Three-dimensional Magnetohydrodynamic Simulations of Buoyant Bubbles in Galaxy Clusters

📝 Abstract

We report results of 3D MHD simulations of the dynamics of buoyant bubbles in magnetized galaxy cluster media. The simulations are three dimensional extensions of two dimensional calculations reported by Jones & De Young (2005). Initially spherical bubbles and briefly inflated spherical bubbles all with radii a few times smaller than the intracluster medium (ICM) scale height were followed as they rose through several ICM scale heights. Such bubbles quickly evolve into a toroidal form that, in the absence of magnetic influences, is stable against fragmentation in our simulations. This ring formation results from (commonly used) initial conditions that cause ICM material below the bubbles to drive upwards through the bubble, creating a vortex ring; that is, hydrostatic bubbles develop into “smoke rings”, if they are initially not very much smaller or very much larger than the ICM scale height. Even modest ICM magnetic fields with beta = P_gas/P_mag ~ 10^3 can influence the dynamics of the bubbles, provided the fields are not tangled on scales comparable to or smaller than the size of the bubbles. Quasi-uniform, horizontal fields with initial beta ~ 10^2 bifurcated our bubbles before they rose more than about a scale height of the ICM, and substantially weaker fields produced clear distortions. On the other hand, tangled magnetic fields with similar, modest strengths are generally less easily amplified by the bubble motions and are thus less influential in bubble evolution. Inclusion of a comparably strong, tangled magnetic field inside the initial bubbles had little effect on our bubble evolution, since those fields were quickly diminished through expansion of the bubble and reconnection of the initial field.

💡 Analysis

We report results of 3D MHD simulations of the dynamics of buoyant bubbles in magnetized galaxy cluster media. The simulations are three dimensional extensions of two dimensional calculations reported by Jones & De Young (2005). Initially spherical bubbles and briefly inflated spherical bubbles all with radii a few times smaller than the intracluster medium (ICM) scale height were followed as they rose through several ICM scale heights. Such bubbles quickly evolve into a toroidal form that, in the absence of magnetic influences, is stable against fragmentation in our simulations. This ring formation results from (commonly used) initial conditions that cause ICM material below the bubbles to drive upwards through the bubble, creating a vortex ring; that is, hydrostatic bubbles develop into “smoke rings”, if they are initially not very much smaller or very much larger than the ICM scale height. Even modest ICM magnetic fields with beta = P_gas/P_mag ~ 10^3 can influence the dynamics of the bubbles, provided the fields are not tangled on scales comparable to or smaller than the size of the bubbles. Quasi-uniform, horizontal fields with initial beta ~ 10^2 bifurcated our bubbles before they rose more than about a scale height of the ICM, and substantially weaker fields produced clear distortions. On the other hand, tangled magnetic fields with similar, modest strengths are generally less easily amplified by the bubble motions and are thus less influential in bubble evolution. Inclusion of a comparably strong, tangled magnetic field inside the initial bubbles had little effect on our bubble evolution, since those fields were quickly diminished through expansion of the bubble and reconnection of the initial field.

📄 Content

Accepted, to appear in ApJ, v694, 2009 April. Preprint typeset using LATEX style emulateapj v. 08/22/09 THREE-DIMENSIONAL MAGNETOHYDRODYNAMIC SIMULATIONS OF BUOYANT BUBBLES IN GALAXY CLUSTERS S. M. O’Neill1, D. S. De Young 2, T. W. Jones3 Accepted, to appear in ApJ, v694, 2009 April. ABSTRACT We report results of 3D MHD simulations of the dynamics of buoyant bubbles in magnetized galaxy cluster media. The simulations are three dimensional extensions of two dimensional calculations reported by Jones & De Young (2005). Initially spherical bubbles and briefly inflated spherical bubbles all with radii a few times smaller than the intracluster medium (ICM) scale height were followed as they rose through several ICM scale heights. Such bubbles quickly evolve into a toroidal form that, in the absence of magnetic influences, is stable against fragmentation in our simulations. This ring formation results from (commonly used) initial conditions that cause ICM material below the bubbles to drive upwards through the bubble, creating a vortex ring; that is, hydrostatic bubbles develop into “smoke rings”, if they are initially not very much smaller or very much larger than the ICM scale height. Even modest ICM magnetic fields with β = Pgas/Pmag ≲103 can influence the dynamics of the bubbles, provided the fields are not tangled on scales comparable to or smaller than the size of the bubbles. Quasi-uniform, horizontal fields with initial β ∼102 bifurcated our bubbles before they rose more than about a scale height of the ICM, and substantially weaker fields produced clear distortions. These behaviors resulted from stretching and amplification of ICM fields trapped in irregularities along the top surface of the young bubbles. On the other hand, tangled magnetic fields with similar, modest strengths are generally less easily amplified by the bubble motions and are thus less influential in bubble evolution. Inclusion of a comparably strong, tangled magnetic field inside the initial bubbles had little effect on our bubble evolution, since those fields were quickly diminished through expansion of the bubble and reconnection of the initial field. Subject headings: galaxies: clusters: general – MHD– galaxies: active–galaxies

1. INTRODUCTION There is now ample evidence from radio and X-ray observations that active galactic nuclei (AGN) gener- ate energetic structures that continue to interact with galaxy cluster environments even after the central engine shuts down. Observations of detached bubbles of radio plasma and coincident X-ray cavities in cluster cores il- lustrate that the AGN jets inflate cocoons displacing the ambient intracluster medium (ICM) (e.g., Boehringer et al. 1993; Slee & Roy 1998; Fabian et al. 2000; Mc- Namara et al. 2001; Slee et al. 2001; Wise et al. 2007). The pdV work required to move the ICM can be esti- mated from X-ray observations, which suggest that up- wards of 1059 −1060 ergs of energy are present in these cavities (Bˆırzan et al. 2004; Dunn et al. 2005; McNa- mara & Nulsen 2007; Wise et al. 2007). As such, they could in principle provide a reservoir of energy needed to stifle cooling flows and maintain the ∼2 keV tem- perature floors observed in cluster cores (Peterson et al. 2001; Fabian et al. 2001; Kaastra et al. 2001; Tamura et al. 2001). The evolution of relic bubbles is an interesting problem in part because their structures are seen to remain coher- ent longer than analytic estimates would suggest. The is- 1 Department of Astronomy, University of Maryland, College Park, MD 20742; soneill@astro.umd.edu 2 National Optical Astronomy Observatory, 950 North Cherry Avenue, Tucson, AZ 85719; deyoung@noao.edu 3 School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455; twj@msi.umn.edu sue of bubble fragmentation and its associated timescale is of importance for models that use “AGN feedback” to reheat the ICM and thus suppress both ICM cool- ing flows and the occurrence of large amounts of star formation in the cluster core. This is because such re- heating needs to be spread throughout the ICM in the central regions, and if radio bubbles do not fragment on timescales comparable to the local ICM cooling time, the distribution of their energy over large volumes requires the assumption of some other, yet unspecified mecha- nism. This fragmentation question is also related to the more general problem of AGN feedback in current cos- mological models and in particular to the use of “radio AGN feedback” to produce the observed distribution of massive galaxy morphologies and colors (e.g., Croton et al. 2006). In particular, because the bubbles are light, presumably being filled with very hot and possibly rela- tivistic plasma, they buoyantly rise in the cluster poten- tial and are subject to disruption by both the Rayleigh- Taylor (R-T) and Kelvin-Helmholtz (K-H) instabilities. Simple linear stability analysis suggests that disruption should take place on timescales of ∼107 years (see Heinz & Churazov 2005,

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