Protoplanetary disks as seen by the IRAM array Vincent Pietu (LAOG) A few important points in the observations and analysis related to the survey we have performed with the IRAM array on TTauri and Herbig HA stars in Taurus-Auriga cloud A few important points in the observations and analysis related to the survey we have performed with the IRAM array on TTauri and Herbig HA stars in Taurus-Auriga cloud Main collaborators: Main collaborators: A. Dutrey (L3AB), S. Guilloteau(L3AB), E. Dartois (IAS)

Protoplanetary disks as seen by the IRAM array Collapse of a prestellar condensation Collapse of a prestellar condensation The conservation of angular momentum gives raise to a flattened structure : disk The conservation of angular momentum gives raise to a flattened structure : disk Evolutionary sequence : Evolutionary sequence : Class 0, I, II, III Also holds for intermediate-mass stars : Herbig HAe stars (3 < Msun) Also holds for intermediate-mass stars : Herbig HAe stars (3 < Msun) Planet formation ? Planet formation ?

Disks emission in mm range Thermalized lines Thermalized lines CO optically thin lines : CO optically thin lines : J=1-0: T b  /T J=1-0: T b  /T J=2-1: T b  J=2-1: T b  CO optically thick lines : T b  Tk T b  Tk Brightness temperatures from a few mK to a few 10 K ( 12 CO J=2-1) Brightness temperatures from a few mK to a few 10 K ( 12 CO J=2-1) Continuum optically thin : Continuum optically thin : T b  T T b  T  0  ν/ν 0    0  ν/ν 0   D= 150 pc Res = 1’

Observations and reduction : strategy 12 CO : (u,v) coverage is the limiting factor. 12 CO : (u,v) coverage is the limiting factor. Snapshot observations (better calibration) Snapshot observations (better calibration) Other molecules : SNR is an issue. Can only image brightest disks and strongest lines. Other molecules : SNR is an issue. Can only image brightest disks and strongest lines. Final error bars on parameters depend on the SNR. Final error bars on parameters depend on 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 CO PdBI : 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 : parametric modelling and inversion Quite complex observations : direct analysis is not possible. Rather use a parametric model. Quite complex observations : direct analysis is not possible. Rather use a parametric model. Need to account for tranfert function of the interferometer for a non-biased analysis. Need to account for tranfert function of the interferometer for a non-biased analysis. Since deconvolution is non-linear, comparison performed in the (u,v) plane Since deconvolution is non-linear, comparison performed in the (u,v) plane  2 =  i  n [ Re(mod i,n ) - Re(obs i,n )] 2 *W i +  i  n [ Im(mod i,n ) - Im(obs i,n )] 2 *W i Weight : W i = 1 /  i 2 where  i is the thermal noise associated with visibility i Standard disk model (Pringle 1981): Standard disk model (Pringle 1981): Power-law parametrisation : Power-law parametrisation : T ( r ) = T 0. (r / r 0 ) -q T ( r ) = T 0. (r / r 0 ) -q  r)  0. (r / r 0 ) -p  r)  0. (r / r 0 ) -p Vertical distribution derived from (isothermal) hydrostatic equilibrium Vertical distribution derived from (isothermal) hydrostatic equilibrium n(r,z ) = n(r,0 ). exp[ - (z / h) 2 ] n(r,z ) = n(r,0 ). exp[ - (z / h) 2 ] Where the scaleheight is : h ( r ) ~ c s / v  Where the scaleheight is : h ( r ) ~ c s / v  Disk in rotation : v ( r ) = v 0. (r / r 0 ) –v Disk in rotation : v ( r ) = v 0. (r / r 0 ) –v (Keplerian case (v=0.5) : dynamical masses measurement : v 0 =√ G.M/r 0 ) 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 : MWC 480 MWC 480 is a isolated Herbig A4 star. MWC 480 is a isolated Herbig A4 star. Observed in 12 CO (2-1) 13 CO (2-1) and 13 CO (1-0) Observed in 12 CO (2-1) 13 CO (2-1) and 13 CO (1-0) The modeling reveals a vertical temperature gradient between the plane of the disk (30 K) and above (50 K) at r = 100 AU The modeling reveals a vertical temperature gradient between the plane of the disk (30 K) and above (50 K) at r = 100 AU Contrary to TTauri stars, CO isotopes are not depleted with respect to TMC-1 Contrary to TTauri stars, CO isotopes are not depleted with respect to TMC-1

