Viscoelastic Tidal Dissipation in Giant Planets and Formation of Hot Jupiters Through High-Eccentricity Migration

We study the possibility of tidal dissipation in the solid cores of giant planets and its implication for the formation of hot Jupiters through high-eccentricity migration. We present a general framework by which the tidal evolution of planetary systems can be computed for any form of tidal dissipation, characterized by the imaginary part of the complex tidal Love number, ${\rm Im}[{\tilde k}_2(\omega)]$, as a function of the forcing frequency $\omega$. Using the simplest viscoelastic dissipation model (the Maxwell model) for the rocky core and including the effect of a nondissipative fluid envelope, we show that with reasonable (but uncertain) physical parameters for the core (size, viscosity and shear modulus), tidal dissipation in the core can accommodate the tidal-Q constraint of the Solar system gas giants and at the same time allows exoplanetary hot Jupiters to form via tidal circularization in the high-e migration scenario. By contrast, the often-used weak friction theory of equilibrium tide would lead to a discrepancy between the Solar system constraint and the amount of dissipation necessary for high-e migration. We also show that tidal heating in the rocky core can lead to modest radius inflation of the planets, particularly when the planets are in the high-eccentricity phase ($e\sim 0.6$) during their high-e migration. Finally, as an interesting by-product of our study, we note that for a generic tidal response function ${\rm Im}[{\tilde k}_2(\omega)]$, it is possible that spin equilibrium (zero torque) can be achieved for multiple spin frequencies (at a given $e$), and the actual pseudo-synchronized spin rate depends on the evolutionary history of the system.Comment: 10 pages, 8 figures, MNRAS in pres

Non-radial Oscillations in Rotating Giant Planets with Solid Cores: Application to Saturn and its Rings

Recent observations have revealed evidence for the global oscillations of Jupiter and Saturn, which can potentially provide a new window into the interior structure of giant planets. Motivated by these observations, we study the non-radial oscillation modes of giant planets containing a solid core. Our calculations include the elastic response of the core and consider a wide range of possible values of the core shear modulus. While the elasticity of the core only slightly changes the frequencies of acoustic modes, which reside mostly in the fluid envelope, it adds two new classes of shear modes that are largely confined to the core. We also calculate the effects of the Coriolis force on the planetary oscillation modes. In addition to changing the mode frequencies, the Coriolis force can cause the shear modes to mix with the f-modes. Such mixing occurs when the frequencies of the shear mode and the f-mode are close to each other, and results in "mixed modes" with similar properties that are slightly split in frequency. We discuss our results in light of the recent work by Hedman & Nicholson (2013), which revealed the presence of density waves in Saturn's C-ring that appear to be excited by the gravitational perturbations associated with the f-mode oscillations within Saturn. We find that the fine splitting in wave frequencies observed in the rings can in principle be explained by the rotation-induced mixing between core shear modes and f-modes, possibly indicating the presence of a solid core within Saturn. However, in our current calculations, which assume rigid-body rotation and include only first-order rotational effects, significant fine-tuning in the planetary model parameters is needed in order to achieve these mode mixings and to explain the observed fine frequency splitting. We briefly discuss other effects that may modify the f-modes and facilitate mode mixing.Comment: 35 pages, 12 figures, submitted to Icaru

Eccentricity and Spin-Orbit Misalignment in Short-Period Stellar Binaries as a Signpost of Hidden Tertiary Companions

Eclipsing binaries are observed to have a range of eccentricities and spin-orbit misalignments (stellar obliquities). Whether such properties are primordial, or arise from post-formation dynamical interactions remains uncertain. This paper considers the scenario in which the binary is the inner component of a hierarchical triple stellar system, and derives the requirements that the tertiary companion must satisfy in order to raise the eccentricity and obliquity of the inner binary. Through numerical integrations of the secular octupole-order equations of motion of stellar triples, coupled with the spin precession of the oblate primary star due to the torque from the secondary, we obtain a simple, robust condition for producing spin-orbit misalignment in the inner binary: In order to excite appreciable obliquity, the precession rate of the stellar spin axis must be smaller than the orbital precession rate due to the tertiary companion. This yields quantitative requirements on the mass and orbit of the tertiary. We also present new analytic expressions for the maximum eccentricity and range of inclinations allowing eccentricity excitation (Lidov-Kozai window), for stellar triples with arbitrary masses and including the non-Keplerian potentials introduced by general relativity, stellar tides and rotational bulges. The results of this paper can be used to place constraints on unobserved tertiary companions in binaries that exhibit high eccentricity and/or spin-orbit misalignment, and will be helpful in guiding efforts to detect external companions around stellar binaries. As an application, we consider the eclipsing binary DI Herculis, and identify the requirements that a tertiary companion must satisfy to produce the observed spin-orbit misalignment.Comment: 19 pages, 15 figures, accepted for publication in MNRA

Chaotic Dynamics of Stellar Spin in Binaries and the Production of Misaligned Hot Jupiters

Many exoplanetary systems containing hot Jupiters are observed to have highly misaligned orbital axes relative to the stellar spin axes. Kozai-Lidov oscillations of orbital eccentricity/inclination induced by a binary companion, in conjunction with tidal dissipation, is a major channel for the production of hot Jupiters. We demonstrate that gravitational interaction between the planet and its oblate host star can lead to chaotic evolution of the stellar spin axis during Kozai cycles. As parameters such as the planet mass and stellar rotation period vary, periodic islands can appear in an ocean of chaos, in a manner reminiscent of other dynamical systems. In the presence of tidal dissipation, the complex spin evolution can leave an imprint on the final spin-orbit misalignment angles.Comment: 26 pages, 13 figures. Includes supplementary materials. To be published in the September 12, 2014 edition of Science Magazine. For additional information, please visit http://astro.cornell.edu/~dong/sciencepaper.htm

