Are transition discs much Are transition discs much commoner in M stars?commoner in M stars?

Recent claim that 50% of discs around M Recent claim that 50% of discs around M stars are in transition (Sicilia-Aguilar et stars are in transition (Sicilia-Aguilar et

al 2008)al 2008)

CAREFUL!

For pure reprocessing

disc with T ~ r^-q

Harder to detect disc at given for

cooler stars

Echoed by Currie et al (25%) and Dahm & Carpenter 2009

L_d() (T_*) ^{2/q-1}

---------

L_*()

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

Ercolano et al 2009: analyseErcolano et al 2009: analyseCoronet SEDs using fitting Coronet SEDs using fitting tool of Robitaille et al 2006tool of Robitaille et al 2006

These turned out to be bona fide transition discs (inner holes >> sublimation radius)

But most weren’tBut most weren’t

• Best fits Best fits were were optically optically thick discs thick discs reprocessireprocessing discs ng discs extending extending in to dust in to dust sublimatiosublimation radiusn radius

MoralMoral

• Detectable excess starting at > 6 Detectable excess starting at > 6 microns doesn’t necessarily mean microns doesn’t necessarily mean that later type stars have inner that later type stars have inner holesholes

• [Doesn’t affect other differences [Doesn’t affect other differences with spectral type, e.g. flatter (more with spectral type, e.g. flatter (more settled) discs in later type stars, settled) discs in later type stars, more anaemic discs…(?)]more anaemic discs…(?)]

Planetesimal growth in self-Planetesimal growth in self-gravitating discsgravitating discs

. Observational . Observational evidence: grain evidence: grain growth to > cm growth to > cm scales in young scales in young massive disc HL massive disc HL TauTau

Greaves et al 2008

(with Peter Cossins, Giuseppe Lodato, Joe Walmswell, Markward Britsch)

Dust accumulation in Dust accumulation in spiral features in self-spiral features in self-

gravitating discs gravitating discs demonstrated by Rice et demonstrated by Rice et al 2004, 2006 ……growth al 2004, 2006 ……growth

to > km scales (?)to > km scales (?)Fundamental Fundamental

principle: gas-dust principle: gas-dust drag makes dust drag makes dust

collect in pressure collect in pressure maximamaxima

Three questions:Three questions:

• Why did Rice et al simulations Why did Rice et al simulations work?work?

• (Where) would this work in real (Where) would this work in real discs (realistic cooling)?discs (realistic cooling)?

• Further planetesimal evolution…….Further planetesimal evolution…….

The issue:The issue:

• Lifetime of spiral features is short Lifetime of spiral features is short (dynamical)(dynamical)

• Should dust concentration be Should dust concentration be effective before features dissolve?effective before features dissolve?

How fast can optimally How fast can optimally coupled (metre size) coupled (metre size)

objects concentrate in objects concentrate in spiral features?spiral features?

To get dust to concentrate in To get dust to concentrate in spiral features need spiral features need // 1 1

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

minimum concentration time ~ /v_max ~ /v = 1/ (/H)^2 (/)^-1

( = scale of pressure maximum)

~ 1Lifetime of spiral features ~ 1/

What determines What determines //??

Empirically Empirically 1/1/t_{cool} t_{cool} (Cossins et al 2009)(Cossins et al 2009)

/

Rice et al 2004,2006

1/t_{cool}

How to understand this How to understand this result?result?

Flow self-adjusts so that Flow self-adjusts so that pattern is sonic cf local flow:pattern is sonic cf local flow:

||_p -_p -|/|/ ~ H/R ~ H/R

Doppler shifted Mach number always

*very* close to unity

Varying

cooling

and disc

mass

radius

Given dominant m and k and dispersion relation can calculate Doppler shifted Mach number

(~ Mach number of relative flow perpendicular to shock)

Shocks are very weak:Shocks are very weak:

Use properties of weak Use properties of weak adiabatic shocks:adiabatic shocks:

Mach = 1 +

Entropy jump at shock 1/ t_{cool}

/

Q.E.D.

How fast can optimally How fast can optimally coupled (metre size) coupled (metre size)

particles concentrate in particles concentrate in spiral features?spiral features?

To get dust to concentrate in To get dust to concentrate in spiral features need spiral features need // 1 1

This implies t_cool is not >> This implies t_cool is not >> t_dynt_dyn

Rice et al simulations had Rice et al simulations had fractional amplitude in fractional amplitude in

range 0.1 to 1range 0.1 to 1

….hence why they worked….hence why they worked

What values of What values of // are are expected in real discs?expected in real discs?

Expect dust aggregation only Expect dust aggregation only beyond ~ 30 A.U.. Implications for beyond ~ 30 A.U.. Implications for

location of planetesimal belts?location of planetesimal belts?

From analytic self-gravitating disc

solutions of Clarke 2009

Clarke & Lodato submitted

Log Mdot

(M_/yr)

Log R (A.U.)

Further evolution of Further evolution of planetesimals in self-planetesimals in self-

gravitating discsgravitating discs

• Pilot study: Britsch et al 2007 - 10 Pilot study: Britsch et al 2007 - 10 test particles demonstrated test particles demonstrated stochastic evolution of a and estochastic evolution of a and e

• Now (Walmswell et al 2009 in prep.) Now (Walmswell et al 2009 in prep.) evolution with 50,000 test particle evolution with 50,000 test particle “planetesimals”“planetesimals”

• If restrict planetesimals to > 30 A.U., find initial If restrict planetesimals to > 30 A.U., find initial relaxation populates inner disc ( ~ 10 % leak inwards)relaxation populates inner disc ( ~ 10 % leak inwards)

• Little change over several thousand years after initial Little change over several thousand years after initial relaxation. relaxation.

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

Evolution on these Evolution on these timescales driven by timescales driven by

attainment of equilibrium attainment of equilibrium eccentricity distributioneccentricity distribution

• Distribution is rapidly pumped up by interaction with Distribution is rapidly pumped up by interaction with the disc.the disc.

• Tends to a steady state, with high mean eccentricity Tends to a steady state, with high mean eccentricity of 0.18. of 0.18.

Note: collisions are

destructive as vrel >>

100 m/s (Leinhardt et al

2007)

CONCLUDECONCLUDE

• If form planetesimals through dust If form planetesimals through dust aggregation in spiral arms, this occurs aggregation in spiral arms, this occurs at > 30 A.U. (scales as M_*^{1/3})at > 30 A.U. (scales as M_*^{1/3})

• Subsequent planetesimal evolution is Subsequent planetesimal evolution is dominated by eccentricity growth - dominated by eccentricity growth - would only fill in inner hole to limited would only fill in inner hole to limited extent - observational signatures?extent - observational signatures?

Debris discs?

CONCLUDE :CONCLUDE :

• Large e of planetesimals implies Large e of planetesimals implies collisions are destructive - re-collisions are destructive - re-supply small grains?supply small grains?

• Means by which to retain solids in Means by which to retain solids in disc during self-gravitating phase? disc during self-gravitating phase?