UNIVERSITY COLLEGE LONDON

University of London

EXAMINATION FOR INTERNAL STUDENTS

For The Following Qualifications:-

B.Sc. M.Sci.

Astronomy 2B12: Astrophysical Processes: Nebulae to Stars

COURSE CODE : ASTR2B12

UNIT VALUE : 0.50

DATE : 18-MAY-05

TIME : 14.30

TIME ALLOWED : 2 Hours 30 Minutes

05-C0075-3-60
© 2005 University College London TURN OVER
Answer ALL questions from Section A and THREE questions from
Section B.

The numbers in square brackets in the right-hand margin indicate the provisional
allocation of maximum marks per sub-section of a question.

Solar l u m i n o s i t y L o = 3.83 x 1026 W

Solar r a d i u s P~ = 6.96×10 s m

Solar m a s s M o = 1.99 × 1030 k g

Parsec pc = 3.09×1016 m

Gravitational constant G = 6 . 6 7 x 1 0 -11 N m 2 kg -2

Boltzmann constant k = 1 . 3 8 x 1 0 -23 J d e g -1

Hydrogen atom mass mH = 1.67X10 -27 k g

Planck constant h = 6 . 6 3 x 1 0 -34 J s
V e l o c i t y of light c = 3 . 0 0 x 1 0 s m s -1
1 year = 3.155 x 107 s e c o n d s
E l e c t r o n S c a t t e r i n g cross s e c t i o n aT = 6.7 × 10 -29 m 2

fo ~ x2e-a2~2dx - V'~
-i-Ja

ASTR2B12/2005 TURN OVER

 SECTION A

1. Define what is meant by an HII region around an OB star. [1]

Contrast the m a i n properties of H II regions and Planetary nebulae, indicating

the n a t u r e of the exciting stars in each c a s e . [3]

Define t h e term Stromgren Sphere for an H II region. Say whether the radius of
a Stromgren sphere would be larger or smaller for an 0 5 star compared to a BO
star and state why. [2]

2. Define what is meant by r e s o n a n c e t r a n s i t i o n s for atomic spectral lines. [2]

Explain why resonance lines are the only ones observed in atomic interstellar
spectra a n d state which wavelength regions of the electromagnetic spectrum the
m a j o r i t y of such lines are found in. [2]

Give three reasons why OB stars are generally used as probes of the interstellar
gas in the Galaxy. [3]

3. Define what is m e a n t by Hydrostatic Equilibrium (H.E.) for a star and

derive the equation of H.E. for a spherically symmetric star. [4]

For a star in H.E. the ViriM Theorem is written as 2U + ~ = 0. Define the terms
U and f~ in this expression. [2]

ASTR2B12/2005 CONTINUED
4. Define the term Mean Molecular weight, (/z), for a gas comprising different
chemical species. [2]

For a fully ionized gas comprising Hydrogen, Helium and heavy elements, with
normalised mass fractions X, Y and Z respectively, show that # can be written: [4]

# = ( 2X + 3Y/4 + Z/2 )-1

Give the value of # for the cases of a gas of pure ionized helium ? [1]

5. Define the term Plane-Parallel geometry for a stellar atmosphere, and indi-
cate for what stellar types this may be valid. [2]

Define what is meant by Local Thermodynamic Equilibrium (LTE) for a gas,

and name the main physical relations that are obeyed by the gas in LTE and the
nature of the associated radiation field. [4]

6. Outline briefly the physical principles by which nuclear fusion reactions

can provide the energy source in stars and explain why such fusion reactions only
occur deep in stellar interiors. [3]

Describe the nuclear fusion reactions of the triple-or process that occurs in the
helium burning phase of a post main-sequence star. [5]

ASTR2B12/2005 TURN OVER

 SECTION B

7. State the condition of Ionization Equilibrium for a pure hydrogen H II

region. [2]

Describe the physical processes by which gas in a typical H II region is heated by

its interaction with radiation from an exciting OB star, indicating the sequence
by which energy is shared between the different particle species. [5]

