EC Daniel Perez-Becker

(Berkeley)

Accretionin Protoplanetary

Disks(conventional

and transitional)

pre-shock flow

heated interior

Calvet & Gullbring 98Muzerolle et al. 05Hartmann et al. 06

Herczeg & Hillenbrand 08

Pre-main-sequence stars accrete

Blue excess powered by accretion

Calvet et al. 05

Transitional Disks

τ10µm ∼ 20 − 200

τ10µm

= 0.05

TW Hyd

Calvet et al. 02

Brown et al. 08

LkHa 330

Holes are not empty

• Mild near-IR excesses in some sourcesτ10µm ∼ 0.002 − 0.05

• Many accreteṀ ∼ 0.1 × median T Tauri rate

• Inner molecular gas disksΣ(H2) > 0.1 g cm

−2 at ∼ 0.2AU

Najita et al. 07 Salyk et al. 07

Theories:

• Grain growth

• Clearing by companion

Puzzle:

Not mutually exclusive

1000 × smaller τ but comparable Ṁ

Clearing by companion (Transitional = Circumbinary)

Ireland & Kraus 08 (Keck AO)Artymowicz & Lubow 94

CoKu Tau/4Binary separationabinary ≈ 8 AU

≈ Hole radiusarim ≈ 10 AU

Ṁ∗ < 10−10M#/yr

D’Alessio et al. 05Najita et al. 07

Blake, Salyk, personal comm.

τ10µm < 0.002

No CO gas out to 2 AU

Mass can still accrete onto star(viscosity / pressure / eccentricity /

mass ratio)

Fast flow (up to radial free-fall)implies low surface density

Resolves the puzzle ofsimilar M but

1000x lower optical depth

.

Hanawa et al. 06

Clearing by companion (Transitional = Circumbinary)

Clearing by multiple planets

Simulation of 4-planet system in viscous disk

Right sign, too small magnitude‒ unless dust is also depleted

Zhu et al. 11 2D FARGO

Planets inside the hole do not explain disk accretion

Outer disk must stillbe viscous

Magneto-rotational instability (MRI)= linear instability

which drives turbulencein weakly magnetized,

outwardly shearing flows

1. Magnetic flux freezing (defeat Ohmic dissipation) (Fleming, Stone, & Hawley 00)

2. Good neutral-ion coupling (defeat ambipolar diffusion) (Blaes & Balbus 94; Hawley & Stone 98; Bai & Stone 11)

ReM ≡csh

η∝

nen

Requirements

> Re∗

M ≈ 102− 10

4

Am ≡ni〈σv〉in

Ω> Am

∗ ≈ 100

Disk accretion

Hawley 2000

1-100

Sideways

N, h

N, �

X− rays

h ≈ N/nH2Σ = Nµ

cosmic rays

1

Surface Layer Accretion by the MRI

Sources of ionization

1. Cosmic rays2. Stellar X-rays3. Stellar UV

Gammie 96

Glassgold et al. 97Sano et al. 00

Ilgner & Nelson 06 Bai & Goodman 09

Turner et al. 10Perez-Becker & EC 11aPerez-Becker & EC 11b

Galactic cosmic raysblocked by stellar wind

sunspot number

cosmic ray flux

interstellar

solar min

Svensmark 98Reedy 87

Pre-main sequence stars are X-ray luminous

Preibisch et al. 05Chandra COUP Orion survey

H+2 + H2 → H

+3 + H

H+3 + CO → HCO

++ H2

e−

dissociativerecombination

H + CO

chargetransfer

Mg+

Mg

βt ∼ 10−9

cm3s−1

e−

Mg

Mg

radiativerecombination

grain−

freemetal

Oppenheimer & Dalgarno 74Umebayashi & Nakano 83Glassgold et al. 86

βdiss ∼ 3 × 10−7

cm3s−1

βrec ∼ 4 × 10−12

cm3s−1

PAH-

neutralization onto charged particles

Mg

Polycyclic Aromatic Hydrocarbons (PAHs)

Allamandola et al. 99Geers et al. 06

PAH abundance ~0.01-10 ppb H2

(in diffuse ISM~1 ppm H)

10−32

10−26

10−20

10−14

10−8

10−2

αPA

H,e

or

αPA

H,M

+[c

m3s−

1]

