arXiv subjects

Yanqin Wu

Publications and source records attributed to Yanqin Wu.

At least 55 records · Page 3Linked to original sources

arXiv2014

A Statistical Reconstruction of the Planet Population Around Kepler Solar-Type Stars

Using the cumulative catalog of planets detected by the NASA Kepler mission, we reconstruct the intrinsic occurrence of Earth- to Neptune-size (1 - 4$R_{\oplus}$) planets and their distributions with radius and orbital period. We analyze 76,711 solar-type ($0.8<R_*/R_{\odot}<1.2 $) stars with 430 planets on 20-200~d orbits, excluding close-in planets that may have been affected by the proximity to the host star. Our analysis considers errors in planet radii and includes an "iterative simulation" technique that does not bin the data. We find a radius distribution that peaks at 2-2.8 Earth radii, with lower numbers of smaller and larger planets. These planets are uniformly distributed with logarithmic period, and the mean number of such planets per star is $0.46 \pm 0.03$. The occurrence is $\sim 0.66$ if planets interior to 20~d are included. We estimate the occurrence of Earth-size planets in the "habitable zone" (defined as 1-2$R_{\oplus}$, 0.99-1.7 AU for solar-like stars) as $6.4^{+3.4}_{-1.1} \%$. Our results largely agree with those of Petigura et al. (2013), although we find a higher occurrence of 2.8-4 Earth-radii planets. The reasons for this excess are the inclusion of errors in planet radius, updated Huber et al. (2014) stellar parameters, and also the exclusion of planets which may have been affected by proximity to the host star.

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arXiv2014

Stability of the Kepler-11 System and its Origin

A significant fraction of Kepler systems are closely-packed, largely coplanar and circular. We study the stability of a 6-planet system, Kepler-11, to gain insights on the dynamics and formation history of such systems. Using a technique called `frequency maps' as fast indicators for long-term stability, we explore the stability of Kepler-11 system by analyzing the neighbourhood space around its orbital parameters. Frequency maps provide a visual representation of chaos and stability, and their dependence on orbital parameters. We find that the current system is stable, but lies within a few percent of several dynamically dangerous 2-body mean-motion resonances. Planet eccentricities are restricted below a small value, $\sim 0.04$, for long-term stability, but planet masses can be more than twice their reported values (thus, allowing for the possibility of mass-loss by past photoevaporation). Based on our frequency maps, we speculate on the origin for instability in closely-packed systems. We then proceed to investigate how the system can have been assembled. The stability constraints on Kepler-11 (mainly, eccentricity constraints) suggest that if the system were assembled in-situ, a dissipation mechanism must have been at work to neutralize eccentricity excitation. On the other hand, if migration was responsible for assembling the planets, there has to be little differential migration among the planets, to avoid them either getting trapped into mean motion resonances, or crashing into each other.

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arXiv2014

Frequency of Close Companions among Kepler Planets - a TTV study

A transiting planet exhibits sinusoidal transit-time-variations (TTVs) if perturbed by a companion near a mean-motion-resonance (MMR). We search for sinusoidal TTVs in more than 2600 Kepler candidates, using the publicly available Kepler light-curves (Q0-Q12). We find that the TTV fractions rise strikingly with the transit multiplicity. Systems where four or more planets transit enjoy roughly five times higher TTV fraction than those where a single planet transits, and about twice higher than those for doubles and triples. In contrast, models in which all transiting planets arise from similar dynamical configurations predict comparable TTV fractions among these different systems. One simple explanation for our results is that there are at least two different classes of Kepler systems, one closely packed and one more sparsely populated.

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arXiv2013

Secular chaos and its application to Mercury, hot Jupiters, and the organization of planetary systems

In the inner solar system, the planets' orbits evolve chaotically, driven primarily by secular chaos. Mercury has a particularly chaotic orbit, and is in danger of being lost within a few billion years. Just as secular chaos is reorganizing the solar system today, so it has likely helped organize it in the past. We suggest that extrasolar planetary systems are also organized to a large extent by secular chaos. A hot Jupiter could be the end state of a secularly chaotic planetary system reminiscent of the solar system. But in the case of the hot Jupiter, the innermost planet was Jupiter- (rather than Mercury-) sized, and its chaotic evolution was terminated when it was tidally captured by its star. In this contribution, we review our recent work elucidating the physics of secular chaos and applying it to Mercury and to hot Jupiters. We also present new results comparing the inclinations of hot Jupiters thus produced with observations.

