The Local Group and Galactic Evolution
I
The Local Group
I
Satellite Galaxies
I
Cepheid Variables
I
Tides and the Roche Limit
I
Local Spirals
I
Chemical Evolution
I
Dwarf Galaxies
I
Future of the Local Group
J.M. Lattimer
AST 346, Galaxies, Part 5
The Local Group
J.M. Lattimer
AST 346, Galaxies, Part 5
The Local Group
J.M. Lattimer
AST 346, Galaxies, Part 5
The Local Group
J.M. Lattimer
AST 346, Galaxies, Part 5
The Large Magellanic Cloud
S Dor
HI gas
⇐=
Large
Magellanic
Cloud
Hα
10◦ or 8.5 kpc
=⇒ ⇐=
7◦ or 6.0 kpc
IR - 24µm
optical
J.M. Lattimer
AST 346, Galaxies, Part 5
=⇒
Bulge
Large Magellanic Cloud
J.M. Lattimer
AST 346, Galaxies, Part 5
Magellanic Clouds
J.M. Lattimer
AST 346, Galaxies, Part 5
Cepheid Variables
MV = −3.525 log(P/d) + 2.88(V − Ic )0
−2.80 − 1.05AV
J.M. Lattimer
AST 346, Galaxies, Part 5
Pulsational Frequency
The Euler equation of motion for a surface layer of mass m and radius R
m
G Mm 1 ∂p
d 2R
=−
−
.
dt 2
R2
ρ ∂r
Use V = 1/ρ and −Vdp = pdV − pV = pdV = 4πR 2 dr (p = 0 at the
top of the layer (surface) and V = 0 at the bottom). In equilibrium, one
has G Mm/R02 = 4πR02 p0 . With perturbation R → R0 + δR; p → p0 + δp
m
d 2 (R + δR)
G Mm
=−
+ 4π(R + δR)2 (p + δp)
dt 2
(R + δR)2
d 2 δR
2G Mm
2
=
m
+
8πR
p
0 0 δR + 4πR0 δp
dt 2
R03
d 2 δR
GM
=
(4 − 3γ)δR
dt 2
R03
We used pV γ = constant or pR 3γ = constant or δp/p0 = −3γδR/R0 .
This equation has a harmonic solution δR = A sin ωt if γ > 4/3.
s
s
GM
GM √
ω = (3γ − 4) 3 '
∼ ρ̄.
R0
R03
J.M. Lattimer
AST 346, Galaxies, Part 5
Pulsational Instability
An instability will occur if opacity
increases with compression
(temperature), which is not normally
the case. Normal stellar opacity is of
the Kramer’s type κ ∝ ρT −3.5 and
ρ ∝ T 3 in adiabatic matter. Thus
κ ∝ ρ−1/6 and decreases upon
compression.
In a partial ionization zone,
H↔ H+ + e − , He ↔ He+ + e − ,
He+ ↔ He++ + e − , the temperature
increases less because of the ionization
energy sink. This is the key to the
kappa mechanism.
