Guillaume Laibe

Discs surrounding binaries, referred to as circumbinary discs, are widely observed to develop central cavities that are carved by the gravitational influence of the binary. Analytical estimates of cavity sizes predict truncation at ∼ 2 3 binary separations, depending on binary properties. However, numerical studies show only qualitative agreement with these predictions, as cavity sizes often evolve on long timescales and can substantially exceed the analytically predicted values. In this work, we revise this paradigm, suggesting that tidal truncation in circumbinary discs responds to additional dynamical parameters that have so far been neglected. -- We analysed a suite of 80 numerical simulations of circumbinary discs to re-examine the physical mechanism responsible for cavity truncation and to provide a prescription for the cavity size independent of the state of evolution of the system. We find that truncation depends not only on the binary parameters a_̊m bin, e_̊m bin and mass ratio q but also on the instantaneous cavity eccentricity e_̊m cav and the relative apsidal orientation ϖ_ ̊m bin -ϖ_ ̊m cav . These quantities jointly determine the pericentre of the innermost stable disc orbit, R_̊m p, in a way that shares some similarities with orbital stability in the restricted three-body problem. Hydrodynamical effects introduce secondary corrections, with the disc scale height H and viscosity α mildly shifting the cavity edge relative to the purely gravitational prediction. We introduce a semi-analytical prescription that captures these dependences for R_̊m p and the cavity semi-major axis a_̊m cav. Additional variability arises from resonant oscillations of the cavity, characterised by anti-phase evolution of e_̊m cav and a_̊m cav, which are not captured by the model. We conclude that cavity truncation for binaries with mass ratios q>0.05 is a process where the instantaneous orbital properties of the disc (e_̊m cav, ϖ_̊m cav) play a fundamental role and should be taken into account to accurately evaluate the truncation efficiency.

Aims. We investigate signatures of pressure extrema on global oscillations in discs. Methods. We used the framework of wave topology to establish a generalised local dispersion relation that includes pressure gradients. We highlight the influence of a previously unrecognised epicyclic–acoustic frequency, and we derive an analytical criterion for the existence of a branch of modes transiting between the inertial and the pressure bands, known as topological modes. Results. We find that pressure extrema consist of wave guides in which such topological modes propagate. The fundamental mode trapped at a pressure bump can propagate at any frequency, allowing it to resonate with any temporal forcing. Conversely, the fundamental mode associated with a pressure dip propagates at any vertical phase velocity. These specific features make them attractive candidates for future discoseismology.

This study investigates the signatures of pressure extrema on global oscillations in discs. To this end, we use the framework of wave topology to establish a generalised local dispersion relation that includes pressure gradients. We highlight the influence of a previously unrecognized epicyclic-acoustic frequency and derive an analytical criterion for the existence of a branch of modes transiting between the inertial and the pressure bands. We find that pressure extrema consist of wave guides in which such topological modes propagate. The fundamental mode trapped at a pressure bump can propagate at all frequencies, allowing it to resonate with any temporal forcing, while the mode associated with a pressure gap propagates at a fixed frequency, propagates with arbitrary vertical phase velocity. These specific features make them attractive candidates for future discoseismology.

Helioseismology has revolutionized our understanding of the Sun by analyzing its global oscillation modes. However, the solar core remains elusive, limiting a full understanding of its evolution. In this work, we study a previously unnoticed global oscillation mode of the Sun using a fully compressible hydrodynamical simulation of the solar interior and assess that it is a mixed f/g-mode with a period of about 1 hr. This is the first global stellar hydrodynamics simulation to successfully couple compressible and gravity modes. To understand this coupling, we invoke a recent theory on the nature of f-modes seen through the prism of wave topology, characterizing their ability to propagate deep into stellar interiors. We demonstrate that the mixed f/g-mode is highly sensitive to the core’s rotation rate, providing a new promising pathway to explore the Sun’s core.

An analytic expression for the frequencies of standing waves in stars, applicable to any radial order n, is derived from ray-tracing equations by the mean of Wigner–Weyl calculus. A correction to previous formulas currently employed in asteroseismology is identified as the Berry phase, which accounts for the vectorial nature of wave propagation in stars. Accounting for this quantity significantly improves upon previous laws for low n modes of the Sun, and we show that the Berry phase is indeed present in the available observational data of solar modes. This phase is due to inhomogeneities of the medium.

