So I've been looking at the formulas for the width of the Gaussian part of the Voigt profile, and I think there might be a factor 2 in the p-winds implementation that shouldn't be there. Eq. 16 of the p-winds paper is taken from Eq. 16 of Lampón et al. (2020) and reads
however, Lampón calls this $\alpha_D$ the "Doppler line width", and comparing his Eq. 15 with the definition of a Gaussian indicates that his $\alpha_D$ is actually not equal to the standard deviation $\sigma$, but to $\sqrt{2} \sigma$. The scipy.voigt_profile() that p-winds uses expects the standard deviation, so I think instead it should be passed $\frac{\nu_0}{c} \sqrt{\frac{kB T}{m{He}}}$.
This would then also be consistent with Eq. 21 of Oklopcic&Hirata (2018), which uses $HWHM = \sqrt{\frac{2 ln 2 kT0}{m{He}}}\frac{\nu_0}{c}$, where the HWHM is related to the standard deviation by a factor $\sqrt{2ln2}$.
(Similarly, I think the turbulence term should be modified to $v_{turb}^2 = \frac{5kT}{6m}$)
Perhaps I am overlooking something, so if someone could verify, that would be great!
Dion
ladsantos
commented
6 months ago
Hi!
So I've been looking at the formulas for the width of the Gaussian part of the Voigt profile, and I think there might be a factor 2 in the p-winds implementation that shouldn't be there. Eq. 16 of the p-winds paper is taken from Eq. 16 of Lampón et al. (2020) and reads
$\alpha = \frac{\nu_0}{c} \sqrt{\frac{2 kB T}{m{He}}}$
however, Lampón calls this $\alpha_D$ the "Doppler line width", and comparing his Eq. 15 with the definition of a Gaussian indicates that his $\alpha_D$ is actually not equal to the standard deviation $\sigma$, but to $\sqrt{2} \sigma$. The
scipy.voigt_profile()that p-winds uses expects the standard deviation, so I think instead it should be passed $\frac{\nu_0}{c} \sqrt{\frac{kB T}{m{He}}}$. This would then also be consistent with Eq. 21 of Oklopcic&Hirata (2018), which uses $HWHM = \sqrt{\frac{2 ln 2 kT0}{m{He}}}\frac{\nu_0}{c}$, where the HWHM is related to the standard deviation by a factor $\sqrt{2ln2}$.(Similarly, I think the turbulence term should be modified to $v_{turb}^2 = \frac{5kT}{6m}$)
Perhaps I am overlooking something, so if someone could verify, that would be great! Dion