Is the xe equation in CAMB correct or not?

YinZhe Ma
Posts: 11
Joined: October 09 2008
Affiliation: University of KwaZulu-Natal

Is the x_e equation in CAMB correct or not?

I am looking at the Antony Lewis' paper

https://arxiv.org/pdf/0804.3865.pdf

for Eq.(B3) on page 11, there is this equation of number of free electron per hydrogen atom.

But for this equation, if $z \rightarrow$ large values, then y=(1+z)3/2 will also become large values, while y(zre) and $\Delta_y$ are fixed. Since "$\tanh(x \rightarrow \infty) \rightarrow 1$", then for large redshift, $x_{\rm e} \rightarrow 1$.

If $z \rightarrow 0$, then $\tanh$ function will becomes a negative value but greater than −1, then $x_{\rm e} \rightarrow 0$.

So this is completely opposite to the trend of Fig.6 on the same page. Can anyone explain what is going on here?

Perhaps I made some stupid mistake, please point it out. Thank you.

Antony Lewis
Posts: 1354
Joined: September 23 2004
Affiliation: University of Sussex
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Re: Is the x_e equation in CAMB correct or not?

I think it's just a typo (code has y(zre)-y in the tanh):

https://github.com/cmbant/CAMB/blob/mas ... on.f90#L80

YinZhe Ma
Posts: 11
Joined: October 09 2008
Affiliation: University of KwaZulu-Natal

Is the x_e equation in CAMB correct or not?

Oh, then this typo affects the Planck reionization paper, the published version of Planck intermediate results XLVII. Planck constraints on reionization history,

page 5, equation 2

also takes this typo.