Protoplanetary disks as Protoplanetary disks as seen by the IRAM arrayseen by the IRAM arrayVincent Pietu (LAOG)Vincent Pietu (LAOG)

A few important points in the A few important points in the observations and analysis related to observations and analysis related to the survey we have performed with the survey we have performed with the IRAM array on TTauri and Herbig the IRAM array on TTauri and Herbig HA stars in Taurus-Auriga cloudHA stars in Taurus-Auriga cloud

Main collaborators:Main collaborators:A. Dutrey (L3AB), S. Guilloteau(L3AB), E. A. Dutrey (L3AB), S. Guilloteau(L3AB), E.

Dartois (IAS) Dartois (IAS)

Protoplanetary disks as Protoplanetary disks as seen by the IRAM arrayseen by the IRAM array

Collapse of a prestellar Collapse of a prestellar condensationcondensation

The conservation of angular The conservation of angular momentum gives raise to a momentum gives raise to a flattened structure : diskflattened structure : disk

Evolutionary sequence : Evolutionary sequence :

Class 0, I, II, IIIClass 0, I, II, III Also holds for intermediate-mass Also holds for intermediate-mass

stars : Herbig HAe stars (3 < Msun)stars : Herbig HAe stars (3 < Msun) Planet formation ?Planet formation ?

Disks emission in mm Disks emission in mm rangerange

Thermalized linesThermalized lines CO optically thin lines CO optically thin lines ::

J=1-0:J=1-0: TTb b /T/T

J=2-1: J=2-1: TTbb

CO optically thick lines CO optically thick lines :: TTbbTkTk

Brightness temperatures Brightness temperatures from a few mK to a few from a few mK to a few 10 K (10 K (1212CO J=2-1CO J=2-1) )

Continuum optically thin Continuum optically thin :: TTb b TT 00νν//νν00

D= 150 pc

Res = 1’

Observations and Observations and reduction : strategyreduction : strategy

1212CO : (u,v) coverage is the limiting factor.CO : (u,v) coverage is the limiting factor. Snapshot observations (better calibration)Snapshot observations (better calibration)

Other molecules : SNR is an issue. Can only Other molecules : SNR is an issue. Can only image brightest disks and strongest lines. image brightest disks and strongest lines.

Final error bars on parameters depend on Final error bars on parameters depend on the SNR.the SNR. PdBI CO observations : physical structure.PdBI CO observations : physical structure. 30-m : line detection.30-m : line detection. PdBI : imaging of molecular lines other than COPdBI : imaging of molecular lines other than CO

Data reduction : flux calibration is an issue !Data reduction : flux calibration is an issue ! Error on Tk proportionnal to flux errors.Error on Tk proportionnal to flux errors.

Method of analysis : Method of analysis : parametric modelling and parametric modelling and

inversioninversion Quite complex observations : direct analysis is not possible. Rather Quite complex observations : direct analysis is not possible. Rather use a parametric model.use a parametric model.

Need to account for tranfert function of the interferometer for a non-Need to account for tranfert function of the interferometer for a non-biased analysis.biased analysis.

Since Since deconvolution is non-lineardeconvolution is non-linear, comparison performed in the , comparison performed in the (u,v) (u,v) planeplane22 = = ii nn [ Re(mod [ Re(modi,ni,n) - Re(obs) - Re(obsi,ni,n)])]2 2 *W*Wii + + ii nn [ Im(mod [ Im(modi,ni,n) - Im(obs) - Im(obsi,ni,n)])]2 2 *W*Wii

Weight : WWeight : Wii = 1 / = 1 / ii2 2 where where i i is the thermal noise associated with is the thermal noise associated with

visibility ivisibility i Standard disk model Standard disk model (Pringle 1981): (Pringle 1981):

Power-law parametrisation :Power-law parametrisation : T ( r ) = TT ( r ) = T00 . (r / r . (r / r

00) ) -q-q

r)r)00 . (r / r . (r / r00) )

-p-p Vertical distribution derived from (isothermal) hydrostatic equilibriumVertical distribution derived from (isothermal) hydrostatic equilibrium

n(r,z ) = n(r,0 ) . exp[ - (z / h) n(r,z ) = n(r,0 ) . exp[ - (z / h) 22 ] ] Where the scaleheight is : h ( r ) ~ cWhere the scaleheight is : h ( r ) ~ c

ss / v / v Disk in rotation : v ( r ) = v Disk in rotation : v ( r ) = v 00 . (r / r . (r / r

00) ) –v –v

(Keplerian case (v=0.5) : dynamical masses measurement : v(Keplerian case (v=0.5) : dynamical masses measurement : v00 =√ G.M/r =√ G.M/r00)) Line width : quadratic sum of thernal width and a turburlent width Line width : quadratic sum of thernal width and a turburlent width Level population : Local Thermodynamic Equilibrium (LTE)Level population : Local Thermodynamic Equilibrium (LTE)

CO isotopes analysis : CO isotopes analysis : MWC 480MWC 480

MWC 480 is a isolated MWC 480 is a isolated Herbig A4 star.Herbig A4 star.

