Depolarization and polarization transfer rates for the C$_2$ $(X ^1\Sigma^+_g, a ^3\Pi_u)$ + H$(^2S_{1/2})$ collisions in the solar photosphere

TL;DR

This study computes collisional depolarization and polarization transfer rates for the C$_2$ molecule in the solar atmosphere, providing new data crucial for interpreting solar polarization signals and magnetic fields.

Contribution

It introduces accurate quantum mechanical calculations and analytical expressions for collisional rates of C$_2$ with hydrogen, filling a key data gap for solar polarization modeling.

Findings

Isotropic hydrogen collisions partially depolarize C$_2$ lower states.

Analytical formulas for rates as functions of temperature and angular momentum.

Collisional data improve interpretation of solar polarization profiles.

Abstract

This paper is a continuation of a series of studies investigating collisional depolarization of solar molecular lines like those of MgH, CN and C$_2$. It is focused on the case of the solar molecule C$_2$ which exhibits striking scattering polarization profiles although its intensity profiles are inconspicuous and barely visible. In fact, interpretation of the C$_2$ polarization in terms of magnetic fields is incomplete due to the almost complete lack of collisional data. This work aims at accurately computing the collisional depolarization and polarization transfer rates for the C$_2$~$(X ^1\Sigma^+_g, a ^3\Pi_u)$ by isotropic collisions with hydrogen atoms H~$(^2S_{1/2})$. We also investigate the solar implications of our findings. We utilize the MOLPRO package to obtain potential energy surfaces (PESs) for the electronic states $X ^1\Sigma^+_g$ and $a^3\Pi_u$ of C$_2$, and the MOLSCAT code to study the quantum dynamics of the C$_2$~$(X ^1\Sigma^+_g, a ^3\Pi_u)$ + H$(^2S_{1/2})$ systems. We use the tensorial irreducible basis to express the resulting collisional cross-sections and rates. Furthermore, sophisticated genetic programming techniques are employed to determine analytical expressions for the temperature and total molecular angular momentum dependence of these collisional rates. We obtain quantum depolarization and polarization transfer rates for the C$_2$ $(X ^1\Sigma^+_g, a ^3\Pi_u)$ + H$(^2S_{1/2})$ collisions in the temperature range T=2,000--15,000~K. We also determine analytical expressions giving these rates as functions of the temperature and total molecular angular momentum. In addition, we show that isotropic collisions with neutral hydrogen can only partially depolarize the lower state of C$_2$ lines, rather than completely. This highlights the limitations of the approximation of neglecting lower-level polarization while modeling the polarization of C$_2$ lines.