Disc-wind planet gaps without MHD:
Can we prescribe disc winds�like we prescribe viscosity?
Michael Hammer (w/ Min-Kai Lin)
ASIAA (Taipei, Taiwan)
Credit: Aoyama & Bai 2023
Has anyone tried simulating� disc winds without MHD before?
Yes!
Question #1
Kimmig et al. 2020 was the first
to do so (with a planet)!
Credit: Tabone et al. 2022
(modified)
Credit: MH (adapted from Scott et al. 2018)
Disc Wind Mechanism
The disc rotates! ➜ Magnetic field lines eject mass!
The disc rotates! ➜ Magnetic field lines eject mass!
Credit: Tabone et al. 2022
(modified)
Credit: MH (adapted from Scott et al. 2018)
Disc Wind Mechanism
To conserve angular momentum, �(some of) the rest of the disc flows inward.
The disc rotates! ➜ Magnetic field lines eject mass!
Credit: Tabone et al. 2022
(modified)
Credit: MH (adapted from Scott et al. 2018)
Step 1: Prescribe a torque to drive accretion flow.
Existing Prescribed Disc Wind Models
Credit: Tabone et al. 2022
(modified)
Credit: MH (adapted from Scott et al. 2018)
Step 1: Prescribe a torque to drive accretion flow.
Existing Prescribed Disc Wind Models
Step 2: Prescribe a mass sink for the mass loss.
Does the two-component model
(torque + mass loss) work?
Let’s find out!
Question #2
We didn’t know!
(No MHD studies of planets with disc winds to compare to)
(Now there are real MHD studies!)
Existing MHD studies of �planetary gaps in wind-driven discs
Aoyama & Bai 2023
Wafflard-Fernandez & Lesur 2023
Hu, Li, Bae, & Zhu 2024
Existing MHD studies of �planetary gaps in wind-driven discs
Aoyama & Bai 2023
Wafflard-Fernandez & Lesur 2023
Hu, Li, Bae, & Zhu 2024
MHD!
Aoyama & Bai 2023
Main feature:
The gap is much deeper!
Actual MHD planetary gap
H/R = 0.10
Mp = 3 MJup
(Because there is extra magnetic torque in the gap!)
Note:
Inner gap is �an MHD gap!
(not planet-related)
Normal
gap depths
(range)
Goal:
Replicate this!
MHD!
𝝰 = 6 ×10-3
𝝰 = 0
Aoyama & Bai 2023
Viscous: Very bad!
Inviscid: They say “good”
Viscous & Inviscid vs. Actual MHD
Gap is less shallow.
Too shallow!
Not wide enough!
Gap width matches!!
H/R = 0.10
Mp = 3 MJup
MHD!
𝝰 = 6 ×10-3
𝝰 = 0
Aoyama & Bai 2023
Viscous: Very bad!
Inviscid: They say “good”
Viscous & Inviscid vs. Actual MHD
Gap is less shallow.
Too shallow!
Not wide enough!
Gap width matches!!
H/R = 0.10
Mp = 3 MJup
Three Criteria for Matching MHD Gap Profiles
Viscous
Inviscid
Prescribed
Gap Depth
Gap Edge Position
Gap Edge Density
Aoyama & Bai 2023
✓
☒
✓
☒
☒
☒
☒
⍰
⍰
⍰
✓
✓
☒
☒
☒
Depth
Edge Position
Edge Density
Gap Criteria?
Components
MH+ 2024, in prep.
Existing Wind Model vs. Actual MHD:
Attempt 1 out of 3
✓
☒
☒
Depth
Edge Position
Edge Density
Gap Criteria?
Components
MH+ 2024, in prep.
𝝰 = 10-3
Existing Wind Model vs. Actual MHD:
Attempt 2 out of 3
☒
☒
Depth
Edge Position
Edge Density
Gap Criteria?
Components
MH+ 2024, in prep.
𝝰 = 10-3
☒
Existing Wind Model vs. Actual MHD:
Attempt 3 out of 3
How else can we improve the� four-component model?
Modify the components!
