Plots of Brightness

Plot of brightness of distortion divided by y.

[Graphics:SoftComptongr373.gif]

[Graphics:SoftComptongr374.gif]

[Graphics:SoftComptongr375.gif]

The curves intersect at the zeros of the coefficients of T2 which are x=3.32956. and x=8.0202

[Graphics:SoftComptongr376.gif]

[Graphics:SoftComptongr377.gif]

[Graphics:SoftComptongr378.gif]

[Graphics:SoftComptongr379.gif]

[Graphics:SoftComptongr380.gif]

[Graphics:SoftComptongr381.gif]

And we can do a figure to compare with Figure 1 of Raphaeli (1995) Ap.J. 445 33-36 which gives nearly identical results.

[Graphics:SoftComptongr382.gif]

[Graphics:SoftComptongr383.gif]

Now we combine 3 plots showing the (brightness) spectrum of the distortion at 5, 10, 15 keV, for a better comparison with Rephaeli.

The 1st is for the classical S-Z distortion

[Graphics:SoftComptongr384.gif]

[Graphics:SoftComptongr385.gif]

[Graphics:SoftComptongr386.gif]

The 2nd is the "scanned in" curves of Rephaeli,  

[Graphics:SoftComptongr387.gif]

[Graphics:SoftComptongr388.gif]

[Graphics:SoftComptongr389.gif]

and the 3rd is our 2nd order approximation

[Graphics:SoftComptongr390.gif]

[Graphics:SoftComptongr391.gif]

[Graphics:SoftComptongr392.gif]

Combining them all and making it look nice (NB we could have put a [Graphics:SoftComptongr393.gif]&Dgr;n label on the y-axis, but when you save to PostScript, the greek letters are changed to roman!)

[Graphics:SoftComptongr394.gif]

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and write it out to disk

[Graphics:SoftComptongr397.gif]

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For conversion from "x" to frequency in GHz

[Graphics:SoftComptongr399.gif]

[Graphics:SoftComptongr400.gif]

Or in black and white: the classical result

[Graphics:SoftComptongr401.gif]

[Graphics:SoftComptongr402.gif]

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Rephaeli's result  

[Graphics:SoftComptongr404.gif]

[Graphics:SoftComptongr405.gif]

[Graphics:SoftComptongr406.gif]

and the 3rd is our 2nd order approximation

[Graphics:SoftComptongr407.gif]

[Graphics:SoftComptongr408.gif]

[Graphics:SoftComptongr409.gif]

Combining them all

[Graphics:SoftComptongr410.gif]

[Graphics:SoftComptongr411.gif]

[Graphics:SoftComptongr412.gif]

[Graphics:SoftComptongr413.gif]

[Graphics:SoftComptongr414.gif]

Document converted by Mathematica of Wolfram Research