Gas dynamics in protoplanetary discs
Clément Baruteau Institute for Research in Astrophysics and Planetology, CNRS/University of Toulouse Millenium ALMA Disk Workshop: Protoplanetary disks and the planets they form, Santiago, 3-7 November 2014
Objectives and outline
□ Give a practical overview of the different physical processes, and related instabilities when relevant, that control the gas dynamics in protoplanetary discs: → magnetohydrodynamics → self-gravity → hydrodynamic vortex-forming instabilities □ Discuss their relevance to observed features (spirals, vortices) observed in young circumstellar discs
Protoplanetary discs: fact sheet □ Geometrically thin (H1Myr, ~2M HD ⊙
142157, H/R~0.1 → Q~2 Armitage 11
e.g., Christiaens+ 2014
→ candidate for GI? → several origins?
Observed spiral waves: origins, constraints? □ Fitting the spirals can help
Surface Brightness (SB) of the scattered light (normalized)
constraint the disc's temperature
~ 100AU
MWC 758 (Grady+ 2013)
polar coordinates of the spiral's launching point
disc's aspect ratio at r = r
c
with
(≠ 1/2)
Rafikov 2002, Muto+ 2012 – see Ogilvie & Lubow 02 for δ=1/2
Observed spiral waves: origins, constraints? □ Fitting the spirals can help
Surface Brightness (SB) of the scattered light (normalized)
constraint the disc's temperature → for MWC 758, hc ~ 0.18 at rc ~ 300 AU
~ 100AU
MWC 758 (Grady+ 2013)
polar coordinates of the spiral's launching point
disc's aspect ratio at r = r
c
with
(≠ 1/2)
Rafikov 2002, Muto+ 2012 – see Ogilvie & Lubow 02 for δ=1/2
Observed spiral waves: origins, constraints? Surface Brightness (SB) of the scattered light (normalized)
□ Fitting the spirals can help constraint the disc's temperature → for MWC 758, hc ~ 0.18 at rc ~ 300 AU
~ 100AU
□ If due to a companion, its MWC 758 (Grady+ 2013)
mass can be estimated as: Mc ≈ Mstar hc3 |ΔSB/SB| → for MWC 758, Mc ≈ 5+3-4 MJup
Overplotted: the gas surface density in a Fargo simulation with most likely disc and planet parameters from Grady+ 13
Take away on self-gravity
□ Gravitational instability (GI) can be active in the outer (>30 AU) parts of protoplanetary discs
→ outcome still uncertain: does GI always lead to fragmentation?
□ Spirals may be used to evaluate the discs temperature, which may help constraint their origin (GI or planet companion)
Hydrodynamic vortex forming instabilities
NEW! Fargo-ADSG now has dust particles implemented!
Vortex forming instabilities 1. The Subcritical Baroclinic Instability (SBI)
□ Driven by a radially decreasing entropy profile: Klahr & Bodenheimer 03
Vortex forming instabilities 1. The Subcritical Baroclinic Instability (SBI)
□ Driven by a radially decreasing entropy profile: Klahr & Bodenheimer 03
□ Non-linear instability: requires finite-amplitude perturbations, could be triggered by linear instabilities: the convective overstability and the vertical shear instability Lesur & Papaloizou 10, Lyra 14, Nelson R.+ 13
Vortex forming instabilities 1. The Subcritical Baroclinic Instability (SBI)
□ Driven by a radially decreasing entropy profile: Klahr & Bodenheimer 03
□ Non-linear instability: requires finite-amplitude perturbations, could be triggered by linear instabilities: the convective overstability r /d dS and the vertical shear instability D C
□ Evolution sensitive to the disc's thermal properties. Sustaining vortices requires short thermalization time
Φ
Petersen+ 07, Lesur & Papaloizou 10, Turner+ 14 (PP6)
gas vorticity:
B
A
R "baroclinic term"
g Armitage 11
Vortex forming instabilities 1. The Subcritical Baroclinic Instability (SBI)
□ Driven by a radially decreasing entropy profile: Klahr & Bodenheimer 03
□ Non-linear instability: requires finite-amplitude perturbations, could be triggered by linear instabilities: the convective overstability and the vertical shear instability Lesur & Papaloizou 10, Lyra 14, Nelson R.+ 13
□ Evolution sensitive to the disc's disc's perturbed vorticity