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arXiv2013

Kepler planets: a tale of evaporation

(Abridged) Inspired by the Kepler planet discoveries, we consider the thermal contraction of planets close to their parent star, under the influence of evaporation. The mass-loss rates are based on hydrodynamic models of evaporation that include both X-ray and EUV irradiation. We find that only low-mass planets with hydrogen envelopes are significantly affected by evaporation, with evaporation being able to remove massive hydrogen envelopes inward of 0.1 AU for Neptune-mass objects. We construct a theoretical population of planets with varying core masses, envelope masses, orbital separations, and stellar spectral types, and compare these against the sizes and densities measured for low-mass planets, both in the Kepler mission and from radial velocity surveys. This exercise leads us to conclude that evaporation is the driving force of evolution for close-in Kepler planets. In fact, some 50% of the Kepler planet candidates may have been significantly eroded. Evaporation explains two striking correlations observed in these objects: a lack of large radius/low density planets close to the stars, and a bimodal distribution in planet sizes with a deficit of planets around 2R_E. Planets that have experienced high X-ray exposures are generally smaller than this size, and those with lower X-ray exposures are typically larger. A bimodal distribution is naturally explained by the evaporation model, where, depending on their X-ray exposure, close-in planets can either hold on to hydrogen envelopes 1% in mass, or be stripped entirely. To quantitatively reproduce the observed features, we argue that not only do low-mass Kepler planets need to be made of rocky cores overlaid with hydrogen envelopes, but few of them should have initial masses above 20 M_E, and the majority of them should have core masses of a few Earth masses.

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arXiv2013

Density and Eccentricity of Kepler Planets

We analyze the transit timing variations obtained by the Kepler mission for 22 sub-jovian planet pairs (17 published, 5 new) that lie close to mean motion resonances. We find that the TTV phases for most of these pairs lie close to zero, consistent with an eccentricity distribution that has a very low RMS value of e ~ 0.01; but about a quarter of the pairs possess much higher eccentricities, up to 0.1 - 0.4. For the low-eccentricity pairs, we are able to statistically remove the effect of eccentricity to obtain planet masses from TTV data. These masses, together with those measured by radial velocity, yield a best fit mass-radius relation M~3 M_E (R/R_E). This corresponds to a constant surface escape velocity of 20km/s. We separate the planets into two distinct groups, "mid-sized" (those greater than 3 R_E), and "compact" (those smaller). All mid-sized planets are found to be less dense than water and therefore contain extensive H/He envelopes, likely comparable in mass to that of their cores. We argue that these planets have been significantly sculpted by photoevaporation. Surprisingly, mid-sized planets are discovered exclusively around stars more massive than 0.8 M_sun. The compact planets, on the other hand, are often denser than water. Combining our density measurements with those from radial velocity studies, we find that hotter compact planets tend to be denser, with the hottest ones reaching rock density. Moreover, hotter planets tend to be smaller in sizes. These results can be explained if the compact planets are made of rocky cores overlaid with a small amount of hydrogen, < 1% in mass, with water contributing little to their masses or sizes. Photoevaporation has exposed bare rocky cores in cases of the hottest planets. Our conclusion that these planets are likely not water-worlds contrasts with some previous studies.

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arXiv2012

On the unusual gas composition in the Beta Pictoris debris disk

The metallic gas associated with the Beta Pic debris disk is not believed to be primordial, but arises from the destruction of dust grains. Recent observations have shown that carbon and oxygen in this gas are exceptionally overabundant compared to other elements, by some 400 times. We study the origin of this enrichment under two opposing hypothesis, preferential production, where the gas is produced with the observed unusual abundance (as may happen if gas is produced by photo-desorption from C/O-rich icy grains), and preferential depletion, where the gas evolves to the observed state from an original solar abundance (if outgassing occurs under high-speed collisions) under a number of dynamical processes. We include ... ... We find ... ...

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arXiv2012

Ohmic Heating Suspends, not Reverses, the Cooling Contraction of Hot Jupiters

We study the radius evolution of close-in extra-solar jupiters under Ohmic heating, a mechanism that was recently proposed to explain the large observed sizes of many of these planets. Planets are born with high entropy and they subsequently cool and contract. We focus on two cases: first, that ohmic heating commences when the planet is hot (high entropy); and second, that it commences after the planet has cooled. In the former case, we use analytical scalings and numerical experiments to confirm that Ohmic heating is capable of suspending the cooling as long as a few percent of the stellar irradiation is converted into Ohmic heating, and the planet has a surface wind that extends to pressures of ~10 bar or deeper. For these parameters, the radii at which cooling is stalled are consistent with (or larger than) the observed radii of most planets. The only two exceptions are WASP-17b and HAT-P-32b. In contrast to the high entropy case, we show that Ohmic heating cannot significantly re-inflate planets after they have already cooled. This leads us to suggest that the diversity of radii observed in hot jupiters may be partially explained by the different epochs at which they are migrated to their current locations.

