Optical Depth

After having crossed an absorbing cloud, the intensity of a source, I, is received by the observer as I() = I, where is the optical depth of the cloud.

Let's connect to the physical parameters.

 
		 N      		: 		 column density

		 a(		 :		 line absorption coefficient

 
				: 		 broadening function

		 a(  		= 		   

		 	l 		: 		lower level of the atomic transition

		      k 		: 		 upper level of the atomic transition

		   		 : 		 rest wavelength of the transition

		     g 		: 		 statistical weight of the lower level

		     g 		: 		 statistical weight of the upper level

		     a 		: 		 spontaneous transition probability

 
		f = upward oscillator strength