  Aims. We aim to investigate the origin of the discrepant results reported in
the literature about the presence of Na I in the atmosphere of HD209458 b,
based on low- and high-resolution transmission spectroscopy. Methods. We
generated synthetic planetary atmosphere models and we compared them with the
transmission light curves and spectra observed in previous studies. Our models
account for the stellar limb-darkening and Rossiter-McLaughlin (RM) effects,
and contemplate various possible scenarios for the planetary atmosphere.
Results. We reconciled the discrepant results by identifying a range of
planetary atmospheres that are consistent with previous low- and
high-resolution spectroscopic observations. Either both datasets are
interpreted as consistent with a total absence of Na I in the planetary
atmosphere (with Hubble Space Telescope data being affected by limb darkening),
or the terminator temperature of HD209458 b has to have an upper limit of about
1000K. In particular, we find that 1D transmission spectra with
lower-than-equilibrium temperatures can also explain the previously reported
detection of absorption signal at low resolution due to differential transit
depth in adjacent bands, while the cores of the Na I D lines may be masked by
the strong RM signal seen at high resolution. We also rule out high-altitude
clouds, which would otherwise mask the absorption signal at low resolution, as
the source of the discrepancies. Conclusions. This work highlights the
synergies between different observing techniques, specifically low- and
high-resolution spectroscopy, to fully characterise transiting exoplanet
systems.
