arXiv subjects
Publications and source records attributed to Bradley S. Meyer.
We show that certain digraphs with the same vertex set but different arc sets have the same sum over the weights of all arborescences with a given root vertex. We relate our results to the Matrix-Tree Theorem and show how they provide a graphical approach for factoring matrix determinants.
We present a version of the matrix-tree theorem, which relates the determinant of a matrix to sums of weights of arborescences of its directed graph representation. Our treatment allows for non-zero column sums in the parent matrix by adding a root vertex to the usually considered matrix directed graph. We use our result to prove a version of the matrix-forest, or all-minors, theorem, which relates minors of the matrix to forests of arborescences of the matrix digraph. We apply the theorems to calculations of the time-evolution of a system with discrete states and then consider two strategies using these theorems to compute determinants.
Nuclear yields are powerful probes of supernova explosions, their engines and their progenitors. In addition, as we improve our understanding of these explosions, we can use nuclear yields to probe dense matter and neutrino physics, both of which play a critical role in the central supernova engine. Especially with upcoming gamma-ray detectors that can directly detect radioactive isotopes out to increasing distances from gamma-rays emitted during their decay, nuclear yields have the potential to provide some of the most direct probes of supernova engines and stellar burning. To utilize these probes, we must understand and limit the uncertainties in their production. Uncertainties in the nuclear physics can be minimized by combining both laboratory experiments and nuclear theory. Similarly, astrophysical uncertainties caused by simplified explosion trajectories can be minimized by higher-fidelity stellar-evolution and supernova-engine models. This paper reviews the physics and astrophysics uncertainties in modeling nucleosynthetic yields, identifying the key areas of study needed to maximize the potential of supernova yields as probes of astrophysical transients and dense-matter physics.
The astrophysical origin of elements synthesized through the rapid neutron capture process ($r-$process) is a long standing mystery. The hot and dense environments of core-collapse supernovae have been suggested as potential $r-$process sites, particularly the neutrino-driven wind from the newly-born protoneutron star (PNS). Wind models that neglect the potential effects of strong magnetic fields and/or rapid rotation of the PNS typically fail to achieve the necessary conditions for production of the third $r-$process peak, but robustly produce a limited or weak $r-$process for neutron-rich winds. Axisymmetric magnetohydrodynamic simulations of rotating and non-rotating PNS winds with magnetar-strength fields reveal that high entropy material is quasi-periodically ejected from the equatorial closed zone of the PNS magnetosphere. Here, we post-process tracer particle trajectories from these simulations using a nuclear reaction network in order to explore the resulting nucleosynthesis across a range of PNS magnetic field strengths, rotation rates, and neutrino luminosities (cooling phase after core-bounce). We find that a robust $r-$process up to and beyond the third peak is generic to magnetar birth, even for magnetic fields as weak as $\sim 5\times 10^{14}$ G. Depending on the distribution of magnetic field strengths and rotation at birth, we estimate that magnetized PNS winds could account for $\sim 5-100\%$ of the Galactic $r-$process inventory, extending up to the third peak. The robust $r-$process in our calculations is accompanied by overproduction of elements with mass number $\rm A\lesssim 120$ compared to the Solar abundances. We also find that $^{92}\rm Mo$ (a $p-$isotope) is produced in significant quantities in neutron-rich winds.
