  High-resolution Doppler spectroscopy has been used to detect several chemical
species in exoplanetary atmospheres. Such detections have traditionally relied
on cross correlation of observed spectra against spectral model templates, an
approach that is successful for detecting chemical species but not optimised
for constraining abundances. Recent work has explored ways to perform
atmospheric retrievals on high-resolution spectra (HRS) and combine them with
retrievals routinely performed for low-resolution spectra (LRS) by developing a
mapping from the cross correlation function to a likelihood metric. We build
upon previous studies and report HyDRA-H, a hybrid retrieval code for
simultaneous analysis of low- and high- resolution thermal emission spectra of
exoplanets in a fully Bayesian approach. We demonstrate HyDRA-H on the hot
Jupiter HD 209458b as a case study. We validate our HRS retrieval capability by
confirming previous results and report a simultaneous hybrid retrieval using
both HRS and LRS data. The LRS data span the HST WFC3 (1.1-1.7 $\mu$m) and
Spitzer photometry (IRAC 3.6-8 $\mu$m) bands, while the HRS data were obtained
with CRIRES on VLT at 2.3 $\mu$m. The constraints on the composition and
temperature profiles for the hybrid retrieval are more stringent than
retrievals with either LRS or HRS datasets individually. We retrieve abundances
of $\log(\mathrm{H_2O)} = -4.11^{+0.91}_{-0.30}$ and $\log(\mathrm{CO}) =
{-2.16}^{+0.99}_{-0.47}$, and $\mathrm{C/O} = 0.99^{+0.01}_{-0.02}$, consistent
with previous works. We constrain the photospheric temperature to be
$1498^{+216}_{-57}$ K, consistent with the equilibrium temperature. Our results
demonstrate the significant advantages of hybrid retrievals by combining
strengths of both HRS and LRS observations which probe complementary aspects of
exoplanetary atmospheres.