Inertial waves in convective regions of stars exhibit topological properties linked to a Chern number of 1. The first of these is a unique, unidirectional, prograde oscillation mode within the cavity, which propagates at arbitrarily low frequencies for moderate azimuthal wave numbers. The second are phase singularities around which the phase winds in Fourier space, with winding numbers ν = ± 1 depending on the hemisphere. Phase winding is a collective effect over waves propagating in all directions that is strongly robust to noise. This suggests a topology-based method for wave detection in noisy observational data. Published by the American Physical Society 2024

Context. Signposts of early planet formation are ubiquitous in substructured young discs. Dense, hot, and high-pressure regions that formed during the gravitational collapse process, integral to star formation, facilitate dynamical mixing of dust within the protostellar disc. This provides an incentive to constrain the role of gas and dust interaction and resolve potential zones of dust concentration during star and disc formation stages. Aims. We explore whether the thermal and dynamical conditions that developed during protostellar disc formation can generate gas flows that efficiently mix and transport the well-coupled gas and dust components. Methods. We simulated the collapse of dusty molecular cloud cores with the hydrodynamics code PLUTO augmented with radiation transport and self-gravity. We used a two-dimensional axisymmetric geometry and followed the azimuthal component of the velocity. The dust was treated as Lagrangian particles that are subject to drag from the gas, whose motion is computed on a Eulerian grid. We considered 1, 10, and 100 µm-sized neutral, spherical dust grains. Importantly, the equation of state accurately includes molecular hydrogen dissociation. We focus on molecular cloud core masses of 1 and 3 M_⊙ and explore the effects of different initial rotation rates and cloud core sizes. Results. Our study underlines mechanisms for the early transport of dust from the inner hot disc regions via the occurrence of two transient gas motions, namely meridional flow and outflow. The vortical flow fosters dynamical mixing and retention of dust, while the thermal pressure driven outflow replenishes dust in the outer disc. Notably, these phenomena occur regardless of the initial cloud core mass, size, and rotation rate. Conclusions. Young dynamical precursors to planet-forming discs exhibit regions with complex hydrodynamical gas features and high-temperature structures. These can play a crucial role in concentrating dust for subsequent growth into protoplanets. Dust transport, especially, from sub-au scales surrounding the protostar to the outer relatively cooler parts, offers an efficient pathway for thermal reprocessing during pre-stellar core collapse.

Context. Protostellar discs are mostly modelled as circular structures of gas and dust orbiting a protostar. However, a number of physical mechanisms, for example, the presence of a (sub)stellar companion or initial axial asymmetry, can cause the gas and dust orbital motion to become eccentric. Theoretical studies have revealed that, when present, disc eccentricity is expected to occur with predictable profiles that can be long-lasting and potentially observable in protostellar systems. Aims. We construct an analytical model predicting the typical features of the kinematics and morphology of eccentric protostellar discs, with the final goal of characterising the observational appearance of eccentricity in discs. Methods. We validate the model using a numerical simulation of a circumbinary disc (where the binary makes the disc eccentric). We finally post-process the simulation with Monte Carlo radiative transfer to study how eccentric features would appear through the ‘eyes’ of ALMA. Results. Besides the motion of the material on eccentric Keplerian orbits in the disc orbital plane, the most characteristic eccentric feature emerging from the analytical model is strong vertical motion with a typical anti-symmetric pattern (with respect to the disc line of pericentres). A circumbinary disc with a ≈ 40 au eccentric cavity (e_cav = 0.2), carved by an a_bin = 15 au binary, placed at a distance d = 130 pc, is expected to host in its upper emission surface vertical oscillations up to v_z ~ 400 m s⁻¹ close to the cavity edge, that is to say, well within ALMA spectral and spatial resolution capabilities. A residual spiral pattern in the vertical velocity Δv_z ~ 150 m s⁻¹ of the simulation cannot be captured by the theoretical model, we speculate it to be possibly linked to the presence of a companion in the system.

We reveal properties of global modes of linear buoyancy instability in stars, characterized by the celebrated Schwarzschild criterion, using non-Hermitian topology. We identify a ring of exceptional points of order 4 that originates from the pseudo-Hermitian and pseudochiral symmetries of the system. The ring results from the merging of a dipole of degeneracy points in the Hermitian stably-stratified counterpart of the problem. Its existence is related to spherically symmetric unstable modes. We obtain the conditions for which convection grows over such radial modes. Those are met at early stages of low-mass stars formation. We finally show that a topological wave is robust to the presence of convective regions by reporting the presence of a mode transiting between the wavebands in the non-Hermitian problem, strengthening their relevance for asteroseismology. Published by the American Physical Society 2024