Post on 23-Aug-2020
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