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  Proposal No.                           **SI**          **DCG**

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**[General LDRD Proposal Template]{.underline}**

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This is a  PRE- or a  FULL (**Check One)** Proposal submitted to the
 Competitive Grants or  Strategic (**Check One**) component of LDRD.

**Project Title:** Nuclear Theory for Supernovae

**Investigator(s):** J.W. Truran, U. Chicago.

**[Check ONE box only for each of the two questions
below:]{.underline}**

The proposed research and investigators  do,  do not comprise a
multidisciplinary effort.

The proposed research is primarily of  basic,  applied,  development
character. \[See General Guidance document for definitions\]

**Fill in percentages for the project character and project relevance
([each line must sum to 100]{.underline}%)**

Project Character: Theory [100]{.underline} % Simulation/Modeling %
Experiment % Software Development %

Project Relevance: National Defense % Homeland Security (HS) %
Non-Defense/Non-HS [100]{.underline} %

+-------------+--------+--------+--------+--------+--------+--------+
| **(1)       | **T    | FY     | FY     | # F    | FY     | FY     |
| Funding     | OTAL** | 2005   | 2006   | Y 2007 | 2008   | 2009   |
| Profile**   |        |        |        |        |        |        |
|             | **(All |        |        |        |        |        |
| **(\$K)**   | Ye     |        |        |        |        |        |
|             | ars)** |        |        |        |        |        |
+-------------+--------+--------+--------+--------+--------+--------+
| **Staff/STA |        |        | 95     | 120    |        |        |
| Effort**    |        |        |        |        |        |        |
+-------------+--------+--------+--------+--------+--------+--------+
| **Post Doc  |        |        | 75     | 86     |        |        |
| Effort**    |        |        |        |        |        |        |
+-------------+--------+--------+--------+--------+--------+--------+
| **M&S**     |        |        |        |        |        |        |
+-------------+--------+--------+--------+--------+--------+--------+
| **Operating |        |        | 170    | 206    |        |        |
| Total**     |        |        |        |        |        |        |
+-------------+--------+--------+--------+--------+--------+--------+
| **Capital   |        |        |        |        |        |        |
| Equip\***   |        |        |        |        |        |        |
+-------------+--------+--------+--------+--------+--------+--------+

