Origin and Evolution of Disk Galaxy Scaling Relations

Transcription

1 Origin and Evolution of Disk Galaxy Scaling Relations Aaron A. Dutton (CITA National Fellow, University of Victoria) Collaborators: Frank C. van den Bosch (Utah), Avishai Dekel (HU Jerusalem), + DEEP2 TEAM Galaxies in the Distant Universe - Ringberg May 2010

2 Outline Star Formation Rate - Stellar Mass Relation (SFR Sequence) (Dutton, van den Bosch, Dekel 2010, MNRAS in press, astro-ph/ ) Velocity - Mass - Radius Relations (Dutton+2010, in prep)

3 Outline 2 things I am going to convince you about in the next ~20min Star Formation Rate - Stellar Mass Relation (SFR Sequence) (Dutton, van den Bosch, Dekel 2010, MNRAS in press, astro-ph/ ) - the evolution is not driven by gas fractions Velocity - Mass - Radius Relations (Dutton, van den Bosch +DEEP2, 2010, in prep) - z=2 disks are smaller than z=0 disks, at fixed stellar mass and maximum circular velocity

4 Part I Evolution of Star Formation Rate Sequence Dutton, van den Bosch, Dekel 2010, MNRAS in press, astro-ph/

5 Observations: SFR Sequence SFR-M star relation (Noeske+07, Elbaz+07, Daddi+07) - scatter is 0.3 dex (1σ) (i.e. factor of 2) (independent of redshift) - slope (independent of redshift) - zero point (SFR) decreases by factor ~20 from z~2 to z=2 Dutton, van den Bosch & Dekel 2010 Vertical error bars are formally the scatter, but are reasonable estimate of systematic uncertainties

6 Theory Overview What is the Origin of the Decline in SSFR since z~2? a) Decrease in gas inflow rate? - (dm halo /dt)/m halo ~ (1+z) 2.25 (Birnboim, Dekel, & Neistein 2007) For a resolved Schmidt-Kennicutt Law: Σ SFR (R) = ε SF Σ gas (R) n, And an exponential gas disk: Σ gas (R) = Σ 0 exp(-r/r g ) SFR = ε SF n -2 M gas Σ 0 n-1 b) Decrease in gas fractions? c) Decrease in gas density?

7 The Star Formation Law Σ SFR Σ gas n (Schmidt 1959) Σ SFR : star formation rate surface density Σ gas : gas surface density (Kennicutt 1998) n 1.4 For disk averaged densities: n 1.4 (Kennicutt 1998) (for Σ gas > ~10 M sun pc -2 ) Star formation suppressed (for Σ gas < ~10 M sun pc -2 ) SFR surface density [M sun yr -1 kpc -2 ] Bigiel et al Gas surface density [M sun pc -2 ]

8 The Molecular Star Formation Law Σ SFR Σ mol n (Schmidt 1959) Σ SFR : star formation rate surface density Σ mol : molecular gas surface density (Kennicutt 1998) n 1.4 For disk averaged densities: n 1.4 (Kennicutt 1998) (for Σ mol > ~100 M sun pc -2 ) For sub-kpc local densities: n 1 (Bigiel et al. 2008) (for Σ mol < ~100 M sun pc -2 ) SFR surface density [M sun yr -1 kpc -2 ] n 1.0 Bigiel et al Similar double power-law derived by Krumholz, McKee & Tumlinson 2009 Molecular Gas surface density [M sun pc -2 ]

9 A simple model for disk galaxy formation (Dutton & van den Bosch 09; Dutton 09) Star formation { 1. Stars form in galactic disks out of molecular gas: double power-law - Σ SFR (R) Σ mol (R) n : n=1 (Σ mol < ~100 M sun pc -2 ); n=1.4 (Σ mol > ~100 M sun pc -2 ) 2. Atomic to molecular transition based on pressure (Blitz & Rosolowski 2006). Disk Structure Mass Accretion { { 3. Growing disk in dynamical equilibrium inside a growing NFW 97 dark matter halo 4. Disk density profile is governed by specific angular momentum distributions from cosmological simulations (Bullock+01,Sharma & Steinmetz 05). 5. Dark Matter Halos and Galaxies grow by Smooth Mass Accretion (Wechsler+02). 6. Hot mode accretion (i.e. virial shock + cooling, Z hot =0.1Z sun ), replicates cold mode for M vir < 5e11M sun 7. Radially dependent mass outflows (V wind (R) = local escape velocity). Caveats, whats missing: -- mergers, quenching, secular evolution, turbulence, reionization, cold streams in M vir > M sun haloes at z>2, recycling of outflow gas, cosmological environment...

