周惑星円盤のガス降着メカニズムについて•藤井悠里1•

奥住聡2, 谷川貴行3, 犬塚修一郎1, 高橋実道14•

1名古屋大学, 2東京工業大学, 3北海道大学, 4京都大学

周惑星円盤周惑星円盤

ガス降着率？
面密度？
温度構造？

周惑星円盤の形成
Protoplanetary Disk

周惑星円盤の形成
Protoplanetary Disk

InfallGas giantCircumplanetary Disk

周惑星円盤の形成
Protoplanetary Disk
原始惑星系円盤からのガス流入のシミュレーション
InfallGas giant• Ayliffe & Bate (2009)• Machida et al. (2010)• Tanigawa et al. (2012)

Circumplanetary Disk

• Uribe et al. (2013)

Tanigawa et al. (2012), Move: by T. Takeda (4D2U, NAOJ)

Tanigawa et al. (2012), Move: by T. Takeda (4D2U, NAOJ)

ガスの流入率Tanigawa, Ohtsuki, & Machida (2012)

Most Promising Gas
Accretion Mechanism:
Magnetorotational
Instability (MRI)MRIFrozen in

Magnetic field(Vertical component)

MRI
Frozen in

Magnetic field(Vertical component)

Rotation

MRI
Frozen inr

Magnetic field(Vertical component)

Rotation

MRI
Frozen inr

Magnetic field(Vertical component)

Rotation

MRI
Frozen inr

Magnetic field

Instability(Vertical component)

Rotation

MRI

Rotation

TurbulenceFlock et al. (2011)

Can CPDs sustain MRI?

Flock et al. (2011)

Ionization & MRIlProtoplanetary disks
X-rays

CRs
Radionuclide

Weakly ionized

MRIAccretion

Ionization & MRIlProtoplanetary disks
X-rays

CRs
Radionuclide

Weakly ionizedProtoplanetary disk

MRI

乱流領域
MRI
磁気乱流不活性領域
MRI-inactive-active

StarAccretion

Ionization & MRIlProtoplanetary disks
CRs

X-raysRadionuclide
Weakly ionizedProtoplanetary disk

MRI

乱流領域
MRI
磁気乱流不活性領域
MRI-inactive-active

Star

Accretion

Circumplanetary disk?

磁気乱流不活性領域

PlanetAim
To understand accretion rate of CPDs...

Investigate accretion rate due to MRIAccretion mechanism ＝ MRI
Estimate sizes of MRI-active regions(Fujii, Okuzumi & Inutsuka, 2011)

Accretion stress, α, can be derived(Okuzumi & Hirose, 2011)

MethodSurface Density• Diffusion equation of disk with infall

Mass infall, f, from PPD

CPD
PlanetViscous diffusion

Surface Density• Diffusion equation of disk with infall

Mass infall, f, from PPD

CPD
PlanetViscous diffusion

Surface Density• Diffusion equation of disk with infall

Mass infall, f, from PPD
CPD
PlanetViscous diffusion

Surface Density

H: scale height of disk
cs: sound speed• Diffusion equation of disk with infall

ν=αcsH

Mass infall, f, from PPD
CPDPlanet

Viscous diffusion

Settings✦ Mass infall rate onto CPD(Tanigawa et al. 2012)

Σ0: surface density of PPD, r: radius of CPD, RJ: Jupiter radius

for r < 20RJ (=0.01AU), f(r>20RJ)=0✦ Ionization model (Fujii et al. 2011)• ionization source

CRs, X-rays, Radionuclide• dust-to-gas mass ratio: fdg=10-2

Condition of MRI Growth
MRI-active region：
Rem > 1(Rem: Magnetic Reynolds number)andH >λmax (=2πvAz/Ω)
H: scale height of disk
λmax:wave length of most unstable modevAz: Alfvén velocity (z component)
Ω: Keplerian frequency

Ionization degree & MRI
MRI-active : Rem > 1
vAz: Alfvén velocity (z component)
η: Magnetic diffusion coefficient
Ω: Keplerian frequency

xe: Ionization degree
T: Temperature(Blaes & Balbus 1994)

Calculate! (Fujii et al. 2011)

Chemical Reaction Network• Neutral gas is ionizedby ionization source

Neutral gas
Cosmic rays

• Ions and electrons arecaptured by grains
Electrons• Balance of thesereactions determines
the ionization degreeIonization
Rec.
IonsCapture

Co mplicate dDifficult to calculate

Dust grains

Basic Equations|Z| is large

So many equations !

e : electron
M+ : metal iond : dust grains
Z : charge of grains: Rate coefficients: Ionization rate

Solve quickly and accurately

Fujii + (2011)

Results

Surface density (f: 100%)
Σ [g/cm2]106

α=0.05

 [g/cm2]

105

104

Galilean satellites
103
51015

20
r [RJ]

25

Radius [RJ]