J.M. Lattimer
V
I A → B: opacity increases during compression
I B → C : heat absorbed ∆SBC = ∆QBC /Thot
I C → D: opacity decreases during expansion
I D → A: heat released ∆SDA = ∆QDA /Tcold
∆QBC + ∆QDA = ∆SBC (Thot − Tcold )/Thot > 0
AST 346, Galaxies, Part 5
Period-Luminosity Relation
I
log L = 3.5 log M + a
I
log L = 2 log R + 4 log Teff
I
log P = − 12 log M +
I
1
log Teff ∼ − 20
log L
3
1
3
log P = ( 4 − 7 + 20
) log L − 3 log Teff
log P = 0.76 log L + b + 7a
2.5
MV = − 0.76
log P + c = −3.3 log P +
I
I
I
3
2
log R + b
J.M. Lattimer
+b+
a
7
c
AST 346, Galaxies, Part 5
Dwarf Spheroidal Galaxies
I
At least as
luminous as
globular clusters
I
Surface
brightness 1% of
LMC
I
> 10 in Local
Group
I
No young stars,
no gas
I
Stars of a wide
range of ages
3 − 10 Gyr
I
Low metallicities
Z = 0.02Z
7
3 Gyr
J.M. Lattimer
AST 346, Galaxies, Part 5
15
Galaxy Encounters
I
Weak or distant encounters
I
I
I
I
Flyby with associated tides
Satellite orbit decay due to
dynamical friction
Tidal evaporation of orbiting
satellite
Tidal or gravitational shocks
I
Strong or close encounters
I
I
I
Analytic cases (mergers can only
be treated numerically)
I
I
I
I
J.M. Lattimer
Mergers
Global gravitational effects
become important
Dynamical friction (small
system moving through a larger
one)
Tidal evaporation
(Jacobi/Roche limit)
Slow encounters (adiabatic
approximation)
Fast (shocking) encounters
(impulse approximation)
AST 346, Galaxies, Part 5
Distant Weak Encounters and Drag
Use the impulse approximation, ignoring
the deviation in the stellar paths. The
impact parameter is b. The perpindicular
pull of star m on star M is GmM/r 2
times b/r , with r 2 = b 2 + V 2 t 2 :
dV⊥
GmMb
=M
F⊥ (t) = 2
dt
(b + V 2 t 2 )3/2
Deflection angle:
Z +∞
1
2Gm
∆V⊥
=
F⊥ dt =
θ=
V
MV −∞
bV 2
The encounter has symmetry about the
vector of closest approach, the line θ/2
backwards from the original perpendicular
impact parameter vector. Newton’s 3rd
law says m∆v = M∆V .
∆t∆Fdrag = −m∆v|| = −
Fdrag
2G 2 M2 m
=−
.
b2 V 3
Z Z
=
nV ∆Fdrag dt2πbdb
=−
4πG 2 M2 nm ln Λ
V2
bmax
Λ=
bmin
Drag is caused by the component of the
force parallel and backwards to M’s
motion. Then
J.M. Lattimer
2G Mm θ
bV 2
AST 346, Galaxies, Part 5
Distant Weak Encounters and Drag
The basic idea is that a moving mass
attracts objects to it, but because of
its motion, the objects tend to gather
behind the mass, pulling it backwards.
I
Open clusters: ln Λ ≈ 6
I
Globular clusters: ln Λ ≈ 11
I
Large elliptical galaxy: ln Λ ≈ 22
I
Galaxy clusters: ln Λ ≈ 7
Allowing for a range of velocities
(Chandrasekhar friction formula):
Z V
4πG 2 M2 m
ln Λ f (v )d 3 v
Fdrag = −
V2
0
I
V << v , use f (v ) ≈ f (0),
resembles Stokes law for motion
through a viscous fluid.
16
Fdrag = − π 2 G 2 M2 mf (0)V ln Λ
3
J.M. Lattimer
I
V >> v , all stars contribute,
drag decreases with V :
Fdrag = −4πG 2 M2 nmV −2 ln Λ
Maxwellian√with dispersion σ,
X = V /(σ 2):
Fdrag = −4πG 2 M2 nmV −2 ln Λ
i
h
2 √
× erf (X ) − 2Xe −X / π
h
i
2
' −4πG 2 M2 nmV −2 ln Λ 1 − e −0.6X
I
AST 346, Galaxies, Part 5
Applications of Dynamical Friction
I
Satellite in circular orbit
Take an isothermal galaxy: √
ρ(r ) = Vc2 /(4πGr 2 ), σ = Vc / 2
or X = 1, L = MVc r
Fdrag = −0.43G (M/r )2 ln λ
dL/dT = Fdrag r =
−0.43G (M2 /r ) ln Λ =
MVc dr /dt
I
Massive galaxy encounter
M = 1010 M , ri = 20 kpc,
V = Vc :
tinfall ' 2 × 108 yr ∼ orbit period.
I
LMC
M ≈ 2 × 1010 M , ri = 60 kpc:
tinfall ≈ 3 × 109 yr.
tinfall = Vc ri2 /(0.86G M ln Λ)
Example: globular cluster orbiting
Milky Way
M = 106 M , Vc = 250 km/s,
bmax = ri = 2 kpc:
tinfall ' 2.6 × 1010 yr
J.M. Lattimer
Why is LMC still there? Not on a
circular orbit; LMC has been
bound to SMC in elliptic
(e = 0.2) orbit. Their orbit has
decayed by factor 2 but will
tidally separate when approaching
Milky Way within 30 kpc.
