= QUESTION 3. (3a) Use the following expression for the virial mass 50 R Muir G to estimate the virial mass of the Virgo

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Question 3 3a Use The Following Expression For The Virial Mass 50 R Muir G To Estimate The Virial Mass Of The Virgo 1 (109.08 KiB) Viewed 27 times

= QUESTION 3. (3a) Use the following expression for the virial mass 50 R Muir G to estimate the virial mass of the Virgo cluster of galaxies in solar masses, treating the cluster like a sphere with radius R=1.5 Mpc and radial-velocity dispersion or = 667 km/s. [6 marks] (3b) Use the visual luminosity of the cluster, Lv = 1.2 x 1012 Lo, to estimate the cluster's luminous mass. [6 marks) (3c) The hot intracluster gas of the Virgo cluster has a temperature of about 70 million K and emits thermal bremsstrahlung with an X-ray luminosity of Lx = 1.5 x 1036 J/s. Use the following relation for the luminosity density of this bremsstrahlung (in Js-'m-) in terms of the electron density ne and the temperature T, Lyol = 1.42 x 10-02T1/2, to estimate the total mass of the hot X-ray gas in solar masses. What conclusions can you draw from a comparison of this mass with the luminous mass and virial mass of the cluster? (10 marks] (3d) Assume that the hot X-ray gas has no energy input, and that it is simply losing energy via thermal bremsstrahlung with a constant luminosity. Estimate the total energy contained in the hot gas, and how long it will take for the gas to lose all of its energy. Compare your answer with the age of the Universe and comment. [8 marks) m