Extreme Eccentricity Research Articles

Binary Mergers in the Centers of Galaxies: Synergy between Stellar Flybys and Tidal Fields

Galactic centers (GCs) are very dynamically active environments, often harboring a nuclear star cluster and supermassive black hole at their cores. Binaries in these environments are subject to strong tidal fields that can efficiently torque its orbit, exciting near-unity eccentricities that ultimately lead to their merger. In turn, frequent close interactions with passing stars impulsively perturb the orbit of the binary, generally softening their orbit until their evaporation, potentially hindering the role of tides to drive these mergers. In this work, we study the evolution of compact object binaries in the GC and their merger rates, focusing for the first time on the combined effect of the cluster’s tidal field and flyby interactions. We find a significant synergy between both processes, where merger rates increase by a factor of ∼10−30 compared to models in which only flybys or tides are taken into account. This synergy is a consequence of the persistent tides-driven eccentricity excitation that is enhanced by the gradual diffusion of j z driven by flybys. The merger efficiency peaks when the diffusion rate is ∼10−100 slower than the tides-driven torquing. Added to this synergy, we also find that the gradual softening of the binary can lift the relativistic quenching of initially tight binaries, otherwise unable to reach extreme eccentricities, and thus expanding the available phase space for mergers. Cumulatively, we conclude that despite the gradual softening of binaries due to flybys, these greatly enhance their merger rates in GCs by promoting the tidal-field-driven eccentricity excitation.

Obliquity Constraints for the Extremely Eccentric Sub-Saturn Kepler-1656 b

The orbits of close-in exoplanets provide clues to their formation and evolutionary history. Many close-in exoplanets likely formed far out in their protoplanetary disks and migrated to their current orbits, perhaps via high-eccentricity migration (HEM), a process that can also excite obliquities. A handful of known exoplanets are perhaps caught in the act of HEM, as they are observed on highly eccentric orbits with tidal circularization timescales shorter than their ages. One such exoplanet is Kepler-1656 b, which is also the only known nongiant exoplanet (<100 M ⊕) with an extreme eccentricity (e = 0.84). We measured the sky-projected obliquity of Kepler-1656 b by observing the Rossiter–McLaughlin effect during a transit with the Keck Planet Finder. Our data are consistent with an aligned orbit but are also consistent with moderate misalignment with λ < 50° at 95% confidence, with the most likely solution of 35.0−21.6+14.9 deg. A low obliquity would be an unlikely outcome of most eccentricity-exciting scenarios, but we show that the properties of the outer companion in the system are consistent with the coplanar HEM mechanism. Alternatively, if the system is not relatively coplanar (≲20° mutual inclination), Kepler-1656 b may be presently at a rare snapshot of long-lived eccentricity oscillations that do not induce migration. Kepler-1656 b is only the fourth exoplanet with e > 0.8 to have its obliquity constrained; expanding this population will help establish the degree to which orbital misalignment accompanies migration. Future work that constrains the mutual inclinations of outer perturbers will be key for distinguishing plausible mechanisms.

Revisiting the Tertiary-induced Binary Black Hole Mergers: The Role of Superthermal Wide Tertiary Eccentricity Distributions

Recent studies show that the eccentricity distribution of wide binaries (semimajor axis ≳103 au) observed by Gaia tends to favor large eccentricities more strongly than the canonical thermal distribution (P(e) ∝ e)—such distributions are termed “superthermal.” Motivated by this observation, we revisit the formation channel of black hole (BH) binary mergers in triple stellar systems and study the impact of superthermal eccentricity distributions in the outer binaries. We explore the persistence of the highly eccentric outer orbits after each component in a stellar triple has undergone mass loss due to supernova explosions. We find that the outer eccentricity distribution can remain significantly superthermal for modestly hierarchical BH triples satisfying a in/a out ≳ 0.005 (where a in and a out are the semimajor axes of the inner and outer orbits), and are otherwise shaped by mass-loss induced kicks and dynamical instability. We then study the impact of these different outer eccentricity distributions of the remaining BH triples on mergers via the tertiary-induced channel. Of interest, we find that mergers can sometimes be produced even when the initial stellar orbits are near alignment (not subject to the von-Zeipel–Lidov–Kozai effect; ZLK effect) as long as the system is sufficiently hierarchical. On the other hand, although the impact of the octupole-order ZLK effect is much greater when the outer binary is more eccentric, we find that the merger fraction only changes modestly for extreme outer eccentricity distributions because the largest eccentricities tend to lead to dynamical instability.

