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Question 1.  Stellar magnitudes (3 marks) 

The Circular No. 4316 of the Central Bureau for Astronomical Telegrams of the International Astronomical Union reported on 24 Feb 1987:

E.M. Bateson, Royal Astronomical Society of New Zealand, informs us that the object was discovered independently by Albert Jones, Nelson, on Feb. 24.37 UT (position  R.A. = 5h35m.8, Decl. = -69 18′).  B. Moreno and S. Walker, Auckland Observatory, obtained m = 4.8 on Feb. 24.454 UT. 

The “object” discovered by a NZ amateur astronomer was proved to be the most famous supernova (SN) in the 20th Century and the brightest visible from Earth since 1604.  It is classified as a SN of the type II in the Large Magellanic Cloud (SN1987a). Its brightness peaked in May 1987, with an apparent magnitude of m = 2.8.

1.Find the absolute magnitude M of the SN1987a at maximum. Distance of the LMC is 51,400 pc.

2.The progenitor (before SN explosion) star was a blue supergiant of the apparent magnitude m = 12.8.  How much brighter (in terms of flux density) this SN was at maximum compared to the progenitor star. Find the ratio FSN / Fbefore

Question 2.  More on stellar magnitudes (3 marks)

The total magnitude of a triple star is 0.0. Two of its components have magnitudes 1.0 and 2.0. What is the magnitude of the third component?

Question 3. Photon density, radiation density (5 marks)

Temperature of the Cosmic Microwave Background radiation (CMB) is T = 2.725 K.

1. Find the maximum wavelength of the CMB (in metres).

Hint: Assume it has a Planck energy distribution; use Wien’s Displacement Law

1. What is the radiation energy density, u (measured in J/m3) of the CMB?
2. Maximum intensity of the CMB occurs at frequency Calculate energy (in Joules, J) of one photon at this frequency.
3. Using the results of (2) and (3), find the number of CMB photons per m3,  .

Question 4. Temperature, luminosity (4 marks)

1. The temperature of plasma in the solar corona can reach 106 Find the average speed of the electrons in such a plasma. Use the formula that relates kinetic energy and temperature:    (1/2) m v2= (3/2) k T, where k is  Boltzmann’s constant and m is the electron mass.
2. The effective temperature of a red giant is T =2500 K with a radius 100 times the solar radius. Find the total luminosity of the star. Express it in solar luminosities.

Question 5.   Radiative processes (5 marks) 

1. An interstellar cloud reduces the intensity of radiation of a background star by the factor of 10. What is the optical depth of the cloud?
2. Using the Rydberg formula, find the frequency of transition between the two bound levels of hydrogen n= 100 and n = 101.
3. In the Figure below (next page)

a.Name all radiative processes shown with arrows. For example, free-free emission, free-bound absorption, etc.

b.Write principal quantum numbers of atomic level in the diagram. (For example, n=3.)

c.Which transition in the Figure corresponds to the Lyman-delta line? (Mark it in the diagram)

d.Which one is a Balmer series transition? (Mark it in the diagram)