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 … )

SFR(t) mstar(t)mgas(t)

central/satellite, r

mhalo(t)

star-f

ormati

on efficie

ncy

mZ(t) mZ,star(t)mZ,gas(t)

mZ,IGM(t)

Zgas(t) Zstar(t)

F(t) morphologymergingquenchingstructure growth dynamics (clumpy disks)IMF

Y(t)

mass-loading

AGNfeedback

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.

SFR(t) mstar(t)mgas(t)

mZ(t) mZ,star(t)mZ,gas(t)

mZ,IGM(t)

Zgas(t) Zstar(t)

F(t) Y(t)

Gas Regulator Model(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)

SFR = e Mgas

SFR

(1 )stardMR SFR

dt

(1 )gasdMR SFR

dt

,gas0(1 )ZdM

y SFR Z R SFR Z Zdt

mass conservation in stars, gas and metals :

definitions of e and l

describe the scaling relations

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

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

1

(1 )eq R

b  halogal

dMf f

dt

First assume F, λ and ε are all constant or only change slowly with time, then test numerically with evolving F, λ and ε

Assumptions:

Do NOT assume any equilibrium/steady state conditions

The dynamics of the gas regulator model

equilibrium or not？1 1

=(1 ) (1 ) 1

gaseq

gas

f

R sSFR R f

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

assume l~1 and R~0.4

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

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.

Timescalesgas depletion timescale tdep = Mgas / SFR =1/e

equilibrium timescale

dilution timescaleFinlator et al. (2008) and Davé et al. (2012)

the scatters in most of the key scaling relations, e.g. Mstar-SFR relation, Mstar-Zgas, Mstar-fgas, are all primarily governed by teq.

1dep

eq R

(1 )eq

t

dil eg s

qa e

M

tdil ≤ teq ≤ tdep

teq is the central timescale that governs the evolution of the galaxy population.

teq is the timescale for a galaxy to return to its equilibrium state from a perturbation or from an (arbitrary) initial condition

The dynamics of the gas regulator model

The dynamics of the gas regulator model

Peng & Maiolino 2014Session- Sp15 

The dynamics of the gas regulator model

Peng, Maiolino & Cochrane 2015, Nature

The dynamics of the gas regulator model

• SFR-Mstar evolution• Stellar MF evolution• SMD(z)• SFRD(z)• Age(z), Metallicity(z)• Quenching historyalmost everything that can be observed on the sky

x 2 x 3000

x 300

Build-up of stars 1 star

star

dmsSFR

m dt 0

( )

0( ) ( )t

tsSFR t dt

star starm t m t e

The critical role of sSFR(t) – cosmic clock

1 Gyr’s evolution at z~3 is “equivalent” to20 Gyr’s evolution at z~0

There are broadly two populations of galaxies on the basis of their specific SFR:

Blue star-forming galaxies that have (sSFR)−1 τ∼ H

Red passive galaxies that have (sSFR)−1 >> τH

The Star-forming Main Sequence

Renzini & Peng 2015

star

-form

ing

mai

n se

quen

ce

pass

ive

sequ

ence

Whitaker et al.2014

The cosmic evolution of the sSFR of thestar-forming galaxies…

…reflects the evolution of the specific accretion of the dark matter halos

The negative logarithmic slope of the sSFR - Mstar relation of the star-forming galaxies

…reflects the equilibrium timescale teq is shorter for massive star-forming galaxies.

These are dynamical features of the star-forming galaxy population, not quenching

The Star-forming Main Sequence

1 1( )

1[1 ]

eq

eq

t

t

eq

esSFR t

Rt e

min

1 1( ) ~

1sSFR t

R t

max

1 2( ) ~

1sSFR t

R t

t >> teq

(equilibrium)

t << teq

(out of equilibrium)

sSFR(t) in the gas-regulator model

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

Whitaker et al. 2014

The slop of the sSFR-M* relation should be less negative at earlier epochs

sSFR(t) determined by using cosmological inflow for different teq

sSFR(t) for star forming main sequence galaxiesAll measurements are converted Mstar ~ 5.0×109M⊙

High redshift measurements are nebular emission line corrected

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

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

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.

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

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

1

(1 )eq R

b  halogal

dMf f

dt

First assume F, λ and ε are all constant or only change slowly with time, then test numerically with evolving F, λ and ε

Assumptions:

Do NOT assume any equilibrium/steady state conditions