<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">kaz29</journal-id><journal-title-group><journal-title xml:lang="ru">Вестник Казахстанско-Британского технического университета</journal-title><trans-title-group xml:lang="en"><trans-title>Herald of the Kazakh-British Technical University</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1998-6688</issn><issn pub-type="epub">2959-8109</issn><publisher><publisher-name>Казахстанско-Британский Технический Университет</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.55452/1998-6688-2024-21-3-258-272</article-id><article-id custom-type="elpub" pub-id-type="custom">kaz29-1387</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИЗИЧЕСКИЕ НАУКИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>PHYSICAL SCIENCES</subject></subj-group></article-categories><title-group><article-title>ВЛИЯНИЕ ОШИБОК НАБЛЮДЕНИЙ ПО GAIA DR3 НА РЕКОНСТРУКЦИЮ ОРБИТ ШАРОВЫХ СКОПЛЕНИЙ НА КОСМОЛОГИЧЕСКОЙ ВРЕМЕННОЙ ШКАЛЕ</article-title><trans-title-group xml:lang="en"><trans-title>THE INFLUENCE OF OBSERVATIONAL ERRORS IN GAIA DR3 ON THE RECONSTRUCTION OF GLOBULAR CLUSTER ORBITS ON A COSMOLOGICAL TIMESCALE</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5937-4985</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Куватова</surname><given-names>Д. Б.</given-names></name><name name-style="western" xml:lang="en"><surname>Kuvatova</surname><given-names>D.</given-names></name></name-alternatives><bio xml:lang="ru"><p>MSc </p><p>050020, г. Алматы</p></bio><bio xml:lang="en"><p>MSc </p><p>050020, Almaty</p></bio><email xlink:type="simple">kuvatova@fai.kz</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-6961-8170</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ищенко</surname><given-names>М. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Ishchenko</surname><given-names>M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>канд. физ.-мат. наук, PhD </p><p>01001, г. Киев;00001, г. Варшава;050020, г. Алматы</p></bio><bio xml:lang="en"><p>c.ph.-m.sc, PhD </p><p>01001, Kyiv;00001, Warsaw;050020, Almaty</p></bio><email xlink:type="simple">marina@mao.kiev.ua</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5004-199X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Берцик</surname><given-names>П. П.</given-names></name><name name-style="western" xml:lang="en"><surname>Berczik</surname><given-names>P.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Dr.Sci </p><p>00001, г. Варшава;050020, г. Алматы;1007, г. Будапешт;01001, г. Киев;</p></bio><bio xml:lang="en"><p>Dr.Sci </p><p>00001, Warsaw;050020, Almaty;1007, Budapest;01001, Kyiv</p></bio><email xlink:type="simple">berczik@mao.kiev.ua</email><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-1672-894X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Омаров</surname><given-names>Ч. Т.</given-names></name><name name-style="western" xml:lang="en"><surname>Omarov</surname><given-names>C.</given-names></name></name-alternatives><bio xml:lang="ru"><p>профессор, PhD </p><p>050020, г. Алматы</p></bio><bio xml:lang="en"><p>Professor, PhD </p><p>050020, Almaty</p></bio><email xlink:type="simple">chingis.omarov@fai.kz</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-0570-7270</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Каламбай</surname><given-names>М. Т.</given-names></name><name name-style="western" xml:lang="en"><surname>Kalambay</surname><given-names>M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>PhD </p><p>050020, г. Алматы;030000, г. Актобе</p></bio><bio xml:lang="en"><p>PhD </p><p>050020, Almaty;030000, Aktobe</p></bio><email xlink:type="simple">kalambay@aphi.kz</email><xref ref-type="aff" rid="aff-4"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru">Астрофизический институт им. В.Г. Фесенкова<country>Казахстан</country></aff><aff xml:lang="en">Fesenkov Astrophysical Institute<country>Kazakhstan</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru">Главная астрономическая обсерватория;&#13;
