Ancient history: N-body experiments tested crucial
aspects of merger hypothesis:
Role of halos in orbit decay
Halos which interpenetrate to half-mass radius merge
on next passage (White 1978, 1979).
Inefficiency of violent relaxation
Merging largely preserves relative binding energy and
radial gradients (White 1978, 1979).
Remnant luminosity profile
Remnant morphology
Remnant Luminosity Profiles
The radial profile at large ris a genuine
signature of merging (violent relaxation & phase mixing)
and tends to
ρ ∝ r-4
since f (E) is continuous at E = 0
(Jaffee 1987, White 1987).
Barnes (1988)
In projection, merger remnants have
r1/4-law profiles, but these are dominated by
pre-existing bulges at small
r.
Conservation of phase-space density precludes an
r1/4-law profile in mergers of pure disks
(Carlberg 1986); the profile flattens out as r
-> 0.
Remnant Morphology
Barnes (1992)
Barnes (1992)
Newly-merged galaxies (left) have lumpy and
irregular structure, including `shells', `ripples', `loops', and
'plumes' commonly noted in peculiar systems (Schweizer 1982).
Within a few crossing times (right), these features fade and a
smooth triaxial object emerges.
Remnant Morphology
Barnes (1992)
Barnes (1992)
Newly-merged galaxies (left) have lumpy and
irregular structure, including `shells', `ripples', `loops', and
'plumes' commonly noted in peculiar systems (Schweizer 1982).
Within a few crossing times (right), these features fade and a
smooth triaxial object emerges.
Remnant Morphology
Barnes (1992)
Barnes (1992)
Newly-merged galaxies (left) have lumpy and
irregular structure, including `shells', `ripples', `loops', and
'plumes' commonly noted in peculiar systems (Schweizer 1982).
Within a few crossing times (right), these features fade and a
smooth triaxial object emerges.
Velocity Profiles: Merging Flunks a Test!
Bendo & Barnes (2000)
Pure N-body remnants have velocity profiles with shallow
leading edges and steep trailing edges -- but in ellipticals
it's the other way around!
(Naab & Burkert 2001)
Bendo & Barnes (2000)
Velocity Profiles: A Resolution?
The line profiles observed in ellipticals can be interpreted
as signatures of embedded stellar disks -- a disk naturally
yields a profile with the correct asymmetry
(anti-correlation of h3 with v).
These observed profiles reinforce other (eg, photometric)
evidence for disks in E galaxies.
Velocity Profiles: A Resolution?
The line profiles observed in ellipticals can be interpreted
as signatures of embedded stellar disks -- a disk naturally
yields a profile with the correct asymmetry
(anti-correlation of h3 with v).
These observed profiles reinforce other (eg, photometric)
evidence for disks in E galaxies.
Mergers of gas-rich galaxies can form disks.
Velocity Profiles: A Resolution?
The line profiles observed in ellipticals can be interpreted
as signatures of embedded stellar disks -- a disk naturally
yields a profile with the correct asymmetry
(anti-correlation of h3 with v).
These observed profiles reinforce other (eg, photometric)
evidence for disks in E galaxies.
Mergers of gas-rich galaxies can form disks.
Moreover, these disks often have interesting
kinematics, including counter-rotation!
(Hernquist & Barnes 1992; Barnes 2002)
A Resolution, but...
But these disks are gas, not stars!
We need to find the right star-formation prescription to
actually make this work.
A challenge for N-body simulators: exhibit a
merger of two gas-rich disk galaxies producing a remnant with an
embedded stellar disk (formed from the gas) and with
velocity profiles similar to those seen in real ellipticals.
Hierarchical Mergers
In groups and clusters, merger remnants are likely
to be invloved in further mergers. What do we know about such
mergers?
One recent study finds that E+E mergers (contours) produce
remnants with less rotation and more anisotropy than D+D
mergers (shaded); most appear consistent with massive, boxy,
slowly-rotating elliptical galaxies (filled squares).
Naab, Khochfar, & Burkert (2006)
Formation of Galactic Nuclei
Massive black holes (MBH) appear to be universal in
early-type galaxies. Models of E+E mergers must
confront the dynamics of binary black holes.
Hypothesis: binary black holes are necessary to
transform the steep cusps of small ellipticals into the
shallow `cores' of bright ellipticals (Ebisuzaki, Makino,
& Okumura 1991; Milosavljevic & Merritt 2001).
Milosavljevic & Merritt (2001)
Are N-body Simulations With MBH Reliable?
MBH particles are not part of the Monte-Carlo
sampling of the phase-space distribution f (r,
v). Interactions between them and other particles
must be treated accurately.
