arXiv subjects

Yanqin Wu

Publications and source records attributed to Yanqin Wu.

70 records · Page 4Linked to original sources

arXiv2007

From mean-motion resonances to scattered planets: Producing the Solar System, eccentric exoplanets and Late Heavy Bombardments

We show that interaction with a gas disk may produce young planetary systems with closely-spaced orbits, stabilized by mean-motion resonances between neighbors. On longer timescales, after the gas is gone, interaction with a remnant planetesimal disk tends to pull these configurations apart, eventually inducing dynamical instability. We show that this can lead to a variety of outcomes; some cases resemble the Solar System, while others end up with high-eccentricity orbits reminiscent of the observed exoplanets. A similar mechanism has been previously suggested as the cause of the lunar Late Heavy Bombardment. Thus, it may be that a large-scale dynamical instability, with more or less cataclysmic results, is an evolutionary step common to many planetary systems, including our own.

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arXiv2006

Formation of Narrow Dust Rings in Circumstellar Debris Disks

Narrow dust rings observed around some young stars (e.g., HR 4796A) need to be confined. We present a possible explanation for the formation and confinement of such rings in optically thin circumstellar disks, without invoking shepherding planets. If an enhancement of dust grains (e.g., due to a catastrophic collision) occurs somewhere in the disk, photoelectric emission from the grains can heat the gas to temperatures well above that of the dust. The gas orbits with super(sub)-Keplerian speeds inward (outward) of the associated pressure maximum. This tends to concentrate the grains into a narrow region. The rise in dust density leads to further heating and a stronger concentration of grains. A narrow dust ring forms as a result of this instability. We show that this mechanism not only operates around early-type stars that have high UV fluxes, but also around stars with spectral types as late as K. This implies that this process is generic and may have occurred during the lifetime of each circumstellar disk. We examine the stringent upper-limit on the H2 column density in the HR 4796A disk and find it to be compatible with the presence of a significant amount of hydrogen gas in the disk. We also compute the OI and CII infrared line fluxes expected from various debris disks and show that these will be easily detectable by the upcoming Herschel mission. Herschel will be instrumental in detecting and characterizing gas in these disks.

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arXiv2006

Resonant Tidal Excitations of Inertial Modes in Coalescing Neutron Star Binaries

We study the effect of resonant tidal excitation of inertial modes in neutron stars during binary inspiral. For spin frequencies less than 100 Hz, the phase shift in the gravitational waveform associated with the resonance is small and does not affect the matched filtering scheme for gravitational wave detection. For higher spin frequencies, the phase shift can become significant. Most of the resonances take place at orbital frequencies comparable to the spin frequency, and thus significant phase shift may occur only in the high-frequency band (hundreds of Hertz) of gravitational wave. The exception is a single odd-paity $m=1$ mode, which can be resonantly excited for misaligned spin-orbit inclinations, and may occur in the low-frequency band (tens of Hertz) of gravitational wave and induce significant (>> 1 radian) phase shift.

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arXiv2006

Braking the Gas in the beta Pictoris Disk

(Abridged) The main sequence star beta Pictoris hosts the best studied circumstellar disk to date. Nonetheless, a long-standing puzzle has been around since the detection of metallic gas in the disk: radiation pressure from the star should blow the gas away, yet the observed motion is consistent with Keplerian rotation. In this work we search for braking mechanisms that can resolve this discrepancy. We find that all species affected by radiation force are heavily ionized and dynamically coupled into a single fluid by Coulomb collisions, reducing the radiation force on species feeling the strongest acceleration. For a gas of solar composition, the resulting total radiation force still exceeds gravity, while a gas of enhanced carbon abundance could be self-braking. We also explore two other braking agents: collisions with dust grains and neutral gas. Grains surrounding beta Pic are photoelectrically charged to a positive electrostatic potential. If a significant fraction of the grains are carbonaceous (10% in the midplane and larger at higher altitudes), ions can be slowed down to satisfy the observed velocity constraints. For neutral gas to brake the coupled ion fluid, we find the minimum required mass to be $\approx$ 0.03 $M_\earth$, consistent with observed upper limits of the hydrogen column density, and substantially reduced relative to previous estimates. Our results favor a scenario in which metallic gas is generated by grain evaporation in the disk, perhaps during grain-grain collisions. We exclude a primordial origin for the gas, but cannot rule out the possibility of its production by falling evaporating bodies near the star. We discuss the implications of this work for observations of gas in other debris disks.