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arXiv2012

Extracting Planet Mass and Eccentricity From TTV data

Most planet pairs in the Kepler data that have measured transit time variations (TTV) are near first-order mean-motion resonances. We derive analytical formulae for their TTV signals. We separate planet eccentricity into free and forced parts, where the forced part is purely due to the planets' proximity to resonance. This separation yields simple analytical formulae. The phase of the TTV depends sensitively on the presence of free eccentricity: if the free eccentricity vanishes, the TTV will be in phase with the longitude of conjunctions. This effect is easily detectable in current TTV data. The amplitude of the TTV depends on planet mass and free eccentricity, and it determines planet mass uniquely only when the free eccentricity is sufficiently small. We proceed to analyze the TTV signals of six short period Kepler pairs. We find that three of these pairs (Kepler-18,24,25) have TTV phase consistent with zero. The other three (Kepler-23,28,32) have small TTV phases, but ones that are distinctly non-zero. We deduce that the free eccentricities of the planets are small, < 0.01, but not always vanishing. Furthermore, as a consequence of this, we deduce that the true masses of the planets are fairly accurately determined by the TTV amplitudes, within a factor < 2. The smallness of the free eccentricities suggests that the planets have experienced substantial dissipation. This is consistent with the hypothesis that the observed pile-up of Kepler pairs near mean-motion resonances is caused by resonant repulsion. But the fact that some of the planets have non-vanishing free eccentricity suggests that after resonant repulsion occurred there was a subsequent phase in the planets' evolution when their eccentricities were modestly excited, perhaps by interplanetary interactions.

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arXiv2012

Resonant Repulsion of Kepler Planet Pairs

Planetary systems discovered by the Kepler space telescope exhibit an intriguing feature. While the period ratios of adjacent low-mass planets appear largely random, there is a significant excess of pairs that lie just wide of resonances and a deficit on the near side. We demonstrate that this feature naturally arises when two near-resonant planets interact in the presence of weak dissipation that damps eccentricities. The two planets repel each other as orbital energy is lost to heat. This moves near-resonant pairs just beyond resonance, by a distance that reflects the integrated dissipation they experienced over their lifetimes. We find that the observed distances may be explained by tides if tidal dissipation is unexpectedly efficient (tidal quality factor ~10). Once the effect of resonant repulsion is accounted for, the initial orbits of these low mass planets show little preference for resonances. This could constrain their origin.

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arXiv2011

Planetesimals in Debris Disks of Sun-like Stars

Observations of dusty debris disks can be used to test theories of planetesimal coagulation. Planetesimals of sizes up to a couple thousand kms are embedded in these disks and their mutual collisions generate the small dust grains that are observed. The dust luminosities, when combined with information on the dust spatial extent and the system age, can be used to infer initial masses in the planetesimal belts. Carrying out such a procedure for a sample of debris disks around Sun-like stars, we reach the following two conclusions. First, if we assume that colliding planetesimals satisfy a primordial size spectrum of the form dn/ds ~ s^{-q}, observed disks strongly favor a value of q between 3.5 and 4, while both current theoretical expectations and statistics of Kuiper belt objects favor a somewhat larger value. Second, number densities of planetesimals are two to three orders of magnitude higher in detected disks than in the Kuiper belt, for comparably-sized objects. This is a surprise for the coagulation models. It would require a similar increase in the solid surface density of the primordial disk over that of the Minimum Mass Solar Nebula, which is unreasonable. Both of our conclusions are driven by the need to explain the presence of bright debris disks at a few Gyrs of age.

