Question

Spectral lines from a Seyfert galaxy are observed to be redshifted by 0.5 percent and to have broadened emission lines indicating an orbital speed of 250 km/s at an angular distance of 0.1" from its center. Assuming circular orbits, use Kepler's laws to estimate the mass within this 0.1" radius.

Answer 1

Here, we need to assume a Hubble constant to find d value

I am assuming as 75 Km/s/Mpc

so,

d = 20 Mpc

Now,

radius within 1'' area is given as

(0.1 / 360 * 3600 ) * d / 2*20e6

solve for d, we get

d = 9.7 pc

we know

1 pc = 206265 AU

so,

d = 9.7 pc = 2e6 AU

Now, we need to find period

P = 2r / v

P = 2*2e6 * 1.48e11 / 250e3

(note that we need to convert AU to meters)

so,

P = 7.439e12 seconds

P = 2.36e5 Years

so,

Mass = d³ / P² (from Kepler's third law)

Note that for Kepler's law to work fine, distance should be in AU and period should be in years.

Mass =   2e6³ / 2.36e5²

Mass = 1.44e8 solar masses