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Should vortices be more ubiquitous in protoplanetary disk observations?

Michael Hammer

ASIAA

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

ASIAA

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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Our 1^st paper said: �“Including the planet’s growth�shortens vortex lifetimes.”

Is that correct?

Not for low-mass planets!

Question #4

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

Not for high-mass planets!

MH, et al., 2022, in prep.

MH, et al. 2017,

MNRAS

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Different ways to grow the planet

Paper(s)

Accretion Method

Vortex Lifetimes

MH, et al., 2022,�in prep.

MH, et al., 2019,

MNRAS

MH, et al., 2021,�MNRAS

MH, et al. 2017,

MNRAS

Prescribe growth:

Accrete gas from disc:

Vary growth time!

(but 1 and 5 M_Jupiter only)

Vary accretion rate!

Higher resolution: 29 / h

Vary disc mass!

Shorter!

(Because elongated, �not compact!)

(H/R = 0.06)

The reason we keep getting different results is because we keep changing how we are growing the planet.

In our first paper, we prescribed the growth of the planet. We just told it to grow to a Jupiter mass and how long it should take to get there. And we get shorter vortex lifetimes because the vortices were elongated instead of compact.

In our most recent paper, we instead started with a small core and had that core accrete its gas from the disc itself, just like how a normal planet would grow. To get different-mass planets, we used different accretion rates.

In our current work, we still accrete gas from the disc, we increased the resolution. And to get different-mass planets, we instead vary the disc mass, assuming that the planet's accretion prescription shouldn't really change the way it did in our last paper.

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

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 low-mass planet)

H/R = 0.06

M_p = 0.20 M_Jup

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Different ways to grow the planet

Paper(s)

Accretion Method

Vortex Lifetimes

MH, et al., 2022,�in prep.

MH, et al., 2019,

MNRAS

MH, et al., 2021,�MNRAS

MH, et al. 2017,

MNRAS

Prescribe growth:

Accrete gas from disc:

Vary growth time!

(but 1 and 5 M_Jupiter only)

Vary accretion rate!

Higher resolution: 29 / h

Vary disc mass!

Shorter!

(Because elongated, �not compact!)

Longer for low-mass planets!

(H/R = 0.06)

(Vortex re-triggered!)

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MH, et al., 2022, in prep.

Vortex re-forms? �Yes! �(unlike high-mass cases at low resolution)

Last vortex? �The last vortex that forms (t = 1660)�is compact!!

Vortex (with high-mass planet AND hi-res)

H/R = 0.06

M_p = 0.64 M_Jup

Dust Surface Density

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MH, et al., 2022, in prep.

Why is the vortex compact? �After 1^st vortex dies, the 2^nd-generation vortex forms a compact core: �a vortex-in-a-vortex!

Vortex (with high-mass planet AND hi-res)

H/R = 0.06

M_p = 0.64 M_Jup

Dust Surface Density

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Different ways to grow the planet

Paper(s)

Accretion Method

Vortex Lifetimes

MH, et al., 2022,�in prep.

MH, et al., 2019,

MNRAS

MH, et al., 2021,�MNRAS

MH, et al. 2017,

MNRAS

Prescribe growth:

Accrete gas from disc:

Vary growth time!

(but 1 and 5 M_Jupiter only)

Vary accretion rate!

Higher resolution: 29 / h

Vary disc mass!

Shorter!

(Because elongated, �not compact!)

Longer for low-mass planets!

Longer for high-mass planets!

(H/R = 0.06)

(Vortex re-triggered!)

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Question #5a

Our 3^rd paper said: �“Low-mass planets induce �longer-lived vortices than high-mass planets.”

Is that correct?

MH, et al. 2021,

MNRAS

Not if the planet is low-mass because the disc is low-mass!

MH, et al., 2022, in prep.

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Lifetime �Survives < 3000 orbits, half the lifetime with high disc mass.

Why so quick? �Planet carves �much deeper gap,�preventing �stronger re-triggers.

Vortex (with low-mass planet & low disc mass)

H/R = 0.06

M_p = 0.20 M_Jup

MH, et al., 2022, in prep.

Dust Surface Density

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Question #5b

Our 3^rd paper said: �“Low-mass planets induce �longer-lived vortices than high-mass planets.”

When is it true?

MH, et al. 2021,

MNRAS

In a high-mass disc.

Or with the VSI! (3-D)

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

MH, et al., 2022, in prep.

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Vortex shape �It is compact!

Lifetime �Survives 3000+ orbits with little sign of decay!

Vortex (with low-mass planet & low disc mass

MH, et al., 2022, in prep.

& VSI in 3-D!!)

M_p = 0.20 M_Jup

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Why not elongated? �

The VSI produces �small compact vortices that seed the �RWI planet-induced vortex!

Vortex (with low-mass planet & low disc mass

M_p = 0.20 M_Jup

MH, et al., 2022, in prep.

& the VSI !!)

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Summary

It is not clear why dust asymmetries associated with planets (i.e. two-sided gaps) are not more common.

Observed dust asymmetries are characterized by �(1) wider azimuthal extents and (2) off-center peaks, matching elongated planet-induced vortex simulations.

(1) Any high-mass planets, (2) low-mass planets in high-mass discs, & (3) low-mass planets in VSI-active discs can all generate long-lived vortices.

Our findings support the idea that vortex lifetimes are being suppressed. Future work should figure out why!

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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)

Let’s take a closer look at the discs in Taurus that don’t have vortices. What chance do each of these systems have of containing a vortex?

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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How does dust feedback affect vortices?

Fu, W. et al. 2014

Normally, the dust doesn’t affect the gas because there is ~100x more gas.

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How does dust feedback affect vortices?

Fu, W. et al. 2014

With dust feedback, gas vortex is destroyed!

But the dust in the vortex never goes away!

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How does dust feedback affect vortices?

Lyra, W. et al., 2018

In 3-D, dust feedback doesn’t destroy the vortex anymore.

Only the midplane (where the dust is) is affected.

(With dust feedback)

Vorticity (No feedback)

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How does dust feedback affect vortices?

Questions about 2-D work�by Fu et al. 2014

Questions about 3-D work�by Lyra et al. 2018

Not stratified.

Not planet-induced vortex.

Their mechanism for creating a vortex never goes away.

Not 3-D.

They told me feedback still kills vortices in 3-D, �but they did not publish it.

Who is correct?

Neither?!

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How does dust feedback affect vortices in 3-D?

Case

Vortex dies at

____ orbits

2-D or 3-D �(no feedback)

2-D �(w/ feedback)

3-D �(w/ feedback)

2200

1300

1700

Artificial waves �go away!

2-D �(w/ feedback)

The dust forms a singular clump that never goes away.

MH, et al., 2022, in prep.

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How does dust feedback affect vortices in 3-D?

Case

Vortex dies at

____ orbits

2-D �(w/ feedback)

3-D �(w/ feedback)

2200

1300

1700

2-D or 3-D �(no feedback)

Hi-res 3-D �(w/ feedback)

2200

The dust spreads out!

And it does go away!

Doubled resolution in z:

32 (6.4 per H) to 64 (12.8 per H)

Why?!?!

MH, et al., 2022, in prep.

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How does dust feedback affect vortices in 3-D?

Vorticity

(With dust feedback)

z > 2 H

z = 0

(midplane)

Lyra, W. et al., 2018

Contrary to above plot, �dust feedback affects vorticity�away from the midplane!