10−5

10−4

10−3

10−2

10−1

1

Norm

alize

dch

arg

edis

trib

ution

−3 −2 −1 0 1 2 3Z

PAHs

Charg

edis

trib

ution

αPAH,eαPAH,M+

10−3

10−2

10−1

100

αgra

in,e

or

αgra

in,M

+[c

m3s−

1]

10−5

10−4

10−3

10−2

10−1

1

Norm

alize

dch

arg

edis

trib

ution

−40 −30 −20 −10 0Z

grains

Chargedistribution

α grain

,e

αgrain,M+

10−15

10−13

10−11

10−9

10−7

10−5

xe

or

(xM

++

xH

CO

+)

10−13 10−11 10−9 10−7 10−5

x�PAH

Possible PAHabundances

limxPA

H�x �PA

H xHCO +

limxPA

H�x �PA

H xe

limxPAH→0

xe, xHCO+

xM = 10−8

�PAH

xPAH

10−110−7 10−5 10−3 101

xM+ + xHCO+

xe

X-rays ⇒ HCO+, Mg+ egrain (1 μm)PAH (6 Å)

---

Charge Balance

0.01

0.1

1

10

100

Am

=(x

M++

xH

CO

+)β

inn

H2/Ω

0.01 0.1 1 10

Σ [g cm−2]

a = 3 AUxM = 10−8

Am∗

109 1010 1011 1012 1013nH2 [cm

−3]

1

102

104

106

108

1010

Re

=c s

h/D

Re∗

a = 3 AUxM = 10−8

0.01 0.1 1 10

Σ [g cm−2]

a = 30 AUxM = 10−8

Am∗

No PAH

Low PAH

High

PAH

Possible PAH

abundances

108 109 1010 1011nH2 [cm

−3]

Re∗

a = 30 AUxM = 10−8

Perez-Becker & EC 11asee also Mohanty, Ercolano, and Turner 11, in prep.

Ohm

ic d

issi

patio

nA

mbi

pola

r di

ffusi

on

region allowedby PAHs

Re

Am

0.01

0.1

1

10

100

Am

=(x

M++

xH

CO

+)β

inn

H2/Ω

0.01 0.1 1 10

Σ [g cm−2]

a = 3 AUxM = 10−8

Am∗

109 1010 1011 1012 1013nH2 [cm

−3]

1

102

104

106

108

1010R

e=

c sh

/D

Re∗

a = 3 AUxM = 10−8

0.01 0.1 1 10

Σ [g cm−2]

a = 30 AUxM = 10−8

Am∗

No PAH

Low PAH

High

PAH

Possible PAH

abundances

108 109 1010 1011nH2 [cm

−3]

Re∗

a = 30 AUxM = 10−8

(0.01-10 ppb H2)

X-ray ionization only

Field may be frozen to plasma ✔

But ions decoupled from neutrals ✗

= 0.1

= 0.01

= 10 3

= 10 4

MRI Prohibited

MRI Permitted

Am

<>

10 2 10 1 100 101 102 103 104100

101

102

103

104

10−11

10−10

10−9

10−8

10−7

10−6

Ṁ[M

⊙/yr]

1 10 100

a [AU]

Conventional Disk

Observed Rates

X-ray

α ≈1/(2β) and βmin(Am)

⇒ αmax (Am)

Bai & Stone 11

Kunz & Balbus 94 Hawley et al. 95

Desch 04Pessah 10

Bai & Stone 11

MRI with ambipolar diffusion

αmax (Am) and Am(Σ)

⇒ M.

X-rays + PAHs =weak accretion

Perez-Becker & EC 11ab

Far-Ultraviolet (FUV) Ionization

912 Å 1109 Å 1198 ÅH H2, C S

HST + FUSE(Bergin et al. 03; Herczeg et al. 02)

LFUV ~ 1030-1032

erg/s

FUV Ionization

912 Å 1109 Å 1198 ÅH H2, C S

Strömgren slab

}LFUVhν 4πa2 · ha ∼ nineαrec · hphotoionizations recombinations(cosmic abundance)Perez-Becker & EC 11ab

∼ 0.1

(

LFUV1030 erg/s

)1/2 (10−5

f

)

g/cm2

⇒ ΣMRI ∼ nH2µh

nH2

ni = ne = fnH2

1

10

102

103

104

Am

=(x

CII

+x

SII)β

inn

tot/

Ω

10−5 10−3 10−1

Σ [g cm−2]

