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Transcript
UNIVERSITY OF SOUTHAMPTON
PHYS2013W1
SEMESTER 1 EXAMINATION 2011/12
GALAXIES
Duration: 120 MINS
Answer all questions in Section A and two and only two questions in
Section B.
Section A carries 1/3 of the total marks for the exam paper and you should aim
to spend about 40 mins on it. Section B carries 2/3 of the total marks for the
exam paper and you should aim to spend about 80 mins on it.
A Sheet of Physical Constants will be provided with this examination paper.
An outline marking scheme is shown in brackets to the right of each question.
Only university approved calculators may be used.
Number of
c University of Southampton
Copyright 2012 Pages 7
2
PHYS2013W1
Section A
A1. Classify the following galaxies according to their Hubble types:
a) A spiral galaxy with a large bulge and tightly wound spiral arms.
b) A spiral galaxy with a bar-shaped bulge and well defined arm-structure that
spirals into a ring around the bar.
c) An elliptical galaxy with an ellipticity of = 0.3.
[3]
A2. The Pleiades are one of the closest open clusters. For this particular cluster,
parallax measurements yield a parallax of 0.00764 arcsec.
The cluster’s
apparent V-band magnitude is 1.6 mag. Assume that the cluster’s luminosity
is dominated by the 14 brightest cluster stars, and let us further assume that
they are all of the same type (that is, they all have the same magnitude). What is
the distance to the cluster in pc, and what is the apparent and absolute V-band
magnitude of each of the 14 bright stars?
[5]
A3. Explain the main evidence that there must be a large amount of dark matter in
the halo of our Galaxy. Give an example of the measurements that were used to
obtain this evidence.
[4]
A4. An elliptical galaxy is observed at a distance of 30 Mpc and a bolometric flux of
Fbol = 2 × 10−14 Wm−2 is measured. Calculate the bolometric luminosity and
state whether the galaxy is a dwarf or a giant. You may assume that 1 pc =
3.086 × 1016 m.
[2]
A5. Explain why the distances to the most distant galaxies cannot be measured from
shifted spectral lines, and describe the methods that can be used instead.
[4]
3
PHYS2013W1
A6. Two stellar populations that both have the same age, distance and stellar mass
are observed. The second stellar population appears fainter and redder than the
first stellar population. Describe the two phenomena that can lead to such an
[2]
effect on magnitude and colour.
TURN OVER
4
PHYS2013W1
Section B
B1.
a) Describe the differences between the stellar content of elliptical and spiral
galaxies and explain the consequences for the galaxies’ colour. Consider
[3]
also variations between the subclasses of the same Hubble type.
b) For a giant elliptical galaxy, the wavelength of its Hα line in the observedframe is measured at 659.6 nm with a line width of 0.5 nm. The rest-frame
wavelength of the line is at Hα,0 = 656.3 nm. Assuming that the galaxy has
no peculiar velocity, show that the galaxy is located at a distance of 20.55
Mpc, and that its internal velocity dispersion is σr = 227 km sec−1 . To
answer this question you may assume that the Hubble constant is H0 = 73
km sec−1 Mpc−1 .
[4]
c) The galaxy has a spherical shape and a density profile that can be described
as ρ(R) = ρ0 R−2 out to a truncation radius Rout (beyond which the density
drops to zero). Show that the kinetic energy of the galaxy can be expressed
as K = 6πρ0 σ2r Rout .
[6]
d) Show that the potential energy of the galaxy described above can be as
expressed as U = −16Gπ2 ρ20 Rout .
e) Show that the mass of the galaxy described above is given by m =
[3]
3Rout σ2r
G ,
and derive the mass that is contained within a radius of 10 kpc in solar
masses M . You may assume that 1 pc = 3.086 × 1016 m.
[4]
5
B2.
PHYS2013W1
a) Describe how the interstellar medium, and thus a galaxy, can become
[7]
enriched in metals.
b) A young star cluster is embedded in an HII region. A spectrum is obtained
from the HII region and the following line fluxes are measured: F Hβ =
0
2.5 × 10−15 W m− 2 and F Hγ = 6.7 × 10−16 W m− 2, where F denotes
0
0
the observed flux. The expected Balmer decrement for these two lines
is
F Hγ
F Hβ
= 0.47, where F denotes the intrinsic flux of the line. The line
extinctions are related by AHγ = 1.76AHβ . What is the extinction AHβ and
[6]
AHγ in magnitudes?
c) The brightest star in the star cluster is a main sequence star with a mass
of 7 M . The initial mass function (IMF) of main sequence stars follows the
Salpeter IMF
n(M) = kM −2.35
where k = 213 is a normalising constant, and M is the stellar mass in
solar masses. Assuming that the lowest-mass stars have masses of 0.8 M ,
what is the total mass of the star cluster? Assuming a mass-to-light ratio of
M/L = 1.2 in B-band, what is the total B-band luminosity of the star cluster?
[4]
d) Compare the two types of star clusters that are found in the Milky Way with
respect to their age, metallicity and location within the Milky Way.
TURN OVER
[3]
6
B3.
PHYS2013W1
a) More than half of the galaxies in the Universe can be found in larger scale
structures called groups and clusters. List the different properties of galaxy
groups and galaxy clusters in terms of their dimension, galaxy numbers,
velocities and types. Describe the distribution of galaxies within a group or
cluster, including a probable explanation of the distribution of galaxy types.
[6]
b) A survey of galaxies has an apparent magnitude limit of mlim = 19 mag and
covers 0.8% of the sky. To what distance can you observe galaxies with
an absolute magnitude of M = −21.5 mag? How many of these galaxies
with M = −21.5 mag do you expect in your survey if the number density is
3.2 × 10−5 Mpc−3 ?
[5]
c) The luminosity function Φ(L) of a galaxy cluster can be well described with
a Schechter function:
Φ(L) =
Φ? − LL L −1
e ?( )
L?
L?
where Φ? is a normalising factor and L? a characteristic luminosity. Show
that the total luminosity density is ρlum = Φ? L? . The following integral may
be useful:
R
eax dx =
eax
a
e) The giant elliptical in the centre of the galaxy cluster is a known AGN. Xray observations measured an X-ray luminosity of LX = 9.75 × 1038 W.
The shortest variability was measured in X-rays on timescales of 1.4 days.
Assuming that the X-ray emission comes from within 5 Schwarzschild radii
(r s =
2GM
c2 )
around the central supermassive black hole, estimate the mass
of the black hole in solar masses. Assuming that the X-ray luminosity is
about 30 % of the bolometric luminosity, at what fraction of the Eddington
[4]
7
PHYS2013W1
luminosity Ledd = 1.3 × 1031 MMBH
(in units of W) is the black hole radiating?
END OF PAPER
[5]