They will settle in Galactic center
in 1010 yr.
AST 346, Galaxies, Part 5
Tidal Limit
Satellite and galaxy are fixed in a
rotating frame. A star’s energy
E = V 2 /2 + Φ is not conserved; but
EJ = V 2 /2 + Φeff is.
Φeff (r) = Φ(r) − |Ω × r|2 /2
Along a line connecting m and M
with origin at m:
GM
Φeff (x) = − |D−x|
−
Gm
|x|
=
Ω2
2 (x
− D)2
Turning points:
xJ ' ±D(m/3M)1/3
is the Jacobi (or tidal, Roche, Hill)
radius.
For an isothermal potential,
xJ ' ±D(m/2M)1/3 .
J.M. Lattimer
AST 346, Galaxies, Part 5
Satellite Evaporation and Destruction
Satellite star with EJ moving away
from satellite has decreasing V , and
turns around when EJ = Φeff .
If EJ > Φeff (rJ ) the star is lost
(evaporated). This differs from slow
evaporation caused by scattering of
stars to V > Ve . Even bound stars
(E < 0) can have EJ > Φeff (rJ ).
A satellite approaching a galaxy has
decreasing rJ and Φeff (rJ ) so it loses
more and more stars.
Since most stars are only marginally
bound (N(E ) peaks near E = 0), a
small decrease in Φeff (rJ ) can result in
the loss of many stars.
J.M. Lattimer
AST 346, Galaxies, Part 5
Slow and Fast Encounters
Although orbits of many stars
significantly affected by a tidal
encounter, the tightly bound ones
(Porb << tencounter ) are not. The tidal
field slowly changes and these stars
respond adiabatically.
The opposite extreme is a tidal shock:
Porb >> tencounter or
Vinternal << ∆Vencounter . These stars
don’t move during the encounter, so
no change in PE. They feel an impulse
and ∆ KE. These stars are thus
heated.
System must expand and cool in
response. A two step process (recall
Eo,f = - KEo,f ):
J.M. Lattimer
I
shock: KEi = KEo + ∆KE,
Ei =Eo + ∆ KE = - KEo + ∆ KE
relaxation: Ef = Ei , KEf =
KEo − ∆KE
Although shock heated system by
∆KE, during relaxation it cooled by
−2∆KE and expanded.
I
Some stars received enough energy to
unbind and evaporate. Repeated
shocks can disintegrate a cluster.
If the encounter is distant, the system
is left elongated, long axis pointing to
the point of closest approach.
AST 346, Galaxies, Part 5
Examples
I
Open clusters are shocked by
passage of dense molecular clouds;
most evaporated after 5 × 108 yr.
I
Globular clusters are shocked by
passing through disk.
If σ = 5 km/s, r = 10 pc,
V⊥ = 170 km/s, R = 3.5 kpc:
tdisrupt ≈ 6 × 109 yr.
I
Galaxies in clusters (galaxy
harassment): disks are heated and
thicken; spiral arm formation is
suppressed; galaxies appear to
evolve to earlier Hubble type.
Stars and dark matter expand and
are lost but join the cluster.
Gas loses angular momentum and
falls to center, triggering star
formation (starburst).
J.M. Lattimer
I
Ring galaxies are formed from
tidal shocks. A perturber passes
rapidly through center of disk,
inducing an inward ∆Vr . Sets
up a synchronized epicyclic
motion, results in an expanding
circular density wave or ring.
These trigger star formation.
AST 346, Galaxies, Part 5
Andromeda Galaxy
I
Large than Milky Way: 50% more
luminous, hR is double,
V (R) ∼ 260 km/s (about 20-30%
larger). Twice the number of
globular clusters (300).
I
Bulge is larger than Milky Way’s,
with about 30-40% of the
luminosity. Stars are older than a
few Gyr and relatively rich in
heavy elements.
I
I
Has a compact, semi-stellar
nucleus, with two concentrations
of light 2pc (0.5 arcsec) apart.
