Physical conditions in Centaurus A's northern filaments II. Does the HCO+ emission highlight the presence of shocks?

We present the first observations of HCO$^+$(1--0) and HCN(1--0) emission in the northern filaments of Centaurus A with ALMA. HCO$^+$(1--0) is detected in nine clumps of the Horseshoe complex, with similar velocities as the CO(1--0) emission. Conversely, HCN(1--0) is not detected, and we derive upper limits on the flux. At a resolution of $ 40\: pc$, the line ratio of the velocity-integrated intensities HCO+ /I_ CO $ varies between 0.03 and 0.08, while $I_ HCO+ /I_ HCN $ is higher than unity, with an average lower limit of 1.51. These ratios are significantly higher than what is observed in nearby star-forming galaxies. Moreover, the ratio $I_ HCO+ /I_ CO $ decreases with increasing CO-integrated intensity, contrary to what is observed in the star-forming galaxies. This indicates that the HCO$^+$ emission is enhanced and may not arise from dense gas within the Horseshoe complex. This hypothesis is strengthened by the average line ratio $I_ HCN /I_ CO <0.03$, which suggests that the gas density is rather low. Using non-local thermal equilibrium, large velocity gradient modelling with RADEX, we explored two possible phases of the gas, which we call `diffuse' and `dense' and are characterised by a significant difference in the HCO$^+$ abundance relative to CO, respectively $N_ HCO+ /N_ CO $ and $N_ HCO+ /N_ CO $. The average CO(1--0) and HCO$^+$(1--0) integrated intensities and the upper limit on HCN(1--0) are compatible with both diffuse ($n_H=10^3\: $, $T_ kin =15-165\: K$) and dense gas ($n_H=10^4\: $, $T_ kin K$). The spectral setup of the present observations also covers SiO(2--1). While undetected, the upper limit on SiO(2--1) is not compatible with the RADEX predictions for the dense gas. We conclude that the nine molecular clouds detected in HCO$^+$(1--0) are likely dominated by diffuse molecular gas. While the exact origin of the HCO$^+$(1--0) emission remains to be investigated, it is likely related to the energy injection within the molecular gas that prevents gravitational collapse and star formation.