MESA inlist and run_star_extras associated with Li & Loeb (2013). MESA version 4298. Publication ... more MESA inlist and run_star_extras associated with Li & Loeb (2013). MESA version 4298. Publication DOI: 10.1093/mnras/sts567
The secular dynamical evolution of a hierarchical three body system, in which a distant third obj... more The secular dynamical evolution of a hierarchical three body system, in which a distant third object orbits around a binary has been studied extensively, demonstrating that the inner orbit can undergo large eccentricity and inclination oscillations. It was shown before that starting with a circular inner orbit, large mutual inclination (40 ◦ − 140◦) can produce long timescale modulations that drive the eccentricity to extremely large value and can flip the orbit. Here, we demonstrate that starting with an almost coplanar configuration, for eccentric inner and outer orbits, the eccentricity of the inner orbit can still be excited to high values, and the orbit can flip by ∼ 180◦, rolling over its major axis. The ∼ 180 ◦ flip criterion and the flip timescale are described by simple analytic expressions that depend on the initial orbital parameters. With tidal dissipation, this mechanism can produce counter-orbiting exo-planetary systems. In addition, we also show that this mechanism ha...
The treatment of hierarchical triple configurations has proven to be very useful in many astrophy... more The treatment of hierarchical triple configurations has proven to be very useful in many astrophysical contexts, from planetary to triple star system. In the secular approximation the orbits may change shape and orientation. In particular, for highly inclined systems, the Kozai-Lidov mechanism can produce large-amplitude oscillations of the eccentricities. Here we re-derive the secular evolution equations including both quadrupole and octupole orders using Hamiltonian perturbation theory. Our new derivation corrects an error in previous treatments of the secular evolution equations. Our new derivation agrees with the “usual” treatment only in the limit where the outer orbit angular momentum is much larger than the inner one is. Assuming, as done in previous treatments, that the inner z-component angular momentum is conserved, ( √ 1− e2 cos i = const) can produce erroneous results for various astrophysical systems, such as planetary systems and triple stars, where the inner orbit’s a...
Gliese 86 is a nearby K dwarf hosting a giant planet on a ≈16 day orbit and an outer white dwarf ... more Gliese 86 is a nearby K dwarf hosting a giant planet on a ≈16 day orbit and an outer white dwarf companion on a ≈century-long orbit. In this study we combine radial velocity data (including new measurements spanning more than a decade) with high angular resolution imaging and absolute astrometry from Hipparcos and Gaia to measure the current orbits and masses of both companions. We then simulate the evolution of the Gl 86 system to constrain its primordial orbit when both stars were on the main sequence; the closest approach between the two stars was then about 9 au. Such a close separation limited the size of the protoplanetary disk of Gl 86 A and dynamically hindered the formation of the giant planet around it. Our measurements of Gl 86 B and Gl 86 Ab’s orbits reveal Gl 86 as a system in which giant planet formation took place in a disk truncated at ≈2 au. Such a disk would be just big enough to harbor the dust mass and total mass needed to assemble Gl 86 Ab’s core and envelope, a...
HD 106906 is a planetary system that hosts a wide-orbit companion, as well as an eccentric and fl... more HD 106906 is a planetary system that hosts a wide-orbit companion, as well as an eccentric and flat debris disk, which hold important constraints on its formation and subsequent evolution. The recent observations of the companion constrain its orbit to be eccentric and inclined relative to the plane of the debris disk. Here, we show that, in the presence of the inclined companion, the debris disk quickly (≲5 Myr) becomes warped and puffy. This suggests that the current configuration of the system is relatively recent. We explore the possibility that a recent close encounter with a free-floating planet could produce a companion with orbital parameters that agree with observations of HD 106906 b. We find that this scenario is able to recreate the structure of the debris disk while producing a companion in agreement with observation.
Mechanisms have been proposed to enhance the merger rate of stellar-mass black hole binaries, suc... more Mechanisms have been proposed to enhance the merger rate of stellar-mass black hole binaries, such as the Von Zeipel–Lidov–Kozai mechanism (vZLK). However, high inclinations are required in order to greatly excite the eccentricity and to reduce the merger time through vZLK. Here, we propose a novel pathway through which compact binaries could merge due to eccentricity increase in general, including in a near coplanar configuration. Specifically, a compact binary migrating in an active galactic nucleus disk could be captured in an evection resonance, when the precession rate of the binary equals the orbital period around the supermassive black hole. In our study we include precession due to first-order post-Newtonian precession as well as that due to disk around one or both components of the binary. Eccentricity is excited when the binary sweeps through the resonance, which happens only when it migrates on a timescale 10–100 times the libration timescale of the resonance. Libration t...
Having a massive moon has been considered as a primary mechanism for stabilized planetary obliqui... more Having a massive moon has been considered as a primary mechanism for stabilized planetary obliquity, an example of which being our Earth. This is, however, not always consistent with the exoplanetary cases. This article details the discovery of an alternative mechanism, namely that planets orbiting around binary stars tend to have low spin-axis variations. This is because the large quadrupole potential of the stellar binary could speed up the planetary orbital precession, and detune the system out of secular spin-orbit resonances. Consequently, habitable zone planets around the stellar binaries in low inclination orbits hold higher potential for regular seasonal changes comparing to their single star analogues.
Studies of active matter—systems consisting of individuals or ensembles of internally driven and ... more Studies of active matter—systems consisting of individuals or ensembles of internally driven and damped locomotors—are of interest to physicists studying nonequilibrium dynamics, biologists interested in individuals and swarm locomotion, and engineers designing robot controllers. While principles governing active systems on hard ground or within fluids are well studied, another class of systems exists at deformable interfaces. Such environments can display mixes of fluid-like and elastic features, leading to locomotor dynamics that are strongly influenced by the geometry of the surface, which, in itself, can be a dynamical entity. To gain insight into principles by which locomotors are influenced via a deformation field alone (and can influence other locomotors), we study robot locomotion on an elastic membrane, which we propose as a model of active systems on highly deformable interfaces. As our active agent, we use a differential driven wheeled robotic vehicle which drives straigh...
We analyze the process of planetary scattering around M0-type stars. To do this, we carry out N-b... more We analyze the process of planetary scattering around M0-type stars. To do this, we carry out N-body simulations with three Jupiter-mass planets close to their instability limit together with an outer planetesimal disk. This paper focuses on the analysis of systems in which a single Jupiter-mass planet survives after the dynamical instability event. The small body reservoirs show different dynamical behaviors. In fact, our simulations produce particles on prograde and retrograde orbits, as well as particles whose orbital plane flips from prograde to retrograde and back again along their evolution. Such particles are called "Type-F particles". We find strong correlations between the inclination $i$ and the ascending node longitude $\Omega$ of such particles. First, $\Omega$ librates around 90$^{\circ}$ or/and 270$^{\circ}$. This property is very important since it represents a necessary and sufficient condition for the flipping of an orbit. Moreover, the libration periods o...
Systems consisting of spheres rolling on elastic membranes have been used as educational tools to... more Systems consisting of spheres rolling on elastic membranes have been used as educational tools to introduce a core conceptual idea of General Relativity (GR): how curvature guides the movement of matter. However, previous studies have revealed that such schemes cannot accurately represent relativistic dynamics in the laboratory. Dissipative forces cause the initially GR-like dynamics to be transient and consequently restrict experimental study to only the beginnings of trajectories; dominance of Earth's gravity forbids the difference between spatial and temporal spacetime curvatures. Here by developing a mapping between dynamics of a wheeled vehicle on a spandex membrane, we demonstrate that an active object that can prescribe its speed can not only obtain steady-state orbits, but also use the additional parameters such as speed to tune the orbits towards relativistic dynamics. Our mapping demonstrates how activity mixes space and time in a metric, shows how active particles do ...
