Transcript No Slide Title

Bars
Galaxy and galactic system mergers
Stefans Quintet
impulse approximation
dynamical friction
dynamical friction in Maxwellian velocity field
applications: dissolution of globular clusters in Andromeda
future merger with LMC and SMC and our Galaxy
Elliptical galaxies: photometry
M87 in Virgo as an example of a giant elliptical (cD) galaxy
- jets, black hole, superluminal motions etc.
BARS
Simulations of spiral structure formation in a 3-component
galaxy model (yellow=bulge stars, blue=disk stars, red=halo)
Tidal forces applied at the beginning of the simulation
Spontaneous growth of the pattern from noise by SWING
N-body calculations by J. Barnes, time between frames ~orbital period.
About 1/2 of all galaxies
have a bar.
Bar formation may be a
by-product of a self-defence
by a disk galaxy against the
approaching gravitational
instability.
MW
sun
A Milky Way-like galaxy
with non-linear waves
(as opposed to ‘linear’,
that is sinusoidal of very
small amplitude; this term has
nothing to do with the shape of
the wave!).
SPH (Smoothed Particle Hydrodynamics) model of gas disk response to the
Milky Way’s force field including a stellar bar. Notice the non-linear response of
gas: shock waves form, as opposed to a smooth and gradual density structure with a
smaller density contrast in the stellar disk. Basic difference in response is due to
velocity dispersion of 7 km/s in gas vs. 35-45 km/s in stars.
Stephan’s Quintet is a small group of galaxies in the constellation Pegasus.
The galaxies are not only close on the sky but are physically close in space.
So close, in fact, that they interact gravationally with each other. A new Chandra X-ray
observatory data details the results of this interaction. The image below (upper left) is a
composite of an X-ray image (shown in blue), superimposed on an optical image
showing the locations of the Quintet galaxies, which are marked A,B,D, E & F on the
lower right image). The X-ray image shows a "blue glow" produced hot gas in a bow
shock in front of the "intruder" galaxy B. The gas in the bow shocked is heated to ~1e6 K
by the motion of galaxy B through the inter-galactic gas in the group.
X-rays
and optical
B
visible
GALAXY MERGERS
NGC4676
mice galaxies
See links to work done at Canadian Inst. For Theoretical Adtrophysics
(CITA) on St. George campus
http://orca.phys.uvic.ca/~patton/openhouse/movies.html
http://www.cita.utoronto.ca/index.php/index_items/nature_of_dark_matter
Estimate of the temperature T of gas after virialization
(thermalization):
The mean energy per particle (ion or electron) and per one dimension, in a
thermalized gas (gas which relaxed to Maxwellian equilibrium) is equal
Ek 
1
2
kBT
The colliding gas flows in a cluster have a specific kinetic energy of relative
motion equal to 1 2 V 2 which is also of order potential energy of the cluster
(by the virial theorem). Temperature of the shocked gas will thus be of order
V2
T
kB
Typical velocities in the center of a clusters reach V~500 km/s. Then, the
temperature T must be of order T~1e7 K.
Conversely, such a high temperature is measured in X-rays, because the
photon energy are ~1 keV, which corresponds to T~1e7 K. From this
observed T we can then derive the virial estimate of the mass M which binds
the cluster: GM/R ~ kBT. That mass usually is significantly, for instance ten
times larger, than the estimate based on the visible matter (stars and gas).
The gravitational potential well and the high velocities seen in the galactic
groups and clusters predominantly due to dark matter.
Interaction of galaxies in pair and groups as a trigger of spirality
While the optical image
suggests separate galaxies, BIMA radio-telescope array
image of M81+M82+NGC3077
shows gas bridges connecting the
interacting galaxies
Cf. Fig. 5.34 in textbook
The future: Milky Way - Andromeda collision (several Gyr from now)
simulation by John Dubinsky (CITA; McKenzie supercomputer, 512 cpus, 10 days)
Another view…
the merger remnant becomes nearly elliptical
The Antennae Galaxies (also known as NGC 4038 / NGC 4039)
are a pair about 20 Mpc away in the constellation Corvus.
