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Solar Oscillations

Oscillations were first detected in the solar photosphere in 1962 by Leighton and students. In 1970 it was calculated that these oscillations, with a period near five minutes, were the manifestations of acoustic waves trapped in the interior. The subsequent measurements of the frequencies of global oscillation modes from the spatio-temporal power spectrum of the waves made possible the refinement of solar interior models. Over the years, increased understanding of the nuclear reaction rates, the opacity, the equation of state, convection, and gravitational settling have resulted. Mass flows shift the frequencies of modes leading to very accurate measurements of the interior rotation as a function of radius and latitude. In recent years, analogues of terrestrial seismology have led to a tomography of the interior, including measurements of global north-south flows and flow and wave speed measurements below features such as sunspots. The future of helioseismology seems bright with the approval of NASA's Solar Dynamics Observatory mission, to be launched in 2008.

Duvall, Thomas↗

eXTP: Enhanced X-Ray Timing and Polarimetry Mission

eXTP is a science mission designed to study the state of matter under extreme conditions of density, gravity and magnetism. Primary goals are the determination of the equation of state of matter at supra-nuclear density, the measurement of QED effects in highly magnetized star, and the study of accretion in the strong-field regime of gravity. Primary targets include isolated and binary neutron stars, strong magnetic field systems like magnetars, and stellar-mass and supermassive black holes. The mission carries a unique and unprecedented suite of state-of-the-art scientific instruments enabling for the first time ever the simultaneous spectral-timing-polarimetry studies of cosmic sources in the energy range from 0.5-30 keV (and beyond). Key elements of the payload are: the Spectroscopic Focusing Array (SFA) - a set of 11 X-ray optics for a total effective area of approx. 0.9 m(exp. 2) and 0.6 m(exp. 2) at 2 keV and 6 keV respectively, equipped with Silicon Drift Detectors offering less than 180 eV spectral resolution; the Large Area Detector (LAD) - a deployable set of 640 Silicon Drift Detectors, for a total effective area of approx. 3.4 m(exp. 2), between 6 and 10 keV, and spectral resolution better than 250 eV; the Polarimetry Focusing Array (PFA) - a set of 2 X-ray telescope, for a total effective area of 250 cm(exp. 2) at 2 keV, equipped with imaging gas pixel photoelectric polarimeters; the Wide Field Monitor (WFM) - a set of 3 coded mask wide field units, equipped with position-sensitive Silicon Drift Detectors, each covering a 90 degrees x 90 degrees field of view. The eXTP international consortium includes major institutions of the Chinese Academy of Sciences and Universities in China, as well as major institutions in several European countries and the United States. The predecessor of eXTP, the XTP mission concept, has been selected and funded as one of the so-called background missions in the Strategic Priority Space Science Program of the Chinese Academy of Sciences since 2011. The strong European participation has significantly enhanced the scientific capabilities of eXTP. The planned launch date of the mission is earlier than 2025.

X-ray astronomy↗

Equation of state at ultrahigh densities. II

Theoretical research into the behavior of matter in the high-density region (at least 2 by 10 to the 14th power g/cu cm) is reviewed. Results of work concerning the appearance of hyperons in the neutron fluid at densities higher than nuclear density are summarized, and it is shown that the presence of hyperons does not severely alter the equation of state from that for a pure neutron gas provided that hyperonic potentials are almost identical to the nucleon-nucleon case. Computations to determine whether neutrons can solidify at a high enough density are described. It is shown that the solidification density is well within the range of values expected in the interior of neutron stars. Several unrelated attempts to analyze the behavior of matter in the relativistic or superhigh-density region (in excess of 10 to the 16th power gm/cu cm) are summarized. It is noted that available data on neutron stars are insufficient to determine a specific value for the speed of sound at superhigh densities.