We consider the long-term tidal heating of a star by the supermassive black hole at the Galactic ... more We consider the long-term tidal heating of a star by the supermassive black hole at the Galactic center, SgrA*. We show that gravitational interaction with background stars leads to a linear growth of the tidal excitation energy with the number of pericenter passages near SgrA*. The accumulated heat deposited by excitation of modes within the star over many pericenter passages can lead to a runaway disruption of the star at a pericenter distance that is 4-5 times farther than the standard tidal disruption radius. The accumulated heating may explain the lack of massive (≳ 10M_) S-stars closer than several tens of AU from SgrA*.
Spin-orbit coupling of planetary systems plays an important role in the dynamics and habitability... more Spin-orbit coupling of planetary systems plays an important role in the dynamics and habitability of planets. However, symplectic integrators that can accurately simulate not only how orbit affects spin but also how spin affects orbit have not been constructed for general systems. Thus, we develop symplectic Lie-group integrators to simulate systems consisting gravitationally interacting rigid bodies. A user friendly package (GRIT) is provided and external forcings such as tidal interactions are also included. As a demonstration, this package is applied to Trappist-I. It shows that the differences in transit timing variations due to spin-orbit coupling could reach a few min in ten year measurements, and strong planetary perturbations can push Trappist-I f, g and h out of the synchronized states.
Ultra-short-period planets (USPs) provide important clues to planetary formation and migration. R... more Ultra-short-period planets (USPs) provide important clues to planetary formation and migration. Recently, it is found that the mutual inclinations of the planetary systems are larger if the inner orbits are closer (≲ 5R_*) and if the planetary period ratios are larger (P_2/P_1 ≳ 5) (Dai et al. 2018). This suggests that the USPs experienced both inclination excitation and orbital shrinkage. Here we investigate the increase in the mutual inclination due to stellar oblateness. We find that the stellar oblateness (within ∼ 1Gyr) is sufficient to enhance the mutual inclination to explain the observed signatures. This suggests that the USPs can migrate closer to the host star in a near coplanar configuration with their planetary companions (e.g., disk migration+tides or in-situ+tides), before mutual inclination gets excited due to stellar oblateness.
The Earth's obliquity is stabilized by the Moon, which facilitates a rapid precession of the ... more The Earth's obliquity is stabilized by the Moon, which facilitates a rapid precession of the Earth's spin-axis, de-tuning the system away from resonance with orbital modulation. It is however, likely that the architecture of the Solar System underwent a dynamical instability-driven transformation, where the primordial configuration was more compact. Hence, the characteristic frequencies associated with orbital perturbations were likely faster in the past, potentially allowing for secular resonant encounters. In this work we examine if at any point in the Earth's evolutionary history, the obliquity varied significantly. Our calculations suggest that even though the orbital perturbations were different, the system nevertheless avoided resonant encounters throughout its evolution. This indicates that the Earth obtained its current obliquity during the formation of the Moon.
We use observed optical to near infrared spectral energy distributions (SEDs) of 266 galaxies in ... more We use observed optical to near infrared spectral energy distributions (SEDs) of 266 galaxies in the COSMOS survey to derive the wavelength dependence of the dust attenuation at high redshift. All of the galaxies have spectroscopic redshifts in the range z = 2 to 6.5. The presence of the CIV absorption feature, indicating that the rest-frame UV-optical SED is dominated by OB stars, is used to select objects for which the intrinsic, unattenuated spectrum has a well-established shape. Comparison of this intrinsic spectrum with the observed broadband photometric SED then permits derivation of the wavelength dependence of the dust attenuation. The derived dust attenuation curve is similar in overall shape to the Calzetti curve for local starburst galaxies. We also see the 2175 \AA~bump feature which is present in the Milky Way and LMC extinction curves but not seen in the Calzetti curve. The bump feature is commonly attributed to graphite or PAHs. No significant dependence is seen with ...
