 #1
Kayla Martin
 7
 0
 Homework Statement

Hi, I can't figure out how to find the optical depth for the following situation:
A supernova remnant has a brightness of I=1.5x10^{19} Wm^{2}Hz^{1}sr^{1} at frequencies around 1.61.7 GHz, but OH molecules in a homogenous foreground cloud produce an absorption line at 1667MHz. The observed intensity at the center of the line is 3.0x10^{20} Wm^{2}Hz^{1}sr^{1} and the width is 16kHz (corresponding to a velocity width of about 3km/s).
Assuming T_{ex}=12K throughout the cloud for this transition I need to use the radiative transfer equation to calculate the optical depth at the center of the line, tau_0.
Can someone please help me figure this out? I know we have been given all the equations for this in our lecture notes, but I am stumped at how to put it all together?
 Relevant Equations

$$\frac{dI}{dS} =  \alpha I + j$$ where $$\alpha$$ is absorption coefficient...
$$\frac{dI}{\tau} =  I + S$$ where S is the source function $$S = \frac{j}{\alpha}$$ and $$\tau$$ is the optical depth.
Last edited: