Secular Excitation Research Articles

Resonant and Ultra-short-period Planet Systems Are at Opposite Ends of the Exoplanet Age Distribution

Exoplanet systems are thought to evolve on secular timescales over billions of years. This evolution is impossible to directly observe on human timescales in most individual systems. While the availability of accurate and precise age inferences for individual exoplanet host stars with ages τ in the interval 1 Gyr ≲ τ ≲ 10 Gyr would constrain this evolution, accurate and precise age inferences are difficult to obtain for isolated field dwarfs like the host stars of most exoplanets. The Galactic velocity dispersion of a thin-disk stellar population monotonically grows with time, and the relationship between age and velocity dispersion in a given Galactic location can be calibrated by a stellar population for which accurate and precise age inferences are possible. Using a sample of subgiants with precise age inferences, we calibrate the age–velocity dispersion relation in the Kepler field. Applying this relation to the Kepler field’s planet populations, we find that Kepler-discovered systems plausibly in second-order mean-motion resonances have 1 Gyr ≲ τ ≲ 2 Gyr. The same is true for systems plausibly in first-order mean-motion resonances, but only for systems likely affected by tidal dissipation inside their innermost planets. These observations suggest that many planetary systems diffuse away from initially resonant configurations on secular timescales. Our calibrated relation also indicates that ultra-short-period (USP) planet systems have typical ages in the interval 5 Gyr ≲ τ ≲ 6 Gyr. We propose that USP planets tidally migrated from initial periods in the range 1 day ≲ P ≲ 2 days to their observed locations at P < 1 day over billions of years and trillions of cycles of secular eccentricity excitation and inside-planet damping.

Precision measurement based on rovibrational spectrum of cold molecular hydrogen ion

A molecular hydrogen ion HD&lt;sup&gt;+&lt;/sup&gt;, composed of a proton, a deuteron, and an electron, has a rich set of rovibrational transitions that can be theoretically calculated and experimentally measured precisely. Currently, the relative accuracy of the rovibrational transition frequencies of the HD&lt;sup&gt;+&lt;/sup&gt; molecular ions has reached 10&lt;sup&gt;–12&lt;/sup&gt;. By comparing experimental measurements with theoretical calculations of the HD&lt;sup&gt;+&lt;/sup&gt; rovibrational spectrum, the precise determination of the proton-electron mass ratio, the testing of quantum electrodynamics(QED) theory, and the exploration of new physics beyond the standard model can be achieved. The experiment on HD&lt;sup&gt;+&lt;/sup&gt; rovibrational spectrum has achieved the highest accuracy (20 ppt, 1 ppt = 10&lt;sup&gt;–12&lt;/sup&gt;) in measuring proton-electron mass ratio. This ppaper comprehensively introduces the research status of HD&lt;sup&gt;+&lt;/sup&gt; rovibrational spectroscopy, and details the experimental method of the high-precision rovibrational spectroscopic measurement based on the sympathetic cooling of HD&lt;sup&gt;+&lt;/sup&gt; ions by laser-cooled Be&lt;sup&gt;+&lt;/sup&gt; ions. In Section 2, the technologies of generating and trapping both Be&lt;sup&gt;+&lt;/sup&gt; ions and HD&lt;sup&gt;+&lt;/sup&gt; ions are introduced. Three methods of generating ions, including electron impact, laser ablation and photoionization, are also compared. In Section 3, we show the successful control of the kinetic energy of HD&lt;sup&gt;+&lt;/sup&gt; molecular ions through the sympathetic cooling, and the importance of laser frequency stabilization for sympathetic cooling of HD&lt;sup&gt;+&lt;/sup&gt; molecular ions. In Section 4, two methods of preparing internal states of HD&lt;sup&gt;+&lt;/sup&gt; molecular ions, optical pumping and resonance enhanced threshold photoionization, are introduced. Both methods show the significant increase of population in the ground rovibrational state. In Section 5, we introduce two methods of determining the change in the number of HD&lt;sup&gt;+&lt;/sup&gt; molecular ions, i.e. secular excitation and molecular dynamic simulation. Both methods combined with resonance enhanced multiphoton dissociation can detect the rovibrational transitions of HD&lt;sup&gt;+&lt;/sup&gt; molecular ions. In Section 6, the experimental setup and process for the rovibrational spectrum of HD&lt;sup&gt;+&lt;/sup&gt; molecular ions are given and the up-to-date results are shown. Finally, this paper summarizes the techniques used in HD&lt;sup&gt;+&lt;/sup&gt; rovibrational spectroscopic measurements, and presents the prospects of potential spectroscopic technologies for further improving frequency measurement precision and developing the spectroscopic methods of different isotopic hydrogen molecular ions.