10 A simple model for disk galaxy formation (Dutton & van den Bosch 09; Dutton 09) Cosmologically motivated model for self - consistent evolution of resolved galaxy disks As a function of galactic radius we calculate: - inflows, outflows (due to SNe), gas (atomic, molecular), star formation, stellar mass, metals, luminosity log Surface Density M vir = Radius [kpc] log Radius [kpc]

11 The Origin of Exponential Galaxy Disks (Dutton 2009) Blow-out of low specific angular momentum material (see also Maller & Dekel 2002, Governato et al. 2010) 25% SNe energy No outflows why: - SF more efficient at small radii (hence lower specific AM gas is ejected) - blow-out mostly occurs at high-z, where disks have lower specific AM M vir =10 10 M sun dwarf galaxy mass halo R/R vir R/R vir

12 The Origin of Exponential Galaxy Disks (Dutton 2009) Blow-out of low specific angular momentum material (see also Maller & Dekel 2002, Governato et al. 2010) 25% SNe energy No outflows why: - SF more efficient at small radii (hence lower specific AM gas is ejected) - blow-out mostly occurs at high-z, where disks have lower specific AM M vir =10 12 M sun Milky Way mass halo R/R vir R/R vir

13 Monte Carlo Sample M vir = h -1 M sun uniform in log 10 <c vir >(M vir ), σ ln c =0.25 WMAP5 (Bullock et al. 2001, Maccio et al. 2008) <λ>=0.035, σ ln λ = 0.5 (Maccio et al. 2008) <α>=0.9, σ ln α = 0.25 (Sharma & Steinmetz 2005)

14 SFR Sequence is independent of our outflow model at redshift z=0 No outflows (NFB) Momentum Driven Outflows (MFB) η = (300 / V wind ) (Murray, Quataert, & Thompson 2005) Model slope ~ 0.95 Observed slope ~ Energy Driven Outflows (EFB) η = ε FB 10 (300 / V wind ) 2, ε FB =0.25 (Dekel & Silk 1986; van den Bosch 2001)

15 SFR Sequence is independent of our outflow model at all redshifts Star Formation Rate Stellar Mass

16 SFR Sequence is independent of our outflow model at all redshifts Star Formation Rate + - Results are more robust since outflows are not well understood Can t use SFR Sequence to constrain feedback models (OK, every other scaling relation for star forming galaxies depends on outflow model, Dutton & van den Bosch 2009) Stellar Mass

17 Evolution of Specific Star Formation Rates Evolution independent of outflow model (FB moves galaxies along SFR sequence) Evolution consistent with change in specific halo accretion rate Factor of ~20 evolution from z~4 to z~0 in agreement of observations Problems: Model underpredicts SSFR in lower mass galaxies (slope problem) Discrepancy of factor 3 at z~2, factor 6 at z~7 Solutions: Systematics in Observations (Herschel => z~2 are overestimated) Variable IMF (Davé 2008) Variation in SF efficiency, recycling of outflow gas (e.g. Weinmann poster)

18 SFR does not follow Gas Accretion Rate Star Formation Rate Cold gas inflow rate

19 SFR ~ follows NET Gas Accretion Rate onto Galaxy Star Formation Rate Net gas inflow rate Galaxies are in a pseudo steady state bewteen inflows, outflows and star formation: SFR ~ dm acc /dt (1+η) -1 ( consensus view, see also Bouche et al. 2010)

20 SFR ~ follows NET Gas Accretion Rate onto Galaxy But WHY? If stars form according to SK type law (and they do in our model), then gas masses or gas densities must evolve

21 Gas fraction - stellar mass relation does not evolve much! GREY: Models (Dutton & van den Bosch 2009), GREEN: Data (Garnett 2002) Gas is neutral atomic and molecular f gas = M gas /(M gas +M star ) f gas = 40% for M star =10 10 at z=0 f gas = 20% for M star =10 11 at z=0

22 Individual galaxies start out gas rich, and evolve ~ along relation GREY: Models (Dutton & van den Bosch 2009), GREEN: Data (Garnett 2002) Gas is neutral atomic and molecular f gas = M gas /(M gas +M star ) f gas = 40% for M star =10 10 at z=0 f gas = 20% for M star =10 11 at z=0

23 Weak evolution in gas fractions * Order of magitude increase in M gas /M star required to explain SSFR evolution Gas / Stars Erb+06 Erb+06 From z=0 to z~2 Observations: factor of ~2 increase in Gas-to-stars ratio Theory: less than factor ~2 increase in Gas-to-stars ratio. Increase in gas fractions in models and observations is no way high enough to explain increase in SSFR

24 Order of magnitude Evolution in Gas Density Σ 50,gas = average gas surface density within gas half mass radius. log Gas density decreases by factor of ~10-30 from z~3 to 0

25 Order of magnitude Evolution in Molecular Gas Mass RED = M mol / M star Dutton, van den Bosch, Dekel 2010 log Gas / Stars * Molecular Gas Mass decreases by factor of ~10 from z~3 to 0 * Evolution consistent with recent observations at z~1-2 (Daddi et al. 2010; Tacconi et al. 2010) * At z=0, molecular gas mass ~ 10% of stellar mass, scatter 0.1dex * Also consistent with observations (COLD GASS project, Saintonge poster)

26 Origin of evolution in the SFR Sequence Thus the evolution in the SFR Sequence from high to low z is driven by both a) Decline in rate of gas supply, and c) Decline in gas surface density. => Decline in molecular gas fractions But not b) an increase in gas fractions.

