Gas dynamics in disks:Planet signatures and dynamical instabilities.

Wladimir (Wlad) Lyra
Tenure-track Professor

California State University Northridge

3rd DTA symposium. The origins of planetary systems: From the current view to new horizons.
Tokyo, June 1st, 2015

Outline•

Observational Evidence•

Dynamical Instabilities• Magnetorotational Instability• Effect of non-ideal MHD• Ohmic dead zone and instabilities• Ambipolar diffusion and Hall MHD• Dead zone instabilities• Vertical shear instability• Convective overstability••••

Planet-disk interaction
Vortex fitting
Spiral fittingHL Tau

Observational evidence: Spirals

Observational evidence: Vortices(?)

Observational evidence: Gaps

Protoplanetary Disks: Observational Perspective

Protoplanetary Disks: Dynamical PerspectiveMagneto-Rotational Instability

Lower effective gravity

B

Moves to LOWER orbit!

Magnetictension

Higher effective gravity
Moves to HIGHER orbit!

Flock et al. (2011)

azimuthA simple dead zone model

radiusLyra et al. (2008b);
See also Varniere & Tagger (2006)Kelvin-Helmholtz Instability

Rossby wave instability

Needs a pressure bump.
Rule of thumb:Modest ~30% local increase
yet SHARP sharper than 2H.

Meheut et al (2010)

Lovelace & Hohlfeld 1978
Toomre 1981
Papaloizou & Pringle 1984,1985
Hawley 1987
Lovelace 1999
Li et al. 2000, 2001
Tagger 2001
Varniere & Tagger 2006de Val Borro et al. 2007
Lyra et al. 2008b, 2009ab
Meheut et al. 2010, 2012abc
Lin & Papaloizou 2011ab,2012
Lyra & Mac Low 2012
Lin 2012,2013

Peggy Varnière & Michel Tagger
Rossby Wave Instability at dead zone boundary
Varnière & Tagger (2006)

3D strat RWI

Meheut et al. (2010, 2012abc, 2013)

3D strat RWI self-gravity

Lin (2012ab, 2013, 2014)

3D strat RWI polytropicInner Active/Dead zone boundary

Unstratified isothermal MHD
with static Ohmic resistivity jumps.

Magnetized inner disk + resistive outer disk
Lyra & Mac Low (2012);
see also Faure et al. (2015)

Active/dead zone boundary

TimeDensity

Magnetized inner disk + resistive outer disk
Lyra & Mac Low (2012)

Vorticity

Mag Energy

Significant angular momentum transport
Active zone

Dead zone

Large mass accretion rates in the dead zone,
comparable to the MRI in the active zone

Lyra & Mac Low (2012)

(Pre-)History of Rossby Wave Instability

Toomre (1981)

Planetary gap RWI(de Val-Borro et al. 2006, 2007)

Pinilla et al. (2012)

Planet tides carve gap
Gap walls are unstable toKelvin-Helmholtz instability

Lyra (2009)

Koller et al. (2003)
RWI at planetary gap

The code comparison
project of 2006(de Val-Borro et al. 2006)

Problem of choice:
2D ‘vanilla’ planet-disk interaction.

Several codes showed
gap-edge vortices.
Follow-up work(de Val-Borro et al. 2007)
showed that to be
the result of RWI

Inner Active/Dead zone boundary

Unstratified isothermal MHD
with static Ohmic resistivity jumps.

