The dynamics of the gas regulator model and the implied cosmic sSFR-history Yingjie Peng Cambridge Roberto Maiolino, Simon J. Lilly, Alvio Renzini + zCOSMOS & COSMOS, SINFONI-SINS, MOONS Team Y. Peng & R. Maiolino 2014 MNRAS (arXiv:1402.5964)

Evolution of the Galaxy Population f (t, SFR, mstar, r, mhalo, morphology, central/satellite, Z, mgas … ) What’s the key parameters that regulate galaxy evolution? What’s the causal relations between different parameters? Need a self-consistent framework to link different parameters together. mZ,IGM(t) mZ,gas(t) mZ(t) Zgas(t) mZ,star(t) Zstar(t) mgas(t) SFR(t) mstar(t) Why the metallicity is extremely important to study the galaxy evolution. Therefore, I would like to take this chance to give a short introduction to our general approach. F(t) mass-loading morphology merging quenching structure growth dynamics (clumpy disks) IMF star-formation efficiency Y(t) AGN feedback mhalo(t) central/satellite, r

Gas Regulator Model mgas(t) SFR = e Mgas (e.g. Finlator et al. 2008, Recchi et al. 2008, Bouche et al. 2010, Davé et al. 2012, Dayal et al. 2013, Lilly et al. 2013, Dekel et al. 2014, Peng et al. 2014) mZ,IGM(t) mZ,gas(t) mZ(t) Zgas(t) mZ,star(t) Zstar(t) mgas(t) SFR(t) mstar(t) F(t) Y(t) describe the scaling relations mass conservation in stars, gas and metals : Gas mass is relatively more hard to observe, the field of view of ALMA is too small to perform large SKY surveys, like SDSS in the local. Therefore, we have to add in Zgas into this picture. but degeneracy still exists between the mass-loading factor and star-formation efficiency. That’s why eventually we have also to add in other constraints such as the mass function to break the degeneracy. Stellar metallicity is also important, for instance, it will give clues on how the galaxy gets quenched. SFR = e Mgas definitions of e and l

Gas Regulator Model Assumptions: SFR = e Mgas (e.g. Finlator et al. 2008, Recchi et al. 2008, Bouche et al. 2010, Davé et al. 2012, Dayal et al. 2013, Lilly et al. 2013, Dekel et al. 2014, Peng et al. 2014) Assumptions: F, λ and ε are all constant or only change slowly with time equilibrium/steady state conditions d Mgas/dt ~ 0 Dave et al. 2012 Lilly et al. 2013 t ≫ τeq Dekel & Mandelker 2014 input specific accretion rate varies on a timescale that is long compared with the gas consumption timescale SFR = e Mgas

The dynamics of the gas regulator model (Peng & Maiolino 2014) Input Parameter Definition gas inflow rate of the galaxy F fb - cosmic baryon fraction fgal - halo penetration efficiency star-formation efficiency e e = SFR / Mgas mass-loading factor l l = Y / SFR Y - outflow rate equilibrium timescale teq R - mass return fraction from stars Mention in terms of control the gas mass, e is degenerated with lambda. Increase e is equivalent to increase l. Assumptions: First assume F, λ and ε are all constant or only change slowly with time, then test numerically with evolving F, λ and ε Do NOT assume any equilibrium/steady state conditions

