turbulence in protoplanetary disks · 2019. 3. 21. · summary ¥ protoplanetary disks are likely...

Jacob B. Simon

June 12, 2012Origins of Stars and Their

Planetary Systems

Turbulence in Protoplanetary Disks

CollaboratorsPhil ArmitageKris Beckwith

Meredith HughesJim Stone

Xuening Bai

JILA Postdoctoral FellowUniversity of Colorado

Courtesy: NASA

Defining the Environment for Planet Formation

Friday, 10 August, 12

We can actually see these systems

Courtesy: NASA

HH30 HD 163296

Hughes et al. (2011)


Dept of Earth & Planetary Sciences, KOBE University

• Dust coagulation is the very earliest stage in planet formation

• Well understood processes involving radial drift and vertical settling in a laminar disk

• But these disks are turbulent

• Global gas evolution will set the conditions for planet formation at various radii

• Turbulence stirs up not only dust, but has importance for mixing of all pre-planetary bodies


Disk turbulence is intimately tied to angular momentum transport

Mass

Angular momentum



Mass

Angular momentum

• Microphysical viscosity is way too small to transport angular momentum.



Mass

• Shakura and Sunyaev (1973) suggested turbulent angular momentum transport.

Angular momentum

• Microphysical viscosity is way too small to transport angular momentum.

Turbulent stresses


Our primary goal is to analyze protoplanetary disk turbulence from first principles and study its influence on the very earliest stages of planet formation


Three likely sources of turbulence

John Hawley

Magnetorotational Instability (MRI)

Kratter et al. (2010)

Self-gravitySubcritical Baroclinic Instability

Hubert Klahr



John Hawley




Hubert Klahr

Needs particular radial entropy profile. Still some

debate about its relevance in low-mass irradiated disks.



John Hawley




Hubert Klahr



Important early on or for very massive disks.



John Hawley




Hubert Klahr




Very likely candidate, but requires sufficient disk

ionization levels



John Hawley




Hubert Klahr




Very likely candidate, but requires sufficient disk

ionization levels

Most relevant for our studies


Hawley (2000)

A weak magnetic field destabilizes orbiting gas: the magnetorotational instability (MRI)


Low ionization levels enhance non-ideal magnetohydrodynamic (MHD) effects

Three effects

1. Ohmic resistivity

2. Hall effect

3. Ambipolar diffusion

e-

ion+ collide with neutrals

e-

ion+ collide with neutralstied to mag. field

e-

ion+tied to mag. field


Low ionization levels enhance non-ideal magnetohydrodynamic (MHD) effects

Armitage (2011)

- Hall effect is important but not on the second image.- Explain each non-ideal term


Our Goals


Our Goals

Our primary goal is to analyze protoplanetary disk turbulence from first principles and study its influence on the very earliest stages of planet formation


Our Goals• To develop high resolution, numerically converged disk simulations that span the range of physical conditions in protoplanetary disks

• To compute observable signatures from this turbulence to constrain theoretical models, particularly the dead zone model

• To study the interaction of turbulence with dust particles for use in planetesimal formation models.


Local simulations: examine small co-rotating disk patch

• Assume Cartesian geometry• Add appropriate source terms• Solve equations of MHD• Shearing periodic boundaries• Valid if H/R << 1• Assume gas is isothermalx

y

z


A state-of-the-art MHD code

Athena

See Stone et al. (2008) for code details


We use a minimum-mass solar nebula model and calculate the Ohmic resistivity at all

radii and heights

Armitage (2011)


Armitage (2011)

Focus on different radial regions

< 0.1 AU

4 AU

10 AU

50 AU


First, let’s consider the limit of ideal MHD



Armitage (2011)

< 0.1 AU



But this limit is also useful as a starting point before adding in more complex physics.


Vary the local domain size

0.5H x 2H x 8H2H x 4H x 8H

4H x 8H x 8H


8H x 16H x 8H


4H x 8H x 8H


8H x 16H x 8H



8H x 16H x 8H


16H x 32H x 8HFriday, 10 August, 12


0.5H x 2H x 8H

16H x 32H x 8HFriday, 10 August, 12

Simon, Beckwith, Armitage (2012)

Results: Ideal MHD and the importance of different length scales

8Hx16Hx8H 16Hx32Hx8H

4Hx8Hx8H2Hx4Hx8H


• These zonal flows may have a scale of ~10H.

• Must determine if they exist in global simulations or are an artifact of local simulations!


Armitage (2011)

Step up complexity by adding in Ohmic resistivity and consider multiple radii

4 AU

10 AU

50 AU

All boxes are 4Hx8Hx8H

box sizes limited to intermediate size due to finite resources


Results: Turbulent velocity distribution

Simon, Armitage, Beckwith (2011)

vertical

horizontalThis is very similar to the ideal MHD distribution for the largest box


Results: Turbulent velocity distribution

vertical

horizontal

Simon, Armitage, Beckwith (2011)


Our turbulent velocities roughly agree with observed measurements

Hughes et al. (2011) probed surface layers in outer disk: |v|/cs ~ 0.4 for HD 163296 |v|/cs < 0.1 for TW Hya

Our results so far suggest |v|/cs ~ 0.1-1


Next


• Simultaneously collaborate with observers to make a more direct comparison between our models and their observations - create synthetic observations (already in progess)


Next


• Simultaneously collaborate with observers to make a more direct comparison between our models and their observations - create synthetic observations (already in progess)

• Calculate interaction of turbulence with dust particles to determine mixing, diffusion, concentration, etc.


Summary

• Protoplanetary disks are likely not quiescent, but turbulent due to the MRI.

• This turbulence generates long-lived ~10 H structures in the density field, which could be important for particle trapping.

• Calculations of the turbulent velocity distribution roughly agree with observations.

• We will continue a first principles approach to studying planet formation in these disks while simultaneously comparing with observations.


Extra slides


We utilize powerful supercomputers to run these simulations


There are new sub-mm observations from which turbulent velocities can be inferred.

Hughes et al. (2011)


turbulence in protoplanetary disks · 2019. 3. 21. · summary ¥ protoplanetary disks are likely...

Documents