arXiv subjects

Dong Lai

Publications and source records attributed to Dong Lai.

At least 91 records · Page 5Linked to original sources

arXiv2021

Jupiter's Dynamical Love Number

Recent observations by the {\it Juno} spacecraft have revealed that the tidal Love number $k_2$ of Jupiter is $4\%$ lower than the hydrostatic value. We present a simple calculation of the dynamical Love number of Jupiter that explains the observed "anomaly". The Love number is usually dominated by the response of the (rotation-modified) f-modes of the planet. Our method also allows for efficient computation of high-order dynamical Love numbers. While the inertial-mode contributions to the Love numbers are negligible, a sufficiently strong stratification in a large region of the planet's interior would induce significant g-mode responses and influence the measured Love numbers.

astro-ph.EP↗

arXiv2021

Inclination Dynamics of Resonant Planets under the Influence of an Inclined External Companion

Recent observations suggest that a large fraction of Kepler super-Earth systems have external giant planet companions (cold Jupiters), which can shape the architecture of the inner planets, in particular their mutual inclinations. The dynamical perturbation from cold Jupiters may account for the population of misaligned planets in the Kepler data. The effectiveness of this mechanism can be hindered by a strong planet--planet coupling in the inner system. In this paper, we study how mean-motion resonances (MMRs) affect this coupling and the expected misalignment. We derive approximate analytical expressions for the mutual inclination excitations in the inner planet system induced by an inclined companion, for various period ratios and perturber properties. In most cases, the mutual inclination is proportional to a dimensionless parameter that characterizes the strength of the perturber relative to the coupling in the inner system. We show that the MMR strengthens the inner coupling, reducing the mutual inclination induced by the perturber by a factor of a few. We find that the resonance is resilient to the perturbation, and derive a criterion for the libration of the resonant angle. Our results have applications for constraining unseen planetary perturbers, and for understanding the architecture of multiplanet systems.

astro-ph.EP↗

arXiv2021

Spin-Orbit Misalignments in Tertiary-Induced Black-Hole Binary 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 $θ_{\rm sl}$ 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 $θ_{\rm sl}$ 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 $χ_{\rm eff}\sim 0$ 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.

gr-qc↗

arXiv2021

Hierarchical Black-Hole Mergers in Multiple Systems: Constrain the Formation of GW190412, GW190814 and GW190521-like events

The merging black-hole (BH) binaries GW190412, GW190814 and GW190521 from the third LIGO/VIRGO observing run exhibit some extraordinary properties, including highly asymmetric masses, significant spin, and component mass in the "mass gap". These features can be explained if one or both components of the binary are the remnants of previous mergers. In this paper, we explore hierarchical mergers in multiple stellar systems, taking into account the natal kick and mass loss due to the supernova explosion (SN) on each component, as well as the merger kick received by the merger remnant. The binaries that have survived the SNe and kicks generally have too wide orbital separations to merge by themselves, but can merge with the aid of an external companion that gives rise to Lidov-Kozai oscillations. The BH binaries that consist of second-generation BHs can also be assembled in dense star clusters through binary interactions. We characterize the parameter space of these BH binaries by merger fractions in an analytical approach. Combining the distributions of the survived binaries, we further constrain the parameters of the external companion, using the analytically formulated tertiary perturbation strength. We find that to produce the three LIGO/VIRGO O3 events, the external companions must be at least a few hundreds $M_\odot$, and fall in the intermediate-mass BH and supermassive BH range. We suggest that GW190412, GW190814 and GW190521 could all be produced via hierarchical mergers in multiples, likely in a nuclear star cluster, with the final merger induced by a massive BH.

astro-ph.HE↗

arXiv2021

Enhanced Lidov-Kozai migration and the formation of the transiting giant planet WD1856+534b

We investigate the possible origin of the transiting giant planet WD1856+534b, 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 an 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 ($e \gtrsim 0.999$), 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 $e \simeq 1$, we obtain an absolute limit of $a_{1} \gtrsim 8 \, {\rm AU} \, (a_{3} / 1500 \, {\rm AU})^{6/7}$ for the planet's semi-major axis just before migration (where $a_{3}$ is the semi-major axis of the 'outer' orbit). We suggest that, to achieve a wide LK window through the 2+2 resonance, WD1856b likely migrated from $30 \, {\rm AU} \lesssim a_{1} \lesssim 60 \, {\rm AU}$, corresponding to $\sim 10$--$20 \, {\rm AU}$ 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.

