Theory of Magnetic Fields in Star and Disk Formation SHANTANU BASU Magnetic Fields or Turbulence: What is the Critical Factor in Star and Disk Formation, National Tsing Hua University, Hsinchu, Taiwan 06 Feb 2018
Theory of Magnetic Fields in
Star and Disk FormationSHANTANU BASUMagnetic Fields or Turbulence: What is the Critical Factor in
Star and Disk Formation, National Tsing Hua University,
Hsinchu, Taiwan
06 Feb 2018
Magnetic Field Can Affect
➢Turbulence
➢Cloud Formation
➢Core/Filament Formation
➢Star Formation Rate/Efficiency
➢Disk Formation
➢Outflow Launching
➢Protostar Formation
➢Accretion Process
My MT thermometer:
0.1
Turbulent ICs from Expanding
Shells
Mol Cloud Progenitors are subcritical H I
Clouds Heiles & Troland (2008)
Column density
Blos
20 -210 cm
subcritical
supercritical
Flux freezing in HI gas Molecular clouds formed by HI
accumulation may have significant subcritical component.
Heiles & Troland (2005)
Can ambipolar diffusion create
supercritical m-t-f post shock?
➢ Inoue & Inutsuka (2008, 2009) conclude
AD in WNM not sufficient to allow MC
formation in flows unless they are largely
parallel to the ambient magnetic.
➢ See also Kortgen & Banerjee (2015),
Chen & Ostriker (2014), Inutsuka et al.
(2015)
Inutsuka et al. (2015)
Molecular Cloud Accumulation
Constraints
1/2 6 3
1
6 3 6
150 pc,2 1 3 10 G 1 cm
150 km/s.1 3 10 G 1 cm 10 yr
B B nL
G
L B n tv
t
Mestel (1999, Stellar Magnetism) quotes 103 above, not 150.
Bottom line: Highly supercritical “initial” condition for MC is unlikely.
Cloud Initial Conditions
Hennebelle, Banerjee, Vazquez-
Semadeni+ 2008
Christie, Wu, Tan (2017) – GMC collisions with AD.See also Vazquez-Semadeni et
al. (2011), Heitsch et al. (2009)
➢ Collision of HI clouds can lead
to cloud formation
➢ Hennebelle et al. (2008) find
flat B-n relation for low
densities and B ~ n0.5 at
densities above 103 cm-3.
B- relation
But what is happening physically at
turnover region?
Crutcher et al. (2010)
0.65
Tritsis et al. (2015)
Basu (2000)
B
1/2
vB
Fit constant value of B at low
density, a turnover point, and
at densities above turnover. Best fit is virial relation
v Av
Model molecular data separated from
atomic data, and include horizontal
error bars.
in driven turbulence ideal MHD
0 16 0 1.6
Driven turbulence. Mach
number =10.
PS Li, McKee, Klein (2015)
1/2 00
0
2 GB
Moderate field model
Weak field model
0 ff1.6 : 0.62 0.11 at 0.57 ,
0.70 0.06.
t
0 16 : 0.57 0.05.
However Mocz et al. (2017)
find ~ 2/3 for weak field
model transitioning to ~ 1/2
for strong field model.
Important Questions
➢ How physically is subcritical to supercritical
transition accomplished? Does it require a
unique density?
➢ Does subcritical to supercritical transition take
place exactly when HI to H2 conversion takes
place?
➢ Or, is there a significant H2 envelope that is also
subcritical?
How to get to supercritical
collapse?
➢ Wait for flow along FLs to create supercritical m-t-f
Or, if cloud has inherited turbulence:➢ Turbulence accelerated fragmentation via
enhanced ambipolar diffusion (AD)
Or, if negligible turbulence:➢ Transcritical fragmentation (gravity-AD hybrid
mode)
➢ Subcritical fragmentation, inevitable win of gravity
due to AD
Transcritical Fragmentation➢ Related to ~ pc scale
clump formation?
➢ Massive prestellar
cores?
➢ Two-stage
fragmentation (Bailey
& Basu 2012, 2014)
2 p
c
Ciolek &
Basu (2006)
flux freezing
with AD
with AD
Ba
su,
Cio
lek, &
Wu
rste
r (2
009
)
Subcritical Fragmentation
➢ Occurs on classical AD timescale ~ 10 tff for
standard xi
➢ Subsonic infall motions
➢ Long gestation period
means subcritical cores
of moderate density
enhancement would
be visible
Basu, Ciolek, &
Wurster (2009)
Turbulence Accelerated AD (TAAD)
yr102 5
0 t
2 4 allowed to decaykv k
Kudoh & Basu (2008) – 3D model similar to thin sheet
models of Li & Nakamura (2004), Nakamura & Li (2005),
Basu, Ciolek, Dapp, & Wurster (2009).
0 00.5, .t Av v
Gas density in midplane (z = 0)
A vertical slice of gas density
Turbulence Accelerated AD
,0 0 0
1 if
3AD t Av v
0 0if .t Av v
Kudoh & Basu (2014)
Ambipolar diffusion time shortened in
predictable manner in oscillatory filamentary
evolution.
Filaments in Molecular Clouds
Is 0.1 pc a universal width?
