Buoyant Bubbles in Galaxy Clusters

Introduction:
As described in O'Neill, De Young, & Jones (2009)^[1], we have conducted a series of 3D magnetohydrodynamic (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)^[2]. 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 = P_gas/P_mag < 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.

Numerical Model:
We employ a second-order, nonrelativistic, Eulerian, total variation diminishing (TVD), ideal 3D MHD code, described in Ryu & Jones (1995)^[3] and Ryu et al. (1998)^[4]. The code is conservative and explicitly enforces the divergence-free condition for magnetic fields through a constrained transport scheme detailed in Ryu et al. (1998)^[4].

Our simulations were conducted on a 3D Cartesian grid of total physical dimensions x_size = 40 kpc, y_size = z_size = 34 kpc, covering the ranges x = [5 kpc : 45 kpc], y = z ≈ [−17 kpc : 17 kpc]. The gravitational acceleration is in the −x direction in this coordinate system. The bubble origin was centered at x_b = 13 kpc, y_b = z_b = 0.

Ambient cluster density and pressure profiles were identical in all models, but ambient magnetic field structure and strength were varied.

For more details on each individual model, see the Table of Bubble Models. A complete discussion of the simulations and analysis is available in O'Neill, De Young, & Jones (2009)^[1].

Animations:
Here, we present a set of animations meant to complement the figures and analysis in O'Neill, De Young, & Jones (2009)^[1]. The Figure numbers listed here correspond to those used in that paper.

• Inflated, Unmagnetized Bubbles in Various Environments (FIGURE 4)
• Inflated, Unmagnetized Bubbles in Tangled, Strong Ambient Fields (FIGURE 7)
• Comparison of Magnetized and Unmagnetized Bubbles (FIGURE 8)

References:
[1] O'Neill, S. M., De Young, D. S., & Jones, T. W. 2009, astro-ph 0901.1673
[2] Jones, T. W. & De Young, D. S. 2005, ApJ, 624, 586.
[3] Ryu, D. & Jones, T. W. 1995, ApJ, 442, 228.
[4] Ryu, D., Miniati, F., Jones, T. W., & Frank, A. 1998, ApJ, 509, 244.