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 15Q
To determine
The maximum mass of a neutron star and the effect of neutrons repulsion force on this mass.
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The typical core-collapse supernova has an energy budget of about 1046 J. This energy comes
from the gravitational potential energy of an inner core with mass Mic, which collapses from an
initial radius of 5 x 106 m down to the final radius of 50 km. Estimate Mic, in solar masses, for
this to be a realistic energy source of the core-collapse supernova. You may assume that the
density before the collapse is uniform.
Discuss briefly how a Type la supernova is different from a core-collapse supernova from a
massive star?
2. Consider a neutron star of radius of 10 km and a mass of 1.4 M⊙ that has a surface layer of pure 1H.
(a) For the given parameters, compute the luminosity and wavelength of peak emission of a neutron star shining at Eddington Luminosity in the rest frame of the neutron star. Assume black body emission.
(b) What is the impact of a) the gravitational redshift and b) the time delay, both caused by general relativity, on the observed wavelength?
(c) What is the wavelength and luminosity seen by an observer at large distance (much larger than neutron star radius)?
Problem 3. Consider a flat, single component universe.
1. For a light source at redshift z that is observed at time to, show that z changes at a rate
dz
dto
=
= Ho(1 + 2) — Ho(1+2)³(¹+w)/2
(2.1)
2. For what values of w does the observed redshift increase with time?
3. Assuming the single component is matter and Ho = 68 km/s/Mpc, you observe a galaxy at z = 1. Using
Equation 2.1, determine how long you will have to keep observing the galaxy in order to see its redshift
change by 1 part in 106.
Chapter 21 Solutions
Universe: Stars And Galaxies
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- In the Check Your Learning section of Example 27.1, you were told that several lines of hydrogen absorption in the visible spectrum have rest wavelengths of 410 nm, 434 nm, 486 nm, and 656 nm. In a spectrum of a distant galaxy, these same lines are observed to have wavelengths of 492 nm, 521 nm, 583 nm, and 787 nm, respectively. The example demonstrated that z=0.20 for the 410 nm line. Show that you will obtain the same redshift regardless of which absorption line you measure.arrow_forward*39 Will the universe continue to expand forever? To attack this question, assume that the theory of dark energy is in error and that the recessional speed v of a galaxy a distance r from us is determined only by the gravitational interaction of the matter that lies inside a sphere of radius r centered on us. If the total mass inside this sphere is M, the escape speed v, from the sphere is v. = V2GMIT (Eq. 13-28). (a) Show that to prevent unlimited expansion, the aver- age density p inside the sphere must be at least equal to ЗН 87G (b) Evaluate this "critical density" numerically; express your an- swer in terms of hydrogen atoms per cubic meter. Measurements of the actual density are difficult and are complicated by the pres- ence of dark matter.arrow_forwardProblem 10. The redshift is defined to be the quantity Job – Xem Xem (5.1) where Aob and Aem are respectively the wavelengths at which radiation is observed and emitted. Find the corresponding definition in terms of observed and emitted frequencies fob and fem.arrow_forward
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