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Stellar-mass binary black holes (BBHs) embedded in active galactic nucleus (AGN) discs offer a distinct dynamical channel to produce black hole mergers detected in gravitational waves by LIGO/Virgo. To understand their orbital evolution through interactions with the disc gas, we perform a suite of two-dimensional high-resolution, local shearing box, viscous hydrodynamical simulations of equal-mass binaries. We find that viscosity not only smooths the flow structure around prograde circular binaries,but also greatly raises their accretion rates. The torque associated with accretion may be overwhelmingly positive and dominate over the gravitational torque at a high accretion rate. However, the accreted angular momentum per unit mass decreases with increasing viscosity, making it easier to shrink the binary orbit. In addition, retrograde binaries still experience rapid orbital decay, and prograde eccentric binaries still experience eccentricity damping. Our numerical experiments further show that prograde binaries are more likely to be hardened if the physical sizes of the accretors are sufficiently small such that the accretion rate is reduced. The dependence of the binary accretion rate on the accretor size can be weaken through boosted accretion either due to a high viscosity or a more isothermal-like equation of state. Our results widen the explored parameter space for the hydrodynamics of embedded BBHs and demonstrate that their orbital evolution in AGN discs is a complex, multifaceted problem.

Stellar-mass black holes (sBHs) embedded in gaseous disks of active galactic nuclei (AGN) can be important sources of detectable gravitational radiation for LIGO/Virgo when they form binaries and coalesce due to orbital decay. In this paper, we study the effect of dynamical friction (DF) on the formation of BH binaries in AGN disks usingN-body simulations. We employ two simplified models of DF, with the force on the BH depending on Δv, the velocity of the sBH relative to the background Keplerian gas. We integrate the motion of two sBHs initially on circular orbits around the central supermassive black hole (SMBH) and evaluate the probability of binary formation under various conditions. We find that both models of DF (with different dependence of the frictional coefficient on ∣Δv∣) can foster the formation of binaries when the effective friction timescaleτsatisfies Ω_Kτ≲ 20–30 (where Ω_Kis the Keplerian frequency around the SMBH): prograde binaries are formed when the DF is stronger (smallerτ), while retrograde binaries dominate when the DF is weaker (largerτ). We determine the distribution of both prograde and retrograde binaries as a function of initial orbital separation and the DF strength. Using our models of DF, we show that for a given sBH number density in the AGN disk, the formation rate of sBH binaries increases with decreasingτand can reach a moderate value with a sufficiently strong DF.

A planetary system can undergo multiple episodes of intense dynamical activities throughout its life, resulting in the production of star-grazing planetesimals (or exocomets) and pollution of the host star. Such activity is especially pronounced when giant planets interact with other small bodies during the system’s evolution. However, due to the chaotic nature of the dynamics, it is difficult to determine the properties of the perturbing planet(s) from the observed planetesimal-disruption activities. In this study, we examine the outcomes of planetesimal-planet scatterings in a general setting. We focus on one-planet systems, and determine the likelihood and time-scale of planetesimal disruption by the host star as a function of the planet properties. We obtain a new analytical expression for the minimum distance a scattering body can reach, extending previous results by considering finite planet eccentricity and non-zero planetesimal mass. Through N-body simulations, we derive the distribution of minimum distances and the likelihood and time-scales of three possible outcomes of planetesimal-planet scatterings: collision with the planet, ejection, and disruption by the star. For planetesimals with negligible mass, we identify four defining dimensionless parameters (the planet eccentricity, planet-to-star mass ratio, planet radius to semimajor axis ratio, and the stellar disruption radius to planet semimajor axis ratio) that enable us to scale the problem and generalize our findings to a wide range of orbital configurations. Using these results, we explore three applications: falling evaporating bodies in the β Pictoris system, white dwarf pollution due to planetesimal disruption and planet engulfment by main-sequence stars.