Question #3
☒
☒
Depth
Edge Position
Edge Density
Gap Criteria?
Components
MH+ 2024, in prep.
𝝰 = 10-3
☒
Existing Wind Model vs. Actual MHD:
Attempt 3 out of 3
Added these two effects
Let’s modify the original two effects!
(to match the actual MHD)
☒
The NEW Wind Model vs. Actual MHD
☒
Depth
Edge Position
Edge Density
Gap Criteria?
Components
MH+ 2024, in prep.
𝝰 = 10-3
☒
✓
✓
✓
✓
✓
✓
The NEW Wind Model vs. Existing Model
MH+ 2024, in prep.
Depth
Edge Position
Edge Density
Gap Criteria?
The NEW Wind Model vs. Existing Model
MH+ 2024, in prep.
✓
✓
✓
Depth
Edge Position
Edge Density
Gap Criteria?
The NEW Wind Model vs. Existing Model
MH+ 2024, in prep.
✓
✓
✓
Depth
Edge Position
Edge Density
Gap Criteria?
Torque: MHD Modifications
Aoyama & Bai 2023
Existing model
NEW model
Note:
Magnetic stress �not directly related to surface density.
, cumulative
MHD Torque Profile: Background
Aoyama & Bai 2023
Old model
NEW model
MHD Torque Profile: Gap
Aoyama & Bai 2023
Mass Loss: MHD Modifications
Existing model
NEW model
Decays
(towards outer disc)
Uniform
Mass Loss: MHD Modifications
Decays
Uniform
Part good!
Outer bump closer to:
Part bad!
Bump ratio closer to:
Why does the viscous model�work now?
It allows vortices!
Question #4
Key to match gap profile w/ viscosity: Vortices
The actual �MHD simulations have �planet-induced vortices �at outer gap edge.
Planet-induced vortices are needed to�match the gap profile!
A vortex!
MH+ 2024, in prep.
Four-component model
Key to not matching gap profile: No vortices
MH+ 2024, in prep.
No vortex!
Four-component model
☒
☒
Depth
Edge Position
Edge Density
☒
H/R = 0.10
Mp = 1 MJup
How does �the planet migrate?
Inward! (mostly normal!)
Question #5
No Wind
Wind
Planet Migration w/ four-component model
The planet migrates qualitatively �similar to viscous case with no disc wind.
Summary
We can match the real MHD planetary gap profiles by adding viscosity & extra gap torque to two-component �(wind torque & mass loss) prescribed models.
It is more difficult to match the gap profiles�for lower-mass planets.
To match the gap profiles with viscosity,�the key is to allow vortices to develop.
Mass Loss: MHD Modifications
Existing model
NEW model
Decays
(towards outer disc)
Uniform
Changes to Existing Model
(1) A torque proportional to dJ/dR, not ∝ Σ�(2) And a uniform mass loss ∝ Ωp, not ΩK(r)
Starting Point: Torque
MHD Torque Profile: Background
Aoyama & Bai 2023
Old model
NEW model
MHD Torque Profile: Gap
Aoyama & Bai 2023
Starting Point: Mass Loss
Old model
NEW model
Mass Loss Profile
Existing Wind Model vs. Actual MHD
Existing Wind Model vs. Actual MHD
Existing Wind Model vs. Actual MHD
Existing Wind Model vs. Actual MHD
NEW Wind Model vs. Actual MHD
Can we simulate planetary gaps
in MHD wind-driven discs?
Yes!
Question #1
Aoyama & Bai 2023
Wafflard-Fernandez & Lesur 2023
Hu, Li, Bae, & Zhu 2024
What changes should we make �to existing prescribed �disc wind models?
Yes!
Question #1
Gap Profiles
MHD!
𝝰 = 6 ×10-3
𝝰 = 0
Aoyama & Bai 2023
Viscous: Very bad
Inviscid: They say it’s good! (The width matches.)
MHD Torque Profile: Background
Aoyama & Bai 2023
MHD Torque Profile: Gap
Aoyama & Bai 2023
Mass Loss Profile