astro-ph.EP↗

arXiv2020

Excitation of Spin-Orbit Misalignments in Stellar Binaries with Circumbinary Disks: Application to DI Herculis

The large spin-orbit misalignments in the DI Herculis stellar binary system have resolved the decades-long puzzle of the anomalously slow apsidal precession rate, but raise new questions regarding the origin of the obliquities. This paper investigates obliquity evolution in stellar binaries hosting modestly-inclined circumbinary disks. As the disk and binary axes undergo mutual precession, each oblate star experiences a torque from its companion star, so that the spin and orbital axes undergo mutual precession. As the disk loses mass through a combination of winds and accretion, the system may be captured into a high-obliquity Cassini state (a spin-orbit resonance). The final obliquity depends on the details of the disk dispersal. We construct a simple disk model to emulate disk dispersal due to viscous accretion and photoevaporation, and identify the necessary disk properties for producing the observed obliquities in DI Herculis. The disk must be massive (at least $10 \%$ of the binary mass). If accretion onto the binary is suppressed, the observed high stellar obliquities are reproduced with a binary-disk inclination of $\sim 5^\circ - 10^\circ$, but if substantial accretion occurs, the inclination must be larger, $\sim 20^\circ - 30^\circ$. If moderate accretion occurs, initially the disk must lose its mass slowly, but eventually lose its remaining mass abruptly, analogous to the observed two-timescale behavior for disks around T-Tauri stars. The spin feedback on the binary orbit causes the binary-disk inclination to decay as the obliquity evolves, a feature that is absent from the standard Cassini state treatment.

astro-ph.SR↗

arXiv2020

High-eccentricity migration of planetesimals around polluted white dwarfs

Several white dwarfs with atmospheric metal pollution have been found to host small planetary bodies (planetesimals) orbiting near the tidal disruption radius. We study the physical properties and dynamical origin of these bodies under the hypothesis that they underwent high-eccentricity migration from initial distances of several astronomical units. We examine two plausible mechanisms for orbital migration and circularization: tidal friction and ram-pressure drag in a compact disc. For each mechanism, we derive general analytic expressions for the evolution of the orbit that can be rescaled for various situations. We identify the physical parameters that determine whether a planetesimal's orbit can circularize within the appropriate time-scale and constrain these parameters based on the properties of the observed systems. For tidal migration to work, an internal viscosity similar to that of molten rock is required, and this may be naturally produced by tidal heating. For disc migration to operate, a minimal column density of the disc is implied; the inferred total disc mass is consistent with estimates of the total mass of metals accreted by polluted WDs.

astro-ph.EP↗

arXiv2020

Evolution of inspiralling neutron star binaries: effects of tidal interactions and orbital eccentricities

Neutron star (NS) binaries formed dynamically may have significant eccentricities while emitting gravitational waves (GWs) in the LIGO/VIRGO band. We study tidal effects in such eccentric inspiralling NS binaries using a set of hybrid equations. The NS is modelled as a compressible ellipsoid, which can deform nonlinearly due to tidal forces, while the orbit evolution is treated with the post-Newtonian (PN) theory up to 2.5-PN order. We find that in general, the tidal interaction can accelerate the inspiral, and cause orbital frequency and phase shifts. For circular inspirals, our calculations reproduce previous linear result at large binary separations, but incorporate the dynamical response of the NS at small separations. For eccentric inspirals, the frequency and phase shifts oscillate considerably near pericenter passages, and the oscillating amplitudes increase with eccentricities. As a result, the GW phase is also significantly influenced by the tidal effect. At merger, the cumulative GW phase shift can reach more than 10 radians (for typical NS mass $1.4M_\odot$ and radius 11.6 km), much larger than the circular inspiral case. Although the event rate of eccentric NS mergers is likely low, the detection of such mergers could provide a useful constraint on the NS equation of state.

