1. 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: )

2. 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

3. 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

4. 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 ~ 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

5. 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

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

7. 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 ) 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 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.

8. 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.

9. 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.

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

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

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

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

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

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

16. 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

17. 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

18. 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

19. 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

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

21. 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

22. 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).

23. 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

24. 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

25. 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.

26. 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.

27. 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.

28. 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.

29. 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

30. 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)

31. 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