# MathSciDoc: An Archive for Mathematician ∫

#### Numerical Analysis and Scientific Computingmathscidoc:1610.25053

The Astrophysical Journal, 772, 3, 2013
We investigate the angular distribution of Ly$\alpha$ photons transferring in or emergent from an optically thick medium. Since the evolutions of specific intensity $I$ in the frequency space and the angular space are coupled with each other, we first develop the WENO numerical solver in order to find the time-dependent solutions of the integro-differential equation of $I$ in frequency and angular space simultaneously. We first show that the solutions with the Eddington approximation, which assume $I$ to be linearly dependent on the angular variable $\mu$, yield similar frequency profiles of the photon flux as that without the Eddington approximation. However, the solutions of the $\mu$ distribution evolution are significantly different from that given by Eddington approximation. First, the angular distribution of $I$ are found to be substantially dependent on the frequency of photons. For photons with the resonant frequency $\nu_0$, $I$ contains only a linear term of $\mu$. For photons with frequency at the double peaks of the flux, the $\mu$-distribution is highly anisotropic, in which most photons are in the direction of radial forward. Moreover, either at $\nu_0$ or at the double peaks, the $\mu$ distributions actually are independent of the initial $\mu$ distribution of photons of the source. This is because the photons with frequency either of $\nu_0$ or of the double peaks undergo the process of forgetting their initial conditions due to the resonant scattering. We also show that the optically thick medium is a collimator of photons at the double peaks. Photons from the double peaks form a forward beam with very small spread angle.
@inproceedings{yang2013angular,
title={Angular distribution of Ly$\alpha$ resonant photons emerging from optically thick medium},
author={Yang Yang, Ishani Roy, Chi-Wang Shu, and Li-Zhi Fang},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012054022297095171},
booktitle={The Astrophysical Journal},
volume={772},
pages={3},
year={2013},
}

Yang Yang, Ishani Roy, Chi-Wang Shu, and Li-Zhi Fang. Angular distribution of Ly$\alpha$ resonant photons emerging from optically thick medium. 2013. Vol. 772. In The Astrophysical Journal. pp.3. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012054022297095171.