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Structure and Stability of Phase Transi5on Layers in the Diffuse Interstellar Medium
Jennifer M. Stone1 Shu-
ichiro Inutsuka1 Ellen G. Zweibel2
1. 2. Nagoya University, Japan University of Wisconsin-
Madison, USA

Phase Transi5ons in the Diffuse ISM, November 2013


Mul5phase Dynamics Mo5va5on
· Interac5ons between ISM phases and their magne5c connec5vity are not well known

Koyama & Inutsuka 2006

Braun & Kanekar 2005

· Can instabili5es in phase transi5on layers sustain turbulence? · Can they generate small-
scale ISM structure? · What are the ramifica5ons for transport processes?
Phase Transi5ons in the Diffuse ISM, November 2013


Phase Transi5on Layer Defini5on
· The balance between radia5ve hea5ng and cooling and photoelectric hea5ng permits a thermally bistable medium (Field et al. 1969, Wolfire et al. 1995, 2003)

cooling dominates

Å

example front solu/on -
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WNM unstable CNM hea5ng dominates

A phase transi/on layer, or thermal front, connects the stable CNM and WNM phases

Phase Transi5ons in the Diffuse ISM, November 2013


Phase Transi5on Characteris5cs
· Consider a steady-
state transi5on layer separa5ng the CNM from the WNM in a plane parallel geometry
EVAPORATION FRONT CNM
net hea5ng

CONDENSATION FRONT WNM
net cooling

WNM

CNM

· The nature of a front is determined by its total pressure · There exists a "satura5on pressure" at which hea5ng and cooling are balanced within a front (Zeldovich & Pikel'ner 1969) P = Psat: STATIC FRONT P < Psat: net hea5ng -
> EVAPORATION FRONT P > Psat: net cooling -
> CONDENSATION FRONT
Phase Transi5ons in the Diffuse ISM, November 2013


Phase Transi5on Layer Instability
evapora5on front

CNM

WNM

A phase transi5on layer separa5ng two uniform media of different densi5es and temperatures undergoes corruga5onal deforma5on ("Darrieus-
Landau instability")
Phase Transi5ons in the Diffuse ISM, November 2013


Corruga5onal Instability Mechanism
· Streamlines bend towards the normal in an unstable front, accelera5ng its displacement

Stone & Zweibel 2009

· Streamlines diverge in a stable front and the corruga5on is smoothed out
Phase Transi5ons in the Diffuse ISM, November 2013


Towards a Full Analysis of Structure and Stability
· Consider perturba5ons at all scales to account for relevant physical processes · Characterize extent of phase transi5on using the Field length, l
lF =

F

(T )T L

: thermal conduc5vity L : cooling func5on

· Thin front (long-
wavelength) analysis: >> lF -
more tractable, discon5nuous front approxima5on · Thick front (short-
wavelength) analysis: < lF -
account for hea5ng, cooling, and thermal conduc5on (PAH photoelectric hea5ng, Ly , [C II] cooling) · Full linear stability analysis without approxima5on · Nonlinear regime
Phase Transi5ons in the Diffuse ISM, November 2013


Modeling of Phase Transi5on Layers
· 1-
D model describing pressure, density, velocity, magne5c field strength, and temperature RT p= equa5on of state µ
+ v = 0

t

x











con5nuity m omentum induc5on






2 v B 2 t + x v + p + 8 = 0

B = - v B t x p

()











R dT dp T - = - L - 1 µ dt dt x x

energy



Phase Transi5ons in the Diffuse ISM, November 2013


Applica5on: Magne5c Field Strength-
Density Rela5on
· The rela5onship between magne5c field strength and gas density in the ISM is a probe of the nature of MHD processes in the interstellar environment

Troland & Heiles 1986

· Zeeman measurements across a range of densi5es suggest there is no correla5on between gas density and magne5c field strength in the diffuse ISM · Strong evidence for diffusion
Phase Transi5ons in the Diffuse ISM, November 2013


Physical Processes in Phase Transi5on Layers
· Inves5gate effects of ambipolar diffusion · Plasma velocity, vp v + vD (Shu 1983)
vD = JâB B =- c i n AD 4 i n
AD

