Gaia Data Release 2 Summary of the variability processing and analysis results

Context. The Gaia Data Release 2 (DR2) contains more than half a million sources that are identified as variable stars. Aims. We summarise the processing and results of the identification of variable source candidates of RR Lyrae stars, Cepheids, long-period variables (LPVs), rotation modulation (BY Dra-type) stars, delta Scuti and SX Phoenicis stars, and short-timescale variables. In this release we aim to provide useful but not necessarily complete samples of candidates. Methods. The processed Gaia data consist of the G, G(BP), and G(RP) photometry during the first 22 months of operations as well as positions and parallaxes. Various methods from classical statistics, data mining, and time-series analysis were applied and tailored to the specific properties of Gaia data, as were various visualisation tools to interpret the data. Results. The DR2 variability release contains 228 904 RR Lyrae stars, 11 438 Cepheids, 151 761 LPVs, 147 535 stars with rotation modulation, 8882 delta( )Scuti and SX Phoenicis stars, and 3018 short-timescale variables. These results are distributed over a classification and various Specific Object Studies tables in the Gaia archive, along with the three-band time series and associated statistics for the underlying 550 737 unique sources. We estimate that about half of them are newly identified variables. The variability type completeness varies strongly as a function of sky position as a result of the non-uniform sky coverage and intermediate calibration level of these data. The probabilistic and automated nature of this work implies certain completeness and contamination rates that are quantified so that users can anticipate their effects. This means that even well-known variable sources can be missed or misidentified in the published data. Conclusions. The DR2 variability release only represents a small subset of the processed data. Future releases will include more variable sources and data products; however, DR2 shows the (already) very high quality of the data and great promise for variability studies

Large-amplitude variables in Gaia Data Release 2. Multi-band variability characterization

The second data release (DR2) of Gaia provides mean photometry in three bands for $\sim$1.4 billion sources, but light curves and variability properties are available for only $\sim$0.5 million of them. Here, we provide a census of large-amplitude variables with amplitudes larger than $\sim$0.2 mag in the $G$ band for objects with mean brightnesses between 5.5 and 19 mag. To achieve this, we rely on variability amplitude proxies in $G$, $G_{BP}$ and $G_{RP}$ computed from the uncertainties on the magnitudes published in DR2. We then apply successive filters to identify two subsets containing respectively sources with reliable mean $G_{BP}$ and $G_{RP}$ (for studies using colours) and sources having compatible amplitude proxies in $G$, $G_{BP}$ and $G_{RP}$ (for multi-band variability studies). The full catalogue gathers $23\,315\,874$ large-amplitude variable candidates, and the two subsets with increased levels of purity contain respectively $1\,148\,861$ and $618\,966$ sources. A multi-band variability analysis of the catalogue shows that different types of variable stars can be globally categorized in four groups according to their colour and blue-to-red amplitude ratios as determined from the $G$, $G_{BP}$ and $G_{RP}$ amplitude proxies. The catalogue constitutes the first census of Gaia large-amplitude variable candidates, extracted from the public DR2 archive. The overview presented here illustrates the added-value of the mission for multi-band variability studies even at this stage when epoch photometry is not yet available for all sources. (Abridged abstract)Comment: Final version, A&A, in press. Main text: 20 pages, 26 figures. Four appendixe

Gaia Data Release 3. The first Gaia catalogue of eclipsing binary candidates

We present the first Gaia catalogue of eclipsing binary candidates released in Gaia DR3, describe its content, provide tips for its usage, estimate its quality, and show illustrative samples. The catalogue contains 2,184,477 sources with G magnitudes up to 20 mag. Candidate selection is based on the results of variable object classification performed within the Gaia Data Processing and Analysis Consortium, further filtered using eclipsing binary-tailored criteria based on the G light curves. To find the orbital period, a large ensemble of trial periods is first acquired using three distinct period search methods applied to the cleaned G light curve. The G light curve is then modelled with up-to two Gaussians and a cosine for each trial period. The best combination of orbital period and geometric model is finally selected using Bayesian model comparison based on the BIC. A global ranking metric is provided to rank the quality of the chosen model between sources. The catalogue is restricted to orbital periods larger than 0.2 days. About 530,000 of the candidates are classified as eclipsing binaries in the literature as well, out of ~600,000 available crossmatches, and 93% of them have published periods compatible with the Gaia periods. Catalogue completeness is estimated to be between 25% and 50%, depending on the sky region, relative to the OGLE4 catalogues of eclipsing binaries towards the Galactic Bulge and the Magellanic Clouds. The analysis of an illustrative sample of ~400,000 candidates with significant parallaxes shows properties in the observational HR diagram as expected for eclipsing binaries. The subsequent analysis of a sub-sample of detached bright candidates provides further hints for the exploitation of the catalogue. The orbital periods, light curve model parameters, and global rankings are all published in the catalogue with their related uncertainties where applicable.Comment: Submitted to A&A. Main text: 23 pages, 35 figures. Four appendices (17 pages) with 38 figure