They were both discovered by Friedrich W. Herschel in 1785
J.Dubinski
(CITA)
Movie of galaxy
formation and mergers
Why do collisions often end in mergers and not just fly-by’s?
(cf. Fig. 5.37 and description in the book)
Dynamical friction provides the braking force. Its basic physics is that
of deflection (gravitational scattering) of stars from the host/target by the
perturber body. The perturber may either be a point mass or a compact
stellar system, all of which stars will be considered to move together.
Let us denote the mass of the perturber as M, and that of a star
from the target galaxy as m. The relative velocity of m and M at infinity is V,
both before and after encounter (due to energy conservation).
We treat all the encounters as independent scatterings, in the limit of weak
encounter (trajectory only slightly bent). While it is sometimes easiest to talk
and draw only the relative motion of the bodies m and M, we must be careful
not to forget about the fact that the lighter body (m) undergoes a stronger
deflection than the more massive one (M), in proportion to the ratio M:(M+m)
vs. m:(M+m).
The dynamical friction decelerates an object travelling through
a sea of stars (perhaps a target galaxy in a merger).
The impulse approximation predicts an inverse quadratic dependence of
the friction force on the velocity of relative motion:
dV/dt = -const.(…)/V^2.
This is because, for any given impact parameter b, the time of interaction is
~1/V, V is large, and the interaction brief and weak.
However, the situation may be quite different, if our chosen test particle
travels around a center of some system together with the
particles providing the dynamical friction. Then, our integration should not
assume that all the stars encountered arrive from one direction.
Rather, we should arrive in the limit of V --> 0 at a final result where the test
particle is NOT subject to any friction force except the isotropic random kicks
from the passing compact objects: dV/dt --> 0 as V-->0. This is a very different
dependence, which looks like across the range of V like this:
Here,  is the velocity dispersion in the
-dV/dt
stellar system. Let’s understand this
a little better.
0

V
How dynamical friction from a stream of particles with Maxwellian velocity
distribution affects a body of mass M
(an explicit formula w/derivation can be found
in Binney & Tremaine 1987; vM = V)
(B&T 1987)
Cf. Problem 5.17 in S&G
erf(x) = error function, an
integral of Gaussian curve
(Maple, Mathematica…)
Notice F~ -M*M
Applications of dynamical friction
Applications of dynamical friction
Applications of dynamical friction
Elliptical galaxies
Ellipticals are not as simple as their projected shape suggests.
Most are triaxial ellipsoids (3 different axial extents)
They are not in a relaxed, Maxwellian state (Trelax >> age of the universe.)
They are most common in dense clusters of galaxies rather
than small groups like the Local Group.
In the centers of dense clusters live the enormous cD-type galaxies like
M87. They are significantly brighter than L* = 2e10 Lsun
(L* corresponds to an absolute magnitude MB = -20 mag.)
De Vaucouleurs’ formula
is a purely empirical formula,
there is no physical derivation
or understanding of ubiquity.
But it works here!
Tricks played by projection
Most galaxies in Virgo are spiral, except in the center which is dominated
by ellipticals and giant ellipticals - a sure sign of environmental influences
(probably mergers)
M87 in the Virgo cluster (also: M84, M86)
[such giant, central elliptical galaxies are given
type designation cD]
M87 sports a one-sided jet
of relativistic electrons and
plasma. It comes from a very
small “central engine” region,
probably a black hole.
The one-sidedness of such jets
is an illusion: the jet is actually
two-sided (bipolar) and
directed almost directly toward
and away from us. Only the
approaching side appears
bright due to a relativistic
boosting (a.k.a. gamma-factor).
A fast-moving object (atom,
electron) radiates mostly in the
direction of motion, and little
in the opposite direction.