Comparison With Challinor and Lasenby

Challinor and Lasenby (astro-ph/9711028) give the following formula for SZ20 (from their eq 2.14)

[Graphics:SoftComptongr446.gif]

[Graphics:SoftComptongr447.gif]

which we verify is equivalent to our computation

[Graphics:SoftComptongr448.gif]

[Graphics:SoftComptongr449.gif]

Challinor and Lasenby have also computed the next order term

[Graphics:SoftComptongr450.gif]

To check that we have transcribed it correctly check that the Rayleigh-Jeans limit is correct

[Graphics:SoftComptongr451.gif]

[Graphics:SoftComptongr452.gif]

So the according to Challinor and Lasenby the 3rd order S-Z distortion is

[Graphics:SoftComptongr453.gif]

Now plot the order results

[Graphics:SoftComptongr454.gif]

[Graphics:SoftComptongr455.gif]

[Graphics:SoftComptongr456.gif]

and comparing with Rephaeli' s numerical results

[Graphics:SoftComptongr457.gif]

[Graphics:SoftComptongr458.gif]

[Graphics:SoftComptongr459.gif]

[Graphics:SoftComptongr460.gif]

[Graphics:SoftComptongr461.gif]

[Graphics:SoftComptongr462.gif]

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