Gaia Data Release 3: The first Gaia catalogue of variable AGN

One of the novelties of the Gaia-DR3 with respect to the previous data releases is the publication of the multiband light curves of about 1 million AGN. The goal of this work was the creation of a catalogue of variable AGN, whose selection was based on Gaia data only. We first present the implementation of the methods to estimate the variability parameters into a specific object study module for AGN. Then we describe the selection procedure that led to the definition of the high-purity variable AGN sample and analyse the properties of the selected sources. We started from a sample of millions of sources, which were identified as AGN candidates by 11 different classifiers based on variability processing. Because the focus was on the variability properties, we first defined some pre-requisites in terms of number of data points and mandatory variability parameters. Then a series of filters was applied using only Gaia data and the Gaia Celestial Reference Frame 3 (Gaia-CRF3) sample as a reference.The resulting Gaia AGN variable sample, named GLEAN, contains about 872000 objects, more than 21000 of which are new identifications. We checked the presence of contaminants by cross-matching the selected sources with a variety of galaxies and stellar catalogues. The completeness of GLEAN with respect to the variable AGN in the last Sloan Digital Sky Survey quasar catalogue is about 47%, while that based on the variable AGN of the Gaia-CRF3 sample is around 51%. From both a comparison with other AGN catalogues and an investigation of possible contaminants, we conclude that purity can be expected to be above 95%. Multiwavelength properties of these sources are investigated. In particular, we estimate that about 4% of them are radio-loud. We finally explore the possibility to evaluate the time lags between the flux variations of the multiple images of strongly lensed quasars, and show one case.Comment: 19 pages, 31 figures, 2 table. This paper is part of Gaia Data Release 3 (DR3). In press for A&

Gaia Focused Product Release: radial velocity time series of long-period variables

