RECENT RESEARCH
(Exo)Moons
Circumbinary Planets
Circumstellar Planets
Solar System Dynamics
Exoplanet Dynamics
Moon Packing Around an Earth-mass Planet
The Earth has only one large natural satellite that we call the Moon, where the giant planets have several that span a range of sizes
and masses. In exoplanetary systems, we find that planets form in multiples that can be tightly packed near mean motion resonances. A similar structure appears within the Saturnian moon system, where it appears possible for multiples moons to form around an extrasolar Earth-mass planet. This work seeks to answer the following questions:
-
What is the size and/or mass limit to the number of moons that can stably orbit an Earth-mass planet?
-
Does outward tidal migration affect the possible number of moons?
Find the full paper here.
An exomoon survey of 70 cool giant exoplanets and the new candidate Kepler-1708 b-i
The search for exomoons (i.e., natural satellites of extrasolar planets) has been underway for about a decade, where David Kipping at Columbia University has led the charge. Due to observational biases and/or constraints, the search for exomoons has focused primarily on giant exoplanets. Early searches have not revealed any viable exomoon candidates when the host exoplanet orbits close to its host star. As a result, Kipping and his team survey a sample of giant exoplanets with large orbital periods (>1 year) from the Kepler Mission. The motivation and main results of the study are summarized by Kipping himself in the following video.
Find the full paper here.
Exomoons in Systems with a Strong Perturber: Applications to α Cen AB
Most exoplanet searches are limited to single stars, however a significant number of Sun-like stars in the Milky Way actually have stellar companions and the pair of stars orbit each other. The α Cen AB stellar binary is only ~4 light years from us, which makes it an appropriate test system to determine the viability of exoplanets hosting moons in binary star systems. Due to the possibly more turbulent formation environment, the host exoplanets may actually orbit in retrograde (i.e., in a direction opposite to the host binary). These considerations lead us to the following science questions:
-
What is the conservative stability limit for retrograde satellites?
-
How does the stellar perturbation affect the stability limit for both prograde and retrograde satellites?
-
Does outward tidal migration also affect the prospects of finding moons in similar systems?
-
What is the observational constraints (e.g., TTVs) for exomoons in binary systems?
Find the full paper here.
Orbital Stability of Circumstellar Planets in Binary Systems
The maximum orbital distance (or stability limit) of circumstellar planets (planets that orbit only one star of a binary) depends on observable parameters (masses & eccentricity) of the host binary. The TESS mission (launched Apr 18 2018) is expected to observe ~500,00 binary stars. By knowing the stability limit, we can better search the TESS data for planets in binaries. This work seeks to answer the following questions:
-
What is the stability limit for circumstellar planets with circular or eccentric binaries?
-
How do does the assumed mutual inclination of the planet change the stability limit?
-
Can orbital stability constraints tell us more about a TESS triple system, LTT 1445ABC?
The first figure shows the orbit (in a rotated frame) of a circumstellar planet that begins at 1/3 of the binary period at two different mutual inclinations (0 & 85 deg.). The gray region is a forbidden for the planet and the binary's orbit is circular. The associated panels on the right illustrate how the resonant angle changes over time for this initial condition. The second figure shows how the stability limit (color-coded) varies with the stellar binary parameters and the mutual inclination. The data used to make these figures can be found on GitHub.com and Zenodo.org.
Find the full paper here. Check out the GitHub repository here.
 |  |
|---|
Obliquity Evolution of Circumstellar Planets in Sun-like Stellar Binaries
Nearly half of Sun-like stars are actually part of a stellar binary, where the most common companion stars have large, eccentric orbits. Gravitational forcing from the secondary star can alter the orbits of planets in residence about the primary and the forcing can be large enough to strip the planets from their host star transforming them into rogue planets. Earth-like planets in the habitable zone of their host star can experience milder forcing on their orbits, but the axial tilt, or obliquity, could be changed dramatically. This work seeks to answer the following questions:
-
How sensitive are the changes in obliquity for an Earth-like planet in α Centauri AB?
-
Can planetary neighbors and/or moons mitigate the effects on obliquity variation in α Centauri AB?
-
How common are Earth-like obliquity variations among a more general set of Sun-like stellar binaries?
The figure shows the obliquity variation (color-coded) for an Earth-like planet in α Centauri A (a), α Centauri B (b), or the Solar System (c) for comparison. The cells vary the initial rotation (α) and tilt (ε) of the planet. The hatched region marks where Earth-like variations can occur. Variations shown in panel (a) are usually mild, while the variations in panel (b) are more substantial. The arrows denote Earth-like initial conditions with (top) and without (bottom) a large moon. For the Solar System (c), a large moon reduces (stabilizes) the obliquity variation, where the opposite occurs for an Earth-like planet orbiting α Centauri B (b).
