On the inconsistency between cosmic stellar mass density and star   formation rate up to $z\sim8$
  In this paper, we test the discrepancy between the stellar mass density and instantaneous star formation rate in redshift range $0<z<8$ using a large observational data sample. We first compile the measurements of the stellar mass densities up to $z\sim 8$. Comparing the observed stellar mass densities with the time-integral of instantaneous star formation history, we find that the observed stellar mass densities are lower than that implied from star formation history at $z<4$. We also use Markov chain monte carlo method to derive the best-fitting star formation history from the observed stellar mass density data. At $0.5<z<6$, the observed star formation rate densities are larger than the best-fitting one, especially at $z\sim2$ where by a factor of about two. However, at lower ($z<0.5$) and higher redshifts ($z>6$), the derived star formation history is consistent with the observations. This is the first time to test the discrepancy between the observed stellar mass density and instantaneous star formation rate up to very high redshift $z\approx8$ using the Markov chain monte carlo method and a varying recycling factor. Several possible reasons for this discrepancy are discussed, such as underestimation of stellar mass density, initial mass function and cosmic metallicity evolution. 
H. Yu, F. Y. Wang (NJU)
astro-ph.GA astro-ph.CO astro-ph.HE