Transcript chapter 26 instructor notes

26. Galactic Evolution
Goals:
1. Examine the characteristics of clusters of
galaxies and peculiar galaxies in search of
potential mechanisms to explain the
differences among them.
2. Determine the importance of various
parameters in the creation and evolution
of galaxies.
3. Consider clusters of galaxies as the
observational test ground for various
ideas about galaxy formation.
Evidence for Interactions of Galaxies:
The centre of the Coma cluster of galaxies, a rich cluster.
The distribution of elliptical galaxies (filled circles) in the
Coma cluster relative to spirals (open circles) peaks
towards the centre of the cluster.
The Coma cluster of galaxies as viewed in X-rays.
The lower density Hercules cluster, on the other hand,
appears to be more heavily populated by spiral galaxies
in its central regions.
The Hercules cluster of galaxies as viewed in X-rays.
Dynamical Friction.
Dynamical friction is a term related to loss of momentum
and kinetic energy of moving bodies as a result of a
gravitational interaction with surrounding matter in
space. It is sometimes referred to as gravitational drag, as
first discussed by Chandrasekhar (1943).
The expression for dynamical friction on a moving object
is related to its speed, vM, and mass, M, as well as the
density, ρ, of the matter through which it is moving. In
standard form:
G 2 M 2  where C probably varies
fd  C
between 20 and 200.
v2
M
The time scale for dynamical capture is given by:
2 vM r
tC 
CGM
2
where r is the orbital radius,
with the obvious C dependence.
The Whirlpool Galaxy (M51) and its companion (M52).
The Whirlpool Galaxy and its companion as modeled by
Toomre & Toomre (1972, ApJ, 178, 623).
The Antennae (NGC 4038/39), optical image.
The Antennae as modeled by Toomre & Toomre (1972,
ApJ, 178, 623).
The ring galaxy II Hz 4, optical images.
The ring galaxy II Hz 4 modeled by Lynds & Toomre
(1976, ApJ, 209, 382).
The polar ring galaxy NGC 4650A.
Centaurus A.
Starburst Galaxies.
These are a group of strongly interacting galaxies that are
bluer in colour than isolated galaxies, presumably
because of the presence of recently-created hot young
stars. Larson and Tinsley (1972) argued that the tidal
interaction with another galaxy has induced star
formation, although the resulting excess luminosity is
hidden behind obscuring clouds of gas and dust. Such
galaxies are bright at infrared wavelengths, however.
Although the starburst activity was initially discovered in
the galaxy nuclei, some spiral galaxies also exhibit diskwide starburst activity. The star formation is assumed to
have been induced by shock waves generated by the
gravitational interaction.
Starburst galaxies often exhibit strong X-ray emission.
Does it originate from gas falling into a deep potential
well at the centre of the galaxy, perhaps a “black hole”?
The starburst galaxy M82, which interacts with M81.
M82 was previously believed to be an irregular galaxy
(left), but in 2005 two symmetric spiral arms were
discovered in near-infrared (NIR) images (right),
detected by subtraction of an axisymmetric exponential
disk from the NIR images. The arms emanate from the
ends of a bar and can be followed for the length of 3 disk
scales. Even though the arms were detected in the NIR
images, they are bluer than the disk.
The rich galaxy cluster Abell 2199 and the multiple
nucleus (cannibalistic?) cD galaxy near its centre.
The curious elliptical galaxy NGC 3923 and the multiple
concentric rings (left, gas?) that surround it.
The butterfly galaxy NGC 6240 as viewed by the Hubble
Space Telescope (left) and by the Chandra Orbiting XRay Observatory (right). What are the multiple strong
sources of X-rays near the galaxy’s centre? How were the
surrounding streams of gas produced?
Models for the Formation of Galaxies.
Models for the formation of galaxies began with ideas on
the formation of the Milky Way Galaxy. One of the first
was that of Eggen, Lynden-Bell, and Sandage (1962), who
suggested that the Galaxy initially collapsed rapidly from
a proto-Galactic nebula, resulting in a collapsing
spheroidal distribution of metal-poor stars in highlyelongated orbits. The collapse slowed as early generations
of stars became supernovae,
thereby enriching the gas content
of the nebula and dissipating the
spheroidal collapse. Combined
with friction and the initial
angular momentum of the cloud,
it resulted in the development of
a flattened metal-rich disk that
eventually produced Population I
stars (akin to ideas about the
formation of the solar system).
Stellar Birthrate Function.
How are stars created: at a constant rate or with an
obvious time dependence as in the model below (Burkert
et al. 1992, ApJ, 391, 651)?
The “G-dwarf problem” is the apparent conflict between
the observed very small proportion of low-metallicity G
dwarfs in the Galactic disk and model predictions for a
sizable fraction (~½), given that the original population of
low-metallicity stars from the Galaxy’s formation has not
had time to evolve away from the main sequence. Perhaps
the amount of matter in stars in the Galactic disk has
increased significantly since the formation of the Galaxy?
Or perhaps very few low-mass stars were formed early in
the Galaxy’s history? Etc., etc.?
And was the Galaxy’s initial collapse rapid or dissipative?
Estimates for the various time scales based on
applications of the Virial Theorem produce typical values
like tff ≈ 200  106 years and tcool ≈ 8  106 years for the
free-fall collapse time scale and cooling time scale,
respectively, implying that tcool << tff. For tcool >> tff one
predicts galaxy masses of 1081012 M, much like what is
observed, but implying that massive cD galaxies have
formed through mergers (hierarchical merger model).
Galactic Disk Dynamics.
The Galactic disk can be pictured as
a thin plane of infinite dimension,
with the density of stars and gas
decreasing exponentially with
height h above the Galactic plane,
i.e.
z h
 ( h )   0e
where z is the distance variation of the gas or stars and ρ0
is the density in the plane. The gravitational form of
Gauss’s Law can be used to approximate the mass within
a cylinder perpendicular to the plane:
M cylinder  1.26  0 Ah
The dependence of gravitational acceleration with
distance from the plane becomes:
g (h)  2.53G0h
The resulting height reached by the gas or stars can be
related to their kinetic energy via the Virial Theorem to
give:
12


