Question

The mass of dark matter in the Milky Way is measured to be about 2×1042 kg. Black holes emit no light, so perhaps they may be responsible for the unseen dark matter? To evaluate this possibility, determine how many black holes must exist to explain the dark matter and what process created them. As far as we know, every black hole was formed as a result of a supernova explosion

A. Find the number of black holes in the Galaxy by dividing the mass of all the dark matter by the mass of a single stellar-mass black hole (5 times the mass of the Sun).

B. Since we believe black holes are created in supernovae, the number of black holes must be equal to the number of supernovae that have occurred. On average, humans have observed about one supernova per century in the Milky Way. At this rate, how long would take to create all enough black holes to explain all the dark matter?

C. If the current rate of supernovae does not appear feasible, consider an alternative hy- pothesis that nearly all the black holes in the galaxy were formed long ago, and we were not around to witness them. What signs of this ancient “burst” of star formation might astronomers look for in our galaxy?

Answer 1

a) Mass of dark matter is given to be M_d= 2 x 10⁴² kg

                Mass of a single Stellar mass Black hole M_b = 5 x Mass of Sun

                                                                                   = 5 x 2 x 10³⁰ kg

                                                                                   = 10³¹ kg

                Thus, Number of black holes       = M_d/M_b

                               = 2 x 10⁴²/ 10³¹

                               = 2 x 10¹¹

b) On the assumption that number of black holes = Number of supernovae

    And that the rate of supernovae is one supernova per century

    Thus, Time taken for enough black holes to be created to explain all dark matter

                = 2 x 10¹¹ x (100 Years)

                = 2 x 10¹³ Years

c) If now we assume that all the black holes were created a long time ago, the astronomers must look for the remnants of it in our galaxy. The cosmic rays are produced in a supernova which can be looked for.