triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · the gas movement...
TRANSCRIPT
Triggered fragmentation in self-gravitating discs: forming fragments at small radii
Farzana Meru!18th February 2015
• Introduction
• Self-gravitating disc properties
• Fragmentation conditions
• Triggered fragmentation
Contents
Self-gravitating discs have characteristic structures that may fragment
Cameron 1978; Boss 1997
Self-gravity drives the evolution of massive
discs (spiral structures form)
Spirals collapse and fragment under the “right” conditions
Meru & Bate 2011a
Fragmentation occurs at large disc radii
Meru & Bate 2010
See movie at www.ast.cam.ac.uk/~fmeru/Movies/GI_disc_fragment.mov
Self-gravitating discs exist on many scales
0 1 2 3
0 1 2 3log Y [g cm-2]
0 1 2 3
-1.0 -0.5 0.0 0.5 1.0-1.0
-0.5
0.0
0.5
1.0
-1.0 -0.5 0.0 0.5 1.0x -1.8 [ 0.04pc ]
-1.0
-0.5
0.0
0.5
1.0
y [ 0
.04p
c ]
-1.0 -0.5 0.0 0.5 1.0-1.0
-0.5
0.0
0.5
1.0
AGN discs: star formation Nayakshin, Cudra & Springel 2007
Brown dwarf formationStamatellos et al 2007
Planet formationMayer et al 2003
Fragmentation occurs locally
The stabilising and destabilising forces fight against each other to determine fragmentation
Centrifugal forces
Pressure forces
Lengthscale
Stability
Instability
The Toomre equation describes when spiral structures develop and fragmentation occurs
Stability determined by:
Centrifugal forces
Pressure forces
Lengthscale
Stability
Instability
Toomre 1964
Q =cs�
��G
For an infinitesimally thin disc:
Toomre 1964
Q > 1 � stableQ < 1 � unstable
Fragmentation is more likely at larger radii
Q =cs�
��G
Toomre parameter generally decreases with radius
Gravitationally unstable discs have a thermostatic nature
High Toomre value Q ≈ 1-2
cool
Q =cs�
��G
The thermostatic control can be overcome to promote fragmentation
Q =cs�
��G
Fast cooling destabilises disc
High mass infall or accretion rate
increases the surface density
!Kratter et al 2008; Zhu et al 2012; Hayfield et
al 2011
Zhu et al 2012; Adapted with
permission from Z. Zhu
Triggered fragmentation
What happens in a gravitationally unstable disc after the first fragment forms?
The fragment will have an effect on the surrounding disc material
3D SPH simulations with radiative transfer !Self-consistent formation and evolution
Before it fragments the disc is relatively calm
log column density [g/cm2]
y [A
U]
x [AU]
50
100
0
-50
-100-100 -50 50 100 -100 -50 0 50 100
0
-5 x 104
5 x 104
1 x 105
-1 x 105
radial velocity [cm/s]
x [AU]0
M? = 1.5M� Mdisc = 1.2M�
The disc fragments in the outer part and then the inner parts
See movie at www.ast.cam.ac.uk/~fmeru/Movies/mass_movement_sigma.mov
The inwards movement of gas triggers further fragmentation
y [A
U]
x [AU]
radi
al ve
locit
y [c
m/s
]
0
-5 x 104
1 x 105
-1 x 105
5 x 104
See movie at www.ast.cam.ac.uk/~fmeru/Movies/mass_movement_vR.mov
The gas movement in the disc is more dynamic after fragmentation
The inwards movement causes the inner spiral to become more dense, lowering the Toomre parameter and allowing further fragmentation
log column density [g/cm2] radial velocity [cm/s]
50
100
0
-50
-100 -50 0 50 100 -100 -50 0 50 100
3
2
1
0
-5 x 104
5 x 104
1 x 105
-1 x 105-100
Q =cs�
��G
y [A
U]
x [AU] x [AU]
Radial velocity increases by up to a factor of 10
The inner disc is pushed into a state of instability
-100
-50
0
50
100
-100 -50 0 50 100
y [A
U]
x [AU]
’./Q_grid040’ u 1:2:3
0
0.5
1
1.5
2
2.5
3
Toom
re p
aram
eter
Inner disc is stable
Before first fragment forms
Q =cs�
��G
Q < 1 � unstable
-100
-50
0
50
100
-100 -50 0 50 100
y [A
U]
x [AU]
’./Q_grid099’ u 1:2:3
0
0.5
1
1.5
2
2.5
3
Toom
re p
aram
eter
Before second fragment forms
Second fragment forms at this radius (≈24au)
Would the inner fragment have formed anyway?
First fragment formation artificially suppressed to see effects
-100
-50
0
50
100
-100 -50 0 50 100
y [A
U]
x [AU]
’./vel_grid293’ u 1:2:($3*vel_conv)
-1e+05
-5e+04
0e+00
5e+04
1e+05
radi
al v
eloc
ity [c
m/s
]
Movement of gas is calm and not dynamic if the outer fragment is not present
Meru, in prep See also Armitage &
Hansen 1999
Triggered fragmentation helps to form planets at radii where in situ formation has been difficult
Core accretion
≈10 AU ≈50 AU
Image reproduced with permission from A. Banzatti
Gravitational instability
Summary
3D radiative transfer simulations to explore mass movement in self-gravitating discs after a fragment forms Model fragment formation and disc evolution self-consistently
Radial velocity enhancements by up to a factor of ≈ 10 push stable regions into state of instability
Fragments may form at smaller radii than otherwise expected