Observed in Observed in 1212CO (2-1) CO (2-1) 1313CO (2-1) and CO (2-1) and 1313CO (1-CO (1-0) 0)

The modeling reveals a The modeling reveals a vertical temperature vertical temperature gradient between the gradient between the plane of the disk (30 K) plane of the disk (30 K) and above (50 K) at r = and above (50 K) at r = 100 AU100 AU

Contrary to TTauri Contrary to TTauri stars, CO isotopes are stars, CO isotopes are not depleted with not depleted with respect to TMC-1respect to TMC-1

Analysis : the (relative) Analysis : the (relative) importance of line importance of line contamination by contamination by

continuumcontinuum MWC 480 possesses a strong (220 mJy @ 230 GHz) and MWC 480 possesses a strong (220 mJy @ 230 GHz) and compact (0.8”) continuum emission (therefore used as compact (0.8”) continuum emission (therefore used as an internal flux calibrator).an internal flux calibrator).

Can contaminate line wings Can contaminate line wings bias on kinematic bias on kinematic properties !properties !

Solution : simultaneous fitting of line and continuum Solution : simultaneous fitting of line and continuum data (the latter are less noisy thanks to a larger data (the latter are less noisy thanks to a larger bandwidth)bandwidth)

Indeed, such a procedure provides an better fit to the Indeed, such a procedure provides an better fit to the data.data.

For example in MWC 480, For example in MWC 480, 1212CO(2-1) :CO(2-1) :MM**= 1.65±0.07 Msol (Simon et al. 2000)= 1.65±0.07 Msol (Simon et al. 2000)

Small difference with prestellar evolution models ? Distance problem ?Small difference with prestellar evolution models ? Distance problem ? Same data : MSame data : M**= 1.97±0.02 Msol (with continum fitting). = 1.97±0.02 Msol (with continum fitting). Perfect agreement with models at the nominal distancePerfect agreement with models at the nominal distance

Sub-arcsecond imaging of Sub-arcsecond imaging of the Herbig A0e star AB the Herbig A0e star AB

AurigaAuriga Continuum Continuum

assymetry also assymetry also present in present in 1313COCO Density effectDensity effect Spiral arm ?Spiral arm ?

Fukagawa et al. 2004

AB Aur : modelling and AB Aur : modelling and analysisanalysis

CO lines modelling reveal thatCO lines modelling reveal that The disk is quite hot, and there is The disk is quite hot, and there is

a vertical temperature between a vertical temperature between the disk plane (30 K) and the disk plane (30 K) and “atmosphere” (80-100 K) at 100 “atmosphere” (80-100 K) at 100 AUAU

Contrary to TTauri disks, CO Contrary to TTauri disks, CO isotopes in HAe disks are not isotopes in HAe disks are not significantly depleted compared significantly depleted compared to TMC-1 CO abundance .to TMC-1 CO abundance .

But some difficulties remain : But some difficulties remain : The rotation is not KeplerianThe rotation is not Keplerian: :

v(r) = 2.44 (r/ro) v(r) = 2.44 (r/ro) 0.4 +\- 0.010.4 +\- 0.01 (as derived from (as derived from 13 13 CO 2-1, 1-0)CO 2-1, 1-0)

Spiral pattern in the diskSpiral pattern in the disk Origin of these disturbances ? Origin of these disturbances ? Companion ? Quite unlikely.Companion ? Quite unlikely. Massive disk ? Stable according to Massive disk ? Stable according to

Toomre’s criterionToomre’s criterion Youth remnant ? (Cassen et al. Youth remnant ? (Cassen et al.

1981, 1983, Stahler et al. 1994)1981, 1983, Stahler et al. 1994) From Grady et al. 1999

Conclusion and Conclusion and perspectiveperspective

Millimeter interferometry is a powerful way to study Millimeter interferometry is a powerful way to study protoplanetary disks, but SNR is an issueprotoplanetary disks, but SNR is an issue

With respect to this concern, the IRAM array is actually the best With respect to this concern, the IRAM array is actually the best instrument in use.instrument in use.

Whenever using a model and inversion techniques, it is very Whenever using a model and inversion techniques, it is very useful to compare with observations in the (u,v) planeuseful to compare with observations in the (u,v) plane

mm interferometry provides a reliable and robust access to mm interferometry provides a reliable and robust access to unique insight onto protoplanetary disks.unique insight onto protoplanetary disks.

In the long term, ALMA In the long term, ALMA will cause a revolution will cause a revolution because ofbecause of Higher angular Higher angular

resolutionresolution

(5 AU @ 230 GHz @ (5 AU @ 230 GHz @ 150 pc)150 pc)

Greater sensitivityGreater sensitivity In that perspective, PdBI In that perspective, PdBI

should be used to prepare should be used to prepare ALMAALMA