Global Mean-Motion Resonances: Part I—An Exceptional Multiplanetary Resonant Chain in TOI-270 and an Exact Laplace-like Resonance in HD 110067
Super-Earth b and sub-Neptunes c and d are orbiting about the M3.0V dwarf TOI-270 in that order from the star. Their global resonant chain (3:5, 1:1, 2:1) is extremely surprising because planet d appears to be the only known planet occupying the 2:1 resonant orbit without participating in a Laplace...
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2025-04-01
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| author | Dimitris M. Christodoulou Nicholas M. Sorabella Sayantan Bhattacharya Silas G. T. Laycock Demosthenes Kazanas |
| author_facet | Dimitris M. Christodoulou Nicholas M. Sorabella Sayantan Bhattacharya Silas G. T. Laycock Demosthenes Kazanas |
| author_sort | Dimitris M. Christodoulou |
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| description | Super-Earth b and sub-Neptunes c and d are orbiting about the M3.0V dwarf TOI-270 in that order from the star. Their global resonant chain (3:5, 1:1, 2:1) is extremely surprising because planet d appears to be the only known planet occupying the 2:1 resonant orbit without participating in a Laplace resonance (LR) or another planet intervening between the 1:1 and 2:1 orbits as in HD 110067. We do not believe that TOI-270 d is an exception to the empirical rule calling for 2:1 vacancy except in 1:2:4 LRs and Laplace-like 2:3:4 chains. Instead, a LR might exist in this system, and we searched (to no avail) the TESS light curves of TOI-270 for hints of an outer planet that would complete the LR chain. Alternative explanations would be an unknown planet more massive than planet c (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>M</mi><mi mathvariant="normal">c</mi></msub><mo>=</mo><mn>6.20</mn><mspace width="0.0pt"></mspace><msub><mi>M</mi><mo>⊕</mo></msub></mrow></semantics></math></inline-formula>) establishing the actual 1:1 orbit, or planet b residing in the 1:2 Laplace orbit with a period shorter by 0.53 days. However, these possibilities are ruled out by current data. This leaves only one other option to explore: the observed orbits could be in a stable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mstyle scriptlevel="0" displaystyle="true"><mfrac><mn>3</mn><mn>5</mn></mfrac></mstyle></semantics></math></inline-formula>:1:2 resonant chain. Preliminary calculations do not preclude this possibility that should be investigated further by numerical orbit integrations. To this end, we determine two potentially resonant angles, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>φ</mi><mo>^</mo></mover></semantics></math></inline-formula>, related via the Laplace phase <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>φ</mi><mi mathvariant="normal">L</mi></msub></semantics></math></inline-formula> by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mi>φ</mi><mo>^</mo></mover><mo>=</mo><msub><mi>φ</mi><mi mathvariant="normal">L</mi></msub><mo>+</mo><mn>2</mn><mspace width="0.0pt"></mspace><mi>φ</mi></mrow></semantics></math></inline-formula>. In contrast, HD 110067 is shown to have planets d-e-f in a Laplace-like 1:<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mstyle scriptlevel="0" displaystyle="true"><mfrac><mn>3</mn><mn>2</mn></mfrac></mstyle></semantics></math></inline-formula>:2 resonance with phase <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>φ</mi><mo>=</mo><mn>2</mn><msub><mi>φ</mi><mi mathvariant="normal">L</mi></msub></mrow></semantics></math></inline-formula> precisely. |
| format | Article |
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| issn | 2075-4434 |
| language | English |
| publishDate | 2025-04-01 |
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| spelling | doaj-art-e26eff51c7c64a80a2d84cd081bb9b182025-08-20T02:18:03ZengMDPI AGGalaxies2075-44342025-04-011324210.3390/galaxies13020042Global Mean-Motion Resonances: Part I—An Exceptional Multiplanetary Resonant Chain in TOI-270 and an Exact Laplace-like Resonance in HD 110067Dimitris M. Christodoulou0Nicholas M. Sorabella1Sayantan Bhattacharya2Silas G. T. Laycock3Demosthenes Kazanas4Lowell Center for Space Science and Technology, University of Massachusetts Lowell, Lowell, MA 01854, USALowell Center for Space Science and Technology, University of Massachusetts Lowell, Lowell, MA 01854, USALowell Center for Space Science and Technology, University of Massachusetts