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

Aims. 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, in which chemistry may be driven by the absorption of X-rays. We estimate the expected number of sources at high redshift in an ALMA deep field. As a specific example for the complex interpretation of sub-mm line observations, we analyze the recently detected z = 6.42 quasar, for which a number of different line fluxes is already available. We note that our diagnostics may also be valuable for future observations in the local universe with space-borne instruments like on SPICA or FIRI. Methods. To estimate the observables from the starburst, we check which emission from the starburst ring of the nearby Seyfert 2 galaxy NGC 1068 falls into the ALMA bands if the galaxy were placed at z = 8. We estimate the sizes of the central X-ray dominated region based on a semi-analytic model, and employ a detailed 1D approach for the chemistry in X-ray irradiated molecular clouds to evaluate the chemistry and the expected line emission under these conditions. We make use of pre-existing chemistry calculations in X-ray dominated regions to show the dependence of different line fluxes on X-ray luminosity, cloud density and cloud column density. We use theoretical models for the high-z black hole population and the local SMBH density to estimate the number of sources at higher redshift. Results. We show that a number of different fine-structure lines may be used to probe the starburst component of high-redshift quasars in considerable detail, providing specific information on the structure of these galaxies by several independent means. We show that the size of the central X-ray dominated region is of the order of a few hundred parsec, and we provide detailed predictions for the expected fluxes in CO, [CII] and [OI]. While the latter fine-structure lines quickly become optically thick and depend mostly on the strength of the X-ray source, the rotational CO lines have a non-trivial dependence on these parameters. We compare our models to XDRs observed in NGC 1068 and APM 08279 and find that the observed emission can indeed be explained with these models. Depending on the amount of X-ray flux, the CO line intensities may rise continuously up to the (17-16) transition. A measurement of such high-J lines allows one to distinguish observationally between XDRs and PDRs. For the recently observed z = 6.42 quasar, we show that the collected fluxes cannot be interpreted in terms of a single gas component. We find indications for the presence of a dense warm component in active star forming regions and a low-density component in more quiescent areas. Near z = 6, an ALMA deep field may find roughly one source per arcmin(2). At higher redshift, one likely has to rely on other surveys like JWST to find appropriate sources.