Analysis : the (relative) importance of line contamination by continuum MWC 480 possesses a strong ( GHz) and compact (0.8”) continuum emission (therefore used as an internal flux calibrator). MWC 480 possesses a strong ( GHz) and compact (0.8”) continuum emission (therefore used as an internal flux calibrator). Can contaminate line wings  bias on kinematic properties ! Can contaminate line wings  bias on kinematic properties ! Solution : simultaneous fitting of line and continuum data (the latter are less noisy thanks to a larger bandwidth) Solution : simultaneous fitting of line and continuum data (the latter are less noisy thanks to a larger bandwidth) Indeed, such a procedure provides an better fit to the data. Indeed, such a procedure provides an better fit to the data. For example in MWC 480, For example in MWC 480, 12 CO(2-1) : M * = 1.65±0.07 Msol (Simon et al. 2000) 12 CO(2-1) : M * = 1.65±0.07 Msol (Simon et al. 2000) Small difference with prestellar evolution models ? Distance problem ? Same data : M * = 1.97±0.02 Msol (with continum fitting). Same data : M * = 1.97±0.02 Msol (with continum fitting).  Perfect agreement with models at the nominal distance

Sub-arcsecond imaging of the Herbig A0e star AB Auriga Continuum assymetry also present in 13 CO Density effect Spiral arm ? Fukagawa et al. 2004

AB Aur : modelling and analysis CO lines modelling reveal that The disk is quite hot, and there is a vertical temperature between the disk plane (30 K) and “atmosphere” ( K) at 100 AU The disk is quite hot, and there is a vertical temperature between the disk plane (30 K) and “atmosphere” ( K) at 100 AU Contrary to TTauri disks, CO isotopes in HAe disks are not significantly depleted compared to TMC-1 CO abundance. Contrary to TTauri disks, CO isotopes in HAe disks are not significantly depleted compared to TMC-1 CO abundance.  But some difficulties remain : The rotation is not Keplerian: The rotation is not Keplerian: v(r) = 2.44 (r/ro) 0.4 +\ (as derived from 13 CO 2-1, 1-0) Spiral pattern in the disk Spiral pattern in the disk  Origin of these disturbances ? Companion ? Quite unlikely. Companion ? Quite unlikely. Massive disk ? Stable according to Toomre’s criterion Massive disk ? Stable according to Toomre’s criterion Youth remnant ? (Cassen et al. 1981, 1983, Stahler et al. 1994) Youth remnant ? (Cassen et al. 1981, 1983, Stahler et al. 1994) From Grady et al. 1999

Conclusion and perspective Millimeter interferometry is a powerful way to study protoplanetary disks, but SNR is an issue Millimeter interferometry is a powerful way to study protoplanetary disks, but SNR is an issue With respect to this concern, the IRAM array is actually the best instrument in use. With respect to this concern, the IRAM array is actually the best instrument in use. Whenever using a model and inversion techniques, it is very useful to compare with observations in the (u,v) plane Whenever using a model and inversion techniques, it is very useful to compare with observations in the (u,v) plane mm interferometry provides a reliable and robust access to unique insight onto protoplanetary disks. mm interferometry provides a reliable and robust access to unique insight onto protoplanetary disks. In the long term, ALMA will cause a revolution because of In the long term, ALMA will cause a revolution because of Higher angular resolution Higher angular resolution ( pc) Greater sensitivity Greater sensitivity In that perspective, PdBI should be used to prepare ALMA In that perspective, PdBI should be used to prepare ALMA