ON THE INCONSISTENCY BETWEEN COSMIC STELLAR MASS DENSITY AND STAR FORMATION RATE UP TO z ∼ 8

In this paper, we test the discrepancy between the stellar mass density (SMD) and instantaneous star formation rate in the redshift range 0 < z < 8 using a large observational data sample. We first compile the measurements of SMDs up to z similar to 8. Comparing the observed SMDs with the time-integral of instantaneous star formation history (SFH), we find that the observed SMDs are lower than that implied from the SFH at z < 4. We also use the Markov chain Monte Carlo (MCMC) method to derive the best-fitting SFH from the observed SMD data. At 0.5 < z < 6, the observed star formation rate densities are larger than the best-fitting one, especially at z similar to 2 where they are larger by a factor of about two. However, at lower (z < 0.5) and higher redshifts (z > 6), the derived SFH is consistent with the observations. This is the first time that the discrepancy between the observed SMD and instantaneous star formation rate has been tested up to very high redshift z approximate to 8 using the MCMC method and a varying recycling factor. Several possible reasons for this discrepancy are discussed, such as underestimation of SMD, initial mass function, and evolution of cosmic metallicity.