(Mock Exam)
UNIVERSITY OF BRISTOL
DEPARTMENT OF PHYSICS
Examination for the Degrees of BSc and MSci (Level H)
Galaxies 301
(PHYS34011)
Date – blank if not known
2 hours
Closed note examination with Formula Sheet.
Calculators may be used.
SECTION A contains 5 questions and carries 50% of the marks for the paper.
SECTION B contains 3 questions and carries 50% of the marks for the paper.
Answer ALL questions from SECTION A and TWO questions from SECTION B.
There are 8 questions on this paper.
PLEASE NOTE that, where a candidate has attempted more than the required number of
questions in any section, only the first answers will be marked unless the candidate clearly
indicates e.g. by crossing through, that an answer should be disregarded.
Answer all questions in a single answer book.
MOCK EXAM
Page 1 of 4
MOCK EXAM MOCK EXAM
DO NOT TURN OVER UNTIL INSTRUCTED TO DO SO
(Mock Exam)
SECTION A
(Answer ALL questions; total 50 marks)
A1
(10 marks)
(a)
How do the Hertzsprung-Russell diagrams of simple stellar populations (with all
their stars formed at the same epoch) vary as the system ages? How is this reflected
in the overall photometric properties of the system?
(b)
A globular cluster has a mass of 106 solar masses and a mass-to-light ratio of 2 (in
solar units). Calculate the maximum distance at which the cluster could be seen in a
survey with a limiting magnitude mB = 22.0. (You may assume that the absolute
magnitude of the Sun is MB = 5.48.)
A2
(10 marks)
(a)
Why does the observed correlation between colour and absolute magnitude
suggest a variation of metallicity with mass for elliptical galxies? How is this correlation
thought to arise physically?
(b)
Assuming that the gas and stars in an elliptical galaxy have the same kinetic energy
per unit mass, deduce the temperature of the gas in terms of the observed radial
velocity dispersion of the stars, r 2. If the X-ray luminosity of the gas is
LX 
1/2
nH2 (T), where nH is the gas density and the cooling function (T)  T ,
dependence of the cooling time tcool on r and nH.
A3
(10 marks)
(a)
What is meant by the Initial Mass Function? Through which two additional factors
is this related to the obseved luminosity function of stars?
(b)
Starting from the equation of hydrostatic equilibrium for a cloud of molecular
hydrogen of constant density , determine an approximate expression for the
pressure P at the centre of the cloud. By also assuming the perfect gas law, use this
to demonstrate that the limiting Jean's mass for collapse of the cloud is
M =
A4
find the
3
32 
½
kT
G mp
3/2
(10 marks)
(a)
State the main contributors to the mass of our Galaxy in (i) the central parsec, (ii)
the bulge, (iii) the disc, and (iv) the halo.
(b)
Consider a uniformly mixed `slab' of stars and dust of physical thickness X and
total
optical depth . If  is the emissivity per unit volume of the stars, write down the
observed intensity (outside the slab) from a volume element of thickness dx a
distance x into the cloud. Hence, by integration, show that the total absorption, as seen by
an external observer is
A = -2.5 log [(1 – e-)/].
A5
(10 marks)
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/Continued
(Mock Exam)
(a)
Describe briefly the distribution of nearby galaxies out to the distance of the Virgo
Cluster, noting the scales involved.
(b)
if the angular effective radius of the Virgo Cluster is 1.7 degrees and the line of
sight velocity dispersion is 700 km s-1, use the virial theorem to calculate the
cluster mass. If the visible galaxies have a total luminosity of 1.3 x 1012 solar
luminosities, what is the overall mass-to-light ratio. What does this tell us about the
matter content of the cluster?
SECTION B
(Answer TWO out of THREE questions; 25 marks each)
B6
(25 marks total)
(a) (6 marks)
What is meant by a de Vaucouleurs (or r1/4) profile and for which galaxy type is it
appropriate? How does the Sersic profile differ from this?
(b) (12 marks)
The bulge and disc components of a certain galaxy are observed to have half light
(effective) radii of 3 arcsec and 15 arcsec, and surface brightnesses at these radii of 22 and
23 B magnitudes per square arcsec, respectively. Calculate the bulge-to-disc ratio. [You
may assume that in the usual notation Re = 1.69a for discs and Re = 3460a for bulges. Hint:
you may find it useful to calculate Io in terms of Ie for each component.]
(c) (7 marks)
By determining which component dominates in the relevant region, estimate the angular
size of the galaxy at the 25 B magnitudes per square arcsec isophote.
B7
(25 marks total)
(a) (6 marks)
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(Mock Exam)
What are meant by”disky” and “boxy” ellipticals? Which other properties of a galaxy are
observed to correlate with whether it is disky or boxy?
(b) (14 marks)
The Fundamental Plane for ellipticals is defined through the relation
5/3
Ie
2
5/2
Re  
where Re is the effective radius, Ie is the surface brightness at that point (in intensity units)
and  is the velocity dispersion. Rewrite this in terms of luminosity L instead of the radius.
Assuming the virial theorem relation between mass, radius and velocity dispersion,
determine how the mass-to-light ratio depends on (i) Ie and L and (ii) Re and .
(c) (5 marks)
How is the Fundamental Plane used in the study of galaxy peculiar velocities and flows?.
B8
(25 marks total)
(a) (6 marks)
What is meant by a flat rotation curve? What does it tell us about the mass
distribution in a spiral galaxy?.
centric
Sun's
it's radial
(b) (15 marks)
Consider a star at Galactic longitude l, a distance D from the Sun and at Galactodistance R, where the rotation velocity is V(R). If we observe this star from the
position at Galacto-centric radius Ro, where the rotation speed is Vo , show that
velocity
vr = Ro sin l (V/R – Vo/Ro).
constant
Now assume that D << R, so that R = Ro + R, with R small. Defining Oort's
A as on the formula sheet, show that we can write the radial velocity as
vr = AD sin 2l .
c) ( 3 marks)
How should Oort's constants A and B be related if the Galaxy had a perfectly flat rotation
curve near the Sun?
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/Continued