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

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 depends on disk parameters only weakly. However, the observed line fluxes cannot always be easily used to infer the column density, much less the abundance of CO. 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 or their combinations can be reliably used to determine disk parameters. Our case is set apart from earlier studies in the literature by the usage of a comprehensive chemical network with grain surface chemistry together with line radiative transfer. We use 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 study how these values change with one parameter varying and others fixed and approximate the dependences log-linearly. We describe 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 $^{13}$CO and C$^{18}$O line fluxes, the mass can be estimated only within two orders of magnitude uncertainty and characteristic radius within one order of magnitude uncertainty. We find that inclusion of grain surface chemistry reduces $^{13}$CO and C$^{18}$O fluxes which can explain the underestimation of disk mass in the previous studies.