Lowell, Lowell, MA 01854, USALowell Center for Space Science and Technology, University of Massachusetts Lowell, Lowell, MA 01854, USANASA Goddard Space Flight Center, Astrophysics Science Division, Code 663, Greenbelt, MD 20771, USASuper-Earth b and sub-Neptunes c and d are orbiting about the M3.0V dwarf TOI-270 in that order from the star. Their global resonant chain (3:5, 1:1, 2:1) is extremely surprising because planet d appears to be the only known planet occupying the 2:1 resonant orbit without participating in a Laplace resonance (LR) or another planet intervening between the 1:1 and 2:1 orbits as in HD 110067. We do not believe that TOI-270 d is an exception to the empirical rule calling for 2:1 vacancy except in 1:2:4 LRs and Laplace-like 2:3:4 chains. Instead, a LR might exist in this system, and we searched (to no avail) the TESS light curves of TOI-270 for hints of an outer planet that would complete the LR chain. Alternative explanations would be an unknown planet more massive than planet c (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>M</mi><mi mathvariant="normal">c</mi></msub><mo>=</mo><mn>6.20</mn><mspace width="0.0pt"></mspace><msub><mi>M</mi><mo>⊕</mo></msub></mrow></semantics></math></inline-formula>) establishing the actual 1:1 orbit, or planet b residing in the 1:2 Laplace orbit with a period shorter by 0.53 days. However, these possibilities are ruled out by current data. This leaves only one other option to explore: the observed orbits could be in a stable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mstyle scriptlevel="0" displaystyle="true"><mfrac><mn>3</mn><mn>5</mn></mfrac></mstyle></semantics></math></inline-formula>:1:2 resonant chain. Preliminary calculations do not preclude this possibility that should be investigated further by numerical orbit integrations. To this end, we determine two potentially resonant angles, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>φ</mi><mo>^</mo></mover></semantics></math></inline-formula>, related via the Laplace phase <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>φ</mi><mi mathvariant="normal">L</mi></msub></semantics></math></inline-formula> by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mi>φ</mi><mo>^</mo></mover><mo>=</mo><msub><mi>φ</mi><mi mathvariant="normal">L</mi></msub><mo>+</mo><mn>2</mn><mspace width="0.0pt"></mspace><mi>φ</mi></mrow></semantics></math></inline-formula>. In contrast, HD 110067 is shown to have planets d-e-f in a Laplace-like 1:<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mstyle scriptlevel="0" displaystyle="true"><mfrac><mn>3</mn><mn>2</mn></mfrac></mstyle></semantics></math></inline-formula>:2 resonance with phase <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>φ</mi><mo>=</mo><mn>2</mn><msub><mi>φ</mi><mi mathvariant="normal">L</mi></msub></mrow></semantics></math></inline-formula> precisely.https://www.mdpi.com/2075-4434/13/2/42exoplanet dynamicsorbital resonancestidal interaction |
| spellingShingle | Dimitris M. Christodoulou Nicholas M. Sorabella Sayantan Bhattacharya Silas G. T. Laycock Demosthenes Kazanas Global Mean-Motion Resonances: Part I—An Exceptional Multiplanetary Resonant Chain in TOI-270 and an Exact Laplace-like Resonance in HD 110067 Galaxies exoplanet dynamics orbital resonances tidal interaction |
| title | Global Mean-Motion Resonances: Part I—An Exceptional Multiplanetary Resonant Chain in TOI-270 and an Exact Laplace-like Resonance in HD 110067 |
| title_full | Global Mean-Motion Resonances: Part I—An Exceptional Multiplanetary Resonant Chain in TOI-270 and an Exact Laplace-like Resonance in HD 110067 |
| title_fullStr | Global Mean-Motion Resonances: Part I—An Exceptional Multiplanetary Resonant Chain in TOI-270 and an Exact Laplace-like Resonance in HD 110067 |
| title_full_unstemmed | Global Mean-Motion Resonances: Part I—An Exceptional Multiplanetary Resonant Chain in TOI-270 and an Exact Laplace-like Resonance in HD 110067 |
| title_short | Global Mean-Motion Resonances: Part I—An Exceptional Multiplanetary Resonant Chain in TOI-270 and an Exact Laplace-like Resonance in HD 110067 |
| title_sort | global mean motion resonances part i an exceptional multiplanetary resonant chain in toi 270 and an exact laplace like resonance in hd 110067 |
| topic | exoplanet dynamics orbital resonances tidal interaction |
| url | https://www.mdpi.com/2075-4434/13/2/42 |
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