MESA inlist and run_star_extras associated with Li & Loeb (2013). MESA version 4298. Publication ... more MESA inlist and run_star_extras associated with Li & Loeb (2013). MESA version 4298. Publication DOI: 10.1093/mnras/sts567
The secular dynamical evolution of a hierarchical three body system, in which a distant third obj... more The secular dynamical evolution of a hierarchical three body system, in which a distant third object orbits around a binary has been studied extensively, demonstrating that the inner orbit can undergo large eccentricity and inclination oscillations. It was shown before that starting with a circular inner orbit, large mutual inclination (40 ◦ − 140◦) can produce long timescale modulations that drive the eccentricity to extremely large value and can flip the orbit. Here, we demonstrate that starting with an almost coplanar configuration, for eccentric inner and outer orbits, the eccentricity of the inner orbit can still be excited to high values, and the orbit can flip by ∼ 180◦, rolling over its major axis. The ∼ 180 ◦ flip criterion and the flip timescale are described by simple analytic expressions that depend on the initial orbital parameters. With tidal dissipation, this mechanism can produce counter-orbiting exo-planetary systems. In addition, we also show that this mechanism ha...
The treatment of hierarchical triple configurations has proven to be very useful in many astrophy... more The treatment of hierarchical triple configurations has proven to be very useful in many astrophysical contexts, from planetary to triple star system. In the secular approximation the orbits may change shape and orientation. In particular, for highly inclined systems, the Kozai-Lidov mechanism can produce large-amplitude oscillations of the eccentricities. Here we re-derive the secular evolution equations including both quadrupole and octupole orders using Hamiltonian perturbation theory. Our new derivation corrects an error in previous treatments of the secular evolution equations. Our new derivation agrees with the “usual” treatment only in the limit where the outer orbit angular momentum is much larger than the inner one is. Assuming, as done in previous treatments, that the inner z-component angular momentum is conserved, ( √ 1− e2 cos i = const) can produce erroneous results for various astrophysical systems, such as planetary systems and triple stars, where the inner orbit’s a...
Gliese 86 is a nearby K dwarf hosting a giant planet on a ≈16 day orbit and an outer white dwarf ... more Gliese 86 is a nearby K dwarf hosting a giant planet on a ≈16 day orbit and an outer white dwarf companion on a ≈century-long orbit. In this study we combine radial velocity data (including new measurements spanning more than a decade) with high angular resolution imaging and absolute astrometry from Hipparcos and Gaia to measure the current orbits and masses of both companions. We then simulate the evolution of the Gl 86 system to constrain its primordial orbit when both stars were on the main sequence; the closest approach between the two stars was then about 9 au. Such a close separation limited the size of the protoplanetary disk of Gl 86 A and dynamically hindered the formation of the giant planet around it. Our measurements of Gl 86 B and Gl 86 Ab’s orbits reveal Gl 86 as a system in which giant planet formation took place in a disk truncated at ≈2 au. Such a disk would be just big enough to harbor the dust mass and total mass needed to assemble Gl 86 Ab’s core and envelope, a...
HD 106906 is a planetary system that hosts a wide-orbit companion, as well as an eccentric and fl... more HD 106906 is a planetary system that hosts a wide-orbit companion, as well as an eccentric and flat debris disk, which hold important constraints on its formation and subsequent evolution. The recent observations of the companion constrain its orbit to be eccentric and inclined relative to the plane of the debris disk. Here, we show that, in the presence of the inclined companion, the debris disk quickly (≲5 Myr) becomes warped and puffy. This suggests that the current configuration of the system is relatively recent. We explore the possibility that a recent close encounter with a free-floating planet could produce a companion with orbital parameters that agree with observations of HD 106906 b. We find that this scenario is able to recreate the structure of the debris disk while producing a companion in agreement with observation.
