PAPER DESCRIPTION: ASTROPHYSICS and SPACE SCIENCE

 ASTR 601

TOTAL MARKS: 100

Question 1.  Evolutionary time scales (25 marks)  

1. The Thermal Time Scale. Which star has a greater thermal time scale: the Sun or an O5-type main sequence star? Hint: use formula (12.3) and tables on pages 264 and 258 of the textbook (the 6thEdition).
2. The Nuclear Time Scale is the time in which a star radiates away (as its luminosity) all the energy that can be released by nuclear reactions. Calculate the Nuclear Time Scale for the Sun ( LꙨ= 3.828×1026 W). Assume that only about 10% of the total mass of hydrogen in the Sun (0.1 MꙨ) can be consumed before other, more rapid evolutionary mechanisms set in. The solar mass MꙨ = 2.0×1030  In addition, when calculating, also take into account that only 0.7% of the “rest mass” (Mc2 ) is turned into energy in hydrogen burning.  
3. The Dynamical Time Scale. Two interstellar molecular clouds start collapsing simultaneously in different parts of the Milky Way.  Both clouds have the density of molecular hydrogen H2= 106 cm-3, but one of them is 10 times more massive than the other (and, therefore, bigger).  Which cloud will collapse first?

Question 2.  Nuclear reactions (30 marks)

1. Which nuclear reaction requires higher temperature of the stellar interior:
   p-p reaction or triple-alpha reaction?  Why?
2. The mass of a proton (1H nucleus) is 1.00728 amu (atomic mass units), and that of the alpha-particle (4He nucleus) is 4.001514 amu.  Find the difference between masses of 4 protons and one alpha-particle (“mass defect”) and present

(a)in amu;

(b)in units of energy. Use conversion: 1 amu is 1.6604×10-27 kg, and E = mc2

(c) as percentage (%) relative to the mass of the alpha-particle

3.Why is this difference (“mass defect”) important for stars?  

1. Find flux density of solar neutrinos at a distance of 1 AU from the Sun (how many neutrinos pass 1 m2in 1 second here on Earth). When answering this question, use the following steps:

a.Assuming that the luminosity of the Sun is provided by p-p reactions only, find how many p-p reactions take place in the Sun every second.

b.How many neutrinos are produced

i.In one p-p reaction?

ii.In all these reactions every second?

c.Assuming that the cross-section of your body is 1 m2, find how many solar neutrinos pass through your body every second (flux density of solar neutrinos at the distance of 1 AU from the Sun).

Question 3. Stars, binary stars, masses of stars, close binaries   (35 marks)  

1. The effective temperature of the Sun is T = 5700 K. The effective temperature of a white dwarf is T= 90,000 K with a radius equal to the radius of the Earth. Find the total luminosity of the white dwarf, L . Express it in solar luminosities, LꙨ.
2. The HR diagram in Figure 1 below is a  “log Lversus  log T ” The diagonal straight lines in this diagram are the “lines of equal radius”, meaning all stars along each diagonal line have the same radius.

a.Explain why lines of equal radii are straight lines.

b.What is the slope of these lines?

Hint: Consider taking the Logarithm of both sides of the formula for luminosity as a function of radius and temperature; show that this is a linear function y = b x + a,  where y = log L ,  x = log T  and  b  is the slope.

Figure 1

3.Name types of binary stars studied in this course. When determining stellar masses, which type of binary system suits best when the inclination

a. i = 90 degrees

b.i = 0 degrees

(Inclination i is the angle between the line of sight and the normal of the orbital plane.)

Explain your answer.

1. It was found from the observation of a binary system’s relative orbit and period that M1+ M2 = 8 solar masses. Observations of the absolute orbits showed that the ratio of the semimajor axes was a1/a2 = 3. Assuming that inclination i = 0, determine the masses of the individual components M1 and M2 (in solar masses).  
2. Close binary systems. We considered the three types of close binary systems: detached, semidetached and contact close binaries.

a.Provide a sketch of each system. Explain.

b.A “TypeI” supernova phenomenon (SN I) can be explained in terms of the evolution of a low-mass close binary system. Which type (types) of close binary system describes the SN I phenomenon?

Question 4. Your presentation in class (10 marks)

1. Which planet did you present in class? What makes this planet special compared to other planets?