thermal properties. Sustaining vortices requires short thermalization time Petersen+ 07, Lesur & Papaloizou 10, Turner+ 14 (PP6)
Petersen+ 07
Vortex forming instabilities 1. The Subcritical Baroclinic Instability (SBI)
□ Driven by a radially decreasing entropy profile: Klahr & Bodenheimer 03
□ Non-linear instability: requires finite-amplitude perturbations, could be triggered by linear instabilities: the convective overstability and the vertical shear instability Lesur & Papaloizou 10, Lyra 14, Nelson R.+ 13
□ Evolution sensitive to the disc's disc's perturbed vorticity
thermal properties. Sustaining vortices requires short thermalization time Petersen+ 07, Lesur & Papaloizou 10, Turner+ 14 (PP6)
□ Both criteria for SBI-induced vortices may not be simultaneously met, notably in outer discs regions where "dust vortices" are observed
Petersen+ 07
Vortex forming instabilities 2. The Rossby-Wave Instability (RWI)
□ Driven by a radial extremum in the quantity Lovelace+ 99
Vortex forming instabilities 2. The Rossby-Wave Instability (RWI)
□ Driven by a radial extremum in the quantity Lovelace+ 99
□ Linear instability saturates into few anticyclonic vortices than tend to merge over time
disc's perturbed pressure
Anticyclonic vortex
Li H.+ 01
Vortex forming instabilities 2. The Rossby-Wave Instability (RWI)
□ Driven by a radial extremum in the quantity Lovelace+ 99
□ Linear instability saturates into few anticyclonic vortices than tend to merge over time
□ RWI in protoplanetary discs a. the edges between magnetically active and dead regions Varnière & Tagger 06, Lyra & MacLow 02, Faure+ 14, Lyra+14
Vortex between a magnetically dead inner region and active outer region →
Lyra+ 14
disc's perturbed density
may be triggered at:
Vortex forming instabilities 2. The Rossby-Wave Instability (RWI)
□ Driven by a radial extremum in the quantity Lovelace+ 99
□ Linear instability saturates into few anticyclonic vortices than tend to merge over time
□ RWI in protoplanetary discs may be triggered at:
de Val Borro+ 07, Lyra+ 09, Lin & Papaloizou 11...
Jupiter-mass planet in an inviscid disc →
Lin M.-K. 12
disc's perturbed density
b. the edges of a planetary gap
Vortices trap dust particles □ Whatever their origin, vortices are pressure maxima and thus are favourable locations to trap dust particles in protoplanetary discs Barge & Sommeria 95, Tanga+ 96...
tailwind
Gas angular frequency:
headwind
From W. Lyra
Vortices trap dust particles □ Whatever their origin, vortices are pressure maxima and thus are favourable locations to trap dust particles in protoplanetary discs Barge & Sommeria 95, Tanga+ 96...
□ Examples of dust concentration in planet-induced vortices:
R
Particles well coupled to the gas (size of 1 mm at ~20 AU) Zhu Z.+ 14
Vortices trap dust particles: case of Oph IRS 48 0.44 mm continuum emisson w/ ALMA
w/ Visir/VLT
van der Marel+ 2013
□ Is the vortex observed in the mm-dust at ~ 63 AU due to a planet ? → gas and dust cavities suggest a 10MJup planet at ~ 20 AU → would generate a vortex at ~40 AU, no further... → eccentric planet / disc? → other vortex forming scenario ?
Take away on vortex-forming instabilities
□ Hydrodynamic vortex-forming instabilities should be active in large parts (>1 AU) of protoplanetary discs
→ the Rossby-wave instability triggered by an unseen planet is one way (but not the only way) to interpret observed dust vortices
□ Further modeling is needed to explore the long-term evolution of dust trapped in vortices (impact of disc turbulence if/when relevant, large dust-to-gas ratios...)
Any questions?
Suggested references: - Armitage 2001, ARA&A, Dynamics of Protoplanetary Disks - Balbus 2003, ARA&A, Enhanced Angular Momentum Transport in Accretion Disks - Clarke & Carswell, Cambridge University Press, Principles of Astrophysical Fluid Dynamics - Turner et al. 2014, Protostars and Planets VI, Transport and Accretion in Planet-Forming Disks
