Long term evolution of circumstellar discs: DM Tau and GM Aur

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: • Numerous Parameterizations. • How to set up values for the most relevant parameters? • Are models of star & disk formation able to compare with observations and give constraints on relevant disk physics? • 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. Circumstellar disks & protoplanets, Nice, February 2003

Models of Disk Formation and Evolution PAREMETERS -Tcloud - wcloud - Mcloud - 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: Viscous evolution + source terms + Simplified radiative transfer + Additional equations for disk properties + Photoevaporation (Long term simulations) Circumstellar disks & protoplanets, Nice, February 2003

Mixing-Length • na=acsH ~ r 3/4 Only a parameterization! Models of MRI a ~ 0.01 - 0.1 Used also when considering others kind of mechanisms for the turbulence Cs H • Non-Linear • shear instability • nb=b(dW/dR)R3 Not easy to study in numerical experiments!! Intensity from experiments in rotating tanks. b ~ 2 x 10-5 Two “models” of turbulence: a and b • na~ r 3/4nb~ r ½ • Are finally both parameterizations so different when applied? Circumstellar disks & protoplanets, Nice, February 2003

Observational characteristics of DM Tau and GM Aur CO Maps of disk emission: Temperature and S retrievals Guilloteau & Dutrey, 1998 Simon, Guilloteau & Dutrey, 2001 • Dust Maps of diffused light: • Retrievals Kitamura et al. 2002 Spectral Energy Dist. (IR) Signatures of Star accretion Rate Hartmann et al. 1998 Circumstellar disks & protoplanets, Nice, February 2003

Comparing model with DM Tau PAREMETERS a = 0.005 wcd = 3 10-14 s-1 Tcd = 10 K M0 = 0.3 M Circumstellar disks & protoplanets, Nice, February 2003

Comparing model with DM Tau a = 0.005 wcd = 3 10-14 s-1 Tcd = 10 K M0 = 0.3 M PAREMETERS Circumstellar disks & protoplanets, Nice, February 2003

Comparing model with DM Tau PAREMETERS a = 0.005 wcd = 3 10-14 s-1 Tcd = 10 K M0 = 0.3 M Explore parameter space. Test parameterizations of turbulence na=acsH nb=b(dW/dR)R3 Circumstellar disks & protoplanets, Nice, February 2003

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

Constraining model parameters: 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

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

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

b models behave globally like a models b models show bigger dispersion in turbulence  Theyhave nalmost unchanged in time while a models evolve from high turbulence to less turbulent stages. a vs. b: DM Tau & GM Aur 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. Circumstellar disks & protoplanets, Nice, February 2003

Conclusions • 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 ofan internal gap in GM Aur? SED of GM Aur seems to suggest a gap! Circumstellar disks & protoplanets, Nice, February 2003

Long term evolution of circumstellar discs: DM Tau and GM Aur