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arXiv2010

Theory of Secular Chaos and Mercury's Orbit

We study the chaotic orbital evolution of planetary systems, focusing on secular (i.e., orbit-averaged) interactions, because these often dominate on long timescales. We first focus on the evolution of a test particle that is forced by multiple massive planets. To linear order in eccentricity and inclination, its orbit precesses with constant frequencies. But nonlinearities can shift the frequencies into and out of secular resonance with the planets' eigenfrequencies, or with linear combinations of those frequencies. The overlap of these nonlinear secular resonances drive secular chaos in planetary systems. We quantify the resulting dynamics for the first time by calculating the locations and widths of nonlinear secular resonances. When results from both analytical calculations and numerical integrations are displayed together in a newly developed "map of the mean momenta" (MMM), the agreement is excellent. This map is particularly revealing for non-coplanar planetary systems and demonstrates graphically that chaos emerges from overlapping secular resonances. We then apply this newfound understanding to Mercury. Previous numerical simulations have established that Mercury's orbit is chaotic, and that Mercury might even collide with Venus or the Sun. We show that Mercury's chaos is primarily caused by the overlap between resonances that are combinations of four modes, the Jupiter-dominated eccentricity mode, the Venus-dominated inclination mode and Mercury's free eccentricity and inclination. Numerical integration of the Solar system confirms that a slew of these resonant angles alternately librate and circulate. We are able to calculate the threshold for Mercury to become chaotic: Jupiter and Venus must have eccentricity and inclination of a few percent. Mercury appears to be perched on the threshold for chaos.

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arXiv2010

Secular Chaos and the Production of Hot Jupiters

In a planetary system with two or more well-spaced, eccentric, inclined planets, secular interactions may lead to chaos. The innermost planet may gradually become very eccentric and/or inclined, as a result of the secular degrees of freedom drifting towards equipartition of angular momentum deficit. Secular chaos is known to be responsible for the eventual destabilization of Mercury in our own Solar System. Here we focus on systems with three giant planets. We characterize the secular chaos and demonstrate the criterion for it to occur, but leave a detailed understanding of secular chaos to a companion paper (Lithwick & Wu, 2010). After an extended period of eccentricity diffusion, the inner planet's pericentre can approach the star to within a few stellar radii. Strong tidal interactions and ensuing tidal dissipation extracts orbital energy from the planet and pulls it inward, creating a hot Jupiter. In contrast to other proposed channels for the production of hot Jupiters, such a scenario (which we term "secular migration") explains a range of observations: the pile-up of hot Jupiters at 3-day orbital periods, the fact that hot Jupiters are in general less massive than other RV planets, that they may have misaligned inclinations with respect to stellar spin, and that they have few easily detectable companions (but may have giant companions in distant orbits). Secular migration can also explain close-in planets as low in mass as Neptune; and an aborted secular migration can explain the "warm Jupiters" at intermediate distances. In addition, the frequency of hot Jupiters formed via secular migration increases with stellar age. We further suggest that secular chaos may be responsible for the observed eccentricities of giant planets at larger distances, and that these planets could exhibit significant spin-orbit misalignment.

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arXiv2010

Gas emission from debris disks around A and F stars

Gas has been detected in a number of debris disk systems. This gas may have arisen from grain sublimation or grain photodesorption. It interacts with the surrounding dust grains through a number of charge and heat exchanges. Studying the chemical composition and physical state of this gas can therefore reveal much about the dust component in these debris disks. We have produced a new code, ontario, to address gas emission from dusty gas-poor disks around A--F stars. This code computes the gas ionization and thermal balance self-consistently, with particular care taken of heating/cooling mechanisms. Line emission spectra are then produced for each species (up to zinc) by statistical equilibrium calculations of the atomic/ionic energy levels. For parameters that resemble the observed beta Pictoris gas disk, we find that the gas is primarily heated by photoelectric emission from dust grains, and primarily cooled through the CII 157.7 micron line emission. The gas can be heated to a temperature that is warmer than that of the dust and may in some cases reach temperature for thermal escape. The dominant cooling line, CII 157.7 micron, should be detectable by Herschel in these disks, while the OI 63.2 micron line will be too faint. We also study the dependence of the cooling line fluxes on a variety of disk parameters, in light of the much improved sensitivity to thermal line emission in the mid/far infrared and at sub-millimeter wavelengths provided by, in particular, Herschel, SOFIA and ALMA. These new instruments will yield much new information about dusty debris disks.

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arXiv2008

The Effect of Charon's Tidal Damping on the Orbits of Pluto's Three Moons

Pluto's recently discovered minor moons, Nix and Hydra, have almost circular orbits, and are nearly coplanar with Charon, Pluto's major moon. This is surprising because tidal interactions with Pluto are too weak to damp their eccentricities. We consider an alternative possibility: that Nix and Hydra circularize their orbits by exciting Charon's eccentricity via secular interactions, and Charon in turn damps its own eccentricity by tidal interaction with Pluto. The timescale for this process can be less than the age of the Solar System, for plausible tidal parameters and moon masses. However, as we show numerically and analytically, the effects of the 2:1 and 3:1 resonant forcing terms between Nix and Charon complicate this picture. In the presence of Charon's tidal damping, the 2:1 term forces Nix to migrate outward and the 3:1 term changes the eccentricity damping rate, sometimes leading to eccentricity growth. We conclude that this mechanism probably does not explain Nix and Hydra's current orbits. Instead, we suggest that they were formed in-situ with low eccentricities. We also show that an upper limit on Nix's migration speed sets a lower limit on Pluto-Charon's tidal circularization timescale of >10^5 yrs. Moreover, Hydra's observed proper eccentricity may be explained by the 3:2 forcing by Nix.

