Some elliptical galaxy has a brightness of 18m and a redshift of 0.1. Estimate the mass of the galaxy. Disregard interstellar absorption.

Let’s find the distance to the galaxy according to the Hubble law:
L = cz / H = 420 Mpc
Here H is the Hubble constant, c is the speed of light. The redshift z is significantly less than unity, and we can calculate the absolute magnitude of this galaxy using the usual formula: m0 = m + 5 – 5logL = –20.
The luminosity of this galaxy is 10 ^ 10 times that of the Sun. As you know, there is practically no gas and dust in elliptical galaxies. Therefore, we can assume that the radiation of all the stars of this galaxy reaches us. Assuming the average mass of a star to be equal to the mass of the Sun, and the average luminosity – the luminosity of the Sun, we find that the mass of all stars in the galaxy is equal to 10 ^ 10 solar masses. But we must also take into account that due to dark matter, the mass of galaxies is about 5 times the mass of their visible matter (in this case, stars). Therefore, the final estimate of the mass will be 5 * 10 ^ 10 (50 billion) solar masses or 10 ^ 41 kg.

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