Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 21, Problem 45Q
To determine
The reason for being able to detect black holes which are members of very short-period binary systems.
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An AGN is emitting with a luminosity of 2×1040W. The AGN's brightness varies by 10% on a time scale of 20 hours. Assuming that the size of the emitting region of the AGN is three Schwarzschild radii, choose which of the following values could give the mass of the central Black Hole, in solar masses.
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Chapter 21 Solutions
Universe: Stars And Galaxies
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- If the book's example of the Schwarzchild radius of the supermassive black hole Sag A* with a mass of ~4 million (aka 4*10^6) solar masses is approximately 1.2*10^10 m (or rewritten as 12*10^9 m), what would be the Schwarzchild radius of something with the mass of Jupiter (~0.001 or 10^(-3) solar masses) be? How does this compare to the size of an average person (~1.5 m)?arrow_forwardThe diagram shows the believed structure of a black hole if viewed from the top and in 3D. Calculate the Schartzchild Radius of a 25 Solar Mass black hole. The Mass of the Sun is 2x10^30kgarrow_forwarda double line The velocity curve for spectroscopic binary is shown in the sketch. The system is viewed edge-on, i.e., with an inclination angle of i = 90°, so that the maximum possible Doppler shifts for this system are observed. 400 U, Aini 300 200 oo - v Ain i 100 -100 -200 -300 400 o 1 2 3 +s 7 8 10 Time (daye) Find the orbital period of this binary in days. Doppler Velocity (2esun)arrow_forward
- Use the Schwarzchild formulaRs =2GM / c2whereRs = Radius of the star, in meters, that would cause it to become a black holeM = Mass of the star, in kilogramsG = A constant, called the gravitational constant= 6.7 x 10-11 m3 / kg . s2c = Speed of light= 3x108 meters per secondto determine to what length the radius of the Sun must be reduced for it to become a black hole. The Sun’s mass is approximately 2 x 1030 kilograms.arrow_forwardWR 68a is a relatively newly discovered (2015) double-lined spectroscopic binary. It has an orbital pe- riod of 5.22 days, a nearly circular orbit, and photometric light curves that are fit best using an inclination, i≈ 80°. Spectral lines show maximum Doppler shifts in the two components of K₁ = 144 km/s and Kg = 295 km/s. Find the masses of the two components. Your answers should be given in units of Mearrow_forwardOnce again in this chapter, we see the use of Kepler’s third law to estimate the mass of supermassive black holes. In the case of NGC 4261, this chapter supplied the result of the calculation of the mass of the black hole in NGC 4261. In order to get this answer, astronomers had to measure the velocity of particles in the ring of dust and gas that surrounds the black hole. How high were these velocities? Turn Kepler’s third law around and use the information given in this chapter about the galaxy NGC 4261-the mass of the black hole at its center and the diameter of the surrounding ring of dust and gas-to calculate how long it would take a dust particle in the ring to complete a single orbit around the black hole. Assume that the only force acting on the dust particle is the gravitational force exerted by the black hole. Calculate the velocity of the dust particle in km/s.arrow_forward
- Say that a particular white dwarf has the mass of the Sun but the radius of Earth. What is the acceleration of gravity at the surface of the white dwarf? How much greater is this than g at the surface of Earth? What would you weigh at the surface of the white dwarf (again granting us the dubious notion that you could survive there)?arrow_forwardHow does a white dwarf differ from a neutron star? How does each form? What keeps each from collapsing under its own weight?arrow_forwardQ1 (oints): A0620-00 is an X-ray binary system, there is a normal star and a compact object. For the normal star the radial orbital velocity is 457 km s and for the compact object it is 43 km s1.They have an orbital period of 0.3226 day. Calculate the mass function.arrow_forward
- velocity curve for a double line spectroscopic binary is shown in the sketch. The system is viewed edge-on, i.e., with an inclination angle of i = 90°, so that the maximum possible Doppler shifts for this system are observed. 400 300 So = U, Ani 200 t0 = v Ain i 100 -100 -200 -300 400 O 1 2 3 1 s 1 8: 10 Time (days) Find the orbital period of this binary in days. Doppler Velocity (krn/sec)arrow_forwardAs a mass m of gas falls into a black hole, at most 0.1mc2 is likely to emerge as radiation; the rest is swallowed by the black hole. Show the Eddington luminosity for a black hole of mass M is equivalent to 2*10-9 Mc2yr-1. Explain why we expect the black hole's mass to grow by at least a factor of e every 5*107 years. Where Edding Luminicity is defined as LE=(4piGMmpc)/(sigmaT), where G is the gravitational constant, M is the mass of the black hole, mp is the mass of a proton, c is the speed of light, and sigmaT is Thomson scattering where sigmaT=6.653*10-25 cm2.arrow_forwardExplain what is meant by the Schwarzschild radius of a black hole. Using a Newtonian approx- imation, derive an expression for the Schwarzschild radius, R, of a black hole of mass MBH- Calculate the Schwarzschild radius for a body with mass equal to the Sun's mass, and express your answer in units of kilometres.arrow_forward
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