Extended Schmidt Law: Role of Existing Stars in Current Star Formation

Abstract

We propose an "extended Schmidt law" with explicit dependence of the star formation efficiency (SFE=SFR/M gas ) on the stellar mass surface density (Σ star ). This relation has a power-law index of 0.48±0.04 and an 1-σ observed scatter on the SFE of 0.4 dex, which holds over 5 orders of magnitude in the stellar density for individual global galaxies including various types especially the low-surfacebrightness (LSB) galaxies that deviate significantly from the Kennicutt-Schmidt law. When applying it to regions at sub-kpc resolution of a sample of 12 spiral galaxies, the extended Schmidt law not only holds for LSB regions but also shows significantly smaller scatters both within and across galaxies compared to the Kennicutt-Schmidt law. We argue that this new relation points to the role of existing stars in regulating the SFE, thus encoding better the star formation physics. Comparison with physical models of star formation recipes shows that the extended Schmidt law can be reproduced by some models including gas free-fall in a stellar-gravitational potential and pressure-supported star formation. By implementing this new law into the analytic model of gas accretion in Λ CDM, we show that it can re-produce the observed main sequence of star-forming galaxies (a relation between the SFR and stellar mass) from z=0 up to z=2.

On the cosmic evolution of the specific star formation rate

“…We will now show that the SFR − M relationship may be explicable through a simple model which relates the overall star formation rate in galaxies to the overall pressure of their ISM (Silk 1997;Blitz & Rosolowsky 2006;Silk & Norman 2009;Shi et al 2011). Here, the star formation rate is limited to regimes where the pressure induced by mechanical energy injection of star formation remains below the hydrostatic mid-plane pressure in galaxies (e.g.…”

“…Recently, Abramson et al (2014) have suggested that slopes less than one for the local ridge line may be due to the contribution from the bulge. If we relax the requirement that m+n = 2, which we adopted because of theoretical arguments (Silk & Norman 2009) and its consistency with observations (Dopita & Ryder 1994;Shi et al 2011), then we can accommodate slopes less than unity for the SFR − M relation (and negative slopes for the sSFR − M relation).…”

“…Dutton et al 2010;Khochfar & Silk 2011;Weinmann et al 2011) other than it is likely to be a complex interaction between the gas supply, the rate at which gas is transformed into stars and material lost from the galaxy (and halo) through outflows (e.g. Bouché et al 2010;Davé et al 2011;Shi et al 2011;Lilly et al 2013). Theoretically, the rate of cosmological baryonic accretion onto a galaxy halo is expected to be a function of mass and time, depending on redshift asṀ acc /M ∝ (1 + z) 2.25−2.5 (Neistein & Dekel 2008;Dekel et al 2009Dekel et al , 2013, contrary to the observed relationship sSFR ∝ (1 + z) 3 at z < ∼ 2 (Oliver et al 2010;Elbaz et al 2011), while at higher redshifts it either remains constant or increases more slowly (e.g.…”

“…When the gas supply drops below the rates necessary to maintain the high rates of star formation required for self regulation, secular processes become important, including the self-gravity provided by stellar disks (e.g. Shi et al 2011). Motivated by the observed slope of the sSFR − z relationship at z < ∼ 2, we suggest that the decline in sSFR is not only driven by declining gas fractions, but also by an evolution in the centrifugal support of the accreting gas (i.e., angular momentum), and by gas and stellar mass surface densities through a generalized Schmidt law (Dopita & Ryder 1994;Shi et al 2011).…”

“…Shi et al 2011). Motivated by the observed slope of the sSFR − z relationship at z < ∼ 2, we suggest that the decline in sSFR is not only driven by declining gas fractions, but also by an evolution in the centrifugal support of the accreting gas (i.e., angular momentum), and by gas and stellar mass surface densities through a generalized Schmidt law (Dopita & Ryder 1994;Shi et al 2011). Thus, the sSFR − z relationship may suggest two epochs of galaxy growth, first of self regulation at z > ∼ 2, which limits the ensemble specific star formation rate, followed by an epoch of secular growth at z < ∼ 2, where galaxies are prevented from consuming their gas too quickly and efficiently because the gas is accreted with relatively high angular momentum.…”