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arXiv2005

Origin of Tidal Dissipation in Jupiter: I. Properties of Inertial-Mode

We study global inertial-modes with the purpose of unraveling the role they play in the tidal dissipation process of Jupiter. For spheres of uniformly rotating, neutrally buoyant fluid, we show that the partial differential equation governing inertial-modes can be separated into two ordinary differential equations when the density is constant, or when the density has a power-law dependence on radius. For more general density dependencies, we show that one can obtain an approximate solution to the inertial-modes that is accurate to the second order in wave-vector. Frequencies of inertial-modes are limited to $ω< 2 Ω$ ($Ω$ is the rotation rate), with modes propagating closer to the rotation axis having higher frequencies. An inertial-mode propagates throughout much of the sphere with a relatively constant wavelength, and a wave amplitude that scales with density as $1/\sqrtρ$. It is reflected near the surface at a depth that depends on latitude, with the depth being much shallower near the special latitudes $θ= \cos^{-1} \pm ω/2Ω$. Around this region, this mode has the highest wave amplitude as well as the sharpest spatial gradient (the ``singularity belt''), thereby incurring the strongest turbulent dissipation. Inertial-modes naturally cause small Eulerian density perturbations, so they are only weakly coupled to the tidal potential. In a companion paper, we attempt to apply these results to the problem of tidal dissipation in Jupiter.

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arXiv2005

Origin of Tidal Dissipation in Jupiter: II. the Value of Q

The process of tidal dissipation inside Jupiter is not yet understood. Its tidal quality factor ($Q$) is inferred to lie between $10^5$ and $10^6$. We examine effects of inertial-modes on tidal dissipation in a neutrally bouyant, core-less, uniformly rotating planet. The rate of dissipation caused by resonantly excited inertial-modes depends on the following three parameters: how well they are coupled to the tidal potential, how strongly they are dissipated (by the turbulent viscosity), and how densely distributed they are in frequency. We find that as a function of tidal frequency, the $Q$ value exhibits large fluctuations, with its maximum value set by the group of inertial-modes that have a typical offset from an exact resonance of order their turbulent damping rates. In our model, inertial-modes shed their tidally acquired energy very close to the surface within a narrow latitudinal zone (the 'singularity belt'), and the tidal luminosity escapes freely out of the planet. Strength of coupling between the tidal potential and inertial-modes is sensitive to the presence of density discontinuities inside Jupiter. In the case of a discreet density jump (as may be caused by the transition between metallic and molecular hydrogen), we find a time-averaged $Q \sim 10^7$. Even though it remains unclear whether tidal dissipation due to resonant inertial-modes is the correct answer to the problem, it is impressive that our simple treatment here already leads to three to five orders of magnitude stronger damping than that from the equilibrium tide. Moreover, our conclusions are not affected by the presence of a small solid core, a different prescription for the turbulent viscosity, or nonlinear mode coupling, but they depend critically on the static stability in the upper atmosphere of Jupiter.