Context. The third Gaia Data Release (DR3) provided photometric time series of more than 2 million long-period variable (LPV) candidates. Anticipating the publication of full radial-velocity data planned with Data Release 4, this Focused Product Release (FPR) provides radial-velocity time series for a selection of LPV candidates with high-quality observations. Aims. We describe the production and content of the Gaia catalog of LPV radial-velocity time series, and the methods used to compute the variability parameters published as part of the Gaia FPR. Methods. Starting from the DR3 catalog of LPV candidates, we applied several filters to construct a sample of sources with high quality radial-velocity measurements. We modeled their radial-velocity and photometric time series to derive their periods and amplitudes, and further refined the sample by requiring compatibility between the radial-velocity period and at least one of the G, GBP, or GRP photometric periods. Results. The catalog includes radial-velocity time series and variability parameters for 9614 sources in the magnitude range 6 ≲ G/mag ≲ 14, including a flagged top-quality subsample of 6093 stars whose radial-velocity periods are fully compatible with the values derived from the G, GBP, and GRP photometric time series. The radial-velocity time series contain a mean of 24 measurements per source taken unevenly over a duration of about three years. We identify the great majority of the sources (88%) as genuine LPV candidates, with about half of them showing a pulsation period and the other half displaying a long secondary period. The remaining 12% of the catalog consists of candidate ellipsoidal binaries. Quality checks against radial velocities available in the literature show excellent agreement. We provide some illustrative examples and cautionary remarks. Conclusions. The publication of radial-velocity time series for almost ten thousand LPV candidates constitutes, by far, the largest such database available to date in the literature. The availability of simultaneous photometric measurements gives a unique added value to the Gaia catalog.This work presents results from the European Space Agency (ESA) space mission Gaia. Gaia data are being processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC is provided by national institutions, in particular the institutions participating in the Gaia MultiLat eral Agreement (MLA). The Gaia mission website is https: //www.cosmos.esa.int/gaia. The Gaia archive website is https://archives.esac.esa.int/gaia. The Gaia mission and data processing have financially been supported by, in alphabetical order by country: the Algerian Centre de Recherche en Astronomie, Astro physique et Géophysique of Bouzareah Observatory; the Austrian Fonds zur Förderung der wissenschaftlichen Forschung (FWF) Hertha Firnberg Programme through grants T359, P20046, and P23737; the BELgian federal Science Policy Office (BEL SPO) through various PROgramme de Développement d’Expériences scientifiques (PRODEX) grants of the European Space Agency (ESA), the Research Foundation Flanders (Fonds Wetenschappelijk Onderzoek) through grant VS.091.16N, the Fonds de la Recherche Scientifique (FNRS), and the Research Council of Katholieke Universiteit (KU) Leuven through grant C16/18/005 (Pushing AsteRoseismology to the next level with TESS, GaiA, and the Sloan DIgital Sky SurvEy PARADISE); the Brazil-France exchange programmes Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Coordenação de Aperfeicoamento de Pessoal de Nível Supe rior (CAPES) - Comité Français d’Evaluation de la Coopération Universitaire et Scientifique avec le Brésil (COFECUB); the Chilean Agencia Nacional de Investigación y Desar rollo (ANID) through Fondo Nacional de Desarrollo Cientí fico y Tecnológico (FONDECYT) Regular Project 1210992 (L. Chemin); the National Natural Science Foundation of China (NSFC) through grants 11573054, 11703065, and 12173069, the China Scholarship Council through grant 201806040200, and the Natural Science Foundation of Shanghai through grant 21ZR1474100; the Tenure Track Pilot Programme of the Croatian Sci ence Foundation and the École Polytechnique Fédérale de Lausanne and the project TTP-2018-07-1171 ‘Mining the Variable Sky’, with the funds of the Croatian-Swiss Research Programme; the Czech-Republic Ministry of Education, Youth, and Sports through grant LG 15010 and INTER-EXCELLENCE grant LTAUSA18093, and the Czech Space Office through ESA PECS contract 98058; the Danish Ministry of Science; the Estonian Ministry of Education and Research through grant IUT40-1; the European Commission’s Sixth Framework Programme through the European Leadership in Space Astrometry (ELSA) Marie Curie Research Training Network (MRTN CT-2006-033481), through Marie Curie project PIOF GA-2009-255267 (Space AsteroSeismology & RR Lyrae stars, SAS-RRL), and through a Marie Curie