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A major motivation of spectroscopic observations of giant exoplanets is tounveil planet formation processes from atmospheric compositions. Several recentstudies suggested that atmospheric nitrogen, like carbon and oxygen, canprovide important constrains on planetary formation environments. Sincenitrogen chemistry can be far from thermochemical equilibrium in warmatmospheres, we extensively investigate under what conditions, and with whatassumptions, the observable NH3 abundances can diagnose an atmosphere's bulknitrogen abundance. In the first paper of this series, we investigateatmospheric T-P profiles across equilibrium temperature, surface gravity,intrinsic temperature, atmospheric metallicity, and C/O ratio using a 1Dradiative-convective equilibrium model. Models with the same intrinsictemperature and surface gravity coincide with a shared "universal" adiabat inthe deep atmosphere, across a wide equilibrium temperature range (250--1200 K),which is not seen in hotter or cooler models. We explain this behavior in termsof the classic "radiative zero solution" and then establish a semi-analyticalT-P profile of the deep atmospheres of warm exoplanets. This profile is thenused to predict vertically quenched NH3 abundances. At solar metallicity, ourresults show that the quenched NH3 abundance only coincides with the bulknitrogen abundance (within 10%) at low intrinsic temperature, corresponding toa planet with a sub-Jupiter mass (< 1 MJ) and old age (> 1 Gyr). If a planethas a high metallicity ($\ge$ 10$\times$ solar) atmosphere, the quenched NH3abundance significantly underestimates the bulk nitrogen abundance at almostall planetary masses and ages. We suggest modeling and observational strategiesto improve the assessment of bulk nitrogen from NH3.

astrophysical journal/the astrophysical journal

Nitrogen as a Tracer of Giant Planet Formation. I.: A Universal Deep  Adiabatic Profile and Semi-analytical Predictions of Disequilibrium Ammonia  Abundances in Warm Exoplanetary Atmospheres