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arXiv2005

Resonance Overlap is Responsible for Ejecting Planets in Binary Systems

A planet orbiting around a star in a binary system can be ejected if it lies too far from its host star. We find that instability boundaries first obtained in numerical studies can be explained by overlap between sub-resonances within mean-motion resonances (mostly of the j:1 type). Strong secular forcing from the companion displaces the centroids of different sub-resonances, producing large regions of resonance overlap. Planets lying within these overlapping regions experience chaotic diffusion, which in most cases leads to their eventual ejection. The overlap region extends to shorter-period orbits as either the companion's mass or its eccentricity increase. Our analytical calculations reproduce the instability boundaries observed in numerical studies and yield the following two additional results. Firstly, the instability boundary as a function of eccentricity is jagged; thus, the widest stable orbit could be reduced from previously quoted values by as much as 20%. Secondly, very high order resonances (e.g., 50:3) do not significantly modify the instability boundary despite the fact that these weak resonances can produce slow chaotic diffusion which may be missed by finite-duration numerical integrations. We present some numerical evidence for the first result. More extensive experiments are called for to confirm these conclusions. For the special case of circular binaries, we find that the Hill criterion (based on the critical Jacobi integral) yields an instability boundary that is very similar to that obtained by resonance overlap arguments, making the former both a necessary and a sufficient condition for planet instability.

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arXiv2005

An algorithm to detect blends with eclipsing binaries in planet transit searches

We present an algorithm that can detect blends of bright stars with fainter, un-associated eclipsing binaries. Such systems contaminate searches for transiting planets, in particular in crowded fields where blends are common. Spectroscopic follow-up observations on large aperture telescopes have been used to reject these blends, but the results are not always conclusive. Our approach exploits the fact that a blend with a eclipsing binary changes its shape during eclipse. We analyze original imaging data from the Optical Gravitational Lensing Experiment (OGLE), which were used to discover planet transit candidates. Adopting a technique developed in weak gravitational lensing to carefully correct for the point spread function which varies both with time and across the field, we demonstrate that ellipticities can be measured with great accuracy using an ensemble of images. Applied to OGLE-TR-3 and OGLE-TR-56, two of the planetary transit candidates, we show that both systems are blended with fainter stars, as are most other stars in the OGLE fields. Moreover, while we do not detect shape change when TR-56 undergoes transits, TR-3 exhibits a significant shape change during eclipses. We therefore conclude that TR-3 is indeed a blend with an eclipsing binary, as has been suggested from other lines of evidence. The probability that its shape change is caused by residual systematics is found to be less than 0.6%. Our technique incurs no follow-up cost and requires little human interaction. As such it could become part of the data pipeline for any planetary transit search to minimize contamination by blends. We briefly discuss its relevance for the Kepler mission and for binary star detection.

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arXiv2003

Planet Migration and Binary Companions: the case of HD 80606b

The exo-solar planet HD 80606b has a highly eccentric (e=0.93) and tight (a=0.47 AU) orbit. We study how it might arrive at such an orbit and how it has avoided being tidally circularized until now. The presence of a stellar companion to the host star suggests the possibility that the Kozai mechanism and tidal dissipation combined to draw the planet inward well after it formed: Kozai oscillations produce periods of extreme eccentricity in the planet orbit, and the tidal dissipation that occurs during these periods of small pericentre distances leads to gradual orbital decay. We call this migration mechanism the 'Kozai migration'. It requires that the initial planet orbit is highly inclined relative to the binary orbit. For a companion at 1000 AU and an initial planet orbit at 5 AU, the minimum relative inclination required is ~ 85. We discuss the efficiency of tidal dissipation inferred from the observations of exo-planets. Moreover, we investigate possible explanations for the velocity residual (after the motion induced by the planet is removed) observed on the host star: a second planet in the system is excluded over a large extent of semi-major axis space if Kozai migration is to work, and the tide raised on the star by HD 80606b is likely too small in amplitude. Lastly, we discuss the relevance of Kozai migration for other planetary systems.