Find the full paper here, a press release here, and an explainer article here.
Could There Be an Undetected Inner Planet Near the Stability Limit in Kepler-1647?
Kepler-1647b is a circumbinary planet (CBP) that was discovered using the chance alignment where multiple transits occur during a single conjunction. This is a unique event that allowed for the confirmation of a Jupiter-like world with an astonishingly long orbital period (~1100 days). As a result, there is a lot of space, dynamically, for another planet to occupy between the binary orbit and the outer gas giant. This work seeks to answer the following questions:
-
What is the probability for an inner planet stably exist and not transit?
-
How would the existence of a planet affect the observations of the outer planet and/or the binary eclipses?
-
Can we place mass constraints on such a planet at the stability limit through using the current observations?
The figure shows the probability that a planet would not have been observed within the 4 years of the Kepler data at the stability limit (a_crit), the average semimajor axis of the other Kepler CBPs (a_aver), or at 2x the stability limit. The probability changes whether we assume a 5 min or 24 min cadence of the data, but we can rule out planets larger than 30x the mass of the Earth because they would have produced a detectable signal.
Find the full paper here.
Instabilities in the Early Solar System Due to a Self-gravitating Disk
The discovery of exoplanets have shown that giant planets can change their orbits relative to where they formed in the protoplanetary disk. The Nice model posits that the Solar System was not very different where the orbits of our giant planets initially began much closer together and an outer disk of small bodies triggered an instability that has sculpted the rest of the Solar System. We investigate under what conditions such instabilities can occur using a more consistent approach with GENGA, an N-body software that utilizes GPUs. This work seeks to answer the following questions:
-
Can a set of giant planets remain static for ~500 million years with a planetesimal disk?
-
Does the gap between the disk and the outermost giant planets affect the instability time?
-
Can we match the properties of the current Solar System with 5 giant planets?
The video illustrates the evolution of the 5 giant planets (black dots) and a massive (20 Earth masses) disk of planetesimals over 50 million years. Each point marks the osculating eccentricity and semimajor axis of a particle. An instability occurs after ~30 Myr (40 sec) leaving a mass distribution similar to the Solar System.
Find the full paper here.
Stability Limits of Circumbinary Planets: Is There a Pile-up in the Kepler CBPs?
The minimum orbital distance of circumbinary planets (CBPs) depends on observable parameters (masses & eccentricity) of the host binary. The TESS mission (launched Apr 18 2018) is expected to observe ~500,00 binary stars. By knowing the smallest orbit or shortest orbital period, we can better search the TESS data for CBPs. This work seeks to answer the following questions:
-
What is the smallest semimajor axis ratio that can a CBP have ?
-
How do mean motion resonances change this minimal semimajor axis ratio?
-
Do the Kepler CBPs cluster near this minimal value?
The first figure shows the minimum semimajor axis ratio, a_c, for a range of binary host star parameters and highlights where the Kepler CBPs lie in this parameter space (identified by the host star number). The second figure shows how the stable parameters space varies over a range of values and how the maximum eccentricity (color scale) of the planet changes. The data used to make these figures can be found on GitHub.com and Zenodo.org.
Find the full paper here. Check out the GitHub repository here.
 |  |
|---|
Planet Packing in the α Centauri System
This paper explores the number of planets that could stably orbit around each star in α Centauri AB for the lifetime of the system. By knowing how many planets can orbit around each star, we can better address the number of planets per star. This work seeks to answer the following questions:
-
How many Earth-like planets can orbit within the habitable zone of each star?
-
What are the dynamical spacings between the planets?
-
Can the number increase if the planets have mutually aligned eccentricity vectors?
The figures show how the system lifetimes (log t) vary with a spacing parameter (β) over the lifetime of the system (~5-6 billion years). Starting from orbits aligned with the forced eccentricity due to the secondary star allows for additional planets in the system. The semimajor axis of the first planet of each system begins at the inner edge of the empirical (black) and conservative (red) habitable zones.
Find the full paper here.
 |  |  |
|---|---|---|
 |
Long Term Stability in the α Centauri System. II: Forced Eccentricities
The forced eccentricity imposed by the secondary star affects the orbital evolution of planets near the stability limit in the α Centauri AB system. Studying the stability limit for planets in binary systems is important for interpreting future observations. If a planet is discovered near the stability limit in α Centauri, it can affect how we understand the process of planet formation in binaries, which make up ~40% of all stars. This work seeks to answer the following questions:
-
How can the stability of Earth-like planets be extended through a mutually aligned eccentricity vector?