Magnetized inner disk + resistive outer disk
Lyra & Mac Low (2012);
see also Faure et al. (2015)

Non-ideal MHD: Ohmic, Hall, Ambipolar terms

Ambipolar diffusion

Ohmic

Ohmic +Ambipolar
Bai & Stone 2013

Ambipolar diffusion

Ohmic

Ohmic +
Ambipolar
Bai & Stone 2013

Ambipolar diffusion

Ohmic

Ohmic +
Ambipolar
Bai & Stone 2013

Magnetic field

Gas parcel

Ambipolar diffusion

Ohmic

Ohmic +
Ambipolar
Bai & Stone 2013

Magnetic fiel

Gas parcel

Global Ambipolar + Ohmic

Gressel et al. (2015)

Hall term

Large-scale azimuthal field generated. Couples toradial field fluctuations to generate large stress.
The flow stays laminar

Ohmic
Ohmic + Hall

The full monty

Ohmic

Ohmic+Ambipolar
Ohmic+ Ambipolar+ Hall

Ambipolar “kills” accretion.
Hall “ressurects” it.
Large scale Bφ couples to δBr, leading to laminar stress.
Wind is also amplified.
Lesur et al. (2014)

Dead zone – Vertical Shear Instability
Taylor-Proudman theorem:
should rotate in cylinders.
For baroclinic disks, that is *not* the case.
StressNon-zero baroclinic term.

Dependecy oncooling times.

Verticalvelocities

Dead zone - Convective Overstability
Klahr & Hubbard (2014), Lyra (2014)

Lyra (2014)

Dead zone - Convective Overstability
Klahr & Hubbard (2014), Lyra (2014)

Lyra (2014)

Saturated state – self-sustenance of vortices

Sketch of the
Baroclinic Instability

Lesur & Papaloizou (2010)
Armitage (2010)

compression
advection

baroclinicity
stretching

dissipation

Saturated state – self-sustenance of vortices
Sketch of the
Baroclinic Instability

Armitage (2010
Lyra & Klahr (2011)

compression
advection

baroclinicity
stretchingdissipation

Vortices and layered accretion

What happens when the vortex is magnetized?

Hydro

MHD

Vorticity

Mag. Energy

Lyra & Klahr (2011)Vortices and layered accretion

What happens when the vortex is magnetized?

Hydro

MHD

Vorticity

Mag. Energy

Vortices and layered accretion

What happens when the vortex is magnetized?

Hydro

MHD

Vorticity

Mag. Energy

Vortices
do not survive magnetization

Lyra & Klahr (2011)

Observational evidence: gaps, spirals, and vortices

Planet-disk interaction: gaps, spirals, and vortices.

Drag-Diffusion Equilibrium

Drag force

Trapped particle

Diffusion

Drag-Diffusion Equilibrium

Dust continuity equation

Drag force

Diffusion
compression
advection

Trapped particle

diffusion

Drag-Diffusion Equilibrium
Steady-state solution

Lyra & Lin (2013)

Drag force

Trapped particle

Diffusion

S=Stδ

a = vortex semi-minor axis
H = disk scale height (temperature)χ = vortex aspect ratio
δ = diffusion parameter
St = Stokes number (particle size)f(χ) = model-dependent scale functionAnalytical solution for dust trapping

Solution

S=Stδ

a = vortex semi-minor axisH = disk scale height (temperature)χ = vortex aspect ratio
δ = diffusion parameter
St = Stokes number (particle size)f(χ) = model-dependent scale function

Solution for

H/r=0.1 χ=4 S=1
Lyra & Lin (2013)

Analytical vs Numerical

S=St
δ
Lyra & Lin (2013)

Raettig et al (2015)

Derived quantities

Lyra & Lin (2013)

Gas distribution

Maximum dust density

Gas contrast

Dust contrast

Total trapped mass

Vortex size

H = disk scale height (temperature) St = Stokes number (particle size)f(χ) = model-dependent scale function
χ = vortex aspect ratio
ε = dust-to-gas ratio
δ = diffusion parameterApplying the model to Oph IRS 48

Observed parameters

asymmetricmm dustat 63 AU

Aspect ratio: 3.1
Dust contrast: 130
Temperature: 60K

Trapped mass: 9 MEarth

Gas detection:
Keplerian rotation

Derived parameters
S=4.8
Stokes number, St=0.008

Micron-sized
dust follows gas

δ = 0.005, vrms = 4% cs

Trapped mass: 11 MEarth
Lyra & Lin (2013)

Turbulence in vortex cores

Lesur & Papaloizou (2010)

Turbulence in vortex cores:
max at ~10% of sound speed
rms at ~3% of sound speed

Lyra & Klahr (2011)

Outer Dead/Active zone transition RWI

Armitage (2010)
Dzyurkevitch et al (2013)

The outer dead zone transition in ionization supposed
TOO SMOOTH
to generate an RWI-unstable bump.

