Cosmic Perspective Fundamentals
Cosmic Perspective Fundamentals
3rd Edition
ISBN: 9780134988504
Author: Bennett, Jeffrey O., Donahue, M. (megan), SCHNEIDER, Nicholas, Voit, Mark
Publisher: Pearson,
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Chapter 10, Problem 3QQ

Choose the best answer to each of the following. Explain your reasoning.

Why does matter falling toward a white dwarf, neutron star, black hole in a binary system form an accertion disk? (a) because the central objects spins very rapidly (b) because the infalling matter has some angular momentum (c) because the gas emits x-rays.

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Using MBH = 6.6 × 10 Mo, calculate the below. a. Find radius of the Schwarzschild sphere (Schwarzschild radius Rs). You can calculated from the appropriate formula or just use the fact that for an object of 1 solar mass Rs = 3 km. b. Express Rs in km, in AU, in parsecs. c. Using the distance to M87 and your result above, find angular radius of the SMBH (Schwarzschild radius). Express it in arcseconds (") and micro- arcseconds (pas) d. Take the radius of Pluto's orbit equal to 40 AU and find its angular size (in micro-arcseconds, pas) at the distance of M87.
Question B1 [This question will required roughly two single-sided A4 pages to answer.] Consider a hypothetical, spherically symmetric star of mass M and radius R, for which the den- sity profile is represented by p(r) = Pc [1 − (r/R)²], where pc is the central density and r is the radial distance from the center of the star. a) If the star is in hydrostatic equilibrium, by considering the forces acting on a volume ele- ment, show that the following expression must apply: dP dr Gm(r) p 12 where P is the pressure as a function of radial position and m(r) is the mass interior to the radius r. b) For the hypothetical star, with the given density as a function of radius p(r) = pc [1-(r/R)²], show that m(r) can be written as m(r) = 1½πr³ p 31.2 5R² c) Show that the average density p of the star (i.e., total mass divided by total volume) is given by p = 0.4pc. d) e) Given that the pressure is zero when r = R, show that the central pressure is given by Pe= 15 G M² 16π R4 ΜΗ The star is…
Match each characteristic below to the appropriate stellar end state. (Select W-White dwarf, N-Neutron star, B-Black hole. If the first is W and the rest N, enter WNNNNNNN). A) Has a mass no greater than 1.4 solar-masses. B) Sometimes appears as a pulsar. C) Size defined by its Schwarzschild radius. D) In a binary system it can explode as a supernova. E) Supported by electron degeneracy pressure. F) Typically about the size of Earth. G) Usually has a very strong magnetic field. H) Viewed from afar, time stops at its event horizon. Answer: Submit All Answers
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