Transfer-of Knowledge (ToK) fellowship (MTKD-CT-2004-014188); the European Commission’s Seventh Framework Programme through grant FP7-606740 (FP7-SPACE-2013-1) for the Gaia European Network for Improved data User Services (GENIUS) and through grant 264895 for the Gaia Research for European Astronomy Training (GREAT-ITN) network; the European Cooperation in Science and Technology (COST) through COST Action CA18104 ‘Revealing the Milky Way with Gaia (MW-Gaia)’; the European Research Council (ERC) through grants 320360, 647208, and 834148 and through the European Union’s Horizon 2020 research and innovation and excel lent science programmes through Marie Skłodowska-Curie grants 687378 (Small Bodies: Near and Far), 682115 (Using the Magellanic Clouds to Understand the Interaction of Galaxies), 695099 (A sub-percent distance scale from bina ries and Cepheids CepBin), 716155 (Structured ACCRE tion Disks SACCRED), 745617 (Our Galaxy at full HD Gal-HD), 895174 (The build-up and fate of self-gravitating systems in the Universe), 951549 (Sub-percent calibration of the extragalactic distance scale in the era of big surveys UniverScale), 101004214 (Innovative Scientific Data Explo ration and Exploitation Applications for Space Sciences EXPLORE), 101004719 (OPTICON-RadioNET Pilot), 101055318 (The 3D motion of the Interstellar Medium with ESO and ESA telescopes ISM-FLOW), and 101063193 (Evolutionary Mechanisms in the Milky waY; the Gaia Data Release 3 revolution EMMY); the European Science Foundation (ESF), in the framework of the Gaia Research for European Astronomy Training Research Network Programme (GREAT-ESF); the European Space Agency (ESA) in the framework of the Gaia project, through the Plan for European Cooper ating States (PECS) programme through contracts C98090 and 4000106398/12/NL/KML for Hungary, through contract 4000115263/15/NL/IB for Germany, through PROgramme de Développement d’Expériences scientifiques (PRODEX) grants 4000132054 for Hungary and through contract 4000132226/20/ES/CM; the Academy of Finland through grants 299543, 307157, 325805, 328654, 336546, and 345115 and the Magnus Ehrn rooth Foundation; the French Centre National d’Études Spatiales (CNES), the Agence Nationale de la Recherche (ANR) through grant ANR-10-IDEX-0001-02 for the ‘Investissements d’avenir’ programme, through grant ANR-15-CE31-0007 for project ‘Modelling the Milky Way in the Gaia era’ (MOD4Gaia), through grant ANR-14-CE33-0014-01 for project ‘The Milky Way disc formation in the Gaia era’ (ARCHEOGAL), through grant ANR-15-CE31-0012-01 for project ‘Unlock ing the potential of Cepheids as primary distance cali brators’ (UnlockCepheids), through grant ANR-19-CE31- 0017 for project ‘Secular evolution of galaxies’ (SEGAL), and through grant ANR-18-CE31-0006 for project ‘Galac tic Dark Matter’ (GaDaMa), the Centre National de la Recherche Scientifique (CNRS) and its SNO Gaia of the Institut des Sciences de l’Univers (INSU), its Programmes Nationaux: Cosmologie et Galaxies (PNCG), Gravitation Références Astronomie Métrologie (PNGRAM), Planétolo gie (PNP), Physique et Chimie du Milieu Interstellaire (PCMI), and Physique Stellaire (PNPS), supported by INSU along with the Institut National de Physique (INP) and the Institut National de Physique nucléaire et de Physique des Particules (IN2P3), and co-funded by CNES; the ‘Action Fédératrice Gaia’ of the Observatoire de Paris, and the Région de Franche-Comté; the German Aerospace Agency (Deutsches Zentrum für Luft- und Raumfahrt e.V., DLR) through grants 50QG0501, 50QG0601, 50QG0602, 50QG0701, 50QG0901, 50QG1001, 50QG1101, 50QG1401, 50QG1402, 50QG1403, 50QG1404, 50QG1904, 50QG2101, 50QG2102, and 50QG2202, and the Centre for Information Services and High Performance Computing (ZIH) at the Technische Universität Dresden for generous allocations of computer time; the Hungarian Academy of Sciences through the János Bolyai Research Scholarship (G. Marton and Z. Nagy), the Lendület Programme grants LP2014-17 and LP2018-7 and the Hungarian National Research, Development, and Inno vation Office (NKFIH) through grant KKP-137523 (‘Seis moLab’); the Science Foundation Ireland (SFI) through a Royal Soci ety - SFI University Research Fellowship (M. Fraser); the Israel Ministry of Science and Technology through grant 3-18143 and the Israel Science Foundation (ISF) through grant 1404/22; the Agenzia Spaziale Italiana (ASI) through contracts I/037/08/0, I/058/10/0, 2014-025-R.0, 2014-025-R.1.2015, and 2018-24-HH.0 and its addendum 2018-24-HH.1-2022 to the Italian Istituto Nazionale di Astrofisica (INAF), contract 2014-049-R.0/1/2, 2022-14-HH.0 to INAF for the Space Science Data Centre (SSDC, formerly known as the ASI Science Data Center, ASDC), contracts I/008/10/0, 2013/030/I.0, 2013-030-I.0.1-2015, and 2016-17-I.0 to the Aerospace Logistics Technology Engineering Company (ALTEC S.p.A.), INAF, and the Italian Ministry of