Extended Sunyaev Zel'dovich Distortion

Here is a Planck Distribution

[Graphics:SoftComptongr357.gif]

[Graphics:SoftComptongr358.gif]

This is the 2nd order distortion written in a simple form

[Graphics:SoftComptongr359.gif]

[Graphics:SoftComptongr360.gif]

which we check agrees with above formulae

[Graphics:SoftComptongr361.gif]

[Graphics:SoftComptongr362.gif]

This is the 1st order (classical) distortion

[Graphics:SoftComptongr363.gif]

[Graphics:SoftComptongr364.gif]

Here we define simpler forms for the 2 different pieces

[Graphics:SoftComptongr365.gif]

[Graphics:SoftComptongr366.gif]

[Graphics:SoftComptongr367.gif]

[Graphics:SoftComptongr368.gif]

which we check

[Graphics:SoftComptongr369.gif]

[Graphics:SoftComptongr370.gif]

Rayleigh-Jeans Limit
Plots of Brightness
Plots of Brightness Temperature
Frequency of Zero Distortion
Document converted by Mathematica of Wolfram Research