Structure of Filaments
Formed by Shock Compression
Kazunari Iwasaki (Doshisha Univ.)
Shu-ichiro Inutsuka, Tsuyoshi Inoue (Nagoya Univ.)

ＤＴＡ シンポジウム 「星形成を軸に俯瞰する役割とその観測的検証」

Star Formation in Filamentary
Molecular Clouds
Herschel Gould Belt Survey
Most of dense cores is associatedwith filamentsfrom PP6 slide by P. AndreWidth of Filaments

column density

Arzoumanian et al. 201110.1
radius [pc]The width of filaments appears to be constantregardless of the central column density.
← contradict simple expectation

Magnetic Field (MF)
TaurusSerpens SouthB

B

Sugitani et al. 2011
Palmeirim et al. 2013

Massive filaments ⊥ B, Striations ∥ B
MF should be important in the dynamics of filaments.

Filament Formation by Shock Compression
ISM is frequently disturbed by shock compression
driven by supernovae, expansion of HII region, …
• Head-on collision along z axis,• Method：AMR (Sfumato,Matsumoto 2006)• Resolution：5123 @ level 0(up to level 4 )• −𝟑. 𝟔 𝐩𝐜 < 𝒙, 𝒚, 𝒛 < 𝟑. 𝟔 𝐩𝐜
• 𝝆𝟎 = 𝟏𝟎𝟎𝝁𝒎𝐇• 𝑽𝟎 = 𝟑 𝐤𝐦/𝐬
• 𝜹𝒗 = 𝟏 𝐤𝐦/𝐬

Two cases
Large B (𝜷 = 𝟎. 𝟏), 𝐁𝟎 = 𝟔. 𝟑𝝁𝐆
Small B (𝜷 = 𝟎. 𝟓), 𝑩𝟎 = 𝟐. 𝟖𝝁𝐆

Filament Formation Mechanism
Inoue & Fukui (2013)

shockshocky axisfilamentz axis

converging flow

At least in the initial stage, filaments are formed by the purely MHD effect.

𝒗𝐜𝐨𝐧𝐯𝐞𝐫𝐠𝐞 > 𝒗𝐟𝐟

Column Density Distribution
red line:
B direction

Large B

Small BMF Configuration for Large B

y axisx axis MF is ordered.
 “Ribbon-like” structure is formed.

MF Configuration for Small B

y axisx axis B has a complex structure
inside the filament.
 B is ordered outside the filamentMF inside Massive Filament
Small B

Large B𝐵2 ∝ 𝜌𝜌 ≥ 100𝜌0time

MF inside the filament increases with the line mass.
 For large B, the increasing rate of MF reduces. → “ribbon-like” filament formation
 For small B, the increasing rate of MF appears to be enhanced.

Dynamics in Postshock Region

Model𝑩𝐬𝐡𝝆𝐬𝐡𝑪𝐀,𝐬𝐡75
75

144𝟏𝟎𝒄𝒔 𝟎. 𝟔𝟕𝐕𝟎𝟓𝒄𝒔 𝟎. 𝟑𝟑𝑽𝟎𝑩𝟐𝐬𝐡∼ 𝝆𝟎 𝑽𝟐𝟎𝟖𝝅

Large B
Small BIf the initial perturbation is nonlinear,shock fronts deform significantly.
→ If B_0 is small,converging flow can be super-Alfvenic.
B is bended during the filament formation.

𝑩𝐜𝐫𝐢𝐭 = 𝑩𝐜𝐫𝐢𝐭 𝐕𝟎 , 𝑩𝟎 , 𝜹𝒗

Radial Profile
filaments are identified by DisPerSE (Soubie et al. 2011)

Large B

Small B
∝ 𝑅−1

∝ 𝑅−1

∝ 𝑅−2

∝ 𝑅−2

• The slope of the radial profile is smaller than the equilibrium profile.

Time Evolution of Width
Large B

Small B

Small Bsupercritical

Large BsubcriticalAt least for the initial phase, the width appears to be 0.1 pc.
For large B, star (sink) forms after the formation of “ribbon” (width decreases)
For small B, the width is remains 0.1 pc at the star (sink) formation.

Summary• We investigate the formation of filament driven by shockcompression.
• At least in the initial phase, filaments are formed by converging
flow whose speed is larger than the free-fall velocity.
• For Large B– MF structure is coherent inside filaments.
– Filament is highly flattened (ribbon-like).

• For Small B– MF structure is complex inside filaments.
– MF is roughly ordered outside filaments (stretching)

Future Works Parameter Survey
 How the structure of MF depends on 𝐵0 , 𝑉0 , 𝛿𝑣.
 Development of Analytical Modelvirial parameter

virial parameter

virial parameter ≡∫ 𝐵2 𝑑𝐴
2∫ 𝑃𝑑𝐴+8𝜋
𝐺𝑀L2

Small B
Large B

Large B (𝜽 = 𝝅/𝟒)

Small B (𝜽 = 𝝅/𝟒)

Small B

Large B