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Stability of Cold Gas Streams in Hot Halos

Nir Mandelker, H.U.J.I.
IGM@50, June 08, 2015
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Collaborators

Dan Padnos, Yuval Birnboim, Avishai Dekel Andi Burkert, Mark Krumholz, John Forbes

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The Plan for Today
Cosmological context (Thanks Avishai!) Linear Theory
(or everything you wanted to know about Kelvin-Helmholtz instability and were afraid to ask)

Preliminary Simulations

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Cosmic-web Streams feed galaxies: mergers and a smoother component
AMR RAMSES Teyssier, Dekel box size 300 kpc resolution 30 pc z ~ 5.0 ­ 2.5
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Streams feeding a high redshift galaxy

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The "Messy" Region
Ceverino, Dekel, Bournaud 2010 ART 35-70pc resolution

streams disk

interaction region

In massive halos, streams may breakup due to shocks, hydro and thermal instabilities, collisions between streams and clumps, heating.

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Main Question
Do the streams breakup before they reach the galaxy? Study growth of various instabilities:
Hydrodynamical: Kelvin-Helmholz instability of dense super-sonic jet in hot medium Thermal: Clumping due to runaway cooling (seeded by KH eddies?) Rayleigh-Taylor instabilities Local Jeans collapse (seeded by KH eddies?) Richtmyer-Meshkov instabilities in feedback induced shocks

Gravitational (external): Gravitational (self ): External shocks:

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Typical numbers
Stream temperature: Surrounding temperature: Pressure equilibrium: 10 ~ 10 10 M 10


Density contrast:
Stream velocity:
$


! "#

10

100

%
& '

Mach number:
Stream radius:

M
R + , 10-./ 0.10

1

1.5

Size ratio:

1

2 2!"#

0.01

0.1

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KHI in Planar Geometry
Standard Hydrodynamic Equations 34 6 47 9 ; 0 : 35 39 : 4 67 ;0 35 Unperturbed Solution 4? ; 4? >C@ 9? ; 9? C D : E Linear Perturbations 4 , 9 , : I ; I C exp M -N D 6 -O P A5 - 9? ; cos>T@ :
?

3 35

34 / ;0 35

; /FGH5

Eigenmodes of the Problem 4 , 9 as a function of = , >4? , 9? , /? @, A, - B : :
UU U 29? U 4? U

4 algebraic equations
;0

9?

A 64 ? -N

-

1

-N -

9? /

A -N

1 ODE Eigenmode equation
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(1) Incompressible Sheet, KKHI
Kindergardener's
Incompressible : / , / 4 ,9 ; 9 5 4 ,9 ; 0
Y

;

16 2Z



[ 9 9 , 100

[ 0 0.010 ,

5 6 05 Y Stream Unstable!
Two complications: 1. Geometry 2. Compressibility

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(2) Incompressible Slab
4 ,9 4

[ 0 0.010 9 100

5 6 05

Y

Stream Unstable!

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(3) Compressible Sheet
Compressible:
4 9
^ ^

;

M

^

4

[ 0 0.010
100 90 80
21 44 67 90 113

; 4 /4

100

; 1.0

70 60 50 40 30 20 10 0.5 1.0 Instabilities DO NOT grow

5 /5

Stream Unstable
100 ; 1.5

Y

136 159 182 205 228

Stream Stable

M ; 9 //

1.5

2.0

2.5

3.0 12

Figure by Dan Padnos


(4) Compressible Slab
; 1.5 ; 100 Each mode decays as [ 0 since sheet is stable ; 1.0 ; 100

A ln>-@

A-

Beware: Non-linear coupling of modes?
Fundamental Mode: Any values of and and all wavelengths Reflected Modes: Only when [ 0 0.010

5 6 05
Y

Y

a b cd 6 ce
Critical wavelengths

[ 0 0.010

[ 0 0.10

5 1 05

Y

5 5

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Reflected mode at Resonance

Analytic

Simulation (RAMSES)

Pressure waves are reflected off the jet boundary Constructive interference at resonance Propagation angle sin i
j
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(5) Compressible Cylinder
See also (e.g.) Birkinshaw 1984; Payne & Cohn 1985; Hardee & Norman 1988; Bodo + 1994 Analysis of hot jets in cold backgrounds

· Axisymmetric modes nearly identical to (P) modes in slab · Additional non-axisymmetric modes have comparable growth rates. Additional coupling?

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The Importance of Eigenmodes
Eigenmodes DO NOT span all possible initial conditions When comparing growth rate in simulations to linear theory, MUST use eigenmode perturbations Random IC must either: · Decay into eigenmodes + additional waves · Go non-linear first
Figure by Dan Padnos 16


k

l

m

(non-eigenmode)

5^no

;5

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Summary and Outlook
First step in systematic study of instabilities in cold, supersonic streams penetrating hot halo Conclusions KHI ­ more complicated than you thought! (Not for kindergardeners) Reflected modes dominate instability of supersonic jet Cold flows in virial halos: Parameters are right at the boundary between two phases of instability ­ fast and slow Immediate term: Quantitative analysis of non-linear evolution with simulations Stream disruption, mass flux / energy / momentum decrease Eigenmode vs non-eigenmode ICs Medium to long term: Add cooling, gravity (convection, magnetic fields...) and study other instabilities
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T HA N K Y O U ! !
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