“The interaction of a giant planet with a disc with MHD turbulence I: The initial turbulent disc models” Papaloizou & Nelson 2003a, MNRAS 339, 923 Brian Gleim February 23rd, 2006 AST 591 Instructor: Rolf Jansen

Introduction n Discovery of giant planets close to their star has led to the idea that they migrated inwards due to gravitational interaction with the gaseous disc

Causes of Migration n Previous studies involving torques between a laminar viscous disc and a Jovian protoplanet produces an inward migration n Balbus & Hawley (1991): inward migration originates from magnetorotational instability (MRI)

Paper I: Turbulent Discs n Focus on turbulent disc models prior to introducing a perturbing protoplanet (Paper II) n Cylindrical disc models; no vertical stratification n Assume disc is adequately ionized for idea MHD conditions; consider models with no net magnetic flux

Initial Model Setup

Models A-E Range from r 1 <r<r 2, 0<  /3 Range from r 1 <r<r 2, 0<  /3 n Keplerian domain imposed within the disc (wherein Ω ~ r -3/2 )

Important Quantities n Magnetic Energy –=> MRI Stress Parameter α Stress Parameter α –=> Ang. Mom. transfer n Radial Fluid Velocity –=> Inward Migration

Model A n Input Moderate Values n At onset of MRI, high initial magnetic energy before relaxation n Stable stress pattern after short time n Radial velocity takes much longer to stability

Model B n Short radius r 2 = 4.0 n Similar results to Model A n Stress Parameter results were initially nonsensical

Models C & D n 50% Thicker discs n Typical magnetic energy Time averages of α are more uniform: may occur because thicker disc loses memory of ini. cond. and relaxes faster Time averages of α are more uniform: may occur because thicker disc loses memory of ini. cond. and relaxes faster

Model E n Long radius r 2 = 8.0 Similar saturation results for α and magnetic energy This model was built to azimuth = 2  to simulate planet-disc interactions

Full 2  Disc n To simulate full disc, transform inertial frame into rotating frame n Would the simulation results change? n No, magnetic energy and stress parameter trends remain

Discussion n All models attain a turbulent state: –α ~ 5x10 -3 and –β -1 ~.001 –Same results for 2  azimuth –Same for rotational frame

Comparison with Theory n Radial velocity results up to 2 orders of magnitude larger than classical viscous disc theory expects n Long duration time-averages required to reveal magnitudes comparable to theoretical viscous inflow velocity

With a Protoplanet? n Expect different dynamic behavior in the gap region n Instantaneous velocity fluctuations too great n Classic theory only applies in quasi- steady regions

References n “The interaction of a giant planet with a disc with MHD turbulence I: The initial turbulent disc models” Papaloizou & Nelson 2003a, MNRAS 339, 923 n Images from: – marcybox4.html – tars.shtml – SciArt/