Download Galaxy interaction and transformation

Galaxy interaction and transformation
Houjun Mo
April 13, 2004
A lot of mergers expected in hierarchical models. The main issues:
• The phenomena of galaxy interaction: tidal tails, mergers, starbursts
• When and where does galaxy interaction most likely to occur
• The properties of merger remnants
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Tidal interaction and tidal radius
When an extended system (galaxy) moves in the gravitational potential of
another object, the system experiences a tidal force which tends to tear the
system apart.
Consider a satellite system with mass m of radius r which is on a circular orbit of
radius D in the potential well of a point mass M.
The accelerations:
a = GM/D2 (at the center of m)
GM/(D + r)2 (farthest end)
GM/(D − r)2 (nearest end)
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Assuming r D, the acceleration difference is
∆a = 2GMr/D3 (between the two ends),
which tends to tear the material apart from the center.
The binding force per unit mass on the two ends of m is Gm/r2.
∆a = Gm/r2 defines a tidal radius: rt = (m/2M)1/3D. A more rigorous derivation
gives:
1/3
m
rt =
D.
M(3 + m/M)
If the radius of the satellite is larger than rt, the material outside rt may be
stripped by the tidal force of M.
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Tidal tails
Tidal force involved in close encounters of spinning galaxies may eject stars into
arcing trajectories, leading to the formation of tidal tails.
But tidal tails are more prominent in prograde encounters than in retrograde
ones.
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Retrograde
Prograde
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Prograde encounter is more violent because of the resonant acceleration.
p
The orbital frequency of a ring of radius r is ωring = GM/r3, whereas the angular
velocity of the line joining the two massive particles at pericenter is
2GM(1 + e)
ωorb =
D3min
1/2
,
where e is the eccentricity of the orbit and Dmin is the minimum separation
of the two massive particles. If ωorb = ωring , i.e., for a ring with radius r =
Dmin/[2(1 + e)]2/3, and if the encounter is prograde, then a test particle in the
ring is in resonance with the tidal acceleration.
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Self-consistent simulations of spinning galaxies
Disk stars have mass, and disk is embedded in extended dark matter halos.
• confirm the importance of mutual alignment of spin and orbital angular
momentum in making prominent tidal tails
• demonstrate that interpenetrating encounters from parabolic orbits generally
leads to mergers of galaxies within a few dynamical time. This happens
because the lauching of tidal tails (now with mass) is at the expense of the
orbital energy, which causes the orbit of the galaxies to decay.
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Dynamical Friction
As an object moves through a
sea of particles, it accelerates the
surrounding particles, and so the
number density of particles down
stream is higher than that up stream,
leading to a net drag force (dynamic
friction) on the object.
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Chandrasekhar dynamical friction formula
Consider the encounter of an object of mass M with a particle with mass m (the
standard gravitational scattering problem). The total change is given by
δVM = δVM|| + δVM⊥.
If ‘M’ goes through a homogeneous sea of particles, ∑ δVM⊥ = 0. For each
scattering with impact parameter b and velocity V0, we have
−1
2 4
2mV0
b V0
δVM|| =
1+ 2
m+M
G (M + m)2
/◦.
If the number density of particles (stars) with velocity vm is f (vm) d3vm, the rate
of encounters of ‘M’ with such stars and with impact parameters in the range
b → b + db is 2πb db × v0 × f (vm) d3vm. The rate of change in vM due to encounters
with these stars is then
dvM
dt
3
bmax
Z
3
|∆vM⊥| · 2πb db
d vm = V0 f (vm) d vm
0
vm
(vm − vM)
= 2π ln 1 + Λ G m(m + M) f (vm) d vm
,
|vm − vM|3
2
2
3
(1)
where Λ ≡
considered.
bmax v20
G(M+m) ,
bmax is the largest impact parameter that needs to be
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Assuming that the distribution of vm is isotropic, the rate of change in vM due
to encounters with stars of all velocities can be obtained by integrating over
vm. Note that this is equivalent to finding the ‘gravitational field’ at ‘position’
vM generated by the ‘mass density’ 4π ln(Λ) G2m(m + M) f (vm). The result is
dvM
vM
= −16π2 ln ΛG2m(m + M) 3
dt
vM
Z
f (vm)v2m dvm .
This is the Chandrasekhar dynamical friction formula.
2
n0
v
If f (vm) is Maxwellian: f (v) = (2πσ2)3/2 exp − 2σ
, then
2
dvM
4π ln ΛG (m + M)ρ
2X −X 2
√
=−
erf(X)
−
e
vM ,
3
dt
π
vM
2
√
where X ≡ vM/( 2σ).
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Dynamical friction in dark halos
As a simple application, let us consider a satellite on circular orbit in the potential
2
2
of a halo of singular
isothermal
sphere:
ρ
(r)
=
V
/(4πGr
). For an isothermal
0
c
√
sphere, σ = Vc/ 2 and so X = 1. Under the assumption that M m the
dynamical friction force experienced by the satellite at radius r is
GM 2
F = −0.428 ln Λ 2 .
r
This force is always tangential, and so the rate of change in the angular
Fr
momentum L is dL
dt = M . Since L = rVc , the radius of the orbit r changes with
time as
r
dr
GM
= −0.428
ln Λ .
dt
Vc
/◦.