Am∗

a = 3 AU

107 108 109 1010 1011ntot [cm−3]

1

102

104

106

108

1010

1012R

e=

c sh

/D

Re∗

Σ∗ Σ∗

LX = 1031 erg s−1

Re

Am

FUV ionization only

Field is frozen to plasma ✔Good ion-neutral coupling ✔

robust against PAHs(PAHs included at

maximum abundance)

sensitive to dust-to-gas ratio(vertical settling of dust)

Perez-Becker & EC 11b

Nτ=1 =1024 cm-2

[S/H] = -1

Nτ=1 =1022 cm-2

[S/H] = 0

102

103

104

105

χ

1 10 100

a [AU]

Nτ=1

VSG= 10

24 cm−2 � = 1/30

FUV

Wardle & Salmeron 11

Hall effect not important

FUV-ionizedsurface layerscan reproduceaccretion ratesat large radius

but not small radius

Perez-Becker & EC 11b

Ṁ ∼ 2 × 3πΣ∗ν

∼ 6πΣ∗αkT

µΩ

10−11

10−10

10−9

10−8

10−7

10−6Ṁ

[M⊙/yr]

1 10 100

a [AU]

ConventionalDisk

ObservedRates

FUV

max

βplas

ma<

1

X-ray

0.1

1

10

t rec

/t d

yn

1 10 100

a [AU]

FUV

Turbulent mixingof plasma to

greater depthscan extend

MRI-active layer

Ion recombinationtime vs.

dynamical time

Ilgner & Nelson 06b

10−12

10−11

10−10

10−9

10−8

10−7

10−6

Ṁtr

ans[M

⊙/yr]

1 10 100

arim [AU]

TransitionalDisk

FUV

X-ray

maxβ

plasm

a<

1

Murray-Clay & EC 07Kim et al. 09

Perez-Becker & EC 11abZhu et al. 11

FUV-driven MRI in Transitional Disks

Rim accretion ratereproduces

observations

Transport problemat small radii

could be solved bycompanions

Extra Slides

Is the required field super-equipartition?

Ṁ ∼ 〈BrBφ〉h/Ω

⇒ minB > 1G

(

Ṁ

10−8M"/yr

)1/2( r

AU

)−5/4

Possible for r > 1 AU

e.g., Bai & Goodman 09

β ≡PgasPmag

=8πnkT

B2< 1

(

Σ

0.1 g/ cm2

) (

10−8M"/yr

Ṁ

)

( r

1 AU

)

On the other hand the field cannot be too strong: β > 1

On the one hand, the field must be strong enough:

Inside-Out Accretion of Transitional Disks

• Dust thickness h/r ≤ R/r ̃ 10-2

• Inclination Ι ̃ 10-1• Warp Δ Ι / Ι < 10-1 (self-gravity) Δ Ι / Ι ̃ ‒10-1 (gas pressure)

Measuring dust layer thicknesses

(e.g., occulting circumbinary diskof KH 15D)

EC & Murray-Clay 07

Ṁ ∼12παN∗a2

rim(kT ∗)3/2

GM∗µ1/2

Rim controlsaccretion rate

X-ray driven MRI

@ 1 AU

• 10-100 x lower density than MMSN• Satisfies CO lower limits• Type II migration

slower than usual

For constant α,

But cannot explainorigin of hole

Σgas ∼ 10 − 100 g cm−2

Kim et al. 09Spitzer Cha I

Planet Clearing

Lubow & D’Angelo 06 Lubow et al. 99

Inner disk fills in

Ṁinner ≈ 0.1Ṁouter • But planetary migration reduces clearing efficiency• Short-lived solution (tdiffusion ~ r2 / ν ~ 104 orbits)• Perhaps multiple planets can help

Initialt = 700 orbits

neglecting migration

Initial profile set toanalytic steady state; note robustness of inner disk

But deeper correlations may exist ...

arim ∝ M2

∗

Ṁ∗ ∝ M2

∗

Ṁ∗ ∝ M2

∗

Same

holds fornon-transitional

disks

How to keep the inner hole

clear of dust?

Leaked dust might concentrate at , restoring :

Gapped(“pre-transitional”) disk

possible

a ! arim

τ10µm > 1

.

