  The elemental ratios of carbon, nitrogen, and oxygen in the atmospheres of
hot Jupiters may hold clues to their formation locations in the protostellar
disc. In this work, we adopt gas phase chemical abundances of C, N and O from
several locations in a disc chemical kinetics model as sources for the envelope
of the hot Jupiter HD 209458b and evolve the planet's atmospheric composition
using a 1D chemical kinetics model, treating both vertical mixing and
photochemistry. We consider two atmospheric pressure-temperature profiles, one
with and one without a thermal inversion. From each of the resulting 32
atmospheric composition profiles, we find that the molecules CH4, NH3, HCN, and
C2H2 are more prominent in the atmospheres computed using a realistic
non-inverted P-T profile in comparison to a prior equilibrium chemistry based
work which used an analytical P-T profile. We also compute the synthetic
transmission and emission spectra for these atmospheres and find that many
spectral features vary with the location in the disc where the planet's
envelope was accreted. By comparing with the species detected using the latest
high-resolution ground-based observations, our model suggests HD 209458b could
have accreted most of its gas between the CO2 and CH4 icelines with a super
solar C/O ratio from its protostellar disc, which in turn directly inherited
its chemical abundances from the protostellar cloud. Finally, we simulate
observing the planet with the James Webb Space Telescope (JWST) and show that
differences in spectral signatures of key species can be recognized. Our study
demonstrates the enormous importance of JWST in providing new insights into hot
Jupiter's formation environments.

Earth and Planetary Astrophysics