For an initial orbit with radius ri, the time for ‘M’ sink to the halo center is
2 Mh Rh
1.17 ri2Vc 1.17 ri
=
.
tdf =
ln Λ GM ln Λ Rh
M Vc
If ri ∼ Rh,
1.17
Mh
1
tdf ≈
,
ln(Mh/M) M 10H(z)
where we have used Rh/Vc = 1/10H(z). Thus, the dynamical friction timescale is
longer than the age of the universe for M/Mh <
∼ 30.
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Galaxy Merging
Criterion for Mergers
What kind of encounters are likely to lead to the merger of two galaxies?
A simple case: two identical spherical galaxies. of mass M and median radius
rmed. The internal mean-square velocity is
hv2i ≈ 0.4GM/rmed.
Such an encounter is specified by Eorb (the specific orbital) and L (the specific
angular momentum) in units derived from hv2i and rmed:
Ê ≡
Eorb
(1/2)hv2i
and
L̂ ≡
L
hv2i1/2r
.
med
Each encounter is then associated with a point in the (Ê, L̂) plane which can be
devided into different reagions
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Orbits in the upper-left region are
forbidden, because for a given orbital
energy the largest possible angular
momentum is that of circular orbit.
Encounters with too high orbital
energy and too high orbital angular
momentum cannot lead to a merger.
Mildly hyperbolic orbits can lead
to a merger if the orbital angular
momentum is sufficiently low.
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Merger requires low Ê, i.e. Eorb < hv2i/2 (or σ2 < hv2i/2) and low L̂ (large rmed).
Conclusion 1:
Galaxies can merge quickly if they are in systems with velocity dispersion
comparable to the internal velocity dispersion of the individual galaxies.
Conclusion 2:
Massive, extended halos can merger more easily than their central galaxies
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Structure of Merger Remnants
• Major mergers of galaxies are expected to be accompanied by violent
changes in the gravitational potential of the system.
• Because of violent relaxation, the merged system generally relax to form a
smooth object near the center of the system, with some irregular structure at
large radii.
The properties of such merger remnants are important to understand. If we
know how merger remnants behave, we can look for merger signatures and
estimate how many mergers have occurred during the history of the universe.
More importantly, the study of the structure of merger remnants can help us to
understand what kind of galaxies may have formed by galaxy merging.
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Simulation results
Being faint, merging structures are in general difficult to observe. Numerical
simulations are used to understand the properties of merger remnants. Some of
the most important results obtained are
1. Major mergers of galaxies generally lead to elliptical-like remnants, with some
irregular structures in the outer regions. Depending on the orbital geometry of
the merger, the remnant can either be prolate or oblate. In general, mergers
of two equal-mass disks lead to rounder remnants if the spins of the merging
progenitors are more tilted relative to the orbital angular momentum. Highly
flattened remnants can be produced in prograte and retrograde encounters.
2. The remnant of a major merger generally rotates slowly in the inner region
but fast in the outer part. This happens because dynamic friction can transfer
angular momentum from particles with high binding energy to the ones with
low binding energy. If merging galaxies have extend massive haloes, the
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effective transfer of angular momentum from the merging galaxies to dark
matter generally leads to slowly-rotating remnants, and so the inner part of
such a remnant is supported by velocity dispersion.
3. The final density profiles of merger remnants in projection are well fitted by
the R−1/4-law profiles over a large radial interval.
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Transformation of Galaxies in Clusters
Although galaxy-galaxy mergers should not be frequent in clusters of galaxies,
cluster environment may play an important role in transforming the morphologies
of their member galaxies. Clusters of galaxies are the largest virialized systems
in the universe, with masses of about 1014 − 1015 M, and velocity dispersions of
about 1000 km s−1. Many clusters are also found to contain large amount of hot
X-ray gas. Thus, galaxies in a cluster can be affected by the cluster environment
in three different ways:
• ram-pressure stripping of their gas components by the hot ICM;
• encounter with other member galaxies and cluster substructures;
• tidal interactions with the global cluster potential.
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Galaxy Interaction and Starbursts
So far only the interactions of gas-free galaxies are discussed. In many cases,
merging progenitors may contain gas. For example, mergers of present disk
galaxies which contain cold gas; high-redshift protogalaxies. It is important to
understand how gas behaves. bbbbbb A parabolic encounter of two gas-rich
disk galaxies. The stellar distribution
is shown on the left; each frame is
about 80 × 96 kpc. Times (-60, 60,
150, 300, 420 Myr, from top to bottom)
are given with respect to pericenter at
t = 0. Hot gas is shown in the middle,
color codes temperature. Cool gas is
shown on the right.
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Because of tidal interaction, merger induces non-axisymmetric structure in the
center. The gas and stars have different response to the tidal force, and gas
and stellar structures have different phases. This phase difference gives rise to
torques that can effectively remove angular momentum from the gas. The gas
then flows towards the central region, forming a dense gas concentration in the
core of the merger remnant.
The surface density of the gas core in the merger remnant is in general many
orders of magnitudes higher than the surface density of the pregenitors. Since
Σ̇? ∝ Σ1.4
gas ,
intense star formation in the center of a gas merger.
This is reminiscent of that for starburst galaxies. There are many reasons to
believe that many starbursts are produced by galaxy interaction.
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Starbursts
• short time scale for star formatio: 107-108 yr, powered by massive young stars.
• large star formation rate per unit area, compact (∼ 1 kpc).
• high star formation rate: a powerful starburst may have a SFR ∼ 1001000 Myr−1
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