Camuto, V.↗

A NICER view of PSR J0030+0451: Implications for the Dense Matter Equation of State

Both the mass and radius of the millisecond pulsar PSRJ0030+0451 have been inferred via pulse-profile modeling of X-ray data obtained by NASA’s Neutron Star Interior Composition Explorer (NICER) mission. In this Letter we study the implications of the mass–radius inference reported for this source by Riley et al. for the dense matter equation of state (EoS), in the context of prior information from nuclear physics at low densities. Using a Bayesian framework we infer central densities and EoS properties for two choices of high-density extensions: a piecewise-polytropic model and a model based on assumptions of the speed of sound in dense matter. Around nuclear saturation density these extensions are matched to an EoS uncertainty band obtained from calculations based on chiral effective field theory interactions, which provide a realistic description of atomic nuclei as well as empirical nuclear matter properties within uncertainties. We further constrain EoS expectations with input from the current highest measured pulsar mass; together, these constraints offer a narrow Bayesian prior informed by theory as well as laboratory and astrophysical measurements. The NICER mass–radius likelihood function derived by Riley et al. using pulse-profile modeling is consistent with the highest-density region of this prior. The present relatively large uncertainties on mass and radius for PSR J0030+0451 offer, however, only a weak posterior information gain over the prior. We explore the sensitivity to the inferred geometry of the heated regions that give rise to the pulsed emission, and find a small increase in posterior gain for an alternative (but less preferred) model. Lastly, we investigate the hypothetical scenario of increasing the NICER exposure time for PSRJ0030+0451.

G Raaijmakers↗

The Radius of PSR J0740+6620 from NICER and XMM-Newton Data

PSR J0740+6620 has a gravitational mass of 2.08±0.07Me, which is the highest reliably determined mass of any neutron star. As a result, a measurement of its radius will provide unique insight into the properties of neutron star core matter at high densities. Here we report a radius measurement based on fits of rotating hot spot patterns to Neutron Star Interior Composition Explorer(NICER)and X-ray Multi-Mirror(XMM-Newton)X-ray observations. We find that the equatorial circumferential radius of PSR J0740+6620 is-+13.71.52.6km(68%).We apply our measurement, combined with the previous NICER mass and radius measurement of PSR J0030+0451,the masses of two other∼2Mepulsars, and the tidal deformability constraints from two gravitational wave events, to three different frameworks for equation-of-state modeling, and find consistent results at∼1.5–5 times nuclear saturation density. For a given framework, when all measurements are included, the radius of a 1.4Meneutron star is known to±4%(68% credibility)and the radius of a 2.08Meneutron star is known to±5%. The full radius range that spans the±1σcredible intervals of all the radius estimates in the three frameworks is 12.45±0.65 km for a 1.4Meneutron star and 12.35±0.75 km for a 2.08Me neutron star.

M C Miller↗

Unpulsed X-rays from pulsars

Preliminary results of several programs to detect thermal X-ray emission from isolated neutron stars are presented. Results of Einstein pulsar surveys indicate that either the majority of supernovas which leave remnants do not produce neutron stars, or the cooling calculations are in need of substantial revision. When appropriate relativistic thermodynamics and updated high energy nuclear physics are included, the new calculations predict significantly lower temperatures for standard neutron star equations of state. X-ray results give strong evidence that five of the seven historical remnants and a large majority of the other remnants of less than 1000 yr do not contain radio pulsars. A survey of known radio pulsars is also presented, which is designed to test the heating mechanisms required by various theories of pulsar emission and neutron star structure, and consists of a survey of all known pulsars within 300 pc.

Helfand, D. J.↗

Transition probabilities of the B-prime 1Sigma(u)(+) to X 1Sigma(g)(+) system of molecular hydrogen

From published potential energy curves and transition dipole moments, there are obtained by numerical integration of the equations of nuclear motion the vibrational eigenfunctions of the X 1Sigma(g)(+) and B-prime 1Sigma(u)(+) states of H2. The probabilities of radiative transitions from the discrete vibrational levels of the excited B-prime 1Sigma(u)(+) electronic state of H2 to the discrete and continuum vibrational levels of the ground X 1Sigma(g)(+) electronic state are calculated. The Franck-Condon factors are also presented.

Kwok, T. L.↗

Harmonic oscillator representation in the theory of scattering and nuclear reactions

The following questions, concerning the application of the harmonic oscillator representation (HOR) in the theory of scattering and reactions, are discussed: the formulation of the scattering theory in HOR; exact solutions of the free motion Schroedinger equation in HOR; separable expansion of the short range potentials and the calculation of the phase shifts; 'isolated states' as generalization of the Wigner-von Neumann bound states embedded in continuum; a nuclear coupled channel problem in HOR; and the description of true three body scattering in HOR. As an illustration the soft dipole mode in the (11)Li nucleus is considered in a frame of the (9)Li+n+n cluster model taking into account of three body continuum effects.

