1 Indiana 3D Hydro Group The Effects of Envelope Irradiation on Gravitational Instabilities in Embedded Protoplanetary Disks Kai Cai Astronomy Department

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Indiana 3D Hydro GroupIndiana 3D Hydro GroupIndiana 3D Hydro GroupIndiana 3D Hydro Group

The Effects of Envelope Irradiation The Effects of Envelope Irradiation onon Gravitational Instabilities Gravitational Instabilities in in EmbeddedEmbedded Protoplanetary Disks Protoplanetary Disks

Kai CaiKai CaiAstronomy Department Astronomy Department

Indiana UniversityIndiana UniversityMay 18May 18, 2006, 2006

(Now at:(Now at: McMaster University)McMaster University)

Richard H. Durisen

Annie C. Mejía

(Univ. of Washington)

Megan K. Pickett

(Purdue Univ. Calumet)

Aaron C. Boley

Scott Michael

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Indiana University - Purdue University Calumet Indiana University - Purdue University Calumet

3D Hydro Group3D Hydro Group



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Gravitational Instabilities in Embedded Disks

Gravitational Instabilities (GIs) in DisksToomre’s stability parameter

for Q = cs/G < 1 ring instability

for Q < 1.5 - 1.7 spiral instability

Several class 0/I disks have low Q’se.g. HL Tau, L1551 IRS5

Why? Disks are massive @ earlier timesDisks are smaller @ earlier times

This Study: Effects of Envelope Irradiation

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3D Hydro Code

Numerical Characteristics:2nd order in space and timeEulerianFixed cylindrical grid (r,,z)

(256,128,32) to (512,512,64)

~ millions of cells !

Runs in parallel on SMP machines

r = 512

z = 64 = 128

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Radiative Cooling:Mejía (2004) & Cai (2006)

– Radiative cooling in the atmosphere (R<2/3)– Flux-limited diffusion in the disk interior (R2/3)– Envelope irradiation: blackbody flux with Tenv

– D’Alessio et al. (2001) mean opacities (dust grains): amax can vary (n(a) ~ a-3.5, amin = 0.005m)

z (A

U)

Atmosphere ( < 2/3)

Interior ( ≥ 2/3)

0 8 16 24 32 40

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0

r (AU)

Envelope

Irradiation

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Initial Axisymmetric Model

Initial modelInitial modelfor for

radiative cooling radiative cooling simulationssimulations

Initial modelInitial modelfor for

radiative cooling radiative cooling simulationssimulations

R = 40 AU

Md = 0.07 M

M = 0.5 M

(r) r-1/2

Qmin=1.5

R = 40 AU

Md = 0.07 M

M = 0.5 M

(r) r-1/2

Qmin=1.5

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The Disk Evolution: four phases

Irr 15K

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The Effects of Envelope Irradiation

Irr 15K

Irr 25KNo Irr.

14 ORPs 3500 yr

Irr 50K

Simulations compared during the asymptotic phase

A = 1.51Global tcool = 2.7 ORPs

A = 1.01 Global tcool = 5 ORPs

A = 1.16Global tcool = 3.2 ORPs

A 0.40Global tcool ~ 9 ORPs

Cai et al. (2007, in prep.)

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Total Nonaxisymmetry

A sum of the amplitudes of all m’s, then averaged temporally A(13 - 14ORPs)

No-Irr: 1.51

Irr 15K: 1.16

Irr 25K: 1.01

Irr 50K: 0.40 - continues to damp

rdrdz

rdrdzA mm

0

Boss (2002) reported a similareffect when he raised outer disk

T.

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Envelope Irradiation: Q(r)

At 14.9 ORPs (= 3725 yrs)

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Total Energies …

∇·F

∫(∇·F)dVdt

∫dVdt

cooling

heating

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The Luminosity of the Envelope Irradiation

Lenv = Tenv42Rd

2 = total energy input rate of the envelope irradiation on the disk

Stellar luminosity L = T44R

2

(T= 4000 K, R= 2 R)

In all cases, net disk luminosity Ldisk ~ 5×1030 erg/s

1.3×1033 1/350K

7.2×1031 2.2×10-2 25K

8.6×1030 2.8×10-3 15K

Lenv(erg/s)Lenv / L Tenv

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Vertical Structure

Irradiation tends to make the disk isothermal vertically

No-I

rrIr

r @

25K

T

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Mass Transport, Modes & Torques

Gravitational torques (A. Boley)-1.5E-06

-1.0E-06

-5.0E-07

0.0E+00

5.0E-07

1.0E-06

1.5E-06

0 10 20 30 40

r (AU)

Mdot (M

o/y

r)

Irr 50K

Irr 25K

Irr 15K

No-Irr

Average mass transport over the last 3 ORPs

<Am> power distribution (13-14 ORPs)

0

0.05

0.1

0.15

0.2

0.25

0.3

1 2 3 4 5 6 7 8 9 10 11 12 m

Am

Irr25KIrr15KNo-IrrIrr 50K

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L1551 IRS 5 system

Osorio et al. (2003)

Lim & Takakuwa (2005)

A triple?

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L1551 IRS 5 : model fit

Osorio et al. (2003)

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A new initial model

M = 0.3 M, Md = 0.2 M, R = 15 AU, (r) r-1, Qmin<1

- close to L1551 IRS 5 northern disk

Setup: Tenv = 120K, amax=200 m

Lenv ~ L⋆ of T Tau star (T= 4000K, R= 2R๏)

2 AU

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Simulating a L1551 IRS 5 Disk

• Disk expands Rfinal ~ 30 AU: unrealistic• Very high midplane & long radiative cooling time

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Q(r) and the Correction Factor

Corrected Qmin = (1 + kmuh)Q0 ~ 1.4-1.5

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Analytic Analyses

Rafikov (2005) min inf[f()]1/5, Tmid Tmin Tinf[f()]2/5, etc.

• 0.07 M disk (at 20 AU): inf 201 g cm-2, Tinf 39 K, but [f()]1/5 might be large (~1.5)

• For L1551 IRS 5 disk (at 10 AU): inf 1220 g cm-2 and Tinf 65.6 K, but [f()]1/5 ~ 5.3

Despite simplifications, Rafikov (2005)’s analytic arguments may be valid out to ~ 20 AU for our disk.

Matzner & Levin (2005): only discussed SLING as global GIs

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Conclusions

Envelope irradiation tends to suppress GIs – it cannot be ignored !No dense clumps produced, so direct giant formation by GIs unlikely. GIs fragmentation! Mild irradiation preferentially suppresses high-order modes

Future

Stellar irradiation – Tirr (r) ~ r-1/2

Consider the gravitational effect of a binary companion – e.g., Mayer et al. (2005), Boss (2006) -> Roche potentialMass infall onto the disk - e.g., Mayer et al. (2004), Banerjee et al. (2004), Vorobyov & Basu (2005)……

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Thank you!

Documents

1 Indiana 3D Hydro Group The Effects of Envelope Irradiation on Gravitational Instabilities in Embedded Protoplanetary Disks Kai Cai Astronomy Department