A hot-Jupiter progenitor on a super-eccentric retrograde orbit.

Giant exoplanets orbiting close to their host stars are unlikely to have formed in their present configurations1. These 'hotJupiter' planets are instead thought to have migrated inward from beyond the ice line and several viable migration channels have been proposed, including eccentricity excitation through angular-momentum exchange with a third body followed by tidally driven orbital circularization2,3. The discovery of the extremely eccentric (e = 0.93) giant exoplanet HD 80606 b (ref. 4) provided observational evidence that hot Jupiters may have formed through this high-eccentricity tidal-migration pathway5. However, no similar hot-Jupiter progenitors have been found and simulations predict that one factor affecting the efficacy of this mechanism is exoplanet mass, as low-mass planets are more likely to be tidally disrupted during periastron passage6-8. Here we present spectroscopic and photometric observations of TIC 241249530 b, a high-mass, transiting warm Jupiter with an extreme orbital eccentricity of e = 0.94. The orbit of TIC 241249530 b is consistent with a history of eccentricity oscillations and a future tidal circularization trajectory. Our analysis of the mass and eccentricity distributions of the transiting-warm-Jupiter population further reveals a correlation between high mass and high eccentricity.

Extreme Resonant Eccentricity Excitation of Stars around Merging Black-Hole Binary.

We study the dynamics of a star orbiting a merging black-hole binary (BHB) in a coplanar triple configuration. During the BHB's orbital decay, the system can be driven across the apsidal precession resonance, where the apsidal precession rate of the stellar orbit matches that of the inner BHB. As a result, the system gets captured into a state of resonance advection until the merger of the BHB, leading to extreme eccentricity growth of the stellar orbit. This resonance advection occurs when the inner binary has a nonzero eccentricity and unequal masses. The resonant driving of the stellar eccentricity can significantly alter the hardening rate of the inner BHB and produce observational signatures to uncover the presence of nearby merging or merged BHBs.

Association between relative peripheral refraction and corresponding electro-retinal signals.

Considering the potential role of the peripheral retina in refractive development and giventhat peripheral refraction varies significantly with increasing eccentricity from the fovea, we investigated the association between relative peripheral refraction (RPR) and corresponding relative peripheral multifocal electroretinogram (mfERG) responses (electro-retinal signals) from the central to the peripheral retina in young adults. Central and peripheral refraction using an open-field autorefractor and mfERG responses using an electrophysiology stimulator were recorded from the right eyes of 17 non-myopes and 24 myopes aged 20-27 years. The relative mfERG N1, P1 and N2 components (amplitude density and implicit time) of a mfERG waveform were compared with the corresponding RPR measurements at the best-matched eccentricities along the principal meridians, that isatthe fovea (0°), horizontal (±5°, ±10° and ± 25°) and vertical meridians (±10° and ± 15°). The mean absolute mfERG N1, P1 and N2 amplitude densities (nV/deg2 ) were maximum at the fovea in both non-myopes (N1: 57.29 ± 14.70 nV/deg2 , P1: 106.29 ± 24.46 nV/deg2 , N2: 116.41 ± 27.96 nV/deg2 ) and myopes (N1: 56.25 ± 15.79 nV/deg2 , P1: 100.79 ± 30.81 nV/deg2 , N2: 105.75 ± 37.91 nV/deg2 ), which significantly reduced with increasing retinal eccentricity (p < 0.01). No significant association was reported between the RPR and corresponding relative mfERG amplitudes at each retinal eccentricity (overall Pearson's correlation, r=-0.25 to 0.26, p ≥ 0.09). In addition, the presence of relative peripheral myopia or hyperopia at extreme peripheral retinal eccentricities did not differentially influence the corresponding relative peripheral mfERG amplitudes (p ≥ 0.24). Relative peripheral mfERG signals are not associated with corresponding RPR in young adults. It is plausible that the electro-retinal signals may respond to the presence of absolute hyperopia (and not relative peripheral hyperopia), which requires further investigation.

