Probing high-redshift quasars with ALMA. I. Expected observables and potential number of sources

(abridged) We explore how ALMA observations can probe high-redshift galaxies in unprecedented detail. We discuss the main observables that are excited by the large-scale starburst, and formulate expectations for the chemistry and the fluxes in the center of active galaxies, where chemistry may be driven by the absorption of X-ray photons. We show that such X-ray dominated regions (XDRs) should be large enough to be resolved with ALMA, and predict the expected amount of emission in CO and various fine-structure lines. We discuss how such XDRs can be distinguished from a strong starburst on the same spatial scales based on the CO line SED. Our models are compared to known sources like NGC 1068 and APM 08279. We also analyze the properties of the z=6.42 quasar SDSS J114816.64+525150.3, and find that the observed emission in CO, [CII] and [CI] requires a dense warm and a low-density cold gas component. We estimate the expected number of sources at redshifts higher than 6, finding that one could expect one black hole with $10^6$ solar masses per arcmin$^2$.