Low cosmic-ray ionisation at parsec scales in G035.39-00.33

Cosmic rays (CRs) regulate the chemical evolution of the gas and its coupling to the magnetic field in the densest and coldest regions of the interstellar medium (ISM). However, the CR ionisation rate of H$_2$ ($\zeta_2$) is one of the most debated parameters characterising molecular clouds due to the uncertainties in its estimation. We developed a new analytical framework based on the chemistry of N$_2$H$^+$, N$_2$D$^+$ and DCO$^+$ to overcome observational limitations in current estimates of $\zeta_2$ and to probe the latter and the electron fraction, $x(e)$, in the gas across multiple density regimes. We applied this method towards the parsec-scale filament of the infrared dark cloud (IRDC) G035.39-00.33 with new observations from the NOrthern Extended Array (NOEMA) at a resolution of $3''$ (or $\sim9000$ au). Ancillary observations of C$^{18}$O complete this survey to measure $x(e)$ and $\zeta_2$ in G035.39-00.33. CO depletion is widespread in G035.39-00.33 with factors, $f_\mathrm{D}$, positively correlated with column and number densities of H$_2$ in the cloud. The deuterium fractions ($R_\mathrm{D}$) are enhanced towards these same sites in which the corresponding electron fraction values cluster below $\lesssim10^{-8}$. $\zeta_2$ varies by three orders of magnitude in G035.39-00.33 ($\sim10^{-18}-10^{-15}$ s$^{-1}$) with a median of $\sim2.3\times10^{-18}$ s$^{-1}$, consistent with those reported for other IRDCs and giant filaments, but on average lower than the typical $\zeta_2$ for the ISM. $\zeta_2$ shows a functional dependence on $N(\mathrm{H_2})$, but with absolute values lower compared to those predicted by theoretical models. This behaviour suggests the presence of an overall attenuation of the CR flux taking place in G035.39-00.33. The CR flux appears to be reduced by the change in magnetic field strength and morphology previously reported in the region.