Are transition discs much commoner in M stars?

Are transition discs much commoner in M stars? Echoed by Currie et al (25%) and Dahm & Carpenter 2009 CAREFUL! Recent claim that 50% of discs around M stars are in transition (Sicilia-Aguilar et al 2008) For pure reprocessing disc with T ~ r^-q L_d()  (T_*) ^{2/q-1} --------- L_*() Harder to detect disc at given  for cooler stars

Disc to star ratio as function of wavelength for pure reprocessing disc extending in to dust sublimation radius for G star(red) and M star (black)

Ercolano et al 2009: analyseCoronet SEDs using fitting tool of Robitaille et al 2006 These turned out to be bona fide transition discs (inner holes >> sublimation radius)

But most weren’t • Best fits were optically thick discs reprocessing discs extending in to dust sublimation radius

Moral • Detectable excess starting at > 6 microns doesn’t necessarily mean that later type stars have inner holes • [Doesn’t affect other differences with spectral type, e.g. flatter (more settled) discs in later type stars, more anaemic discs…(?)]

Planetesimal growth in self-gravitating discs (with Peter Cossins, Giuseppe Lodato, Joe Walmswell, Markward Britsch) . Observational evidence: grain growth to > cm scales in young massive disc HL Tau Greaves et al 2008

Dust accumulation in spiral features in self-gravitating discs demonstrated by Rice et al 2004, 2006 ……growth to > km scales (?) Fundamental principle: gas-dust drag makes dust collect in pressure maxima

Three questions: • Why did Rice et al simulations work? • (Where) would this work in real discs (realistic cooling)? • Further planetesimal evolution…….

The issue: • Lifetime of spiral features is short (dynamical) • Should dust concentration be effective before features dissolve?

How fast can optimally coupled (metre size) objects concentrate in spiral features? ( = scale of pressure maximum) V_^2 = G M + 1 P --------- ----- - --- r r^2  r -------------------------------- V_ = v_k  1 + (c_s/v_k)^2 / r/   v = v_ - v_k = v_k (H/r)^2 (r/) /  Maximum radial drift speed To get dust to concentrate in spiral features need / 1  minimum concentration time ~ /v_max ~ /v = 1/ (/H)^2 (/)^-1  ~ 1 Lifetime of spiral features ~ 1/

What determines /?Empirically 1/t_{cool} (Cossins et al 2009) / 1/t_{cool}  Rice et al 2004,2006

Given dominant m and k and dispersion relation can calculate Doppler shifted Mach number (~ Mach number of relative flow perpendicular to shock) How to understand this result?Flow self-adjusts so that pattern is sonic cf local flow:|_p -|/ ~ H/R  Varying cooling and disc mass  Doppler shifted Mach number always *very* close to unity radius

Shocks are very weak: Mach = 1 +  Use properties of weak adiabatic shocks: Entropy jump at shock    1/ t_{cool} Q.E.D. /  

How fast can optimally coupled (metre size) particles concentrate in spiral features? To get dust to concentrate in spiral features need / 1 This implies t_cool is not >> t_dyn

Rice et al simulations had fractional amplitude in range 0.1 to 1….hence why they worked

What values of / are expected in real discs? From analytic self-gravitating disc solutions of Clarke 2009 Log Mdot (M_/yr)     Expect dust aggregation only beyond ~ 30 A.U.. Implications for location of planetesimal belts? Log R (A.U.) Clarke & Lodato submitted

Further evolution of planetesimals in self-gravitating discs • Pilot study: Britsch et al 2007 - 10 test particles demonstrated stochastic evolution of a and e • Now (Walmswell et al 2009 in prep.) evolution with 50,000 test particle “planetesimals”

If restrict planetesimals to > 30 A.U., find initial relaxation populates inner disc ( ~ 10 % leak inwards) • Little change over several thousand years after initial relaxation.

Understand in terms of lack of evolution in energy distribution of particles

Evolution on these timescales driven by attainment of equilibrium eccentricity distribution • Distribution is rapidly pumped up by interaction with the disc. • Tends to a steady state, with high mean eccentricity of 0.18. Note: collisions are destructive as vrel >> 100 m/s (Leinhardt et al 2007)

CONCLUDE • If form planetesimals through dust aggregation in spiral arms, this occurs at > 30 A.U. (scales as M_*^{1/3}) • Subsequent planetesimal evolution is dominated by eccentricity growth - would only fill in inner hole to limited extent - observational signatures? Debris discs?

CONCLUDE : • Large e of planetesimals implies collisions are destructive - re-supply small grains? • Means by which to retain solids in disc during self-gravitating phase?

Are transition discs much commoner in M stars?