The hidden heart of the luminous infrared galaxy IC 860 I. A molecular inflow feeding opaque, extreme nuclear activity

High-resolution (0."03 - 0."09) (9 - 26 pc)) ALMA (100 - 350 GHz (3 - 0.8 mm)) and VLA 45 GHz measurements have been used to image continuum and spectral line emission from the inner region of the nearby infrared luminous galaxy IC 860. We detect compact (r=8-10 pc), luminous, mm continuum emission in the core of IC 860, with brightness temperatures $T_{\rm B}>$ 280 K. The 45 GHz continuum is equally compact, but fainter in flux. We suggest that the 3 to 0.8 mm continuum is opaque at mm-wavelengths, implying a very large H$_2$ column density $N$(H$_2$) of 1e26 cm-2, and that it emerges from hot dust with temperature $T_{\rm d} \sim 280$ K. Vibrationally excited lines of HCN $\nu_2$=1f J=4-3 and 3-2 (HCN-VIB) are seen in emission and resolved on scales of 40-50 pc. The HCN-VIB emission reveals a north-south nuclear velocity gradient with projected rotation velocities of v=100 kms$^{-1}$ at r=10 pc. The brightest HCN-VIB emission is oriented perpendicular to the velocity gradient. Ground state lines of HCN 3-2, 4-3, HC$^{15}$N 4-3, HCO$^+$ 3-2, 4-3 and CS 7-6, show complex line absorption and emission features. HCN and HCO$^+$ have red-shifted, reversed P-Cygni profiles consistent with gas inflows of $\sim$50 kms$^{-1}$. The absorption features can be traced from the north-east into the nucleus. In contrast, CS 7-6 shows blue-shifted line wings extending to -180 kms$^{-1}$. We suggest that a dense and slow outflow is hidden behind a foreground layer of inflowing gas. It appears that the centre of IC 860 is in a phase of rapid evolution where an inflow is building up the nuclear column density of gas. A slow, dense outflow may be signalling the onset of feedback. The inner, r=10 pc, IR luminosity can be powered by an accreting black hole and/or a compact starburst with a top-heavy initial mass function.