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Date: 3/12/05
Indian Institute of Technology Kanpur
Department of Physics
The End-semester Examination: 2005-06-I
SE311/PHY 305: Physics of the Universe
Max. Marks: 120
Time: 4:00pm—7:00 pm
[Note: (1) You can make any reasonable assumptions while solving the problems, provided you
state them. (2) Use of class-notes (only) is allowed. (3) Some values (SI units, unless otherwise
stated) : hc=12,340 eV-A0, Radius of the Sun: 6.96 x 108 m, Stefan-Boltzmann constant  = 5.6705x
10-8, Boltzmann constant k =1.3807x10-23, Planck's constant h =6.6261x 10-34, 1 AU =1.5 x 1011m.,
1 parsec = 3.0857x1016m = 206,265AU, L =3.9x1026W, T =5,7800K; Hubble const. = 72± 5 km
s-1Mpc-1 ; Radius of Earth= 6,400 km, ]
1. Give brief answers (Write the answers sequentially, each in a line: Do rough work
elsewhere. You need not copy down the question.):
(i) What is the most significant source of broadening of spectral lines in the Sun?
(ii) A star of mass 2M  ,at the end of its post-main sequence evolution, will primarily
have the following elements in its composition: ………………
(iii) Two cepheids from nearby galaxies have equal periods but their apparent
magnitudes differ by 5. The ratio of their distances r/r' (where r>r') is: …………
(iv) A white dwarf (Te=30,000) cools with time. In what manner will its color index
(B − V) be affected?
(v) A visual binary shows very small and nearly constant Doppler red-shifts in its
spectrum. What information do you gather from it?
(vi) If the universe has Ω0 = 1.5, what lowest value of the temperature would CMBR
ever reach according to the Newtonian cosmology?
(vii) A star is classified as M2V. What information do you gather from it? Will it be
more or less luminous than the Sun?
(viii) In a very large baseline radio interferometry, one uses data from two (correlated)
radio telescopes far apart. What could forbid this for optical telescopes?
(ix) The absolute magnitude of a star in Andromeda galaxy (distance 690 kpc) is M=5.
It explodes as a supernova and becomes one billion times brighter. Find its apparent
magnitude.
(x) The largest redshift, in an astronomical object, so far observed is about 7. What is
the corresponding look-back time t in terms of the present age t0? (Assume a flat
universe and Newtonian cosmology).
(2x5+4x5=30)
2. The color temperature can be determined from two magnitudes corresponding
to two different wavelengths. Show that Tc = 7000 K/ { (B – V) + 0.47}. State the
approximations made. The wavelengths of the B and V bands are 440 nm and 548 nm,
respectively, and we assume that B = V for stars of the spectral class A0, the color
temperature of which is about 15,000 K.
(10)
3. Explain briefly:
(a) He core of a star with mass 1 M  can become degenerate, while that with mass
5M  cannot become degenerate.
(b) Stars with mass  1.5 M  live much shorter than those with mass  1.5 M .
(c) Why do we NOT find stars of surface temperatures >> 30,000 0K in the main
sequence stage?
(d) In primordial nucleosynthesis, unlike in many stars, He burning does not take
place.
(20)
4 . Suppose that a binary star system like that of Sirius is located at a distance of 30
kpc at 450 to the plane of the sky. With the current observational power, would it be
possible to locate it as a binary system and if so what type of a binary system would it
be called? [For reference, Sirius A and B have absolute magnitudes MA =1.33, MB =
8.57; RA ~R  , RB~R E and Sirius system subtends a maximum angle of 7.62'' at the
Earth. The Hubble space telescope can observe stars of apparent magnitude of 30 or
less and has resolution of about 0.1'' in the visible region. Distance of Sirius from
Earth =2.65 pc. Ignore extinction.]
(15)
5.
The Carbon absorption lines that form when a quasar, Q1331+70, passes
through an intergalactic cloud indicate that the temperature of the cloud is 7.4 ±
0.08 0K and the lines show a redshift of z = 1.776. How does the temperature of the
cloud compare with temperature of the CMBR at that redshift?
(10)
6. Andromeda galaxy is at a distance of 4.3 Mpc and shows a blue-shift of z =
−0.001. What is the component of peculiar velocity of the galaxy in direction
joining the galaxy to earth?
(10)
7. Suppose that a white dwarf and a neutron star have (nearly) the same mass (~ 1.4
M  ). In both cases, we have degeneracy pressure of some kind supporting against
the gravitational pull towards the center. One has a large radius of ~RE and other has
radius ~ 10 km, i.e. much smaller. Explain quantitatively what makes this possible.
[Hint: Consider (i) How the pressure at the center, in each case, depends on the
radius; (ii) How the expressions for the degeneracy pressure differ in the two cases.
Use non-relativistic expressions.]
(15)
8. You are given (only) that there is an unknown astronomical object (beyond Solar
system) in a photograph that is reddish in appearance. List the possibilities regarding
what the object could be and what the reddish color could correspond to. What
additional information(s), that is/are readily accessible experimentally, could
distinguish between those possibilities?
(10)