On the Cosmic Evolution of the Specific Star Formation Rate

A&A 577, A112 (2015) Astronomy DOI: 10.1051/0004-6361/201322630 & c ESO 2015 Astrophysics On the cosmic evolution of the specific star formation rate M. D. Lehnert1, W. van Driel2, L. Le Tiran2;3, P. Di Matteo2, and M. Haywood2 1 Institut d’Astrophysique de Paris, UMR 7095, CNRS, Université Pierre et Marie Curie, 98bis boulevard Arago, 75014 Paris, France e-mail: [email protected] 2 GEPI, Observatoire de Paris, UMR 8111, CNRS, Université Paris Diderot, 5 place Jules Janssen, 92190 Meudon, France 3 Departamento de Astronomia, IAG/USP, rua do Matão 1226, 05508-090, Cidade Universitária, 1280 São Paulo, SP, Brazil Received 9 September 2013 / Accepted 3 February 2015 ABSTRACT The apparent correlation between the specific star formation rate (sSFR) and total stellar mass (M?) of galaxies is a fundamental relationship indicating how they formed their stellar populations. To attempt to understand this relation, we hypothesize that the relation and its evolution is regulated by the increase in the stellar and gas mass surface density in galaxies with redshift, which is itself governed by the angular momentum of the accreted gas, the amount of available gas, and by self-regulation of star formation. With our model, we can reproduce the specific SFR− M? relations at z ∼ 1–2 by assuming gas fractions and gas mass surface densities similar to those observed for z = 1–2 galaxies. We further argue that it is the increasing angular momentum with cosmic time that causes a decrease in the surface density of accreted gas. The gas mass surface densities in galaxies are controlled by the centrifugal 3 support (i.e., angular momentum), and the sSFR is predicted to increase as, sSFR(z) = (1 + z) =tH0, as observed (where tH0 is the Hubble time and no free parameters are necessary). In addition, the simple evolution for the star-formation intensity we propose is in agreement with observations of Milky Way-like galaxies selected through abundance matching. At z ∼> 2, we argue that star formation is self-regulated by high pressures generated by the intense star formation itself. The star formation intensity must be high enough to either balance the hydrostatic pressure (a rather extreme assumption) or to generate high turbulent pressure in the molecular medium which maintains galaxies near the line of instability (i.e. Toomre Q ∼ 1). We provide simple prescriptions for understanding these self-regulation mechanisms based on solid relationships verified through extensive study. In all cases, the most important factor is the increase in stellar and gas mass surface density with redshift, which allows distant galaxies to maintain high levels of sSFR. Without a strong feedback from massive stars, such galaxies would likely reach very high sSFR levels, have high star formation efficiencies, and because strong feedback drives outflows, ultimately have an excess of stellar baryons. Key words. galaxies: high-redshift – galaxies: evolution – galaxies: kinematics and dynamics – galaxies: ISM 1. Introduction Currently there is no widely accepted explanation as to why the relative rate of growth of galaxies depends on redshift in The evolution of the star formation rate (SFR) and the relation this manner (e.g. Dutton et al. 2010; Khochfar & Silk 2011; between the specific star formation rate (SFR per unit stellar Weinmann et al. 2011) other than it is likely to be a complex in- mass, sSFR) and total stellar mass (M?) of galaxies has garnered teraction between the gas supply, the rate at which gas is trans- considerable observational and theoretical attention (e.g. Elbaz formed into stars and material lost from the galaxy (and halo) et al. 2007, 2011; Daddi et al. 2007; Weinmann et al. 2011; Stark through outflows (e.g. Bouché et al. 2010; Davé et al. 2011; Shi et al. 2013; Behroozi et al. 2013). Observations of galaxies over et al. 2011; Lilly et al. 2013). Theoretically, the rate of cosmo- a wide range of redshifts suggest that the slope of the SFR − M? logical baryonic accretion onto a galaxy halo is expected to be a relation is about unity (e.g. Elbaz et al. 2007; Salmi et al. 2012), function of mass and time, depending on redshift as M˙ acc/M / which implies that their sSFR does not depend strongly on stel- (1 + z)2:25−2:5 (Neistein & Dekel 2008; Dekel et al. 2009, 2013), lar mass. Specific star formation rates increase out to z ≈ 2 contrary to the observed relationship sSFR / (1 + z)3 at z ∼< 2 (Elbaz et al. 2007, 2011; Daddi et al. 2007, 2009; Noeske et al. (Oliver et al. 2010; Elbaz et al. 2011), while at higher redshifts it 2007; Dunne et al. 2009; Stark et al. 2009; Oliver et al. 2010; either remains