The Warm Neptune GJ 3470b Has a Polar Orbit

The warm Neptune GJ 3470b transits a nearby (d = 29 pc) bright slowly rotating M1.5-dwarf star. Using spectroscopic observations during two transits with the newly commissioned NEID spectrometer on the WIYN 3.5 m Telescope at Kitt Peak Observatory, we model the classical Rossiter–McLaughlin effect, yielding a sky-projected obliquity of and a . Leveraging information about the rotation period and size of the host star, our analysis yields a true obliquity of , revealing that GJ 3470b is on a polar orbit. Using radial velocities from HIRES, HARPS, and the Habitable-zone Planet Finder, we show that the data are compatible with a long-term radial velocity (RV) slope of over a baseline of 12.9 yr. If the RV slope is due to acceleration from another companion in the system, we show that such a companion is capable of explaining the polar and mildly eccentric orbit of GJ 3470b using two different secular excitation models. The existence of an outer companion can be further constrained with additional RV observations, Gaia astrometry, and future high-contrast imaging observations. Lastly, we show that tidal heating from GJ 3470b’s mild eccentricity has most likely inflated the radius of GJ 3470b by a factor of ∼1.5–1.7, which could help account for its evaporating atmosphere.

Secular resonance sweeping and orbital excitation in decaying disks

We revisit the problem of secular resonance sweeping during the dissipation of a protoplanetary disk and its possible role in exciting the orbits of primordial asteroids, in the light of recent models of solar system evolution. We develop an integrator that incorporates the gravitational effect of a uniformly (or not) depleting, axisymmetric disk with arbitrary surface density profile; its performance is verified by analytical calculations. The secular response of fictitious asteroids, under perturbations from Jupiter, Saturn and a decaying disk, is thoroughly studied. Note that the existence of a symmetry plane induced by the disk, lifts the inherent degeneracy of the two-planet system, such that the '$s_5$' nodal frequency can also play a major role. We examine different resonant configurations for the planets (2:1, 3:2, 5:3), disk models and depletion scenarios. For every case we compute the corresponding time paths of secular resonances, which show when and where resonance crossing occurs. The excitation of asteroids, particularly in inclination, is studied in the various models and compared to analytical estimates. We find that inclination excitation in excess of $\sim 10^{\circ}$ is possible in the asteroid belt, but the nearly uniform spread of $\Delta i\sim 20^{\circ}$ observed calls for the combined action of secular resonance sweeping with other mechanisms (e.g. scattering by Mars-sized embryos) that would be operating during terrestrial planet formation. Our results are also applicable to extrasolar planetary systems.