One is a star cluster, one is a
black hole of 4 × 106 M .
Nucleus is free of gas and dust.
Metal-poor globular clusters have
deeply plunging trajectories.
J.M. Lattimer
I
Most stars within a few kpc of
disk are not metal-poor, as if the
bulge was overflowing. These are
about 6 Gyrs old and may be the
remnant of a merger with a
metal-rich (and therefore
massive) galaxy.
I
A “ring of fire” circles at 10 kpc
and contains most of the young
stars. Marked by HII regions and
CO emission.
I
Less pronounced, and tightly
wound, spiral features makes this
an Sb galaxy, compared to Milky
Way (SBc).
I
4 − 6 × 106 M of HI, 50% more
than Milky Way.
AST 346, Galaxies, Part 5
M31
J.M. Lattimer
AST 346, Galaxies, Part 5
Formation of Local Group
Denser clumps collapse, and are already clustered.
Tidal torques induce slow rotation
J.M. Lattimer
AST 346, Galaxies, Part 5
Galactic Chemical Evolution
Evolution of total mass
M(t) = Mg (t) + M∗ (t) in terms of
inflows f (t) and outflows o(t):
In the Closed Box Model, f (t) = o(t).
The evolution of the gas mass Mg (t)
The Initial Mass Function (IMF) is ξ.
Integrate over stars dying at time t,
i.e., from Mt to the upper limit of the
IMF MU .
The evolution of species i with mass
Mg Zi in the gas is
dMg /dt = −Ψ + E + f − o
dMg Zi /dt = −ΨZi + Ei + fZi,f − oZi,o
dM/dt = f − o
in terms of the Star Formation Rate
(SFR, Ψ(t)) and the rate of mass
ejection by dying stars E (t).
A star of mass M is created at time
t − τM and dies at time t > τM ,
leaving a remnant of mass CM .
Z
MU
E (t) =
The rate of stellar ejection of species i:
Z
MU
Ei (t) =
Yi (M)Ψ(t−τM )ξ(M)dM
Mt
where Yi (M) is the stellar yield and
could depend on t.
(M−CM )Ψ(t−τM )ξ(M)dM
Mt
J.M. Lattimer
AST 346, Galaxies, Part 5
Inputs
Stellar lifetimes strongly decrease
with M.
Stellar remnants include white
dwarfs, neutron stars and black
holes. Their masses depend on
the extent of mass loss by winds.
Ejected mass fractions increase
with M.
Stellar yields are better expressed
in terms of net yields
yi (M) = Yi (M) − Zi (M − CM ),
the newly created mass of i minus
what was originally there.
J.M. Lattimer
AST 346, Galaxies, Part 5
Initial Mass Function
Two simplified cases:
Luminosity function
f (L) = dN/dL and M − L
relation for MS stars
φ(L) = dM/dL. The present-day
mass function (PDMF, F (M)) is
F (M) = dN/dM = f φ.
The IMF can be derived if the SFR
is known as it is an integral over
time of the star creation rate ΦΨ.
If the IMF doesn’t depend on t:
Z T
ξ(M) = F (M)/
Ψ(t)dt.
T −τM
Return Mass Fraction R is mass
fraction of a stellar generation
returned
Z to ISM
I
Short-lived stars
ξ(M) =
I
Eternal stars
F (M)
hΨiτM
R
−1 T
Ψ(t)dt is
where hΨi = T
0
the past average SFR.
ξ(M) =
Salpeter formula (α = 2.35)
ξ(M) = dN/dM = ξo M−α
Z MU
1=
ξ(M)MdM
ML
MU
(M − CM )ξ(M)dM
R=
MT
ξo = ξ0 Mα−1
R = 0.28 (S), 0.30 (K + S),
0.34 (C + S)
J.M. Lattimer
F (M)
.
Ψ0 τM
AST 346, Galaxies, Part 5
IMF and Its Evolution
J.M. Lattimer
AST 346, Galaxies, Part 5
Star Formation Rate
Schmidt (1959): Ψ(t) = νMg (t)N
N ∼ 2 theoretically if referring to mass density
N ∼ 1.4 observationally if referring to surface density, more easily
measured.
