Turbulence in TW Hya

Measuring Turbulence in TW HyaRichard Teague, max planck institute for astronomy Stephane Guilloteau, Dima Semenov, Thomas Henning, Anne Dutrey, Vincent piétu

Til birnstiel, Edwige Chapillon, David Hollenbach, uma gorti

Can we measure turbulence in protoplanetary disks?

Richard Teague, MPIA

Can we measure turbulence in protoplanetary disks?

Yes! We can fit models to

the observations.

Dartois et al. (2003), Piétu et al. (2007), Hughes et al. (2011) Guilloteau et al. (2012), Rosenfeld et al. (2012), Flaherty et al. (2015)

ALMA Consortium

Unfortunately, disks are not azimuthally symmetric nor smoothly varying along the radius.


Can we measure turbulence in protoplanetary disks

in a model independent way?


Can we measure turbulence in protoplanetary disks

in a model independent way?

Sort of.


To measure the turbulent broadening:


• Disk: TW Hya

• Molecules: CO, CN and CS

Nearby and nearly face-on.

Range of locations in the disk and molecular masses.

• Product: SpectraBoth radial profiles and de-projected maps.

Picture credit: NRAO

Try two ‘direct’ approaches.

1. Temperature is known.

2. Co-Spatial molecular tracers.

Where we can derive Tex from the spectra.

Exploit different molecular masses to derive Tkin.


�1.0 �0.5 0.0 0.5 1.0

Velocity (km s�1)

0.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ized

Flu

x

CO

�3 �2 �1 0 1 2 3

Velocity (km s�1)

CN

�1.0 �0.5 0.0 0.5 1.0

Velocity (km s�1)

CS

CO CN CS

All molecules yield line centres and widths .

CO and CN yield while CS yields .

Extract physical parameters from spectra.

Richard Teague, MPIAMethods 1 & 2. Direct methods.

�1.0 �0.5 0.0 0.5 1.0

Velocity (km s�1)

0.0

0.2

0.4

0.6

0.8

1.0

Norm

alize

dFlu

x

�1.0 �0.5 0.0 0.5 1.0

Velocity (km s�1)

0.0

0.2

0.4

0.6

0.8

1.0

Norm

alize

dFlu

x�1.0 �0.5 0.0 0.5 1.0

Velocity (km s�1)

0.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ized

Flu

x

Gaussian Optically thin wings

Temperature from a single emission line.


40 60 80 100 120 140 160 180 200

Distance (au)

0

5

10

15

20

25

30

�vK

ep

(ms�

1)

6.0

7.0

8.0

Beam

Account for beam smearing.


Gorti et al. (2011)

0 20 40 60 80 100 120 140

Radius (au)

0

50

100

150

Hei

ght

(au)

0 2 4 6 8 10

log10 n(H2) (cm�3)

Assume local thermal equilibrium.

Method 1. Temperature is known. Richard Teague, MPIA

�4 �2 0 2 4

O↵set (arcsec)

�4

�2

0

2

4

O↵se

t(a

rcse

c)

�4 �2 0 2 4

O↵set (arcsec)

0

10

20

30

40

50

Tem

peratu

re(K

)

Fully recover the kinetic temperature.

CO CN


40 60 80 100 120 140 160 180

Radius (au)

0

20

40

60

Tkin

(K)

Tmaxkin

Tkin

Supra-thermal excitation of CN?


Also see poster of Ryan Loomis.

�4 �2 0 2 4

O↵set (arcsec)

�4

�2

0

2

4

O↵se

t(a

rcse

c)

�4 �2 0 2 4

O↵set (arcsec)

0

30

60

90

120

150

Velocity

Disp

ersion(m

s �1)

CO CN

Turbulent broadening.


Assume CN and CS are co-spatial.

Method 2. Co-spatial molecular tracers.

Where molecule B is the heavier of the two.


Assume CN and CS are co-spatial.


Where molecule B is the heavier of the two.