Extreme secular excitation of eccentricity inside mean motion resonance

Context. It is well known that asteroids and comets fall into the Sun. Metal pollution of white dwarfs and transient spectroscopic signatures of young stars like β-Pic provide growing evidence that extra solar planetesimals can attain extreme orbital eccentricities and fall into their parent stars. Aims. We aim to develop a general, implementable, semi-analytical theory of secular eccentricity excitation of small bodies (planetesimals) in mean motion resonances with an eccentric planet valid for arbitrary values of the eccentricities and including the short-range force due to General Relativity. Methods. Our semi-analytic model for the restricted planar three-body problem does not make use of series expansion and therefore is valid for any eccentricity value and semi-major axis ratio. The model is based on the application of the adiabatic principle, which is valid when the precession period of the longitude of pericentre of the planetesimal is much longer than the libration period in the mean motion resonance. In resonances of order larger than 1 this is true except for vanishingly small eccentricities. We provide prospective users with a Mathematica notebook with implementation of the model allowing direct use. Results. We confirm that the 4:1 mean motion resonance with a moderately eccentric (e′ ≲ 0.1) planet is the most powerful one to lift the eccentricity of planetesimals from nearly circular orbits to star-grazing ones. However, if the planet is too eccentric, we find that this resonance is unable to pump the planetesimal’s eccentricity to a very high value. The inclusion of the General Relativity effect imposes a condition on the mass of the planet to drive the planetesimals into star-grazing orbits. For a planetesimal at ~ 1 AU around a solar mass star (or white dwarf), we find a threshold planetary mass of about 17 Earth masses. We finally derive an analytical formula for this critical mass. Conclusions. Planetesimals can easily fall into the central star even in the presence of a single moderately eccentric planet, but only from the vicinity of the 4:1 mean motion resonance. For sufficiently high planetary masses the General Relativity effect does not prevent the achievement of star-grazing orbits.

On the formation of hot and warm Jupiters via secular high-eccentricity migration in stellar triples

Hot Jupiters (HJs) are Jupiter-like planets orbiting their host star in tight orbits of a few days. They are commonly believed not to have formed in situ, requiring inwards migration towards the host star. One of the proposed migration scenarios is secular high-eccentricity or high-$e$ migration, in which the orbit of the planet is perturbed to high eccentricity by secular processes, triggering strong tidal evolution and orbital migration. Previous theoretical studies have considered secular excitation in stellar binaries. Recently, a number of HJs have been observed in stellar triple systems. In the latter, the secular dynamics are much richer compared to stellar binaries, and HJs could potentially be formed more efficiently. Here, we investigate this possibility by modeling the secular dynamical and tidal evolution of planets in two hierarchical configurations in stellar triple systems. We find that the HJ formation efficiency is higher compared to stellar binaries, but only by at most a few tens of per cent. The orbital properties of the HJs formed in the simulations are very similar to HJs formed in stellar binaries, and similarly to studies of the latter we find no significant number of warm Jupiters. HJs are only formed in our simulations for triples with specific orbital configurations, and our constraints are approximately consistent with current observations. In future, this allows to rule out high-$e$ migration in stellar triples if a HJ is detected in a triple grossly violating these constraints.

Compensating for excess micromotion of ion crystals**Project supported by the National Basic Research Program of China (Grant Nos. 2012CB821301 and 2010CB832803), the National Natural Science Foundation of China (Grant Nos. 11004222 and 91121016), and the Fund from Chinese Academy of Sciences.

A new method of compensating for the excess micromotion along two directions in three-dimensional Coulomb crystals is reported in this paper; this method is based on shape control and optical imaging of a Coulomb crystal in a sectioned linear ion trap. The characteristic parameters, such as the ion numbers, temperatures, and geometric factors of different ion crystals are extracted from the images and secular motion excitation spectra. The method of controlling the shape of the ion crystals can be used in cold ion experiments, such as sympathetically cooling, structural phase transitions, and selective-control of ions, etc.

PLANET FORMATION IN SMALL SEPARATION BINARIES: NOT SO SECULARLY EXCITED BY THE COMPANION

Existence of planets is binaries with relatively small separations (around 20 AU), such as \alpha Centauri or \gamma Cephei poses severe challenges to standard planet formation theories. The problem lies in the vigorous secular excitation of planetesimal eccentricities at separations of several AU, where some of the planets are found, by the massive, eccentric stellar companions. High relative velocities of planetesimals preclude their growth in mutual collisions for a wide range of sizes, from below 1 km up to several hundred km, resulting in fragmentation barrier to planet formation. Here we show that rapid apsidal precession of planetesimal orbits, caused by the gravity of the circumstellar protoplanetary disk, acts to strongly reduce eccentricity excitation, lowering planetesimal velocities by an order of magnitude or even more at 1 AU. By examining the details of planetesimal dynamics we demonstrate that this effect eliminates fragmentation barrier for in-situ growth of planetesimals as small as < 10 km even at separations as wide as 2.6 AU (semi-major axis of the giant planet in HD 196885), provided that the circumstellar protoplanetary disk is relatively massive, ~0.1 M_Sun.

