Cosmic Explosions in Three Dimensions: Asymmetries in Supernovae and Gamma-Ray Bursts
392
Cosmic Explosions in Three Dimensions: Asymmetries in Supernovae and Gamma-Ray Bursts
392Hardcover
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Product Details
| ISBN-13: | 9780521842860 |
|---|---|
| Publisher: | Cambridge University Press |
| Publication date: | 12/16/2004 |
| Series: | Cambridge Contemporary Astrophysics |
| Pages: | 392 |
| Product dimensions: | 6.69(w) x 9.61(h) x 0.87(d) |
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Cambridge University Press
0521842867 - Cosmic Explosions in Three Dimensions - Asymmetries in Supernovae and Gamma-Ray Bursts - Edited by Peter Höflich
Excerpt
Part I
Introduction
1
3-D explosions: a meditation on rotation (and magnetic fields)
J. C. Wheeler
Department of Astronomy University of Texas at Austin
1.1 Introduction: a brief time for history
There has been a great deal of progress in the thirty-five years or so that I have been working on supernovae and related topics. Two of the classical problems have been with us the whole time: what makes core collapse explode, and what are the progenitors of Type Ia supernovae? This workshop, indeed, the perspectives of three-dimensional astrophysics applied to these problems, gave encouraging evidence that breakthroughs may be made in both of these venerable areas.
On the other hand, what a marvelous array of progress has rolled forth with ever increasing speed. We have an expanded botany of supernovae classification: Type Ia, Ib, Ic, Type IIP, IIL IIb, IIn; but, of course, more than mere classification, a growing understanding of the physical implications of these categories. Neutron stars were discovered as rotating, magnetized pulsars when I was a graduate student, and the extreme form, magnetars, has now been revealed (Duncan & Thompson 1992). The evidence that we are seeing black holes in binary systems and the centers of galaxies has grown from suspicion to virtual certainty, awaiting only the final nail of detecting the black spot in a swirl of high-gravity effects. Supernova 1987A erupted upon us over 16 years ago and is still teaching us important lessons as it reveals its distorted ejecta and converts to a young supernova remnant before our eyes.
There have also been immense theoretical developments. Focus on core collapse has stimulated so much great work on neutrino transport: the invocation of weak neutral currents and neutrino-nucleon scattering; the understanding that neutrinos can and will become degenerate at the highest densities and the concomitant implications for the dynamics and the formation of the homologous core. More recently we have come to general understanding that a prompt shock is unlikely to make an explosion, but that significant layers of the proto-neutron star will be convective with important implications for the neutrino transport. Techniques of neutrino transport have evolved from simple diffusion to full Boltzmann transport. SN 1987A showed dramatically that we are on the right track, even if the details, even important physics, may be missing: core collapse with the predicted production of neutrinos does occur! In terms of the "other mechanism," our understanding has evolved from detonations to deflagrations, to the current paradigm of delayed detonation models. The recent understanding of the associated combustion physics has blossomed with the computational ability to do the required three-dimensional modeling.
Finally, the last few years have seen the birth and maturation of a field that was hinted at long ago, but came to fruition only recently, the systematic study of the polarization of supernovae. This technique has substantially altered our view of core collapse. It was only a few years ago that polarization was still regarded as an oddity, perhaps limited to a few peculiar events. In the last year, the idea that core collapse is asymmetric has become sufficiently accepted that papers are now written saying "as is well known, core collapse is asymmetric" without providing any reference to the hard labor required to establish that! Overnight, it seems, the wonders of the three-dimensional world have become revealed wisdom. The revelations of polarized core collapse have been the most distinct so far, but their implications are far from understood. The application of polarization to Type Ia supernovae had lagged somewhat in drama because the polarization is generally smaller, but this workshop served to provide evidence that important three-dimensional distortions are ubiquitous, and important, in Type Ia as well.
Besides all these developments that have been so central to the development of supernova science, the last few years have seen two outstanding developments that have cast supernovae research, already one of the most central and important in astrophysics, onto broader stages. What a time was 1997/1998! Careful studies of Type Ia supernovae revealed the acceleration of the Universe with the implication of the pervading dark energy. In virtually the same time frame, the discovery of optical transients associated with gamma-ray bursts and then SN 1998bw led to the connection of gamma-ray bursts with supernovae, probably some variety of Type Ic. For a mature field, the study of supernovae had a great deal of life left! Since Type Ia and Type Ic have been especially near and dear to me, this was about more excitement than my mature heart could stand.
I cannot do justice to all the great work on supernovae that has been done over my career, but I would like to touch on one other bit of history, a development that was critical for so much else that followed. I distinctly recall that when I was in graduate school there was a raging debate concerning the nature of the spectra of Type Ia, then called just Type I, supernovae. Some people argued that the spectrum near maximum consisted only of absorption lines and provided the interpretation of the absorption minima in terms of atomic features. Others insisted that the spectrum consisted purely of emission lines and provided an interpretation of the flux peaks, totally incongruent with the first interpretation, of course. David Branch provided the insight that we were looking at P-Cygni lines, hence a blended mix of emission and blue-shifted absorption. That was the insight needed to convince the world that the key feature in the spectrum of a Type Ia was Si Ⅱ. From that it followed that the presence of silicon and other intermediate mass elements ruled out pure detonation models. This was the base on which so much subsequent analysis of supernovae of all types was built. More work, especially from Bob Kirshner and colleagues revealed that, with patience, the spectrum does evolve to be dominated by emission lines. Type Ia, like all supernovae, eventually evolve to a "supernebular" phase.