40 60 80 100 120 140 160 180

Radius (au)

0

20

40

60

80

100

Tkin

(K)

Tmaxkin

Tkin

60 80 100 120 140 160 180

Radius (au)

0

30

60

90

120

150

vtu

rb(m

s �1)

vturb

Derive Tkin and vturb directly.


Failed co-spatial assumption.


40 60 80 100 120 140 160 180 200

Radius (au)

0.4

0.6

0.8

1.0

1.2p

µ·�

V(k

ms�

1)

CN

CS

Mass scaled linewidths.

Failed co-spatial assumption.

Method 2. Co-spatial molecular tracers. Richard Teague, MPIA

Comparison of ‘Direct Methods’

Methods 1 & 2. Direct methods.

40 60 80 100 120 140 160 180

Radius (au)

0

50

100

150

200

v turb

(ms�

1)

CO

CN

CS

60 80 100 120 140 160 180

Radius (au)

0.0

0.2

0.4

0.6

0.8

1.0

vtu

rb(c

s )

CO

CN

CS

Sound speed.Absolute value.


How far can we go?

0.00 0.05 0.10 0.15 0.20

�Tkin / Tkin

0.00

0.05

0.10

0.15

0.20

v turb

/c s

3 �5 �10�

0.0

0.2

0.4

0.6

0.8

1.0

�vtu

rb/v

turb

ALMA will achieve a flux calibration of ~3%.Minimum of vturb / cs ~0.13

Method 1. If absolute values are required. Richard Teague, MPIA

0.00 0.01 0.02 0.03 0.04 0.05

��V / �V

0.00

0.05

0.10

0.15

0.20

v turb

/c s

3�

5�

10�

0.0

0.2

0.4

0.6

0.8

1.0

�vtu

rb/v

turb

0.00 0.01 0.02 0.03 0.04 0.05

��V / �V

0.00

0.05

0.10

0.15

0.20

v turb

/c s 5

�

10�

0.0

0.1

0.2

0.3

0.4

0.5

�Tkin

/T

kin

0.00 0.01 0.02 0.03 0.04 0.05

��V / �V

0.00

0.05

0.10

0.15

0.20

v turb

/c s 5

�

10�

0.0

0.1

0.2

0.3

0.4

0.5

�Tkin

/T

kin

Better precision but not as accurate?


Kinetic temperature.Turbulent broadening.

Typical accuracy of ~0.4% on linewidths with ALMA. Minimum of vturb / cs ~0.08


ConclusionsWe observed turbulent widths of 50 - 150 ms-1 in TW Hya.

Consistent with predictions from disks pervaded by the MRI.Flux calibration sets an absolute limit on what we can detect.

What do we need?What molecules are co-spatial?

Well constrained thermal structure.


ConclusionsWe observed turbulent widths of 50 - 150 ms-1 in TW Hya.

Consistent with predictions from disks pervaded by the MRI.Flux calibration sets an absolute limit on what we can detect.

What do we need?What molecules are co-spatial?

Well constrained thermal structure.


“The truth springs from an argument amongst friends.” DAVID HUME


40 60 80 100 120 140 160 180 200

Distance (au)

0

20

40

60

80

100

Tem

per

atu

re(K

)

CO (2 � 1)Tmax

kin

Tkin

Fit

60 80 100 120 140 160 180 200

Distance (au)

CN (2 � 1)Tmax

kin

Tkin

Fit

60 80 100 120 140 160 180 200

Distance (au)

CS (5 � 4)Tmax

kin

Tkin

Fit

Derived temperature profiles.


Comparison with Hughes et al. (2011)

40 60 80 100 120 140 160 180 200

Radius (au)

0

20

40

60

80

Tem

per

ature

(K)

Hughes et al. (2011) : CO (3�2)

This work: CO (2�1)

Hughes et al. (2011)

Global Fit

Direct Method

Science

Turbulence in TW Hya