astro-ph.HE↗

arXiv2020

Dynamics of Colombo's Top: Generating Exoplanet Obliquities from Planet-Disk Interactions

Large planetary spin-orbit misalignments (obliquities) may strongly influence atmospheric circulation and tidal heating in the planet. A promising avenue to generate obliquities is via spin-orbit resonances, where the spin and orbital precession frequencies of the planet cross each other as the system evolves in time. One such mechanism involves a dissipating (mass-losing) protoplanetary disk that drives orbital precession of an interior planet. We study this scenario analytically in this paper, and obtain the mapping between the general initial spin orientation and the final obliquity. We show that (i) under adiabatic evolution (i.e. the disk dissipates at a sufficiently slow rate), the final planetary obliquity as a function of the initial spin orientation bifurcates into distinct tracks governed by interactions with the resonance; (ii) under nonadiabatic evolution, a broad range of obliquities can be excited. We obtain analytical expressions for the final obliquities for various regimes of parameter space. The dynamical system studied in this paper is an example of "Colombo's top", and our analysis and results can be adapted to other applications.

astro-ph.EP↗

arXiv2020

Tidal Evolution of Eccentric Binaries Driven by Convective Turbulent Viscosity

Tidal dissipation due to convective turbulent viscosity shapes the evolution of a variety of astrophysical binaries. For example, this type of dissipation determines the rate of orbital circularization in a binary with a post-main sequence star that is evolving toward a common envelope phase. Viscous dissipation can also influence binaries with solar-type stars, or stars with a close-in giant planet. In general, the effective viscosity in a convective stellar envelope depends on the tidal forcing frequency $ω_{\rm tide}$; when $ω_{\rm tide}$ is larger than the turnover frequency of convective eddies, the viscosity is reduced. Previous work has focused on binaries in nearly circular orbits. However, for eccentric orbits, the tidal potential has many forcing frequencies. In this paper, we develop a formalism for computing tidal dissipation that captures the effect of frequency-dependent turbulent viscosity and is valid for arbitrary binary eccentricities. We also present an alternative simpler formulation that is suitable for very high eccentricities. We apply our formalisms to a giant branch (GB) star model and a solar-type star model. We find that a range of pseudosynchronous rotation rates are possible for both stellar models, and the pseudosynchronous rate can differ from the prediction of the commonly-used weak tidal friction theory by up to a factor of a few. We also find that tidal decay and circularization due to turbulent viscosity can be a few orders of magnitude faster than predicted by weak tidal friction in GB stars on eccentric, small pericentre orbits, but is suppressed by a few orders of magnitude in solar-type stars due to viscosity reduction.

astro-ph.SR↗

arXiv2020

Merging Compact Binaries Near a Rotating Supermassive Black Hole: Eccentricity Excitation due to Apsidal Precession Resonance

We study the dynamics of merging compact binaries near a rotating supermassive black hole (SMBH) in a hierarchical triple configuration. We include various general relativistic effects that couple the inner orbit, the outer orbit and the spin of the SMBH. During the orbital decay due to gravitational radiation, the inner binary can encounter an "apsidal precession resonance" and experience eccentricity excitation. This resonance occurs when the apsidal precession rate of the inner binary matches that of the outer binary, with the precessions driven by both Newtonian interactions and various post-Newtonian effects. The eccentricity excitation requires the outer orbit to have a finite eccentricity, and is most effective for triples with small mutual inclinations, in contrast to the well-studied Lidov-Kozai effect. The resonance and the associated eccentricity growth may occur while the binary emits gravitational waves in the low-frequency band, and may be detectable by future space-based gravitational wave detectors.

astro-ph.HE↗

arXiv2020

Giant Planet Scatterings and Collisions: Hydrodynamics, Merger-Ejection Branching Ratio, and Properties of the Remnants