> **(2) Scientific/Technical Opportunity**
>
> The origin of heavy elements in the universe is a key problem of
> longstanding which requires collaboration between nuclear physics and
> astrophysics. An accurate description of stellar nucleosynthesis
> demands further investigation of supernovae, neutron stars and the
> physics of dense nuclear matter. A future exotic beam facility will
> enable the terrestrial measurement of reaction rates that are expected
> to play an important role in nucleosynthesis. Argonne researchers in
> experimental nuclear physics are already active in addressing critical
> reaction rate and other nuclear physics needs for astrophysical
> problems. Argonne also needs a consolidated nuclear theory and
> theoretical nuclear astrophysics capacity to secure a frontline
> position in this field.
>
> **(3) Benefits/beneficiaries/customers**
>
> Our approach will lead to a material growth in capacity and expertise
> in Theory at Argonne. The substantial nature of the problems we
> propose to address means that progress will require the full-time
> attention of a postdoctoral fellow, and a commitment of effort from a
> senior researcher. The proposed research will result in both nuclear
> theory inputs for specific astrophysical problems and refined
> theoretical methods that will be of use far into the future. It will
> have a major impact on the experimental programs on-site.
>
> \(4\) Hypothesis/Objectives/Approach (nature of work, deliverables,
> milestones, leveraging of external\
> activities, FY2007 work and expected results)
>
> **Focus**
>
> We propose to build efforts at the forefront of modern nuclear theory
> that emphasize applications to astrophysics, to current experimental
> research at Argonne, and to planning for a future exotic beam
> facility. A key area of research in nuclear astrophysics focuses on
> nucleosynthesis. The heavy element content of the Universe at any
> point in its history reflects the integrated nucleosynthesis
> contributions from earlier stellar generations, and can be used as a
> tool both to probe its dynamical and star formation histories and to
> constrain models of stellar and supernova nucleosynthesis. A correct
> reading of this history requires knowledge of the nuclear processes
> occurring in stars and supernovae which contribute to nucleosynthesis
> -- and of the underlying nuclear physics. Progress in this field is
> built on a strong interaction between experimental and theoretical
> nuclear physicists and researchers in stellar astronomy and nuclear
> astrophysics. This proposal will create a new strength at Argonne that
> can address this fundamentally important research area at the
> forefront of modern physics.
>
> **Background**
>
> James Truran, who holds a joint position in the ANL Physics Division
> and the Astronomy and Astrophysics Department of the University
> Chicago, is an internationally recognized pioneer of, and expert in,
> nuclear astrophysics. He has particular expertise in the nuclear
> physics of the *r*-process, and an active program in this area. This
> forms an ideal complement to existing expertise in the Physics
> Division, which focuses on nuclear data needs for astrophysics.
>
> **Proposed Research**
>
> Recent results from spectroscopic analyses of metal-poor stars are
> serving to impose increasingly stringent constraints upon the possible
> sites of the *r*-process. Researchers in both experimental and
> theoretical nuclear physics at Argonne are addressing critical
> problems in nucleosynthesis. Using the best available nuclear physics
> input, we propose to perform nucleosynthesis calculations appropriate
> to diverse astrophysical environments -- e.g. massive stars, Type Ia
> supernovae and Type II supernovae. This will also involve the use of
> theoretical estimates of relevant nuclear properties, such as beta
> decay lifetimes and neutron capture cross-sections, notably for nuclei
> far from the Valley of Beta Stability. Our calculations will test
> stellar and supernova model predictions, help us to better interpret
> recent observations of the compositions of stars in our and other
> galaxies, and by so doing provide significant constraints on the
> natures of the earliest stellar populations in the Universe.
>
> **Mode of Operation**
>
> Achieving the project goals will require a dedicated application of
> effort, combining expertise in nuclear physics and astrophysics. The
> Theory Group provides the former, and James Truran provides the
> latter. In particular, he provides a strong connection to the
> ASC/Alliances Center for Astrophysical Thermonuclear Flashes, based at
> the University of Chicago, and a theory link with the Joint Institute
> for Nuclear Astrophysics, a Physics Frontier Center. This combination
> joins capability and resources in large scale computation dedicated to
> explosive astrophysical events with a center whose goal is to enable
> communication and collaborations across field boundaries. An
> appropriately trained postdoctoral fellow is required at the focal
> point of our effort. The fellow will capitalize on the environment
> provided and work with us to build a modern and quantitative
> understanding of *r*-process conditions.
>
> **FY07 Work and Expected Results**
>
> We will obtain a detailed and comprehensive picture of the nuclear
> evolution of matter in galaxies resulting from stellar and supernova
> processing, through the use of complex and quantitative nuclear
> reaction networks. This will be used to address broader astrophysical
> questions, such as the observed trends in galactic enrichment by heavy
> elements as reflected in the abundance history of our Milky Way galaxy
> and nearby galaxies. These results will also serve both to identify
> critical nuclear parameters to be determined with future experiments
> and to better constrain stellar evolution and supernova models.
>
> \(5\) Resources required (dependencies, key skills, new hires)
>
> We propose to provide 49% of the academic year effort of James Truran
> and 100% support for a postdoctoral fellow in FY07. Large-scale
> computing resources will be provided by the state-of-the-art
> facilities at Argonne National Laboratory.
>
> **(6) Future funding opportunities (direct follow-on and related
> programs) for next year and subsequent\
> years**
>
> This proposal will expand contemporary nuclear astrophysics in the
> Physics Division. The most recent *University of Chicago Review* of
> the Physics Division and the *2005* *Nationwide Review of National
> Laboratory Nuclear Theory* identified this as an essential part of the
> Division's development plans into future. We are currently seeking
> program funds to support this expansion. In addition, the development
> of on-site expertise that we secure with this program will establish
> the kernel of a Topical Center focused on the theory necessary for
> full capitalization on the nation\'s investment in an exotic beam
> facility. Topical Centers of this type were recommended in the Report
> of the NSAC Nuclear Theory Subcommittee. The research effort we
> propose will guarantee our competitiveness in bidding for related new
> program funds from DOE.
>
> **(7) Prior year(s) accomplishments relative to milestones listed in
> paragraph (4) above**

