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Jonathan Dursi

Research: Buoyant Bubbles

Flows involving the rise of buoyant bubbles have long been well understood when &madash; as with air bubbles in water — viscosity or surface tension can play an important role in regularizing the problem and stabilizing the interface. However, there are real systems where such diffusivities or tensions are so vanishingly small that they can play no role on any length scale of interest. In these systems, often some other physical effect rises to the occasion and acts to provide the necessary stabilization of the interface; but then the resulting dynamics are quite different from the more familiar cases. I have been working in particular on the cases of a rising bubble in a magnetized medium, and a buoyant reactive `flame bubble'.

[ Magnetic Draping of Bubbles | Propagation of Flame Bubbles | Papers | Talks ]

Magnetic Draping of Galaxy Cluster Bubbles

A projectile in a magnetized medium `draping' the field over itself, modifying its later dynamics. From Dursi & Pfrommer (2007).
Recent observations of galaxy cluster cooling flows have revealed X-ray emission voids up to twice the size of our own galaxy in size that have been identified with buoyant, magnetized bubbles, presumably inflated by the central Active Galactic Nucleus (AGN) of the cluster. These hot bubbles potentially help explain an important mystery in understanding the Inter-Cluster Medium (ICM) by providing a heat source; however, the mechanism by which the hot bubble heats the surrounding medium remains unclear. Complicating the issue of bubble/ICM interaction is that the interface is still poorly understood; it is known that the interface remains quite sharp, and it's not clear why that would be.

Recent numerical and linear stability theory work of mine, however, (Dursi 2007, Dursi & Pfrommer 2007) has shown that for the case of a small overdense core merging into a magnetized medium — even one quite weakly magnetized,as one might expect in this context — the projectile `plows up' field lines, building magnetic field strength up to dynamically important and even dominant levels, as shown in the figure above. This magnetic layer can have significant dynamic effects, from partly stabilizing against instabilities (as shown in the linear theory work) to more surprising effects including acting to decelerate the projectile.

A bubble self-disrupting as it rises. From Robinson, Dursi, et al. (2004).
These dynamical effects may be quite important, as earlier work of mine done while supervising undergraduate research student K. Robinson at Chicago (Robinson, Dursi, et al. (2004)) showed that such a coherent magnetic showed that such a coherent magnetic field may be necessary for the maintenance of these bubbles, as absent any such features, a hydrodynamic bubble will shred itself into at best a `smoke ring' in one buoyant rise time (eg, the figure below), making it very difficult to see how purely hydrodynamic flow could explain both AGN heating and the persistence of such bubbles.

We now largely understand this behaviour for an over-dense core; however, there in principle could be significant differences for an under-dense bubble which is prone to breaking up. There there is some evidence that they are similar, and our analysis has confirmed that the timescales could well be sort enough for the draping to successfully provide a protective `bubble wrap' for these objects, as well. Further, there is the intriguing possibility that these magnetized layers may be directly observable. I plan to continue this work to examine these two questions, and apply this effect of `magnetic draping' to other systems.

The work considered above includes only ideal magnetohydrodynamics (MHD), and it is inferred that, because of the magnetic field geometry, thermal conductivity across the drape will be strongly suppressed, maintaining the sharpness of the interface. However, confirming this requires self-consistent inclusion of the relevant thermal and magnetic diffusivities — which in this context are themselves open research topics. But therein lies opportunity; coupled with the possibility of the direct observation of these drapes, one may be able to constrain what the diffusivities must look like, and therefore contribute to the understanding of another problem.



Propagation of Flame Bubbles

Early simulations by M. Zingale, in part for Zingale & Dursi (2007), of a rising flame being distorted and experiencing shear instabiliites.
Another situation in which some other effect provides a stabilization of a buoyant bubble is the case of a rising reactive bubble, or a `flame bubble' (eg, the figure to the right). There are a number of situations such studies relate to; an important system is Supernovae of Type Ia, which are extremely interesting objects in their own right, but are also used in measuring global parameters of the Universe (the discovery that the Universe is accelerating its expansion, and thus the inference of the existence of a `dark energy', is largely based on the unexplained apparent uniformity of these objects).