constant or increases more slowly (e.g. Stark et al. Rodighiero et al. 2010) and are constant, or perhaps slowly in- 2013). Of course, there are several caveats in making a direct creasing, from z = 2 out to z = 6, though with a large scatter, link between the specific halo accretion rate and the sSFR, such sSFR ≈ 2−10 Gyr−1 (Feulner et al. 2005; Dunne et al. 2009; as assuming that the ratio of halo mass to stellar mass is con- Magdis et al. 2010; Stark et al. 2013). stant at constant halo mass with redshift (Behroozi et al. 2013). It is important to emphasize that neither the observed While many variables come into play in determining the mass SFR − M? nor the sSFR − M? relationship implies a correla- accretion rate, it appears that the general increase in the sSFR tion, but that both are actually ridge lines in the distribution of with redshift is not simply controlled by the gas supply, and that actively star-forming galaxies – galaxies that are evolving pas- other processes must come into play. sively or forming stars at moderate rates lie below these relation- Any plausible explanation must reconcile the available gas ships at a given mass (Rodighiero et al. 2010; Elbaz et al. 2011; supply with the evolution of the sSFR. Currently, the most di- Karim et al. 2011). Depending on epoch, the fraction of pas- rect ways of relating the specific growth of galaxies to the spe- sively evolving galaxies can be significant, in particular among cific accretion rate is to use AGN and starburst driven outflows very massive objects (Karim et al. 2011). and gas consumption timescales to regulate the star formation in Article published by EDP Sciences A112, page 1 of 13 A&A 577, A112 (2015) galaxies (e.g. Dekel et al. 2009; Lilly et al. 2013). The effects for local and distant galaxies. In Sect.3, we discuss the evolution of feedback from massive stars and active galactic nuclei allow of the sSFR in a more general context, specifically commenting this direct coupling of star formation with the gas supply to be on why there is a change in the apparent evolution of the sSFR broken (e.g. Peirani et al. 2012; Lehnert et al. 2013). This de- above and below z ≈ 2. Finally, in Sect.4, we provide a brief coupling is important as not only do we need the relative growth summary. of galaxies not to track the gas supply too closely, as observed in the evolution of the sSFR, but also because baryonic mass fraction in galaxies is small and does not follow the halo mass 2. The ridge line in the SFR – M? plane function (Baldry et al. 2008; Papastergis et al. 2012) suggesting that either a fraction of the baryons are not accreted or they are The apparent SFR − M? relation and its evolution from z ≈ 0–7 efficiently removed from the galaxy. Galaxy growth and baryon (e.g. Elbaz et al. 2007; Daddi et al. 2007; Stark et al. 2009, 2013; content must be limited by the way in which gas is accreted, Oliver et al. 2010; Magdis et al. 2010) provides valuable insight cools and collapses, or alternatively, by processes that are inter- into how galaxies convert their gas into stars. As a ridge line to nal to the galaxy or the physics of star formation (e.g. Dutton the distribution of galaxies in the SFR−M? plane it shows in par- et al. 2010). In fact, breaking this coupling may be necessary ticular how the sSFR of vigorously star-forming galaxies evolves to explain some aspects of the evolution of the sSFR within the with stellar mass and redshift. Although the slope of the ridge context of simulations, which often produce too little star forma- in this plane is roughly the same at every epoch, high-redshift galaxies can reach much higher sSFR values than galaxies at tion at recent epochs and exhibit a positive correlation between < the sSFR and stellar mass (similar to that of the specific dark more moderate redshifts (z ∼ 2). matter accretion rate; Weinmann et al. 2013). The lack of a direct coupling between accretion and star for- 2.1. A simple model relating overall SFR to ISM pressure mation would favor an explanation of the sSFR−M? relationship through local processes such as star formation controlling the We will now show that the SFR − M? relationship may be ex- pressure of the interstellar medium (ISM), and hence self regula- plicable through a simple model which relates the overall star tion (e.g. Silk 1997). One observational signature of this self reg- formation rate in galaxies to the overall pressure of their ISM ulation is galaxy-wide outflows, which are observed in intensely (Silk 1997; Blitz & Rosolowsky 2006; Silk & Norman 2009; Shi star-forming galaxies across all cosmic epochs (e.g. Lehnert & et al. 2011).

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