Detecting water ice and vapor disks originating from icy planetary bodies around white dwarfs with future PRIMA observations

Observations of atmospheres of polluted white dwarfs provide insights into the elemental composition of accreted exoplanets and exo-asteroids. However, they poorly constrain the abundance of ice-forming volatile elements due to the properties of white dwarf atmospheres. Instead of focusing solely on atmospheric observations, we propose observing circumstellar water ice and vapor disks formed by the tidal disruption of icy bodies using the future PRobe far-Infrared Mission for Astrophysics (PRIMA) far-infrared enhanced survey spectrometer. PRIMA has the potential to measure volatile abundances in colder circumstellar regions inaccessible by shorter-wavelength observations. We employ a simple disk emission model with disk parameter ranges inferred from previous observations and disk evolution simulations. We find the 44-$μ$m water ice feature promising for observing icy disks. For white dwarfs within 60 pc, 1-hour PRIMA observations could detect water ice with a mass above $10^{20}$ g, representing a potential lower limit of circumstellar disk mass. Water vapor rotational lines also abundantly emerge within the PRIMA wavelength coverage, and 5-hour observations for white dwarfs within 20 pc could detect water vapor with a total disk mass $\gtrsim 10^{20}$ g, depending on the H$_2$/H$_2$O ratio. 19 metal polluted white dwarfs within 20 pc and 210 within 60 pc could be optimal targets for water vapor and ice observations, respectively.