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: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-04-01
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| Series: | Galaxies |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-4434/13/2/42 |
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| Summary: | 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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| ISSN: | 2075-4434 |