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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Main Authors: Dimitris M. Christodoulou, Nicholas M. Sorabella, Sayantan Bhattacharya, Silas G. T. Laycock, Demosthenes Kazanas
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Galaxies
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Online Access:https://www.mdpi.com/2075-4434/13/2/42
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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
collection DOAJ
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.
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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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