12M Manual Appendix B


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The Relationship Between Flux and Brightness Temperature


In the following we derive the relationship between the flux of a source and its brightness temperature for a gaussian beam measuring two different source geometries, uniform disk and gaussian. The general relation between flux and brightness temperature is

Sν =          (B.1)

 

Note that throughout this discussion when we refer to a “temperature” we are actually referring to the effective source radiation temperature J(ν; T), which is defined by Equation C.1.

 

B.1 Uniform Disk Source

Sν =       (B.2)
Sν =        (B.3)

 

where we have used the fact that

=   (B.4)
=   (B.5)

 

Plugging in some constants into Equation B.2 yields the following

Sν(Jy) =    
  =   (B.6)

 

The peak flux densities of the planets are calculated by the planets program using Equation B.6.

 

B.2 Elliptical Gaussian Source

Sν =    
  =    
  =   (B.7)

 

Plugging in some constants into Equation B.7 yields the following

Sν(Jy) =    
  =   (B.8)

 

 


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Last updated: 11/08/11.