AY202a Galaxies

1
AY202a Galaxies DynamicsLecture 22Galaxy
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) ? ? ?(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)?t
j k (n-j-1)?t
3

• This is piecewise, time-weighted summation in an
  Age-Flux table for stars
• ?(k,j) is the birth rate function of stars of
  type k in the jth time step
• ?(k,j) ? ?(m,t) ma eßt
• The Initial Mass Function (IMF) is often
  parameterized as ma
• with a 2.35 as the Salpeter slope
• The Star Formation Rate (SFR) is often
  parameterized as an exponential in time R(t) A
  eßt
• or as R(t) m0/t e(t/t) t 1 Bruzual
  C Model
• ?
  1 - e (1 Gyr / t)

4
Gaseous line Continuum Emission
5
(No Transcript)
6
(No Transcript)
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 ?L x2
9

• Spectrum
• vs
• Type
• Kennicutt 92

10
Hß as a diagnostic
Bursts
Young
Old a 0.35 a 3.35
11
Age
C Model vs time
12
µ 0.7 model vs time

13

• BC 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

16
(No Transcript)
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!

18

19
(No Transcript)
20
Star Formation Rates - redux

• What drives SFR?
• Schmidt 59 SFR ? ?g ? d?g / dt
• which leads to ?g(t) ? ?0 e -t/r
• An exponentially declining SFR which is the
  justification for the Tinsley, SSB, JPH, BC
  models
• More general form has d?g/dt ? ?gn
• Best fitting current law (Kennicutt 98)
• ?SFR (2.5 0.7)x10-4 (?gas/ 1 M? pc-2)1.40.5
• M? yr-1 kpc-2
  (disk averaged SFR)

21

• Relative Star Formation Rate RP/ltRgt

RP/ltRgt Present Rate ? Average Rate dt
b RP/ltRgt
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
• ?v(z,?) comoving luminosity density at ?

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 Alices
  Restaurant
• 
  A. Guthrie

26
Galaxy Formation Dynamical Evolution

• Simple formation picture ? Gravitational
  Instability
• Start with Eulers Equations and Newton
• ??/?t ?( ? v) 0
  continuity
• ?v/?t (v ?) v 1/??p ?f 0
  energy
• ?2f 4pG ?
  potential
• Static solution ?0 const P0 const v 0
• Apply linear ? ?0 ?1
• perturbation p p0 p1
• analysis v v0 v1
• f f0 f1

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/??)adiabatic
• Then
• VS2

p1 ?1
28

• We can write the perturbed Euler equations
  (substituting for p) as
• ??1/?t ?0 ? v1 0
• ?v1/?t (VS2/?0) ??1 ?f 0
• ?2f1 4pG?1
• Which can be combined as
• ??2/?t2 -VS2 ?2?1 4pG?0?1
• which is a second order DE with solutions
• ?1(r,k) d(r,t)?0 A e-i kr i ?t ?0

29

• Where ? and k satisfy the dispersion relation
• ?2 VS2 ?2 - 4pG?0 ? k
• if ? is imaginary, then ? exponentially growing
  modes
• and for k less than some value, ? is imaginary
  and modes grow or decay exponentially
• define kJ (4pG?0 / VS2) Jeans wave number
• with a dynamical timescale tdyn (4pG?0)
  -1/2
• Jeans mass is the total mass inside a sphere of
  radius
• ?J/2 p/kJ
• MJ (4p/3) (p/ kJ)3 ?0

p 5/3 VS3 6 G3/2 ?1/2
Masses gt 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 gt 10
• Dark Halos z 5
• Rich Clusters z 1-2
• Spiral Disks z 1
• Superclusters, walls, voids z 1
• Details depend on O and the cause of structure
  formation

31

• Rule of thumb from Peebles
• Rich clusters have d?/? 100 inside ra
• 1 zf 2.5 O -1/3
• Globular Cluster systems
• 1 zf 8 h-2/3 O -1/3
• so for our favorite numbers of h 0.7
• and OM 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 1980s we know that
• ?(r), gal ¼ ?(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) OM 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
• d?

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
• ?(r)Galaxies b2 ?(r)Dark matter
• and
• (d?/?)Baryons b (d?/?)DM
• and b2 s82(galaxies) / s82(mass)
• where s8 is the variance in 8 Mpc spheres
• (roughly where ?(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?
• PS assumed that the amplitudes of the
  fluctuations could be described by a Gaussian
  distribution
• p(?) exp -
  
• where ? d?/? is the density contrast
  associated with perturbations of mass M

1 ?2 (2p)1/2
s(M) 2 s2(M)
36

• The mean of the distribution is zero, but the
  variance s2(M), the mean squared fluctuation, is
  finite.
• If only those fluctuations with ? gt ?C collapse,
  the fraction is
• F(M) ? exp-
  d? ½ 1 F(tc)
• where tc ?c/ v2 s and F(x) is the
  probability integral defined by
• F(x) (2/vp) ? et2
  dt

8
1 ?2 (2p)½
s(M) 2s2(M)
?c
x
0
37

• We can then relate the mean square density
  perturbation to the power spectrum
• s2(M) lt ?2gt A M (3n)/3
• and we can write tc in terms of the mass
• tc M(3n)/6
  (M/M)(3n)/6
• with M as a reference mass (2A/?c2) 3/(3n)
• With some effort, we can write the mass function
  as
• N(M) ( )?/2 exp -(
  )?

?c ?c v2 s(M) v2 A½
lt?gt ? M M vp
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 p R2 ltvrelgt N t
• P probability of a merger in time t
• R impact parameter N density vrel relative
  velocities

41

• 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 50s, then Ostriker Tremaine, Toomre2
  and others in the 70s

N h-3 rc h vrel
0.05 Mpc-3 20 kpc 300 km/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 ? with dispersion
  s and of velocity v is dragged by tidal forces
• 
  wake formed
• 
  exerts a
• 
  negative pull
• (Schombert)

45

• dv/dt -4pG2 MS ? v-2 f(x) xf(x) ln?
• where
• f error function
• x v2 v/s
• ? 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 Es in
  clusters are a special case.

46

• Ostriker Hausman 78
• Simulations for 1st ranked galaxies (BCGs)
• 1. Galaxies get brighter with time due to
  cannibalism (L)
• 2. Galaxies get bigger with time (ß)
• 3. Galaxies get bluer with time by eating lower
  L, thus lower Fe/H galaxies

L
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 0.16ltzlt0.47, 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 z1000 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 z0.35 and z1089
  to 4 fractional accuracy and the absolute
  distance to z0.35 to 5 accuracy. From the
  overall shape of the correlation function, we
  measure the matter density Omh2 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 Om0.273/ 0.0250.123 (1w0)0.137OK.
  Including the CMB acoustic scale, we find that
  the spatial curvature is OK-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 contours of CDM models as a function
of O mh2 and DV(0.35). The likelihood has been
taken to be proportional to exp(- ? 2/2), and
contours corresponding to 1 through 5 s   for a
two-dimensional Gaussian have been plotted. The
one-dimensional marginalized values are O mh2
0.130 0.010 and DV(0.35) 1370 64 Mpc.
49

• w -1, non zero curvature
• Solid lines constant curvature
• Dashed lines constant ?m

50

• w -1, non-zero curvature
• Dashed lines are constant H0