COMPARING THE ORTHO-TO-PARA RATIOS OF H$_2$ AND H$_3^+$ IN DIFFUSE INTERSTELLAR CLOUDS

Abstract

The ratio between the populations of the two lowest rotational levels of H$_2$, $J=0$ and $J=1$, can be used to determine the temperature of interstellar gas (referred to as $T_{01}$). Likewise, a temperature can be inferred from the populations of the $(J,K)=(1,0)$ and $(J,K)=(1,1)$ states of H$_3^+$. However, the average temperatures derived from these methods ($T_{01}\approx60$~K, $T({\rm H}_3^+)\approx30$~K) do not agree. Theories predict that the deviation from a Boltzmann distribution in both species is due to collisions between H$_2$ and H$_3^+$ which can change the spin alignment. Recent laboratory results confirm this deviation from a thermal distribution, and provide a relationship between the (1,0)/(1,1) ratio of H$_3^+$ and the (1)/(0) ratio of H$_2$. We have made observations searching for H$_3^+$ in several sight lines with measured H$_2$ abundances for the purpose of determining this relationship in interstellar clouds. With such a relationship, we then show that IR observations probing the (1,0) and (1,1) states of H$_3^+$ can be used to estimate the H$_2$ temperature in highly extincted sight lines where UV spectroscopy is not possible.