AY202a Galaxies & Dynamics Lecture 22: Galaxy Evolution

1. AY202a Galaxies & DynamicsLecture 22:Galaxy Evolution

2. Population Evolution Tinsley ‘68, SSB ’73, JPH ’77 and the death of the Hubble/Sandage cosmology program … The Flux from a galaxy at time t and in band i is FG(i,t) =   [ Ψ(k,j) ∫ FK(i,t’) dt’ ] where FK(i,t’) is the flux of star of type k in bandpass i at age t’ and ∫ F is the integrated flux in the jth timestep n-1 (n-j)Δt j k (n-j-1)Δt

3. This is piecewise, time-weighted summation in an Age-Flux table for stars Ψ(k,j) is the birth rate function of stars of type k in the jth time step Ψ(k,j)  Ψ(m,t) = m–α e–βt The Initial Mass Function (IMF) is often parameterized as m–α with α = 2.35 as the Salpeter slope The Star Formation Rate (SFR) is often parameterized as an exponential in time R(t) = A e–βt or as R(t) = m0/τ e–(t/τ)τ = 1 Bruzual “C” Model  = 1 - e– (1 Gyr / τ)

4. Gaseous line + Continuum Emission

7. Starbursts a.k.a. Composite galaxes --- its all in a name

8. How Fast They Change! A 25 Myr Burst on an old Spiral ΔL = x2

9. Spectrum vs Type Kennicutt ‘92

10. Hβ as a diagnostic Bursts Young Old α = 0.35 α = 3.35

11. Age C Model vs time

12. μ = 0.7 model vs time

13. B&C = Bruzual & Charlot GW = Worthey BBCFN = Bertelli et al. From Charlot, Worthy & Bressan ‘96

14. Comparison to Observations Charlot, Worthy & Bressan ‘96

15. Early Tracks from I. Iben X =0.708 Y = 0.272 Z = 0.020

17. Modern tracks from Maeder & Meynet (and there are others!) Predicted Evolution depends on [Fe/H] and various assumptions re opacity, mixing, reaction rates, etc. ! There is not yet agreement on these!

20. Star Formation Rates - redux What drives SFR? Schmidt ’59 SFR  ρg dρg / dt which leads to ρg(t)  ρ0 e -t/r • An exponentially declining SFR which is the justification for the Tinsley, SSB, JPH, BC models More general form has dρg/dt ρgn Best fitting current law (Kennicutt ’98) SFR = (2.5 ±0.7)x10-4 (gas/ 1 M pc-2)1.4±0.5 M yr-1 kpc-2 (disk averaged SFR)

21. Relative Star Formation Rate RP/<R> RP/<R> = Present Rate ∫ Average Rate dt b = RP/<R> Im Sb Sc Sa 0.2 0.4 B-V 0.8 1.0

22. SFR(z) = SFR(t) Star Formation history of the Universe Integrated Rate ρv(z,λ) = comoving luminosity density at λ Dust? Madau, Pozzetti & Dickinson ‘98

23. GOODS Giavalisco et al. ’04 Blue = observed Red = corrected to 0.2L* Red = observed Blue = corrected for dust

24. SF Histories can be complex even in simple appearing systems! Smecker-Hane et al. Carina Dwarf

25. Population Synthesis Models Depend on IMF -- shape, slope , upper & lower mass limits of integration SFR -- detailed history [Fe/H] – affects stellar colors, evolutionary history Y -- Helium content affects age, etc. Gas -- Chemistry, density, distribution, infall etc. Dust – related to [Fe/H], etc. Non-thermal activity – presence of an AGN “You can get anything you want at Alice’s Restaurant” A. Guthrie

26. Galaxy Formation & Dynamical Evolution Simple formation picture  Gravitational Instability Start with Euler’s Equations and Newton ρ/t + ·( ρ v) = 0 continuity v/t + (v ·) v + 1/ρp + φ = 0 energy 2φ = 4πG ρ potential Static solution ρ0 = const P0 = const v = 0 Apply linear ρ = ρ0 + ρ1 perturbation p = p0 + p1 analysis v = v0 + v1 φ = φ0 + φ1

27. Now need an equation of state to relate pressure and energy density. Assume adiabatic (no spatial variation in Entropy) Define the sound speed VS2≡ (p/ρ)adiabatic Then VS2 = p1 ρ1

