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Should vortices be more ubiquitous in protoplanetary disk observations?

Michael Hammer

(No institution, …but ASIAA soon!! :-)

Collaborators: Min-Kai Lin (ASIAA), Paola Pinilla (MPIA), Kaitlin Kratter (Arizona)

Credit: �Nienke van der Marel

(nienkevandermarel.com/)

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Should vortices be more ubiquitous in protoplanetary disk observations?

Michael Hammer

(No institution, …but ASIAA soon!! :-)

Collaborators: Min-Kai Lin (ASIAA), Paola Pinilla (MPIA), Kaitlin Kratter (Arizona)

Credit: �Nienke van der Marel

(nienkevandermarel.com/)

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Do protoplanetary disks

typically contain vortices?

ALMA suggests no!

Question #1

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How common are large-scale asymmetries*?

Credit: Nienke van der Marel

(nienkevandermarel.com/)

ALMA observations of mm dust

* (vortex candidates)

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V1247 Ori

HD 135344B

AB Aur

CQ Tau

RY Lup

Only about 25% of disks* contain asymmetries!

HD 142527

Oph IRS 48

HD 34282

MWC 758

HD 143006

SR 21

Credit: Nienke van der Marel

(nienkevandermarel.com/)

van der Marel, N., �et al. 2021

* (resolved transition disks)

ALMA observations of mm dust

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V1247 Ori

HD 135344B

AB Aur

CQ Tau

RY Lup

HD 142527

Oph IRS 48

HD 34282

MWC 758

HD 143006

SR 21

Credit: Nienke van der Marel

(nienkevandermarel.com/)

Only 2 disks have two-sided gaps* with an* asymmetry!

* (one or more)

ALMA observations of mm dust

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V1247 Ori

HD 135344B

AB Aur

CQ Tau

RY Lup

Only 2 disks have two-sided gaps* with an* asymmetry!

HD 142527

Oph IRS 48

HD 34282

MWC 758

HD 143006

SR 21

* (one or more)

HD 135344 B

V1247 Ori

Cazzoletti, P., et al. 2018

Kraus, S., et al. 2017

* (with a planet??)

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Can planets generate �these large-scale asymmetries?

.

Question #2

Yes, but…

…only if they just formed

AND

you may need to consider �the planet’s growth time.

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Vortex Evolution (with Slow Planet Growth)

MH, Kratter, K., Lin, M.-K. 2017, MNRAS, 466, 3533

Extent �>180 degrees.

Lifetime �Lasts ~1500 orbits.

(~5x shorter than instant growth case!)

Notice:

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MH, Lin, M.-K., Kratter, K., Pinilla, P., 2021�MNRAS, 504, 3963

ALMA Observation

Synthetic Image

HD 135344 B

(Dust at λ = 1.9 mm)

Cazzoletti, P., et al. 2018

~50 AU

Matching ALMA Observations

Beam

Elongated Vortex

(w/ slow growth)

Off-center peak!

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Beam

ALMA Observation

Synthetic Image

HD 135344 B

(Dust at λ = 1.9 mm)

Cazzoletti, P., et al. 2018

~50 AU

(Not) Matching ALMA Observations

MH, Pinilla, P., Kratter, K., Lin, M.-K. 2019, MNRAS, 482, 3609

Compact Vortex

(w/ instant growth)

Too �compact!!

Peak not�off-center!!

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Why do these vortices �look different?

There are two types�of vortices!!

Question #3

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Two types of vortices!!

Compact

Gaussian model (Surville + Barge 2015)

Rossby number: Ro < -0.15

Elongated

GNG model (Goodman et al. 1987)

Rossby number: Ro > -0.15

INSTANT growth!!

SLOWER (realistic) growth!!

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Why is the final vortex elongated?

MH, Lin, M.-K., Kratter, K., Pinilla, P., 2021�MNRAS, 504, 3963

The initial set of vortices are elongated!�(Ro > -0.15)

The final vortex has�no clear� vorticity minimum �at the center!

The Rossby number never drops to compact!

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Why do elongated vortices�have off-center peaks?

The dust circulates �around the vortex.

Question #4

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Different Vortex Structures

Compact Vortex

Elongated Vortex

Contour Levels:

1.10,

Gas

1.20,

1.30, 1.40, …, 2.70

[Σ / Σ₀]

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The dust circulates around the vortex!

Vortex is also elongated in the dust.

The peak is usually �off-center.

MH, Pinilla, P., Kratter, K., Lin, M.-K. 2019, MNRAS, 482, 3609

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Does incorporating �the planet’s growth time� always shorten vortex lifetimes?

Not for lower-mass planets!

Question #5

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Growing the planet even more realistically

Our Past Work:

More Realistic Approach:

Prescribe the growth of the planet.

�Have the planet accrete gas directly from the disk.