Outer Dead/Active zone transition: 3D MHD

Resistive inner disk + magnetized outer disk
Lyra et al (2015)

Outer Dead/Active zone transition RWIResistive inner disk + magnetized outer disk
Lyra, Turner, & McNally (2015)

Outer Dead/Active zone transition RWI

MHD

Hydro

Lyra, Turner, & McNally (2015)

Outer Dead/Active zone transition RWI

Lyra, Turner, & McNally (2015)

Outer Dead/Active zone transition RWISano & Stone (2002)

Too big to be vortices?

An offset stellar potential leads to horseshoe orbits

Mittal & Chiang (2015)

Tail trapping

The Lyra-Lin
solution is for thecore only.
But the logarithmic
tail is significant forsmaller particles.

Global wrapping of tailLesur & Papaloizou (2009)

Lyra et al 2015 (in prep)Waiting for ALMA cycle 3

Zhu & Stone (2014)

Outer Dead/Active zone transition:
Spirals without planets

Waves launched at the active zonepropagate into the dead zone as a coherent spiral.

Spirals in transition disks

Muto et al. (2012)

Lyra (2009)

SPHERE-ALMA-VLA overlay of MWC 758

SPHEREALMAVLA

Marino et al. (2015)

Spiral arm fitting leads to problems

Analytical spiral fit
Spirals are too wide,
hotter (300K) thanambient gas (50K).

Benisty et al. (2015)

Spiral has little
polarization. Must be
thermal emission at 1000K.
Rafikov (2002)
Muto et al. (2012)

Currie et al. (2014)

Hot spirals

Richert et al. (2015)

Some crazy turbulence showing up at high planet mass….

Isothermal vs Adiabatic

Richert et al. (2015)

Shows up for long cooling times….

The energy source: shock heating!

Adiabatic

Adiabatic, but no shock heating

Richert et al. (2015)

The spiral is buoyantly unstable

Richert et al. (2015)

The spiral has Ma >~ 1

3D shocks: ascending bores and breaking waves

Boley & Durisen (2006)

3D shocks: ascending bores and breaking waves

Temperature

Div u(shock)Lyra et al. (2015, in prep)3D shocks: ascending bores and breaking waves

Lyra et al. (2015, in prep)

Observational evidence: Gaps

Possible Interpretation?

Dead zone boundary:density enhancement

Super-Keplerian:Magnetic pressure build-up

Flock et al. (2015)

Magnetic pressure
expels gas

Shallow gaps located aticelines of common volatiles.

Zheng et al. (2015)

Summary and Conclusions• Observational evidence: spirals, gaps, and vortices.
Planet-disk interaction: spirals, gaps, and vortices.
Disk dynamical instabilities: spirals, gaps, and vortices.

Muto et al. (2012)

ALMA et al. (2015)

van der Marel et al. (2013)

Summary and Conclusions
Observational evidence: spirals, gaps, and vortices.
• Planet-disk interaction: spirals, gaps, and vortices.
Disk dynamical instabilities: spirals, gaps, and vortices.

Summary and Conclusions
Observational evidence: spirals, gaps, and vortices.
Planet-disk interaction: spirals, gaps, and vortices.
• Disk dynamical instabilities: spirals, gaps, and vortices.

Dipierro et al. (2015)

Flock et al. (2015)

Lyra et al. (2015)