Long term evolution of circumstellar discs: DM Tau and GM Aur Ricardo Hueso (*) & Tristan Guillot Laboratoire Cassini, Observatoire de la Côte d’Azur, Nice, France (*) Now at: E.T.S. Ing. Ind. y Telecom. UPV, Bilbao, Spain Circumstellar disks & protoplanets, Nice, February 2003

Initial questions: Are models of star & disk formation able to compare with observations and give constraints on relevant disk physics? Numerous Parameterizations. How to set up values for the most relevant parameters? Circumstellar disks & protoplanets, Nice, February 2003 Is it viscous evolution the most important factor determining disk properties on the long term? Different models of turbulence a prescription, b prescription, Shear, convection, MRI, surface MRI, waves Statistics about protoplanetary disks begin to be available. Life-span, disk masses, star accretion rates with time … This work: Make simple models of disk formation & evolution and compare with available observations. Set up model parameters and test turbulence prescriptions.

Models of Disk Formation and Evolution Circumstellar disks & protoplanets, Nice, February 2003 PAREMETERS - T cloud - w cloud - M cloud - a, b Several long term simulations of DM Tau and GM Aur Compare with observations Fast 1D models Including gravitational collapse of rotating isothermal spheres: + Additional equations for disk properties + Simplified radiative transfer + Photoevaporation (Long term simulations) Viscous evolution + source terms

Two “models” of turbulence: a and b Non-Linear shear instability  n b = b ( d W/ dR ) R 3 Non-Linear shear instability  n b = b ( d W/ dR ) R 3 Not easy to study in numerical experiments!! Intensity from experiments in rotating tanks. b ~ 2 x Not easy to study in numerical experiments!! Intensity from experiments in rotating tanks. b ~ 2 x HCsCs Mixing-Length  n a = a c s H ~ r 3/4 Mixing-Length  n a = a c s H ~ r 3/4 Only a parameterization! Models of MRI a ~ Used also when considering others kind of mechanisms for the turbulence Only a parameterization! Models of MRI a ~ Used also when considering others kind of mechanisms for the turbulence  n a ~ r 3/4 n b ~ r ½  Are finally both parameterizations so different when applied?  n a ~ r 3/4 n b ~ r ½  Are finally both parameterizations so different when applied? Circumstellar disks & protoplanets, Nice, February 2003

Observational characteristics of DM Tau and GM Aur Guilloteau & Dutrey, 1998 Simon, Guilloteau & Dutrey, 2001 CO Maps of disk emission: Temperature and S retrievals Dust Maps of diffused light: S Retrievals Kitamura et al Spectral Energy Dist. (IR) Signatures of Star accretion Rate Hartmann et al Circumstellar disks & protoplanets, Nice, February 2003

Comparing model with DM Tau a = w cd = s -1 T cd = 10 K M 0 = 0.3 M  PAREMETERS Circumstellar disks & protoplanets, Nice, February 2003

Comparing model with DM Tau a = w cd = s -1 T cd = 10 K M 0 = 0.3 M  PAREMETERS Circumstellar disks & protoplanets, Nice, February 2003

Comparing model with DM Tau a = w cd = s -1 T cd = 10 K M 0 = 0.3 M  PAREMETERS n a =a c s H n b =b ( d W/ dR ) R 3 n a =a c s H n b =b ( d W/ dR ) R 3 Explore parameter space. Test parameterizations of turbulence Explore parameter space. Test parameterizations of turbulence Circumstellar disks & protoplanets, Nice, February 2003

Constraining model parameters: All Models Circumstellar disks & protoplanets, Nice, February 2003 Selecting models

All Models CO + Star age & mass Circumstellar disks & protoplanets, Nice, February 2003 Constraining model parameters: Selecting models

All Models CO + Star age & mass CO + Dust Circumstellar disks & protoplanets, Nice, February 2003 Constraining model parameters: Selecting models

All Models CO + Star age & mass CO + Dust CO + Dust + Accretion Rate Circumstellar disks & protoplanets, Nice, February 2003 Constraining model parameters: Selecting models

All Models CO + Star age & mass CO + Dust CO + Dust + Accretion Rate Circumstellar disks & protoplanets, Nice, February 2003 Constraining model parameters: Selecting models

Set of model parameters fitting the observational constraints: Circumstellar disks & protoplanets, Nice, February 2003 Practically a standard accretion disk.

Set of model parameters fitting the observational constraints: More mass is needed Less Turbulence Greater Temperature (15 K) (Faster early formation) Less dispersion with Temperature Circumstellar disks & protoplanets, Nice, February 2003

a vs. b : DM Tau & GM Aur b models behave globally like a models b models show bigger dispersion in turbulence  They have n almost unchanged in time while a models evolve from high turbulence to less turbulent stages. Circumstellar disks & protoplanets, Nice, February 2003 Knowing the data for the disk within an order of 5 doesn’t improve these plots. Iincertitudes come also from the assumed star age and its mass.

Conclusions Circumstellar disks & protoplanets, Nice, February 2003 Models of purely viscous discs are able to explain presently observed characteristics of circumstellar disks like DM Tau and GM Aur. We can obtain valuable information about the relevant parameters governing disk formation and evolution. Large incertitudes on the determination of physical properties. Results depends on assumptions such as CO depletion or dust abundance. Incertitudes give rise to one-two orders of magnitude indetermination of disk viscosity. Alpha an Beta parameterizations of turbulence work equally well (or bad) to fit the observations. GM Aur requires 10 times less turbulence than DM Tau. Consequence of a more massive disk combined with a lower accretion rate. Why? Simply more massive system, older, or... A procative posibility. Can this reduced “accretion” be interpreted in terms of an internal gap in GM Aur? SED of GM Aur seems to suggest a gap!