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_⨀ then what must its mass accretion rate be?

Question

Quizplus · Accepted Answer

From the given luminosity and assuming 50% of accreted mass is converted into energy, we can use the following equation to calculate the mass accretion rate:

Luminosity = (0.5) x (mass accretion rate) x (speed of light^2)

Substituting the given values, we get:

10^14 L⊙ = (0.5) x (mass accretion rate) x (3 x 10^8)^2

Solving for mass accretion rate, we get:

mass accretion rate = (2 x 10^44) / (9 x 10^16)

mass accretion rate ≈ 2.22 x 10^27 kg/year

Converting this to solar masses per year, we get:

mass accretion rate ≈ 11 MSun/year

Therefore, the best choice is B) 10 MSun/year, since it is closest to the calculated value of 11 MSun/year.

Assume That When a Supermassive Black Hole Accretes Gas,approximately 50