1次元モデルによる初代星周りの円盤進化
Evolution of the Disk around Pop III Starby One-Dimensional Model木村 和貴 (京都大学)
共同研究者
細川 隆史 (京都大学)
杉村 和幸 (メリーランド大学)

1. Introduction

Fragmentation of Circumstellar Disk
- observed in many simulations of pop III star formation- affect accretion rate and evolution of central star
- formation channel of binary or multiple stars→ Gravitational Wave ?
- change IMF from the cases of single star
Grief et al. (2012)

Chon, Hosokawa & Yoshida (2018)

Previous Study and Motivation
Matsukoba et al (2019) : Primordial Case- one-dimensional and steady disk model- discuss the condition for disk fragmentation- not compared with simulation
Takahashi et al (2013) : Solar Metallicity Case- one-dimensional and non-steady disk model- One-dimensional model is in good agreement with 3D simulation

We incorporated the physical processes in pop III
star formation into Takahashi’s model( and want to compare with 3D simulation )The advantages of one-dimensional model are- long time evolution with high resolution( but in limited situation)- parameter search2. Model

Model・model accretion from envelope to the disk analyticallyΩ0collapse

accretionfrom envelope

𝑇 = 250 K
𝑛𝑐 = 103 𝑓 /cm3
Critical Bonnor-Ebert Sphere

Central star・One-dimensional equation of the Disk
・Mass Conservation
・Angular Momentum Conservation (EOM)・Energy Conservation𝜕𝜕
2𝜋𝑟Σ +2𝜋𝑟Σ𝑣𝑟𝜕𝑡𝜕𝑟= 𝑀𝑖𝑛𝑓𝑎𝑙𝑙

Thermal Evolution : visocosity , radiation , advection , chemistry
Chemical Evolution (Saha) : H , H2 , H + , H − , eModel・Viscosity : 𝜶 𝐦𝐨𝐝𝐞𝐥
Gravitational Torque𝜈 = 𝛼𝑐𝑠 𝐻

𝛼=exp(−𝑄4 )If 𝛼 > 0.1 somewhere in the disk,
clumpy structures transfer
angular momentum globally

0.01 + exp −𝑄4 (if 𝛼𝑚𝑎𝑥 > 0.1)

・Parameter𝐸rot
Ω20 𝑅03𝛽0 === 10−3 ~10−2 , 𝑓 = 1.4𝐸grav 3𝐺𝑀𝐵𝐸

accretionfrom envelope

・Initial Condition of the Disk
Central Star 𝑀∗ = 10−2 M⊙
No Disk𝑀∗

3. Result

𝐎𝐮𝐭𝐞𝐫 𝐫𝐞𝐠𝐢𝐨𝐧 𝐢𝐬 𝐦𝐚𝐠𝐢𝐧𝐚𝐥𝐥𝐲 𝐬𝐭𝐚𝐛𝐥𝐞・𝛽0 = 10−2 , 𝑓 = 1.4

snapshot at 𝑀∗ = 0.1 , 1 , 10 𝑀⊙
26𝑀∗ = 0.1𝑀⊙
𝑀∗ = 1𝑀⊙
𝑀∗ = 10𝑀⊙

5𝑄

log 𝑇[K] 413012

log 𝑟 [AU]3012

log 𝑟 [AU]outer region (optically thin) : viscous heating = H2 coolinginner region (optically thick) : viscous heating dominant
Temperature gradually increase3

𝐂𝐢𝐫𝐜𝐮𝐦𝐬𝐭𝐞𝐥𝐥𝐚𝐫 𝐝𝐢𝐬𝐤 𝐢𝐬 𝐦𝐚𝐬𝐬𝐢𝐯𝐞・𝛽0 = 10−2 , 𝑓 = 1.4 ,−25−3log 𝑀

𝑀𝑑𝑖𝑠𝑘
3𝑀∗

𝑀⊙ /year−5−61
1.90

−4

1.92

1.94

1.90

𝑡 [Myr]to the Disk
to the Star

1.92

𝑡 [Myr]Central star

1.94

The radius where Q takes least value
・𝛽 = 10−3 , 10−2.5 , 10−2 𝑓 = 1.4 snapshot at 𝑀∗ = 10𝑀⊙
26log 𝑇𝑄[K]𝛽0 = 10−3𝛽0 = 10−2.5
𝛽0 = 10−210125433log 𝑟 [AU]012log 𝑟 [AU]- 𝛽0 ≤ 10−2.5

𝑛𝑐 ~1016 where disk becomes optically thick- 𝛽0 = 10−3more outer region

3Comparison with Different Viscosity Model・heating and cooling processes , snapshot at 𝑀∗ = 10𝑀⊙
107

107

105

105viscosity
H2 lineH2 CIEchemicaladvection
radiation

erg/g ∙ s103

103

10101023log 𝑟 [AU]

only gravitational torque𝛼=exp(−𝑄4 )0.01 + exp −𝑄4 (if 𝛼𝑚𝑎𝑥 > 0.1)0123log 𝑟 [AU]MRI + gravitational torque𝛼 = 0.01 + exp(−𝑄4 )Summary・We investigated time evolution of the disk
around pop III star by one-dimensional model
Result・In outer region, viscous heating = H2 cooling・In inner region, viscous heating is dominant・The radius where Q takes least value depends on 𝛽0
・If MRI viscosity is added ,viscous heating = radiative cooling in inner region

Future Work・Calculation in other parameter ranges
・Comparison with 3D simulation