Planetesimal dynamics in self-gravitating discs Giuseppe Lodato IoA - Cambridge.
Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement...
Transcript of Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement...
![Page 1: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/1.jpg)
Triggered fragmentation in self-gravitating discs: forming fragments at small radii
Farzana Meru!18th February 2015
![Page 2: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/2.jpg)
• Introduction
• Self-gravitating disc properties
• Fragmentation conditions
• Triggered fragmentation
Contents
![Page 3: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/3.jpg)
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
![Page 4: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/4.jpg)
Fragmentation occurs at large disc radii
Meru & Bate 2010
See movie at www.ast.cam.ac.uk/~fmeru/Movies/GI_disc_fragment.mov
![Page 5: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/5.jpg)
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
![Page 6: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/6.jpg)
Fragmentation occurs locally
![Page 7: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/7.jpg)
The stabilising and destabilising forces fight against each other to determine fragmentation
Centrifugal forces
Pressure forces
Lengthscale
Stability
Instability
![Page 8: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/8.jpg)
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
![Page 9: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/9.jpg)
Fragmentation is more likely at larger radii
Q =cs�
��G
Toomre parameter generally decreases with radius
![Page 10: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/10.jpg)
Gravitationally unstable discs have a thermostatic nature
High Toomre value Q ≈ 1-2
cool
Q =cs�
��G
![Page 11: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/11.jpg)
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
![Page 12: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/12.jpg)
Triggered fragmentation
![Page 13: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/13.jpg)
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
![Page 14: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/14.jpg)
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�
![Page 15: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/15.jpg)
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
![Page 16: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/16.jpg)
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
![Page 17: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/17.jpg)
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
![Page 18: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/18.jpg)
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)
![Page 19: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/19.jpg)
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
![Page 20: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/20.jpg)
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
![Page 21: Triggered fragmentation in self-gravitating discs: forming … · 2020-05-21 · The gas movement in the disc is more dynamic after fragmentation The inwards movement causes the inner](https://reader034.fdocuments.net/reader034/viewer/2022050404/5f812e2a42d03b6401744a46/html5/thumbnails/21.jpg)
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