E x p l a i n what is m e a n t by C a s e - B recombination for Hydrogen and indicate the

physical basis for its use in H II region analyses. [3]

Discuss the physical process by which Forbidden Lines provide an important cool-
ing source for H II regions. [5]

Derive expressions for the outer radius R~ and total mass Ms for a Strom-
gren Sphere of uniform Hydrogen number density n surrounding an OB star
which emits S. ionizing photons per second. Calculate values of R~, in par-
secs, and Ms, in Mo, for the case where n = 10l° m -3, S. = 1 x 10 49 s -1 and
~ B - - 2 X 10 -19 m 3 s - 1 . [5]

8. Describe the chain of nuclear reactions involved in the Hydrogen burning

P P - I process t h a t operates in the Sun. [6]

E s t i m a t e the Main Sequence lifetime for a 2/14o star undergoing P P - I fusion, as-
suming t h a t the energy production rate is CH ---- 6.3 × 1014 J Kg -1. [NB assume
a m a s s - l u m i n o s i t y relation: L o¢ M 3 ] [3]

O u t l i n e how the s and r processes can give rise to the production of elements
heavier t h a n Iron in stars. [6]

Discuss briefly the m a i n observational properties of Type I and Type II Su-

pernovae, indicating why T y p e Ia supernovae are used as standard candles for
distance determinations in the Universe. [5]

ASTP~2B12/2005 CONTINUED
9. List the main sources of opacity in a stellar atmosphere, indicating the
wavelength dependence for each opacity source. [4]

Define, using a diagram to illustrate the geometry, the Specific Intensity, Iv, of a
radiation field. [3]

Define the Mean Intensity, J~ and Physical Flux, F~ of a radiation field and write
down integral expressions for these quantities in terms of I~ in the case of a plane-
parallel atmosphere. [4]

Write down expressions for the optical depth, (T~), and the Source Function, (S~),
defining all quantities, and write down the form of the equation of radiative trans-
fer for a plane-parallel atmosphere. [5]

Outline the main steps involved in the calculation of realistic LTE model atmo-
spheres to determine the emergent radiative flux distribution, F~, when radiative
equilibrium is obeyed, r. [4]

10. Derive the equations of Continuity of Mass and Continuity of Energy used
in stellar structure models, assuming spherical geometry. [5]

The Boltzmann Distribution for the relative populations of two bound-levels ra

and n can be written:

Show that the ionization balance of the gas can be derived from this, relating the
total number densities of neutral and ionized species, No and Ni respectively, as
given by the Saha law, defining all terms in this expression: [a2]

N00- U0 h3 Pe exp .

Draw a rough sketch of how the ionization fraction of (a) hydrogen and (b) helium
varies with temperature, for a given, constant electron pressure. [3]

ASTR2BI2/2005 TURN OVER

11. Discuss briefly the direct observational evidence for the existence of dust
particles in the general interstellar medium. [5]

Illustrate in a diagram the wavelength dependence, of the average interstellar dust

extinction curve, in the form of A ~ / E s - v vs. A, from infrared to far-ultraviolet
wavelengths. [A~ is the amount of extinction in magnitudes at wavelength A and
E B - V is the colour excess]. [3]

Define what is meant by the Equivalent Width, W~, of an absorption line, and
the column density, Ni of absorbing species i in the line-of-sight. [2]

For a single interstellar absorption line arising from an atomic species i, with a
volume number density ni, the line opacity can be written as:

7re 2
-
meC
where ¢~(v) is the normalised line profile, and f is the line oscillator strength.
Show, using this expression, that the Equivalent Width, W~, of a weak line in
terms of the column density, Ni of the absorbers, can be written as:

71-e2
W~ -- - - Ni f ~i 2
meC2

Indicate briefly how the relative abundances of different elements can de deter-
mined from interstellar absorption line studies.

ASTR2B12/2005 END OF PAPER