Smirnov, Yuri F.↗

The computation of standard solar models

Procedures for calculating standard solar models with the usual simplifying approximations of spherical symmetry, no mixing except in the surface convection zone, no mass loss or gain during the solar lifetime, and no separation of elements by diffusion are described. The standard network of nuclear reactions among the light elements is discussed including rates, energy production and abundance changes. Several of the equation of state and opacity formulations required for the basic equations of mass, momentum and energy conservation are presented. The usual mixing-length convection theory is used for these results. Numerical procedures for calculating the solar evolution, and current evolution and oscillation frequency results for the present sun by some recent authors are given.

Ulrich, Roger K.↗

Our Sun IV: The Standard Model and Helioseismology: Consequences of Uncertainties in Input Physics and in Observed Solar Parameters

Helioseismic frequency observations provide an extremely accurate window into the solar interior; frequencies from the Michaelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft, enable the adiabatic sound speed and adiabatic index to be inferred with an accuracy of a few parts in 10(exp 4) and the density with an accuracy of a few parts in 10(exp 3). This has become a Serious challenge to theoretical models of the Sun. Therefore, we have undertaken a self-consistent, systematic study of the sources of uncertainties in the standard solar models. We found that the largest effect on the interior structure arises from the observational uncertainties in the photospheric abundances of the elements, which affect the sound speed profile at the level of 3 parts in 10(exp 3). The estimated 4% uncertainty in the OPAL opacities could lead to effects of 1 part in 10(exp 3); the approximately 5%, uncertainty in the basic pp nuclear reaction rate would have a similar effect, as would uncertainties of approximately 15% in the diffusion constants for the gravitational settling of helium. The approximately 50% uncertainties in diffusion constants for the heavier elements would have nearly as large an effect. Different observational methods for determining the solar radius yield results differing by as much as 7 parts in 10(exp 4); we found that this leads to uncertainties of a few parts in 10(exp 3) in the sound speed int the solar convective envelope, but has negligible effect on the interior. Our reference standard solar model yielded a convective envelope position of 0.7135 solar radius, in excellent agreement with the observed value of 0.713 +/- 0.001 solar radius and was significantly affected only by Z/X, the pp rate, and the uncertainties in helium diffusion constants. Our reference model also yielded envelope helium abundance of 0.2424, in good agreement with the approximate range of 0.24 to 0.25 inferred from helioseismic observations; only extreme Z/X values yielded envelope helium abundance outside this range. We found that other current uncertainties, namely, in the solar age and luminosity, in nuclear rates other than the pp reaction, in the low-temperature molecular opacities, and in the low-density equation of state, have no significant effect on the quantities that can be inferred from helioseismic observations. The predicted pre-main-sequence lithium depletion is uncertain by a factor of 2. The predicted neutrino capture rate is uncertain by approximately 30% for the Cl-27 experiment and by approximately 3% for Ga-71 experiments, while the B-8 neutrino flux is uncertain by approximately 30%.

Boothroyd, Arnold I.↗

An optical model for composite nuclear scattering

The optical model of composite particle scattering is considered and compared to the accuracies of other models. A nonrelativistic Schroedinger equation with two-body potentials is used for the scattering of a single particle by an energy-dependent local potential. The potential for the elastic channel is composed of matrix elements of a single scattering operator taken between the ground states of the projectile and the target; the coherent amplitude is considered as dominating the scattering in the forward direction. A multiple scattering series is analytically explored and formally summed by the solution of an equivalent Schroedinger equation. Cross sections of nuclear scattering are then determined for He-4 and C-12 nuclei at 3.6 GeV/nucleus and O-16 projectiles at 2.1 GeV/nucleus, and the optical model approximations are found to be consistently lower and more accurate than approximations made by use of Glauber's theory.

Wilson, J. W.↗

Applications of NASTRAN to nuclear problems

The extent to which suitable solutions may be obtained for one physics problem and two engineering type problems is traced. NASTRAN appears to be a practical tool to solve one-group steady-state neutron diffusion equations. Transient diffusion analysis may be performed after new levels that allow time-dependent temperature calculations are developed. NASTRAN piecewise linear anlaysis may be applied to solve those plasticity problems for which a smooth stress-strain curve can be used to describe the nonlinear material behavior. The accuracy decreases when sharp transitions in the stress-strain relations are involved. Improved NASTRAN usefulness will be obtained when nonlinear material capabilities are extended to axisymmetric elements and to include provisions for time-dependent material properties and creep analysis. Rigid formats 3 and 5 proved to be very convenient for the buckling and normal-mode analysis of a nuclear fuel element.