Planetary systems with sufficiently small orbital spacings can experience planetary mergers and ejections. The branching ratio of mergers vs ejections depends sensitively on the treatment of planetary close encounters. Previous works have adopted a simple "sticky-sphere" prescription, whose validity is questionable. We apply both smoothed particle hydrodynamics and $N$-body integrations to investigate the fluid effects in close encounters between gas giants and the long-term evolution of closely-packed planetary systems. Focusing on parabolic encounters between Jupiter-like planets with $M_J$ and $2M_J$, we find that quick mergers occur when the impact parameter $r_p$ (the pericenter separation between the planets) is less than $2R_J$, and the merger conserved 97% of the initial mass. Strong tidal effects can affect the "binary-planet" orbit when $r_p$ is between $2R_J$ and $4R_J$. We quantify these effects using a set of fitting formulae that can be implemented in $N$-body codes. We run a suite of $N$-body simulations with and without the formulae for systems of two giant planets initially in unstable, nearly circular coplanar orbits. The fluid (tidal) effects significantly increase the branching ratio of planetary mergers relative to ejections by doubling the effective collision radius. While the fluid effects do not change the distributions of semi-major axis and eccentricity of each type of remnant planets (mergers vs surviving planets in ejections), the overall orbital properties of planet scattering remnants are strongly affected due to the change in the branching ratio. We also find that the merger products have broad distributions of spin magnitudes and obliquities.

astro-ph.EP↗

arXiv2020

Physics of Tidal Dissipation in Early-Type Stars and White Dwarfs: Hydrodynamical Simulations of Internal Gravity Wave Breaking in Stellar Envelopes

In binaries composed of either early-type stars or white dwarfs, the dominant tidal process involves the excitation of internal gravity waves (IGWs), which propagate towards the stellar surface, and their dissipation via nonlinear wave breaking. We perform 2D hydrodynamical simulations of this wave breaking process in a stratified, isothermal atmosphere. We find that, after an initial transient phase, the dissipation of the IGWs naturally generates a sharp critical layer, separating the lower stationary region (with no mean flow) and the upper "synchronized" region (with the mean flow velocity equal to the horizontal wave phase speed). While the critical layer is steepened by absorption of these waves, it is simultaneously broadened by Kelvin-Helmholtz instabilities such that, in steady state, the critical layer width is determined by the Richardson criterion. We study the absorption and reflection of incident waves off the critical layer and provide analytical formulae describing its long-term evolution. The result of this study is important for characterizing the evolution of tidally heated white dwarfs and other binary stars.

astro-ph.SR↗

arXiv2020

Planetary Spin and Obliquity from Mergers

In planetary systems with sufficiently small inter-planet spacing, close encounters can lead to planetary collisions/mergers or ejections. We study the spin property of the merger products of two giant planets in a statistical manner using numerical simulations and analytical modeling. Planetary collisions lead to rapidly rotating objects and a broad range of obliquities. We find that, under typical conditions for two-planet scatterings, the distributions of spin magnitude $S$ and obliquity $Θ_{\rm SL}$ of the merger products have simple analytical forms: $f_{S} \propto S$ and $f_{\cosΘ_{\rm SL}} \propto (1-\cos^2Θ_{\rm SL})^{-1/2}$. Though parameter studies, we determine the regime of validity for the analytical distributions of spin and obliquity. Since planetary mergers is a major outcome of planet-planet scatterings, observational search for the spin/obliquity signatures of exoplanets would provide important constraints on the dynamical history of planetary systems.

astro-ph.EP↗

arXiv2020

Periodic Fast Radio Bursts with Neutron Star Free/Radiative Precession

The CHIME/FRB collaboration recently reported the detection of a 16 day periodicity in the arrival times of radio bursts from FRB 180916.J0158+65. We study the possibility that the observed periodicity arises from free precession of a magnetized neutron star, and put constraints on different components of the star's magnetic fields. Using a simple geometric model, where radio bursts are emitted from a rotating neutron star magnetosphere, we show that the emission pattern as a function of time can match that observed from FRB 180916.J0158+65.

