Self-consistent Spin, Tidal, and Dynamical Equations of Motion in the REBOUNDx Framework

The Astrophysical Journal · 2023 · 31 citations

• Physics
• Classical mechanics
• Statistical physics

Abstract We introduce self-consistent spin, tidal, and dynamical equations of motion into REBOUNDx , a library of additional effects for the popular N -body integrator REBOUND . The equations of motion used are derived from the constant time lag approximation to the equilibrium tide model of tidal friction. These effects will allow the study of a variety of systems of which the full dynamical picture cannot be encapsulated by point particle dynamics. We provide several test cases and benchmark the code’s performance against analytic predictions. The open-source code is available in the most recent release of REBOUNDx .

The Warm Neptune GJ 3470b Has a Polar Orbit

The Astrophysical Journal Letters · 2022 · 77 citations

• Computer Science
• Algorithm
• Geology

Abstract The warm Neptune GJ 3470b transits a nearby ( d = 29 pc) bright slowly rotating M1.5-dwarf star. Using spectroscopic observations during two transits with the newly commissioned NEID spectrometer on the WIYN 3.5 m Telescope at Kitt Peak Observatory, we model the classical Rossiter–McLaughlin effect, yielding a sky-projected obliquity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>λ</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>98</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>12</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>15</mml:mn> <mml:mspace width="0.33em"/> <mml:mo>◦</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> and a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>v</mml:mi> <mml:mi>sin</mml:mi> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>0.85</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.33</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.27</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:mi>km</mml:mi> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> . Leveraging information about the rotation period and size of the host star, our analysis yields a true obliquity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>ψ</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>95</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>8</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>9</mml:mn> <mml:mspace width="0.33em"/> <mml:mo>◦</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> , revealing that GJ 3470b is on a polar orbit. Using radial velocities from HIRES, HARPS, and the Habitable-zone Planet Finder, we show that the data are compatible with a long-term radial velocity (RV) slope of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mn>0.0022</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.0011</mml:mn> <mml:mspace width="0.25em"/> <mml:mi mathvariant="normal">m</mml:mi> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi>day</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> over a baseline of 12.9 yr. If the RV slope is due to acceleration from another companion in the system, we show that such a companion is capable of explaining the polar and mildly eccentric orbit of GJ 3470b using two different secular excitation models. The existence of an outer companion can be further constrained with additional RV observations, Gaia astrometry, and future high-contrast imaging observations. Lastly, we show that tidal heating from GJ 3470b’s mild eccentricity has most likely inflated the radius of GJ 3470b by a factor of ∼1.5–1.7, which could help account for its evaporating atmosphere.