Large Interferometer For Exoplanets (LIFE): XIII. The Value of Combining Thermal Emission and Reflected Light for the Characterization of Earth Twins

Following the recommendations to NASA and ESA, the search for life on exoplanets will be a priority in the next decades. Two direct imaging space mission concepts are being developed: the Habitable Worlds Observatory (HWO) and the Large Interferometer for Exoplanets (LIFE). HWO focuses on reflected light spectra in the ultraviolet/visible/near-infrared (UV/VIS/NIR), while LIFE captures the mid-infrared (MIR) emission of temperate exoplanets. We assess the potential of HWO and LIFE in characterizing a cloud-free Earth twin orbiting a Sun-like star at 10 pc, both separately and synergistically, aiming to quantify the increase in information from joint atmospheric retrievals on a habitable planet. We perform Bayesian retrievals on simulated data from an HWO-like and a LIFE-like mission separately, then jointly, considering the baseline spectral resolutions currently assumed for these concepts and using two increasingly complex noise simulations. HWO would constrain H$_2$O, O$_2$, and O$_3$, in the atmosphere, with ~ 100 K uncertainty on the temperature profile. LIFE would constrain CO$_2$, H$_2$O, O$_3$ and provide constraints on the thermal atmospheric structure and surface temperature (~ 10 K uncertainty). Both missions would provide an upper limit on CH$_4$. Joint retrievals on HWO and LIFE data would accurately define the atmospheric thermal profile and planetary parameters, decisively constrain CO$_2$, H$_2$O, O$_2$, and O$_3$, and weakly constrain CO and CH$_4$. The detection significance is greater or equal to single-instrument retrievals. Both missions provide specific information to characterize a terrestrial habitable exoplanet, but the scientific yield is maximized with synergistic UV/VIS/NIR+MIR observations. Using HWO and LIFE together will provide stronger constraints on biosignatures and life indicators, potentially transforming the search for life in the universe.