BUILDING TATOOINE: SUPPRESSION OF THE DIRECT SECULAR EXCITATION IN KEPLER CIRCUMBINARY PLANET FORMATION

Circumbinary planetary systems recently discovered by Kepler represent an important testbed for planet formation theories. Planetesimal growth in disks around binaries has been expected to be inhibited interior to ~10 AU by secular excitation of high relative velocities between planetesimals, leading to their collisional destruction (rather than agglomeration). Here we show that gravity of the gaseous circumbinary disk in which planets form drives fast precession of both the planetesimal and binary orbits, resulting in strong suppression of planetesimal eccentricities beyond 2-3 AU and making possible growth of 1-100 km objects in this region. The precise location of the boundary of accretion-friendly region depends on the size of the inner disk cavity cleared by the binary torques and on the disk mass (even 0.01 M_Sun disk strongly suppresses planetesimal excitation), among other things. Precession of the orbit of the central binary, enhanced by the mass concentration naturally present at the inner edge of a circumbinary disk, plays key role in this suppression, which is a feature specific to the circumbinary planet formation.

NEPTUNE ON TIPTOES: DYNAMICAL HISTORIES THAT PRESERVE THE COLD CLASSICAL KUIPER BELT

The current dynamical structure of the Kuiper belt was shaped by the orbital evolution of the giant planets, especially Neptune, during the era following planet formation, when the giant planets may have undergone planet-planet scattering and/or planetesimal-driven migration. Numerical simulations of this process, while reproducing many properties of the belt, fail to generate the high inclinations and eccentricities observed for some objects while maintaining the observed dynamically "cold" population. We present the first of a three-part parameter study of how different dynamical histories of Neptune sculpt the planetesimal disk. Here we identify which dynamical histories allow an in situ planetesimal disk to remain dynamically cold, becoming today's cold Kuiper belt population. We find that if Neptune undergoes a period of elevated eccentricity and/or inclination, it secularly excites the eccentricities and inclinations of the planetesimal disk. We demonstrate that there are several well-defined regimes for this secular excitation, depending on the relative timescales of Neptune's migration, the damping of Neptune's orbital inclination and/or eccentricity, and the secular evolution of the planetesimals. We model this secular excitation analytically in each regime, allowing for a thorough exploration of parameter space. Neptune's eccentricity and inclination can remain high for a limited amount of time without disrupting the cold classical belt. In the regime of slow damping and slow migration, if Neptune is located (for example) at 20 AU, then its eccentricity must stay below 0.18 and its inclination below 6{\deg}.

Observation of the v′=8←v=0 vibrational overtone in cold trapped HD+

We report the observation of the hitherto undetected v′=8←v=0 vibrational overtone in trapped HD+ molecular ions, sympathetically cooled by laser-cooled Be+ ions. The overtone is excited using 782 nm laser radiation, after which HD+ ions in v=8 are photodissociated by the 313 nm laser used for Be+ cooling. The concomitant loss of HD+ is detected by the method of secular excitation (Roth et al. in Phys. Rev. A. 74:040501(R), 2006). We furthermore present details of the experimental setup, and we show that results from spectroscopy of v′=8←v=0 overtones in combination with accurate ab initio calculations may yield a new value for the proton–electron mass ratio with an accuracy of order 1 ppb.

