M A G N E T I C F I E L D S A N D T H E H E L I U M C O N T E N T I N T H E I N T R A C L U S T E R M E D I U M

T H O M A S B E R L O K & M A R T I N E . P E S S A H N I E L S B O H R I N S T I T U T E

È C O L E D E P H Y S I Q U E D E S H O U C H E S , M A R C H 2 0 1 5

N G C 4 9 1 1

1 M I O . L I G H T Y E A R S

Image courtesy of U. Briel, MPE Garching. ESA

B R E M S S T R A H L U N G E M I S S I O N

+

-E L E C T R O N

I O N

X - R A Y

T H E T E M P E R A T U R E A N D D E N S I T Y P R O F I L E

20 50 100 200 500 10000.00

0.02

0.04

0.06

0.08

0.10

r !kpc"

n e#cm!3

$

20 50 100 200 500 1000

456789

r !kpc"

T#keV$

Model from Bulbul et al. (2010, 2011)

dS

dr> 0

Piffaretti et al. 2005, A&A

Radius

Entro

pyI C M S TA B L E A C C O R D I N G T O S C H W A R Z S C H I L D

S / ln p⇢��

S TA B L E A T M O S P H E R E W I T H O U T M A G N E T I C F I E L D S

rT

Time

g

M A G N E T I C F I E L D S : I C M I S U N S TA B L E !

rT g

Time

Balbus (2001) Quataert (2008)

Parrish & Stone 2005Parrish & Quataert 2008

Kunz et. al 2012and others

B U T W H Y S H O U L D T H E I C M B E H O M O G E N E O U S ?

• Sedimentation of He • Consider magnetic fields!

20 50 100 200 500 1000r !kpc"0.60

0.65

0.70

0.75

0.80

Μ

Using model from Peng & Nagai (2009)

I S O T H E R M A L A T M O S P H E R E W I T H O U T M A G N E T I C F I E L D S

rµg

Time

U N S TA B L E ONLY B E C A U S E I T ’ S W E A K LY M A G N E T I Z E D

Berlok & Pessah (in prep.)

rµg

TimeTime

Anisotropic effects

Heat conduction

Diffusion of particles

Braginskii viscosity

Qs = ��b̂b̂ ·rT

Qc = �Db̂b̂ ·rc

The ICM is magnetized

H � �mfp � ⇢

characteristic size.

Larmor radius.

mean free path�mfp

H

⇢

T H E E Q U A T I O N S O F K I N E T I C M H D W I T H H E L I U M

DRAFT VERSION MAY 26, 2014Preprint typeset using LATEX style emulateapj v. 12/16/11

LOCAL SIMULATIONS OF WEAKLY-COLLISIONAL PLASMAS WITH COMPOSITION GRADIENTS

Niels Bohr Institute, University of CopenhagenDraft version May 26, 2014

ABSTRACTUnderstanding whether Helium can sediment to the core of galaxy clusters is important for a number of prob-lems in cosmology and astrophysics. For example, our ignorance in the distribution of Helium leads to sys-tematic uncertainties in estimating the density and masses of galaxy cluster. All current models addressingthis questions are one-dimensional, and ignore the fact that the intracluster medium is a dilute, magnetizedplasma, which can effectively channel ions and electrons, leading to anisotropic transport of momentum, heat,and particle diffusion. This anisotropy can lead to a wide variety of instabilities, which could be relevant forunderstanding the dynamics of the heterogeneous medium. In this paper, we shed light into this problem byinvestigating the dynamical role played by gradients in the temperature and mean molecular weight in a mag-netized tenuous plasma, such as the ICM. We analyze a wide spectrum of instabilities, and discuss the futureprospects of studying the long term evolution of Helium sedimentation in more realistic settings.