Spreeuw, E.↗

Transport methods and interactions for space radiations

This report presents a brief history leading to the involvement of the Langley Research Center of the National Aeronautics and Space Administration (NASA) in space-radiation physics and protection. Indeed, a relatively complete summary of technical capability as of the summer of 1990 is given. The Boltzmann equations for coupled ionic and neutronic fields are presented and inversion techniques for the Boltzmann operator are discussed. Errors generated by the straight ahead approximation are derived and are shown to be negligible for most problems of space-radiation protection. A decoupling of projectile propagation from the target fields greatly simplifies the Boltzmann equations and allows an analytic solution of the target fragment transport. Analytic and numerical methods of solving the projectile transport equations are discussed. The nuclear physics underlying the coefficients in the Boltzmann equation is discussed. A coupled-channel optical model is found as a consequence of the loose binding of nuclear matter and closure of the nuclear states in high-energy reactions. Transport solutions with the developed data base are used with laboratory experiments to validate both the transport code and the data base. Numerical benchmarks and comparison with Monte Carlo calculations are also used for code validation.

Wilson, John W.↗

Computing Highly Accurate Spectroscopic Line Lists for Characterization of Planetary Atmospheres: CO2 and SO2 Line Lists Needed for Modeling Venus

Over the last decade, it has become apparent that the most effective approach for determining highly accurate rotational and rovibrational line lists for molecules of interest in planetary atmospheres and other astrophysical environments is through a combination of highresolution laboratory experiments coupled with state-of-the art ab initio quantum chemistry methods. The approach involves computing the most accurate potential energy surface (PES) possible using state-of-the art electronic structure methods, followed by computing rotational and rovibrational energy levels using an exact variational method to solve the nuclear Schrödinger equation. Then, reliable experimental data from high-resolution experiments is used to refine the ab initio PES in order to improve the accuracy of the computed energy levels and transition energies. From the refinement step, we have been able to achieve an accuracy of approximately 0.015 cm-1 for rovibrational transition energies, and even better for purely rotational transitions. This combined "experiment / theory" approach allows for determination of essentially a complete line list, with hundreds of millions of transitions, and having the transition energies and intensities be highly accurate. Our group has successfully applied this approach to determine highly accurate line lists for NH3, CO2 and isotopologues, and SO2 and isotopologues. Here I will report our latest results for CO2 and SO2 including all isotopologues. Comparisons to the available data in HITRAN2012 and other available databases will be shown, though we note that our line lists for SO2 are significantly more complete than any other databases. Since it is important to span a large temperature range in order to model the spectral signature of Venus as well as exoplanets, we will demonstrate how the spectra change on going from low temperatures (100 K) to higher temperatures (500 K to 1500 K).

potential energy surface (PES)5405 PLANETARY SCIEN↗

PSR J0030+0451 Mass and Radius from NICER Data and Implications for the Properties of Neutron Star Matter

Neutron stars are not only of astrophysical interest, but are also of great interest to nuclear physicists because their attributes can be used to determine the properties of the dense matter in their cores. One of the most informative approaches for determining the equation of state (EoS) of this dense matter is to measure both a star’s equatorial circumferential radius Re and its gravitational mass M. Here we report estimates of the mass and radius of the isolated 205.53 Hz millisecond pulsar PSRJ0030+0451 obtained using a Bayesian inference approach to analyze its energy-dependent thermal X-ray waveform, which was observed using the Neutron Star Interior Composition Explorer (NICER). This approach is thought to be less subject to systematic errors than other approaches for estimating neutron star radii. We explored a variety of emission patterns on the stellar surface. Our best-fit model has three oval, uniform-temperature emitting spots and provides an excellent description of the pulse waveform observed using NICER. The radius and mass estimates given by this model are Re = 13.02+1.24-1.06 km andM = 1.44+0.15-0.14 Mmoon (68%). The independent analysis reported in the companion paper by Riley et al. explores different emitting spot models, but finds spot shapes and locations and estimates of Re and M that are consistent with those found in this work. We show that our measurements of Re and M for PSRJ0030+0451 improve the astrophysical constraints on the EoS of cold, catalyzed matter above nuclear saturation density.

M C Miller↗