Universe: Stars And Galaxies
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 51Q
To determine

The difference between gamma ray and X-ray bursts and the reason for X-ray bursts to emit repeated pulses, whereas gamma ray bursts emit just once.

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1.2 1.0 0.8 0.6 Cosmic background data from COBE 0.4 0.2 0.0 0.5 10 Wavelength A in mm c) Background (CMB) undertaken by the COBE satellite. Use this diagram to estimate the current temperature of the CMB. Based on your estimate, what would the temperature of the CMB have been at a redshift of z = 5000? The left hand diagram above shows the results from observations of the Cosmic Microwave Radiated Intensity per Unit Wavelength (16° Watts/m per mm)
Problem 2: Black hole – the ultimate blackbody A black hole emits blackbody radiation called Hawking radiation. A black hole with mass M has a total energy of Mc², a surface area of 167G²M² /c*, and a temperature of hc³/167²KGM. a) Estimate the typical wavelength of the Hawking radiation emitted by a 1 solar mass black hole (2 × 103ºkg). Compare your answer to the size of the black hole. b) Calculate the total power radiated by a one-solar mass black hole. c) Imagine a black hole in empty space, where it emits radiation but absorbs nothing. As it loses energy, its mass must decrease; one could say "evaporates". Derive a differential equation for the mass as a function of time, and solve to obtain an expression for the lifetime of a black hole in terms of its mass.
Imagine that you are observing the light from a distant star that is located in a galaxy 100 million lightyears away from you. By analysis of the starlight received, you are able to tell that the image we see is of a 10- million-year-old star. You are also able to predict that the star will have a total lifetime of 50 million years, at which point it will end in a catastrophic supernova. a) How old does the star appear to be to us here on Earth now? b) How long will it be before we receive the light from the supernova event? c) Has the supernova already occurred? If so, when did it occur?
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