Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTidal heating in multilayer planets: Application to the TRAPPIST-1 system
75
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
TRAPPIST-1 (Gillon et al. 2017) is an extremely compact planetary system: seven earth-sized planets orbit at distances lower than 0.07 AU around one of the smallest M-dwarf known in the close neighborhood of the Sun (with a mass of less than 0.09 $M_odot$). With 3 planets within the classical habitable zone, this system represents an interesting observational target for future instruments such as the JWST (e.g. Barstow & Irwin 2016). As the planets are close-in, tidal interactions play a crucial role in the evolution of the system by controlling both orbital configurations and rotational states of the planets. For the closest planets, the associated tidal dissipation could have an influence on their internal evolution and potentially on their climate and habitability Turbet et al. (2018). Following (Tobie et al. 2005), we build multilayer models of the internal structure of the TRAPPIST-1 planets accounting for the mass and radius of Grimm et al. (2018), then we compute the tidal response and estimate the tidal heat flux of each planet as well as the profile of tidal heating with depth. Finally, we compare our results to the homogeneous model of Efroimsky (2012) and assess the impact heating rate on the thermal state of each layer of the planet.
rate research
Read More
We perform numerical simulations of the TRAPPIST-1 system of seven exoplanets orbiting a nearby M dwarf, starting with a previously suggested stable configuration. The long-term stability of this configuration is confirmed, but the motion of planets is found to be chaotic. The eccentricity values are found to vary within finite ranges. The rates of tidal dissipation and tidal evolution of orbits are estimated, assuming an Earth-like rheology for the planets. We find that under this assumption the planets b, d, e were captured in the 3:2 or higher spin-orbit resonances during the initial spin-down but slipped further down into the 1:1 resonance. Dependent on its rheology, the innermost planet b may be captured in a stable pseudosynchronous rotation. Non-synchronous rotation ensures higher levels of tidal dissipation and internal heating. The positive feedback between the viscosity and the dissipation rate -- and the ensuing runaway heating -- are terminated by a few self-regulation processes. When the temperature is high and the viscosity is low enough, the planet spontaneously leaves the 3:2 resonance. Further heating is stopped either by passing the peak dissipation or by the emergence of partial melt in the mantle. In the post-solidus state, the tidal dissipation is limited to the levels supported by the heat transfer efficiency. The tides on the host star are unlikely to have had a significant dynamical impact. The tides on the synchronized inner planets tend to reduce these planets orbital eccentricity, possibly contributing thereby to the systems stability.
We study the dynamical evolution of the TRAPPIST-1 system under the influence of orbital circularization through tidal interaction with the central star. We find that systems with parameters close to the observed one evolve into a state where consecutive planets are linked by first order resonances and consecutive triples, apart from planets c, d and e, by connected three body Laplace resonances. The system expands with period ratios increasing and mean eccentricities decreasing with time. This evolution is largely driven by tides acting on the innermost planets which then influence the outer ones. In order that deviations from commensurability become significant only on $Gy$ time scales or longer, we require that the tidal parameter associated with the planets has to be such that $Q > sim 10^{2-3}.$ At the same time, if we start with two subsystems, with the inner three planets comprising the inner one, $Q$ associated with the planets has to be on the order (and not significantly exceeding) $10^{2-3}$ for the two subsystems to interact and end up in the observed configuration. This scenario is also supported by modelling of the evolution through disk migration which indicates that the whole system cannot have migrated inwards together. Also in order to avoid large departures from commensurabilities, the system cannot have stalled at a disk inner edge for significant time periods. We discuss the habitability consequences of the tidal dissipation implied by our modelling, concluding that planets d, e and f are potentially in habitable zones.