Kim et al. 09

1023 cm-2

tdiff ∼ a2rim / ν

ν = α csh

MRI simulations give 10-4-10-1

Mrim = 2πarim × 2h × N∗ µ

photo-ionization heating CO ro-vibrational cooling

230 K

*

Glassgold, Najita, & Igea 04EC & Murray-Clay 07

Ṁ ∼Mrimtdiff

∼

12παN∗a2rim(k T∗ )3/2

GM∗µ1/2

LXσXe−N

∗σX fheatn

4πa2rim

∼ ΛCO(T∗)

*

X-rays

}N*

T*a rim

X-rays

dustygasrim

MRI-active

Inside-Out MRI

tblow ∼1

Ω

(

1

Ωtstop

)

N*τrim ∼ 0.1

• Leaked dust might concentrate at , restoring : Gapped (“pre-transitional”) disk possible

a ! arim

τ10µm > 1

EC & Murray-Clay 07

-▽Ppoints in

Aerodynamic filter Radiation pressure

Gas is super-Keplerian

Dust is Keplerian ∴ dragged out

Keeping inner hole clear of dust

• Filtering is inefficient

Rice et al. 06

“Pre-Transitional” Gapped Disks

Espaillat et al. 08

Espaillat et al. 07

1600 K blackbody fit to excess

0.12 AU

< 0.15 AU

LkCa 15 46 AU

But deeper correlations may exist ...

˙

arim ∝ M2

∗

Ṁ∗ ∝ M2

∗

Ṁ∗ ∝ M2

∗

Why?

And does similarrelation hold

for debris disks?

Same

holds fornon-transitional

disks

(T̂ > 1)

Sustaining MRI at a

Outer diskphotoevaporationstarves inner disk

t=0

t=6 Myr

t=6.02 Myr

t=6.18 Myr

Alexander 08

x4e+

(

βgrβrec

)

x3e+

(

ζ

nβdiss

βtβrec

)

x2e−

(

ζ

nβdiss

βtβrec

) (

βgrβt

+ xmet,tot

)

xe−βt

βrec

(

ζ

nβdiss

)2

= 0

n = 2N/arim ζ =LXσXe

−NσX ξsecondary

4πEXa2rim

Estimating N*

xmet,tot = 10−6

10−7

10−8

EC & Murray-Clay 07

0

Am*

N*

Theories for transitional disks are not mutually exclusive

Planets + MRI +

smaller Ṁ∗ smaller τ10µmorigin

of viscosityMultiple planetsmight explainfactor of 10

and prolong Type II migration

Grain growth +Radiative /

aerodynamic blowout

smaller τ10µm

Imperfectclearing can

lead to gapped disks(e.g. LkCa 15)

0.01

0.1

1

10

100

Am

=(x

M++

xH

CO

+)β

inn

H2/Ω

0.01 0.1 1 10

Σ [g cm−2]

Am∗

109 1010 1011 1012 1013nH2 [cm

−3]

1

102

104

106

108

1010

Re

=c s

h/D

Re∗

LX = 1031 erg s−1

0.01 0.1 1 10

Σ [g cm−2]

Am∗

No PAH

Low PAHHigh

PAH

PossiblePA

H

abundances

109 1010 1011 1012 1013nH2 [cm

−3]

Re∗

Std. Model (a = 3 AU)

0.01 0.1 1 10

Σ [g cm−2]

Am∗

109 1010 1011 1012 1013nH2 [cm

−3]

Re∗

xM = 10−6

0.01

0.1

1

10

100

Am

=(x

M++

xH

CO

+)β

inn

H2/Ω

0.01 0.1 1 10

Σ [g cm−2]

Am∗

109 1010 1011 1012 1013nH2 [cm

−3]

1

102

104

106

108

1010

Re

=c s

h/D

Re∗

LX = 1031 erg s−1

0.01 0.1 1 10

Σ [g cm−2]

Am∗

No PAH

Low PAH

High

PAH

PossiblePA

H

abundances

109 1010 1011 1012 1013nH2 [cm

−3]

Re∗

Std. Model (a = 3 AU)

0.01 0.1 1 10

Σ [g cm−2]

Am∗

109 1010 1011 1012 1013nH2 [cm

−3]

Re∗

xM = 10−6

0.01

0.1

1

10

100

Am

=(x

M++

xH

CO

+)β

inn

H2/Ω

0.01 0.1 1 10

Σ [g cm−2]

Am∗

109 1010 1011 1012 1013nH2 [cm

−3]