Астрономический центр имени Николая Коперника Польской академии наук;&#13;
Астрофизический институт им. В.Г. Фесенкова<country>Казахстан</country></aff><aff xml:lang="en">Main Astronomical Observatory;&#13;
Nicolaus Copernicus Astronomical Centre Polish Academy of Sciences;&#13;
Fesenkov Astrophysical Institute<country>Kazakhstan</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru">Астрономический центр имени Николая Коперника Польской академии наук;&#13;
Астрофизический институт им. В.Г. Фесенкова;&#13;
Обсерватория Конколи, Исследовательский центр астрономии и наук о Земле;&#13;
Главная астрономическая обсерватория;<country>Казахстан</country></aff><aff xml:lang="en">Nicolaus Copernicus Astronomical Centre Polish Academy of Sciences;&#13;
Fesenkov Astrophysical Institute;&#13;
Konkoly Observatory, Research Centre for Astronomy and Earth Sciences;&#13;
Main Astronomical Observatory<country>Kazakhstan</country></aff></aff-alternatives><aff-alternatives id="aff-4"><aff xml:lang="ru">Астрофизический институт им. В.Г. Фесенкова;&#13;
Хериот-Уатт Международный факультет, Актюбинский региональный университет им. К. Жубанова<country>Казахстан</country></aff><aff xml:lang="en">Fesenkov Astrophysical Institute;&#13;
Heriot-Watt International Faculty, Zhubanov University<country>Kazakhstan</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>02</day><month>10</month><year>2024</year></pub-date><volume>21</volume><issue>3</issue><fpage>258</fpage><lpage>272</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Куватова Д.Б., Ищенко М.В., Берцик П.П., Омаров Ч.Т., Каламбай М.Т., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Куватова Д.Б., Ищенко М.В., Берцик П.П., Омаров Ч.Т., Каламбай М.Т.</copyright-holder><copyright-holder xml:lang="en">Kuvatova D., Ishchenko M., Berczik P., Omarov C., Kalambay M.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://vestnik.kbtu.edu.kz/jour/article/view/1387">https://vestnik.kbtu.edu.kz/jour/article/view/1387</self-uri><abstract><p>В последнее время набирает популярность развивающаяся область астрономии, занимающаяся историей формирования галактик, – галактическая археология. Шаровые скопления принимали участие во многих ключевых процессах, происходивших в Млечном Пути, поэтому их изучение, в частности реконструкция орбит, имеет существенное значение в этой области. Каталог Gaia DR3 предоставляет параметры 165 шаровых скоплений, такие как собственные движения, радиальная скорость и гелиоцентрическое расстояние, с некоторой точностью, поэтому важно изучить влияние ошибок измерений данных параметров на начальные данные при преобразовании в галактоцентрическую систему координат и, как следствие, на форму орбит. Нами были проинтегрированы орбиты шаровых скоплений на 10 миллиардов лет назад. Для физической обоснованности при интегрировании использовался внешний динамический потенциал под индивидуальным номером 411321 из базы космологического моделирования IllustrisTNG-100, наилучшим образом воспроизводящий потенциал Млечного Пути. Интегрирование производилось с помощью параллельного N-body кода φ-GPU, основанного на схеме Эрмита четвертого порядка с иерархическими индивидуальными блок-временными шагами. Было создано 1000 рандомизаций начальных данных с учетом нормального распределения ошибок и рассмотрено влияние ошибок на разброс начальных скоростей и на форму орбит. Наибольшие относительные ошибки имеют собственные движения и радиальная скорость, наименьшие – гелиоцентрическое расстояние. Обнаружено, что 85% шаровых скоплений от общего числа имеют относительные ошибки по всем параметрам не более 10%, а 5.4% – не более 1%. Исследовав влияние ошибок измерений для скоплений с различными величинами относительных ошибок, мы пришли к выводу, что для большинства шаровых скоплений влияние ошибок измерений на форму орбит не существенно и, следовательно, для них возможна реконструкция орбит с высокой точностью. Так как реконструкция орбит шаровых скоплений подразумевает космологические