My research focuses on the orbital dynamics of multi-body systems, such as binary and triple stars and exoplanet systems. In particular I am studying systems for which the eccentric Kozai-Lidov (EKL) mechanism comes into play. This dynamical effect occurs in hierarchical three-body systems, where two bodies are orbited by a distant third body. In this case the system is stable in the long term, but the eccentricities and inclinations of the orbits can change over time due to the gravitational perturbations from the third body. This can have interesting effects, such as, for example, stellar or planetary collisions or the formation of retrograde orbits (see Naoz 2016 for a full explanation).
I personally am especially interested in the effects that stellar evolution has on the dynamical evolution of these systems. As stars age, they expand and lose mass, becoming red giants, and, depending on their initial mass, end as supernovae, black holes, neutron stars, or white dwarfs, among other possibilities. This can have important effects on these systems by changing the orbital parameters, or, for example, the strength of tides. I have worked to implement these effects into models of the EKL mechanism.
Hierarchical three-body dynamics has been used as a possible explanation for so-called "Hot Jupiters", giant gas planets that orbit their host stars on short-period orbits (P<10 days), and which are heated to very high temperatures due the close proximity to the star. In this scenario, a giant planet initially orbits its star initially on a wider orbit, but a companion star or second large planet leads to EKL excitations of the gas giant's orbital eccentricity. As the planet gets closer to the star for part of its orbit, tidal effects become stronger and shrink and circularize the gas giant's orbit, turning it into a Hot Jupiter. However, another way to enhance the strength of tidal effects is to expand the star, such as when it becomes a Red Giant towards the end of its life. I therefore lead a project that investigated the significance of stellar evolution for Hot Jupiter formation in the case of A-type host stars. A-type main-sequence stars have masses about 1.6 to 2.4 times the mass of our Sun and evolve on timescales of about 1 Gyr,
much faster than sunlike stars. They also nearly always possess stellar companions, leading to EKL effects for any planets orbiting either planet. We found that the enhanced tidal effects during the Red Giant phase of the stars can lead to the formation of "Temporary Hot Jupiters", Hot Jupiters that only exist for a few hundred thousand years before they become engulfed by their evolving host star. Overall we found that A-type stars would destroy about 70 % of all gas giant planets orbiting them, by turning them into Hot Jupiters or Temporary Hot Jupiters and subsequently engulfing them. Our work was published in A.P. Stephan, S. Naoz, B.S. Gaudi, 2018, A-type Stars, the Destroyers of Worlds: The Lives and Deaths of Jupiters in Evolving Stellar Binaries, AJ, Vol. 156, Issue 3, article id. 128, 12 pp., doi: 10.3847/1538-3881/aad6e5 and has been featured as a Nature Research Highlight.
Some of my previous work has been concerned with the pollution of white dwarfs in evolving wide binary star systems. Over recent decades many studies have revealed that about a quarter to a half of all white dwarf stars, the last life-stage of most stars, contain heavy elements in their atmosphere. However, these elements are expected to sink to the core of the star over short time-scales, indicating that they have been recently polluted by planetary or asteroidal material. In our work, published in A.P. Stephan, S. Naoz, B. Zuckerman, 2017, Throwing Icebergs at White Dwarfs, ApJL, Vol. 844, L16, doi: 10.3847/2041-8213/aa7cf3, we show that some of these white dwarfs can be polluted by planets that orbited far from the star during the main sequence, if they have a stellar companion on a very distant orbit. This is
due to the mass loss that a star undergoes during its evolution, which changes the orbital configuration of the systems and allows the EKL mechanism to become stronger. Thus, objects that did not get destroyed during the main sequence might instead end up coming close to the white dwarf, potentially polluting it. This work perfectly explains recent observations by Xu et al. 2017 that have for the first time found nitrogen pollution in a white dwarf. In our own solar system nitrogen is only abundant in the Kuiper belt, as it is a volatile element. In fact, Earth's atmospheric nitrogen probably came from a Kuiper belt asteroid. The white dwarf in Xu et al. is also part of an extremely wide binary star system, and was therefore most likely polluted by such a Kuiper belt analog object through the EKL mechanism. Our work has also been featured by AAS Nova and Physics Today.
My Master Thesis project, in collaboration with the UCLA Galactic Center Group, studied the EKL mechanism in the context of binary stars that are orbiting the massive black hole at the center of the Milky Way. For these systems we included the effects of general relativity, tides, and stellar evolution into our calculations, in order to accurately model the possibility of binary mergers in the galactic center. We see a binary merger as a good candidate to explain the G2 object that has been discovered by Gillessen et al. (2012). Our findings were published in:
A.P. Stephan, S. Naoz, A.M. Ghez et al., 2016, Merging Binaries in the Galactic Center: The eccentric Kozai-Lidov mechanism with stellar evolution, MNRAS, Vol. 460, 3494-3504, doi: 10.1093/mnras/stw1220
The EKL mechanism, including tides and stellar evolution, can be used to study a large variety of different astronomical systems. A project I have been part of was a study by my adviser, Prof. Smadar Naoz, investigating the formation of low-mass X-ray (LMXR) binaries through the EKL perturbations by a third companion. For this study the inclusion of stellar evolution effects, which I assisted with, was of crucial importance. The study was recently published by ApJ Letters:
S. Naoz, T. Fragos, A. Geller, A.P. Stephan, and F.A. Rasio, 2016, Formation of Black Hole Low-Mass X-Ray Binaries in Hierarchical Triple Systems, ApJ, 822, L24, doi: 10.3847/2041-8205/822/2/L24
Another study I have been involved with was concerned with the stability of multi-planet systems in the presence of an outer companion. In particular, the project considered two planets orbiting a star in a co-planar configuration that are being perturbed by an outer, inclined fourth body, and showed for what configurations such an ensemble would be stable or unstable.. The project was lead by a former undergraduate mentee of my adviser, Paul Denham, and is currently under review for publication. The arXiv version can be found here: P. Denham, S. Naoz, B.-M. Hoang, A.P. Stephan, W.M. Farr, 2018, Hidden Planetary Friends: On the Stability Of 2-Planet Systems in the Presence of a Distant, Inclined Companion, arXiv:1802.00447
When comparing the results of my recent binary mergers paper to observations in the galactic center, one problem that arises is the fact that only very massive stars can be observed, since smaller stars are usually not bright enough to be detected. However, my work did not focus on this stellar population, and can therefore only make very limited predictions on the effect of mergers on the high-mass stellar population. I plan to study this population in one of my next projects, which will also require us to expand the models we are using by including the effects of asymmetric mass loss and supernova kicks. This is currently in development, together with Prof. Smadar Naoz and one of her undergraduate mentees, Cicero Lu.
Another topic I have been interested in is the study of exoplanet system dynamics, especially in the context of evolving stars. I am currently developing a project to study some of the aspects of these systems.
During my time at the University of Chicago I had the great opportunity to work with Prof. James W. Truran and Michael Florian on problems concerning the chemical evolution of galaxies and dwarf galaxies. While I am not currently working on chemical evolution problems, I continue to be interested in these systems. In particular I wish to further explore the role of galaxy dynamics in these circumstances, at some point.
I also had the great fortune to have had Prof. Michael D. Gladders as my bachelor thesis adviser. The project for my bachelor thesis was concerned with strong gravitationally lensing galaxy clusters and the relation between the brightest cluster galaxy (BCG) mass and the strength of the lens. This was an extraordinarily fascinating project, exploring the structure of galaxy clusters with general relativity.