Extreme Eccentricities of Triple Systems: Analytic Results

Triple stars and compact objects are ubiquitously observed in nature. Their long-term evolution is complex; in particular, the von Zeipel–Lidov–Kozai (ZLK) mechanism can potentially lead to highly eccentric encounters of the inner binary. Such encounters can lead to a plethora of interacting binary phenomena, as well as stellar and compact-object mergers. Here we find implicit analytical formulae for the maximal eccentricity, , of the inner binary undergoing ZLK oscillations, where both the test-particle limit (parameterized by the inner-to-outer angular momentum ratio η) and the double-averaging approximation (parameterized by the period ratio, ϵ SA) are relaxed, for circular outer orbits. We recover known results in both limiting cases (either η or ϵ SA → 0) and verify the validity of our model using numerical simulations. We test our results with two accurate numerical N-body codes, rebound for Newtonian dynamics and tsunami for general-relativistic dynamics, and find excellent correspondence. We discuss the implications of our results for stellar triples and both stellar and supermassive triple black hole mergers.

Quasi-periodic eruptions from galaxy nuclei

ABSTRACT I consider quasi-periodic eruptions (QPEs) from galaxy nuclei. All the known cases fit naturally into a picture of accretion from white dwarfs (WDs) in highly eccentric orbits about the central black holes which decay through gravitational wave emission. I argue that ESO 243-39 HLX–1 is a QPE source at an earlier stage of this evolution, with a correspondingly longer period, more extreme eccentricity, and a significantly more massive WD donor. I show explicitly that mass transfer in QPE systems is always highly stable, despite recent claims to the contrary in the literature. This stability may explain the alternating long-short eruptions seen in some QPE sources. As the WD orbit decays, the eruptions occupy larger fractions of the orbit and become brighter, making searches for quasi-periodicities in bright low-mass galaxy nuclei potentially fruitful.

Secular chaos in white dwarf planetary systems: origins of metal pollution and short-period planetary companions

ABSTRACT Secular oscillations in multiplanet systems can drive chaotic evolution of a small inner body through non-linear resonant perturbations. This ‘secular chaos’ readily pushes the inner body to an extreme eccentricity, triggering tidal interactions or collision with the central star. We present a numerical study of secular chaos in systems with two planets and test particles using the ring-averaging method, with emphasis on the relationship between the planets’ properties and the time-scale and efficiency of chaotic diffusion. We find that secular chaos can excite extreme eccentricities on time-scales spanning several orders of magnitude in a given system. We apply our results to the evolution of planetary systems around white dwarfs (WDs), specifically the tidal disruption and high-eccentricity migration of planetesimals and planets. We find that secular chaos in a planetesimal belt driven by large (≳10 M⊕), distant ($\gtrsim 10 \, \mathrm{au}$) planets can sustain metal accretion on to a WD over Gyr time-scales. We constrain the total mass of planetesimals initially present within the chaotic zone by requiring that the predicted mass delivery rate to the Roche limit be consistent with the observed metal accretion rates of WDs with atmospheric pollution throughout the cooling sequence. Based on the occurrence of long-period exoplanets and exo-asteroid belts, we conclude that secular chaos can be a significant (perhaps dominant) channel for polluting solitary WDs. Secular chaos can also produce short-period planets and planetesimals around WDs in concert with various circularization mechanisms. We discuss prospects for detecting exoplanets driving secular chaos around WDs using direct imaging and microlensing.

Kepler-1656b’s Extreme Eccentricity: Signature of a Gentle Giant

Highly eccentric orbits are one of the major surprises of exoplanets relative to the solar system and indicate rich and tumultuous dynamical histories. One system of particular interest is Kepler-1656, which hosts a sub-Jovian planet with an eccentricity of 0.8. Sufficiently eccentric orbits will shrink in the semimajor axis due to tidal dissipation of orbital energy during periastron passage. Here our goal was to assess whether Kepler-1656b is currently undergoing such high-eccentricity migration, and to further understand the system’s origins and architecture. We confirm a second planet in the system with M c = 0.40 ± 0.09 M jup and Pc = 1919 ± 27 days. We simulated the dynamical evolution of planet b in the presence of planet c and find a variety of possible outcomes for the system, such as tidal migration and engulfment. The system is consistent with an in situ dynamical origin of planet b followed by subsequent eccentric Kozai–Lidov perturbations that excite Kepler-1656b’s eccentricity gently, i.e., without initiating tidal migration. Thus, despite its high eccentricity, we find no evidence that planet b is or has migrated through the high-eccentricity channel. Finally, we predict the outer orbit to be mutually inclined in a nearly perpendicular configuration with respect to the inner planet orbit based on the outcomes of our simulations and make observable predictions for the inner planet’s spin–orbit angle. Our methodology can be applied to other eccentric or tidally locked planets to constrain their origins, orbital configurations, and properties of a potential companion.

