This

**preview**shows pages 1-3. to view the full**12 pages of the document.**Astronomy 142 Practice Midterm Exam #2

Spring 2013

This practice exam will do you very little good unless (1) you have mastered the

homework and workshop problems, and tried to understand everything discussed in

the online solutions for all these problems; (2) you have already composed your one-

page Cheat Sheet and want to see if it really has everything you need on it, and nothing

you don’t. If you’ve done (1) and (2), feel free to proceed.

If this were a real exam, you would be advised here of the exam rules:

“You may consult only one page of formulas and constants and a calculator while

taking this test. You may not consult any books, nor each other. All of your work must

be written on the attached pages, using the reverse sides if necessary. The final answers,

and any formulas you use or derive, must be indicated clearly. Exams are due an hour

and fifteen minutes after we start, and will be returned to you during the next lecture.

Good luck.

“Note:

• “Work first on the problems you find easiest, and come back to harder or less

familiar material later. Don’t get stuck.

• “The amount of space left for each problem is not necessarily an indication of the

amount of writing it takes to solve it.”

Name: _______________________

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- 2 -

Problem 1. (40 points)

a. A

8

10 M

black hole at the center of an elliptical galaxy accretes matter from a

surrounding disk at a rate limited by radiation pressure. What is the luminosity

thus produced (in

L

)?

b. We usually think of the radiated energy in black hole accretion as originally

comprising a fraction

0.1

ε

=

of the rest energy of the infalling material. What is

the rate (in

-1

yearM

) at which the black hole in part (a) must accrete mass in

order to produce its luminosity?

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

- 3 -

Problem 1. (continued)

c. A very young

1M

protostar, still completing its formation, accretes matter from

a surrounding disk at a rate limited by radiation pressure. What is the luminosity

thus produced (in

L

)?

d. In this case we account for the radiated energy in the gravitational potential

energy of the infalling material. Gas originating hundreds of AU away from the

star is passed through the disk and deposited on the surface of the star,

considered here to lie 1

R

from the star’s center. According to the virial theorem

only half of the potential energy drop shows up as an increase in thermal kinetic

energy; the rest is available for radiation. What is the rate (in

-1

yearM

) at

which the star in part (c) must accrete mass in order to produce its luminosity?

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