1

102

104

106

108

1010

Re

=c s

h/D

Re∗

LX = 1031 erg s−1

0.01 0.1 1 10

Σ [g cm−2]

Am∗

No PAH

Low PAH

High

PAH

PossiblePA

H

abundances

109 1010 1011 1012 1013nH2 [cm

−3]

Re∗

Std. Model (a = 3 AU)

0.01 0.1 1 10

Σ [g cm−2]

Am∗

109 1010 1011 1012 1013nH2 [cm

−3]

Re∗

xM = 10−6

X-ray ionized MRI-active surface layer

Σactive ~ 1 g cm-2

Am ~ 1 (α ~ 10-3)

Perez-Becker & EC 10

At 3 AU,

0.01

0.1

1

10

100

Am

=(x

M++

xH

CO

+)β

inn

H2/Ω

0.01 0.1 1 10

Σ [g cm−2]

Am∗

108 109 1010 1011nH2 [cm

−3]

1

102

104

106

108

1010

Re

=c s

h/D

Re∗

xM = 0

0.01 0.1 1 10

Σ [g cm−2]

Am∗

No PAH

Low PAH

High

PAH

Possible PAH

abundances

108 109 1010 1011nH2 [cm

−3]

Re∗

Std. Model (a = 30 AU)

0.01 0.1 1 10

Σ [g cm−2]

Am∗

108 109 1010 1011nH2 [cm

−3]

Re∗

ζCR = 1/4 × 10−17 s−1

0.01

0.1

1

10

100

Am

=(x

M++

xH

CO

+)β

inn

H2/Ω

0.01 0.1 1 10

Σ [g cm−2]

Am∗

108 109 1010 1011nH2 [cm

−3]

1

102

104

106

108

1010

Re

=c s

h/D

Re∗

xM = 0

0.01 0.1 1 10

Σ [g cm−2]

Am∗

No PAH

Low PAH

High

PAH

Possible PAH

abundances

108 109 1010 1011nH2 [cm

−3]

Re∗

Std. Model (a = 30 AU)

0.01 0.1 1 10

Σ [g cm−2]

Am∗

108 109 1010 1011nH2 [cm

−3]

Re∗

ζCR = 1/4 × 10−17 s−1

Sideways

N, h

N, �

X− rays

h ≈ N/nH2Σ = Nµ

cosmic rays

1

Σactive ~ 0.1 g cm-2if no cosmic rays

At 30 AU,

Am ~ 1 (α ~ 10-3)

Σactive ~ 10 g cm-2if cosmic rays

X-ray ionized MRI-active surface layer

Far-UV (912-1100 Å) ionized MRI-active surface layer

H2 + hν→ H + HH + H + grain → H2 + grain

C + hν ⇄ C+ + e-

xCO = 10-4

Σactive ~ 0.01 g cm-2

At 3-30 AU,

Am > 102 (α ~ 0.1)

1

10

102

103

104

Am

=(x

C+)β

inn

H/Ω

0.01 0.1 1 10

Σ [g cm−2]

Am∗

109

1010

1011

1012

nH [cm−3]

1

102

104

106

108

1010

1012

Re

=c s

h/D

Re∗

fC = 10−4

a = 3 AULX = 1031 erg s−1

0.01 0.1 1 10

Σ [g cm−2]

Am∗

108

109

1010

1011

nH [cm−3]

Re∗

fC = 10−4

a = 30 AU

0.01 0.1 1 10

Σ [g cm−2]

Am∗

109

1010

1011

1012

nH [cm−3]

Re∗

xM = 10−6fC = 10−4

a = 3 AU

Planet Clearing

Run duration = 100 orbits ≪ Viscous time ~ 10000 orbits

Initial Σinner / Σouter = 0.01

∴ Hole in simulation reflects assumed initial conditions

Quillen et al. 2004

tdiff ∼ a2rim / ν

ν = α csh

0.004 (assumed)

tdiff

0.1MJ

10AU

arim =

3 AUX-ray3 AU

Far-UV30 AUX-ray+CR

30 AUFar-UV

αΣactive(g/cm2)T

(K)Ṁ

(M☉/yr)

10-118010-31

3010-30.1-10 10-11-10-9

0.1

0.1

0.01 300 4 x 10-11

0.01 300 10-9

200 AU

Protoplanetary Disks

disk mass ~ 0.001-0.1 stellar mass