временные масштабы, то учет ошибок измерений является важным аспектом в подготовительной процедуре перед основным интегрированием. </p></abstract><trans-abstract xml:lang="en"><p>In recent years, the emerging field of astronomy focused on the history of galaxy formation, known as Galactic Archaeology, has been gaining popularity. Globular clusters have been involved in many key processes occurring in the Milky Way, making their study, particularly the reconstruction of their orbits, significantly important. The Gaia DR3 catalog provides parameters for 165 globular clusters, such as proper motions, radial velocity, and heliocentric distance, with certain accuracy. Therefore, it is important to examine the influence of measurement errors in these parameters on the initial data when converting to the Galactocentric coordinate system and, consequently, on the shape of the orbits. We integrated the orbits of globular clusters 10 billion years lookback. For physical justification during the integration, we used the external dynamic potential with the individual number 411321 from the cosmological simulation database IllustrisTNG-100, which best reproduces the potential of the Milky Way. The integration was performed using the parallel N-body code φ-GPU, based on a fourth-order Hermite scheme with hierarchical individual block timesteps. A total of 1,000 randomizations of the initial data were created considering a normal distribution of errors, and the influence of errors on the scatter of initial velocities and on the shape of the orbits was examined. The parameters with the largest relative errors are proper motions and radial velocity, while the smallest errors are in heliocentric distance. It was found that 85% of the globular clusters have relative errors in all parameters of no more than 10%, and 5.4% have errors of no more than 1%. Investigating the influence of measurement errors for clusters with different magnitudes of relative errors, we concluded that for most globular clusters, the influence of measurement errors on the shape of the orbits is not significant. Consequently, it is possible to reconstruct the orbits with high accuracy for these clusters. Since the reconstruction of globular cluster orbits involves cosmological timescales, accounting for measurement errors is an important aspect of the preparatory procedure before the main integration.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>шаровые скопления</kwd><kwd>Млечный Путь</kwd><kwd>внешний динамический потенциал IllustrisTNG-100</kwd><kwd>численное моделирование</kwd><kwd>Gaia DR3 каталог</kwd></kwd-group><kwd-group xml:lang="en"><kwd>globular clusters</kwd><kwd>Milky Way</kwd><kwd>external dynamic potential IllustrisTNG-100</kwd><kwd>numerical simulation</kwd><kwd>Gaia DR3 catalog</kwd></kwd-group><funding-group xml:lang="ru"><funding-statement>Исследование финансируется Комитетом науки Министерства науки и высшего образования Республики Казахстан (грант № AP14869395).</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Buder S. et al. The GALAH+ survey: Third data release. Mon. Not. R. Astron. Soc. Oxford Academic, 2021, vol. 506, no. 1, pp. 150–201. https://doi.org/10.1093/mnras/stab1242.</mixed-citation><mixed-citation xml:lang="en">Buder S. et al. The GALAH+ survey: Third data release. Mon. Not. R. Astron. Soc. Oxford Academic, 2021, vol. 506, no. 1, pp. 150–201. https://doi.org/10.1093/mnras/stab1242.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Vallenari A. et al. Gaia Data Release 3 - Summary of the content and survey properties. Astron. Astrophys. Suppl. Ser. EDP Sciences, 2023, vol. 674, p. A1. https://doi.org/10.1051/0004-6361/202243940.</mixed-citation><mixed-citation xml:lang="en">Vallenari A. et al. Gaia Data Release 3 - Summary of the content and survey properties. Astron. Astrophys. Suppl. Ser. EDP Sciences, 2023, vol. 674, p. A1. https://doi.org/10.1051/0004-6361/202243940.