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 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) 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
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
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)
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.
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 5 different simulations of eating 30 neighbors Profile
Chemical Evolution 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)
dMz/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.
S Process Silver to Antimony Slow neutron capture in stars. Neutron capture slower than beta decay.
R Process Rapid neutron capture relative to beta decay. Primarily in core collapse SN.
Tayler’s Disk Model 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 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
Curve of Growth for a typical Voigt line profile – Linear Log Sq Root
Model Cumulative histogram of N vs z N z The G dwarf problem --- most nearby stars are metal rich Data
Possible solutions 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 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
= 0.00 = 2.35 = 4.00
SN II Production SN Ia Production Element Ratios
Population Box Baade’s simple view
Hodge’s population box SFR [Fe/H] AGE