Chaotic dynamics of wide triples induced by galactic tides: a novel channel for producing compact binaries, mergers, and collisions

ABSTRACT Recent surveys show that wide (&amp;gt;104 AU) binaries and triples are abundant in the field. We study the long-term evolution of wide hierarchical triple systems and the role played by the Galactic tidal (GT) field. We find that when the time-scales of the secular von–Ziepel–Lidov–Kozai and the GT oscillations are comparable, triple evolution becomes chaotic which leads to extreme eccentricities. Consequently, the close pericentre approaches of the inner-binary components lead to strong interactions, mergers, and collisions. We use a novel secular evolution code to quantify the key parameters and carry out a population-synthesis study of low and intermediate-mass wide-orbit triples. We find that in $\sim 9{{\ \rm per\ cent}}$ of low-mass wide-triples the inner main-sequence binaries collide or tidally-inspiral within $10\ \rm Gyr$, with direct collisions are 6 times more likely to occur. For the intermediate-mass sample, $\sim 7.6{{\ \rm per\ cent}}$ of the systems merge or inspiral with roughly equal probabilities. We discuss the relative fractions of different stellar merger/inspiral outcomes as a function of their evolutionary stage (Main Sequence, MS; Red Giant, RG; or White Dwarf, WD), their transient electromagnetic signatures and the final products of the merger/inspiral. In particular, the rate of WD–WD direct-collisions that lead to type-Ia Supernovae is comparable to other dynamical channels and accounts for at most $0.1{{\ \rm per\ cent}}$ of the observed rate. RG inspirals provide a novel channel for the formation of eccentric common-envelope-evolution binaries. The catalysis of mergers/collisions in triples due to GT could explain a significant fraction, or even the vast majority, of blue-stragglers in the field, produce progenitors for cataclysmic-variables, and give-rise to mergers/collisions of double-RG binaries.

A parameterized model to achieve orbit extrapolation on-board for highly elliptical orbits

<p indent="0mm">In general, both numerical and analytical methods can be used to predict the orbit. Numerical integrations are often adopted to achieve high accuracy, while analytical methods are more efficient. Many methods can be successfully used to predict the orbit for near-circular orbits. However, when it comes to orbit extrapolation on-board for orbits of extreme eccentricities, these existing methods are impractical. Conventional numerical integrators are extremely slow and analytical methods cannot reach sufficient accuracy because of the simplified force model. To find an appropriate solution to achieve orbit extrapolation on-board for highly elliptical orbits, a parameterized model comprising a polynomial fitting formula is proposed herein. The exact form of the fitting formula was determined after the analysis of the analytical solution of perturbations. Different functions were used to reflect the periodic term and secular term under the effect of perturbations. Five orbital elements <italic>σ</italic> (true anomaly <italic>f</italic>, argument of perigee<italic> ω</italic>, right ascension of ascending node <italic>Ω</italic>, orbital inclination <italic>i</italic> and geocentric distance <italic>r</italic>) were first fitted and then calculated using the fitting formula. Real positions of satellites were also calculated using these five orbital elements and presented in an inertial coordinate system. A total of 33 Molniya orbits were tested using this method. Twenty-eight groups of tests were performed for each satellite, and each extrapolation spanned three days. The numerical test results indicate that residuals of orbital elements (<italic>f</italic>, <italic>w</italic>, <italic>i</italic> and <italic>r</italic>) are affected by the eccentricity of orbits. Position errors are generally several hundred meters in three days.