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Kollmeier J. et al. SDSS-V: Pioneering Panoptic Spectroscopy. arXiv: Astrophysics of Galaxies, 2017. https://assets.pubpub.org/nubevd6h/01598545751555.pdf.</mixed-citation><mixed-citation xml:lang="en">Kollmeier J. et al. SDSS-V: Pioneering Panoptic Spectroscopy. arXiv: Astrophysics of Galaxies, 2017. https://assets.pubpub.org/nubevd6h/01598545751555.pdf.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Ackerl C. et al. Galaxy archaeology - The quest for ancient mergers, 2024, pp. 1.01.</mixed-citation><mixed-citation xml:lang="en">Ackerl C. et al. Galaxy archaeology - The quest for ancient mergers, 2024, pp. 1.01.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Merrow A. et al. Did the Gaia Enceladus/Sausage merger form the Milky Way’s bar? Mon. Not. R. Astron. Soc. Oxford University Press, 2024, p. stae1250. https://academic.oup.com/mnras/advance-articleabstract/doi/10.1093/mnras/stae1250/7671147.</mixed-citation><mixed-citation xml:lang="en">Merrow A. et al. Did the Gaia Enceladus/Sausage merger form the Milky Way’s bar? Mon. Not. R. Astron. Soc. Oxford University Press, 2024, p. stae1250. https://academic.oup.com/mnras/advance-articleabstract/doi/10.1093/mnras/stae1250/7671147.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Marin-Franch A. et al. THE ACS SURVEY OF GALACTIC GLOBULAR CLUSTERS. VII.* RELATIVE AGES. Astrophys. J. IOP Publishing, 2009, vol. 694, no. 2, p. 1498. https://iopscience.iop.org/article/10.1088/0004-637X/694/2/1498/meta</mixed-citation><mixed-citation xml:lang="en">Marin-Franch A. et al. THE ACS SURVEY OF GALACTIC GLOBULAR CLUSTERS. VII.* RELATIVE AGES. Astrophys. J. IOP Publishing, 2009, vol. 694, no. 2, p. 1498. https://iopscience.iop.org/article/10.1088/0004-637X/694/2/1498/meta</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Valcin D. et al. Inferring the Age of the Universe with Globular Clusters. arXiv [astro-ph.CO], 2020. https://doi.org/10.1088/1475-7516/2020/12/002</mixed-citation><mixed-citation xml:lang="en">Valcin D. et al. Inferring the Age of the Universe with Globular Clusters. arXiv [astro-ph.CO], 2020. https://doi.org/10.1088/1475-7516/2020/12/002</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Vandenberg D.A. et al. The Ages of 55 Globular Clusters as Determined Using an Improved delta V_TO^HB Method Along with Color-Magnitude Diagram Constraints, and Their Implications for Broader Issues. arXiv [astro-ph.GA], 2013. https://doi.org/10.1088/0004-637X/775/2/134.</mixed-citation><mixed-citation xml:lang="en">Vandenberg D.A. et al. The Ages of 55 Globular Clusters as Determined Using an Improved delta V_TO^HB Method Along with Color-Magnitude Diagram Constraints, and Their Implications for Broader Issues. arXiv [astro-ph.GA], 2013. https://doi.org/10.1088/0004-637X/775/2/134.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Baumgardt H. et al. Mean proper motions, space orbits, and velocity dispersion profiles of Galactic globular clusters derived from Gaia DR2 data, mnras, 2019, vol. 482, no. 4, pp. 5138–5155. https://doi.org/10.1093/mnras/sty2997</mixed-citation><mixed-citation xml:lang="en">Baumgardt H. et al. Mean proper motions, space orbits, and velocity dispersion profiles of Galactic globular clusters derived from Gaia DR2 data, mnras, 2019, vol. 482, no. 4, pp. 5138–5155. https://doi.org/10.1093/mnras/sty2997</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Baumgardt H., Vasiliev E. Accurate distances to Galactic globular clusters through a combination of Gaia EDR3, HST, and literature data, mnras, 2021, vol. 505, no. 4, pp. 5957–5977. https://doi.org/10.1093/mnras/stab1474.</mixed-citation><mixed-citation xml:lang="en">Baumgardt H., Vasiliev E. Accurate distances to Galactic globular clusters through a combination of Gaia EDR3, HST, and literature data, mnras, 2021, vol. 505, no. 4, pp. 5957–5977. https://doi.org/10.1093/mnras/stab1474.