Retrieval of Thermally-Resolved Water Vapor Distributions in Disks Observed with JWST-MIRI

The mid-infrared water vapor emission spectrum provides a novel way to characterize the delivery of icy pebbles towards the innermost ($<5$ au) regions of planet-forming disks. Recently, JWST MIRI-MRS showed that compact disks exhibit an excess of low-energy water vapor emission relative to extended multi-gapped disks, suggesting that icy pebble drift is more efficient in the former. We carry out detailed emission line modeling to retrieve the excitation conditions of rotational water vapor emission in a sample of four compact and three extended disks within the JDISC Survey. We present two-temperature H$_2$O slab model retrievals and, for the first time, constrain the spatial distribution of water vapor by fitting parametric radial temperature and column density profiles. Such models statistically outperform the two-temperature slab fits. We find a correlation between the observable hot water vapor mass and stellar mass accretion rate, as well as an anti-correlation between cold water vapor mass and sub-mm dust disk radius, confirming previously reported water line flux trends. We find that the mid-IR spectrum traces H$_2$O with temperatures down to 180-300 K, but the coldest 150-170 K gas remains undetected. Furthermore the H$_2$O temperature profiles are generally steeper and cooler than the expected `super-heated' dust temperature in passive irradiated disks. The column density profiles are used to estimate icy pebble mass fluxes, which suggest that compact and extended disks may produce markedly distinct inner-disk exoplanet populations if local feeding mechanisms dominate their assembly.