High-excitation OH and H$_2$O lines in Markarian 231: the molecular signatures of compact far-infrared continuum sources

The far-infrared spectrum of the ultraluminous galaxy Mkn 231 obtained with the Long Wavelength Spectrometer aboard ISO shows high-excitation OH and H$_2$O lines in absorption in energy levels up to 300 K above the ground state, and emission in the [O I] 63 $\mu$m and [C II] 158 $\mu$m lines. Our analysis shows that OH and H$_2$O are radiatively pumped by the far-infrared continuum emission of the galaxy. The observed absorptions in the high-excitation lines require high far-infrared radiation densities, allowing us to constrain the size, temperature, and opacity of the underlying continuum source. The bulk of the far-infrared continuum arises from warm ($T_{{\rm dust}}=70-100$ K), optically thick ($\tau_{100\mu{\rm m}}=1-2$), environments with an effective diameter of 200-400 pc. In our best-fit model, the observed OH line with highest excitation at 65 $\mu$m arises from a luminous ($L/L_{{\rm IR}}\sim0.56$) region with radius $\sim100$ pc. The high surface brightness of this component suggest that its infrared emission is dominated by the AGN. In this context the observed molecules with derived $N({\rm OH})\gtrsim10^{17}$ cm$^{-2}$ and $N({\rm H_2O})\gtrsim6\times10^{16}$ cm$^{-2}$ may be tracers of an XDR, although significant starburst chemistry cannot be ruled out. The lower-lying OH lines, as well as the [C II] 158 $\mu$m and [O I] 63 $\mu$m lines, are expected to arise from a more extended ($\sim350$ pc) starburst region. We show that the [C II] deficit in Mkn 231 is compatible with a high average abundance of C$^+$ because of the extreme overall luminosity to gas mass ratio ($\sim500$ \Lsun/\Msun). Thus, we suggest that a low [C II] to far-infrared flux ratio may be an indication of an important contribution to the luminosity by an AGN, and/or by star formation with extreme efficiency.