27 Part II Evolution of Velocity-Mass-Radius relations Dutton, van den Bosch, +DEEP2, 2010, in prep

28 Scaling Relations of Dark Matter Haloes Spherical Collapse: M vir (z) = 4/3 π R vir (z) 3 Δ vir (z) ρ crit (z) Virial theorem: M vir (z) = V vir (z) 2 R vir (z) / G => V vir R vir M vir 1/3 Critical density of universe M vir (z)/m vir,0 = [V vir (z)/v vir,0 ] 3 [H(z)/H 0 ] -1 [Δ vir (z)/δ vir,0 ] -1/2 R vir (z)/r vir,0 = [V vir (z)/v vir,0 ] [H(z)/H 0 ] -1 [Δ vir (z)/δ vir,0 ] -1/2 R vir (z)/r vir,0 = [M vir (z)/m vir,0 ] 1/3 [H(z)/H 0 ] -2/3 [Δ vir (z)/δ vir,0 ] -1/3 Hubble Parameter: H(z)/H 0 = [Ω Λ + Ω M (1+z) 3 ] 1/2

29 Scaling Relations of Dark Matter Haloes in LCDM cosmology (Ω M =0.3, Ω Λ =0.7), Δ vir (z) (Bryan & Norman 1998) ΔM vir (z)(v vir ) ΔR vir (z)(m vir ) ΔR vir (z)(v vir ) z=2 z=2 x2.5 x3.5 x3.5 z=2 ΔM vir (z)(v vir ) ~ (1+z) -1.3 ΔR vir (z)(m vir ) ~ (1+z) -0.8 ΔR vir (z)(v vir ) ~ (1+z) -1.3 Simplest model of disk galaxy formation: V max = V vir, M d = m d M vir, R d = R vir λ d / 2, m d & λ d independent of z

30 Observed Evolution Observed evolution of V max -M star -R 50 weaker than predicted DEEP2 (MV): S0.5>90 km/s (Kassin et al. 2007) DEEP2 (RM): M star >1e10 M sun (Dutton et al. in prep) SINS: V max >150 km/s, M star >1e10 M sun (Cresci et al. 2009) GEMS+FIRES (RM): M star >3e10 M sun (Trujillo et al. 2006) Similar RM evolution from z~1 to 0 from COSMOS (Carollo talk)

31 More realistic model 25% galaxy formation efficiency Median spin of LCDM haloes Disk formation model in evolving NFW haloes, m d =0.04, λ d =0.035 Model Reproduces M-V and R-M evolution. Factor of 3 discrepancy with SINS R-V relation Similar evolution of R 50 -M star relation in other models: (Somerville et al. 2008; Firmani & Avila-Reese 2009)

32 More realistic model Disk formation model in evolving NFW haloes, m d =0.04, λ d =0.035 Model Reproduces M-V and R-M evolution. Factor of 3 discrepancy with SINS R-V relation Factor of 3 discrepancy with SINS R-M relation => observations are inconsistent

33 Solutions to factor 3 discrepancy HWHM not equal to disk scale lengths Hα sizes over estimate stellar sizes (e.g. by factor 1.8 Sales et al. 2009) - most interesting from galaxy formation point of view Selection bias towards large disks

34 Observations almost self consistent Using Hα R 1/2 instead of HWHM (interpreted as R d ) removes most of the discrepancy SINS galaxies are smaller at fixed M star and V max than z=0 disks

35 Does Hα trace stellar mass density? In disk model half mass radii R SF ~ 2 R star (inside-out disk growth) Smaller differences w.r.t. optical sizes R SF ~ 1.4 R I ~ 1.25 R V Molecular gas sizes slightly smaller than SF sizes (due to almost linear molecular SK law)

36 Models and Observations consistent Observed evolution of V max -M star -R 50 in consistent with simple model of evolving disks in NFW haloes with m d =0.04, λ d =0.035 High spin parameters (λ d =0.1) are not necessary to explain evolution of VMR relations from z=0 to z~2 as argued by Bouche et al and Burkert et al. 2009

37 Summary Evolution of SSFRs can be understood on 3 levels: 1) Steady state: SFR = net inflow rate (cosmological accretion - outflow) 2) Inflow in turned into stars via SK law a) density of gas disks evolves strongly b) but gas fraction evolves weakly 3) (2a =>) molecular gas fraction evolves strongly (in agreement with recent observations, Daddi et al. 2010, Tacconi et al. 2010) Observed evolution of V max -M star -R 50 in consistent with simple model of evolving disks in NFW haloes m d =0.04, λ d =0.035 High spin parameters (λ d =0.1) at z~2 are not necessary to explain evolution of VMR relations from z=0 to z~2 as argued by Bouche et al and Burkert et al. 2009