MH, Lin, M.-K., Kratter, K., Pinilla, P., 2021�MNRAS, 504, 3963

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MH, Lin, M.-K., Kratter, K., Pinilla, P., 2021�MNRAS, 504, 3963

Notice:

Vortex re-forms? �Yes, multiple times:

t = 2610�t = 3150�t = 3660

Lifetime �Vortex is still alive at the end of this movie:�t = 6000

Vortex (with H/R = 0.06 and 0.20 M_Jup planet)

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MH, Lin, M.-K., Kratter, K., Pinilla, P., 2021, MNRAS, 504, 3963

Dust snapshots (with 0.2 M_Jup planet)

Note:

Dust asymmetry survives in-between gas vortices.

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MH, Lin, M.-K., Kratter, K., Pinilla, P., 2021�MNRAS, 504, 3963

Vortex Lifetimes

Note:

Because of �later-generation vortices,�

the low-mass planets�produce �longer vortex lifetimes.

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How do you kill a vortex?

Question #6

(from the planet’s spiral waves)

Viscosity!

but not always!

(but only if 𝜶 > 10^-4)

Shocks!

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MH, Lin, M.-K., Kratter, K., Pinilla, P., 2021�MNRAS, 504, 3963

Vortex Evolution (with H/R = 0.08)

Notice:

Vortex Growth�

After first 200 orbits,

nothing happens!

The vortex is still alive �at the end.

The shocks passing through the vortex �are weaker!

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Do these trends occur �with higher viscosity?

Question #7

No, viscosity still shortens vortex lifetimes.

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MH, Lin, M.-K., Kratter, K., Pinilla, P., 2021�MNRAS, 504, 3963

Vortex Lifetimes ( at 𝝂 = 10^-7 and 𝝂 = 10^-6 )

With 𝝂 = 10^-6,�vortices are�short-lived regardless of �planet mass.

𝝂 = 10^-7

𝝂 = 10^-6

Viscosity

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At least in some cases, yes!

AND

Should vortices be more ubiquitous in protoplanetary disc observations?

Question #8

Figuring out why may constrain planet or disc properties.

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DS Tau

FT Tau

MWC 480

DL Tau

9.65 M_Jup

0.44 M_Jup

0.40 M_Jup

0.34 M_Jup

Disc w/ Gap

Planet mass

CI Tau

0.40 M_Jup

0.42 M_Jup

Chances of Observing Vortices in Taurus

Sample from �Long, F., et al. 2018

(NO asymmetries!)

Mass estimates by �Lodato, G., et al. 2019��(over-estimates assuming �a low viscosity)

(per solar mass)

Gap location

33 AU

73 AU

48 AU

25 AU

89 AU

120 AU

Chance

(Lifetime = 1000 orbits)

(Cluster Age = 2 Myr)

12%

23%

10%

42%

68%

18%

There should be� at least ONE vortex!

(but there are none)

We attempted to quantify that idea by looking at a sample of gaps in Taurus associated with planets massive enough to trigger vortices and estimating the probability we would see an asymmetry at the edge of the gap. If we assume the vortex has a lifetime of 1000 orbits and the cluster is 2 Myr old, then based on the gap in FT Tau being located at 25 AU, we can estimate that if a vortex was triggered, it would have lasted for 10% of the current age of the system. Some of the other gaps are located farther out, and so they have slightly higher percentages. And the last two are in the outer part of the disc, so you would expect a vortex to be present for a significant fraction of the disc lifetime. Overall, these percentages are high enough that you would expect at least one of these gaps to have an asymmetry, but not of them do. And this is just for an estimated vortex lifetime of 1000 orbits. We saw that the low viscosity cases in our study have characteristic lifetimes of at least 2000 orbits, and even 6000 orbits can be common for certain parameters. If we assumed a vortex lifetime of 3000 orbits here, we would expect half of these systems to have vortices. So why is it the case that none of them have vortices?

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Why are there so few asymmetries?

(and what can we learn?)

Higher viscosity?

Planet migration?

Vortex forms later?

Strong dust feedback?

Sub-optimal cooling time?

Strong disc self-gravity?

Planet formed early!

Dust-to-gas ratio must be high!

Not in 3-D?!!

Viscosity may not be so low!

Planet massive enough to create vortex, but not if it is migrating!

Planet can’t be too massive!

(more relevant for outer disc)

𝞫 ≳ 1.0 Ω^-1 weakens vortices

Lyra, W., et al. 2018;

MH, et al. in prep. b

Fung, J. + Ono, T. 2021; Rometsch, T., et al. 2021

May be realistic in outer disc?!!

Bae, J., et al. 2021; Malygin, M., et al. 2017

MH, et al. 2021

e.g. MH, et al. 2021

Kanagawa et al. 2021;

MH, et al. in prep. a

Relevant for Q < (H/R)^-1, but weaker for lower-mass discs

The simplest explanation might be that discs still have a moderate amount of viscosity.

