Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHow Close are Compact Multi-Planet Systems to the Stability Limit?
97
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Transit surveys have revealed a significant population of compact multi-planet systems, containing several sub-Neptune-mass planets on close-in, tightly-packed orbits. These systems are thought to have formed through a final phase of giant impacts, which would tend to leave systems close to the edge of stability. Here, we assess this hypothesis, comparing observed eccentricities in systems exhibiting transit-timing variations (TTVs), with the maximum eccentricities compatible with long-term stability. We use the machine-learning classifier SPOCK (Tamayo et al. 2020) to rapidly classify the stability of numerous initial configurations and hence determine these stability limits. While previous studies have argued that multi-planet systems are often maximally packed, in the sense that they could not host any additional planets, we find that the existing planets in these systems have measured eccentricities below the limits allowed by stability by a factor of 2--10. We compare these results against predictions from the giant impact theory of planet formation, derived from both $N$-body integrations and theoretical expectations that in the absence of dissipation, the orbits of such planets should be distributed uniformly throughout the phase space volume allowed by stability. We find that the observed systems have systematically lower eccentricities than this scenario predicts, with a median eccentricity about 4 times lower than predicted. These findings suggest that if such systems formed through giant impacts, then some dissipation must occur to damp their eccentricities. This may take place during formation, perhaps through interactions with the natal gas disk or a leftover population of planetesimals, or over longer timescales through the coupling of tidal and secular processes.
rate research
Read More
Multi-planetary systems are prevalent in our Galaxy. The long-term stability of such systems may be disrupted if a distant inclined companion excites the eccentricity and inclination of the inner planets via the eccentric Kozai-Lidov mechanism. However, the star-planet and the planet-planet interactions can help stabilize the system. Here, we extend the previous stability criterion that considered only the companion-planet and planet-planet interactions by also accounting for short-range forces or effects, specifically, relativistic precession induced by the host star. A general analytical stability criterion is developed for planetary systems with $N$ inner planets and a far-away inclined perturber by comparing precession rates of relevant dynamical effects. Furthermore, we demonstrate as examples that in systems with $2$ and $3$ planets, the analytical criterion is consistent with numerical simulations using a combination of Gausss averaging method and direct N-body integration. This new stability criterion extends the parameter space in which inclined companions of multi-planet systems can inhabit.
The dynamical stability of tightly packed exoplanetary systems remains poorly understood. While for a two-planet system a sharp stability boundary exists, numerical simulations of three and more planet systems show that they can experience instability on timescales up to billions of years. Moreover, an exponential trend between the planet orbital separation measured in units of Hill radii and the survival time has been reported. While these findings have been observed in numerous numerical simulations, little is known of the actual mechanism leading to instability. Contrary to a constant diffusion process, planetary systems seem to remain dynamically quiescent for most of their lifetime before a very short unstable phase. In this work, we show how the slow chaotic diffusion due to the overlap of three-body resonances dominates the timescale leading to the instability for initially coplanar and circular orbits. While the last instability phase is related to scattering due to two-planet mean motion resonances (MMR), for circular orbits the two-planets MMR are too far separated to destabilize systems initially away from them. We develop an analytical model to generalize the empirical trend obtained for equal mass and equally-spaced planets to general systems. We obtain an analytical estimate of the survival time consistent with simulations over four orders of magnitude for the planet to star mass ratio $epsilon$, and 6 to 8 orders of magnitude for the instability time. We also confirm that measuring the orbital spacing in terms of Hill radii is not adapted and that the right spacing unit scales as $epsilon^{1/4}$. We predict that beyond a certain spacing, the three-planet resonances are not overlapped, which results in an increase of the survival time. We finally discuss the extension of our result to more general systems, containing more planets on initially non circular orbits.
The SIM Lite mission will undertake several planet surveys. One of them, the Deep Planet Survey, is designed to detect Earth-mass exoplanets in the habitable zones of nearby main sequence stars. A double blind study has been conducted to assess the capability of SIM to detect such small planets in a multi-planet system where several giant planets might be present. One of the tools which helped in deciding if the detected planets were actual was an orbit integrator using the publicly available HNBody code so that the orbit solutions could be analyzed in terms of temporal stability over many orbits. In this contribution, we describe the implementation of this integrator and analyze the different blind test solutions. We discuss also the usefulness of this method given that some planets might be not detected but still affect the overall stability of the system.
We combine analytical understanding of resonant dynamics in two-planet systems with machine learning techniques to train a model capable of robustly classifying stability in compact multi-planet systems over long timescales of $10^9$ orbits. Our Stability of Planetary Orbital Configurations Klassifier (SPOCK) predicts stability using physically motivated summary statistics measured in integrations of the first $10^4$ orbits, thus achieving speed-ups of up to $10^5$ over full simulations. This computationally opens up the stability constrained characterization of multi-planet systems. Our model, trained on $approx 100,000$ three-planet systems sampled at discrete resonances, generalizes both to a sample spanning a continuous period-ratio range, as well as to a large five-planet sample with qualitatively different configurations to our training dataset. Our approach significantly outperforms previous methods based on systems angular momentum deficit, chaos indicators, and parametrized fits to numerical integrations. We use SPOCK to constrain the free eccentricities between the inner and outer pairs of planets in the Kepler-431 system of three approximately Earth-sized planets to both be below 0.05. Our stability analysis provides significantly stronger eccentricity constraints than currently achievable through either radial velocity or transit duration measurements for small planets, and within a factor of a few of systems that exhibit transit timing variations (TTVs). Given that current exoplanet detection strategies now rarely allow for strong TTV constraints (Hadden et al., 2019), SPOCK enables a powerful complementary method for precisely characterizing compact multi-planet systems. We publicly release SPOCK for community use.
Using a sample of nine massive compact galaxies at z ~ 2.3 with rest-frame optical spectroscopy and comprehensive U through 8um photometry we investigate how assumptions in SED modeling change the stellar mass estimates of these galaxies, and how this affects our interpretation of their size evolution. The SEDs are fit to Tau-models with a range of metallicities, dust laws, as well as different stellar population synthesis codes. These models indicate masses equal to, or slightly smaller than our default masses. The maximum difference is 0.16 dex for each parameter considered, and only 0.18 dex for the most extreme combination of parameters. Two-component populations with a maximally old stellar population superposed with a young component provide reasonable fits to these SEDs using the models of Bruzual & Charlot (2003); however, using models with updated treatment of TP-AGB stars the fits are poorer. The two-component models predict masses that are 0.08 to 0.22 dex larger than the Tau-models. We also test the effect of a bottom-light IMF and find that it would reduce the masses of these galaxies by 0.3 dex. Considering the range of allowable masses from the Tau-models, two-component fits, and IMF, we conclude that on average these galaxies lie below the mass-size relation of galaxies in the local universe by a factor of 3-9, depending on the SED models used.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
