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Register a new userInvestigating protoplanetary disc cooling through kinematics: analytical GI wiggle
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Added by
Cristiano Longarini
Publication date
2021
fields
Physics
and research's language is
English
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It is likely that young protostellar discs undergo a self-gravitating phase. Such systems are characterised by the presence of a spiral pattern that can be either in a quasi-steady state or in a non-linear unstable condition. This spiral wave affects both the gas dynamics and kinematics, resulting in deviations from the Keplerian rotation. Recently, a lot of attention has been devoted to kinematic studies of planet forming environments, and we are now able to measure even small perturbations of velocity field thanks to high spatial and spectral resolution observations of protostellar discs. In this work, we investigate the kinematic signatures of gravitational instability: we perform an analytical study of the linear response of a self-gravitating disc to a spiral-like perturbation, focusing our attention on the velocity field perturbations. We show that unstable discs have clear kinematic imprints into the gas component across the entire disc extent, due to the GI spiral wave perturbation, resulting in deviations from Keplerian rotation. The shape of these signatures depends on several parameters, but they are significantly affected by the cooling factor: by detecting these features, we can put constraints on protoplanetary discs cooling.
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Exoplanets form in protoplanetary accretion discs. The total protoplanetary disc mass is the most fundamental parameter, since it sets the mass budget for planet formation. Although observations with the Atacama Large Millimeter/Submillimeter array (ALMA) have dramatically increased our understanding of these discs, total protoplanetary disc mass remains difficult to measure. If a disc is sufficiency massive ($gtrsim$ 10% of the host star mass), it can excite gravitational instability (GI). Recently, it has been revealed that GI leaves kinematic imprints of its presence known as the ``GI Wiggle. In this work, we use numerical simulations to empirically determine an approximately linear relationship between the amplitude of the wiggle and the host disc-to-star mass ratio, and show that measurements of the amplitude are possible with the spatial and spectral capabilities of ALMA. These measurements can therefore be used to constrain disc-to-star mass ratio.
The Protoplanetary Discussions conference --- held in Edinburgh, UK, from 7th --11th March 2016 --- included several open sessions led by participants. This paper reports on the discussions collectively concerned with the multiphysics modelling of protoplanetary discs, including the self-consistent calculation of gas and dust dynamics, radiative transfer and chemistry. After a short introduction to each of these disciplines in isolation, we identify a series of burning questions and grand challenges associated with their continuing development and integration. We then discuss potential pathways towards solving these challenges, grouped by strategical, technical and collaborative developments. This paper is not intended to be a review, but rather to motivate and direct future research and collaboration across typically distinct fields based on textit{community driven input}, to encourage further progress in our understanding of circumstellar and protoplanetary discs.
Circumstellar discs may become warped or broken into distinct planes if there is a stellar or planetary companion with an orbit that is misaligned with respect to the disc. There is mounting observational evidence for protoplanetary discs with misaligned inner discs and warps that may be caused by such interactions with a previously undetected companion, giving us a tantalising indication of possible planets forming there. Hydrodynamical and radiative transfer models indicate that the temperature varies azimuthally in warped discs due to the variable angle at which the disc surface faces the star and this impacts the disc chemistry. We perform chemical modelling based on a hydrodynamical model of a protoplanetary disc with an embedded planet orbiting at a 12$^{circ}$ inclination to the disc. Even for this small misalignment, abundances of species including CO and HCO$^+$ vary azimuthally and this results in detectable azimuthal variations in submillimetre line emission. Azimuthal variations in line emission may therefore indicate the presence of an unseen embedded companion. Nonaxisymmetric chemical abundances should be considered when interpreting molecular line maps of warped or shadowed protoplanetary discs.
We perform numerical simulations of solid particle motion in a shearing box model of a protoplanetary disc. The accretion flow is turbulent due to the action of the magnetorotational instability. Aerodynamic drag on the particles is modelled using the Epstein law with the gas velocity interpolated to the particle position. The effect of the magnetohydrodynamic turbulence on particle velocity dispersions is quantified for solids of different stopping times t_s, or equivalently, different sizes. The anisotropy of the turbulence is reflected upon the dispersions of the particle velocity components, with the radial component larger than both the azimuthal and vertical components for particles larger than ~ 10 cm (assuming minimum-mass solar nebula conditions at 5 AU). The dispersion of the particle velocity magnitude, as well as that of the radial and azimuthal components, as functions of stopping time, agree with previous analytical results for isotropic turbulence. The relative speed between pairs of particles with the same value of t_s decays faster with decreasing separation than in the case of solids with different stopping time. Correlations in the particle number density introduce a non-uniform spatial distribution of solids in the 10 to 100 cm size range. Any clump of particles is disrupted by the turbulence in less than one tenth on an orbital period, and the maximally concentrated clumps are stable against self-gravitational collapse.
We carry out three-dimensional hydrodynamical simulations to study planet-disc interactions for inclined high mass planets, focusing on the discs secular evolution induced by the planet. We find that, when the planet is massive enough and the induced gap is deep enough, the disc inside the planets orbit breaks from the outer disc. The inner and outer discs precess around the systems total angular momentum vector independently at different precession rates, which causes significant disc misalignment. We derive the analytical formulae, which are also verified numerically, for: 1) the relationship between the planet mass and the depth/width of the induced gap, 2) the migration and inclination damping rates for massive inclined planets, and 3) the condition under which the inner and outer discs can break and undergo differential precession. Then, we carry out Monte-Carlo radiative transfer calculations for the simulated broken discs. Both disc shadowing in near-IR images and gas kinematics probed by molecular lines (e.g. from ALMA) can reveal the misaligned inner disc. The relationship between the rotation rate of the disc shadow and the precession rate of the inner disc is also provided. Using our disc breaking condition, we conclude that the disc shadowing due to misaligned discs should be accompanied by deep gaseous gaps (e.g. in Pre/Transitional discs). This scenario naturally explains both the disc shadowing and deep gaps in several systems (e.g. HD 100453, DoAr 44, AA Tau, HD 143006) and these systems should be the prime targets for searching young massive planets ($>M_J$) in discs.
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