Gaia is a cornerstone mission in the science programme of the European Space Agency (ESA). The spacecraft construction was approved in 2006, following a study in which the original interferometric concept was changed to a direct-imaging approach. Both the spacecraft and the payload were built by European industry. The involvement of the scientific community focusses on data processing for which the international Gaia Data Processing and Analysis Consortium (DPAC) was selected in 2007. Gaia was launched on 19 December 2013 and arrived at its operating point, the second Lagrange point of the Sun-Earth-Moon system, a few weeks later. The commissioning of the spacecraft and payload was completed on 19 July 2014. The nominal five-year mission started with four weeks of special, ecliptic-pole scanning and subsequently transferred into full-sky scanning mode. We recall the scientific goals of Gaia and give a description of the as-built spacecraft that is currently (mid-2016) being operated to achieve these goals. We pay special attention to the payload module, the performance of which is closely related to the scientific performance of the mission. We provide a summary of the commissioning activities and findings, followed by a description of the routine operational mode. We summarise scientific performance estimates on the basis of in-orbit operations. Several intermediate Gaia data releases are planned and the data can be retrieved from the Gaia Archive, which is available through the Gaia home page.

Context. At about 1000 days after the launch of Gaia we present the first Gaia data release, Gaia DR1, consisting of astrometry and photometry for over 1 billion sources brighter than magnitude 20.7. Aims. A summary of Gaia DR1 is presented along with illustrations of the scientific quality of the data, followed by a discussion of the limitations due to the preliminary nature of this release. Methods. The raw data collected by Gaia during the first 14 months of the mission have been processed by the Gaia Data Processing and Analysis Consortium (DPAC) and turned into an astrometric and photometric catalogue. Results. Gaia DR1 consists of three components: a primary astrometric data set which contains the positions, parallaxes, and mean proper motions for about 2 million of the brightest stars in common with the Hipparcos and Tycho-2 catalogues -a realisation of the Tycho-Gaia Astrometric Solution (TGAS) -and a secondary astrometric data set containing the positions for an additional 1.1 billion sources. The second component is the photometric data set, consisting of mean G-band magnitudes for all sources. The G-band light curves and the characteristics of ∼3000 Cepheid and RR Lyrae stars, observed at high cadence around the south ecliptic pole, form the third component. For the primary astrometric data set the typical uncertainty is about 0.3 mas for the positions and parallaxes, and about 1 mas yr −1 for the proper motions. A systematic component of ∼0.3 mas should be added to the parallax uncertainties. For the subset of ∼94 000 Hipparcos stars in the primary data set, the proper motions are much more precise at about 0.06 mas yr −1 . For the secondary astrometric data set, the typical uncertainty of the positions is ∼10 mas. The median uncertainties on the mean G-band magnitudes range from the mmag level to ∼0.03 mag over the magnitude range 5 to 20.7. Conclusions. Gaia DR1 is an important milestone ahead of the next Gaia data release, which will feature five-parameter astrometry for all sources. Extensive validation shows that Gaia DR1 represents a major advance in the mapping of the heavens and the availability of basic stellar data that underpin observational astrophysics. Nevertheless, the very preliminary nature of this first Gaia data release does lead to a number of important limitations to the data quality which should be carefully considered before drawing conclusions from the data.

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This document describes the Multi-Order Coverage map method (MOC) to specify arbitrary sky regions. The goal is to be able to provide a very fast comparison mechanism between coverage maps. The mechanism is based on the HEALPix sky tessellation algorithm. It is essentially a simple way to map regions of the sky into hierarchically grouped predefined cells.

We show how a configurational lattice dynamics technique, in which the free energy of a number of configurations is determined directly by means of a fully dynamic structural minimization, can be used to calculate thermodynamic properties of solid solutions and phase diagrams. No assumptions are made as to the nature of the solution and both configurational and vibrational entropy contributions are determined directly. Only a small number of configurations are required. We illustrate the method using MnO/MgO, for which our results support the recent experiments of Wood, Hackler, and Dobson ͓Contrib. Mineral. Petrol. 115, 438 ͑1994͔͒ who, in contrast to previous workers, suggest the formation of a complete solid solution at temperatures only above 1100 K.Solid solutions, alloys, and grossly nonstoichiometric compounds present considerable challenges to the theoretician, as does the calculation of absolute free energy. Ceramic solid solutions in particular are often strongly nonideal and approaches such as the cluster variation method ͑CVM͒, 1 widely used for metallic alloys, often perform poorly. In addition, despite the importance of accurate thermodynamic data for oxide solid solutions in such areas as ceramic fabrication and design and mineralogy, accurate thermodynamic data are rare.We have recently developed a highly efficient method for the fully dynamic structure optimization of large unit cells 2 that uses lattice statics and quasiharmonic lattice dynamics ͑QLD͒. We calculate the full set of free-energy first derivatives analytically, and a full minimization of the free energy with respect to all structural variables for large unit cells is possible. The accurate calculation of the free energy via QLD is quick and computationally efficient and does not resort to lengthy thermodynamic integration. Here we show this can be used for the free energies of solid solutions ͑in-cluding ⌬H mix and ⌬S mix ͒ and phase diagrams. The method is readily extended to elevated T and high P; no a priori assumptions are made regarding the configurational entropy contribution and the vibrational contribution is also evaluated straightforwardly.We illustrate our approach using MnO/MgO, for which not only are there several sets of experimental enthalpy data 3,4 but also conflicting reports of the phase diagram. As shown in Ref. 5, the experiments of Raghavan, Iyengar, and Abraham 6 suggest a consolute temperature, T c , as low as 600 K, whereas the results of Wood, Hackler, and Dobson 7 are consistent with a much larger T c ͑Ϸ1100 K͒ and a markedly asymmetric phase diagram. The data of Ref. 6 are indeed surprising given the CaO/MgO phase diagram, in which there is a large two-phase region, and the mismatch in ionic radii between Mn 2ϩ and Mg 2ϩ , which is substantial although smaller than between Ca 2ϩ and Mg 2ϩ . A further aim of this paper is to attempt to resolve this issue.In principle the solid solution can assume any state, i.e., each atom can be at any position. However, the only states of practical importance away from t...