Dancing on the grain: Variety of CO and its isotopologue fluxes as a result of surface chemistry and T Tauri disk properties

Context. One of the most important problems in the study of protoplanetary disks is the determination of their parameters, such as their size, age, stellar characteristics, and, most importantly, gas mass in the disk. At the moment, one of the main ways to infer the disk mass is to use a combination of CO isotopologue line observations. A number of theoretical studies have concluded that CO must be a reliable gas tracer, as its relative abundance only depends weakly on disk parameters. However, the observed line fluxes cannot always be easily used to infer the column density, much less the abundance of CO. Aims. The aim of this work is to study the dependence of the CO isotopologue millimeter line fluxes on the astrochemical model parameters of a standard protoplanetary disk around a T Tauri star and to conclude whether they can be used individually or in combinations to reliably determine the disk parameters. Our case is set apart from earlier studies in the literature by the adoption of a comprehensive chemical network with grain-surface chemistry, together with line radiative transfer. Methods. We used the astrochemical model ANDES together with the radiative transfer code RADMC-3D to simulate CO isotopologue line fluxes from a set of disks with varying key parameters (disk mass, disk radius, stellar mass, and inclination). We studied how these values change with one parameter varying and others fixed and approximated the dependences log-linearly. Results. We described the dependences of CO isotopologue fluxes on all chosen disk parameters. Physical and chemical processes responsible for these dependences are analyzed and explained for each parameter. We show that using a combination of the 13CO and C18O line fluxes, the mass can be estimated only within two orders of magnitude uncertainty and a characteristic radius with an uncertainty of one order of magnitude. We find that the inclusion of the grain-surface chemistry reduces 13CO and C18O fluxes, which can help explain the underestimation of disk mass in the previous studies.