Ay202a galaxies dynamics lecture 23 galaxy evolution
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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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Ay202a galaxies dynamics lecture 23 galaxy evolution
AY202a Galaxies & DynamicsLecture 23:Galaxy Evolution


CMD’s for local dwarfs

Tolstoy. Hill & Tosi 2009

LG Dwarfs SFR


Dynamical evolution
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


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


Mergers occur

depending on the Energy and Angular Momentum of the interaction


Milky way andromeda collision dubinski
Milky Way Andromeda collision (Dubinski)

M31

MW

Androway


NGC3923

Shell galaxy

D. Malin


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

wake formed

& exerts a

negative pull

(Schombert)


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

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.


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

Core radius

5 different simulations of eating 30 neighbors

Profile


Chemical evolution
Chemical Evolution and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the disk

Simplest Model

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 *

(winds, SN)


dM and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the diskz/dt

dM*/dt

Yield

y(t) =

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.


Neutron capture
Neutron Capture and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the disk


S process
S Process and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the disk

Silver to Antimony

Slow neutron capture in stars. Neutron capture slower than beta decay.


R process
R Process and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the disk

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


Where the elements come from
Where the elements come from and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the disk


Element production pagel
Element Production and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the disk(Pagel)


Sn ia
SN Ia and a spheroid of mass 100x in units of the circular period. Bar under 0 is ten scale lengths for the disk


Tayler s disk model
Tayler’s Disk Model 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

Then

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


Substituting for S and

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




Model and

Cumulative histogram of N vs z

N

z

The G dwarf problem --- most nearby stars are metal rich

Data


Possible solutions and

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


Metallicity gradients
Metallicity Gradients and

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

Element Ratios


Population box
Population Box and

Baade’s simple view


Hodge’s population box and

SFR

[Fe/H]

AGE




Theoretical basis for the IMF? and

Shu, Li & Allen 2004

Magnetic fields set scaling with mass. YSO Winds and radiation pressure depress the high mass end.


Summary
Summary and

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.


References
References and

Longair, M. 2008, Galaxy Formation, Springer.

Pagel, B. 1997, Nucleosynthesis & Chemical Evolution of Galaxies, Cambridge


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