We provide an overview of the isotopic signatures of presolar supernova grains, specifically focusing on 44Ti-containing grains with robustly inferred supernova origins and their implications for nucleosynthesis and mixing mechanisms in supernovae. Recent technique advancements have enabled the differentiation between radiogenic (from 44Ti decay) and nonradiogenic 44Ca excesses in presolar grains, made possible by enhanced spatial resolution of Ca-Ti isotope analyses with the Cameca NanoSIMS (Nano-scale Secondary Ion Mass Spectrometer) instrument. Within the context of presolar supernova grain data, we discuss (i) the production of 44Ti in supernovae and the impact of interstellar medium heterogeneities on the galactic chemical evolution of 44Ca/40Ca, (ii) the nucleosynthesis processes of neutron bursts and explosive H-burning in Type II supernovae, and (iii) challenges in identifying the progenitor supernovae for 54Cr-rich presolar nanospinel grains. Drawing on constraints and insights derived from presolar supernova grain data, we also provide an overview of our current understanding of the roles played by various supernova types - including Type II, Type Ia, and electron capture supernovae - in accounting for the diverse array of nucleosynthetic isotopic variations identified in bulk meteorites and meteoritic components. We briefly overview the potential mechanisms that have been proposed to explain these nucleosynthetic variations by describing the transport and distribution of presolar dust carriers in the protoplanetary disk. We highlight existing controversies in the interpretation of presolar grain data and meteoritic nucleosynthetic isotopic variations, while also outlining potential directions for future research.
We report C, N, Si, and Al-Mg isotope data for 39 presolar X silicon carbide (SiC) and four silicon nitride grains - a group of presolar grains that condensed in the remnants of core-collapse Type II supernovae (CCSNe) - isolated from the Murchison meteorite. Energy dispersive X-ray (EDX) data were used to determine the Mg and Al contents of the X SiC grains for comparison with the Mg/Al ratios determined by secondary ion mass spectroscopy (SIMS). Previous SIMS studies have used O-rich standards in the absence of alternatives. In this study, the correlated isotopic and elemental data of the X SiC grains enabled accurate determination of the initial 26Al/27Al ratios for the grains. Our new grain data suggest that (i) the literature data for X grains are affected to varying degrees by asteroidal/terrestrial contamination, and (ii) the Al/Mg ratios in SiC are a factor of two (with +/-6% 1 sigma uncertainties) lower than estimated based on the SIMS analyses that used O-rich standards. The lowered Al/Mg ratios result in proportionally higher inferred initial 26Al/27Al ratios for presolar SiC grains. In addition, the suppression of asteroidal/terrestrial contamination in this study leads to the observation of negative trends for 12C/13C-30Si/28Si and 26Al/27Al-30Si/28Si among our CCSN grains. We discuss these isotope trends in the light of explosive CCSN nucleosynthesis models, based on which we provide new insights into several non-traditional CCSN nucleosynthesis processes, including explosive H burning, the existence of a C/Si zone in the outer regions of CCSNe, and neutrino-nucleus reactions in deep CCSN regions.
Nuclear isomers are populated in the rapid neutron capture process (r process) of nucleosynthesis. The r process may cover a wide range of temperatures, potentially starting from several tens of GK (several MeV) and then cooling as material is ejected from the event. As the r-process environment cools, isomers can freeze out of thermal equilibrium or be directly populated as astrophysical isomers (astromers). Two key behaviors of astromers -- ground state<->isomer transition rates and thermalization temperatures -- are determined by direct transition rates between pairs of nuclear states. We perform a sensitivity study to constrain the effects of unknown transitions on astromer behavior. We also introduce a categorization of astromers that describes their potential effects in hot environments. We provide a table of neutron-rich isomers that includes the astromer type, thermalization temperature, and key unmeasured transition rates.