Giant Outer Transiting Exoplanet Mass (GOT ‘EM) Survey. II. Discovery of a Failed Hot Jupiter on a 2.7 Yr, Highly Eccentric Orbit*

Abstract Radial velocity (RV) surveys have discovered giant exoplanets on au-scale orbits with a broad distribution of eccentricities. Those with the most eccentric orbits are valuable laboratories for testing theories of high-eccentricity migration. However, few such exoplanets transit their host stars, thus removing the ability to apply constraints on formation from their bulk internal compositions. We report the discovery of Kepler-1704 b, a transiting 4.15 M J giant planet on a 988.88 day orbit with an extreme eccentricity of 0.921 − 0.015 + 0.010 . Our decade-long RV baseline from the Keck I telescope allows us to measure the orbit and bulk heavy-element composition of Kepler-1704 b and place limits on the existence of undiscovered companions. A failed hot Jupiter, Kepler-1704 b was likely excited to high eccentricity by scattering events that possibly began during its gas accretion phase. Its final periastron distance was too large to allow for tidal circularization, so now it orbits its host from distances spanning 0.16–3.9 au. The maximum difference in planetary equilibrium temperature resulting from this elongated orbit is over 700 K. A simulation of the thermal phase curve of Kepler-1704 b during periastron passage demonstrates that it is a remarkable target for atmospheric characterization from the James Webb Space Telescope, which could potentially also measure the planet’s rotational period as the hot spot from periastron rotates in and out of view. Continued characterization of the Kepler-1704 system promises to refine theories explaining the formation of hot Jupiters and cool giant planets like those in the solar system.

SpaceHub: A high-performance gravity integration toolkit for few-body problems in astrophysics

ABSTRACT We present the open source few-body gravity integration toolkit SpaceHub. SpaceHub offers a variety of algorithmic methods, including the unique algorithms AR-Radau, AR-Sym6, AR-ABITS, and AR-chain+ which we show outperform other methods in the literature and allow for fast, precise, and accurate computations to deal with few-body problems ranging from interacting black holes to planetary dynamics. We show that AR-Sym6 and AR-chain+, with algorithmic regularization, chain algorithm, active round-off error compensation and a symplectic kernel implementation, are the fastest and most accurate algorithms to treat black hole dynamics with extreme mass ratios, extreme eccentricities, and very close encounters. AR-Radau, the first regularized Radau integrator with round off error control down to 64 bits floating point machine precision, has the ability to handle extremely eccentric orbits and close approaches in long-term integrations. AR-ABITS, a bit efficient arbitrary precision method, achieves any precision with the least CPU cost compared to other open source arbitrary precision few-body codes. With the implementation of deep numerical and code optimization, these new algorithms in SpaceHub prove superior to other popular high precision few-body codes in terms of performance, accuracy, and speed.

Spin-orbit misalignments in tertiary-induced binary black-hole mergers: Theoretical analysis

Black-hole (BH) binary mergers driven by gravitational perturbations of tertiary companions constitute an important class of dynamical formation channels for compact binaries detected by LIGO/VIRGO. Recent works have examined numerically the combined orbital and spin dynamics of BH binaries that undergo large Lidov-Kozai (LK) eccentricity oscillations induced by a highly inclined companion and merge via gravitational wave radiation. However, the extreme eccentricity variations make such systems difficult to characterize analytically. In this paper, we develop an analytical formalism for understanding the spin dynamics of binary BHs undergoing LK-induced mergers. We show that, under certain conditions, the eccentricity oscillations of the binary can be averaged over to determine the long-term behavior of the BH spin in a smooth way. In particular, we demonstrate that the final spin-orbit misalignment angle $\theta_{\rm sl}$ is often related to the binary's primordial spin orientation through an approximate adiabatic invariant. Our theory explains the "$90^\circ$ attractor" (as found in recent numerical studies) for the evolution of $\theta_{\rm sl}$ when the initial BH spin is aligned with the orbital axis and the octupole LK effects are negligible -- such a "$90^\circ$ attractor" would lead to a small binary effective spin parameter $\chi_{\rm eff}\sim 0$ even for large intrinsic BH spins. We calculate the deviation from adiabaticity in closed form as a function of the initial conditions. We also place accurate constraints on when this adiabatic invariant breaks down due to resonant spin-orbit interactions. We consider both stellar-mass and supermassive BH tertiary companions, and provide simple prescriptions for determining analytically the final spin-orbit misalignment angles of the merging BH binaries.