Edu cation, University, and Research (Ministero dell’Istruzione, dell’Università e della Ricerca) through the Premiale project ‘MIning The Cosmos Big Data and Innovative Italian Tech nology for Frontier Astrophysics and Cosmology’ (MITiC); the Netherlands Organisation for Scientific Research (NWO) through grant NWO-M-614.061.414, through a VICI grant (A. Helmi), and through a Spinoza prize (A. Helmi), and the Netherlands Research School for Astronomy (NOVA); the Polish National Science Centre through HARMO NIA grant 2018/30/M/ST9/00311 and DAINA grant 2017/27/L/ST9/03221 and the Ministry of Science and Higher Education (MNiSW) through grant DIR/WK/ 2018/12; the Portuguese Fundação para a Ciência e a Tecnologia (FCT) through national funds, grants 2022.06962.PTDC and 2022.03993.PTDC, and work contract DL 57/2016/CP1364/ CT0006, grants UIDB/04434/2020 and UIDP/04434/2020 for the Instituto de Astrofísica e Ciências do Espaço (IA), grants UIDB/00408/2020 and UIDP/00408/2020 for LASIGE, and grants UIDB/00099/2020 and UIDP/00099/ 2020 for the Centro de Astrofísica e Gravitação (CENTRA); the Slovenian Research Agency through grant P1-0188; the Spanish Ministry of Economy (MINECO/FEDER, UE), the Spanish Ministry of Science and Innovation (MCIN), the Spanish Ministry of Education, Culture, and Sports, and the Spanish Government through grants BES-2016-078499, BES-2017-083126, BES-C-2017-0085, ESP2016-80079-C2-1-R, FPU16/03827, RTI2018-095076- B-C22, PID2021-122842OB-C22, PDC2021-121059-C22, and TIN2015-65316-P (‘Computación de Altas Prestaciones VII’), the Juan de la Cierva Incorporación Programme (FJCI-2015-2671 and IJC2019-04862-I for F. Anders), the Severo Ochoa Centre of Excellence Programme (SEV2015-0493) and MCIN/AEI/10.13039/501100011033/ EU FEDER and Next Generation EU/PRTR (PRTR C17.I1); the European Union through European Regional Development Fund ‘A way of making Europe’ through grants PID2021-122842OB-C21, PID2021-125451NA-I00, CNS2022-13523 and RTI2018-095076-B-C21, the Institute of Cosmos Sciences University of Barcelona (ICCUB, Unidad de Excelencia ‘María de Maeztu’) through grant CEX2019-000918-M, the University of Barcelona’s official doctoral programme for the development of an R+D+i project through an Ajuts de Personal Investigador en For mació (APIF) grant, the Spanish Virtual Observatory project funded by MCIN/AEI/10.13039/501100011033/ through grant PID2020-112949GB-I00; the Centro de Investigación en Tecnologías de la Información y las Comunicaciones (CITIC), funded by the Xunta de Galicia through the collaboration agreement to reinforce CIGUS research centers, research consolidation grant ED431B 2021/36 and scholarships from Xunta de Galicia and the EU - ESF ED481A-2019/155 and ED481A 2021/296; the Red Española de Supercomputación (RES) computer resources at MareNostrum, the Barcelona Supercomputing Centre - Centro Nacional de Supercomputación (BSC-CNS) through activities AECT-2017-2-0002, AECT-2017-3-0006, AECT 2018-1-0017, AECT-2018-2-0013, AECT-2018-3-0011, AECT-2019-1-0010, AECT-2019-2-0014, AECT-2019-3- 0003, AECT-2020-1-0004, and DATA-2020-1-0010, the Departament d’Innovació, Universitats i Empresa de la Generalitat de Catalunya through grant 2014-SGR-1051 for project ‘Models de Programació i Entorns d’Execució Parallels’ (MPEXPAR), and Ramon y Cajal Fellowships RYC2018-025968-I, RYC2021-031683-I and RYC2021- 033762-I, funded by MICIN/AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR and the European Science Foundation (‘Investing in your future’); the Port d’Informació Científica (PIC), through a collaboration between the Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT) and the Institut de Física d’Altes Energies (IFAE), supported by the call for grants for Scientific and Technical Equipment 2021 of the State Program for Knowledge Generation and Scientific and Technological Strengthening of the R+D+i System, financed by MCIN/AEI/ 10.13039/501100011033 and the EU NextGeneration/PRTR (Hadoop Cluster for the comprehensive management of massive scientific data, reference EQC2021-007479-P); the Swedish National Space Agency (SNSA/Rymdstyrelsen); the Swiss State Secretariat for Education, Research, and Innovation through the Swiss Activités Nationales Com plémentaires and the Swiss National Science Founda tion through an Eccellenza Professorial Fellowship (award PCEFP2_194638 for R. Anderson); the United Kingdom Particle Physics and Astronomy Research Council (PPARC), the United Kingdom Sci ence and Technology Facilities Council (STFC), and the United Kingdom Space Agency (UKSA) through the following grants to the University of Bristol, Brunel University London, the Open University, the Uni versity of Cambridge, the University of Edinburgh, the University of Leicester, the Mullard Space Sci ences Laboratory of University College London, and the United Kingdom Rutherford Appleton Laboratory (RAL