Lead (Pb) is predominantly produced by the slow neutron-capture process (s process) in asymptotic giant branch (AGB) stars. In contrast to significantly enhanced Pb abundances predicted by low-mass, low-metallicity AGB-models, observations of Magellanic post-AGB stars show incompatibly low Pb abundances. Observations of carbon-enhanced metal-poor (CEMP) stars whose s-process enrichments are accompanied by heavy elements traditionally associated with the rapid neutron-capture process (r process) have raised the need for a neutron-capture process operating at neutron densities intermediate to the s and r process: the so-called i process. We study i-process nucleosynthesis with single-zone nuclear-network calculations. Our i-process models can explain the heavy-element abundance patterns measured in Magellanic post-AGB stars including their puzzlingly low Pb abundances. Furthermore, the heavy-element enhancements in the post-AGB and CEMP-i stars, particularly their Pb abundance, allow us to characterise the neutron densities and exposures of the i process that produced the observed abundance patterns. We find that the lower-metallicity CEMP-i stars ($\left[ \mathrm{Fe} / \mathrm{H} \right] \approx -2.5$) have heavy-element abundances best matched by models with higher neutron densities and exposures ($τ> 2.0 \, \mathrm{mbarn}^{-1}$) compared to the higher-metallicity post-AGB stars ($\left[ \mathrm{Fe} / \mathrm{H} \right] \approx -1.3$, $τ< 1.3 \, \mathrm{mbarn}^{-1}$). This offers new constraints and insights regarding the properties of i-process sites and demonstrates that the responsible process operates on time scales of the order of a few years or less.
We report Mo isotopic data for 16 15N-rich presolar SiC grains of type AB (14N/15N solar), thus providing further support to the division of the two AB subgroups recently proposed by Liu et al. (2017a), who showed that AB1 grains most likely originated from Type II supernovae (SNe) with explosive H burning. Comparison of the Sr, Mo, and Ba isotopic compositions of the AB1 grains with SN model predictions indicates that the s-process isotopic compositions of AB1 grains resulted from neutron-capture processes occurring during the progenitor massive stars' pre-SN evolution rather than from an explosive neutron-capture process. In addition, the observations of (1) explosive H burning occurring in the C-rich regions of the progenitor SNe of SN X grains as suggested by the isotopic compositions of X grains, and (2) explosive H burning occurring both at the bottom of the He/C zone and at the top of the He/N zone as suggested by model simulations, imply that explosive H burning is a common phenomenon in outer SN zones.
Carbon-enhanced metal-poor (CEMP) stars in the Galactic Halo display enrichments in heavy elements associated with either the s (slow) or the r (rapid) neutron-capture process (e.g., barium and europium respectively), and in some cases they display evidence of both. The abundance patterns of these CEMP-s/r stars, which show both Ba and Eu enrichment, are particularly puzzling since the s and the r processes require neutron densities that are more than ten orders of magnitude apart, and hence are thought to occur in very different stellar sites with very different physical conditions. We investigate whether the abundance patterns of CEMP-s/r stars can arise from the nucleosynthesis of the intermediate neutron-capture process (the i process), which is characterised by neutron densities between those of the s and the r processes. Using nuclear network calculations, we study neutron capture nucleosynthesis at different constant neutron densities n ranging from $10^7$ to $10^{15}$ cm$^{-3}$. With respect to the classical s process resulting from neutron densities on the lowest side of this range, neutron densities on the highest side result in abundance patterns that show an increased production of heavy s-process and r-process elements but similar abundances of the light s-process elements. Such high values of n may occur in the thermal pulses of asymptotic giant branch (AGB) stars due to proton ingestion episodes. Comparison to the surface abundances of 20 CEMP-s/r stars show that our modelled i-process abundances successfully reproduce observed abundance patterns that could not be previously explained by s-process nucleosynthesis. Because the i-process models fit the abundances of CEMP-s/r stars so well, we propose that this class should be renamed as CEMP-i.
This white paper informs the nuclear astrophysics community and funding agencies about the scientific directions and priorities of the field and provides input from this community for the 2015 Nuclear Science Long Range Plan. It summarizes the outcome of the nuclear astrophysics town meeting that was held on August 21-23, 2014 in College Station at the campus of Texas A&M University in preparation of the NSAC Nuclear Science Long Range Plan. It also reflects the outcome of an earlier town meeting of the nuclear astrophysics community organized by the Joint Institute for Nuclear Astrophysics (JINA) on October 9- 10, 2012 Detroit, Michigan, with the purpose of developing a vision for nuclear astrophysics in light of the recent NRC decadal surveys in nuclear physics (NP2010) and astronomy (ASTRO2010). The white paper is furthermore informed by the town meeting of the Association of Research at University Nuclear Accelerators (ARUNA) that took place at the University of Notre Dame on June 12-13, 2014. In summary we find that nuclear astrophysics is a modern and vibrant field addressing fundamental science questions at the intersection of nuclear physics and astrophysics. These questions relate to the origin of the elements, the nuclear engines that drive life and death of stars, and the properties of dense matter. A broad range of nuclear accelerator facilities, astronomical observatories, theory efforts, and computational capabilities are needed. With the developments outlined in this white paper, answers to long standing key questions are well within reach in the coming decade.