astro-ph.HE↗

arXiv2020

Fast radio burst counterparts and their implications for the central engine

While the radiation mechanism of fast radio bursts (FRBs) is unknown, coherent curvature radiation and synchrotron maser are promising candidates. We find that both radiation mechanisms work for a neutron star (NS) central engine with $B\gtrsim 10^{12}$ G, while for the synchrotron maser, the central engine can also be an accreting black hole (BH) with $B\gtrsim 10^{12}$ G and a white dwarf (WD) with $B\sim 10^8-10^9$ G. We study the electromagnetic counterparts associated with such central engines, i.e., nebulae for repeating FRBs and afterglows for non-repeating FRBs. In general, the energy spectrum and flux density of the counterpart depend strongly on its size and total injected energy. We apply the calculation to the nebula of FRB 121102 and find that the persistent radio counterpart requires the average energy injection rate into the nebula to be between $2.7\times10^{39}~{\rm erg/s}$ and $1.5\times10^{44}~{\rm erg/s}$, and the minimum injected energy be $6.0\times10^{47}~{\rm erg}$ in around $7$ yr. Consequently, we find that for FRB 121102 and its nebula: (1) WD and accretion BH central engines are disfavored; (2) a rotation-powered NS central engine works when $1.2\times10^{12}~{\rm G}\lesssim B\lesssim 7.8\times10^{14}~{\rm G}$ with initial period $P<180$ ms, but the radio emission must be more efficient than that in typical giant pulses of radio pulsars; and (3) a magnetic-powered NS central engine works when its internal magnetic field $B\gtrsim 10^{16}$ G. We also find that the radio-emitting electrons in the nebula could produce a significant rotation measure (RM), but cannot account for the entire observed RM of FRB 121102.

astro-ph.HE↗

arXiv2019

Circumbinary Accretion from Finite and Infinite Disks

We carry out 2D viscous hydrodynamics simulations of circumbinary disk (CBD) accretion using {\footnotesize AREPO}. We resolve the accretion flow from a large-scale CBD down to the streamers and disks around individual binary components. Extending our recent studies \citep{mun19}, we consider circular binaries with various mass ratios ($0.1\leq q_{\rm{b}}\leq1$) and study accretion from ``infinite'', steady-supply disks and from finite-sized, viscously spreading tori. For ``infinite'' disks, a global steady state can be reached, and the accretion variability has a dominant frequency ${\sim}0.2Ω_{\rm{b}}$ for $q_{\rm{b}}>0.5$ and $Ω_{\rm{b}}$ for $q_{\rm{b}}<0.5$, ($Ω_{\rm{b}}$ is the binary angular frequency). We find that the accretion ``eigenvalue'' $l_0$ -- the net angular momentum transfer from the disk to the binary per unit accreted mass -- is always positive and falls in the range ($0.65$-$0.85)a_{\rm b}^2Ω_{\rm{b}}$ (with $a_{\rm{b}}$ the binary separation), depending weakly on the mass ratio and viscosity. This leads to binary expansion when $q_{\rm{b}}\gtrsim0.3$. Accretion from a finite torus can be separated into two phases: an initial transient phase, corresponding to the filling of the binary cavity, followed by a viscous pseudo-stationary phase, during which the torus viscously spreads and accretes onto the binary. In the viscous phase, the net torque on the binary per unit accreted mass is close to $l_0$, the value derived for ``infinite'' disks. We conclude that similar-mass binaries accreting from CBDs gain angular momentum and expand over long time scales. This result significantly impacts the coalescence of supermassive binary black holes and newly formed binary stars. We offer a word of caution against conclusions drawn from simulations of transient accretion onto empty circumbinary cavities.

astro-ph.HE↗

arXiv2019

Pulsed Disc Accretion Driven by Hot Jupiters

We present 2D hydrodynamical simulations of hot Jupiters orbiting near the inner edge of protoplanetary discs. We systemically explore how the accretion rate at the inner disc edge is regulated by a giant planet of different mass, orbital separation and eccentricity. We find that a massive (with planet-to-star mass ratio $\gtrsim 0.003$) eccentric ($e_p\gtrsim 0.1$) planet drives a pulsed accretion at the inner edge of the disc, modulated at one or two times the planet's orbital frequency. The amplitude of accretion variability generally increases with the planet mass and eccentricity, although some non-monotonic dependences are also possible. Applying our simulation results to the T Tauri system CI Tau, where a young hot Jupiter candidate has been detected, we show that the observed luminosity variability in this system can be explained by pulsed accretion driven by an eccentric giant planet.

astro-ph.EP↗