Gaia Data Release 2: All-sky classification of high-amplitude pulsating stars

Out of the 1.69 billion sources in the Gaia Data Release 2 (DR2), more than half a million are published with photometric time series that exhibit light variations during 22 months of observation. An all-sky classification of common high-amplitude pulsators (Cepheids, long-period variables, Delta Scuti / SX Phoenicis, and RR Lyrae stars) is provided for stars with brightness variations greater than 0.1 mag in the G band. A semi-supervised classification approach was employed, firstly training multi-stage Random Forest classifiers with sources of known types in the literature, followed by a preliminary classification of the Gaia data and a second training phase that included a selection of the first classification results to improve the representation of some classes, before the application of the improved classifiers to the Gaia data. Dedicated validation classifiers were used to reduce the level of contamination in the published results. A relevant fraction of objects were not yet sufficiently sampled for reliable Fourier series decomposition, so classifiers were based on features derived from statistics of photometric time series in the G, BP, and RP bands, as well as from some astrometric parameters. The published classification results include 195,780 RR Lyrae stars, 150,757 long-period variables, 8550 Cepheids, and 8882 Delta Scuti / SX Phoenicis stars. All of these results represent candidates, whose completeness and contamination are described as a function of variability type and classification reliability. Results are expressed in terms of class labels and classification scores, which are available in the vari_classifier_result table of the Gaia archive

Gaia Data Release 2. All-sky classification of high-amplitude pulsating stars

More than half a million of the 1.69 billion sources in Gaia Data Release 2 (DR2) are published with photometric time series that exhibit light variations during the 22 months of observation. An all-sky classification of common high-amplitude pulsators (Cepheids, long-period variables, Delta Scuti / SX Phoenicis, and RR Lyrae stars) is provided for stars with brightness variations greater than 0.1 mag in G band. A semi-supervised classification approach was employed, firstly training multi-stage random forest classifiers with sources of known types in the literature, followed by a preliminary classification of the Gaia data and a second training phase that included a selection of the first classification results to improve the representation of some classes, before the improved classifiers were applied to the Gaia data. Dedicated validation classifiers were used to reduce the level of contamination in the published results. A relevant fraction of objects were not yet sufficiently sampled for reliable Fourier series decomposition, consequently classifiers were based on features derived from statistics of photometric time series in the G, BP, and RP bands, as well as from some astrometric parameters. The published classification results include 195,780 RR Lyrae stars, 150,757 long-period variables, 8550 Cepheids, and 8882 Delta Scuti / SX Phoenicis stars. All of these results represent candidates whose completeness and contamination are described as a function of variability type and classification reliability. Results are expressed in terms of class labels and classification scores, which are available in the vari_classifier_result table of the Gaia archive.Comment: 21 pages, 33 figures, with minor revisions, in press (Astronomy & Astrophysics

All-Sky RR Lyrae Stars in the Gaia Data

The second Gaia data release is expected to contain data products from about 22 months of observation. Based on these data, we aim to provide an advance publication of a full-sky Gaia map of RR Lyrae stars. Although comprehensive, these data still contain a significant fraction of sources which are insufficiently sampled for Fourier series decomposition of the periodic light variations. The challenges in the identification of RR Lyrae candidates with (much) fewer than 20 field-of-view transits are described. General considerations of the results, their limitations, and interpretation are presented together with prospects for improvement in subsequent Gaia data releases.Comment: 5 pages, 1 figure, Proceedings of the RR Lyrae 2017 Conference (Revival of the Classical Pulsators: from Galactic Structure to Stellar Interior Diagnostics), to be published in the Proceedings of the Polish Astronomical Societ