We explore heavy-element nucleosynthesis by rapid neutron capture (r-process) in the decompressing ejecta from the surface of a neutron star. The decompression is triggered by a violent phase transition to strange quark matter (quark-nova scenario). The presence of neutron-rich large Z nuclei (40,95) < (Z,A) < (70,177), the large neutron-to-seed ratio, and the low electron fraction Ye ~ 0.03 in the decompressing ejecta present favorable conditions for the r-process. We perform network calculations that are adapted to the quark-nova conditions, and which mimic usual (n-gamma) equilibrium r-process calculations during the initially cold decompression phase. They match to dynamical r-process calculations at densities below neutron drip (4.10^11 g cm-3). We present results for the final element abundance distribution with and without heating from nuclear reactions, and compare to the solar abundance pattern of r-process elements. We highlight the distinguishing features of quark-novae by contrasting it with conventional nucleosynthetic sites such as type II supernovae and neutron star mergers, especially in the context of heavy-element compositions of extremely metal-deficient stars.
We present a detailed study of s-process nucleosynthesis in massive stars of solar-like initial composition and masses 15, 20,25, and 30 Msun. We update our previous results of s-process nucleosynthesis during the core He-burning of these stars and then focus on an analysis of the s-process under the physical conditions encountered during the shell-carbon burning. We show that the recent compilation of the Ne22(alpha,n)Mg25 rate leads to a remarkable reduction of the efficiency of the s-process during core He-burning. In particular, this rate leads to the lowest overproduction factor of Kr80 found to date during core He-burning in massive stars. The s-process yields resulting from shell carbon burning turn out to be very sensitive to the structural evolution of the carbon shell. This structure is influenced by the mass fraction of C12 attained at the end of core helium burning, which in turn is mainly determined by the C12(alpha,gamma)O16 reaction. The still present uncertainty in the rate for this reaction implies that the s-process in massive stars is also subject to this uncertainty. We identify some isotopes like Zn70 and Rb87 as the signatures of the s-process during shell carbon burning in massive stars. In determining the relative contribution of our s-only stellar yields to the solar abundances, we find it is important to take into account the neutron exposure of shell carbon burning. When we analyze our yields with a Salpeter Initial Mass Function, we find that massive stars contribute at least 40% to s-only nuclei with mass A <= 87. For s-only nuclei with mass A >90, massive stars contribute on average ~7%, except for Gd152, Os187, and Hg198 which are ~14%, \~13%, and ~11%, respectively.
We present a detailed study of the evolution of massive stars of masses 15, 20, 25 and 30 $\msun$ assuming solar-like initial chemical composition. The stellar sequences were evolved through the advanced burning phases up to the end of core oxygen burning. We present a careful analysis of the physical characteristics of the stellar models. In particular, we investigate the effect of the still unsettled reaction $^{12}$C($α$,$γ$)$^{16}$O on the advanced evolution by using recent compilations of this rate. We find that this rate has a significant impact on the evolution not only during the core helium burning phase, but also during the late burning phases, especially the shell carbon-burning. We have also considered the effect of different treatment of convective instability based on the Ledoux criterion in regions of varying molecular weight gradient during the hydrogen and helium burning phases. We compare our results with other investigations whenever available. Finally, our present study constitutes the basis of analyzing the nucleosynthesis processes in massive stars. In particular we will present a detail analysis of the {\it s}-process in a forthcoming paper.
