A low cosmic-ray ionisation rate in the pre-stellar core Ophiuchus/H-MM1. Mapping of the molecular ions ortho-H2D+, N2H+, and DCO+

We test the use of three common molecular ions, ortho-htwodplus (ohtwodplus ), diaz , and dcoplus , as probes of the internal structure and kinematics of a dense, starless molecular cloud core. The pre-stellar core H-MM1 in Ophiuchus was mapped in the ohtwodplusline , $ and $ lines with the Large APEX sub-Millimeter Array (LAsMA) multi-beam receiver of the Atacama Pathfinder EXperiment (APEX) telescope. We also ran a series of chemistry models to predict the abundance distributions of the observed molecules, and to estimate the effect of the cosmic-ray ionisation rate on their abundances. The three line maps show different distributions. The ohtwodplus map is extended and outlines the general structure of the core, diaz mainly shows the density maxima, and the dcoplus emission peaks are shifted towards one edge of the core where a region of enhanced desorption had previously been found. According to the chemical simulation, the fractional ohtwodplus abundance remains relatively high in the centre of the core, and its column density correlates strongly with the cosmic-ray ionisation rate, $ htwo $. Simulated line maps constrain the cosmic-ray ionisation rate to be low, between $5 and $1 in the H-MM1 core. This estimate agrees with the gas temperature measured in the core. The present observations show that very dense, cold gas in molecular clouds can be traced by mapping the ground-state line of ohtwodplus and high-$J$ transitions of dcoplus and diaz , despite the severe depletion of the latter two molecules. Modelling line emission of ohtwodplus provides a straightforward method of determining the cosmic-ray ionisation rate in dense clouds, where the primary ion, hthreeplus , is not observable.