Kennicutt (1998): Ψ ∝ Σ/τdyn where τdyn = R/V (R).
J.M. Lattimer
AST 346, Galaxies, Part 5
Analytical Chemical Evolution
Analytical solutions are possible if Instantaneous Recycling
Approximation (IRA) is adopted (Schmidt 1963). Stars are either
I “eternal”, M < M , τM ≥ T ∼ 12 Gyr, or
I “dead at birth”, M < M , τM ≈ 0.
With IRA, Ψ(t − τM ) = Ψ(t) 6= f (M). Define pi to be the amount of i
created by a stellar generation per unit mass of “eternal” stars and
remnants:
Z
MU
pi = (1 − R)−1
yi (M)ξ(M)dM,
MT
For a closed box, IRA model
dMg Zi
dMg
= −(1 − R)Ψ(t),
= Ψ(t)(1 − R)(pi − Zi ).
dt
dt
Eliminating Ψ and t, and setting Mg (t = 0) = M:
Mg dZi = −pi dMg ;
Zi = Zi,0 + pi ln
M
Mg
Assuming a Schmidt Law with N = 1:
Mg = Me −ν(1−R)t ,
J.M. Lattimer
Zi = Zi,0 + pi ν(1 − R)t.
AST 346, Galaxies, Part 5
Models
Parameters of the model should be constrained to produce the
present-day metallicity. Assuming Zi,0 = 0, R ' 0.3, non-IRA models
imply N = 1 and ν = 1.2 Gyr−1 . IRA predicts
Mg (T )/M = e −ν(1−R)T ' 4 × 10−5
compared to the observed value Mg (T ) ' 0.2M. Also
p = −(Z − Z0 )/ ln(Mg /M) ' 0.6Z ' 0.012
J.M. Lattimer
AST 346, Galaxies, Part 5
Metallicity Evolution
Nearby F and G stars
r v < 80 km/s
b v > 80 km/s
J.M. Lattimer
AST 346, Galaxies, Part 5
Metallicity Distribution
Mg = Me −[Z (t)−Z (0)]/p .
Where the gas abundance is high relative to stars (outer disk regions) the
metallicity is low.
Disk gas in M33
J.M. Lattimer
AST 346, Galaxies, Part 5
Metal Abundances in Bulge Giant Stars
Mass of stars with metallicity between Z and Z + ∆Z is
dM∗
∆Z = Me −[Z (t)−Z (0)]/p ∆Z .
dZ
Consistency indicates bulge retained all its gas, turning it into stars.
p = 0.7Z , G and K giant stars in Galactic bulge.
dM∗ /dZ
dM∗ /d ln Z
J.M. Lattimer
AST 346, Galaxies, Part 5
Metal Abundances in Solar-Neighborhood Dwarf Stars
If Z (0) = Z0 6= 0, Z0 ∼ 0.15Z :
Z − Z0 ' p ln (M/Mg ) and p ' 0.63Z .
Closed box model with IRA and
Z (0) = 0 suggests for solar
neighborhood
Z (T ) ' Z ' p ln(
M∗ (< 0.25Z )
1 − e (Z0 −0.25Z )/p
=
M∗ (< 0.7Z )
1 − e (Z0 −0.7Z )/p
' 0.25.
M
)
Mg
50
),
13
p ' 0.74Z .
≈p ln(
Fraction of metal-poor stars with
Z < Z /4:
M∗ (< 0.25Z )
1 − e −0.25Z /p
=
M∗ (< 0.7Z )
1 − e −0.7Z /p
' 0.52.
Observed fraction ∼ 25%. Known
as the G-dwarf problem.
d[N(Z < Z 0 )/N(Z < ZT )]/d ln Z
Pre-enrichment: Z0 = 0.08Z
Infall: exponential τ = 7 Gyr
J.M. Lattimer
AST 346, Galaxies, Part 5
Evidence For Infall
There is another inconsistency with the closed box model.
Note Ψ ∼ 3 − 5M yr−1 in the solar neighborhood.
Present disk gas mass is Mg ∼ 5 − 10 × 109 M .
Remaining epoch of star formation should last no longer than
Mg /[Ψ(1 − R)] ∼ 1.4 − 4.8 Gyr.