The newly detected TRAPPIST-1 system, with seven low-mass, roughly Earth-sized planets transiting a nearby ultra-cool dwarf, is one of the most important exoplanet discoveries to date. The short baseline of the available discovery observations, however, means that the planetary masses (obtained through measurement of transit timing variations of the planets of the system) are not yet well constrained. The masses reported in the discovery paper were derived using a combination of photometric timing measurements obtained from the ground and from the Spitzer spacecraft, and have uncertainties ranging from 30% to nearly 100%, with the mass of the outermost, $P=18.8,{rm d}$, planet h remaining unmeasured. Here, we present an analysis that supplements the timing measurements of the discovery paper with 73.6 days of photometry obtained by the K2 Mission. Our analysis refines the orbital parameters for all of the planets in the system. We substantially improve the upper bounds on eccentricity for inner six planets (finding $e<0.02$ for inner six known members of the system), and we derive masses of $0.79pm 0.27 ,M_{oplus}$, $1.63pm 0.63,M_{oplus}$, $0.33pm 0.15,M_{oplus}$, $0.24^{+0.56}_{-0.24},M_{oplus}$, $0.36pm 0.12,M_{oplus}$, $0.566pm 0.038,M_{oplus}$, and $0.086pm 0.084,M_{oplus}$ for planets b, c, d, e, f, g, and h, respectively.
With the discovery of TRAPPIST-1 and its seven planets within 0.06 au, the correct treatment of tidal interactions is becoming necessary. The eccentricity, rotation, and obliquity of the planets of TRAPPIST-1 are indeed the result of tidal evolution over the lifetime of the system. Tidal interactions can also lead to tidal heating in the interior of the planets, which can then be responsible for volcanism and/or surface deformation. In the majority of studies to estimate the rotation of close-in planets or their tidal heating, the planets are considered as homogeneous bodies and their rheology is often taken to be a Maxwell rheology. We investigate here the impact of considering a multi-layer structure and an Andrade rheology on the way planets dissipate tidal energy as a function of the excitation frequency. We use an internal structure model, which provides the radial profile of structural and rheological quantities to compute the tidal response of multi-layer bodies. We then compare the outcome to the dissipation of a homogeneous planet. We find that for purely rocky bodies, it is possible to approximate the response of a multi-layer planet by that of a homogeneous planet. However, using average profiles of shear modulus and viscosity to compute the homogeneous planet response leads to an overestimation of the averaged dissipation. We provide fitted values of shear modulus and viscosity to be able to reproduce the response of various types of rocky planets. However, we find that if the planet has an icy layer, its tidal response can no longer be approximated by a homogeneous body because of the very different properties of the icy layers, which lead to a second dissipation peak at higher frequencies. We also compute the tidal heating profiles for the outer TRAPPIST-1 planets (e to h).
After publication of our initial mass-radius-composition models for the TRAPPIST-1 system in Unterborn et al. (2018), the planet masses were updated in Grimm et al. (2018). We had originally adopted the data set of Wang et al., 2017 who reported different densities than the updated values. The differences in observed density change the inferred volatile content of the planets. Grimm et al. (2018) report TRAPPIST-1 b, d, f, g, and h as being consistent with <5 wt% water and TRAPPIST-1 c and e has having largely rocky interiors. Here, we present updated results recalculating water fractions and potential alternative compositions using the Grimm et al., 2018 masses. Overall, we can only reproduce the results of Grimm et al., 2018 of planets b, d and g having small water contents if the cores of these planets are small (<23 wt%). We show that, if the cores for these planets are roughly Earth-sized (33 wt%), significant water fractions up to 40 wt% are possible. We show planets c, e, f, and h can have volatile envelopes between 0-35 wt% that are also consistent with being totally oxidized and lacking an Fe-core entirely. We note here that a pure MgSiO$_3$ planet (Fe/Mg = 0) is not the true lowest density end-member mass-radius curve for determining the probability of a planet containing volatiles. All planets that are rocky likely contain some Fe, either within the core or oxidized in the mantle. We argue the true low density end-member for oxidizing systems is instead a planet with the lowest reasonable Fe/Mg and completely core-less. Using this logic, we assert that planets b, d and g likely must have significant volatile layers because the end-member planet models produce masses too high even when uncertainties in both mass and radius are taken into account.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
