Stellar Mass Function of Active and Quiescent Galaxies via the Continuity Equation

Abstract

The continuity equation is developed for the stellar mass content of galaxies, and exploited to derive the stellar mass function of active and quiescent galaxies over the redshift range z ∼ 0 − 8. The continuity equation requires two specific inputs gauged on observations: (i) the star formation rate functions determined on the basis of the latest UV+far-IR/sub-mm/radio measurements; (ii) average star-formation histories for individual galaxies, with different prescriptions for discs and spheroids. The continuity equation also includes a source term taking into account (dry) mergers, based on recent numerical simulations and consistent with observations. The stellar mass function derived from the continuity equation is coupled with the halo mass function and with the SFR functions to derive the star formation efficiency and the main sequence of star-forming galaxies via the abundance matching technique. A remarkable agreement of the resulting stellar mass function for active and quiescent galaxies, of the galaxy main sequence and of the star-formation efficiency with current observations is found; the comparison with data also allows to robustly constrain the characteristic timescales for star formation and quiescence of massive galaxies, the star formation history of their progenitors, and the amount of stellar mass added by in-situ star formation vs. that contributed by external merger events. The continuity equation is shown to yield quantitative outcomes that must be complied by detailed physical models, that can provide a basis to improve the (sub-grid) physical recipes implemented in theoretical approaches and numerical simulations, and that can offer a benchmark for forecasts on future observations with multi-band coverage, as it will become routinely achievable in the era of JWST.

New Analytic Solutions for Galaxy Evolution: Gas, Stars, Metals, and Dust in Local ETGs and Their High-z Star-forming Progenitors

“…Our result at z obs ≈ 0 is compared with the local data for ETGs from various authors, determined via weak lensing (see Velander et al 2014;Hudson et al 2015;Rodriguez-Puebla et al 2015;Mandelbaum et al 2016) and satellite kinematics (see More et al 2011;Wojtak & Mamon 2013), while the outcome at z ≈ 2 should be compared with the estimates by Burkert et al (2016) via Hα data and mass profile modeling; we find very good agreement in normalization and scatter within the still large observational uncertainties. Our results as a function of redshift are also similar, within a factor of 2, to the determinations via abundance matching technique by Moster et al (2013), Behroozi et al (2013), Aversa et al (2015), and Lapi et al (2017).…”

“…We have checked that our results are rather insensitive to the specific shape of such a phenomenological parameterization. With a similar formula Mancuso et al (2016a,b) have reproduced the main sequence of starforming galaxies at z ≈ 2, and Lapi et al (2017) have linked the statistics of starforming galaxies, AGNs and massive quiescent galaxies via a continuity equation approach.…”

Growth of Supermassive Black Hole Seeds in ETG Star-forming Progenitors: Multiple Merging of Stellar Compact Remnants via Gaseous Dynamical Friction and Gravitational-wave Emission

“…In Fig. 3 we illustrate the merger rate dṄ DF /d log m • per unit logarithmic bin of compact remnant mass m • , for a galaxy with redshift z = 2 and spatially-integrated SFR ψ = 300 M /yr, at different galactic ages τ ; this SFR is a typical value for a star-forming ETG progenitors at z ∼ 2, that characterizes galaxies at the knee of the SFR function (e.g., Gruppioni et al 2013;Mancuso et al 2016;Lapi et al 2017Lapi et al , 2018. At early times (say 10 7 yr, which are anyway needed for the most massive stars to explode as supernovae) only the most massive compact remnants with m • 30 M contribute to the merging rate, since the dynamical friction timescale is shorter for them (see Eq.…”

“…In the right panel of the same Fig. 4 we show the mass growth of a BH, in a galaxy at z ≈ 2 with SFR ψ ∼ 300 M yr −1 , representative of a typical ETG progenitor at the peak of the cosmic star formation history and at the knee of the SFR function (e.g., Gruppioni et al 2013Gruppioni et al , 2015Mancuso et al 2016;Lapi et al 2017Lapi et al , 2018. In this case the evolutionary tracks with dynamical friction and disk accretion for λ = 1 and λ = 0.3 are compared to that for pure disk accretion with λ = 1.…”

“…1 and 3.1). Finally, an integration over the possible values of the SFR ψ is performed, by weighting with the galaxy SFR functions dN/dV dψ at cosmic time t z ; these galaxy statistics have been determined observationally over a wide range of SFRs ψ ∼ 10 − 3000 M yr −1 and redshifts z ∼ 0 − 8 thanks the combination of deep UV/near-IR/far-IR/submm/radio surveys (see Mancuso et al 2016a,b;Lapi et al 2017;Boco et al 2019, their Fig. 1).…”