Numerical simulation of ﬁlamentary
molecular cloud in magnetic ﬁeld
（磁場に貫かれたフィラメント状分子雲の安定性）
工藤哲洋（長崎大）
花輪知幸（千葉大）
富阪幸治（国立天文台）

Introduction•Many molecular clouds show
ﬁlamentary structures. Interstellar
magnetic ﬁeld are perpendicular
to the ﬁlamentary axis.

•However, the stability of theseclouds are not well known.

•We study the nonlinear stabilitiesof the clouds by MHD numericalsimulation.

The Astrophysical Journal, 807:5 (10pp), 2015 July 1

Figure 4. Obtained polarization degree vectors overlaid on the IRAS 100 μm emission map of Lupus I and its surrounding region. T
linearly with the measured degree of polarization according to the scale indicated in the upper left corner, and its orientation gives
component of the local magnetic ﬁeld. The positions of different classes of young stellar objects, from Rygl et al. (2013), are indcode: unbound cores (white circles), prestellar cores (green circles), class 0 (red circle), class I (triangles), class II (squares), andincreasing Galactic longitude (l ) and latitude (b) are shown in the upper left corner.

black line:

direction of magnetic ﬁeldand Rizzo et al. (1998), who obtained a mean polarization
angle of 52° with a standard deviation ofTR  23n, for stars
close to the rim of Lupus I.

Schematic picture of the ﬁlamentary molecular cloudmagnetic ﬁelds

molecular cloud

coreMethod
initial setup•

The initial ﬁlamentary cloud is
dynamically equilibrium(Stodolkiewicz 1963, Ostriker 1964).

•

Magnetic ﬁelds are uniform andMag. F.

perpendicular to the ﬁlamentaryaxis.
•Input rondom noise.
Mag. F.

•

Ideal MHD, self-gravity, isothermal.

Results
no mag. FTime = 22.7
1.5
1.0

weak mag. F
1.5
1.0

200.5

Time = 35.7

= 1.00Time = 50.0

= 1.00
1.5
1.0

20

0.5

strong mag. F

0.0

0.0

-0.5-0.5

-0.5

-1.0

-1.0

10-1.010-1.5-2.0

0-10-10-10-20-20-20-50x

510-10= 1.00z

420-2-4-10-50x

510-50x

510-10= 1.00420-2-4z-10

z

0

y

0

10-1.5-2.0

yy-1.5-2.0

20

0.5

0.0

= 1.00-10-50x510-50x510= 1.00

420-2-4-10-50x510

Comparison to linear analysis (Hanawa)no mag. F

p0(Fourier component)

10p=110strong mag. F

p

=2L0
=2L0
=
4-1

⇢kweak mag. F

= 0.5

L0
=
210-2
10-3
10-4
10-5
0

10203040

timesolid lines:
numerical simulations
dashed lines: linear analysis

50

Results : Nonlinear evolution
runaway collapse

no mag. F
Time = 22.7
1.5
1.0

weak mag. F
1.5
1.0

20

0.5

Time = 35.7

= 1.00Time = 50.0

= 1.001.5
1.0

20

0.5

no runaway collapse
strong mag. F

0.0

0.0-0.5-0.5-0.5

-1.0

-1.0

10-1.010-1.5-2.00-10-10-10-20-20-20-50x

510-10= 1.00z

420-2-4-10-5

0x

510-50x

510-10= 1.004
20-2-4

z-10

z

0

y

0

10-1.5-2.0

yy-1.5
-2.0

20

0.5

0.0

= 1.00-10-50x510-50x510= 1.00420-2-4-10

-50x

510

strong magnetic ﬁeld

initial plasma β on the axis.

= 0.36= 0.49no runaway collapse= 0.64runaway collapse

Theoretical estimation
pBcr ⌘ 2⇡ G⌃(0)in the case of ﬁlaments，✓◆ 222x +z⇢(x, y) = ⇢0 1 +8⇡H 2p⌃(0) = 2⇡⇢0 H✓cs
H=p4⇡G⇢0therefore，

p 2 p
Bcr = 2 2⇡ ⇢0 GH
8⇡⇢0 c2s4= 2 ' 0.405
cr =Bcr⇡◆

= 0.49

sinusoidal long wave perturb.

runaway collapse near critical

Velocity
4.02.0verticalVycollapse

y1.00.5

horizontal

VxexpansionxSummary•

Magnetic ﬁelds do not stabilize the self-gravitational
instability of ﬁlamentary molecular clouds.

•When the magnetic ﬁeld is not strong, the coreshows runaway collapse. When the magnetic ﬁeld isstrong enough, the starless core is formed.

•Near the critical magnetic ﬁeld, the core collapses
along the ﬁlamentary axis but expands to theperpendicular direction.