1. INTRODUCTION

Astrophysical dilute plasmas which are magnetized can besubject to a variety of instabilities when they are stratifiedin the direction of gravity. This is the case because even amechanically weak magnetic field can effectively channelelectrons and ions, leading to anisotropic heat conduction,Braginskii viscosity and particle diffusion.Previous studies have considered plane-parallel, fully ionizedhomogenous atmospheres with a temperature gradient in thedirection of gravity. The magneto-thermal instability (MTI)acts when the magnetic field has a horizontal component andthe temperature decreases with height Balbus (2000, 2001).The heat-buoyancy instability (HBI) is on the other handactive when the magnetic field has a vertical component andthe temperature increases with height Quataert (2008). Thedynamics of the MTI and the HBI have been investigatedextensively by using ideal MHD simulations with anisotropicheat conduction (). The importance of Braginskii viscositywas recently recognized analytically Kunz (2011) andnumerically Kunz et al. (2012); ?.

The motivation to understand the various instabilities isthat these mechanisms play a key role in the dynamics ofthe intracluster medium (ICM). Various authors have pointedout the importance of a good description of the He contentin the ICM since the assumption of a homogeneous plasmaleads to systematic uncertainties in cluster density and massestimates Peng & Nagai (2009); Bulbul et al. (2011). Inorder to more realistically capture the role of He in the ICMPessah & Chakraborty (2013) included a mass concentrationof He, c, in the equations of kinetic MHD and derived adispersion relation. As a result, it was seen that the plasmacan be unstable both when the mean molecular weight, µ, isincreasing and when it is decreasing with height. In analogyto the instabilities that feed off temperature gradients (theMTI and the HBI), instabilities that feed off gradients incomposition were named the magneto-thermo-compositionalinstability (MTCI, maximally unstable with horizontalmagnetic field) and the heat-buoyo-compositional instability(HBCI, maximally unstable with vertical magnetic field).Furthermore, it was shown that there exists atmosphereswhich are only unstable when anisotropic diffusion of He istaken into account.

In this paper we have generalized the result of Pessah &Chakraborty (2013) to include the effects of the magneticfield strength on the stability properties of the stratified atmo-sphere. This is an important result because magnetic tensionis thought to influence some parts of the ICM. We extend thediscussion of the instabilities to inclined magnetic field ge-ometries and discuss the available wave number space.

2. DERIVATION OF THE DISPERSION RELATION

The kinetic MHD equations for a binary mixture of Hydro-gen and Helium can be written as

@⇢

@t+r·(⇢v) = 0 , (1)

@

@t(⇢v) +r·

✓⇢vv + P+

B2

8⇡I� B2

4⇡b̂b̂

◆= ⇢g , (2)

@B

@t= r⇥(v⇥B) , (3)

P

� � 1

d

dt(lnP⇢��) = (p? � pk)

d

dtln

B

⇢2/3�r·Qs , (4)

dc

dt= �r·Qc . (5)

Here, the Lagrangian and Eulerian derivatives are relatedvia d/dt ⌘ @/@t + v·r, ⇢ is the mass density, v is the fluidvelocity, g is the gravitational acceleration, � is the adiabaticindex, and I stands for the 3⇥ 3 identity matrix. The symbols? and k refer respectively to the directions perpendicular andparallel to the magnetic field B whose direction is given bythe versor b̂ ⌘ B/B = (b

x

, 0, bz

).The evolution of the plasma is influenced by three different

non-ideal effects, namely anisotropic heat conduction drivenby the electrons given by

Q

s

= ��b̂b̂ ·rT, (6)

anisotropic diffusion of Helium given by

Q

c

= �Db̂b̂ ·rc (7)

and the anisotropic pressure which gives rise to Braginskii

Pessah & Chakraborty 2013

A N I S O T R O P I C E F F E C T S : A N E X A M P L E

Modification to ATHENA (Stone et al. 2008)Parrish & Stone 2005, Sharma & Hammett 2007

Image courtesy of U. Briel, MPE Garching. ESA

1 M I O . L I G H T Y E A R S

L O C A L M O D E L S : M I X I N G O F C O M P O S I T I O N

0.1H0

L O C A L M O D E L S : M I X I N G O F C O M P O S I T I O N

Berlok & Pessah (in prep.) TimeWith Braginskii

Without Braginskii

See Kunz et. al 2012 for details on Braginskii viscosity

Image courtesy of U. Briel, MPE Garching. ESA

1 M I O . L I G H T Y E A R S

2H0

Thermal profile as in Latter & Kunz 2012 but including a composition gradient