The dynamics of the gas regulator model Mention my talk in Wednesday s8

equilibrium or not？ assume l~1 and R~0.4 z~3, Mstar ~1011M⊙ fgas ~10% (e.g. Troncoso et al. 2014) sSFR ~ 3 Gyr-1 teq~ 0.02 Gyr << tH fgas ~ 40 % (e.g. Tacconi et al. 2013 ) teq~ ~ 0.14 Gyr << tH z~0, Mstar ~1011M⊙ fgas ~5% sSFR ~ 0.1 Gyr-1 teq~ 0.33 Gyr << tH massive galaxies are likely to live around the equilibrium state over most of the cosmic time. z~3, Mstar ~109M⊙ fgas ~90% (e.g. Troncoso et al. 2014) sSFR ~ 3 Gyr-1 teq~ 1.88 Gyr ~ tH Mstar ~108M⊙ teq > tH Low mass galaxies (Mstar ~ 109M⊙) at z~3 are expected to be the progenitors of today’s Milky Way-like galaxies (i.e. L* galaxies). Therefore, today’s typical L* galaxies may live around the equilibrium state locally, but when we trace them back to earlier epochs, they are likely to be completely out of the equilibrium. z~0, Mstar ~109M⊙ fgas ~ 60% sSFR ~ 0.1 Gyr-1 teq~ 9.4 Gyr ~ tH Mstar ~108M⊙ fgas ~ 80% teq~ 25 Gyr > tH low mass galaxies and dwarf galaxies are very unlikely to live around the equilibrium state at any epoch.

Timescales tdil ≤ teq ≤ tdep gas depletion timescale tdep = Mgas / SFR =1/e equilibrium timescale dilution timescale Finlator et al. (2008) and Davé et al. (2012) tdil ≤ teq ≤ tdep The equilibrium timescale, by definition, is the timescale for a galaxy to return to its equilibrium state from a perturbation or from an (arbitrary) initial condition teq is the timescale for a galaxy to return to its equilibrium state from a perturbation or from an (arbitrary) initial condition teq is the central timescale that governs the evolution of the galaxy population. the scatters in most of the key scaling relations, e.g. Mstar-SFR relation, Mstar-Zgas, Mstar-fgas, are all primarily governed by teq.

The dynamics of the gas regulator model I would say it would be useless if we could not use these dynamical properties of the galaxies to guide observations and help to interpreted the data in an analytic way. Again, the best feature of this simple framework is that it’s fully analytical.

The dynamics of the gas regulator model Peng & Maiolino 2014 Session- Sp15  Mention my talk in Wednesday s8

The dynamics of the gas regulator model Peng, Maiolino & Cochrane 2015, Nature Mention my talk in Wednesday s8

The dynamics of the gas regulator model And there are several coming papers…

The dynamics of the gas regulator model (Peng & Maiolino 2014)

The dynamics of the gas regulator model (Peng & Maiolino 2014)

Apparently d Mgas/dt ~ 0 (Dave et al. 2012) is not a good assumption however… sSFR ~ 1/t

The critical role of sSFR(t) – cosmic clock Build-up of stars x 2 x 3000 x 300 SFR-Mstar evolution Stellar MF evolution SMD(z) SFRD(z) Age(z), Metallicity(z) Quenching history almost everything that can be observed on the sky 1 Gyr’s evolution at z~3 is “equivalent” to 20 Gyr’s evolution at z~0

The Star-forming Main Sequence There are broadly two populations of galaxies on the basis of their specific SFR: Blue star-forming galaxies that have (sSFR)−1 ∼ τH Red passive galaxies that have (sSFR)−1 >> τH star-forming main sequence Mention the mass-quenched cloud, and the environment-quenched one (if you plot only central, the transitional mass, At low mass, the bimodality is getting more blurred. passive sequence Renzini & Peng 2015

The Star-forming Main Sequence The negative logarithmic slope of the sSFR - Mstar relation of the star-forming galaxies The cosmic evolution of the sSFR of the star-forming galaxies… Whitaker et al.2014 Mention the discrepancy between ssfr and smir …reflects the evolution of the specific accretion of the dark matter halos …reflects the equilibrium timescale teq is shorter for massive star-forming galaxies. These are dynamical features of the star-forming galaxy population, not quenching

sSFR(t) in the gas-regulator model t >> teq (equilibrium) t << teq (out of equilibrium) sSFR(t) can differ by only a factor of few at any epoch  existence of the Main-Sequence sSFR(t) is insensitive to teq (i.e. e and l)  insensitive to feedback teq may strongly depend on M* , but there is only a weak dependence of the sSFR on M* teq is shorter for more massive galaxies  lower sSFR  the slop of the sSFR-M* relation is negative