Closely packed multiplanet systems are known to experience dynamical instability if the spacings between the planets are too small. Such instability can be tempered by the frictional forces acting on the planets from gaseous discs. A similar situation applies to stellar-mass black holes embedded in active galactic nuclei discs around supermassive black holes. We use N-body integrations to evaluate how the frictional damping of orbital eccentricity affects the growth of dynamical instability for a wide range of K (the difference in the planetary semimajor axes in units of the mutual Hill radius) and (unequal) planet masses. We find that, in general, the stable region (large K) and unstable region (small K) are separated by a “grey zone”, where the (in)stability is not guaranteed. We report the numerical values of the critical spacing for stability Kcrit and the “grey zone” range in different systems, and provide fitting formulae for arbitrary frictional forcing strength. We show that the stability of a system depends on the damping time-scale τ relative to the zero-friction instability growth time-scale tinst: two-planet systems are stable if tinst ≳ τ; three-planet systems require tinst ≳ 10τ−100τ. When K is sufficiently small, tinst can be less than the synodic period between the planets, which makes frictional stabilization unlikely to occur. As K increases, tinst tends to grow exponentially, but can also fluctuate by a few orders of magnitude. We also devise a linear map to analyse the dynamical instability of the “planet + test mass” system, and find qualitative agreement with N-body simulations.

We present a new mechanism of generating large planetary eccentricities. This mechanism applies to planets within the inner cavities of their companion protoplanetary disks. A massive disk with an inner truncation may become eccentric due to nonadiabatic effects associated with gas cooling and can retain its eccentricity in long-lived coherently precessing eccentric modes; as the disk disperses, the inner planet will encounter a secular resonance with the eccentric disk when the planet and the disk have the same apsidal precession rates; the eccentricity of the planet is then excited to a large value as the system goes through the resonance. In this work, we solve the eccentric modes of a model disk for a wide range of masses. We then adopt an approximate secular dynamics model to calculate the long-term evolution of the “planet + dispersing disk” system. The planet attains a large eccentricity (between 0.1 and 0.6) in our calculations even though the disk eccentricity is quite small (≲0.05). This eccentricity excitation can be understood in terms of the mode conversion (“avoided crossing” between two eigenstates) phenomenon associated with the evolution of the “planet + disk” eccentricity eigenstates.

Hydrodynamical interaction in circumbinary discs (CBDs) plays a crucial role in various astrophysical systems, ranging from young stellar binaries to supermassive black hole binaries in galactic centres. Most previous simulations of binary-disc systems have adopted locally isothermal equation of state. In this study, we use the grid-based code Athena++ to conduct a suite of two-dimensional viscous hydrodynamical simulations of circumbinary accretion on a Cartesian grid, resolving the central cavity of the binary. The gas thermodynamics is treated by thermal relaxation towards an equilibrium temperature (based on the constant − β cooling ansatz, where β is the cooling time in units of the local Keplerian time). Focusing on equal mass, circular binaries in CBDs with (equilibrium) disc aspect ratio H/R = 0.1, we find that the cooling of the disc gas significantly influences the binary orbital evolution, accretion variability, and CBD morphology, and the effect depends sensitively on the disc viscosity prescriptions. When adopting a constant kinematic viscosity, a finite cooling time (β ≳ 0.1) leads to a binary inspiral as opposed to an outspiral and the CBD cavity becomes more symmetric. When adopting a dynamically varying α-viscosity, binary inspiral only occurs within a narrow range of cooling time (corresponding to β around 0.5).

Tidal heating on Io due to its finite eccentricity was predicted to drive surface volcanic activity, which was subsequently confirmed by the Voyager spacecraft. Although the volcanic activity in Io is more complex, in theory volcanism can be driven by runaway melting in which the tidal heating increases as the mantle thickness decreases. We show that this runaway melting mechanism is generic for a composite planetary body with liquid core and solid mantle, provided that (i) the mantle rigidity,μ, is comparable to the central pressure, i.e.,μ/(ρgR_P) ≳ 0.1 for a body with densityρ, surface gravitational accelerationg, and radiusR_P; (ii) the surface is not molten; (iii) tides deposit sufficient energy; and (iv) the planet has nonzero eccentricity. We calculate the approximate liquid core radius as a function ofμ/(ρgR_P), and find that more than 90% of the core will melt due to this runaway forμ/(ρgR_P) ≳ 1. From all currently confirmed exoplanets, we find that the terrestrial planets in the L 98-59 system are the most promising candidates for sustaining active volcanism. However, uncertainties regarding the quality factors and the details of tidal heating and cooling mechanisms prohibit definitive claims of volcanism on any of these planets. We generate synthetic transmission spectra of these planets assuming Venus-like atmospheric compositions with an additional 5%, 50%, and 98% SO₂component, which is a tracer of volcanic activity. We find a ≳3σpreference for a model with SO₂with 5–10 transits with JWST for L 98-59bcd.