30

3540

Infall rate f: 100%
Rem> 1 & H >λmax

MRI-active region

4↑Rem> 1z/H32

H >max 

10dust free
10H: disk scale height

=10420] J]
r [RJ[RRadius

3040(Pressure)Infall rate f: 100%
Rem> 1 & H >λmax

MRI-active region

4↑Rem> 1z/H

3
2

No MRI-active layerH >max 

10dust free
10H: disk scale height

=10420] J]
r [RJ[RRadius

3040(Pressure)5f: 100%, β=10Rem> 1 & H >λmax

MRI-active region

4↑Rem> 1z/H

3

↓H >λmax

2
10dust free
102030Radiusr [RJ][RJ]=10540

5f: 100%, β=10Rem> 1 & H >λmax

MRI-active region

4z/H

3

No MRI-activelayer↑Rem> 1

↓H >λmax

2
10

dust free
102030Radiusr [RJ][RJ]=10540f: ×10-5, β=1044z/H

3↑R2em >

1

a=10−5cm

0size ofdust grains1
H >max

a=10−3cm
dust free10

=104203040

r [RJ[R] J] Active region
Radiusf: ×10-5, β=1054z/H

3↑Rem >

1↓H >λmax210

a=10−5cm
a=10−3cm
dust free10

=105203040

Radiusr [RJ] [RJ] Active regionSurface density (f: ×10-5)1022 2] ]Σ [g/cm[g/cm101

100

10-110-25101520r [RJ]25

Radius [RJ]

303540Surface density (f: ×10-5)
Satellite formation timescale (Lissauer & Stewrt 1993; Ward 1996)

107yr
102

2 2] ]
Σ [g/cm[g/cm101

100

10-110-2

5101520r [RJ]25

Radius [RJ]

303540Surface density (f: ×10-5)
Satellite formation timescale (Lissauer & Stewrt 1993; Ward 1996)

107yr
102

2 2] ]
Σ [g/cm[g/cm

101

100

10-110-25101520r [RJ]25

Radius [RJ]303540

Satellite formation
not realistic forreduced infall rates

Why so little MRI?
cs: sound speed
η: magnetic diffusivity
β: plasma beta
Ω: Keplerian frequency

Protoplanetary disk@5AU

Circumplanetary disk@15RJ

Why so little MRI?
cs: sound speed
η: magnetic diffusivity
β: plasma beta
Ω: Keplerian frequency

Protoplanetary disk@5AUxe≅4x10-10

Circumplanetary disk@15RJ

xe≅3x10-10

Why so little MRI?
cs: sound speed
η: magnetic diffusivity
β: plasma beta
Ω: Keplerian frequency

Protoplanetary disk@5AU

Circumplanetary disk@15RJ

xe≅4x10-10xe≅3x10-10Ω≅2x10-8 s-1

Ω≅1x10-5 s-1

Why so little MRI?
cs: sound speed
η: magnetic diffusivity
β: plasma beta
Ω: Keplerian frequency

Protoplanetary disk@5AU

Circumplanetary disk@15RJ

xe≅4x10-10xe≅3x10-10Ω≅2x10-8 s-1

Ω≅1x10-5 s-1

3 orders of magnitude!

Infall rate

Surface density

Accretion rate, αInfall rate

Surface density

Gravitational Instability
Toomre parameter

Pressure
Rotation
Gravity

1<Q<2spiral arms
effective viscosity
Takahashi et al. (2013)

cs : Sound speed
G : Gravitational constant
Σ: Surface density

重力不安定を考慮して再計算
Mass infall, f, from PPD

CPD

Viscous diffusionmass infall rate

Σ0: surface density of PPD, RJ: Jupiter radius(Tanigawa et al. 2012)

calculatesurface density

重力不安定を考慮して再計算
Mass infall, f, from PPD

CPD

Viscous diffusionmass infall rate

Σ0: surface density of PPD, RJ: Jupiter radius(Tanigawa et al. 2012)

ν=αcsHcalculatesurface density面密度分布Surface density evolution of CPD
with Gravitational Instability (GI)1010

6.0e11s
4.5e11s
2.5e11s
9.5e10s

equilibrium

Y [g/cm2]

108

just pile up
GI turned on106

104

110r [RJ]Viscous Heating
Gravitational energy

HeatingΔr

Mp

σ: Stefan-Boltzmann constantIf mid-plane temperature
exceed 1000K, thermalionization kicked on MRI

mid-plane temperature

τ: optical depth
κ: opasityr

κ= 5cm2/g

160 < T < 1350

κ= 10-4cm2/g

T > 1350K(Pollack et al. 1994)

熱電離も考慮Surface density evolution with thermal ionization104

mid-plane temperatureeasily exceed 1000K

Y [g/cm2]

N.B. opacity at 1000K (κ=5cm2/g) is used
103
50000

2110r [RJ]

thermal ionization: αMRI=0.01

10000
T [K]

10steady state:1000
110r [RJ]まとめ• 角運動量輸送の有力候補であるMRIが周惑星円盤で起こるかどうか調べた• 非熱的電離ではMRIは期待できない• 他に降着メカニズムがないと重力不安定によるスパイラル波で角運動が輸送される• 粘性加熱で熱電離によるMRIが駆動される• 加熱源は必ずしも重力不安定に限られない
e.g. 恒星からのトルク Rivier et al. (2013)