A new proxy to estimate the cosmic-ray ionisation rate in dense cores
  Cosmic rays are a global source of ionisation, and the ionisation fraction
represents a fundamental parameter in the interstellar medium. Ions couple to
magnetic fields, affect the chemistry, and the dynamics of star-forming regions
as well as planetary atmospheres. However, the cosmic-ray ionisation rate
represents one of the bottlenecks for astrochemical models, and its
determination is one of the most puzzling problems in astrophysics. While for
diffuse clouds reasonable values have been provided from H$_3^+$ observations,
for dense clouds, due to the lack of rotational transitions, this is not
possible, and estimates are strongly biased by the employed model. We present
here an analytical expression, obtained from first principles, to estimate the
cosmic-ray ionisation rate from observational quantities. The theoretical
predictions are validated with high-resolution three-dimensional numerical
simulations and applied to the well known core L1544; we obtained an estimate
of $\zeta_2 \sim 2-3 \times 10^{-17}$ s$^{-1}$. Our results and the analytical
formulae provided represent the first model-independent, robust tool to probe
the cosmic-ray ionisation rate in the densest part of star-forming regions (on
spatial scales of $R \leq 0.05$ pc). An error analysis is presented to give
statistical relevance to our study.