1.2 Type Ia
The combination of ever more thorough searches both by people at the eyepiece and by computer-driven telescopes, subsequent multi-wavelength follow-up, and theoretical and computational study has brought the study of Type Ia supernova to an impressive level of maturity. After a spirited debate, the conclusion that Type Ia are not merely thermonuclear explosions in white dwarfs, but specifically explosions in carbon/oxygen white dwarfs of mass very nearly the Chandrasekhar mass is now essentially universally accepted (Höflich & Khokhlov 1996; Nugent et al. 1997; Lentz et al. 2001). Even more precisely, the paradigm of a slow initial subsonic deflagration phase followed by a rapid supersonic, shock-mediated detonation phase (Khokhlov 1991) has been richly successful in accounting for the observed properties of Type Ia (Höflich 1995). It accounts for the existence of iron-peak elements in the center of the explosion and layers of intermediate mass elements in the outer layers, essentially by design. It also gives a framework in which to understand the variety of light curve shapes with lower transition densities leading to less nickel, and dimmer, cooler, faster light curves (Höflich et al. 1996), and it has successfully made predictions about infrared spectra (Höflich et al. 2002) and polarization properties (Wang, Wheeler & Höflich 1997; Howell et al. 2001). Delayed detonation works!
This success has put focus on a wonderful physics problem, the deflagration to detonation transition, or DDT, that astrophysics shares with a host of terrestrial combustion issues. This is a hard problem on Earth or off! One of the most interesting developments in recent years has been the resonance of terrestrial and astrophysical combustion studies. There has been dramatic progress in understanding DDT in laboratory, shock-tube environments by means of sophisticated computational studies of shock-flame interactions (Khokhlov & Oran 1999) and DDT in enclosed environments where boundaries and reflected shocks play a key role (Khokhlov, Oran & Thomas 1999). Still, the astrophysical problem, one of unconfined DDT, remains elusive. This is a quintessential multi-dimensional problem, one for which several promising lines of attack are underway.
The wealth of knowledge of Type Ia revealed by optical studies is too large to summarize here, but it has been amplified and complemented in recent years by studies in the near infra-red. The NIR is an especially powerful spectral range to study because lines are less blended and the continuum is nearly transparent so one sees all the way through the ejecta with a single spectrum probing all the important layers simultaneously. This technique was pioneered for all supernovae by Peter Miekle and his collaborators and is rapidly coming to the fore as a major tool in the study of Type Ia. SN 1999by was a subluminous Type Ia that was, not incidentally, significantly polarized (Howell et al. 2001). Höflich et al. (2002) showed that a delayed detonation model selected to match the light curve provided a good agreement with the NIR spectra and revealed the products of explosive carbon burning in the outer layers and products of incomplete silicon burning in deeper layers. The results were inconsistent with pure deflagration models or merger models that leave substantial unburned matter on the outside. The data also seemed incompatible with the mixing of unburned elements into the center as predicted by pure deflagration 3-D models. Three-dimensional models in which the inner unburned matter undergoes a detonation, the current most realistic manifestation of the delayed detonation paradigm as presented here by Gamezo et al. alleviate that problem. Marion et al. (2003) have presented NIR spectra of "normal" Type Ia (see also Hamuy 2002) and shown that the outer layers of intermediate mass elements are not mixed, that very little unburned carbon remains in the outer layers, and perhaps revealed Mn, a sensitive probe of burning conditions.
Another important development concerns work on the quasi-static phase of carbon burning that follows carbon ignition and precedes dynamic runaway. This important "smoldering" phase had not been critically re-examined since the initial study of Arnett (1969). Höflich & Stein (2002) showed that the convective velocities in this phase can exceed the initial speeds of the subsequent deflagration front. This means that the "pre-processing" of the white dwarf by this smoldering phase and the resulting velocity field, rather than the pure Rayleigh-Taylor driven deflagration, will dominate the early propagation of the burning front. This is a crucial, multidimensional, insight that will foment much work in the near future to understand all the implications.
Finally, it is necessary to repeat that polarization studies have revealed that Type Ia are polarized and hence asymmetric (Wang, Wheeler & Höflich 1997). It may be that the subluminous variety are more highly polarized and perhaps more rapidlly rotating than the "normal" type (Howell et al. 2001). It may also be that, although the polarization is generally low, all Type Ia are polarized at an interesting level if appropriate, sufficiently accurate observations are made (Wang et al. 2003a). This has clear implications for the quest to answer the old problem of whether Type Ia arise in binary systems and, if so, as we all believe, what sort? The asymmetries might also be teaching us lessons yet ungleaned about the combustion process which is undoubtedly complex and three dimensional. The asymmetries must be understood in order to use Type Ia with great confidence as we move to the next phase of cosmological studies where exceptionally precise photometry and tight control of systematic effects will be necessary to probe the equation of state of the dark energy.