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Harris G.L.H., Poole G.B., Harris W.E. Globular clusters and supermassive black holes in galaxies: further analysis and a larger sample. Mon. Not. R. Astron. Soc. Oxford Academic, 2014, vol. 438, no. 3, pp. 2117–2130. https://doi.org/10.1093/mnras/stt2337.</mixed-citation><mixed-citation xml:lang="en">Harris G.L.H., Poole G.B., Harris W.E. Globular clusters and supermassive black holes in galaxies: further analysis and a larger sample. Mon. Not. R. Astron. Soc. Oxford Academic, 2014, vol. 438, no. 3, pp. 2117–2130. https://doi.org/10.1093/mnras/stt2337.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Kharchenko N.V. et al. Global survey of star clusters in the Milky Way II. The catalogue of basic parameters. arXiv [astro-ph.GA], 2013. https://doi.org/10.1051/0004-6361/201322302.</mixed-citation><mixed-citation xml:lang="en">Kharchenko N.V. et al. Global survey of star clusters in the Milky Way II. The catalogue of basic parameters. arXiv [astro-ph.GA], 2013. https://doi.org/10.1051/0004-6361/201322302.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Ibata R. et al. Charting the galactic acceleration field. I. a search for stellar streams with Gaia DR2 and EDR3 with follow-up from ESPaDOnS and UVES. Astrophys. J. American Astronomical Society, 2021, vol. 914, no. 2, pp. 123. https://doi.org/10.3847/1538-4357/abfcc2.</mixed-citation><mixed-citation xml:lang="en">Ibata R. et al. Charting the galactic acceleration field. I. a search for stellar streams with Gaia DR2 and EDR3 with follow-up from ESPaDOnS and UVES. Astrophys. J. American Astronomical Society, 2021, vol. 914, no. 2, pp. 123. https://doi.org/10.3847/1538-4357/abfcc2.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Mateu C. galstreams: A library of Milky Way stellar stream footprints and tracks. Mon. Not. R. Astron. Soc. Oxford Academic, 2023, vol. 520, no. 4, pp. 5225–5258. https://doi.org/10.1093/mnras/stad321.</mixed-citation><mixed-citation xml:lang="en">Mateu C. galstreams: A library of Milky Way stellar stream footprints and tracks. Mon. Not. R. Astron. Soc. Oxford Academic, 2023, vol. 520, no. 4, pp. 5225–5258. https://doi.org/10.1093/mnras/stad321.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Snaith O.N. et al. The dominant epoch of star formation in the Milky Way formed the thick disk. Astrophys. J. Lett. IOP Publishing, 2014, vol. 781, no. 2, p. L31. https://iopscience.iop.org/article/10.1088/2041-8205/781/2/L31/meta.</mixed-citation><mixed-citation xml:lang="en">Snaith O.N. et al. The dominant epoch of star formation in the Milky Way formed the thick disk. Astrophys. J. Lett. IOP Publishing, 2014, vol. 781, no. 2, p. L31. https://iopscience.iop.org/article/10.1088/2041-8205/781/2/L31/meta.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Xiang M., Rix H.-W. A time-resolved picture of our Milky Way’s early formation history. Nature, 2022, vol. 603, no. 7902, pp. 599–603. https://doi.org/10.1038/s41586-022-04496-5.</mixed-citation><mixed-citation xml:lang="en">Xiang M., Rix H.-W. A time-resolved picture of our Milky Way’s early formation history. Nature, 2022, vol. 603, no. 7902, pp. 599–603. https://doi.org/10.1038/s41586-022-04496-5.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Brown A.G.A. et al. Gaia Early Data Release 3 - Summary of the contents and survey properties. Astron. Astrophys. Suppl. Ser. EDP Sciences, 2021, vol. 649, p. A1. https://doi.org/10.1051/0004-6361/202039657.</mixed-citation><mixed-citation xml:lang="en">Brown A.G.A. et al. Gaia Early Data Release 3 - Summary of the contents and survey properties. Astron. Astrophys. Suppl. Ser. EDP Sciences, 2021, vol. 649, p. A1. https://doi.org/10.1051/0004-6361/202039657.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Gaia C. et al. Gaia data release 2 summary of the contents and survey properties. Astron. Astrophys. Suppl. Ser. EDP Sciences, 2018, vol. 616, no. 1. https://real.mtak.hu/84690/1/gaia6.pdf.