The instability of aself-gravitating gaseous disk

by

Chi YuanInstitute of Astronomy & Astrophysics

Academia Sinica, Taipei11-01-2006

Collaborators: David C.C. Yen, L.H. Lin, H.H. Wang, C.C. Yang

Two kinds of instabilityin astrophysical disks

• Toomre’s instability: starburst rings, star formation

• Shear instability of Rayleigh’s type: associated with shocks, causing substructure, chaos and turbulence

Governing Equations

,0v

t

~,

,

,4

,Iv v v

2

02

bd0

d2

2

PaP

r

zG

at

The Antares Code

• Second-order 2-D Godunov codes

• Based on exact Riemann solver

• Coupled with the fft Poisson solver (non-periodic BC) for disk self-gravity

• True radiation (non-reflecting) boundary conditions.

• Cartesian and polar coordinates

• Isothermal and polytropic gas

• All codes parallelized

大火程序

Starburst Rings

NGC1512 NGC6782NGC4313

Circumnuclear Disk in ngc1068

Center of M51

NGC 1068

9.5 arcmin

• Type : Sb / AGN

• Distance : 14.4 Mpc

( H0 = 75 km s-1 Mpc-1 )

1 arcsec = 74 pc

Nearly Flat Rotation Curve

01.0,)( 2

1

0

r

rvv

Cases of Double Resonances: OLR-OILR

Toomre’s Instability

densitysurface

frequencyepicyclic

eeda:sound spG

aQ

:

:

1

Onset of Instability

G

aQ

Disk Instability

G

aQ

m

Sub-structure, feathers, chaos

Sub-structure of M81

M81

Shear Instability

Sub-structure, Patches, Chaos

Rayleigh’s Shear Instability: (vorticity in the axisymmetric flow flield has a local

extremum)

vorticity divided by surface density orSpecific vorticity has a local extremum

.0 ,0

problems D-2for

. ,

Fluids ibleIncompress Fluids leCompressib

Dt

D

Dt

D

uDt

Du

Dt

D

Specific Vorticity

STuhu

Dt

D

Dt

D

uuDt

D

zzz

pzsz

)2

1(

shockat created vorticity

0v)( y

u)( x

t

0,v)( y

u)( x

t

frame) (rotating .02

,0

problems D-2for

x ,

vorticityspecific

2

The Mechanism of Rayleigh’s Criterion for Shear Instability (C.C. Lin 1944)

Simple Explanation of Rayleigh’s shear instability

Specific Vorticity distribution

Vorticity Creation by Shock(Cocco, Truesdell, Lighthill, Hayes, Berndt, Kevlahan)

s

r

r

Dt

Du

Cs

C)(

1

)1(21

1

)1(21

1

22

sra

r

a Dt

Du

Cs

C)(

1

)1(21

1

)1(21

)1()(

2

2

2

1a

b

,ACCr

Creation of Vorticity along Shocks

Conclusions

• Disk instability is extremely important in astrophysics.• Toomre’s instability at work, giving rise starburst an

d star formation activities. It also explains the origin of the dense circumnuclear molecular disks observed in the center of many nearby galaxies.

• Shear instability creates substructures, patches and chaos in the middle of the galactic disk where shocks are present.

• We believe that the origin of the shear instability lies on the vorticity creation on shocks.

Evolution of Streamlines

Specific Vorticity at different resolution