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arXiv2001

Tidal Evolution Of the Planetary System around HD 83443

Two planets with orbital period ratio approximately 10:1 have been discovered around the star HD 83443. The inner and more massive planet, HD 83443b, has the smallest semi-major axis among all currently known exoplanets. Unlike other short period exoplanets, it maintains a substantial orbital eccentricity, e_1=0.079+/- 0.008, in spite of efficient tidal damping. This is a consequence of its secular interactions with HD 83443c whose orbital eccentricity e_2=0.42+/-0.06. Dissipation, associated with tides the star raises in the inner planet, removes energy but not angular momentum from its orbit, while secular interactions transfer angular momentum but not energy from the inner to the outer planet's orbit. The outward transfer of angular momentum decreases the tidal decay rate of the inner planet's orbital eccentricity while increasing that of the outer planet. The alignment of the apsides of the planets' orbits is another consequence of tidal and secular interactions. In this state the ratio of their orbital eccentricities, e_1/e_2, depends upon the secular perturbations the planets exert on each other and on additional perturbations that enhance the inner planet's precession rate. Tidal and rotational distortions of the inner planet along with general relativity provide the most important of these extra precessional perturbations, each of which acts to reduce e_1/e_2. Provided the planets' orbits are coplanar, the observed eccentricity ratio uniquely relates sin i and C=(k_2/k_{2J})(R_1/R_J)^5, where the tidal Love number, k_2, and radius, R_1, of the inner planet are scaled by their Jovian equivalents.

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arXiv2001

Inferring Initial Spin Periods for Neutron Stars in Composite Remnant

We propose a method to infer the initial spin period of pulsars residing in composite supernova remnants. Such a remnant consists of both a plerionic and a shell type component, corresponding respectively to the pulsar wind nebula driven by the spindown luminosity of the central pulsar, and the blastwave bounding the supernova remnant. Theoretical investigations including hydrodynamical simulations have shown that at late times (~ 1,000 - 10,000 years), a simple scaling law connects the radius of the supernova shell to the radius of the plerion. The energy content of the plerion and the total mechanical energy of the supernova remnant enter into this scaling law. One can use this scaling law to estimate the initial spin period of pulsars residing in composite remnants. We discuss potential pitfalls of this method, including the effect of a small remnant age and of strong radiative losses in the plerion.

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arXiv2000

R-modes in Neutron Stars with Crusts: Turbulent Saturation, Spin-down, and Crust Melting

Rossby waves (r-modes) have been suggested as a means to regulate the spin periods of young or accreting neutron stars, and also to produce observable gravitational wave radiation. R-modes involve primarily transverse, incompressive motions of the star's fluid core. However, neutron stars gain crusts early in their lives: therefore, r-modes also imply shear in the fluid beneath the crust. We examine the criterion for this shear layer to become turbulent, and derive the rate of dissipation in the turbulent regime. Unlike dissipation from a viscous boundary layer, turbulent energy loss is nonlinear in mode energy and can therefore cause the mode to saturate at amplitudes typically much less than unity. This energy loss also reappears as heat below the crust. We study the possibility of crust melting as well as its implications for the spin evolution of low-mass X-ray binaries. Lastly, we identify some universal features of the spin evolution that may have observational consequences.

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arXiv2000

Gravity-Modes in ZZ Ceti Stars: IV. Amplitude Saturation by Parametric Instability

ZZ Ceti stars exhibit small amplitude photometric pulsations in multiple gravity-modes. We demonstrate that parametric instability, a form of resonant 3-mode coupling, limits overstable modes to amplitudes similar to those observed. In particular, it reproduces the observed trend that longer period modes have larger amplitudes. Parametric instability involves the destabilization of a pair of stable daughter modes by an overstable parent mode. The 3-modes must satisfy exact angular selection rules and approximate frequency resonance. The lowest instability threshold for each parent mode is provided by the daughter pair that minimizes $(δω^2+γ_d^2)/κ^2$, where $κ$ is the nonlinear coupling constant, $δω$ is the frequency mismatch, and $γ_d$ is the energy damping rate of the daughter modes. The overstable mode's amplitude is maintained at close to the instability threshold value. Although parametric instability defines an upper envelope for the amplitudes of overstable modes in ZZ Ceti stars, other nonlinear mechanisms are required to account for the irregular distribution of amplitudes of similar modes and the non-detection of modes with periods longer than $1,200\s$. Resonant 3-mode interactions involving more than one excited mode may account for the former. Our leading candidate for the latter is Kelvin-Helmholtz instability of the mode-driven shear layer below the convection zone.