</mixed-citation><mixed-citation xml:lang="en">Gaia C. et al. Gaia data release 2 summary of the contents and survey properties. Astron. Astrophys. Suppl. Ser. EDP Sciences, 2018, vol. 616, no. 1. https://real.mtak.hu/84690/1/gaia6.pdf.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Malhan K. et al. The global dynamical atlas of the Milky Way mergers: Constraints from Gaia EDR3–based orbits of globular clusters, stellar streams, and satellite galaxies. Astrophys. J. American Astronomical Society, 2022, vol. 926, no. 2, p. 107. https://doi.org/10.3847/1538-4357/ac4d2a.</mixed-citation><mixed-citation xml:lang="en">Malhan K. et al. The global dynamical atlas of the Milky Way mergers: Constraints from Gaia EDR3–based orbits of globular clusters, stellar streams, and satellite galaxies. Astrophys. J. American Astronomical Society, 2022, vol. 926, no. 2, p. 107. https://doi.org/10.3847/1538-4357/ac4d2a.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Massari D., Koppelman H.H., Helmi A. Origin of the system of globular clusters in the Milky Way. Astron. Astrophys. Suppl. Ser. EDP Sciences, 2019, vol. 630, p. L4. https://doi.org/10.1051/0004-6361/201936135.</mixed-citation><mixed-citation xml:lang="en">Massari D., Koppelman H.H., Helmi A. Origin of the system of globular clusters in the Milky Way. Astron. Astrophys. Suppl. Ser. EDP Sciences, 2019, vol. 630, p. L4. https://doi.org/10.1051/0004-6361/201936135.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Myeong G.C. et al. Evidence for two early accretion events that built the Milky Way stellar halo. Mon. Not. R. Astron. Soc. Oxford Academic, 2019, vol. 488, no. 1, pp. 1235–1247. https://doi.org/10.1093/mnras/stz1770.</mixed-citation><mixed-citation xml:lang="en">Myeong G.C. et al. Evidence for two early accretion events that built the Milky Way stellar halo. Mon. Not. R. Astron. Soc. Oxford Academic, 2019, vol. 488, no. 1, pp. 1235–1247. https://doi.org/10.1093/mnras/stz1770.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Dwek E., Arendt R.G., Hauser M.G. Morphology, near-infrared luminosity, and mass of the Galactic bulge from COBE DIRBE observations. Journal, Part 1 …. adsabs.harvard.edu, 1995. https://adsabs.harvard.edu/full/1995ApJ...445..716D.</mixed-citation><mixed-citation xml:lang="en">Dwek E., Arendt R.G., Hauser M.G. Morphology, near-infrared luminosity, and mass of the Galactic bulge from COBE DIRBE observations. Journal, Part 1 …. adsabs.harvard.edu, 1995. https://adsabs.harvard.edu/full/1995ApJ...445..716D.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Wegg C., Gerhard O. Mapping the three-dimensional density of the Galactic bulge with VVV red clump stars. Mon. Not. R. Astron. Soc. Oxford Academic, 2013, vol. 435, no. 3, pp.1874–1887. https://doi.org/10.1093/mnras/stt1376.</mixed-citation><mixed-citation xml:lang="en">Wegg C., Gerhard O. Mapping the three-dimensional density of the Galactic bulge with VVV red clump stars. Mon. Not. R. Astron. Soc. Oxford Academic, 2013, vol. 435, no. 3, pp.1874–1887. https://doi.org/10.1093/mnras/stt1376.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Conroy C. et al. All-sky dynamical response of the Galactic halo to the Large Magellanic Cloud. Nature, 2021, vol. 592, no. 7855, pp. 534–536. https://doi.org/10.1038/s41586-021-03385-7.</mixed-citation><mixed-citation xml:lang="en">Conroy C. et al. All-sky dynamical response of the Galactic halo to the Large Magellanic Cloud. Nature, 2021, vol. 592, no. 7855, pp. 534–536. https://doi.org/10.1038/s41586-021-03385-7.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Gómez F.A. et al. And yet it moves: the dangers of artificially fixing the Milky Way center of mass in the presence of a massive Large Magellanic Cloud. Astrophys. J. Iop Publishing, 2015, vol. 802, no. 2, p.128. https://iopscience.iop.org/article/10.1088/0004-637X/802/2/128/meta.</mixed-citation><mixed-citation xml:lang="en">Gómez F.A. et al. And yet it moves: the dangers of artificially fixing the Milky Way center of mass in the presence of a massive Large Magellanic Cloud. Astrophys. J. Iop Publishing, 2015, vol. 802, no. 2, p.128. https://iopscience.iop.org/article/10.1088/0004-637X/802/2/128/meta.