Hopf Categories

We introduce Hopf categories enriched over braided monoidal categories. The notion is linked to several recently developed notions in Hopf algebra theory, such as Hopf group (co)algebras, weak Hopf algebras and duoidal categories. We generalize the fundamental theorem for Hopf modules and some of its applications to Hopf categories.Comment: 47 pages; final version to appear in Algebras and Representation Theor

Gaia Early Data Release 3: Summary of the contents and survey properties

ABSTRACT: Context. We present the early installment of the third Gaia data release, Gaia EDR3, consisting of astrometry and photometry for 1.8 billion sources brighter than magnitude 21, complemented with the list of radial velocities from Gaia DR2. Aims. A summary of the contents of Gaia EDR3 is presented, accompanied by a discussion on the differences with respect to Gaia DR2 and an overview of the main limitations which are present in the survey. Recommendations are made on the responsible use of Gaia EDR3 results. Methods. The raw data collected with the Gaia instruments during the first 34 months of the mission have been processed by the Gaia Data Processing and Analysis Consortium and turned into this early third data release, which represents a major advance with respect to Gaia DR2 in terms of astrometric and photometric precision, accuracy, and homogeneity. Results. Gaia EDR3 contains celestial positions and the apparent brightness in G for approximately 1.8 billion sources. For 1.5 billion of those sources, parallaxes, proper motions, and the (GBP ? GRP) colour are also available. The passbands for G, GBP, and GRP are provided as part of the release. For ease of use, the 7 million radial velocities from Gaia DR2 are included in this release, after the removal of a small number of spurious values. New radial velocities will appear as part of Gaia DR3. Finally, Gaia EDR3 represents an updated materialisation of the celestial reference frame (CRF) in the optical, the Gaia-CRF3, which is based solely on extragalactic sources. The creation of the source list for Gaia EDR3 includes enhancements that make it more robust with respect to high proper motion stars, and the disturbing effects of spurious and partially resolved sources. The source list is largely the same as that for Gaia DR2, but it does feature new sources and there are some notable changes. The source list will not change for Gaia DR3. Conclusions. Gaia EDR3 represents a significant advance over Gaia DR2, with parallax precisions increased by 30 per cent, proper motion precisions increased by a factor of 2, and the systematic errors in the astrometry suppressed by 30-40% for the parallaxes and by a factor ~2.5 for the proper motions. The photometry also features increased precision, but above all much better homogeneity across colour, magnitude, and celestial position. A single passband for G, GBP, and GRP is valid over the entire magnitude and colour range, with no systematics above the 1% levelThe Gaia mission and data processing have financially been supported by ; the Spanish Ministry of Economy (MINECO/FEDER, UE) through grants ESP2016-80079-C2-1-R, ESP2016-80079-C2-2-R, RTI2018-095076-B-C21, RTI2018-095076-B-C22, BES-2016-078499, and BES-2017-083126 and the Juan de la Cierva formación 2015 grant FJCI-2015-2671, the Spanish Ministry of Education, Culture, and Sports through grant FPU16/03827, the Spanish Ministry of Science and Innovation (MICINN) through grant AYA2017-89841P for project “Estudio de las propiedades de los fósiles estelares en el entorno del Grupo Local” and through grant TIN2015-65316-P for project “Computación de Altas Prestaciones VII

Pulsations in main sequence OBAF-type stars

CONTEXT: The third Gaia data release provides photometric time series covering 34 months for about 10 million stars. For many of those stars, a characterisation in Fourier space and their variability classification are also provided. This paper focuses on intermediate- to high-mass (IHM) main sequence pulsators (M ≥  1.3 M⊙) of spectral types O, B, A, or F, known as β Cep, slowly pulsating B (SPB), δ Sct, and γ Dor stars. These stars are often multi-periodic and display low amplitudes, making them challenging targets to analyse with sparse time series. AIMS: We investigate the extent to which the sparse Gaia DR3 data can be used to detect OBAF-type pulsators and discriminate them from other types of variables. We aim to probe the empirical instability strips and compare them with theoretical predictions. The most populated variability class is that of the δ Sct variables. For these stars, we aim to confirm their empirical period-luminosity (PL) relation, and verify the relation between their oscillation amplitude and rotation. METHODS: All datasets used in this analysis are part of the Gaia DR3 data release. The photometric time series were used to perform a Fourier analysis, while the global astrophysical parameters necessary for the empirical instability strips were taken from the Gaia DR3 gspphot tables, and the v sin i data were taken from the Gaia DR3 esphs tables. The δ Sct PL relation was derived using the same photometric parallax method as the one recently used to establish the PL relation for classical Cepheids using Gaia data. RESULTS: We show that for nearby OBAF-type pulsators, the Gaia DR3 data are precise and accurate enough to pinpoint them in the Hertzsprung-Russell (HR) diagram. We find empirical instability strips covering broader regions than theoretically predicted. In particular, our study reveals the presence of fast rotating gravity-mode pulsators outside the strips, as well as the co-existence of rotationally modulated variables inside the strips as reported before in the literature. We derive an extensive period–luminosity relation for δ Sct stars and provide evidence that the relation features different regimes depending on the oscillation period. We demonstrate how stellar rotation attenuates the amplitude of the dominant oscillation mode of δ Sct stars. CONCLUSIONS: The Gaia DR3 time-series photometry already allows for the detection of the dominant (non-)radial oscillation mode in about 100 000 intermediate- and high-mass dwarfs across the entire sky. This detection capability will increase as the time series becomes longer, allowing the additional delivery of frequencies and amplitudes of secondary pulsation modes

