White dwarfs with rapid rotation
| dc.citation.epage | 302 | |
| dc.citation.issue | 2 | |
| dc.citation.journalTitle | Математичне моделювання та комп'ютинг | |
| dc.citation.spage | 278 | |
| dc.contributor.affiliation | Львівський національний університет імені Івана Франка | |
| dc.contributor.affiliation | Ivan Franko National University of Lviv | |
| dc.contributor.author | Ваврух, М. | |
| dc.contributor.author | Дзіковський, Д. | |
| dc.contributor.author | Смеречинський, С. | |
| dc.contributor.author | Vavrukh, M. | |
| dc.contributor.author | Dzikovskyi, D. | |
| dc.contributor.author | Smerechynskyi, S. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-03-04T11:14:29Z | |
| dc.date.created | 2022-02-28 | |
| dc.date.issued | 2022-02-28 | |
| dc.description.abstract | На основі рівняння рівноваги розраховано характеристики холодних білих карликів з осьовим обертанням і кулонівськими міжчастинковими взаємодіями у рамках електрон-ядерної моделі з повністю виродженою електронною підсистемою і статичною ядерною підсистемою. На першому етапі знайдено наближені розв’язки диференціального рівняння рівноваги, в якому фігурують два безрозмірні параметри: x0— параметр релятивізму у центрі зорі та Ω — безрозмірна кутова швидкість. З метою коректного розрахунку набору сталих інтегрування використано інтегральну форму цього рівняння. На цій основі обчислено масу карлика, екваторіальний і полярний радіуси, момент інерції, повну енергію, прискорення на екваторі як функції параметрів x0 та Ω. Проаналізовано зміну характеристик під впливом обертання. Описану модель узагальнено шляхом врахування кулонівських взаємодій. Досліджено конкуренцію між обертанням і міжчастинковими взаємодіями. На основі результатів розрахунку виконано оцінки характеристик недавно відкритих білих карликів зі швидким обертанням за відомою зі спостережень їхньою кутовою швидкістю або ж кутовою швидкістю та масою. | |
| dc.description.abstract | A new analytical approach for calculation of white dwarfs characteristics that accounts for two important competing factors — axial rotation and Coulomb interparticle interactions, is proposed. The feature of our approach is simultaneous usage of differential and integral forms of equilibrium equation. In dimensionless form the differential equilibrium equation is strongly nonlinear inhomogeneous equation of the second order in partial derivatives with two dimensionless parameters — the relativistic parameter in stellar center x0 and dimensionless angular velocity Ω. In inner stellar region, rotation is taken into account as perturbation in the linear approximation for Ω2. In stellar periphery rotation is considered as the main factor. Usage of the integral equation provides correct calculations of integration constants. Dwarf's mass, moment of inertia relative to the axis of rotation, equatorial and polar radii, equatorial gravity in the following parameter space 1≤x0≤24, 0≤Ω<Ωmax(x0) have been calculated based on the solutions of equilibrium equation. For the first time it was calculated the total energy of dwarf as function of these parameters. By the extrapolation, it was calculated the maximal values Ωmax(x0), as well as the observed angular velocity ωmax(x0). The considered model is generalized by taking into account Coulomb interparticle interactions. Also, we provide the examples of application of obtained results. It was shown that the characteristics of observed massive dwarfs do not contradict the calculated values for the model with consideration of solid body rotation and Coulomb interparticle interactions. | |
| dc.format.extent | 278-302 | |
| dc.format.pages | 25 | |
| dc.identifier.citation | Vavrukh M. White dwarfs with rapid rotation / M. Vavrukh, D. Dzikovskyi, S. Smerechynskyi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 2. — P. 278–302. | |
