Download PC2491 Examples 2

PC2491 Examples 2
Hand in to the Physics Office by Friday 8th December. More beer for
the best six papers.
(1) The optical surface brightness of a spiral galaxy follows the usual disk exponential
law
I r   I o e

r
ro
If the scale length (ro) is 4 kpc and the central surface brightness (Io) is 150 solar
luminosities pc-2, what is the total luminosity of the galaxy?
(2) A spiral galaxy is observed to have major and minor axes 0.3o and 0.15o in extent.
The frequencies of the 1420.4MHz line from neutral hydrogen at the ends of the
major axis are observed to differ by 1421 kHz. If the galaxy is at a distance of 5 Mpc,
estimate the mass of the galaxy in solar masses.
(3). If the gas in the Milky Way is travelling in purely circular obits, show that the
radial velocity of an object distance r from the galactic centre in galactic longitude l is
given by
Vr   r   o Ro sin l
where Ro is the distance from the galactic centre to the Sun, o is the angular velocity
of the Sun and (r) is the angular velocity at radius r.
An H1 cloud in the galactic plane at l=30o is observed to have a velocity
relative to the local standard of rest of +80 km s-1. Assume the galactic rotation curve
is flat with an amplitude of 220 km s-1 , and that Ro = 8.2 kpc and estimate the two
possible distances to this cloud.
(4) Estimate the mean free path of a star in a region where the stellar density is 1 star
pc-3 and typical stellar velocities are 10 km s-1 (assume all stars 1Mo).
In the same region hydrogen atoms have a density of 106 m-3. Assume the hydrogen
atoms to be elastic spheres of radius 10-8 m and only interact by direct collision.
Estimate their mean free path.
(5) A spiral galaxy has a rotation curve that is flat with Vcirc= 180 km s-1. Estimate
the values of Oort’s constants at a radius of 3kpc and hence, or otherwise, the
epicyclic frequency in km s-1 kpc-1
If the galaxy has a two armed spiral pattern, and the inner Lindblad resonance is
observed to be 3kpc from the galactic centre, estimate the pattern speed and the radius
of corotation of the galactic density wave.
(6) An atomic hydrogen cloud has a uniform density of 109 atoms m-3 and a
temperature of 100K. Estimate how large the cloud can be before it begins to collapse
under its own gravity.
(7) Explain why it is more difficult to study the dynamics of elliptical galaxies than
spiral galaxies. Summarise the main observational results of such studies in elliptical
galaxies.
(8) Explain what is meant by the ‘fundamental plane’ for elliptical galaxies. Why is it
used rather than the Luminosity –Dispersion (‘Faber-Jackson’) relation to determine
the distances of elliptical galaxies?
Show that, using reasonable arguments, the ‘half light radius’ (Re) of an
elliptical galaxy mass M, luminosity L is related to the stellar dispersion (the
average surface brightness within Re (e) via
1
M 
Re  k    o2  e1
 L
where k is structure parameter.
Show that the above relation is approximately consistent with the fundamental plane
if
M 
k 1    L0.25
 L
(9) The Large Magellanic Cloud (LMC) has a mass of 1010 Mo and is 50kpc from the
centre of the Milky Way. Assume it is a circular orbit around the Milky Way with a
circular velocity of 200 km/s and estimate the distance from the centre of the LMC
that stars and gas will be significantly tidally affected by the Milky Way.
(10) A galaxy cluster contains 1000 galaxies and has a total mass of 1014 Mo. If the
cluster has an extent of 3 Mpc and the dynamics of the galaxies are governed by the
virial theorem, what would be the velocity dispersion of the cluster galaxies?