Calculating the output of Seyferrt Galaxy

[skydivephil]

Im trying to calcuate the energy output of Saigtarius A star if it were to accrete material at the same rate as a typical Seyfert Galaxy which I understand to be about 1 solar mass per year (correct?). I am getting an answer that looks way too low. As I understand it we should get a number something like 10^37
Here are my calculations:

The radius of Sagittarius A star, the black hole at the centre of our galaxy is a number I couldn’t find. However it’s mass is easily available: 3.6 mio solar mass
We can compute the radius using the Schwarzschild formula
Rs=2GM/c^2
Where Rs is the Schwarzschild radius
G is the gravitational constant = 6.67*10^-11
M is the mass in kg is 7.2*10^36
C is the speed of light 3*10*8
So we have 2*6.67*10-11*7.2*10^36/9*10^16
= 1.07*10^10
No we can calculate the accretion energy using
GM/R = 6.67*10^-11*2*10^30/1.0*10^10
=1.25*10^10
Mauybe the radisu of Sag A* is much alrgher than normal AGn, or I've made a mistake somehwere. Any ideas?

 

[Adrmay]

Actually, the correct formula for calculating the Schwarzschild radius is Rs = 2GM/c^2, where G is the gravitational constant (6.67x10^-11 m^3 kg^-1 s^-2) and M is the mass of the black hole (in kg). Using this formula, we can calculate the Schwarzschild radius of Sagittarius A* as Rs = 2*6.67x10^-11*7.2x10^36/(3x10^8)^2 = 1.07x10^9 m. Now, to calculate the accretion energy we can use the equation E = GMm/R, where G is the gravitational constant, M is the mass of the black hole (7.2x10^36 kg), m is the mass of the material being accreted (1 solar mass per year, or 1.99x10^30 kg) and R is the Schwarzschild radius (1.07x10^9 m). Plugging in these values, we get E = 6.67x10^-11*7.2x10^36*1.99x10^30/1.07x10^9 = 1.25x10^37 J/s. This is the energy output when Sagittarius A* accretes material at a rate of 1 solar mass per year.