However, increasing scrutiny shows Type Ia aren't as uniform as previously thought; what's more, new observations suggest that there may be populations of Type Ia which are very difficult to produce in the standard picture. Understanding these events requires a more detailed understanding of the ignition and early burning. The burning in this situation is likely to ignite at points, meaning that the initial behaviour is that of a rising flame bubble.

My earlier work has largely focused on planar (thermonuclear) burning waves in this regime, both supersonic detonations (Dursi & Timmes (2006), Timmes et al. (2000)) and subsonic deflagrations or `flames' , (Dursi (2004), Dursi et al. (2003)) including the instabilities of these propagating burning fronts and their interaction with turbulence (see, eg, the figure to the left). They are similar enough to the more familiar terrestrial equivalents to be able to bring over much of the well-developed theory from the combustion literature, but different enough to be extremely interesting, and fundamental questions remain unanswered. My work on these flows themselves are discussed in a later section.

With M. Zingale (SUNY SB), in collaboration with researchers at Lawrence Berkeley National Laboratory, I have used a novel computational method along with analytic arguments to examine the balance of flame propagation, flame instabilities, and buoyancy the early behaviour of flame bubbles in Type Ia supernovae (Zingale & Dursi 2007). The analytics are essential to understand the dynamics of the situation, and the simulations are extremely large-scale computations, due to the large range of scales between the flame thickness and the hydrodynamic scales. We have considered such questions as when the centre of the star is consumed by the first flames; we have also shown the tendency of a rising flame bubble to fragment (assisted by my earlier work in non-reactive bubbles), and calculated a characteristic fragmentation scale. This fragmentation scale drops precipitously as degeneracy lifts in the star, providing a rapid cascade of fragmentation — and thus an increase in burning area — at just the time that an increase in burning rate is needed to match observations. This novel burning model will be examined in future work.

Results from a simulation of spherically compressed reactive turbulence.
My work so far, then, examines ignition in one-zone (0d) (eg, Dursi & Timmes (2006)) models and early stages of burning in 2d and 3d. My next goal is to extend the work in both directions to build a model which goes from ignition points to early burning phases. This area is currently the biggest unanswered question in Type Ia supernovae models; while the technology has developed to do very sophisticated large-scale simulations of the explosions given some set of initial large-scale burning, they must be initialized with some guess as to what that burning looks like. The goal of my current work is to give a prescription for what that large-scale burning should look like given some progenitor model and the convective turbulence expected from the long-term simmering.

To do this will require extending the consideration of ignition from one-zone models to 1d and higher; this brings in a great deal more physics, and while estimates can be done analytically, precision in the ignition conditions will require very large parameter studies (but of very modest individual computations) to demarcate the `flammability conditions' for given hotspots. From there, it will be necessary to extend the early burning work done already to include in a more sophisticated way the effects of turbulence and instabilities; the result of these two efforts will be a significant step towards a `soup-to-nuts' model of the ignition and early burning stages of Type Ia supernovae, which would apply in many different scenarios beyond the standard model, such as models where the initial reactive turbulence is highly compressed (as in the figure to the right.)

Papers

L. J. Dursi, C. Pfrommer. Draping of Cluster Magnetic Fields over Bullets and Bubbles -- Morphology and Dynamic Effects, arXiv:0711.0213, ApJ submitted, 2007. (3D renderings can be investigated in this manuscript if Adobe Acrobat Reader 8.01 or better is used)

M. Zingale, L. J. Dursi. Propagation of the First Flames in Type Ia Supernovae, ApJ, 656:333-346, 2007.

L. J. Dursi. The Linear Stability of Astrophysical Flames in Magnetic Fields, ApJ, 606:1039-1056, May 2004.

L. J. Dursi, F. X. Timmes. Local Ignition in Carbon/Oxygen White Dwarfs -- I: One-zone Ignition and Spherical Shock Ignition of Detonations. ApJ, 641:1071, Apr 2006.