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arXiv2000

Combination Frequencies in the Fourier Spectra of White Dwarfs

Combination frequencies are observed in the Fourier spectra of pulsating DA and DB white dwarfs. They appear at sums and differences of frequencies associated with the stellar gravity-modes. Brickhill (1992) proposed that the combination frequencies result from mixing of the eigenmode signals as the surface convection zone varying in depth when undergoing pulsation. This depth changes cause time-dependent thermal impedance, which mix different harmonic frequencies in the light curve. Following Brickhill's proposal, we developed analytical expressions to describe the amplitudes and phases of these combination frequencies. The parameters that appear in these expressions are: the depth of the stellar convection zone when at rest, the sensitivity of this depth towards changes in stellar effective temperature, the inclination angle of the stellar pulsation axis with respect to the line of sight, and lastly, the spherical degrees of the eigenmodes involved in the mixing. Adopting reasonable values for these parameters, we apply our expressions to a DA and a DB variable white dwarf. We find reasonable agreement between theory and observation, though some discrepancies remain unexplained. We show that it is possible to identify the spherical degrees of the pulsation modes using the combination frequencies.

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arXiv1998

Gravity-Modes in ZZ Ceti Stars III. Eigenvalues and Eigenfuctions

We report on numerical calculations of nonadiabatic eigenvalues and eigenfunctions for g-modes in ZZ Ceti variables. The spectrum of overstable $l=1$ modes delineates the instability strip. Its blue edge occurs where $ωτ_c \approx 1$ for the $n=1$ mode. Here $ω$ is radian frequency and $τ_c$ is about four times the thermal timescale at the bottom of the surface convection zone. As a ZZ Ceti cools, its convection zone deepens, longer period modes become overstable, but the critical value of $ωτ_c$ separating overstable and damped modes rises. The latter is a consequence of enhanced radiative damping for modes which propagate immediately below the convection zone. The critical value of $ωτ_c$ is of observational significance because modes with the smallest value of $ωτ_c$ are most observable photometrically. Maximum periods for overstable modes predicted for our cooler model envelopes are about a factor two longer than the observational upper limit of $1,200\s$. We assess a number of plausible resolutions for this discrepancy among which convective overshoot and nonlinear saturation look promising. The nonadiabatic eigenfunctions enable us to predict relative amplitudes and phases of photospheric variations of flux and velocity, quantities made accessible by recent observations. We also present asymptotic formula for damping rates of high order modes, a result of consequence for future investigations of nonlinear saturation of the amplidues of overstable modes.

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arXiv1998

Gravity-Modes in ZZ Ceti Stars: I.Quasiadiabatic Analysis of Overstability

We analyze the stability of g-modes in variable white dwarfs with hydrogen envelopes. In these stars, the radiative layer contributes to mode damping because its opacity decreases upon compression and the amplitude of the Lagrangian pressure perturbation increases outward. The overlying convective envelope is the seat of mode excitation because it acts as an insulating blanket with respect to the perturbed flux that enters it from below. A crucial point is that the convective motions respond to the instantaneous pulsational state. Driving exceeds damping by as much as a factor of two provided $ωτ_c\geq 1$, where $ω$ is the radian frequency of the mode and $τ_c\approx 4τ_{th}$ with $τ_{th}$ being the thermal time constant evaluated at the base of the convective envelope. As a white dwarf cools, its convection zone deepens, and modes of lower frequency become overstable. However, the deeper convection zone impedes the passage of flux perturbations from the base of the convection zone to the photosphere. Thus the photometric variation of a mode with constant velocity amplitude decreases. These factors account for the observed trend that longer period modes are found in cooler DAVs. The linear growth time, ranging from hours for the longest period observed modes ($P\approx 20$ minutes) to thousands of years for those of shortest period ($P\approx 2 $ minutes), probably sets the time-scale for variations of mode amplitude and phase. This is consistent with observations showing that longer period modes are more variable than shorter period ones. Our investigation confirms many results obtained by Brickhill in his pioneering studies of ZZ Cetis.

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