Chaotic Dynamics of Stellar Spin Driven by Planets Undergoing Lidov-Kozai Oscillations: Resonances and Origin of Chaos

Many exoplanetary systems containing hot Jupiters are found to possess significant misalignment between the spin axis of the host star and the planet's orbital angular momentum axis. A possible channel for producing such misaligned hot Jupiters involves Lidov-Kozai oscillations of the planet's orbital eccentricity and inclination driven by a distant binary companion. In a recent work (Storch, Anderson & Lai 2014), we have shown that a proto-hot Jupiter undergoing Lidov-Kozai oscillations can induce complex, and often chaotic, evolution of the spin axis of its host star. Here we explore the origin of the chaotic spin behavior and its various features in an idealized non-dissipative system where the secular oscillations of the planet's orbit are strictly periodic. Using Hamiltonian perturbation theory, we identify a set of secular spin-orbit resonances in the system, and show that overlaps of these resonances are responsible for the onset of wide-spread chaos in the evolution of stellar spin axis. The degree of chaos in the system depends on the adiabaticity parameter $\epsilon$, proportional to the ratio of the Lidov-Kozai nodal precession rate and the stellar spin precession rate, and thus depends on the planet mass, semi-major axis and the stellar rotation rate. For systems with zero initial spin-orbit misalignment, our theory explains the occurrence (as a function of $\epsilon$) of "periodic islands" in the middle of a "chaotic ocean" of spin evolution, and the occurrence of restricted chaos in middle of regular/periodic spin evolution. Finally, we discuss a novel "adiabatic resonance advection" phenomenon, in which the spin-orbit misalignment, trapped in a resonance, gradually evolves as the adiabaticity parameter slowly changes. This phenomenon can occur for certain parameter regimes when tidal decay of the planetary orbit is included.Comment: 15 pages, 17 figures, submitted to MNRA

Aero-resonant migration

The process of planet conglomeration, which primarily unfolds in a geometrically thin disc of gas and dust, is often accompanied by dynamical excitation of the forming planets and planetesimals. The ensuing orbital crossing can lead to large-scale collisional fragmentation, populating the system with icy and rocky debris. In a gaseous nebula, such leftover solid matter tends to spiral down towards the host star due to aerodynamic drag. Along the way, the inward drifting debris can encounter planets and gravitationally couple to them via mean-motion resonances, sapping them of their orbital energy and causing them to migrate. Here, we develop a simple theory for this migration mechanism, which we call ‘aero-resonant migration’ (ARM), in which small planetesimals (10 m ≲ s ≲ 10 km) undergo orbital decay due to aerodynamic drag and resonantly shepherd planets ahead of them. Using a combination of analytical calculations and numerical experiments, we show that ARM is a robust migration mechanism, able to significantly transport planets on time-scales ≲1 Myr, and present simple formulae for the ARM rate

The Light Curve and Internal Magnetic Field of the Mode-Switching Pulsar PSR B0943+10

A number of radio pulsars exhibit intriguing mode-switching behavior. Recent observations of PSR B0943+10 revealed correlated radio and X-ray mode switches, providing a new avenue for understanding this class of objects. The large X-ray pulse fraction observed during the radio quiet phase (Q mode) was previously interpreted as a result of changing obscuration of X-rays by dense magnetosphere plasma. We show that the large X-ray pulse fraction can be explained by including the beaming effect of a magnetic atmosphere, while remaining consistent with the dipole field geometry constrained by radio observations. We also explore a more extreme magnetic field configuration, where a magnetic dipole displaced from the center of the star produces two magnetic polar caps of different sizes and magnetic field strengths. These models are currently consistent with data in radio and X-rays and can be tested or constrained by future X-ray observations.Comment: 5 pages, 5 figures, submitted to ApJ

Formation and stellar spin-orbit misalignment of hot Jupiters from Lidov–Kozai oscillations in stellar binaries

Observed hot Jupiter (HJ) systems exhibit a wide range of stellar spin-orbit misalignment angles. This paper investigates the inward migration of giant planets due to Lidov–Kozai (LK) oscillations induced by a distant stellar companion. We conduct a large population synthesis study, including the octupole gravitational potential from the stellar companion, mutual precession of the host stellar spin axis and planet orbital axis, tidal dissipation in the planet and stellar spin-down in the host star due to magnetic braking. We consider a range of planet masses (0.3–5 MJ) and initial semimajor axes (1–5 au), different properties for the host star, and varying tidal dissipation strengths. The fraction of systems that result in HJs depends on planet mass and stellar type, with fHJ = 1–4 per cent (depending on tidal dissipation strength) for M_p = 1 MJ, and larger (up to 8 per cent) for more massive planets. The production efficiency of ‘hot Saturns’ (M_p = 0.3MJ) is much lower, because most migrating planets are tidally disrupted. We find that the fraction of systems that result in either HJ formation or tidal disruption, f_(mig) ≃ 11–14 per cent is roughly constant, having little variation with planet mass, stellar type and tidal dissipation strength. The distribution of final HJ stellar obliquities exhibits a complex dependence on the planet mass and stellar type. For M_p = (1–3)MJ, the distribution is always bimodal, with peaks around 30° and 130°. The distribution for 5MJ planets depends on host stellar type, with a preference for low obliquities for solar-type stars, and higher obliquities for more massive (1.4 M_⊙) stars