B x

AD/(i+n) (Draine et al. 1983)



· Hea5ng and cooling L = n [ n - (PAH + AD )] analy5c func5ons chosen to fit -
: radia5ve cooling Wolfire et al. 2003 models -
PAH: photoelectric hea5ng 1 B dB g nAD = i n AD v D 2 = -
AD: ion-
neutral driu hea5n
i n
AD

2

4 dx

· Thermal conduc5on dominated by neutral atoms (Parker 1953) = 2.5 10 3 T1 / 2 erg s-
1 cm-
1 K-
1 â
Phase Transi5ons in the Diffuse ISM, November 2013




Problem Setup
· Magne5c field tangen5al to front · Choose appropriate boundary condi5ons to establish an eigenvalue problem
z CNM BC F R O N vCNM T


WNM BWNM

NM

Derive front solu5on that connects CNM and WNM phases in thermal equilibrium Control ini5al ambipolar driu hea5ng rate in CNM

vWNM x

Phase Transi5ons in the Diffuse ISM, November 2013


Example Phase Transi5on Profiles
10000 100

1000

10

100

1

Thin phase transi5on layers featuring steep temperature gradients at small scales

0 -0.002

1 0.9 0.8

-0.004 0.7 -0.006 0.6 -0.008 -0.01 0.5

Magne5c field profile becomes fla{er as the ini5al field strength is increased
Phase Transi5ons in the Diffuse ISM, November 2013

Stone & Zweibel 2010


Profiles Assuming Flux-
Freezing
10000 1

1000

0.1

100

0.01

Assume magne5c field strength is propor5onal to density

0.001



0

Flux-
freezing is ruled out as the resul5ng profiles imply huge hea5ng rates and driu veloci5es that are unphysical

Stone & Zweibel 2010

Phase Transi5ons in the Diffuse ISM, November 2013


Diffusive Phase Transi5ons
· Compare thermal and ambipolar diffusivi5es:
v~

th lF




AD

= v A 2

th ni n iT 1 / = 10 -2 AD th Bµ 2
ni

2

· Find ni << th, so the driu 5me is always much smaller than th e 5me to flow through the front · Suggests the magne5c field becomes close to uniform · Previous studies argue that ambipolar diffusion is too slow; invoke turbulence · Ambipolar diffusion is efficient in thin phase transi/on layers
Phase Transi5ons in the Diffuse ISM, November 2013


Phase Transi5on Linear Stability Analyses

· Knowledge of the structure of a phase transi5on enables us to undertake a full stability analysis · However, to date this has proven prohibi5vely difficult · Full problem is ill-
condi/oned, even for the hydrodynamic case
·

Conven5onal numerical techniques do not converge Approximate overall stability behavior by s5tching together various approxima5ons and assump5ons

Inoue et al. 2006

Phase Transi5ons in the Diffuse ISM, November 2013


Summary of Stability Proper5es
Magne5c field orthogonal to phase transi5on Front Type Evaporation Condensation Stone & Zweibel 2009 Hydrodynamic Unstable Stable Trans-
AlfvÈnic Super-AlfvÈnic Unstable Stable Sub-AlfvÈnic Stable Unstable

· Magne5c fields can have a drama5c effect on stability proper5es · If condensa5on proceeds sufficiently rapidly, instability may be important for cloud forma5on dynamics · Sophis5cated numerical methods currently being inves5gated for full stability calcula5on · Nonlinear studies likely required to understand physical mechanism
Phase Transi5ons in the Diffuse ISM, November 2013


Summary
· Our models of phase transi5ons between the CNM and WNM include: various hea5ng and cooling mechanisms, thermal conduc5on, ambipolar diffusion · Methods can be applied to any mul5phase system · ISM phase transi5on layer structure and stability is a rich, mathema5cally difficult problem with a large number of applica5ons (e.g. numerical methods, shock theory) · ISM Phase transi/ons are important for transport processes and should be resolved! · How can we combine observa5ons and modeling to diagnose physical processes in the diffuse ISM?
Phase Transi5ons in the Diffuse ISM, November 2013