Question

We observe a B-type main sequence star (MV = -1.1) in the direction of a large region of interstellar gas and dust. The visual extinction looking through the cloud is 1.1 magnitudes. The thickness of the nebula is estimated to be 20 pc and its center is located 700 pc from Earth.

a. If the star is in front of the nebula, what would be its apparent visual magnitude?

b. If the star is behind the nebula, what would be its apparent visual magnitude?

c. If the extinction coefficient in the nebula (assume constant ρ) is κV = 0.035 m2 kg-1 what is the density, ρ, of the nebula?

d. If the star were behind the nebula, but we were not aware of any extinction, how far away would we think the star was?

Answer 1

We know that the relationship between the apparent magnitude, absolute magnitude, and distance is given by

where AV - visual extinction

Distance between the center of nebula and earth = 700 pc

let us assume that the nebula is spherical in shape. then the diameter of the sphere = 20 pc

the radius of the nebula = 10 pc

Given that

AV  = 1.1 magnitude

MV = -1.1 magnitude

a. star is infront of nebula

distance fro earth = 700-10 = 690 pc

b. star is behind the nebula

distance fro earth = 700+10 = 710 pc

d. if there is no idea of extinction and the star is behind the nebula, then

MV = -1.1 magnitude

c. given that extinction coefficient

density of the nebula

here r- radius of the nebula = 10 pc