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As the Kepler mission has done for hot exoplanets, the ESA Euclid and NASA Roman missions have the potential to create a breakthrough in our understanding of the demographics of cool exoplanets, including unbound, or free-floating, planets (FFPs). Roman will dedicate part of its core survey program to the detection of cool exoplanets via microlensing, while Euclid may undertake a microlensing program as an ancillary science goal. In this study, we demonstrate the complementarity of the two missions and propose two joint surveys to better constrain the mass and distance of microlensing events. We first demonstrate that an early brief Euclid survey (~7 h) of the Roman microlensing fields will allow the measurement of at least 30% of the events’ relative proper motions µ rel and 42% of the lens magnitudes. This survey would place strong constraints on the mass and distance on thousands of microlensing events observed by Roman just after the first year of observation. Then, we study the potential of simultaneous observations by Roman and Euclid to enable the measurement of the microlensing parallax for the shortest microlensing events and, ultimately, obtain a direct measurement of the masses, distances, and transverse motions of FFPs. Using detailed simulations of the joint detection yield we show that within one year Roman-Euclid observations will be at least an order of magnitude more sensitive than current ground-based measurements. The recent tentative detection of an excess of short-duration events by the OGLE survey is consistent with a scenario of up to ten Earth-mass FFPs per Galactic star. For such a scenario a joint Roman-Euclid campaign should detect around 130 FFP events within a year, including 110 with measured parallax that strongly constrain the FFP mass, and around 30 FFP events with direct mass and distance measurements. The ability of the joint survey to completely break the microlens mass-distance-velocity degeneracy for a significant subset of events provides a unique opportunity to verify unambiguously the FFP hypothesis or else place abundance limits for FFPs between Earth and Jupiter masses that are up to two orders of magnitude stronger than provided by ground-based surveys. Finally, we study the capabilities of the joint survey to enhance the detection and characterization of exomoons, and find that it could lead to the detection of the first exomoon. 

Context. The ESA Gaia mission provides a unique time-domain survey for more than 1.6 billion sources with G ≲ 21 mag. Aims. We showcase stellar variability in the Galactic colour-absolute magnitude diagram (CaMD). We focus on pulsating, eruptive, and cataclysmic variables, as well as on stars that exhibit variability that is due to rotation and eclipses. Methods. We describe the locations of variable star classes, variable object fractions, and typical variability amplitudes throughout the CaMD and show how variability-related changes in colour and brightness induce “motions”. To do this, we use 22 months of calibrated photometric, spectro-photometric, and astrometric Gaia data of stars with a significant parallax. To ensure that a large variety of variable star classes populate the CaMD, we crossmatched Gaia sources with known variable stars. We also used the statistics and variability detection modules of the Gaia variability pipeline. Corrections for interstellar extinction are not implemented in this article. Results. Gaia enables the first investigation of Galactic variable star populations in the CaMD on a similar, if not larger, scale as was previously done in the Magellanic Clouds. Although the observed colours are not corrected for reddening, distinct regions are visible in which variable stars occur. We determine variable star fractions to within the current detection thresholds of Gaia . Finally, we report the most complete description of variability-induced motion within the CaMD to date. Conclusions. Gaia enables novel insights into variability phenomena for an unprecedented number of stars, which will benefit the understanding of stellar astrophysics. The CaMD of Galactic variable stars provides crucial information on physical origins of variability in a way that has previously only been accessible for Galactic star clusters or external galaxies. Future Gaia data releases will enable significant improvements over this preview by providing longer time series, more accurate astrometry, and additional data types (time series BP and RP spectra, RVS spectra, and radial velocities), all for much larger samples of stars.