Assume that when a supermassive black hole accretes gas, approximately 50 percent of its mass is converted directly into energy, which is radiated away. If a quasar has a luminosity of 10¹⁴ L _$\odot$ then what must its mass accretion rate be?

Question

Quizplus · Accepted Answer

The mass accretion rate can be calculated using the formula: $L = \eta\dot{M}c^2$ where $L$ is the luminosity, $\dot{M}$ is the mass accretion rate, $c$ is the speed of light, and $\eta$ is the efficiency factor, which is 0.5 based on the assumption given in the problem. Rearranging the formula: $\dot{M} = \frac{L}{\eta c^2} = \frac{10^{14} ext{L}_\odot}{0.5 imes 3 imes 10^{10} ext{cm/s}^2} \approx 6.67 imes 10^7 ext{M}_\odot/ ext{year}$ Converting to units of MF2S2S2W1_F1F1F10 per year, we get: $\dot{M} \approx 6.67 imes 10^4$ MF2S2S2W1_F1F1F10/year which is closest to answer choice B, 10 MF2S2S2W1_F1F1F10 per year.

Assume That When a Supermassive Black Hole Accretes Gas, Approximately ⊙\odot⊙

Assume That When a Supermassive Black Hole Accretes Gas, Approximately $\odot$