A large fraction of white dwarfs (WDs) have metal-polluted atmospheres, which are produced by accreting material from remnant planetary systems. The composition of the accreted debris broadly resembles that of rocky Solar system objects. Volatile-enriched debris with compositions similar to long-period comets (LPCs) is rarely observed. We attempt to reconcile this dearth of volatiles with the premise that exo-Oort clouds (XOCs) occur around a large fraction of planet-hosting stars. We estimate the comet accretion rate from an XOC analytically, adapting the ‘loss cone’ theory of LPC delivery in the Solar system. We investigate the dynamical evolution of an XOC during late stellar evolution. Using numerical simulations, we show that 1–30 per cent of XOC objects remain bound after anisotropic stellar mass-loss imparting a WD natal kick of ${\sim}1 \, {\rm km \, s^{-1}}$. We also characterize the surviving comets’ distribution function. Surviving planets orbiting a WD can prevent the accretion of XOC comets by the star. A planet’s ‘dynamical barrier’ is effective at preventing comet accretion if the energy kick imparted by the planet exceeds the comet’s orbital binding energy. By modifying the loss cone theory, we calculate the amount by which a planet reduces the WD’s accretion rate. We suggest that the scarcity of volatile-enriched debris in polluted WDs is caused by an unseen population of 10–$100 \, \mathrm{au}$ scale giant planets acting as barriers to incoming LPCs. Finally, we constrain the amount of volatiles delivered to a planet in the habitable zone of an old, cool WD.

Stellar-mass binary black holes (BBHs) embedded in active galactic nucleus (AGN) discs offer a promising dynamical channel to produce black hole mergers that are detectable by LIGO/Virgo. Modelling the interactions between the disc gas and the embedded BBHs is crucial to understand their orbital evolution. Using a suite of 2D high-resolution simulations of prograde equal-mass circular binaries in local disc models, we systematically study how their hydrodynamical evolution depends on the equation of state (EOS; including the γ-law and isothermal EOS) and on the binary mass and separation scales (relative to the supermassive black hole mass and the Hill radius, respectively). We find that binaries accrete slower and contract in orbit if the EOS is far from isothermal such that the surrounding gas is diffuse, hot, and turbulent. The typical orbital decay rate is of the order of a few times the mass doubling rate. For a fixed EOS, the accretion flows are denser, hotter, and more turbulent around more massive or tighter binaries. The torque associated with accretion is often comparable to the gravitational torque, so both torques are essential in determining the long-term binary orbital evolution. We carry out additional simulations with non-accreting binaries and find that their orbital evolution can be stochastic and is sensitive to the gravitational softening length, and the secular orbital evolution can be very different from those of accreting binaries. Our results indicate that stellar-mass BBHs may be hardened efficiently under ideal conditions, namely less massive and wider binaries embedded in discs with a non-isothermal EOS.

About ten percent of Sun-like (1–2M_⊙) stars will engulf a 1–10M_Jplanet as they expand during the red giant branch (RGB) or asymptotic giant branch (AGB) phase of their evolution. Once engulfed, these planets experience a strong drag force in the star’s convective envelope and spiral inward, depositing energy and angular momentum. For these mass ratios, the inspiral takes ∼10–10²yr (∼10²–10³orbits); the planet undergoes tidal disruption at a radius of ∼1R_⊙. We use the Modules for Experiments in Stellar Astrophysics (MESA) software instrument to track the stellar response to the energy deposition while simultaneously evolving the planetary orbit. For RGB stars, as well as AGB stars withM_p≲ 5M_Jplanets, the star responds quasi-statically but still brightens measurably on a timescale of years. In addition, asteroseismic indicators, such as the frequency spacing or rotational splitting, differ before and after engulfment. For AGB stars, engulfment of anM_p≳ 5M_Jplanet drives supersonic expansion of the envelope, causing a bright, red, dusty eruption similar to a “luminous red nova.” Based on the peak luminosity, color, duration, and expected rate of these events, we suggest that engulfment events on the AGB could be a significant fraction of low-luminosity red novae in the Galaxy. We do not find conditions where the envelope is ejected prior to the planet’s tidal disruption, complicating the interpretation of short-period giant planets orbiting white dwarfs as survivors of common envelope evolution.