  Thermal dominated X-ray spectra of neutron stars in quiescent transient X-ray
binaries and neutron stars that undergo thermonuclear bursts are sensitive to
mass and radius. The mass-radius relation of neutron stars depends on the
equation of state that governs their interior. Constraining this relation
accurately is thus of fundamental importance to understand the nature of dense
matter. In this context we introduce a pipeline to calculate realistic model
spectra of rotating neutron stars with hydrogen and helium atmospheres. An
arbitrarily fast rotating neutron star with a given equation of state generates
the spacetime in which the atmosphere emits radiation. We use the
Lorene/nrotstar code to compute the spacetime numerically and the ATM24 code to
solve the radiative transfer equations self-consistently. Emerging specific
intensity spectra are then ray-traced through the neutron star's spacetime from
the atmosphere to a distant observer with the Gyoto code. Here, we present and
test our fully relativistic numerical pipeline. To discuss and illustrate the
importance of realistic atmosphere models we compare our model spectra to
simpler models like the commonly used isotropic color-corrected blackbody
emission. We highlight the importance of considering realistic model-atmosphere
spectra together with relativistic ray tracing to obtain accurate predictions.
We also insist on the crucial impact of the star's rotation on the observables.
Finally, we close a controversy that has been appearing in the literature in
the recent years regarding the validity of the ATM24 code.