In any case, the lesson of recent history and of this workshop is that Type Ia supernovae are three dimensional!
1.3 Asymmetric core collapse
If anything, the polarization studies have had even more dramatic impact on core collapse supernovae. All core collapse supernovae adequately observed are found to be polarized and hence asymmetric in some way (Wang et al. 1996; Wang et al. 2001, 2002, 2003b; Leonard et al. 2000; Leonard & Filippenko 2001; Leonard et al. 2001, 2002). Many of these events are substantially bi-polar (Wang et al. 2001). The fact that the polarization is higher as one sees deeper in and is higher when the hydrogen envelope is less, strongly indicates that the very machine of the explosion deep in the stellar core is asymmetric and probably predominantly bi-polar. SN 1987A reveals similar evidence (Wang et al. 2002). Other famous "spherically symmetric" supernovae are those that gave rise to the Crab Nebula and to Cas A.
Complementary computational work has shown that jet-induced explosions can produce the qualitative asymmetries that are observed (Khokhlov et al. 1999, see also MacFadyen et al. 2001 Zhang, et al. 2003). Khokhlov & Höflich (2001) and Höflich, Khokhlov & Wang (2001) have shown that asymmetric nickel deposition by a jet-like flow can produce polarization by asymmetric heating and ionization even in an otherwise spherically-symmetric density distribution. This very plausibly accounts for the early low polarization in Type Ⅱ supernovae that grows as the underlying asymmetry is revealed.
The large question remains as to what causes the jet-like flow. My bet is that this involves rotation and magnetic fields at the deepest level. Rotation alone can affect neutrino deposition, but the case can be made that rotation without magnetic fields is highly unlikely. Akiyama et al. (2003) have presented a proof of principle that the physics of the magneto-rotational instability (MRI: Balbus & Hawley 1991, 1998) is inevitable in the context of the differentially-rotating environment of protoneutron stars. The magnetic fields can in turn affect the neutrino transport. The ultimate problem of core collapse is intrinsically three-dimensional involving rotation, magnetic fields, and neutrino transport. We have known this all along (despite, not because of, cheap shots after core collapse talks in which some joker always asks "but what about rotation?" or "but what about magnetic fields?"), but the new polarization observations demand a new, integrated view. This makes a devilishly hard problem even harder. Progress will come by isolating and understanding pieces of the problem and eventually sticking them together.
1.4 The magneto-rotational instability and core collapse
The advantage of the MRI to generate magnetic field is that while it works on the rotation time scale of Ω-1 (as does field-line wrapping), the strength of the field grows exponentially. This means that from a plausible seed field of 1010 to 1012 G that might result from field compression during collapse, only ∼7-12 e-folds are necessary to grow to a field of 1015 G. That is only (7-12)/2π ∼ 1-2 full rotations or ∼10-20 ms for expected initial rotation periods of order 10 ms. Furthermore, while the growth time may depend on the seed field, the final saturation field is independent of the seed field (unlike a linear wrapping model that ignores the complications of reconnection, see Wheeler et al. 2000, 2002, for examples and other references).
Core collapse will lead to strong differential rotation near the surface of the protoneutron star even for initial solid-body rotation of the iron core (Kotake, Yamada & Sato 2003; Ott et al. 2004). The criterion for instability to the MRI is a negative gradient in angular velocity, as opposed to a negative gradient in angular momentum for the Rayleigh dynamical instability. This condition is broadly satisfied at the surface of a newly formed neutron star during core collapse and so the growth of magnetic field by the action of the MRI is inevitable. More quantitatively, when the magnetic field is small and/or the wavelength is long (kvA < Ω) the instability condition can be written (Balbus & Hawley 1991, 1998):
where N is the Brunt-Väisälä frequency. Convective stability will tend to stabilize the MRI, and convective instability to reinforce the MRI. The saturation field given by general considerations and simulations is approximately given by the condition: va ∼ λΩ where λ ≲ r or B2 ∼ 4πρr2Ω2 where vA is the Alfvén velocity.
These physical properties were illustrated in the calculations of Akiyama et al. (2003) who used a spherically-symmetric collapse code to compute the expected conditions, instability, field growth and saturation. Akiyama et al. assumed initial rotation profiles, solid body or differential, invoked conservation of angular momentum on shells that should, at least, give some idea of conditions in the equatorial
Fig. 1.1. Angular velocity, field strength and MHD luminosity (in units of 1051 erg s-1) for a representative initial differential rotation of the iron core as a function of time from Akiyama et al. (2003)
plane and computed regions of MRI instability. They assumed exponential growth to saturation. For sub-Keplerian post-collapse rotation, Akiyama et al. found that fields can be expected to grow to 1015 to 1016 G in a few tens of milliseconds. The resulting characteristic MHD luminosity (cf. Blandford & Payne 1982) is:
If this power can last for a significant fraction of a second, a supernova could result. Figure 1.1 shows the results for a model in which the iron core began with a smoothly decreasing distribution of angular velocity and a central value of Ω = 1 s-1.
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