Mechanisms have been proposed to enhance the merger rate of stellar-mass black hole binaries, suc... more Mechanisms have been proposed to enhance the merger rate of stellar-mass black hole binaries, such as the Von Zeipel–Lidov–Kozai mechanism (vZLK). However, high inclinations are required in order to greatly excite the eccentricity and to reduce the merger time through vZLK. Here, we propose a novel pathway through which compact binaries could merge due to eccentricity increase in general, including in a near coplanar configuration. Specifically, a compact binary migrating in an active galactic nucleus disk could be captured in an evection resonance, when the precession rate of the binary equals the orbital period around the supermassive black hole. In our study we include precession due to first-order post-Newtonian precession as well as that due to disk around one or both components of the binary. Eccentricity is excited when the binary sweeps through the resonance, which happens only when it migrates on a timescale 10–100 times the libration timescale of the resonance. Libration t...
Having a massive moon has been considered as a primary mechanism for stabilized planetary obliqui... more Having a massive moon has been considered as a primary mechanism for stabilized planetary obliquity, an example of which being our Earth. This is, however, not always consistent with the exoplanetary cases. This article details the discovery of an alternative mechanism, namely that planets orbiting around binary stars tend to have low spin-axis variations. This is because the large quadrupole potential of the stellar binary could speed up the planetary orbital precession, and detune the system out of secular spin-orbit resonances. Consequently, habitable zone planets around the stellar binaries in low inclination orbits hold higher potential for regular seasonal changes comparing to their single star analogues.
Studies of active matter—systems consisting of individuals or ensembles of internally driven and ... more Studies of active matter—systems consisting of individuals or ensembles of internally driven and damped locomotors—are of interest to physicists studying nonequilibrium dynamics, biologists interested in individuals and swarm locomotion, and engineers designing robot controllers. While principles governing active systems on hard ground or within fluids are well studied, another class of systems exists at deformable interfaces. Such environments can display mixes of fluid-like and elastic features, leading to locomotor dynamics that are strongly influenced by the geometry of the surface, which, in itself, can be a dynamical entity. To gain insight into principles by which locomotors are influenced via a deformation field alone (and can influence other locomotors), we study robot locomotion on an elastic membrane, which we propose as a model of active systems on highly deformable interfaces. As our active agent, we use a differential driven wheeled robotic vehicle which drives straigh...
We analyze the process of planetary scattering around M0-type stars. To do this, we carry out N-b... more We analyze the process of planetary scattering around M0-type stars. To do this, we carry out N-body simulations with three Jupiter-mass planets close to their instability limit together with an outer planetesimal disk. This paper focuses on the analysis of systems in which a single Jupiter-mass planet survives after the dynamical instability event. The small body reservoirs show different dynamical behaviors. In fact, our simulations produce particles on prograde and retrograde orbits, as well as particles whose orbital plane flips from prograde to retrograde and back again along their evolution. Such particles are called "Type-F particles". We find strong correlations between the inclination $i$ and the ascending node longitude $\Omega$ of such particles. First, $\Omega$ librates around 90$^{\circ}$ or/and 270$^{\circ}$. This property is very important since it represents a necessary and sufficient condition for the flipping of an orbit. Moreover, the libration periods o...
Systems consisting of spheres rolling on elastic membranes have been used as educational tools to... more Systems consisting of spheres rolling on elastic membranes have been used as educational tools to introduce a core conceptual idea of General Relativity (GR): how curvature guides the movement of matter. However, previous studies have revealed that such schemes cannot accurately represent relativistic dynamics in the laboratory. Dissipative forces cause the initially GR-like dynamics to be transient and consequently restrict experimental study to only the beginnings of trajectories; dominance of Earth's gravity forbids the difference between spatial and temporal spacetime curvatures. Here by developing a mapping between dynamics of a wheeled vehicle on a spandex membrane, we demonstrate that an active object that can prescribe its speed can not only obtain steady-state orbits, but also use the additional parameters such as speed to tune the orbits towards relativistic dynamics. Our mapping demonstrates how activity mixes space and time in a metric, shows how active particles do ...