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arXiv2008

On the Origin of Pluto's Minor Moons, Nix and Hydra

How did Pluto's recently discovered minor moons form? Ward and Canup propose an elegant solution in which Nix and Hydra formed in the collision that produced Charon, then were caught into corotation resonances with Charon, and finally were transported to their current location as Charon migrated outwards. We show with numerical integrations that, if Charon's eccentricity is judiciously chosen, this scenario works beautifully for either Nix or Hydra. However, it cannot work for both Nix and Hydra simultaneously. To transport Nix, Charon's eccentricity must satisfy e_C< 0.024; otherwise, the second order Lindblad resonance at 4:1 overlaps with the corotation resonance, leading to chaos. To transport Hydra, e_C > 0.7 R_p/a_C > 0.04; otherwise migration would be faster than libration, and Hydra would slip out of resonance. These two restrictions conflict. Having ruled out this scenario, we suggest an alternative: that many small bodies were captured from the nebular disk, and they were responsible for forming, migrating and damping Nix and Hydra. If this is true, small moons could be common around large Kuiper belt objects.

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arXiv2008

Outer edges of debris discs: how sharp is sharp?

Ring-like features have been observed in several debris discs. Outside the main ring, while some systems exhibit smooth surface brightness profiles (SB) that fall off roughly as r**-3.5, others display large luminosity drops at the ring's outer edge and steeper radial SB profiles. We seek to understand this diversity of outer edge profiles under the ``natural'' collisional evolution of the system, without invoking external agents such as planets or gas. We use a statistical code to follow the evolution of a collisional population, ranging from dust grains (submitted to radiation pressure) to planetesimals and initially confined within a belt (the 'birth ring'). The system typically evolves toward a "standard" steady state, with no sharp edge and SB \propto r**-3.5 outside the birth ring. Deviations from this standard profile, in the form of a sharp outer edge and a steeper fall-off, occur only when two parameters take their extreme values: 1) When the birth ring is so massive that it becomes radially optically thick for the smallest grains. However, the required disc mass is here probably too high to be realistic. 2) When the dynamical excitation of the dust-producing planetesimals is so low ( <0.01) that the smallest grains, which otherwise dominate the total optical depth, are preferentially depleted. This low-excitation case, although possibly not generic, cannot be ruled out by observations. Our "standard" profile provides a satisfactory explanation for a large group of debris discs with outer edges and SB falling as r**-3.5. Systems with sharper outer edges, barring other confining agents, could still be explained by ``natural'' collisional evolution if their dynamical excitation is very low. We show that such a dynamically-cold case provides a satisfactory fit for HR4796A

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arXiv2007

Hot Jupiters in binary star systems

Radial velocity surveys find Jupiter mass planets with semi-major axes a less than 0.1 AU around ~1% of solar-type stars; counting planets with $a$ as large as 5 AU, the fraction of stars having planets reaches ~ 10% {Marcy,Butler}. An examination of the distribution of semi-major axes shows that there is a clear excess of planets with orbital periods around 3 or 4 days, corresponding to a~0.03$ AU, with a sharp cutoff at shorter periods (see Figure 1). It is believed that Jupiter mass planets form at large distances from their parent stars; some fraction then migrate in to produce the short period objects. We argue that a significant fraction of the `hot Jupiters' (a<0.1 AU) may arise in binary star systems in which the orbit of the binary is highly inclined to the orbit of the planet. Mutual torques between the two orbits drive down the minimum separation or periapse r_p between the planet and its host star (the Kozai mechanism). This periapse collapse is halted when tidal friction on the planet circularizes the orbit faster than Kozai torque can excite it. The same friction then circularizes the planet orbit, producing hot Jupiters with the peak of the semimajor axis distribution lying around 3 days. For the observed distributions of binary separation, eccentricity and mass ratio, roughly 2.5% of planets with initial semimajor axis a_p ~ 5au will migrate to within 0.1au of their parent star. Kozai migration could account for 10% or more of the observed hot Jupiters.

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