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.
ABSTRACT
Evolving the size distribution of solid aggregates challenges simulations of young stellar objects. Among other difficulties, generic formulae for stability conditions of explicit solvers ...provide severe constraints when integrating the coagulation equation for astrophysical objects. Recent numerical experiments have reported that these generic conditions may be much too stringent. By analysing the coagulation equation in the Laplace space, we explain why this is indeed the case and provide a novel stability condition that avoids time oversampling.
Discrete symmetries have found numerous applications in photonics and quantum mechanics, but remain little studied in fluid mechanics, particularly in astrophysics. We aim to show how $ PT $ and ...anti-$ PT $ symmetries determine the behaviour of linear perturbations in a wide class of astrophysical problems. They set the location of `exceptional points' in the parameter space and the associated transitions to instability, and are associated with the conservation of quadratic quantities that can be determined explicitly. We study several classical local problems: the gravitational instability of isothermal spheres and thin discs, the Schwarzschild instability, the Rayleigh-Bénard instability and acoustic waves in dust--gas mixtures. We calculate the locations and the order of the exceptional points using the resultant of two univariate polynomials, as well as the conserved quantities in the different regions of the parameter space using Krein theory. All problems studied here exhibit discrete symmetries, even though Hermiticity is broken by different physical processes (self-gravity, buoyancy, diffusion, and drag). This analysis provides genuine explanations for certain instabilities, and for the existence of regions in the parameter space where waves do not propagate. Those two aspects correspond to regions where $ PT $ and anti-$ PT $ symmetries are broken respectively. Not all instabilities are associated to symmetry breaking (e.g. the Rayleigh-Benard instability).
We study the dynamics of a viscous protoplanetary disc hosting a population of dust grains with a range of sizes. We compute steady-state solutions and show that the radial motion of both the gas and ...the dust can deviate substantially from those for a single-size dust population. Although the aerodynamic drag from the dust on the gas is weaker than in the case where all grains are optimally coupled to the gas, the cumulative `back-reaction' of the dust particles can still alter the gas dynamics significantly. In typical protoplanetary discs, the net effect of the dust back-reaction decreases the gas accretion flow compared to the dust-free (viscous) case, even for dust-to-gas ratios of the order of 1 per cent. In the outer disc, where dust grains are typically less strongly coupled to the gas and settle towards the midplane, the dust back-reaction can even drive outward gas flow. Moreover, the radial inward drift of large grains is reduced below the gas motion in the inner disc regions, while small dust grains follow the gas dynamics over all the disc extent. The resulting dust and gas dynamics can give rise to observable structures, such as gas and dust cavities. Our results show that the dust back-reaction can play a major role in both the dynamics and observational appearance of protoplanetary discs, and cannot be ignored in models of protoplanetary disc evolution.
Abstract
Planet formation is thought to occur in discs around young stars by the aggregation of small dust grains into much larger objects. The growth from grains to pebbles and from planetesimals to ...planets is now fairly well understood. The intermediate stage has however been found to be hindered by the radial-drift and fragmentation barriers. We identify a powerful mechanism in which dust overcomes both barriers. Its key ingredients are (i) backreaction from the dust on to the gas, (ii) grain growth and fragmentation and (iii) large-scale gradients. The pile-up of growing and fragmenting grains modifies the gas structure on large scales and triggers the formation of pressure maxima, in which particles are trapped. We show that these self-induced dust traps are robust: they develop for a wide range of disc structures, fragmentation thresholds and initial dust-to-gas ratios. They are favoured locations for pebbles to grow into planetesimals, thus opening new paths towards the formation of planets.
Abstract
We present a new algorithm, multigrain, for modelling the dynamics of an entire population of small dust grains immersed in gas, typical of conditions that are found in molecular clouds and ...protoplanetary discs. The multigrain method is more accurate than single-phase simulations because the gas experiences a backreaction from each dust phase and communicates this change to the other phases, thereby indirectly coupling the dust phases together. The multigrain method is fast, explicit and low storage, requiring only an array of dust fractions and their derivatives defined for each resolution element.
Dusty gas with one fluid Laibe, Guillaume; Price, Daniel J.
Monthly notices of the Royal Astronomical Society,
05/2014, Letnik:
440, Številka:
3
Journal Article
Recenzirano
Odprti dostop
In this paper, we show how the two-fluid equations describing the evolution of a dust and gas mixture can be re-formulated to describe a single fluid moving with the barycentric velocity of the ...mixture. This leads to evolution equations for the total density, momentum, the differential velocity between the dust and the gas phases and either the dust-to-gas ratio or the dust fraction. The equations are similar to the usual equations of gas dynamics, providing a convenient way to extend existing codes to simulate two-fluid mixtures without modifying the code architecture. Our approach avoids the inherent difficulties related to the standard approach where the two phases are separate and coupled via a drag term. In particular, the requirements of infinite spatial and temporal resolution as the stopping time tends to zero are no longer necessary. This means that both small and large grains can be straightforwardly treated with the same method, with no need for complicated implicit schemes. Since there is only one resolution scale the method also avoids the problem of unphysical trapping of one fluid (e.g. dust) below the resolution of the other. We also derive a simplified set of equations applicable to the case of strong drag/small grains, consisting of the standard fluid equations with a modified sound speed, plus an advection-diffusion equation for the dust-to-gas ratio. This provides a simple and fast way to evolve the mixture when the stopping time is smaller than the Courant time step. We present a smoothed particle hydrodynamics implementation in a companion paper. PUBLICATION ABSTRACT
We describe a simple method for simulating the dynamics of small grains in a dusty gas, relevant to micron-sized grains in the interstellar medium and grains of centimetre size and smaller in ...protoplanetary discs. The method involves solving one extra diffusion equation for the dust fraction in addition to the usual equations of hydrodynamics. This ‘diffusion approximation for dust’ is valid when the dust stopping time is smaller than the computational timestep. We present a numerical implementation using smoothed particle hydrodynamics that is conservative, accurate and fast. It does not require any implicit timestepping and can be straightforwardly ported into existing 3D codes.
On the origin of horseshoes in transitional discs Ragusa, Enrico; Dipierro, Giovanni; Lodato, Giuseppe ...
Monthly notices of the Royal Astronomical Society,
01/2017, Letnik:
464, Številka:
2
Journal Article
Recenzirano
Odprti dostop
We investigate whether the rings, lopsided features and horseshoes observed at millimetre (mm) wavelengths in transitional discs can be explained by the dynamics of gas and dust at the edge of the ...cavity in circumbinary discs. We use 3D dusty smoothed particle hydrodynamics calculations to show that binaries with mass ratio ... drive eccentricity in the central cavity, naturally leading to a crescent-like feature in the gas density, which is accentuated in the mm dust grain population with intensity contrasts in mm continuum emission of 10 or higher. We perform mock observations to demonstrate that these features closely match those observed by the Atacama Large Millimetre/Submillimetre Array, suggesting that the origin of rings, dust horseshoes and other non-axisymmetric structures in transition discs can be explained by the presence of massive companions. (ProQuest: ... denotes formulae/symbols omitted.)
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