Why do we live so near the end of star formation?
Additional gas must be accumulating in the Galactic disk.
J.M. Lattimer
AST 346, Galaxies, Part 5
Models with Infall
If it is assumed gas infalls with a metallicity Z0 = Z (t = 0) and an infall
rate proportional to star formation rate:
f (t) = Λ(1 − R)Ψ(t).
The parameter Λ ≤ 1; if Λ = 1 then Mg (t) = Mg (0).
Λ−1 −1
Λ/(1−Λ) !
Λ
p
Mg (t)
Mg (t)
= 1 − [Z (t) − Z0 ]
, Z (t) =
1−
.
Mg (0)
p
Λ
Mg (0)
When Z = Z0 + p/Λ, the maximum metallicity, Mg → 0. Introducing
Z
M(t) − M(0)
1−R t
Mg (t) − M(0) Λ
=Λ
Ψ(t 0 )dt 0 =
,
µ(t) =
M(0)
M(0) 0
M(0)
Λ−1
Λ/(1−Λ) Z (t) = Z0 + pΛ−1 1 − 1 − (Λ−1 − 1)µ(t)
, Λ 6= 1
h
i
Z (t) = Z0 + p 1 − e −µ(t) .
Λ=1
Z t0
M(0)
N(Z < Z 0 )
µ(t 0 )
N(Z < Z 0 ) =
Ψ(t)dt =
µ(t 0 ),
=
Λ(1 − R)
N(Z < Z (T ))
µ(T )
0
J.M. Lattimer
AST 346, Galaxies, Part 5
Evolution of the Solar Neighborhood (the Thin Disk)
Assume exponentially decreasing infall with timescale τf = 7 Gyr and
Mg (0) = Z (0) = 0. Use surface densities:
I Infall normalized to observed value:
Z T
ΣT =
f (t)dt = Σg + Σ∗ ' 12 + 38 = 50M pc−2
0
f (t) = Ae −t/τf
=⇒ ΣT = Aτf 1 − e −t/τf
−1
=⇒ A = (50/7) 1 − e −12/7
' 8.7M pc−2 Gyr−1
I
Assume Schmidt SFR Ψ(t) = νΣg (t) and Σg (T )/ΣT (T ) = 0.24:
dΣg
A
= −(1 − R)Ψ(t) + Ae −t/τf ,
Σg (t) = e −t/τf 1 − e −αt ,
dt
α
α = (1 − R)ν − τf−1
=⇒ ν ' 0.32 Gyr−1 , Ψ(T ) ' 3.8M pc−2 G
Constrain to solar metallicity Z = Z (t = 7.5 Gyr) ' 0.02:
1 − R e αt − αt − 1
Z (t) = pν
=⇒ p = 1.17Z
α
e αt"− 1
#
Z t0
0
Aν
e −t /τf
0
−(1−R)νt 0
N(Z < Z ) =
Ψdt =
α+
− (1 − R)νe
.
α
τf
0
J.M. Lattimer
AST 346, Galaxies, Part 5
Evolution of the Solar Neighborhood (the Thin Disk)
J.M. Lattimer
AST 346, Galaxies, Part 5
Oxygen Evolution
Oxygen is characteristic of a primary α−nucleus, originating primarily in
Type II supernovae.
Iron is also primary, produced in a 2:1 proportion by Type I and Type II
supernovae, but the former don’t ”turn on” until [Fe/H]> −1.5.
thick disk
halo
thin disk
J.M. Lattimer
AST 346, Galaxies, Part 5
CNO Evolution
Carbon and oxygen are characteristic
of primary nuclei, originating primarily
in Type II supernovae.
Nitrogen thought to originate from
Hot Bottom Burning in AGB stars,
but the most massive of these (8M )
have lifetimes too long to explain its
primary character.
It is also produced as a secondary
nucleus.
Now known to be a primary nucleus
produced by rotationally-induced
mixing in massive stars, from
H-burning of C and O produced inside
the star.
Requires low-metallicity stars to be
rotating muich faster (800 km/s) than
high-metallicity stars (300 km/s).