28. We can write the perturbed Euler equations (substituting for p) as ρ1/t + ρ0· v1 = 0 v1/t + (VS2/ρ0) ρ1 + φ = 0 2φ1 = 4πGρ1 Which can be combined as ρ2/t2 -VS22ρ1 = 4πGρ0ρ1 which is a second order DE with solutions ρ1(r,k) = δ(r,t)ρ0 = A e[-i k·r + i ωt]ρ0

29. Where ω and k satisfy the dispersion relation ω2 = VS2κ2- 4πGρ0 ; κ≡ | k | if ω is imaginary, then  exponentially growing modes and for k less than some value, ω is imaginary and modes grow or decay exponentially define kJ = (4πGρ0 /VS2) ≡ Jeans wave number with a dynamical timescale τdyn = (4πGρ0) -1/2 Jeans mass is the total mass inside a sphere of radius λJ/2 = π/kJ MJ = (4π/3) (π/ kJ)3ρ0 = π5/3 VS3 6 G3/2ρ1/2 Masses > MJ are unstable and will collapse

30. The Jeans problem can also be solved in an expanding universe (c.f. Bonnor 1957, MNRAS 117, 104) • Characteristic formation times Galaxy Spheroids z ~ 20 AGN z > 10 Dark Halos z ~ 5 Rich Clusters z ~ 1-2 Spiral Disks z ~ 1 Superclusters, walls, voids z ~ 1 Details depend on Ω and the cause of structure formation

31. Rule of thumb from Peebles Rich clusters have δρ/ρ ~ 100 inside ra 1 + zf ~ 2.5 Ω-1/3 & Globular Cluster systems 1 + zf ~ 8 h-2/3Ω-1/3 so for our favorite numbers of h = 0.7 and ΩM = 0.25 GC formation is at z ~ 16 Time to go hunting in the dark ages!

32. Biased Galaxy Formation Two themes (1) By the mid 1980’s we know that ξ(r), gal ~ ¼ ξ(r), rich clusters so the amplitude of clustering for clusters is much larger (20x) than that of galaxies. Clustering also appears to be a function of galaxy mass (2) ΩM from galaxy clustering etc. is only 0.25 not 1.00000… So how could galaxies, etc. form efficiently?

33. N.Kaiser (’84) solved this by introducing the idea of biased galaxy formation δρ 1/f noise fluctuation spectrum Galaxies form Cut for formation Mean cluster

34. And galaxies will cluster more than the underlying dark matter. If b is the linear biasing factor, then ξ(r)Galaxies = b2ξ(r)Dark matter and (δρ/ρ)Baryons = b (δρ/ρ)DM and b2 = σ82(galaxies) / σ82(mass) where σ8 is the variance in 8 Mpc spheres (roughly where ξ(r)gal 1) Real bias need not be linear, can be a function of environment, etc. Current values ~ 1 to 1.5 Coles & Luchin ‘98

35. Press Schechter Formalism Galaxies and larger structures should be build up by heirarchical clustering --- what happens after fluctuations grow enough to form bound objects? P&S assumed that the amplitudes of the fluctuations could be described by a Gaussian distribution p(Δ) = exp -[ ] where Δ = δρ/ρ is the density contrast associated with perturbations of mass M 1 Δ2 (2π)1/2σ(M) 2 σ2(M)

36. The mean of the distribution is zero, but the variance σ2(M), the mean squared fluctuation, is finite. If only those fluctuations with Δ > ΔC collapse, the fraction is F(M) =  exp-[ ] dΔ = ½ [1 – Φ(tc)] where tc = Δc/ √2 σ and Φ(x) is the probability integral defined by Φ(x) = (2/√π)  e–t2 dt ∞ 1 Δ2 (2π)½σ(M) 2σ2(M) Δc x 0

37. We can then relate the mean square density perturbation to the power spectrum σ2(M) = < Δ2> = A M –(3+n)/3 and we can write tc in terms of the mass tc = = M(3+n)/6 = (M/M*)(3+n)/6 with M* as a reference mass (2A/Δc2) 3/(3+n) With some effort, we can write the mass function as N(M) = ( )γ/2 exp [-( )γ] ΔcΔc √2 σ(M) √2 A½ <ρ> γ M M √π M2 M* M*