| dc.identifier.citationen | Vavrukh M. White dwarfs with rapid rotation / M. Vavrukh, D. Dzikovskyi, S. Smerechynskyi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 2. — P. 278–302. | |
| dc.identifier.doi | doi.org/10.23939/mmc2022.02.278 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/63452 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та комп'ютинг, 2 (9), 2022 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 2 (9), 2022 | |
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| dc.relation.references | [2] Fowler R. H. On dense matter. Monthly Notices of the Royal Astronomical Society. 87 (2), 114–122 (1926). | |
| dc.relation.references | [3] Chandrasekhar S. The Maximum Mass of Ideal White Dwarfs. Astrophysical Journal. 74, 81–82 (1931). | |
| dc.relation.references | [4] Vavrukh M. V., Smerechynskyi S. V. Hot degenerate dwarfs in a two-phase model. Astronomy Reports. 57, 913–983 (2013). | |
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| dc.relation.references | [8] James R. A. The Structure and Stability of Rotating Gas Masses. Astrophysical Journal. 140, 552–582 (1964). | |
| dc.relation.references | [9] Tassoul J.-L. Theory of Rotating Stars. (PSA-1), Vol. 1. Princeton University Press (2016). | |
| dc.relation.references | [10] Shapiro S. L. Teukolsky S. A. Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects. Wiley, New York (1983). | |
| dc.relation.references | [11] Vavrukh M. V., Kostrobij P. P., Markovych B. M. Reference system approach in the theory of manyelectrons systems. Rastr-7, Lviv (2017), (in Ukrainian). | |
| dc.relation.references | [12] Vavrukh M. V., Dzikovskyi D. V. Method of integral equations in the polytropic theory of stars with axial rotation. II. Polytrope with indices n > 1. Mathematical Modeling and Computing. 8 (3), 474–485 (2021). | |
| dc.relation.references | [13] Monaghan J. J., Roxburgh I. W. The Structure of Rapidly Rotating Polytropes. Monthly Notices of the Royal Astronomical Society. 131 (1), 13–22 (1965). | |
| dc.relation.references | [14] Vavrukh M. V., Tyshko N. L., Dzikovskyi D. V. New approach in the theory of stellar equilibrium with axial rotation. Journal of Physical Studies. 24 (3), 3902-1–3902-20 (2020). | |
| dc.relation.references | [15] Vavrukh M. V., Dzikovskyi D. V. Exact solution for the rotating polytropes with index unity, its approximations and some applications. Contrib. Astron. Obs. Skalnat´e Pleso. 50 (4), 748–771 (2020). | |
| dc.relation.references | [16] Vavrukh M., Krokhmalskii T. Reference System Approach in the Electron Liquid Theory. I. General Relations. Physica Status Solidi (b). 168 (2), 519–532 (1991). | |
| dc.relation.references | [17] Vavrukh M. V., Krokhmalskii T. E. Reference System Approach in the Electron Liquid Theory. II. Ground State Characteristics in the Medium Density Region. Physica Status Solidi (b). 169 (2), 451–462 (1992). | |
| dc.relation.references | [18] Vavrukh M., Dzikovskyi D., Solovyan V., Tyshko N. Correlation functions of the degenerate relativistic electron gas with high density. Mathematical Modeling and Computing. 3 (1), 97–110 (2016). | |
| dc.relation.references | [19] Pines D., Nozi´eres P. The Theory of Quantum Liquids: Normal Fermi Liquids. CRC Press (1966). | |
| dc.relation.references | [20] Fuchs K. A quantum mechanical investigation of the cohesive forces of metallic copper. Proceedings of the Royal Society of London. Series A – Mathematical and Physical Sciences. 151 (874), 585–602 (1935). | |
| dc.relation.references | [21] Carr W. J. Energy, Specific Heat, and Magnetic Properties of the Low-Density Electron Gas. Physical Review. 122 (5), 1437–1446 (1961). | |
| dc.relation.references | [22] Vavrukh M. V., Smerechynskyi S. V., Tyshko N. L. New models in the theory of white dwarfs structure. Rastr-7, Lviv (2018). | |
