strongly dependent on the disk surface brightness mu_{d}, with lower surface brightness galactic disks having steeper color gradients. We quantify the intrinsic correlation between color gradients and surface brightness as G_{gr}=-0.011mu_{d}+0.233 and G_{rz}=-0.015mu_{d}+0.324. These quantified correlations provide tight observational constraints on the formation and evolution models of spiral galaxies.
We have examined some basic properties of damped Ly$alpha$ systems(DLAs) by semi-analytic model. We assume that DLA hosts are disk galaxies whose mass function is generated by Press-Schechter formulism at redshift 3. Star formation and chemical evolu
tion undergo in the disc. We select modelled DLAs according to their observational criterion by Monte Carlo simulation using random line of sights and disk inclinations. The DLA ages are set to be 1 to 3 Gyr. By best-fitting the predicted metallicity distribution to the observed ones, we get the effective yield for DLAs about $0.25Z_{odot}$. On the basis of this constrain, we further compared our model predictions with observations at redshift 3 in the following items: number density; gas content; HI frequency distribution; star formation rate density; relationship between metallicity and HI column density. We found that the predicted number density at redshift 3 agree well with the observed value, but the gas content $Omega_{DLA}$ is about 3 times larger than observed since our model predicts more DLA systems with higher column density. The frequency distribution at higher HI column density is quite consistent with observation while some difference exists at lower HI end. The predicted star formation rate density contributed by DLAs is consistent with the most recent observations. Meanwhile, the connection between DLAs and Lyman Break galaxies(LBGs) is discussed by comparing their UV luminosity functions which shows that the DLAs host galaxies are much fainter than LBGs. However, there is a discrepancy between model prediction and observation in the correlation between metallicity and HI column density for DLAs. Further investigations are needed for the star formation mode at high redshift environments.
Based on the disk galaxy formation theory within the framework of standard LCDM hierarchical picture, we selected modelled DLAs, according to their observational criterion, by Monte Carlo simulation with the random inclinations being considered, to e
xamine their observed properties. By best-fitting the predicted metallicity distribution to the observed ones, we get the effective yield for DLAs about 0.25Z_sun, which is comparable to those for SMC and LMC. And the predicted distribution is the same as that of observation at the significant level higher than 60%. The predicted column density distribution of modelled DLAs is compared with the observed ones with the corresponding number density, gas content being discussed. We found that the predicted number density n(z) at redshift 3 agree well with the observed value, but the gas content Omega_DLA is about 3 times larger than observed since our model predicts more DLA systems with higher column density. It should be noted that the predicted star formation rate density contributed by DLAs is consistent with the most recent observations if the star formation timescale in DLAs is assumed to be 1 to 3 Gyr. Meanwhile, the connection between DLAs and LBGs is discussed by comparing their UV luminosity functions which shows that the DLAs host galaxies are much fainter than LBGs. We also predict that only few percent of DLAs can host LBGs which is also consistent with current observations. However, there is a discrepancy between model prediction and observation in the correlation between metallicity and HI column density for DLAs. We suggest that this could result from either the inadequacy of Schmidt-type star formation law at high redshift, the diversities of DLA populations, or the model limitations.