Acoustic fields for monopole logging while drilling with an eccentric collar

The acoustic problem of an eccentric drill collar in a fluid-filled borehole has been of interest in the field of acoustic logging while drilling (ALWD) in recent years. To reduce the effects of tool eccentricity on ALWD measurements, studies on acoustic responses under such conditions are essential. This study therefore has developed an analytical method to investigate borehole wavefields with an off-center monopole ALWD tool in fast and slow formations. By evaluating the contributions of compressional and shear branch points, the effects of the tool eccentricity on individual formation primary and shear head waves are investigated. Results illustrate that tool eccentricity only affects the excitation properties and has almost no effect on the extracted velocities. The joint analysis of synthetic full waveforms and dispersion diagrams with varying eccentricity degrees indicates that multipole modes are excited when the tool is off center, and their excitation amplitudes gradually increase with the increasing eccentricity, especially in the direction of tool movement. Moreover, the dispersion analysis reveals that the two modes with intersections in the centered case are coupled when the tool becomes eccentric. In particular, the coupling performance between the Stoneley and flexural modes is the most prominent. Furthermore, the effects of tool eccentricity on the monopole acquisition method, that is, the sum of waveforms received at four orthogonal azimuths, are evaluated. Results show that the above summation method can effectively reduce the effects of slight or moderate eccentricity. However, for large or extreme eccentricity, reducing or eliminating the effects of eccentricity on the Stoneley wave is a challenge for this method. Based on the above analyses, measurements may not be reliable for formation evaluation in the case of extreme eccentricity, especially for Stoneley wave applications.

Enhanced Lidov–Kozai migration and the formation of the transiting giant planet WD 1856+534 b

ABSTRACT We investigate the possible origin of the transiting giant planet WD 1856+534 b, the first strong exoplanet candidate orbiting a white dwarf, through high-eccentricity migration (HEM) driven by the Lidov–Kozai (LK) effect. The host system’s overall architecture is a hierarchical quadruple in the ‘2 + 2’ configuration, owing to the presence of a tertiary companion system of two M-dwarfs. We show that a secular inclination resonance in 2 + 2 systems can significantly broaden the LK window for extreme eccentricity excitation (e ≳ 0.999), allowing the giant planet to migrate for a wide range of initial orbital inclinations. Octupole effects can also contribute to the broadening of this ‘extreme’ LK window. By requiring that perturbations from the companion stars be able to overcome short-range forces and excite the planet’s eccentricity to e ≃ 1, we obtain an absolute limit of $a_{1} \gtrsim 8 \, \mathrm{au}\, (a_{3} / 1500 \, \mathrm{au})^{6/7}$ for the planet’s semimajor axis just before migration (where a3 is the semimajor axis of the ‘outer’ orbit). We suggest that, to achieve a wide LK window through the 2 + 2 resonance, WD 1856 b likely migrated from $30 \, \mathrm{au}\lesssim a_{1} \lesssim 60 \, \mathrm{au}$, corresponding to ∼10–$20 \, \mathrm{au}$ during the host’s main-sequence phase. We discuss possible difficulties of all flavours of HEM affecting the occurrence rate of short-period giant planets around white dwarfs.

Planet–planet scattering as the source of the highest eccentricity exoplanets

Most giant exoplanets discovered by radial velocity surveys have much higher eccentricities than those in the solar system. The planet–planet scattering mechanism has been shown to match the broad eccentricity distribution, but the highest-eccentricity planets are often attributed to Kozai-Lidov oscillations induced by a stellar companion. Here we investigate whether the highly eccentric exoplanet population can be produced entirely by scattering. We ran 500 N-body simulations of closely packed giant-planet systems that became unstable under their own mutual perturbations. We find that the surviving bound planets can have eccentricities up to e &gt; 0.99, with a maximum of 0.999017 in our simulations. This suggests that there is no maximum eccentricity that can be produced by planet–planet scattering. Importantly, we find that extreme eccentricities are not extremely rare; the eccentricity distribution for all giant exoplanets with e &gt; 0.3 is consistent with all planets concerned being generated by scattering. Our results show that the discovery of planets with extremely high eccentricities does not necessarily signal the action of the Kozai-Lidov mechanism.

