ASTROPHYSICS I
Practice Question for Mid-Term
SN Numerical
1 The chemical composition of gases in a star is as follows: 85% Hydrogen
and 10% Helium.
(a) Assume complete ionization and calculate mean molecular weight in
terms of atomic mass unit.
What will be the value of mean molecular weight if
(b) Hydrogen is 50% ionized and heavier gases (He and others) are
neutral?
(c) Hydrogen and Helium are is 80% and 50% ionized, heavier gases
remain neutral.
(d) Discuss your results.
2 The chemical composition of gases in a degenerate star is as follows:
65% Hydrogen and 30% Helium.
(a) What will be the value of mean molecular weight of free electron?
(b) What will be the value of mean molecular weight of particles?
(c) Discuss your results.
3 Use hydrostatic equilibrium and mass continuity relation to find the central
density and central pressure of a star having density profile
𝑟
𝜌 = 𝜌𝑐𝑒𝑛 [1 − ].
2𝑅
4 Calculate the value of radiation pressure in the Sun at one-third of its
radius [Chemical Composition: X=0.71, Y = 0.27 at one-third = 1800
kg/m3 , Msun = 1.989 x 1030 kg, Rsun = 6.98 x 108 m].
5 Calculate the value of radiation pressure at the half the solar radius
assuming hydrostatic equilibrium. [Chemical Composition: X=0.71, Y =
0.27 at half = 3000 kg/m3 , Msun = 1.989 x 1030 kg, Rsun = 6.98 x 108 m].
SN Long Questions
1 Find the expression for degenerate gas pressure in the star assuming
non-relativistic electrons. Discuss why degeneracy pressure is
independent of temperature.
2 Assume that the electrons in the degenerate stars are relativistic. Find the
expression for degenerate gas pressure exerted by those relativistic
electrons. Discuss how this pressure depends upon chemical composition
of gases.
3 Assume isotropy in the stellar interior and find the expression for radiation
pressure. Discuss why this pressure is independent of density and
chemical composition of the star.
4 What do you mean by polytropy? Set up Lane Emden Differential
equation in terms of pressure and density parameter. Find its analytical
solution assuming polytropic index n = 0.
5 Assume linear density profile 𝜌 = 𝜌𝑐𝑒𝑛 [1 − 𝑟 ] and find mass, pressure
𝑅
and temperature profile (or distribution) in the star. Normalize these
expressions and find central density and central pressure. Discuss the
relevance of these distributions.
6 What do you mean by electron degenerate star? Assume non-relativistic
electrons and find appropriate polytropic index. Use this polytropic index
to find density, mass, pressure and temperature profile in the star.
Discuss the trend shown by these expressions.
SN Short Questions
1 Find the expression for non-degenerate gas pressure in the star in terms
of chemical composition.
2 How mean molecular weight can be calculated for non-degenerate star?
3 How mean molecular weight is calculated for degenerate star? Find the
expression for mean molecular weight for free electrons.
4 Set up hydrostatic equilibrium in the star and find expression for pressure
gradient.
5 Use hydrostatic equilibrium and mass continuity relation to find the central
limiting density in the star.
6 Define stellar parallax and proper motion of the star and discuss it.
7 Discuss the main features of stellar spectra.
8 Discuss the basis of Harvard Classification of the star.
12 Dec 2018