IOAA 2013, theory — Задача 3

*$7^{th}$ International Olympiad on Astronomy & Astrophysics 27 July – 5 August 2013, Volos Greece

Theoretical Exam - Long Questions · 27 юли 2013 г.*

Условие

Question 3

(1) Using the $\textit{virial theorem}$ for an isolated, spherical system, i.e, that $-2\langle K\rangle=\langle U\rangle$, where “K” is the average kinetic energy and “U” is the average potential energy of the system, determine an expression for the total mass of a cluster of galaxies if we know the radial velocity dispersion, $\sigma$, of the cluster’s galaxy members and the cluster’s radius, $R$. Assume that the cluster is isolated, spherical, has a homogeneous density and that it consists of galaxies of equal mass.

(2) Find the $\textit{virial mass}$, i.e. the mass calculated from the $\textit{virial theorem}$, of the Coma cluster, which lies at a distance of 90 Mpc from us, if you know that the radial velocity dispersion of its member galaxies is $\sigma_{v_r}=1000km/s$ and that its angular diameter (on the sky) is about $4^\circ$.

(3) From observations, the total luminosity of the galaxies comprising the cluster is approximately $L=5\times10^{12}L_{\odot}$. If the mass to luminosity ratio, $M/L$, of the cluster is $\sim1$ (assume that all the mass of the cluster is visible mass), this should correspond to a total mass $M\sim5\times10^{12}M_{\odot}$ for the mass of the cluster. Give the ratio of the luminous mass to the total mass of the cluster you derived in question (2).

Решение

Теми и трудност

Трудност: неоценена.

Галактики и космология · Светлина и астрономически измервания · Купове и тъмна материя · Поток и светимост

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Оригинал в Архива: LongQuestions.pdf