Supernova of Type Ia are both fascinating phenomenon in and of
themselves, and play an important role in cosmology. However, the
underlying mechanism of these explosions remains something of a mystery,
and scenarios previously considered `exotic' may be required to explain
recent observations. My past research on these objects has focused on
understanding the ignition and burning microphysics that occurs in white
dwarfs, including a surprising finding about metallicity dependence; this
work is applicable to all plausible scenarios, and is aimed at creating
microphysical inputs suitable for use in large-scale simulations.
I intend to continue this work, and incorporate it into simulations
of large-scale exotic models. Future work will involve putting these
microphysical inputs into large-scale simulations to consider two
`non-standard' mechanisms for explosions; white dwarf mergers and
pulsational detonations.
Increasing scrutiny shows Type Ia aren't as uniform
as previously thought. What's more, new observations suggest that there
may be a `prompt' population of Type Ia, as well as super-Chandrasekhar
mass progenitors, both of which are very difficult to produce in the
standard model of supernovae. Understanding these events requires better
constraining the scenario which leads to explosion, and a more detailed
understanding of the ignition and burning. However, critically examining
both ignition/burning and the large scale mechanism simultaneously has
been impossible, making distinguishing between scenarios difficult.
Early simulations by M. Zingale, in part for
Zingale & Dursi (2007), of a rising flame being distorted and experiencing shear instabilities.
My most recent work on Type Ia supernova has focused on the small-scale
physics of burning and ignition, with the goal of producing inputs to
large-scale simulations. While the overall mechanism remains unclear,
it is almost certain that the source of the explosion is the incineration
of a carbon-oxygen white dwarf. Thus, questions of how burning would
proceed in a degenerate mixture of carbon and oxygen are relevant to
all Type Ia scenarios.
However, critically examining both the ignition/burning mechanisms
and the large scale mechanism simultaneously has been impossible,
which has made distinguishing between scenarios difficult.
I and others have put much work recently into understanding
important microphysical effects which are necessary inputs to large-scale
simulations. One example of my own work is the effect of flow on flame
speed. Another is work done this past summer
with two undergraduate students measuring ignition limits very accurately.
Both of these are important because large scale models cannot possibly
resolve both the ignition scenario under consideration and the ignition
or burning. Turbulent ignition, in particular, is likely to happen
first at extremely small scales. Now that these small scale effects are
better understood, they can be used as sub-grid inputs to large
scale simulations. I plan to perform these large-scale simulations
for at least the following two scenario in the coming three years.
Early work of this type that I was involved with concerned the
behaviour of detonations — supersonic combustion that propagates
by shock heating. Real detonations are highly multidimensional
structures, caused by a cellular instability that corrugates
the front, greatly modifying the structure behind the detonation.
In particular, the cellular structure can leave material that is only
partially burned. This is of great interest for Type Ia supernovae
because normally the existence of intermediate-mass (eg,
only partially-burned) elements in the ejecta would disfavor
detonations as an explosion mechanism; more detailed understanding
of cellular structure allows us to better understand the constraints
that observations place on detonation models. This work (Timmes
et al. 2000) placed an upper limit on the density at which
the cellular instability is likely to produce significant pockets of
partially-burned material.
I have also worked extensively on the behaviour of subsonic burning
- deflagrations, or flames - which almost certainly are the
first stage of burning of these supernovae. The instabilities
of these flames are crucial for understanding the speed of the
initial burning phase, and has been the focus of most of my work
(Dursi (2003),
Dursi, Zingale, et al., (2003).
Zingale & Dursi (2007)) , explaining the scales
on which these flames are stable (see, eg, the figure below).
Flame-turbulence interaction in Type Ia. Note that
the flame suppresses small-scale wrinkling at the front, while material
behind the front is greatly wrinkled.
Although much work has now gone into how burning propagates in a white
dwarf, the question of how the burning ignites remains an open question
— despite the fact that this is a necessary input to any model of a
Type Ia, and that differing ignition geometries can strongly affect the
final outcome of the explosion. Only recently has attention been focused
on ignition physics in a white dwarf.
