Tidal Resonance: A Factor Worth Considering in the Orbital Evolution of Heartbeat Stars
Heartbeat star systems have been reported to exhibit two distinct different orbital dynamic evolution processes: apsidal precession (e.g., KIC 4544587) and orbital decay (e.g., KIC 3766353). While experiencing similar dynamic tidal interactions, these binary systems display different dynamical behav...
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MDPI AG
2023-12-01
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| Online Access: | https://www.mdpi.com/2218-1997/9/12/514 |
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| author | Jian-Wen Ou Chen Jiang Ming Yang Cong Yu Dong-Yang Gao Guangbo Long |
| author_facet | Jian-Wen Ou Chen Jiang Ming Yang Cong Yu Dong-Yang Gao Guangbo Long |
| author_sort | Jian-Wen Ou |
| collection | DOAJ |
| description | Heartbeat star systems have been reported to exhibit two distinct different orbital dynamic evolution processes: apsidal precession (e.g., KIC 4544587) and orbital decay (e.g., KIC 3766353). While experiencing similar dynamic tidal interactions, these binary systems display different dynamical behaviors, which is a puzzling phenomenon. In this work, we deduced a theoretical relation between the timescale of stellar pulsation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>pul</mi></msub></semantics></math></inline-formula> and orbital periods <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>orb</mi></msub></semantics></math></inline-formula> of heartbeat stars based on the resonance criteria representing the orbital local low-energy configuration. The theoretical relation shows that when the ratio of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>orb</mi></msub></semantics></math></inline-formula> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>pul</mi></msub></semantics></math></inline-formula> is an integer, the specific orbital period is captured in the resonance state, resulting in resonance locking. The resonance criteria are verified by periodograms of the pulsations and orbits of the two systems KIC 4544587 and KIC 3766353 from observations. KIC 4544587 is an apsidal precession heartbeat star with eight observed resonant frequencies available from observations and has an almost integer ratio of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>P</mi><mi>pul</mi></msub><mo>/</mo><msub><mi>P</mi><mi>orb</mi></msub><mo>=</mo><mn>67.968</mn></mrow></semantics></math></inline-formula>. On the contrary, KIC 3766353 is undergoing the process of orbital shrinkage with only three weak pulsation–orbital resonance frequencies available and shows a non-integer ratio of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>P</mi><mi>pul</mi></msub><mo>/</mo><msub><mi>P</mi><mi>orb</mi></msub><mo>=</mo><mn>83.163</mn></mrow></semantics></math></inline-formula>. Given the results, the theoretical relation is a potential proxy to distinguish between apsidal precession and orbital decay binary systems. Furthermore, we predict that the orbital period of KIC 3766353 will be reduced to 2.492 days, at which time it will be transformed into apsidal precession. |
| first_indexed | 2024-03-08T20:19:11Z |
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| last_indexed | 2024-03-08T20:19:11Z |
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| series | Universe |
| spelling | doaj.art-7aeb1f98dde244a8a944478fc8bd3ded2023-12-22T14:46:38ZengMDPI AGUniverse2218-19972023-12-0191251410.3390/universe9120514Tidal Resonance: A Factor Worth Considering in the Orbital Evolution of Heartbeat StarsJian-Wen Ou0Chen Jiang1Ming Yang2Cong Yu3Dong-Yang Gao4Guangbo Long5School of Intelligent Engineering, Shaoguan University, Shaoguan 512005, ChinaMax-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, GermanyCollege of Surveying and Geo-Informatics, Tongji University, Shanghai 200092, ChinaSchool of Physics and Astronomy, CSST Science Center for the Guangdong-Hongkong-Macau Greater Bay Area, Sun Yat-sen University, Zhuhai 519082, ChinaShandong Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment, Institute of Space Sciences, School of Space Science and Physics, Shandong University, Weihai 264209, ChinaSchool of Intelligent Engineering, Shaoguan University, Shaoguan 512005, ChinaHeartbeat star systems have been reported to exhibit two distinct different orbital dynamic evolution processes: apsidal precession (e.g., KIC 4544587) and orbital decay (e.g., KIC 3766353). While experiencing similar dynamic tidal interactions, these binary systems display different dynamical behaviors, which is a puzzling phenomenon. In this work, we deduced a theoretical relation between the timescale of stellar pulsation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>pul</mi></msub></semantics></math></inline-formula> and orbital periods <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>orb</mi></msub></semantics></math></inline-formula> of heartbeat stars based on the resonance criteria representing the orbital local low-energy configuration. The theoretical relation shows that when the ratio of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>orb</mi></msub></semantics></math></inline-formula> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mi>pul</mi></msub></semantics></math></inline-formula> is an integer, the specific orbital period is captured in the resonance state, resulting in resonance locking. The resonance criteria are verified by periodograms of the pulsations and orbits of the two systems KIC 4544587 and KIC 3766353 from observations. KIC 4544587 is an apsidal precession heartbeat star with eight observed resonant frequencies available from observations and has an almost integer ratio of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>P</mi><mi>pul</mi></msub><mo>/</mo><msub><mi>P</mi><mi>orb</mi></msub><mo>=</mo><mn>67.968</mn></mrow></semantics></math></inline-formula>. On the contrary, KIC 3766353 is undergoing the process of orbital shrinkage with only three weak pulsation–orbital resonance frequencies available and shows a non-integer ratio of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>P</mi><mi>pul</mi></msub><mo>/</mo><msub><mi>P</mi><mi>orb</mi></msub><mo>=</mo><mn>83.163</mn></mrow></semantics></math></inline-formula>. Given the results, the theoretical relation is a potential proxy to distinguish between apsidal precession and orbital decay binary systems. Furthermore, we predict that the orbital period of KIC 3766353 will be reduced to 2.492 days, at which time it will be transformed into apsidal precession.https://www.mdpi.com/2218-1997/9/12/514eclipsing binariesstellar oscillationstidal resonanceKIC 3766353KIC 4544587 |
| spellingShingle | Jian-Wen Ou Chen Jiang Ming Yang Cong Yu Dong-Yang Gao Guangbo Long Tidal Resonance: A Factor Worth Considering in the Orbital Evolution of Heartbeat Stars Universe eclipsing binaries stellar oscillations tidal resonance KIC 3766353 KIC 4544587 |
| title | Tidal Resonance: A Factor Worth Considering in the Orbital Evolution of Heartbeat Stars |
| title_full | Tidal Resonance: A Factor Worth Considering in the Orbital Evolution of Heartbeat Stars |
| title_fullStr | Tidal Resonance: A Factor Worth Considering in the Orbital Evolution of Heartbeat Stars |
| title_full_unstemmed | Tidal Resonance: A Factor Worth Considering in the Orbital Evolution of Heartbeat Stars |
| title_short | Tidal Resonance: A Factor Worth Considering in the Orbital Evolution of Heartbeat Stars |
| title_sort | tidal resonance a factor worth considering in the orbital evolution of heartbeat stars |
| topic | eclipsing binaries stellar oscillations tidal resonance KIC 3766353 KIC 4544587 |
| url | https://www.mdpi.com/2218-1997/9/12/514 |
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