The intrinsic SFRF and sSFRF of galaxies: comparing SDSS observation with IllustrisTNG simulation

The star formation rate function (SFRF) and specific star formation rate function (sSFRF) from the observation are impacted by the Eddington bias, due to the uncertainties on the estimated SFR. We develop a novel method to correct the Eddington bias and obtained the intrinsic SFRF and sSFRF from the Sloan Digital Sky Survey Data Release 7. The intrinsic SFRF is in good agreement with measurements from previous data in the literature that relied on UV SFRs but its high star-forming end is slightly lower than those IR and radio tracers. We demonstrate that the intrinsic sSFRF from SDSS has a bi-modal form with the one peak found at ${\rm sSFR \sim 10^{-9.7} yr^{-1}}$ representing the star-forming objects while the other peak is found at ${\rm sSFR \sim 10^{-12} yr^{-1}}$ representing the quenched population. Furthermore, we compare our observations with the predictions from the IllustrisTNG and Illustris simulations and show that the ``TNG'' model performs much better than its predecessor. However, we show that the simulated SFRF and cosmic star formation density (CSFRD) of TNG simulations are highly dependent on resolution, reflecting the limitations of the model and today state-of-the-art simulations. We demonstrate that the bi-modal, two peaked sSFRF implied by the SDSS observations does not appear in TNG regardless of the adopted box-size or resolution. This tension reflects the need for inclusion of an additional efficient quenching mechanism to the TNG model.