-   *The Strange Star Surface: A Crust with Nuggets*

> Strange quark stars, made entirely of quark matter in a deconfined
> state, can exist if dense quark matter at sufficiently high density is
> absolutely stable at zero pressure. Based upon a picture of
> homogeneous quark matter satisfying local charge neutrality, it was
> widely accepted that the surface of quark stars was characterized by
> an enormous density gradient (10^26^ g/cm^4^) and large electric
> fields (10^16^ V/cm). We re-examined the surface composition of
> strange stars and found that, provided the surface tension of quark
> matter is small enough, the homogeneous phase is unstable against the
> formation of a heterogenous one consisting of quark nuggets immersed
> in a uniform background of electrons.We analyzed the phase stability
> and structure of quark matter in a model-independent way by
> identifying two quantities, the charge density and the charge
> susceptibility, that determine the criterion for phase separation into
> quarks and electrons. We evaluated this criterion in the framework of
> the Bag model of dense quark matter, and found that the Gibbs free
> energy would be lower in a mixed phase in which quark matter lumps
> together to form positively charged nuggets of size \~10 fm. The mixed
> phase satisfies global charge neutrality and its structure is
> particularly sensitive to finite size effects.If strange quark stars
> possess a heterogeneous crust, the thermal conductivity and neutrino
> opacity is very similar to that in the crust of neutron stars, making
> a distinction between the two classes of stars quite difficult. The
> presence of a solid crust at low temperatures can also help explain
> the observed glitches in the spin-period of neutron stars. An article
> describing this work was published^1^ and a précis appeared in
> Physical Review Focus.^2^
>
> ^1^ P. Jaikumar, S. Reddy and A. W. Steiner, Phys. Rev. Lett. 96,
> 041101 (2006).
>
> ^2^ P. Jaikumar, *et al*., Phys. Rev. Focus, 3 February 2006.

-   *Bremsstrahlung neutrinos from electron-electron scattering in a
    relativistic degenerate electron plasma*

> Energy loss through neutrino emission is the driving force in the
> evolution of supernovae and neutron stars. We studied neutrino pair
> bremsstrahlung emission in collisions of relativistic particles
> (electrons) including medium modifications of photons exchanged in the
> collision and other many-body effects. Soft photon exchange in the
> magnetic sector is Landau damped, and we provided the first estimate
> of this effect on the neutrino emission rate. Our results revealed
> that bremsstrahlung pair emission can dominate over other sources of
> neutrino emission, particularly in the superfluid crust of neutron
> stars just above nuclear saturation density and in the core, if it is
> in a superfluid state. The photon exchange in electron-electron
> scattering was described by the one-loop resummed photon propagator in
> the hard dense loop limit, and corrections to the emissivity from
> multiple photon exchange, vertex dressing, as well as non-Fermi liquid
> effects were shown to be small. The neutrino emissivity was found to
> be enhanced by several orders of magnitude at low temperatures
> (T≤10^8^K) in comparison with previous works that neglected Landau
> damping effects. Based upon a comparison with other neutrino emission
> mechanisms, we also established the relevance of neutrino
> bremsstrahlung rates for cooling of black-hole accretion tori.
> Neutrino pair bremsstrahlung becomes the dominant cooling process in
> the low density (ρ≤ 10^10^ g/cm^3^) and low temperature ((T≤10^10^K)
> regions of the black-hole accretion torus. It also provides the most
> copious source for antineutrinos which are believed to play an
> important role in triggering Gamma ray bursts in the collapsar
> scenario. An article describing this work was published.^1^
>
> ^1^P. Jaikumar, C. Gale and D. Page, Phys. Rev. D**72**, 123004
> (2005).

-   *Direct urca neutrino rate in color superconducting quark matter*

> The direct urca process of neutrino emission in quark matter
> (*d→u*+*e*+¯*ν*~e~ and *u*+*e→d*+*ν~e~*) is the most eﬃcient cooling
> mechanism for neutron stars containing unpaired quark matter in their
> core. If the quark matter is in a superconducting phase, neutrino
> emission is modiﬁed by the presence of the pairing gap. We evaluated
> the impact of pairing on the neutrino emission rate in fully and
> partially gapped regimes. Our results showed that the pairing-induced
> suppression of the rate below the critical temperature *T*~c~ was not
> as severe as previously believed, and that Cooper pair-breaking and
> recombination makes an important contribution to the total neutrino
> emissivity. We explored a minimal realistic scenario of two-ﬂavour
> (*u*, *d*) quark matter, with spin-singlet pairing, constrained by
> charge neutrality and *β--*equilibrium. In this case, we found that
> the quark dispersion relation could be either fully or partially
> gapped. Including interaction corrections linear in the strong
> coupling parameter *α~s~*, pairing-induced phase space corrections and
> Cooper pair-breaking and recombination eﬀects, we found the neutrino
> rate was: (1) suppressed only linearly on a material domain of
> temperatures below the critical temperature *T*~c~ for the fully
> gapped phase; and (2) moderately enhanced above that of unpaired quark
> matter at low temperatures in the partially gapped phase. Our
> calculation in the two-ﬂavor regime is indicative of similar results
> for the neutrino rate in phases of gapped quark matter with three
> ﬂavors. Considered together with neutrino opacities, which are large
> at *T\~T~c~*, our results are pertinent to any detailed computation of
> the cooling history of a star that undergoes a phase transition from
> nuclear matter to superconducting quark matter. An article describing
> this work was published.^1^
>
> ^1^ P. Jaikumar, C. D. Roberts and A. Sedrakian, Phys. Rev. C **73**,
> 042801(R) (2006).

