Is the x_e equation in CAMB correct or not?

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

Is the x_e equation in CAMB correct or not?

Post by YinZhe Ma » July 31 2017

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 [tex]z \rightarrow[/tex] large values, then y=(1+z)^3/2 will also become large values, while y(z_re) and [tex]\Delta_y[/tex] are fixed. Since "[tex]\tanh(x \rightarrow \infty) \rightarrow 1[/tex]", then for large redshift, [tex]x_{\rm e} \rightarrow 1[/tex].

If [tex]z \rightarrow 0[/tex], then [tex]\tanh[/tex] function will becomes a negative value but greater than -1, then [tex]x_{\rm e} \rightarrow 0[/tex].

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
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Affiliation: University of Sussex
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Re: Is the x_e equation in CAMB correct or not?

Post by Antony Lewis » July 31 2017

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?

Post by YinZhe Ma » July 31 2017

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.

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