In Dursi & Timmes (2006),
we examined the one-zone ignition timescale
for degenerate white dwarf material as temperature, density, and
composition vary. This work was initially planned to be a useful but
unremarkable tabulation of ignition times, which is a necessary step to
more complicated models; however, we found something rather surprising
— even quite modest increases in the metallicity of the white dwarf,
and in particular the Neon abundances, can significantly decrease the
ignition time, significantly raising the probability of a hotspot ignition
for more Neon-rich white dwarfs. This, as far as the authors are aware,
is the first hint that there could be a difference in the mechanism of
ignition between younger and older white dwarfs.
We also examined the ignition of a detonation from a point, and
find that a detonation requires a much larger energy input —
or coordination on much larger scales — to be successful than is
generally understood. Detonations are extremely sensitive to curvature,
and even modest curvatures make the propagation of a steady-state
detonation impossible. This means detonations at interesting densities
in a white dwarf likely require `matchheads' of up to kilometers in
size to launch a detonation. The stage in the explosion of a Type Ia
supernovae after ignition is propagation of a burning front and, while
detonations may play a role later, at early times the burning propagates
as a flame. In this case, where the burning occurs depends sensitively
on the balance of the burning, turbulence, and buoyancy; if the buoyancy
dominates, then the flame bubble will float harmlessly out of the star,
leaving intermediate-mass elements on the surface of the white dwarf
but not igniting the star. If the turbulence dominates, the flame
surface may be spread over a wide region of the core of the white dwarf,
aiding the explosion. In between these regimes, the flame bubble may
rise some distance and then become disrupted, essentially beginning the
large-scale burning at some finite radius from the center.
Stability diagram for a flame in a parallel magnetic field from
Dursi (2004).
I have also examined the effect of magnetic fields on flame instabilities.
Magnetic fields can have only limited roles in terrestrial flames,
where the relatively high magnetic resistivity mean that no local
variations in magnetic field strengths can persist for dynamically
interesting periods of time. For flames in astrophysical plasmas,
however, a strong enough magnetic field — one for which the Alfvén
speed exceeds the flame speed — can suppress the flame instability.
This can easily occur in X-ray bursts, but is less likely to play a
global role in the evolution of a Type Ia supernovae. However,
another interesting regime was uncovered in this work; when the flame
is trans-Alfvénic, the flame becomes non-evolutionary (as is the
case with trans-Alfvénic shocks), and flame-generated MHD turbulence
becomes possible.
Although much work has now gone into how burning propagates in a white
dwarf, the question of how the burning ignites remains an open question,
despite the fact that this is a necessary input to any model of a Type Ia,
and that it is known that differing ignition geometries can strongly effect
the final outcome of the explosion. Only recently has much work focused
on ignition physics in a white dwarf.
In Dursi & Timmes
(2005), we examine the one-zone ignition timescale for degenerate
white dwarf material as temperature, density, and composition vary.
This work was initially planned to be a useful but unremarkable tabulation
of ignition times, which is a necessary step to more complicated models;
however, we find something rather remarkable — even quite modest
increases in the metallicity of the white dwarf, and in particular
the Neon abundances, can significantly decrease the ignition time,
significantly raising the probability of a hotspot ignition for more
Neon-rich white dwarfs. This, as far as the authors are aware, is
the first hint that there could be a difference in the ignition of
younger and older white dwarfs.
We also examined the ignition of a detonation from a point, and
find that a detonation requires a much larger energy input —
or coordination on much larger scales — to be successful than is
generally understood. Detonations are extremely sensitive to curvature,
and even modest curvatures make the propagation of a steady-state
detonation impossible. This means detonations at interesting densities
in a white dwarf likely require `matchheads' of up to kilometers in
size to launch a detonation. The stage in the explosion of a Type Ia
supernovae after ignition is propagation of a burning front and, while
detonations may play a role later, at early times the burning propagates
as a flame. In this case, where the burning occurs depends sensitively
on the balance of the burning, turbulence, and buoyancy; if the buoyancy
dominates, then the flame bubble will float harmlessly out of the star,
leaving intermediate-mass elements on the surface of the white dwarf
but not igniting the star. If the turbulence dominates, the flame
surface may be spread over a wide region of the core of the white dwarf,
aiding the explosion. In between these regimes, the flame bubble may
rise some distance and then become disrupted, essentially beginning the
large-scale burning at some finite radius from the center.
