Contents

## The Magnetothermal Instability in addition to its Application to Clusters of Galaxies Motivation Talk Outline Algorithm: MHD with Athena Algorithm: Heat Conduction

Martinez, Jennifer, Contributing Writer has reference to this Academic Journal, PHwiki organized this Journal The Magnetothermal Instability in addition to its Application to Clusters of Galaxies Ian Parrish Advisor: James Stone Dept. of Astrophysical Sciences Princeton University/ UC Berkeley October 10, 2007 Motivation Hydra A Cluster (Ch in addition to ra) Collisionless Transport T ~ 4.5 keV n ~ 10-3-10-4 Sgr A T ~ 1 keV, n ~ 10 cm-3 Rs ~ 1012 cm Motivating example suggested by E. Quataert Talk Outline Idea: Stability, Instability, in addition to Backward Transport in Stratified Fluids, Steve Balbus, 2000. Physics of the Magnetothermal Instability (MTI). Algorithm: Athena: State of the art, massively parallel MHD solver. Anisotropic thermal conduction module. Verification in addition to Exploration Verification of linear growth rates. Exploration of nonlinear consequences. Application to Galaxy Clusters

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Idea: Magnetothermal Instability Qualitative Mechanism Convective Stability in a Gravitational Field Clasically: Schwarzschild Criterion Long MFP: Balbus Criterion New Stability Criterion! Q Q Q Magnetic Field Lines Anisotropic heat flux given by Braginskii conductivity. Algorithm: MHD with Athena Athena: Higher order Godunov Scheme Constrained Transport as long as preserving divergence free. Unsplit CTU integrator Algorithm: Heat Conduction B Verification Gaussian Diffusion: 2nd order accurate. Circular Field Lines. Implemented through sub-cycling diffusion routine.

Algorithm: Per as long as mance Dispersion Relation Dimensionless Growth Rate Dimensionless Wavenumber Dispersion Relation Linear Regime Dimensionless Growth Rate Dimensionless Wavenumber ~3% error Linear Regime: Verification

Exploration: 3D Nonlinear Behavior Subsonic convective turbulence, Mach ~ 1.5 x 10-3. Magnetic dynamo leads to equipartition with kinetic energy. Efficient heat conduction. Steady state heat flux is 1/3 to 1/2 of Spitzer value. Magnetic Energy Density = B2/2 g Exploration: 3D Nonlinear Behavior Subsonic convective turbulence, Mach ~ 1.5 x 10-3. Magnetic dynamo leads to equipartition with kinetic energy. Efficient heat conduction. Steady state heat flux is 1/3 to 1/2 of Spitzer value. RMS Mach Exploration: 3D Nonlinear Behavior MTI-Unstable Region Subsonic convective turbulence, Mach ~ 1.5 x 10-3. Magnetic dynamo leads to equipartition with kinetic energy. Efficient heat conduction. Steady state heat flux is 1/3 to 1/2 of Spitzer value. Temperature profile can be suppressed significantly. Temperature

Expectations from Structure Formation Hydro Simulation: CDM Cosmology, Eulerian Expect: steep temperature profile Rv ~ 1-3 Mpc M ~ 1014 1015 solar masses (84% dark matter, 13% ICM, 3% stars) T ~ 1-15 keV LX ~ 1043 1046 erg/s B ~ 1.0 µG Anisotropic Thermal Conduction Dominates Loken, Norman, et al (2002) Application: Clusters of Galaxies Application: Clusters of Galaxies Plot from DeGr in addition to i in addition to Molendi 2002 ICM unstable to the MTI on scales greater than Observational Data Simulation: Clusters of Galaxies Temperature Profile becomes Isothermal

Simulation: Clusters of Galaxies Magnetic Dynamo: B2 amplified by ~ 60 Vigorous Convection: Mean Mach: ~ 0.1 Peak Mach: > 0.6 Summary Physics of the MTI. Verification in addition to validation of MHD + anisotropic thermal conduction. Nonlinear behavior of the MTI. Application to the thermal structure of clusters of galaxies. Future Work Galaxy cluster heating/cooling mechanisms: jets, bubbles, cosmic rays, etc. Application to neutron stars. Mergers of galaxy clusters with dark matter. DOE CSGF Fellowship, Ch in addition to ra Fellowship Many calculations per as long as med on Princetons Orangena Supercomputer Acknowledgements Questions

Adiabatic Single Mode Example Single Mode Evolution Magnetic Energy Density Kinetic Energy Density Single Mode Perturbation Single Mode Evolution Saturated State should be new isothermal temperature profile Analogous to MRI Saturated State where angular velocity profile is flat.

Dependence on Magnetic Field Instability Criterion: Conducting Boundaries Temperature Fluctuations Models with Convectively Stable Layers Heat flux primarily due to Advective component. Very efficient total heat flow MTI Stable MTI Stable MTI Unstable

Future Work & Applications Full 3-D Calculations Potential as long as a dynamo in three-dimensions (early evidence) Convection is intrinsically 3D Application-Specific Simulations Clusters of Galaxies Atmospheres of Neutron Stars Acknowledgements: Aristotle Socrates, Prateek Sharma, Steve Balbus, Ben Ch in addition to ran, Elliot Quataert, Nadia Zakamska, Greg Hammett Funding: Department of Energy Computational Science Graduate Fellowship (CSGF) SUPPLEMENTARY MATERIAL Analogy with MRI Magneto-Rotational Magneto-Thermal Keplerian Profile Conserved Quantity: Angular Momentum Free Energy Source: Angular Velocity Gradient Weak Field Required Convectively Stable Profile Conserved Quantity: Entropy Free Energy Source: Temperature Gradient Weak Field Required Unstable When: Unstable When:

Heat Conduction Algorithm Magnetic Fields Defined at Faces Interpolate Fields Calculate Unit Vectors +Symmetric Term Heat Flux with Stable Layers Outline & Motivation Goal: Numerical simulation of plasma physics with MHD in astrophysics. Verification of algorithms Application to Astrophysical Problems Outline: Physics of the Magnetothermal Instability (MTI) Verification of Growth Rates Nonlinear Consequences Application to Galaxy Clusters Solar Corona Around 2 R: n ~ 3 x 1015, T ~ few 106 K mfp > distance from the sun

Conducting Boundary Temperature Profiles Extension to 3D How to get there ATHENA is already parallelized as long as 3D Need to parallelize heat conduction algorithm Parallel scalability up to 2,048 processors What can be studied Confirm linear in addition to non-linear properties in 2D Convection is intrinsically 3Dmeasure heat conduction Possibility of a dynamo Initial Conditions Pressure Profile Bx g Convectively Stable Atmosphere Ideal MHD (ATHENA) Anisotropic Heat Conduction (Braginskii) BCs: adiabatic or conducting at y-boundary, periodic in x

## Martinez, Jennifer Contributing Writer

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