-   *Sedimentation and Type I X-ray Bursts at Low Accretion Rates*

> An ionized plasma in a gravitational field develops an electric field
> sufficient to levitate the ions and ensure overall charge neutrality.
> When there is more than one species of ion present, the ions will
> experience a differential force: lighter ions float upward (defined by
> the local gravitational field) and heavier ions sink downward. The
> high surface gravity of compact objects makes the timescale for
> isotopes to stratify often comparable to or faster than other
> timescales of interest. In particular, sedimentation of heavier
> isotopes 1 is important in understanding the surface compositions of
> white dwarf stars (Vauclair et al. 1979) and isolated neutron stars
> (Chang & Bildsten 2003). For accreting white dwarfs, diffusion between
> the accreted envelope and underlying white dwarf was proposed as a
> means to enrich the ejecta of classical novae in CNO isotopes
> (Prialnik & Kovetz 1984; Iben, Fujimoto, & MacDonald 1992).
>
> Accreting neutron stars, with their strong surface gravity ≈ 2×10^14^
> cm s^-2^, are an ideal place to look for the effects of sedimentation.
> The sedimentation of heavy elements and resulting nucleosynthesis in
> the envelope of isolated neutron stars cooling from birth was first
> described by Rosen (1969) and has more recently been studied in detail
> by Chang & Bildsten (2003, 2004). For accreting neutron stars, the
> rapid stratification removes heavy nuclei from the photosphere for
> accretion rates dM/dt ≤ 10^-12^ M~~ yr^-1^ (Bildsten, Salpeter, &
> Wasserman 1992). Deeper in the neutron star envelope, the
> differentiation of the isotopes can alter the nuclear burning, namely
> unstable H/He burning and the rapid proton-capture process
> (rp-process), that powers Type I X-ray bursts. Some estimates of the
> relative importance of sedimentation and diffusion were made by
> Wallace, Woosley, & Weaver (1982), who studied accretion at rates
> dM/dt = 2×10^-11^ M~~ yr^-1^ and argued that the partial separation
> of the H and He layers might play a role in setting the ignition
> conditions and subsequent burst nucleosynthesis.
>
> Neutron stars, with their strong surface gravity, have interestingly
> short timescales for the sedimentation of heavy elements. Motivated by
> observations of Type I X-ray bursts from sources with extremely low
> persistent accretion luminosities, L~X~ \< 10^36^ ergs s^-1^ (0.01
> L~Edd~), we studied how sedimentation effects the distribution of
> isotopes and the ignition of H and He in the envelope of an accreting
> neutron star. For local mass accretion rates dm/dt \< 10-2 dm~Edd~/dt
> (for which the ignition of H is unstable), where dm~Edd~/dt = 8.8 x
> 10^4^ g cm^-2^ s^-1^, the helium and CNO elements settle out of the
> accreted fuel layer before the temperature is reached at which H would
> ignite. Using one-zone calculations of the thermonuclear burning, we
> identified a range of accretion rates for which the unstable ignition
> of hydrogen does not trigger unstable helium burning. This range
> depends on the emergent flux from reactions in the deep neutron star
> crust; for F = 0.1 MeV ((dm/dt)/m~u~), the range is 3x10^-3^
> dm~Edd~/dt ≤ dm/dt ≤ 10^-2^ dm~Edd~/dt. We speculated that sources
> accreting in this range will build up a massive He layer that later
> produces an energetic and long X-ray burst. At mass accretion rates
> lower than this range, we found that the hydrogen flash leads to a
> strong mixed H/He flash. Surprisingly, even at accretion rates dm/dt ≥
> 0.1 dm~Edd~/dt, although the H and He do not completely segregate, the
> H abundance at the base of the accumulated layer is still reduced.
> While following the evolution of the X-ray burst was beyond the scope
> of this introductory study, we noted that the reduced proton-to-seed
> ratio favors the production of 12C, an important ingredient for
> subsequent superbursts.