| dc.relation.references | [23] Ceperley D. M., Alder B. J. Ground State of the Electron Gas by a Stochastic Method. Physical Review Letters. 45 (7), 566–569 (1980). | |
| dc.relation.references | [24] Salpeter E. E. Energy and Pressure of a Zero-Temperature Plasma. Astrophysical Journal. 134, 669–682 (1961). | |
| dc.relation.references | [25] Davydov A. C. Quantum mechanics. Nauka, Moscow (1973). | |
| dc.relation.references | [26] Bond H. E., Schaefer G. H., Gilliland R. L., Holberg J. B., Mason B. D., Lindenblad I. W., SeitzMcLeese M., David A. W., Demarque Pi., Spada F., Young P. A., Barstow M. A., Burleigh M. R., Gudehus D. The Sirius System and Its Astrophysical Puzzles: Hubble Space Telescope and Ground-based Astrometry. The Astrophysical Journal. 840 (2), 70 (2017). | |
| dc.relation.references | [27] Kong D., Zhang K., Schubert G. An exact solution for arbitrarily rotating gaseous polytropes with index unity. Monthly Notices of the Royal Astronomical Society. 448 (1), 456–463 (2015). | |
| dc.relation.references | [28] Knopik J., Mach P., Odrzywo lek A. The shape of a rapidly rotating polytrope with index unity. Monthly Notices of the Royal Astronomical Society. 467 (4), 4965–4969 (2017). | |
| dc.relation.references | [29] Tricomi F. G. Integral Equations. Dover Publications (1985). | |
| dc.relation.referencesen | [1] Adams W. S. The Spectrum of the Companion of Sirius. Publications of the Astronomical Society of the Pacific. 27 (161), 236–237 (1915). | |
| dc.relation.referencesen | [2] Fowler R. H. On dense matter. Monthly Notices of the Royal Astronomical Society. 87 (2), 114–122 (1926). | |
| dc.relation.referencesen | [3] Chandrasekhar S. The Maximum Mass of Ideal White Dwarfs. Astrophysical Journal. 74, 81–82 (1931). | |
| dc.relation.referencesen | [4] Vavrukh M. V., Smerechynskyi S. V. Hot degenerate dwarfs in a two-phase model. Astronomy Reports. 57, 913–983 (2013). | |
| dc.relation.referencesen | [5] Pelisoli I., Marsh T. R., Dhillon V. S., Breedt E., Brown A. J., Dyer M. J., Green M. J., Kerry P., Littlefair S. P., Parsons S. G., Sahman D. I., Wild J. F. Found: a rapidly spinning white dwarf in LAMOST J024048.51+195226.9. Monthly Notices of the Royal Astronomical Society: Letters. 509 (1), L31–L36 (2022). | |
| dc.relation.referencesen | [6] Lopes de Oliveira R., Bruch A., Rodrigues C. V., Oliveira A. S., Mukai K. CTCV J2056-3014: An X-Rayfaint Intermediate Polar Harboring an Extremely Fast-spinning White Dwarf. The Astrophysical Journal Letters. 898 (2), L40 (2020). | |
| dc.relation.referencesen | [7] Ashley R. P., Marsh T. R., Breedt E., G¨ansicke B. T., Pala A. F., Toloza O., Chote P., Thorstensen J. R., Burleigh M. R. V1460 Her: a fast spinning white dwarf accreting from an evolved donor star. Monthly Notices of the Royal Astronomical Society. 499 (1), 149–160 (2020). | |
| dc.relation.referencesen | [8] James R. A. The Structure and Stability of Rotating Gas Masses. Astrophysical Journal. 140, 552–582 (1964). | |
| dc.relation.referencesen | [9] Tassoul J.-L. Theory of Rotating Stars. (PSA-1), Vol. 1. Princeton University Press (2016). | |
| dc.relation.referencesen | [10] Shapiro S. L. Teukolsky S. A. Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects. Wiley, New York (1983). | |
| dc.relation.referencesen | [11] Vavrukh M. V., Kostrobij P. P., Markovych B. M. Reference system approach in the theory of manyelectrons systems. Rastr-7, Lviv (2017), (in Ukrainian). | |
| dc.relation.referencesen | [12] Vavrukh M. V., Dzikovskyi D. V. Method of integral equations in the polytropic theory of stars with axial rotation. II. Polytrope with indices n > 1. Mathematical Modeling and Computing. 8 (3), 474–485 (2021). | |
| dc.relation.referencesen | [13] Monaghan J. J., Roxburgh I. W. The Structure of Rapidly Rotating Polytropes. Monthly Notices of the Royal Astronomical Society. 131 (1), 13–22 (1965). | |