K. Robinson, L. J. Dursi, P. M. Ricker, R. Rosner, A. C. Calder, M. Zingale, J. W. Truran, T. Linde, A. Caceres, B. Fryxell, , K. Olson, K. Riley, A. Siegel, and N. Vladimirova. Morphology of Rising Hydrodynamic and Magnetohydrodynamic Bubbles from Numerical Simulations. ApJ , 601(2):621-643, February 2004.

L. J. Dursi, M. Zingale, A. C. Calder, B. Fryxell, F. X. T. Timmes, N. Vladimirova, R. Rosner, A. Caceres, D. Q. Lamb, K. Olson, P. M. Ricker, K. Riley, A. Siegel, and J. W. Truran. The Response of Model and Astrophysical Thermonuclear Flames to Curvature and Stretch. ApJ , 595(2):955-979, October 2003.

F. X. Timmes, M. Zingale, K. Olson, B. Fryxell, P. Ricker, A. C. Calder, L. J. Dursi, H. Tufo, P. MacNeice, J. W. Truran, and R. Rosner. On the Cellular Structure of Carbon Detonations. ApJ , 543:938-954, November 2000.

M. Zingale, L. J. Dursi, J. ZuHone, A. C. Calder, B. Fryxell, T. Plewa, J. W. Truran, A. Caceres, K. Olson, P. Ricker, K. Riley, R. Rosner, A. Siegel, F. X. Timmes, and N. Vladimirova. Mapping Initial Hydrostatic Models in Godunov Codes. ApJSS , 143(2):539-566, December 2002.


Talks

Sweeping up a Magnetic Sheath: Magnetic Draping over Moving Cores and Bubbles in Galaxy Clusters
Accretion and Explosion: the Astrophysics of Degenerate Stars, KITP, May 17 2007
[PDF] [Keynote]
A talk given while I was in residence at the KITP program on supernovae in May 2007. The talk is on work examining `magnetic draping' in galaxy clusters. Video or audio of the talk, as well as the slides, are available at the KITP website.

First Flames: Burning, Turbulence, and Buoyancy
Paths to Exploding Stars: Accretion and Eruption, KITP, Mar 2007
[PDF] [Keynote]
An invited talk to the KITP conference during the program Accretion and Explosion: the Astrophysics of Degenerate Stars at KITP. The talk discusses the ignition and earliest burning phases (eg, burning bubbles) in a Type Ia supernovae. (Choppy) video or audio of the talk, as well as the slides, is available at the conference webpage.

Simulating Astrophysical Combustion with the FLASH code
CAIMS/MITACS Joint Annual Conference, June 2006
[PDF] [OpenDocument]
An invited talk to the Scientific Computing session of the annual Canadian applied mathematics conference discussing simulating combustion in an astrophysical context, and the computational choices that this regime suggests.

Local Ignition in Carbon-Oxygen White Dwarfs: One Zone Ignition, and Spherical Shock Ignition of Detonations
208th AAS meeting, June 2006
[PDF] [OpenDocument]
A presentation describing recent work on the physics of local ignition in Type Ia supernovae.

Towards Understanding some Astrophysical Flows using Multiscale Approaches with the FLASH code
HPCS 2006, May 2006
[PDF] [OpenDocument]
A discussion of some of our attempts to simulate turbulent astrophysical flows with interesting physics on disparate scales using simple multiscale approaches.

Grungy Gastrophysics and Cosmology
class="bold" href="http://www.ap.stmarys.ca/">St. Mary's University, Nov 2005
[PDF] [OpenDocument]
This discusses the Type Ia supernovae problem, the very detailed interplay of physics needed to really understand how they blow up, and arguing that the problem is really still very much wide-open.

Buoyancy and Astrophysics
Toronto Astrophysical Gas Dynamics Seminar, Oct 2004
[PDF] [OpenOffice .sxi]
Rayleigh-Taylor, RT-plus burning, and rising bubbles; an overview of some astrophysical problems involving buoyancy and why such simple problems are so surprisingly difficult to deal with.

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