Arzoumanian (2013)
Palmeirim et al.
(2012) – B
perpendicular to
massive filament
B211/213
Arzoumanian et al. (2011)
IC 5146
Ribbon Model Auddy, Basu, & Kudoh (2016)
Quasi-magnetohydrostatic ribbon
viewed at various viewing angles yields relatively flat observed width-N
correlation.
Tomisaka (2014):
Ribbon tends to
fragment along
length if line
mass to flux ratio above critical
value
Image of TAAD
scenario – Basu
et al. (2009).
Striations
Tritsis & Tassis (2016)
➢ Alfvén modes couple to
magnetosonic modes
➢ Density enhancements due
to magnetosonic modes
Density map
from 2D
simulation
with
spectrum of
Alfvén waves
initially
present.
CO integrated intensity
map of striations in
Taurus
Column Density PDFAuddy, Basu, & Kudoh (2018)Three distinct outcomes.
Supercritical fragmentation – Subcritical fragmentation – Turbulence Accelerated AD in subcritical cloud
Pure power laws of different slope in supercritical and subcritical fragmentation respectively.
For TAAD, a natural transition from lognormal pdf to power law at transition from subcritical to
supercritical gas.
Supercritical
contraction
consistent with
2.ln
dN
d
Effect of feedback – SFR/SFE
Federrath 2014
Wang, ZYLi, Abel, Nakamura (2010)
Add sink cells and protostellar outflow prescription to track long term
evolution.
Nakamura & Li (2008)
Subcritical cloud,
including AD
Supercritical clouds
Top to bottom: HD, +turbulence,
+MHD, +outflows
B is effective at spreading
outflow energy, keeps
cloud stirred up.
HD
+turbulence
+B
+outflow
Zoom in on Disk Formation
Magnetic Braking Catastrophe
Allen, Li, Shu (2001)
➢ 1990s: MB effective in subcritical
cloud, but ineffective in supercritical
prestellar core collapse: Tomisaka et
al. (1990), Basu & Mouschovias (1994)
➢ Allen, Li, & Shu (2001) – No! MB is
revitalized in protostellar phase, ideal
MHD
➢ MB catastrophe firmly established by
Mellon & Li 2008, 2009, Galli et al. 2006,
Hennebelle & Ciardi 2009
Magnetic Flux Loss in aligned rotator – enables
small class 0 disk within first core region
Tomida+ (2015)
used 3D
nonideal MHD
calculation to
find ~ 5 AU disk
at end of first
core phase
• Dashed lines are for flux-freezing model (no magnetic diffusion)extreme flaring of field lines long lever arm magnetic braking catastrophe
• Solid lines are for model with magnetic diffusion; field lines more relaxed (straight)
-4
0
-2
0
0
2
0
40
AU
Dapp, Basu & Kunz (2012)
– thin disk calculation
MB catastrophe
Centrifugal disk
Other causes of disk formation –
possibly large class 0 disks
➢ Misaligned rotation and magnetic axes (Hennebelle &
Ciardi 2009; Li, Krasnopolsky & Shang 2013)
➢ Magnetic flux loss due to turbulence induced
reconnection (Santos-Lima et al. 2012, 2013)
➢ Tangling of field lines due to turbulence leading to lower
efficiency of magnetic braking (Seifried et al. 2012, 2013)
➢ Enhanced magnetic flux loss due to pseudodisk warping
(Li et al. 2014)
3D nested grid resistive MHD
simulations: self consistent outflows
Outflows launched from
edge of first core
Machida et al. (2008)
and later papers
Jets launched
from just outside
second core
r zB B B
r zB B BSignificant Ohmic
resistivity within first
core region.Simulations typically
followed to early class 0
phase.
New insight into outflowsF. Alves, Girart, Caselli + 2017
➢ Class I object BHB07-11, in B59: outflow
launch site is ~ 100 AU from center
➢ Coincides with disk edge/centrifugal barrier
as revealed by gas kinematics
Velocity channel map
Magnetocentrifugal effect
at disk edge in late
accretion phase?
Alignment of B and J – Effect of the
Hall term
➢ Effect of an additional Hall current due to
e-i drift
➢ When B and J are parallel, the Hall effect
aids magnetic braking. When B and J
antiparallel, it weakens magnetic braking.
Can get bimodal disk size evolution
(Tsukamoto+2015, Wurster+2016, also
Braiding & Wardle 2012).
➢ In antiparallel case, can get a counter-
rotating envelope (Krasnopolsky et al.
2011, Tsukamoto et al. 2015, Wurster et al.
2016)Tsukamoto et al. (2015) – details
depend on value of Hall resistivity
Small
disk: B, J
parallel
Large
disk: B, J
anti-
parallel
Summary and Key Questions
➢ Exactly how/when is supercritical gas created? This
affects fragmentation mode, B-rho relation, column
density pdf
➢ Magnetic fields can explain ribbon-like and striation
features in molecular clouds
➢ Magnetic fields provide an efficient means of
spreading turbulent energy in clouds
➢ Disk and outflow formation depend sensitively on B
and non-ideal MHD. Are there self-regulation
mechanisms in play?