Question

The smallest known blackhole is XTE J1650-500 in a binary system in the Milky Way. It’s mass is with just 3.8 times the mass of the sun. On the other hand, the most massive blackhole known is located in a super massive galaxy named Holm 15A, which is thought to have already formed from the collision of at least 8 smaller galaxies. The BH’s mass is 40 billion times that of the Sun. Calculate the Schwarzschild radius of both blackholes.

You have discovered a new galaxy and you think you have identified an Type II Cepheid star with a period of 30 days. You measure its brightness and with the Period-Luminosity function you calculate the distance to the galaxy d. However, you later find out that in fact the star you had identified is a Type I Cepheid. Is the galaxy further than, or, close to, us than we previously expected? By what factor should you multiply d to get the correct distance to the new galaxy?

Answer 1

The numerical value of the Schwarzschild radius, Rs, is given bMy the equation:

where G is Newton's gravitational constant, c is the speed of light and M is mass.

In practical units, Rs = kilometers.

Given : Mass of XTE J1650-500 = 3.8 Msun

Mass of massive blackhole = 40 x 109 Msun

Rs of XTE J1650-500 = 3 x 3.8 = 11.4 km

Rs of massive blackhole = 1.2 x 1011 km

From Inverse Square Law, we know apparent brightness of an object decreases as the square of its distance. If you know both the apparent and intrinsic brightness of a star, you can calculate its distance. The period at which Cepheids pulse is related to their average intrinsic luminosity. More luminous Cepheids pulse more slowly. Thus Type 1 Cepheids are more luminious than type 2 Cepheids. By measuring the period of a Cepheid we can calculate its intrinsic luminosity, and thus its distance.