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Petersen M.S., Peñarrubia J. Detection of the Milky Way reflex motion due to the Large Magellanic Cloud infall. Nature Astronomy. Nature Publishing Group, 2020, vol. 5, no. 3, pp. 251–255. https://doi.org/10.1038/s41550-020-01254-3.</mixed-citation><mixed-citation xml:lang="en">Petersen M.S., Peñarrubia J. Detection of the Milky Way reflex motion due to the Large Magellanic Cloud infall. Nature Astronomy. Nature Publishing Group, 2020, vol. 5, no. 3, pp. 251–255. https://doi.org/10.1038/s41550-020-01254-3.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Bajkova A.T., Bobylev V.V. Orbits of 152 globular clusters of the Milky Way galaxy constructed from the Gaia DR2 data. arXiv [astro-ph.GA], 2020. https://doi.org/10.1088/1674-4527/21/7/173/meta</mixed-citation><mixed-citation xml:lang="en">Bajkova A.T., Bobylev V.V. Orbits of 152 globular clusters of the Milky Way galaxy constructed from the Gaia DR2 data. arXiv [astro-ph.GA], 2020. https://doi.org/10.1088/1674-4527/21/7/173/meta</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Vasiliev E., Baumgardt H. Gaia EDR3 view on galactic globular clusters. Mon. Not. R. Astron. Soc. Oxford Academic, 2021, vol. 505, no. 4, pp. 5978–6002. https://doi.org/10.1093/mnras/stab1475.</mixed-citation><mixed-citation xml:lang="en">Vasiliev E., Baumgardt H. Gaia EDR3 view on galactic globular clusters. Mon. Not. R. Astron. Soc. Oxford Academic, 2021, vol. 505, no. 4, pp. 5978–6002. https://doi.org/10.1093/mnras/stab1475.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Reid M.J., Brunthaler A. The proper motion of Sagittarius A*. ii. The mass of Sagittarius A. Astrophys. J. American Astronomical Society, 2004, vol. 616, no. 2, pp. 872–884. https://doi.org/10.1086/424960.</mixed-citation><mixed-citation xml:lang="en">Reid M.J., Brunthaler A. The proper motion of Sagittarius A*. ii. The mass of Sagittarius A. Astrophys. J. American Astronomical Society, 2004, vol. 616, no. 2, pp. 872–884. https://doi.org/10.1086/424960.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Bennett M., Bovy J. Vertical waves in the solar neighbourhood in Gaia DR2. Mon. Not. R. Astron. Soc. Oxford Academic, 2018, vol. 482, no. 1, pp. 1417–1425. https://doi.org/10.1093/mnras/sty2813.</mixed-citation><mixed-citation xml:lang="en">Bennett M., Bovy J. Vertical waves in the solar neighbourhood in Gaia DR2. Mon. Not. R. Astron. Soc. Oxford Academic, 2018, vol. 482, no. 1, pp. 1417–1425. https://doi.org/10.1093/mnras/sty2813.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Bovy J. et al. The Milky Way’s circular-velocity curve between 4 and 14 kpc from APOGEE data. Astrophys. J. IOP Publishing, 2012, vol. 759, no. 2, p. 131. https://iopscience.iop.org/article/10.1088/0004-637X/759/2/131/meta</mixed-citation><mixed-citation xml:lang="en">Bovy J. et al. The Milky Way’s circular-velocity curve between 4 and 14 kpc from APOGEE data. Astrophys. J. IOP Publishing, 2012, vol. 759, no. 2, p. 131. https://iopscience.iop.org/article/10.1088/0004-637X/759/2/131/meta</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Drimmel R., Poggio E. On the solar velocity. Res. Notes AAS. American Astronomical Society, 2018, vol. 2, no. 4, p. 210. https://doi.org/10.3847/2515-5172/aaef8b.</mixed-citation><mixed-citation xml:lang="en">Drimmel R., Poggio E. On the solar velocity. Res. Notes AAS. American Astronomical Society, 2018, vol. 2, no. 4, p. 210. https://doi.org/10.3847/2515-5172/aaef8b.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Chemerynska I.V. et al. Kinematic characteristics of the Milky Way globular clusters based on Gaia DR2 data. arXiv [astro-ph.GA], 2022. http://arxiv.org/abs/2201.07221.</mixed-citation><mixed-citation xml:lang="en">Chemerynska I.V. et al. Kinematic characteristics of the Milky Way globular clusters based on Gaia DR2 data. arXiv [astro-ph.GA], 2022. http://arxiv.org/abs/2201.07221.