Another simple explanation could be that although the minimum planet mass needed to trigger a vortex is very low in a low-viscosity disc, but it might double or so if the planet is migrating.

Another simple explanation for the planets in the very outer disc is that they haven’t had orbits to trigger a vortex yet, but they will eventually as the planet continues to open up a gap. This would apply to relatively low mass planets.

In terms of physical effects, two recent works showed that cooling timescale a bit larger than the orbital timescale are optimal shortening vortex lifetimes. Those cooling times may be realistic in the outer disc in at least a few models.

Another relevant physical effect that weakens self-gravity. This would be interesting because it would be consistent with the idea that planets form relatively early, but although self-gravity can affect discs that aren’t close to self-gravitating, it doesn’t affect vortices in those discs as much.

It’s also been suggested that dust feedback could shorten vortex lifetimes, but this doesn’t seem to hold up in 3-D.

Overall, I don’t think we know exactly why there are so few asymmetries, but figuring it out could provide some helpful constraints!

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Elongated planet-induced vortices are characterized by (1) wider azimuthal extents and (2) off-center peaks.

Summary

With H / R ≤ 0.06, lower-mass planets create longer-lived asymmetries because of the vortex re-forming.

With H / R ≥ 0.08, vortices are long-lived �because of weaker shocks from the planet.

Have questions? Contact�mhammer@email.arizona.edu

Test vortex-killing mechanisms w/ large H / R values!

It’s still problematic that so few systems have �large-scale asymmetries that could be vortices.

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Other Signatures of Elongated Vortices

(1) Dust extent not always as wide as �gas extent!

(2) Double peak�also possible!!

Dust supply is cut off!

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Double Peak Signature in Real Discs

Boehler, Y. et al. 2021

Kraus, S. et al. 2017

V1247 Orionis

HD 142527

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What does it take to�re-form a vortex?

A sharp spike in .

Question #7

A new sharp pressure bump?

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Pressure Bumps (with 0.6 M_Jup planet)

Initial Vortex

End State

MH, Lin, M.-K., Kratter, K., Pinilla, P., 2021�MNRAS, 504, 3963

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P (with 0.6 M_Jup planet)

Initial Vortex

End State

MH, Lin, M.-K., Kratter, K., Pinilla, P., 2021�MNRAS, 504, 3963

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Pressure Bumps (with 0.6 M_Jup planet)

Initial Vortex

End State

MH, Lin, M.-K., Kratter, K., Pinilla, P., 2021�MNRAS, 504, 3963

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P (with 0.6 M_Jup planet)

Initial Vortex

End State

MH, Lin, M.-K., Kratter, K., Pinilla, P., 2021�MNRAS, 504, 3963

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MH, Lin, M.-K., Kratter, K., Pinilla, P., 2021�MNRAS, 504, 3963

Evolution (with 0.6 M_Jup planet)

Notice:

A spike appears after the initial vortex dies�(t > 1350 orbits).

But it doesn’t affect�the pressure bump!

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MH, Lin, M.-K., Kratter, K., Pinilla, P., 2021�MNRAS, 504, 3963

Vortex Evolution (with 0.6 M_Jup planet)

Notice:

Vortex re-forms? �No, not at the pressure bump.

But vortices do re-form�inside the �pressure bump!

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MH, Lin, M.-K., Kratter, K., Pinilla, P., 2021�MNRAS, 504, 3963

Vortex Evolution (with 0.2 M_Jup planet)

Notice:

Vortex re-forms? �Yes, multiple times:

t = 2610�t = 3150�t = 3660

Lifetime �Vortex is still alive at the end of this movie:�t = 6000

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MH, Lin, M.-K., Kratter, K., Pinilla, P., 2021�MNRAS, 504, 3963

Evolution (with 0.2 M_Jup planet)

Notice:

Tiny spikes �appears after �the initial vortex dies�(t = 2350 orbits).

They affect the whole pressure bump!

Separation must be �less than �3 scale heights!

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Early Vortex Evolution

…with Instant Growth:

…with Slower Growth:

(1) Planet grows to full size.

(2) Disk becomes unstable.

(3) A compact vortex forms.

(Ro < -0.15)

(4) Vortex smooths gap edge.

(1) Disk becomes unstable.

(2) An elongated vortex forms.� (Ro > -0.15)

(3) Vortex smooths gap edge.

(4) Planet grows to full size.

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MH, Lin, M.-K., Kratter, K., Pinilla, P., 2020�to be submitted

Vortex (with H/R = 0.06 and 0.6 M_Jup planet)

Notice:

Extent �Still very elongated!

Lifetime �Lasts ~1200 orbits.

�(similar to the prescribed�slow growth case)

Vortex re-forms? �No.