Gaia Data Release 3: Mapping the asymmetric disc of the Milky Way

With the most recent Gaia data release the number of sources with complete 6D phase space information (position and velocity) has increased to well over 33 million stars, while stellar astrophysical parameters are provided for more than 470 million sources, in addition to the identification of over 11 million variable stars. Using the astrophysical parameters and variability classifications provided in Gaia DR3, we select various stellar populations to explore and identify non-axisymmetric features in the disc of the Milky Way in both configuration and velocity space. Using more about 580 thousand sources identified as hot OB stars, together with 988 known open clusters younger than 100 million years, we map the spiral structure associated with star formation 4-5 kpc from the Sun. We select over 2800 Classical Cepheids younger than 200 million years, which show spiral features extending as far as 10 kpc from the Sun in the outer disc. We also identify more than 8.7 million sources on the red giant branch (RGB), of which 5.7 million have line-of-sight velocities, allowing the velocity field of the Milky Way to be mapped as far as 8 kpc from the Sun, including the inner disc. The spiral structure revealed by the young populations is consistent with recent results using Gaia EDR3 astrometry and source lists based on near infrared photometry, showing the Local (Orion) arm to be at least 8 kpc long, and an outer arm consistent with what is seen in HI surveys, which seems to be a continuation of the Perseus arm into the third quadrant. Meanwhile, the subset of RGB stars with velocities clearly reveals the large scale kinematic signature of the bar in the inner disc, as well as evidence of streaming motions in the outer disc that might be associated with spiral arms or bar resonances. (abridged

Gaia Data Release 3 The extragalactic content⋆

The Gaia Galactic survey mission is designed and optimized to obtain astrometry, photometry, and spectroscopy of nearly two billion stars in our Galaxy. Yet as an all-sky multi-epoch survey, Gaia also observes several million extragalactic objects down to a magnitude of G ∼ 21 mag. Due to the nature of the Gaia onboard-selection algorithms, these are mostly point-source-like objects. Using data provided by the satellite, we have identified quasar and galaxy candidates via supervised machine learning methods, and estimate their redshifts using the low resolution BP/RP spectra. We further characterise the surface brightness profiles of host galaxies of quasars and of galaxies from pre-defined input lists. Here we give an overview of the processing of extragalactic objects, describe the data products in Gaia DR3, and analyse their properties. Two integrated tables contain the main results for a high completeness, but low purity (50−70%), set of 6.6 million candidate quasars and 4.8 million candidate galaxies. We provide queries that select purer sub-samples of these containing 1.9 million probable quasars and 2.9 million probable galaxies (both ∼95% purity). We also use high quality BP/RP spectra of 43 thousand high probability quasars over the redshift range 0.05−4.36 to construct a composite quasar spectrum spanning restframe wavelengths from 72−1000 nm

Gaia Data Release 3: Chemical cartography of the Milky Way

Context. The motion of stars has been used to reveal details of the complex history of the Milky Way, in constant interaction with its environment. Nevertheless, to reconstruct the Galactic history puzzle in its entirety, the chemo-physical characterisation of stars is essential. Previous Gaia data releases were supported by a smaller, heterogeneous, and spatially biased mixture of chemical data from ground-based observations. Aims. Gaia Data Release 3 opens a new era of all-sky spectral analysis of stellar populations thanks to the nearly 5.6 million stars observed by the Radial Velocity Spectrometer (RVS) and parametrised by the GSP-Spec module. In this work, we aim to demonstrate the scientific quality of Gaia’s Milky Way chemical cartography through a chemo-dynamical analysis of disc and halo populations. Methods. Stellar atmospheric parameters and chemical abundances provided by Gaia DR3 spectroscopy are combined with DR3 radial velocities and EDR3 astrometry to analyse the relationships between chemistry and Milky Way structure, stellar kinematics, and orbital parameters. Results. The all-sky Gaia chemical cartography allows a powerful and precise chemo-dynamical view of the Milky Way with unprecedented spatial coverage and statistical robustness. First, it reveals the strong vertical symmetry of the Galaxy and the flared structure of the disc. Second, the observed kinematic disturbances of the disc – seen as phase space correlations – and kinematic or orbital substructures are associated with chemical patterns that favour stars with enhanced metallicities and lower [α/Fe] abundance ratios compared to the median values in the radial distributions. This is detected both for young objects that trace the spiral arms and older populations. Several α, iron-peak elements and at least one heavy element trace the thin and thick disc properties in the solar cylinder. Third, young disc stars show a recent chemical impoverishment in several elements. Fourth, the largest chemo-dynamical sample of open clusters analysed so far shows a steepening of the radial metallicity gradient with age, which is also observed in the young field population. Finally, the Gaia chemical data have the required coverage and precision to unveil galaxy accretion debris and heated disc stars on halo orbits through their [α/Fe] ratio, and to allow the study of the chemo-dynamical properties of globular clusters. Conclusions. Gaia DR3 chemo-dynamical diagnostics open new horizons before the era of ground-based wide-field spectroscopic surveys. They unveil a complex Milky Way that is the outcome of an eventful evolution, shaping it to the present day