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Nelson D. et al. The IllustrisTNG simulations: public data release. Computational Astrophysics and Cosmology, 2019, vol. 6, no. 1, p. 2. https://doi.org/10.1186/s40668-019-0028-x</mixed-citation><mixed-citation xml:lang="en">Nelson D. et al. The IllustrisTNG simulations: public data release. Computational Astrophysics and Cosmology, 2019, vol. 6, no. 1, p. 2. https://doi.org/10.1186/s40668-019-0028-x</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Miyamoto M., Nagai R. Three-dimensional models for the distribution of mass in galaxies, 1975, vol. 27, no. 4, pp. 533–543. adsabs.harvard.edu, 1975. https://adsabs.harvard.edu/full/1975PASJ...27..533M.</mixed-citation><mixed-citation xml:lang="en">Miyamoto M., Nagai R. Three-dimensional models for the distribution of mass in galaxies, 1975, vol. 27, no. 4, pp. 533–543. adsabs.harvard.edu, 1975. https://adsabs.harvard.edu/full/1975PASJ...27..533M.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Navarro J.F., Frenk C.S., White S.D.M. A universal density profile from hierarchical clustering. Astrophys. J. American Astronomical Society, 1997, vol. 490, no. 2, pp. 493–508. https://doi.org/10.1086/304888.</mixed-citation><mixed-citation xml:lang="en">Navarro J.F., Frenk C.S., White S.D.M. A universal density profile from hierarchical clustering. Astrophys. J. American Astronomical Society, 1997, vol. 490, no. 2, pp. 493–508. https://doi.org/10.1086/304888.</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Ishchenko M. et al. Milky Way globular clusters on cosmological timescales - I. Evolution of the orbital parameters in time-varying potentials. Astron. Astrophys. Suppl. Ser. EDP Sciences, 2023, vol. 673, p.A152. https://doi.org/10.1051/0004-6361/202245117.</mixed-citation><mixed-citation xml:lang="en">Ishchenko M. et al. Milky Way globular clusters on cosmological timescales - I. Evolution of the orbital parameters in time-varying potentials. Astron. Astrophys. Suppl. Ser. EDP Sciences, 2023, vol. 673, p.A152. https://doi.org/10.1051/0004-6361/202245117.</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Mardini M.K. et al. Cosmological insights into the early accretion of r-process-enhanced stars. I. a comprehensive chemodynamical analysis of LAMOST J1109+0754. Astrophys. J. American Astronomical Society, 2020, vol. 903, no. 2, p. 88. https://doi.org/10.3847/1538-4357/abbc13.</mixed-citation><mixed-citation xml:lang="en">Mardini M.K. et al. Cosmological insights into the early accretion of r-process-enhanced stars. I. a comprehensive chemodynamical analysis of LAMOST J1109+0754. Astrophys. J. American Astronomical Society, 2020, vol. 903, no. 2, p. 88. https://doi.org/10.3847/1538-4357/abbc13.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Berczik P. et al. High performance massively parallel direct N-body simulations on large GPU clusters. International conference on high performance computing, 2011, pp. 8–18. ftp://ftp.mao.kiev.ua/pub/berczik/phi-GPU/paper/1.1(8).pdf.</mixed-citation><mixed-citation xml:lang="en">Berczik P. et al. High performance massively parallel direct N-body simulations on large GPU clusters. International conference on high performance computing, 2011, pp. 8–18. ftp://ftp.mao.kiev.ua/pub/berczik/phi-GPU/paper/1.1(8).pdf.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">Berczik P. et al. Up to 700k GPU Cores, Kepler, and the Exascale Future for Simulations of Star Clusters Around Black Holes. Supercomputing. Springer Berlin Heidelberg, 2013, pp. 13–25. https://doi.org/10.1007/978-3-642-38750-0_2.</mixed-citation><mixed-citation xml:lang="en">Berczik P. et al. Up to 700k GPU Cores, Kepler, and the Exascale Future for Simulations of Star Clusters Around Black Holes. Supercomputing. Springer Berlin Heidelberg, 2013, pp. 13–25. https://doi.org/10.1007/978-3-642-38750-0_2.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