sSFR(t) determined by using cosmological inflow for different teq The slop of the sSFR-M* relation should be less negative at earlier epochs

sSFR(t) determined by using cosmological inflow for different teq Whitaker et al. 2014 The slop of the sSFR-M* relation should be less negative at earlier epochs

sSFR(t) for star forming main sequence galaxies All measurements are converted Mstar ~ 5.0×109M⊙ High redshift measurements are nebular emission line corrected the green solid squares show the dust corrected values from Bouwens et al. (2012). The red dots, purple dots and black square show the nebular emission line corrected values from Stark et al. (2013), Tilvi et al. (2013) and Ouchi et al. (2013), respectively. The red line shows the fitting function of sSFR = 26 t -2.2 Gyr-1 up to z ~ 3 from Elbaz et al. (2011).

the predicted sSFR(t) from the gas regulator model is in good agreement with the prediction from typical SAMs the observed sSFR(t) is fundamentally different from the predicted sSFR(t) from both typical SAMs and gas regulator model. some key process is missing in both SAMs and gas regulator model

Dekel & Mandelker 2014 the predicted sSFR history from the gas regulator model is in good agreement with the prediction from typical SAMs the observed sSFR history is fundamentally different from the predicted sSFR history from both typical SAMs and gas regulator model. some key process is missing in both SAMs and gas regulator model

The required mass loading factor l to reproduce the observed sSFR(t) A tremendous (physically unrealistic) mass-loading factor is required in the first two or three billion years to suppress the early star formation.

Model largely underestimates the sSFR at z~2 is not because it underestimates the SFR at z~2, but because it has overproduced too many stars at z>2.

The dynamics of the gas regulator model Mention is not meant to provide precise matches of the observational data, which is the aim of hydro-dynamical simulations and SAMs. The aim of this approach is to use these dynamical properties of the galaxies to guide observations and help to interpreted the data in an analytic way. since the best feature of this simple framework is that it’s fully analytical. We have many forthcoming papers to show how to demonstrate how to use these equations to guide observations and find interesting results.

The required star formation efficiency e and the associated gas faction to reproduce the observed sSFR history As the direct consequence of the small value of e, the associated gas fraction is almost 100% at z>~2, which clearly contradicts to the observed gas faction at similar redshifts.

The dynamics of the gas regulator model (Peng & Maiolino 2014) Input Parameter Definition gas inflow rate of the galaxy F fb - cosmic baryon fraction fgal - halo penetration efficiency star-formation efficiency e e = SFR / Mgas mass-loading factor l l = Y / SFR Y - outflow rate equilibrium timescale teq R - mass return fraction from stars Assumptions: First assume F, λ and ε are all constant or only change slowly with time, then test numerically with evolving F, λ and ε Do NOT assume any equilibrium/steady state conditions

A New Approach to Galaxy Evolution translate complex data into several simple equations number conservation distribution functions gas-regulator model link Galaxies to Halos Gas Cosmological framework: more or less well understood Stellar population: P10 framework Link them together. SAM, Hydro-... From halo to galaxy, is fundamentally different from my approach HOD/Abundance Matching mathematical model mass conservation scaling relations Cosmological Context fhalo (mh, r, t)

From Galaxies to Halos - Reverse Engineering of the Galaxy Population Input Halo mass function SMIRDM(t) parameters baryonic accretion timescale tacc (fgal) star-formation efficiency e mass-loading factor l quenching rate Observations sSFR(t) Power law form of the MF Z - Mstar Initial Conditions almost arbitrary MF + fred Star-forming MS sSFR(t) All the continuity-approach results Power law form of the MF of star-forming galaxies with as ~ -1.45 The evolution of the stellar-to-halo mass (SHM) relation and the SHM ratio Use the gas/stellar metallicity and gas content to understand quenching Reproduce the observed star-formation efficiency Gas fraction evolution The distribution of metals in gas, stars and IGM (Renzini+2014) FMR and its break down at z~2.5 Z - Mstar – SFR - fgas - redshift Study the scatters in various scaling relations