| dc.relation.referencesen | [14] Vavrukh M. V., Tyshko N. L., Dzikovskyi D. V. New approach in the theory of stellar equilibrium with axial rotation. Journal of Physical Studies. 24 (3), 3902-1–3902-20 (2020). | |
| dc.relation.referencesen | [15] Vavrukh M. V., Dzikovskyi D. V. Exact solution for the rotating polytropes with index unity, its approximations and some applications. Contrib. Astron. Obs. Skalnat´e Pleso. 50 (4), 748–771 (2020). | |
| dc.relation.referencesen | [16] Vavrukh M., Krokhmalskii T. Reference System Approach in the Electron Liquid Theory. I. General Relations. Physica Status Solidi (b). 168 (2), 519–532 (1991). | |
| dc.relation.referencesen | [17] Vavrukh M. V., Krokhmalskii T. E. Reference System Approach in the Electron Liquid Theory. II. Ground State Characteristics in the Medium Density Region. Physica Status Solidi (b). 169 (2), 451–462 (1992). | |
| dc.relation.referencesen | [18] Vavrukh M., Dzikovskyi D., Solovyan V., Tyshko N. Correlation functions of the degenerate relativistic electron gas with high density. Mathematical Modeling and Computing. 3 (1), 97–110 (2016). | |
| dc.relation.referencesen | [19] Pines D., Nozi´eres P. The Theory of Quantum Liquids: Normal Fermi Liquids. CRC Press (1966). | |
| dc.relation.referencesen | [20] Fuchs K. A quantum mechanical investigation of the cohesive forces of metallic copper. Proceedings of the Royal Society of London. Series A – Mathematical and Physical Sciences. 151 (874), 585–602 (1935). | |
| dc.relation.referencesen | [21] Carr W. J. Energy, Specific Heat, and Magnetic Properties of the Low-Density Electron Gas. Physical Review. 122 (5), 1437–1446 (1961). | |
| dc.relation.referencesen | [22] Vavrukh M. V., Smerechynskyi S. V., Tyshko N. L. New models in the theory of white dwarfs structure. Rastr-7, Lviv (2018). | |
| dc.relation.referencesen | [23] Ceperley D. M., Alder B. J. Ground State of the Electron Gas by a Stochastic Method. Physical Review Letters. 45 (7), 566–569 (1980). | |
| dc.relation.referencesen | [24] Salpeter E. E. Energy and Pressure of a Zero-Temperature Plasma. Astrophysical Journal. 134, 669–682 (1961). | |
| dc.relation.referencesen | [25] Davydov A. C. Quantum mechanics. Nauka, Moscow (1973). | |
| dc.relation.referencesen | [26] Bond H. E., Schaefer G. H., Gilliland R. L., Holberg J. B., Mason B. D., Lindenblad I. W., SeitzMcLeese M., David A. W., Demarque Pi., Spada F., Young P. A., Barstow M. A., Burleigh M. R., Gudehus D. The Sirius System and Its Astrophysical Puzzles: Hubble Space Telescope and Ground-based Astrometry. The Astrophysical Journal. 840 (2), 70 (2017). | |
| dc.relation.referencesen | [27] Kong D., Zhang K., Schubert G. An exact solution for arbitrarily rotating gaseous polytropes with index unity. Monthly Notices of the Royal Astronomical Society. 448 (1), 456–463 (2015). | |
| dc.relation.referencesen | [28] Knopik J., Mach P., Odrzywo lek A. The shape of a rapidly rotating polytrope with index unity. Monthly Notices of the Royal Astronomical Society. 467 (4), 4965–4969 (2017). | |
| dc.relation.referencesen | [29] Tricomi F. G. Integral Equations. Dover Publications (1985). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2022 | |
| dc.subject | вироджені карлики | |
| dc.subject | осьове обертання | |
| dc.subject | кулонівські міжчастинкові взаємодії | |
| dc.subject | рівняння механічної рівноваги | |
| dc.subject | обернена задача | |
| dc.subject | white dwarfs | |
| dc.subject | axial rotation | |
| dc.subject | Coulomb interparticle interactions | |
| dc.subject | mechanical equilibrium equation | |
| dc.subject | inverse problem | |
| dc.title | White dwarfs with rapid rotation | |
| dc.title.alternative | Вироджені карлики зі швидким обертанням | |
| dc.type | Article |
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