RETENTION OF A PRIMORDIAL COLD CLASSICAL KUIPER BELT IN AN INSTABILITY-DRIVEN MODEL OF SOLAR SYSTEM FORMATION

The cold classical population of the Kuiper belt exhibits a wide variety of unique physical characteristics, which collectively suggest that its dynamical coherence has been maintained through out the solar system's lifetime. Simultaneously, the retention of the cold population's relatively unexcited orbital state has remained a mystery, especially in the context of a solar system formation model, that is driven by a transient period of instability, where Neptune is temporarily eccentric. Here, we show that the cold belt can survive the instability, and its dynamical structure can be reproduced. We develop a simple analytical model for secular excitation of cold KBOs and show that comparatively fast apsidal precession and nodal recession of Neptune, during the eccentric phase, are essential for preservation of an unexcited state in the cold classical region. Subsequently, we confirm our results with self-consistent N-body simulations. We further show that contamination of the hot classical and scattered populations by objects of similar nature to that of cold classicals has been instrumental in shaping the vast physical diversity inherent to the Kuiper belt.

Long‐Term Evolution of Close Planets Including the Effects of Secular Interactions

This paper studies the long-term evolution of planetary systems containing short-period planets, including the effects of tidal circularization, secular excitation of eccentricity by companion planets, and stellar damping. For planetary systems subject to all of these effects, analytic solutions (or approximations) are presented for the time evolution of the semimajor axes and eccentricities. Secular interactions enhance the inward migration and accretion of hot Jupiters, while general relativity tends to act in opposition by reducing the effectiveness of the secular perturbations. The analytic solutions presented herein allow us to understand these effects over a wide range of parameter space and to isolate the effects of general relativity in these planetary systems.

Resonant instability of ducted free supersonic mixing layers induced by periodic Mach waves

It is known that the mixing or spreading rate of free mixing layers decreases with an increase in the convective Mach number of the flow. At supersonic convective Mach number the natural rate of mixing of the shear layers is very small. It is believed that the decrease in mixing rate is directly related to the decrease in the rate of growth of the instabilities of these flows. In an earlier study (Tarn &amp; Hu 1989) it was found that inside a rectangular channel supersonic free shear layers can support two families of instability waves and two families of acoustic wave modes. In this paper the possibility of driving these normal acoustic wave modes into resonant instability by using a periodic Mach wave system is investigated. The Mach waves can be generated by wavy walls. By properly choosing the wavelength of the periodic Mach wave system mutual secular excitation of two selected acoustic wave modes can be achieved. In undergoing resonant instability, the acoustic modes are locked into mutual simultaneous forcing. The periodic Mach waves serve as a catalyst without actually being involved in energy transfer. The resonant instability process is analysed by the method of multiple scales. Numerical results indicate that by using wavy walls with an amplitude-to-wavelength ratio of 1½% it is possible to obtain a total spatial growth of e9 folds over a distance of ten channel heights. This offers reasonable promise for mixing enhancement. The results of a parametric study of the effects of flow Mach numbers, temperature ratio, shear-layer thickness, modal numbers as well as three-dimensional effects on the spatial growth rate of the resonant instability are reported and examined so as to provide basic information needed for future feasibility analysis.

The Elasticity Theory of Dislocations in Real Earth Models and Changes in the Rotation of the Earth

Summary Steketee's Elasticity Theory of Dislocations is generalized to real Earth models. Taken into account are; (i) self-gravitation, (ii) radial variation of elastic properties, density and gravity, (iii) initial hydrostatic stress, (iv) the presence of the liquid core. Volterra's formula for the displacement field is found to hold in the more general circumstances for slip faults. The dilemma, previously pointed out by Jeffreys and Vicente, which arises when the Adams and Williamson condition is assumed not to hold everywhere perfectly in the core, is resolved. This result also bears on the theory of Earth tides and tidal loading. Changes in the inertia tensor are shown to arise only from spheroidal displacement fields of degree zero and two. These fields have virtually no attenuation with distance from the fault. In the one example in which a direct comparison can be made, the present theory gives a factor of 7.5 increase over a mapped half-space theory and a factor of 2.9 increase over the result for a uniform, spherical Earth, in the contribution to secular polar shift and excitation of Chandler wobble. Calculated and observed levels appear now to be in agreement.