We consider the long-term tidal heating of a star by the supermassive black hole at the Galactic ... more We consider the long-term tidal heating of a star by the supermassive black hole at the Galactic center, SgrA*. We show that gravitational interaction with background stars leads to a linear growth of the tidal excitation energy with the number of pericenter passages near SgrA*. The accumulated heat deposited by excitation of modes within the star over many pericenter passages can lead to a runaway disruption of the star at a pericenter distance that is 4-5 times farther than the standard tidal disruption radius. The accumulated heating may explain the lack of massive (≳ 10M_) S-stars closer than several tens of AU from SgrA*.
Spin-orbit coupling of planetary systems plays an important role in the dynamics and habitability... more Spin-orbit coupling of planetary systems plays an important role in the dynamics and habitability of planets. However, symplectic integrators that can accurately simulate not only how orbit affects spin but also how spin affects orbit have not been constructed for general systems. Thus, we develop symplectic Lie-group integrators to simulate systems consisting gravitationally interacting rigid bodies. A user friendly package (GRIT) is provided and external forcings such as tidal interactions are also included. As a demonstration, this package is applied to Trappist-I. It shows that the differences in transit timing variations due to spin-orbit coupling could reach a few min in ten year measurements, and strong planetary perturbations can push Trappist-I f, g and h out of the synchronized states.
Ultra-short-period planets (USPs) provide important clues to planetary formation and migration. R... more Ultra-short-period planets (USPs) provide important clues to planetary formation and migration. Recently, it is found that the mutual inclinations of the planetary systems are larger if the inner orbits are closer (≲ 5R_*) and if the planetary period ratios are larger (P_2/P_1 ≳ 5) (Dai et al. 2018). This suggests that the USPs experienced both inclination excitation and orbital shrinkage. Here we investigate the increase in the mutual inclination due to stellar oblateness. We find that the stellar oblateness (within ∼ 1Gyr) is sufficient to enhance the mutual inclination to explain the observed signatures. This suggests that the USPs can migrate closer to the host star in a near coplanar configuration with their planetary companions (e.g., disk migration+tides or in-situ+tides), before mutual inclination gets excited due to stellar oblateness.
The Earth's obliquity is stabilized by the Moon, which facilitates a rapid precession of the ... more The Earth's obliquity is stabilized by the Moon, which facilitates a rapid precession of the Earth's spin-axis, de-tuning the system away from resonance with orbital modulation. It is however, likely that the architecture of the Solar System underwent a dynamical instability-driven transformation, where the primordial configuration was more compact. Hence, the characteristic frequencies associated with orbital perturbations were likely faster in the past, potentially allowing for secular resonant encounters. In this work we examine if at any point in the Earth's evolutionary history, the obliquity varied significantly. Our calculations suggest that even though the orbital perturbations were different, the system nevertheless avoided resonant encounters throughout its evolution. This indicates that the Earth obtained its current obliquity during the formation of the Moon.
We use observed optical to near infrared spectral energy distributions (SEDs) of 266 galaxies in ... more We use observed optical to near infrared spectral energy distributions (SEDs) of 266 galaxies in the COSMOS survey to derive the wavelength dependence of the dust attenuation at high redshift. All of the galaxies have spectroscopic redshifts in the range z = 2 to 6.5. The presence of the CIV absorption feature, indicating that the rest-frame UV-optical SED is dominated by OB stars, is used to select objects for which the intrinsic, unattenuated spectrum has a well-established shape. Comparison of this intrinsic spectrum with the observed broadband photometric SED then permits derivation of the wavelength dependence of the dust attenuation. The derived dust attenuation curve is similar in overall shape to the Calzetti curve for local starburst galaxies. We also see the 2175 \AA~bump feature which is present in the Milky Way and LMC extinction curves but not seen in the Calzetti curve. The bump feature is commonly attributed to graphite or PAHs. No significant dependence is seen with ...
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