-
What is the difference in stability if we assume initially prograde or retrograde orbits?
The figures demonstrate how eccentricity variation can be minimized by starting the planet near the forced eccentricity of the binary system. The planetary orbit needs to be aligned (∆ varpi ~ 0 deg.) for prograde and anti-aligned (∆ varpi ~ 180 deg.) for retrograde.
Find the full paper here.
 |  |
|---|---|
 |
TRAPPIST-1 -- A 7 planet system only 40 light years away.
This paper explores the possible compositions of the TRAPPIST-1 planets through the lens of orbital stability. Long-term orbital solutions tell us the most likely orbital parameters because the system is old, but also can narrow the range of planetary parameters. This work seeks to answer the following questions:
-
How close to Earth-like can we claim for these planets?
-
What are the dynamical spacings between the planets?
-
How does the TRAPPIST-1 system compare with other known systems of multiple planets?
The figure shows a top-down view of the TRAPPIST-1 system with orbits drawn from numerical simulations that are stable on a million year timescale. The dispersion of the orbits further elucidates the need for continued observation to better understand the system.
Find the full paper here.
Early Venus Obliquity Evolution
Venus has a long history that has been masked by interactions with its atmosphere, within its interior, and tidal interactions with the Sun. My colleagues and I investigate the possible obliquity, or axial tilt, of hypothetical Venus-like planets that have yet undergone the radical changes of our sister planet. The evolution of the axial tilt of Earth-like worlds is important to increase our understanding of the general aspects of planet habitability. Some of the questions we seek to answer are:
-
How do fast do obliquity variations occur in our Solar System?
-
Can we estimate changes in obliquity for exoplanets?
-
What does the speed of a changing obliquity mean for habitability?
The figure shows the variations of a hypothetical (thin atmosphere) Venus with an Earth-like tilt in prograde (bottom) and retrograde (top) rotations considering a range of initial rotation periods.
Find the full paper here.
 |
|---|
 |
 |
 |
Long-term Stability of Planets in the α Centauri System
The closest Sunlike stars to the Earth are only ~4 light years away in a triple star system, where the 2 more massive stars orbit each other as a binary (α Cen AB). As a result, any Earthlike planets in residence around α Cen AB will experience periodic "tugs" from the secondary star that may alter or disrupt its orbit. I investigate how strong Earth-like planets respond to these tugs on billion year timescales. Some of the questions we seek to answer are:
-
How does the initial mutual inclination between the binary and planet affect the stability of Earthlike planets?
-
How does the initial planetary eccentricity affect the stability of Earthlike planets?
-
What area of the sky could Earthlike planets occupy?
The figures show how test particles initially in orbit around α Cen A respond to the forcing by α Cen B at different inclinations and eccentricities. Additionally the coplanar stable particles are plotted on the sky plane and the final figure shows the lifetimes of circumbinary test particles around α Cen AB. Find the full paper here.
Selected Proposals
-
Debris Disk Morphology due to Stellar Encounters
-
Role: Co-Investigator
-
Program: NASA Astrophysics Theory
-
Term: 2020 -- 2022
-
-
Where to Search for Habitable Worlds
-
Role: Co-Investigator
-
Term: 2019 -- 2021
-
-
Tidal Obliquity Variations of Potentially Habitable Planets
-
Role: Co-Investigator
-
Program: NASA Habitable Worlds
-
Term: 2019 -- 2020
-
-
Warm, Large Exoplanets
-
Role: Co-Investigator
-
Program: NASA Exoplanets Research
-
Term: 2016 -- 2019
-
-
Comprehensive Analyses of Comet Siding Spring, Before, During and After Its Mars Encounter
-
Role: Collaborator
-
Program: NASA Solar System Workings
-
Term: 2016 -- 2019
-
-
Obliquity Stability of Potentially Habitable Worlds
-
Role: Postdoctoral Associate
-
Program: NASA Exobiology
-
Term: 2014 -- 2017
-
-
Eclipsing Binary Stars: Indispensable Astrophysical Laboratories for Studying Stellar Populations
-
Role: Postdoctoral Associate
-
Program: NASA K2 Guest Observer
-
Term: 2015 - Observing Campaigns 4 & 5
-
-
Rotation Period of the Mars Flyby Comet C/2013 A1 (Siding Spring)
-
Role: Postdoctoral Associate
-
Program: NASA K2 Guest Observer
-
Term: 2014 - Observing Campaign 2
-