The r-process of nucleosynthesis requires a large neutron-to-seed nucleus ratio. This does not, however, that there be an excess of neutrons over protons. If the expansion of the material is sufficiently rapid and the entropy per nucleon is sufficiently high, the nucleosynthesis enters a heavy-element synthesis regime heretofore unexplored. In this extreme regime, characterized by a persistent disequilibrium between free nucleons and the abundant alpha particles, heavy r-process nuclei can form even in matter with more protons than neutrons. This observation bears on the issue of the site of the r-process, on the variability of abundance yields from r-process events, and on cnstraints on neutrino physics derived from nucleosynthesis. It also clarifies the difference between nucleosynthesis in the early universe and that in less extreme stellar explosive environments.
We solve the general-relativistic steady-state eigenvalue problem of neutrino-driven protoneutron star winds, which immediately follow core-collapse supernova explosions. We provide velocity, density, temperature, and composition profiles and explore the systematics and structures generic to such a wind for a variety of protoneutron star characteristics. Furthermore, we derive the entropy, dynamical timescale, and neutron-to-seed ratio in the general relativistic framework essential in assessing this site as a candidate for $r$-process nucleosynthesis. Generally, we find that for a given mass outflow rate ($\dot{M}$), the dynamical timescale of the wind is significantly shorter than previously thought. We argue against the existence or viability of a high entropy ($\gtrsim300$ per k$_{B}$ per baryon), long dynamical timescale $r$-process epoch. In support of this conclusion, we model the protoneutron star cooling phase, calculate nucleosynthetic yields in our steady-state profiles, and estimate the integrated mass loss. We find that transonic winds enter a high entropy phase only with very low $\dot{M}$ ($\lesssim1\times10^{-9}$ M$_\odot$ s$^{-1}$) and extremely long dynamical timescale ($τ_ρ\gtrsim0.5$ seconds). Our results support the possible existence of an early $r$-process epoch at modest entropy ($\sim150$) and very short dynamical timescale, consistent in our calculations with a very massive or very compact protoneutron star that contracts rapidly after the preceding supernova. We explore possible modifications to our models, which might yield significant $r$-process nucleosynthesis generically. Finally, we speculate on the effect of fallback and shocks on both the wind physics and nucleosynthesis.
We explore neutrino capture during r-process nucleosynthesis in neutrino-driven ejecta from nascent neutron stars. We focus on the interplay between charged-current weak interactions and element synthesis, and we delineate the important role of equilibrium nuclear dynamics. During the period of coexistence of free nucleons and light and/or heavy nuclei, electron neutrino capture inhibits the r-process. At all stages, capture on free neutrons has a larger impact than capture on nuclei. However, neutrino capture on heavey nuclei by itself, if it is very strong, is also detrimental to the r-process until large nuclear equilibrium clusters break down and the classical neutron-capture phase of the r-process begins. The sensitivity of the r-process to neutrino irradiation means that neutrino-capture effects can strongly constrain the r-process site, neutrino physics, or both. These results apply also to r-process scenarios other than neutrino-heated winds.
We investigate the possibility that inhomogeneous nucleosynthesis may eventually be used to explain the abundances of \li6, \be9 and B in population II stars. The present work differs from previous studies in that we have used a more extensive reaction network. It is demonstrated that in the simplest scenario the abundances of the light elements with $A\le7$ constrain the separation of inhomogeneities to sufficiently small scales that the model is indistinguishable from homogeneous nucleosynthesis and that the abundances of \li6, \be9\ and B are then below observations by several orders of magnitude. This conclusion does not depend on the \li7 constraint. We also examine alternative scenarios which involve a post-nucleosynthesis reprocessing of the light elements to reproduce the observed abundances of Li and B, while allowing for a somewhat higher baryon density (still well below the cosmological critical density). Future B/H measurements may be able to exclude even this exotic scenario and further restrict primordial nucleosynthesis to approach the homogeneous model conclusions.