AY202a Galaxies & Dynamics Lecture 23: Galaxy Evolution. CMD’s for local dwarfs Tolstoy. Hill & Tosi 2009 LG Dwarfs SFR. Dynamical Evolution. Galaxy shapes affected by dynamical interactions with other galaxies (& satellites) Galaxy luminosities will change with accretion & mergers
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Tolstoy. Hill & Tosi 2009
LG Dwarfs SFR
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
N h-3 rc h vrel
0.05 Mpc-3 20 kpc 300 km/s
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
depending on the Energy and Angular Momentum of the interaction
Time evolution of an encounter between an exponetial disk and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the disk
Velocity-Radius Shells Quinn ‘84 and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the disk
Results from n-body simulations: and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the disk
(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
An additional effect is and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the diskDynamical 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
& exerts a
dv/dt = -4 and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the diskπG2 MSρ v-2 [φ(x) – xφ’(x)] lnΛ
φ = error function
x = √2 v/σ
Λ = rmax/rmin (maximum & minimum
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.
L and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the disk
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
5 different simulations of eating 30 neighbors
Closed Box Reprocessing
= - +
MG(t) = MG0 –M*(t) + ME(t)
ME complicated ME(m,t)
usually assume for M < 3 M, ME(t) ~0
dMG dM* dME
dt dt dt
Gas Stars Ejecta from evolving *
dM and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the diskz/dt
dMz/dt = rate at which newly formed metals are
ejected from stars
To make this work we need the theory of element formation.
BBFH 1957 etc.
see Arnett ARAA 1995
also work bya variety of other authors.
Silver to Antimony
Slow neutron capture in stars. Neutron capture slower than beta decay.
Rapid neutron capture relative to beta decay. Primarily in core collapse SN.
Structure of an evolved 25 M and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the disk Star
Predicted Yields and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the disk
SFR = dM*/dt = C μn μ = gas surface density
and assume the Instantaneous Recycling approximation some fraction α of gas is not returned to the gas mass and a fraction 1- α is returned instantaneously, metal enriched
μ = μ0 – α s , s= stellar density
dμ/dt = -α ds/dt = -α Cμn = -μn /t0
where t0 = 1/αC is the characteristic time constant for significant changes in the disk gas density
If z is the fraction of heavy elements by mass in the gas, and λ is the fraction of mass in stars which is converted completely to heavy elements and ejected into the ISM. If we define zμ as the fraction of heavy elements per unit mass+ in the disk
d(zμ)/dt = -z ds/dt + (1-α –λ) z ds/dt + λ ds/dt
then the yield Y = λ/α = the ratio of the mass converted into heavy elements to the mass locked up in stars, and we have
d(zμ)/ds = λ (1 – z) - αz
loss due to SF
return due to winds w no processing
return of completely processed material
+ mass includes both stellar and gas
d(zμ)/ds = μ dz/ds + z dμ/ds = -αμ dz/dμ – α z
-μ dz/dμ = dz/d(ln 1/μ) = λ (1 – z) /α
λ/α is usually termed the yield Y, the ratio of the mass completely converted to heavy elements to the mass locked up in stars. (in the limit of small z)
dz/d(ln 1/μ) = Y
z = Y ln(1/μ)
so the heavy element abundance is simply related to the net fraction of the mass of gas turned into stars
For the simple Tayler model the yield is ~ 0.004
Cumulative histogram of N vs z
The G dwarf problem --- most nearby stars are metal rich
1. Prompt Initial Enrichment (PIE)
2. Variable IMF with increased yields in the past
3. Metal enhanced star formation stars for preferentially in high [Fe/H] regions
4. Infall --- gas not described by a closed box
“4” may be best – we expect infall in most formation scenarios, but we need a variable infall rate
MG(t) = MG0 + ME(t) - M*(t) + MI(t)
all of 1-4 probably operate in the galaxy
Simple model has one important success ---
successfully predicts linear metallicity gradients in spirals
z(r) = z0 – r (1/rT – 1/rG)
rT = scale length of total mass density
rG = scale length of total gas density
Ages from ubvyH and photometry
SN II Production and
SN Ia Production
Baade’s simple view
Shu, Li & Allen 2004
Magnetic fields set scaling with mass. YSO Winds and radiation pressure depress the high mass end.
Galaxies evolve both dynamically and via stellar populations.
Dynamics driven by mergers and acquisitions which depend on environment and such variables as the energy and angular momentum of encounters.
Populations depend on a host of variables but primarily IMF, SFR, gas processes and chemistry. Chemistry can be complicated.
Dynamics can induce Star Formation.
Longair, M. 2008, Galaxy Formation, Springer.
Pagel, B. 1997, Nucleosynthesis & Chemical Evolution of Galaxies, Cambridge