38. Now

39. Press-Schechter vs simulations Extended PS (includes non-sphericity) Its surprising that it works at all!

40. Dynamical Evolution Galaxy shapes affected by dynamical interactions with other galaxies (& satellites) Galaxy luminosities will change with accretion & mergers SFR will be affected by interactions Mergers – the simple model Rate P = π R2 <vrel> N t P = probability of a merger in time t R = impact parameter N = density vrel = relative velocities

41. N h-3 rc h vrel 0.05 Mpc-3 20 kpc 300 km/s Roughly P = 2x10-4()( )2( ) 1/H0 a small number, but we see a lot in clusters N ~ 103 – 104 N field V rel ~ 3-5 V rel field The problem was worked first by Spitzer & Baade in the ’50’s, then Ostriker & Tremaine, Toomre2 and others in the ’70’s

42. Mergers occur depending on the Energy and Angular Momentum of the interaction

43. Results from n-body simulations: (1) Cross sections for merging are enhanced if angular momenta of the galaxies are aligned (prograde) and reduced of antialigned (retrograde) (2) Merger remnants will have both higher central surface density and larger envelopes --- peaks and puffs (3) Head on collisions  prolate galaxies along the line of centers, off center collisions  oblate galaxies

44. An additional effect is Dynamical Friction (Chandrasekhar ’60) A satellite galaxy, Ms, moving though a background of stars of density ρ with dispersion σ and of velocity v is dragged by tidal forces wake formed & exerts a negative pull (Schombert)

45. dv/dt = -4πG2 MSρ v-2 [φ(x) – xφ’(x)] lnΛ where φ = error function x = √2 v/σ Λ = rmax/rmin (maximum & minimum impact parameters) usually rmin = max (rS, GMS/v2) If you apply this to typical galaxy clustering distributions, on average a large E galaxy has eaten about ½ its current mass. Giant E’s in clusters are a special case.

46. L Ostriker & Hausman ’78 Simulations for 1st ranked galaxies (BCG’s) 1. Galaxies get brighter with time due to cannibalism (L) 2. Galaxies get bigger with time (β) 3. Galaxies get bluer with time by eating lower L, thus lower [Fe/H] galaxies Core radius Profile

47. Eisenstein et al…. BAO We present the large-scale correlation function measured from a spectroscopic sample of 46,748 luminous red galaxies from the Sloan Digital Sky Survey. The survey region covers 0.72 h-3 Gpc3 over 3816 deg2 and 0.16<z<0.47, making it the best sample yet for the study of large-scale structure. We find a well-detected peak in the correlation function at 100 h-1 Mpc separation that is an excellent match to the predicted shape and location of the imprint of the recombination-epoch acoustic oscillations on the low-redshift clustering of matter. This detection demonstrates the linear growth of structure by gravitational instability between z~1000 and the present and confirms a firm prediction of the standard cosmological theory. The acoustic peak provides a standard ruler by which we can measure the ratio of the distances to z=0.35 and z=1089 to 4% fractional accuracy and the absolute distance to z=0.35 to 5% accuracy. From the overall shape of the correlation function, we measure the matter density Ωmh2 to 8% and find agreement with the value from cosmic microwave background (CMB) anisotropies. Independent of the constraints provided by the CMB acoustic scale, we find Ωm=0.273+/ 0.025+0.123 (1+w0)+0.137ΩK. Including the CMB acoustic scale, we find that the spatial curvature is ΩK=-0.010+/-0.009 if the dark energy is a cosmological constant. More generally, our results provide a measurement of cosmological distance, and hence an argument for dark energy, based on a geometric method with the same simple physics as the microwave background anisotropies. The standard cosmological model convincingly passes these new and robust tests of its fundamental

48. Likelihood contoursof CDM models asa function of Ωmh2 and DV(0.35). The likelihoodhas been taken tobe proportional to exp(- χ2/2),and contours corresponding to1 through 5 σfor a two-dimensional Gaussianhave been plotted. Theone-dimensional marginalized values areΩmh2 = 0.130 ±0.010 and DV(0.35) =1370 ± 64 Mpc.

49. w = -1, non zero curvature Solid lines constant curvature Dashed lines constant Ωm

50. w =-1, non-zero curvature Dashed lines are constant H0