J.M. Lattimer
AST 346, Galaxies, Part 5
Halo Evolution and Hierarchical Galaxy Formation
The metallicity distribution of halo
field stars is well fit by a closed box,
IRA model dN/d ln Z ∝ (Z /p)e −Z /p .
This peaks at Z = p. [Fe/H]= −1.6
implies p ' Z /40.
The reduced yield could be explained
by an outflow during halo formation,
with a rate 8 times the SFR.
It could also be interpreted as due to
hierarchical galaxy formation. The
halo metallicities are lower by more
than 3 times than those of nearby
galaxies of the same mass as the halo.
Those small galaxies show a linear
relation between stellar mass and
metallicity which results from mass
loss: hot supernova ejecta escape more
easily from smaller mass galaxies.
J.M. Lattimer
AST 346, Galaxies, Part 5
The R-Process
Elements heavier than Fe
are produced by proton
capture (p) or by neutron
capture, either slow (s)
or rapid (s).
J.M. Lattimer
AST 346, Galaxies, Part 5
Element Evolution
Primary α-elements show less
scatter and small trends
with metallicity. Secondary r-process
elements show large scatter.
J.M. Lattimer
AST 346, Galaxies, Part 5
R-Process and Heirarchical Galaxy Formation
J.M. Lattimer
AST 346, Galaxies, Part 5
Dwarf Spheroidals and Metallicity Distributions
J.M. Lattimer
AST 346, Galaxies, Part 5
Neutron Star Mergers and the R-Process
Mergers have minimum evolution
lifetimes of 10-100 Myrs.
But high r-process abundance can
be made in small metallicity places.
Different places have different [Fe/H].
[Fe/H] is decoupled from time.
Ishimaru, Wanajo & Prantzos 2010
J.M. Lattimer
AST 346, Galaxies, Part 5
Dwarf Galaxies
I
Types:
I
I
I
I
Dwarf Spheroidals - diffuse and devoid of
gas and star formation
Dwarf Ellipticals - devoid of gas and star
formation
Dwarf Irregulars -diffuse and abundant
gas and star formation
I
Gas in dwarf irregulars
extends beyond stellar disk
HI gas on R band image of IC10
Properties:
I
I
I
All have horizontal branch stars, i.e.,
some stars older than 10 Gyr. This is
predicted by cold dark matter.
M32 is anomalous, with extremely high
central surface density. Perhaps the core
remnant of a larger galaxy with a
massive black hole at its center
Metallicities in dwarf galaxies correlates
with their masses. This suggests
outflow, caused by star formation, which
is easier the more shallow is the
gravitational potential.
J.M. Lattimer
AST 346, Galaxies, Part 5
M33
Wolf-Rayet
J.M. Lattimer
AST 346, Galaxies, Part 5
History of the Local Group
Treat the Local Group as the galaxies
M31 (M) and the Milky Way (m).
They are separated by r = 770 kpc
and approaching each other
dr /dt = −120 km/s.
It can be shown that the equation of
motion for two arbitrarily massive
objects (m, M) is the same as for a
small mass m moving in the field of a
much larger mass M + m. In this
case, the relative positions of the two
masses satisifies
d 2r
L2
G (M + m)
= 3z −
2
dt
r
r2
r
dr
2G (M + m) L2z
=±
− 2
dt
r
r
Since dr /dt < 0, we use − sign.
J.M. Lattimer
Pericenter is reached when dr /dt = 0
or rmin = L2z /[2G (M + m)].
Using rmin = 0 gives M + m >
(dr /dt)2 r /(2G ) ∼ 1.3 × 1012 M .
There is a cyclic solution
r = a(1 − e cos η)
a3/2 (η − e sin η)
t= p
G (M + m)
where a = L2z /[G (M + m)(1 − e)].
Galaxies began moving apart at t = 0
(η = 0) and are now approaching.
η = π(2π) corresponds to apocenter
(pericenter). M + m, η, a can be
determined from r , dr /dt, t if e is
known. We find a minimum
12
M+m >
∼ 5.1 × 10 M when e = 1,
12 times larger than we estimated from
circular velocities.
p Pericenter time is
t2π = 2πa3/2 / G (M + m) = 15 Gyr.
AST 346, Galaxies, Part 5