Formation of hot Jupiters through secular chaos and dynamical tides

Abstract The population of giant planets on short-period orbits can potentially be explained by some flavours of high-eccentricity migration. In this paper, we investigate one such mechanism involving ‘secular chaos’, in which secular interactions between at least three giant planets push the inner planet to a highly eccentric orbit, followed by tidal circularization and orbital decay. In addition to the equilibrium tidal friction, we incorporate dissipation due to dynamical tides that are excited inside the giant planet. Using the method of Gaussian rings to account for planet–planet interactions, we explore the conditions for extreme eccentricity excitation via secular chaos and the properties of hot Jupiters formed in this migration channel. Our calculations show that once the inner planet reaches a sufficiently large eccentricity, dynamical tides quickly dissipate the orbital energy, producing an eccentric warm Jupiter, which then decays in semimajor axis through equilibrium tides to become a hot Jupiter. Dynamical tides help the planet avoid tidal disruption, increasing the chance of forming a hot Jupiter, although not all planets survive the process. We find that the final orbital periods generally lie in the range of 2–3 d, somewhat shorter than those of the observed hot Jupiter population. We couple the planet migration to the stellar spin evolution to predict the final spin-orbit misalignments. The distribution of the misalignment angles we obtain shows a lack of retrograde orbits compared to observations. Our results suggest that high-eccentricity migration via secular chaos can only account for a fraction of the observed hot Jupiter population.

J'aime ta joie parce qu'elle est folle: écrivains en fête (XVIe et XVIIe siècles) by Michel Jeanneret

Reviewed by: J'aime ta joie parce qu'elle est folle: écrivains en fête (XVIe et XVIIe siècles) by Michel Jeanneret Gregory B. Stone Jeanneret, Michel. J'aime ta joie parce qu'elle est folle: écrivains en fête (XVIe et XVIIe siècles). Droz, 2018. ISBN 978-2-600-00562-3. Pp. 232. This book draws upon a host of remarkable sixteenth- and seventeenth-century European (nearly exclusively French) writers, including the famous, infamous, marginal, and unknown, to craft an essayistic Ode to Joy—not the lofty joy of intellectual or mystical pleasure but joy as enjoyment, especially of life's material pleasures. Against the background of the Counter-Reformation's restraint of a variety of modes of freedom, Jeanneret brings to light an overlooked yet abundant element of the cultural defense of an increasingly endangered liberty: the key role played by partisans of laughter and play. As antidotes to interdiction, moral imperatives, the repression of natural instincts, and the assignment of guilt, this host of witting fools celebrates gaiety, utter lack of constraint, the unhindered pursuit of appetites, extreme eccentricity, and absolute freedom of thought, language, and lifestyle—all while violating, mocking, and deflating classicizing norms of beauty, refinement, and order. Festival or carnival for these writers is not a brief contained release of repressed energy but rather constant unregulated activity. They assume the guise of madman, buffoon, and "comedian" (in the modern English sense) both for no reason whatsoever (thus eschewing utility and purposefulness) and for a good reason—to point toward an egalitarian and tolerant social order and to re-balance human life away from aspirations of transcendence toward enjoyment and acceptance of our imperfect reality. Opening with somewhat perfunctory treatment of perhaps unavoidable giants of the sixteenth century (Erasmus, Rabelais, Montaigne), the book gains the reader's sustained interest with its chapter on Béroalde de Verville's Le moyen de parvenir—a work that, flaunting its own inanity, is a wildly inventive unrestrained mess (described by Jeanneret as a massive outburst of creative verve and linguistic innovation nearly unparalleled in French literature and as the most vast collection of gauloiseries ever compiled in France). Not a book of theses and arguments but rather an archaeology of mostly buried and often stunning curiosities, J'aime ta joie parce qu'elle est folle nonetheless does offer, in its latter half, two significant claims: first, that the vogue for undignified genres such as farce and the copious production of pornography in the first half of the seventeenth century was a final salvo of resistance to the Counter-Reformation's prudery and its designation of virtually all desire as sin; secondly, that, as the rising disciplinary regime that increasingly ostracized madness and deviance spelled the end of such institutions as the official position of fool to the king, there was a sort of return of the repressed, as that expelled official was informally reintroduced to the centers of power, in the person of scandal-provoking figures such as Molière, who performed nearly all of the once-recognized functions of the court buffoon. Jeanneret offers numerous sketches of fascinating, sometimes appealing, sometimes disgusting, often perverse rogues and bohemians (both professional and nonprofessional authors) who shuttled back-and-forth between the palaces and the [End Page 203] taverns with ease and impunity. The book is an outstanding adventurer's guide to the other side and the underside of the literature of the French Renaissance. Gregory B. Stone Louisiana State University Copyright © 2019 American Association of Teachers of French