The one-zone paper lays the groundwork for projects done
with two undergraduate students, D. Doucette and C. Hiratsuka,
examining more realistic hotspot ignition, including thermal diffusion physics
and hydrodynamics. These projects, which are underway now, will accurately
nail down the `flammability limits' for hotspots in a turbulent medium.
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 these
flows on the propagation of flames in Type Ia supernovae ( Zingale
& Dursi 2007). Beyond considering when the centre of the star is consumed by the
first flames, I have also shown the tendency of a rising flame bubble to
fragment (see also the first figure), 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 densities that an
increase in burning rate is needed to match observations. This novel
burning model will be examined in future work.
Future Work:
My work so far, then, examines burning instabilities, ignition in one-zone
(0d) 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.
Results from a simulation of spherically compressed reactive turbulence.
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.
Because the physics of the small-scale ignition does not depend
on the large-scale mechanism of the explosion, it will be possible to
use this model to critically examine `exotic' Type&nsbp;Ia mechanisms such
as mergers of white dwarf binaries, or pulsational detonation (eg,
as in the figure above.)
Pulsational Detonation
The questions I intend to answer through simulations are: Can any
reasonable infall from a failed explosion produce a detonation that will
then propagate through the star? Can it succeed without hotspots in
the center? If not, what sort of hotspots must exist - ie, how intense
does the central turbulence have to be for this to be a viable model?
And what roles do diffusive and turbulent transport have in preparing
the central regions?
Preliminary work on this project has begun; a parameter study of
small-scale spherical hotspot compression simulations have been run,
as have preliminary two-dimensional simulations of compressed reactive
turbulence. Next is to perform increasingly large-scale
simulations connecting these small scale results to the global problem
of a partially burned white dwarf re-collapse.
The first step is to perform one-dimensional simulations of the
re-collapse of a realistic burned white dwarf. This allows us
to connect to work already done, as well as extend it by including
more recent information as to how the initial
deflagration phase proceeds. These 1d global simulations then provide
the compression time profile for 2d and 3d simulations of compressed
reactive turbulence with and without rotation.
These computationally large-scale (but physically small-scale) simulations
will then give constraints for the properties of the turbulence and the
central region for the collapse to successfully ignite a detonation.
Meso-scale simulations then connect the two, determining if these
constraints are realizable.
White Dwarf Mergers
Some recent work has gone into examining the merging of white dwarfs as
a mechanism for more than a Chandrasekhar mass of carbon and oxygen to
ignite. The secondary dwarf is seen to be completely disrupted, and -
after some transient mass transfer - form an accretion disk. While a
‘flash’ is seen, no propagating burning occurs in the models to date.
But such models could not observe such an event; a typical size for a
detonation ignition would be hundreds of metres, while for a flame that
might be millimetres.
I propose to perform a series of large-scale white dwarf merger
simulations, with an eye to trying to better resolve the initial flash
from the transient transfer of material before a steady accretion
disk forms. Because resolving the white dwarf structure during the
merger is important, these are extremely large simulations; however,
the merger itself happens relatively quickly, meaning the total amount
of computational resources per simulation is reasonable. At least one
of the merger simulations will be computed with both SPH and AMR codes
to ensure that different numerical methods do not lead to significantly
different effects.
The global merger simulations and the initial mass transfer provide the
initial conditions for meso-scale and small-scale simulations examining
whether propagating burning can be ignited by the merger. If it is shown
that a detonation can be ignited, then the detonation can be mapped into
the global simulation to confirm that the detonation can disrupt the
system.
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.
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.
Grungy Gastrophysics and Cosmology 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 argues that the problem is really still very
much wide-open.
Really, Really Hot Flames, and How, In My Small Way, I Helped Save The Universe Wopat Student Talks, University of Chicago, Feb 2004 [PDF]
A (much!) less formal presentation of the same material above, for the
world famous Wopat talks.
![[Supernova 1994D]](./research/sn94d_hiz.jpg "[HST Image of Type Ia Supernova 1994D]")