-   *Capturing the Fire: Flame Energetics and Neutronization for Type Ia
    Supernova Simulations*

> Type Ia supernovae (SNe) are bright explosions characterized by a lack
> of hydrogen spectral features and strong silicon P Cygni features near
> maximum light. The currently favored interpretation is the disruption
> of a near-Chandrasekhar-mass C/O white dwarf by a thermonuclear
> runaway. These events are fascinating in and of themselves and are
> important both for their contribution to the cosmic abundance of
> iron-peak elements and for their role as standard candles.
>
> Models of Type Ia SNe necessarily involve a mechanism for incinerating
> the star by a thermonuclear runaway, and the nature of this mechanism
> is the subject of contemporary research. In the explosion, a
> thermonuclear flame propagates through the C/O fuel of the white dwarf
> as either a subsonic deflagration front or a supersonic detonation
> wave and releases sufficient energy to unbind the star. However,
> models involving either a pure deflagration or a pure detonation have
> traditionally been unable to provide an explanation for both the
> observed expansion velocities and the spectra produced by ejecta that
> is rich in both intermediate-mass and iron-peak elements. Recent work,
> however, suggests th at a fast deflagration alone may provide
> sufficient energy to unbind the star.
>
> There has been considerable progress recently in hydrodynamic
> simulations of deflagrations of C/O white dwarfs that model the entire
> star. This is a complicated endeavor, predominantly due to the vast
> range of length scales: the laminar flame width is \~ 10^-3^ -- 10 cm,
> some 8 to 12 orders of magnitude smaller than the stellar radius.
> Because the computational requirements for simulations with these
> disparate scales demand resources well beyond current capabilities,
> multidimensional Type Ia models must make use of an appropriate
> sub-grid-scale model for the evolution of the thermonuclear burning
> front. Moreover, large-scale simulations are very demanding of
> computational resources, and it is not feasible at present to include
> enough isotopes to allow for directly computing the reaction kinetics.
> A realistic model must nevertheless accurately describe the nuclear
> energy that is released, the timescale on which it is released, and
> the compositional changes that occur in the flame. In addition, the
> burned material continues to evolve after the passage of the flame due
> to both weak interactions and hydrodynamic evolution, and realistic
> simulations must describe this \`\`post-flame\" evolution.
>
> We studied the nuclear burning that occurs during C/O deflagrations,
> with the goal of providing a realistic flame model for simulations of
> Type Ia supernovae. Our flame model builds on the
> advection-diffusion-reaction model of Khokhlov and includes electron
> screening and Coulomb corrections to the equation of state in a
> self-consistent way. We calibrated this model flame\-\--its energetics
> and timescales for energy release and neutronization\-\--with
> self-heating reaction network calculations that include both these
> Coulomb effects and up-to-date weak interactions. The burned material
> evolves post-flame due to both weak interactions and hydrodynamic
> changes in density and temperature. We developed a scheme to follow
> the evolution, including neutronization, of the NSE state subsequent
> to the passage of the flame front. As a result, our model flame is
> suitable for deflagration simulations over a wide range of initial
> central densities and can track the temperature and electron fraction
> of the burned material through the explosion and into the expansion of
> the ejecta.
>
> The importance of such a detailed consideration of the consequences of
> nuclear burning and neutronization via electron captures is to provide
> an accurate determination of the ^56^Ni abundance in the ejecta of a
> Type Ia supernova. For a value of Y~e~ ≈ 0.5, the matter in nuclear
> statistical equilibrium following expansion and cooling is dominated
> by the self-conjugate nucleus ^56^Ni. At high densities, however,
> electron captures on both protons and heavy nuclei effect
> neutronization of the matter and Y~e~ falls below 0.5. Such neutron
> enrichment favors neutron-rich isotopes at the expense of ^56^Ni.
> Since the brightness of SNe Ia at maximum is a direct function of the
> mass of ^56^Ni ejected, an accurate determination of the composition
> of the ejecta is critical to the use of SNe Ia as distance indicators.

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