Depolarization and polarization transfer rates for the C₂ (X¹ Σ⁺_g, a ³Π_u) + H(²S_1/2) collisions in the solar photosphere

¹ Astronomy and Space Science Department, Faculty of Science, King Abdulaziz University, PO Box 80203, Jeddah 21589, Saudi Arabia
² Department of Optics and Spectroscopy, Tomsk State University, 36 Lenin av., Tomsk 634050, Russia
³ Institute of Spectroscopy, Russian Academy of Sciences, Fizicheskaya St. 5, 108840 Troitsk, Moscow, Russia

^★ Corresponding author; derouichmoncef@gmail.com

Received: 8 April 2024
Accepted: 31 December 2024

Abstract

Context. This paper is a continuation of a series of studies that investigated the collisional depolarization of solar molecular lines such as those of MgH, CN and C₂. It is focused on the solar molecule C₂, which exhibits striking scattering polarization profiles, although its intensity profiles are inconspicuous and barely visible. The current interpretation of the C₂ polarization in terms of magnetic fields is incomplete because collisional data are almost completely lacking.

Aims. We accurately compute the collisional depolarization and polarization transfer rates for the C₂(X¹Σ_g⁺,α³Π_u) by isotropic collisions with hydrogen atoms H (²S _l/2). We also investigate the solar implications of our findings.

Methods. We used the package MOLPRO to obtain potential energy surfaces for the electronic states X¹Σ_g⁺ and a³Π_u of C₂, and the code MOLSCAT to study the quantum dynamics of the C₂(X¹Σ_g⁺,α³Π_u) + H(²S_1/2) systems. We used the tensorial irreducible basis to express the resulting collisional cross sections and rates. Furthermore, sophisticated genetic programming techniques were employed to determine analytical expressions for the temperature and total molecular angular momentum dependence of these collisional rates.

Results. We obtained quantum depolarization and polarization transfer rates for the C₂(X¹Σ_g⁺,α³Π_u) + H(²S_1/2) collisions in the temperature range T = 2000−15 000 K. We also determined analytical expressions that write 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 the C₂ lines. This highlights that the approximation of neglecting lower-level polarization is limited in modeling the polarization of C₂ lines.

Conclusions. Isotropic collisions with neutral hydrogen atoms are a fundamental ingredient for understanding C₂ polarization.