As a MBH binary hardens, it becomes efficient at ejecting
stars. As a result, its decay will stall until the loss cone is
refilled by 2-body relaxation. This is faster in N-body models
than in real galaxies (Milosavljevic & Merritt 2003, Berczik
et al. 2005).
However, in rotating triaxial systems, the loss cone may be
refilled by chaotic diffusion, permitting the binary to coalesce
in less than 10 Gyr (Berczik et al. 2006).
Worth doing... but validity of results remains
uncertain.
Hierarchical Mergers: Questions
Do E+E merger simulations produce remnants with the
right structure? Are line profiles consistent with observations?
Can decoupled cores and other kinematic features
survive hierarchical mergers? If not (and it seems unlikely that
they can) do detections of decoupled cores in cluster galaxies
constrain hierarchical merging?
Can binary MBHs coalesce fast enough to avoid the
formation of triple MBH systems and the inevitable slingshot
ejections which would spoil the relationship between MBH and galaxy
mass/velocity dispersion?
Feedback from Star Formation and AGN
Modeling the behavior of the ISM is hard even for
in-active galaxies! A promising two-phase model
leads to a simple effective equation of state; below some
threshold density star formation is inoperative and the gas is
isothermal, while at higher densities energy from supernovae
boosts the pressure (Springel & Hernquist 2003).
Springel, DiMatteo, & Hernquist (2005a)
The accretion rate onto MBH particles is evaluated
from the local gas density and pressure, and a small fraction (5%)
of the energy liberated is coupled back to the surrounding gas.
(This choice matches the observed MBH - σ
relation.)
One possible consequence of feedback is to produce `red and
dead' ellipticals. Without AGN feedback, too much gas is left
to fuel star formation and remnants remain relatively blue.
By terminating star formation, AGN feedback allows mergers to
quickly transition to the red population (Springel, Di Matteo,
& Hernquist 2005b).
Springel, Di Matteo, & Hernquist (2005b)
AGN feedback is most effective in massive galaxies
(where MBH growth is most pronounced). Thus, this mechanism helps
account for massive red galaxies at high redshift.
Feedback: Questions
Are galactic-scale outflows driven by energy input
to the ISM alone, or are momemtum inputs (SN ejecta, AGN jets)
significant?
In ultra-luminous IR galaxies, the energy
reprocessed by the ISM from UV to IR is sufficient to unbind the
baryons in a few Myr. Can models of this reprocessing justify the
5% coupling of AGN luminosity to gas used by Springel et al.?
In the Springel et al. simulations, feedback can
stabilize pure gas disks. Can real galaxies do the
same trick? Is there any evidence for such high gas fractions at
early times?
Modeling Interacting Galaxies
Fitting a simulation to a real pair of interacting
disk galaxies involves exploring a large parameter space.
Orbit
p , e , μ
3
Orientations
i 1 , ω1 , i 2 , ω2
4
Time
t P
1
View
θX , θY , θZ
3
Scale
S L , S V
2
Center
α , δ , cz
3
Total
16
Parameter Space
The parameter space may be abstracted using
cylindrical coordinates. The vertical coordinate represents
parameters which can be chosen after a simulation has been run.
The azimuthal coordinate represents disk orientations. The
radial coordinate represents orbit parameters.
Model Matching
The parameter space may be abstracted using
cylindrical coordinates. The vertical coordinate represents
parameters which can be chosen after a simulation has been run.
The azimuthal coordinate represents disk orientations. The
radial coordinate represents orbit parameters.
Simulating a real system involves guessing some set of
initial conditions and integrating forward to see if they match
the data. Trial and error may eventually yield a satisfactory
match.
Matching the Mice
Finding a good match to both morphology and kinematics can
require many experiments. Here is a subset of the runs John
Hibbard and I did to match the Mice (NGC 4676).
Earlier stages of tidal interactions can be
modeled with test-particle disks in massive spheroids. A
spherical cloud of particles on circular orbits represents
all possible disk orientations. The disk particles to
display are selected interactively after simulation is run.
Galactic Identakit
Earlier stages of tidal interactions can be
modeled with test-particle disks in massive spheroids. A
spherical cloud of particles on circular orbits represents
all possible disk orientations. The disk particles to
display are selected interactively after simulation is run.
Model Matching: Objectives
Produce `look-alikes' of interacting galaxies in COSMOS and
other surveys.
Use radial velocity data to upgrade look-alikes to real
dynamical models.
Test schemes for quantifying goodness-of-fit to observational
data.
Develop automated procedures for matching models to
observations.