3kT

h(t )  
 2.53Gm 0 
The scale height derived for the thick disk and thin disk
is used to infer characteristics about the temperature of
the gas from which the stars formed originally.
The stars orbiting the Galactic centre appear to be blue
in colour, but are not necessarily young. Demarque &
Virani (2007, A&A, 461, 651), for example, argue that
they are low-mass, low-metallicity, blue horizontal
branch stars. The presence of high-velocity blue stars at
high galactic latitude has been interpreted as stars being
ejected from the Galaxy through interactions with the
high-mass compact object at the Galactic centre.
The Formation of Elliptical Galaxies.
While the Eggen, Lynden-Bell, and Sandage mechanism
has been proposed for the formation of disk galaxies like
spirals and lenticulars, the formation of ellipticals has
generally been considered to have been a faster process in
which star formation was extremely efficient, leaving
nothing for the creation of a disk and later generations.
The observational evidence, however, also suggests that
galaxy collisions may also be important for the creation of
giant ellipticals through cannibalism. Ellipticals are more
abundant than spirals in rich clusters of galaxies, for
example. Computer simulations have confirmed the
possibility of such a mechanism, but keep in mind that
computer simulations have reproduced a variety of
possible galaxy scenarios, some of which have not yet
been observed.
Sample Questions
1. The mass density of stars in the solar neighbourhood is
estimated to be 0.05 M pc−3. If that value is constant in
the Galactic plane and all of the stars are M dwarfs,
estimate the fraction of the Galactic disk’s volume
occupied by stars. Suppose that an intruder M dwarf
moves perpendicularly through the Galactic disk. What
are the chances of the intruder colliding with another star
during disk passage? Assume a disk thickness of 1 kpc.
Answer: An average M dwarf (Appendix G) has a mass of
~0.3 M and a radius of ~0.4 R. If the mass density of
stars near the Sun is ρ = 0.05 M pc−3, the number
density of M dwarfs can be estimated from:
The average volume occupied by a single M dwarf is
therefore given by:
The volume occupied by an M dwarf of radius ~0.4R is
given by:
The fraction of Galactic space occupied by M dwarfs is
therefore given by:
If an intruder M dwarf traverses the Galactic plane, the
mean free path between collisions is given by Equation
9.12, i.e. l = 1/nσ, where the collision cross-section is:
The mean free path for the intruder is therefore:
For a disk thickness of 1 kpc = 1000 pc, the probability of
a stellar collision for the intruder star is given by:
2. Equate the cooling time scale for a sphere of gas to its
free-fall time scale to find the maximum mass of a
protogalactic nebula. Note that anything less will not
necessarily collapse on a free-fall time scale.
Answer. See equations 12.26, 26.6, 26.7, and 26.8 of text.
Equating tff to tcool yields:
The density ρ0 and number of particles n can be written
as:
and
So:
or
or
or
The minimum mass for a protogalactic nebula of radius
60 kpc for Λ  10−37 W m3 with μ = 0.6 is therefore given
by:
corresponding to about 35 Milky Way galaxies and fairly
typical of giant ellipticals.
3. The Large Magellanic Cloud has a distance modulus of
18.43, orbiting our Galaxy in the Magellanic Stream. If it
has a mass of 2  1010 M, what is the time scale for its
dynamical capture by the Milky Way for C = 23?
Answer. The distance to the LMC, its “orbital radius” r,
is determined from:
so:
The orbital speed of the LMC can be inferred from
Kepler’s 3rd Law:
for m1 and m2 in M, a in AU, P in yrs.
where:
Since 1 pc = 206265 AU, MMW  2  1011 M, then:
So:
and:
The time scale for dynamical capture can now be
evaluated:
2 vM r
tC 
CGM
2
2  1.3968  10  48.5  10  206265  1.496  10

23  6.6726  1011  2  1010  1.989  1030
1.9657  1048
3.2198  1016 s
9


 1.0203  10 yr
31
7
6.105  10
3.1557  10 s/yr
5
3

11 2
Which implies dynamical capture of the LMC in only
half of its orbital period. But that assumes that Milky
Way matter extends as far as the LMC so that there is
friction occurring constantly, whereas there is some
evidence that the LMC has orbited the Milky Way
several times.