Cosmic rays cannot explain the high ionisation rates in the Galactic centre

Context. The H-2 ionisation rate in the central molecular zone, located in the Galactic centre, is estimated to be zeta similar to 2 x 10(-14) s(-1), based on observations of H-3(+) lines. This value is two to three orders of magnitude larger than that measured anywhere else in the Galaxy. Aims. Due to the high density of the gas in the central molecular zone, UV and X-ray photons do not penetrate this region. Hence, cosmic rays are expected to be the exclusive agents of ionisation. A high cosmic-ray density has been invoked to explain the unusually high ionisation rate. However, this excess is not seen in the gamma-ray emission from this region, which is produced by high-energy cosmic rays. Therefore, an excess is expected only in the low-energy cosmic-ray spectrum. Here, we derive constraints on this hypothetical low-energy component in the cosmic-ray spectra, and we question its plausibility. Methods. To do so, we numerically solved the cosmic-ray transport equation in the central molecular zone, considering spatial diffusion, advection in the Galactic wind, re-acceleration in the ambient turbulence, and energy losses due to interactions with matter and radiation in the interstellar medium. We derived stationary solutions under the assumption that cosmic rays are continuously injected by a source located in the Galactic centre. The high-energy component in the cosmic-ray spectrum was then fitted to available gamma-ray and radio data, and a steep low-energy component was added to the cosmic-ray spectrum to explain the large ionisation rates. Results. We find that injection spectra of p(-7) for protons below p(enh, p)c similar or equal to 780 MeV and p(-5.2) for electrons below p(enh, e)c = 1.5 GeV are needed to reach the observed ionisation rates. This corresponds to a cosmic-ray power of the order of similar to 10(40 - 41) erg s(-1) injected at the Galactic centre. Not only is this unrealistic, but it is also impossible to reproduce a constant ionisation rate across the region, as observations suggest. Conclusions. We conclude that cosmic rays alone cannot explain the high ionisation rates in the Galactic centre.