Effective field theory calculation of two-deuteron radiative capture reaction at astrophysical energies

Two-deuteron radiative capture reaction is one of the deuterium-burning processes that the cross section is not well known at very low-energies. We develop the formalism based on pionless Effective Field Theory (EFT) for deuteron–deuteron (dd) scattering to derive the cross section of two-deuteron radiative capture. Within this formalism the two- and three-body forces, should also be included in the capture cross section calculations. The aim of the present work is to calculate the observables of the low-energy dd photonuclear reactions. The cross section and the astrophysical S-factor for the ²H(d,γ)⁴He reaction have been calculated. The ⁴He is studied as four-body bound states in the pionless EFT. The theoretical uncertainties for observables are estimated based on the variation of the cutoffs. The astrophysical S-factor is accurately determined to be 6.9×10^?6 keV?b (6.1×10^?6 keV?b) for two-body (two- and three-body) at zero energy. A satisfactory agreement between theory and experiment for dd radiative capture observables up to order of calculation has been found by insertion of three-body force.     

A postulate leading to the Titius-Bode law

The revised Titius-Bode law (Balsano and Hughes, 1979) giving distances of planets from the Sun shows integers that recall the Bohr law in the early quantum theory of hydrogen atom. The author searchs for a formalism, similar to the Sommerfeld's one accounting for the planetary distribution of the solar system. It is shown that such a formalism might be started with the assumed relation $$\int_{r_0 }^{r_n } {U(r)dr = nk,} $$ whereU(r) stands for the gravitation potential created by the Sun at distancer,k=cte,r _o=cte,r _n=distance of then ^th planet andn=1, 2, 3... Although the inspiration of the present note came from the early quantum theory, it is emphasized that there is no connection between the above assumed equation and the Sommerfeld quantum rule, but a pure formal similarity. the true significance of that equation is still unknown. It is either a fortuitous coincidence leading to the T-B law or any possible unsuspected property of gravitation.     

Fading Hawking radiation

In this study, we explore a particular type Hawking radiation which ends with zero temperature and entropy. The appropriate black holes for this purpose are the linear dilaton black holes. In addition to the black hole choice, a recent formalism in which the Parikh-Wilczek’s tunneling formalism amalgamated with quantum corrections to all orders in ? is considered. The adjustment of the coefficients of the quantum corrections plays a crucial role on this particular Hawking radiation. The obtained tunneling rate indicates that the radiation is not pure thermal anymore, and hence correlations of outgoing quanta are capable of carrying away information encoded within them. Finally, we show in detail that when the linear dilaton black hole completely evaporates through such a particular radiation, entropy of the radiation becomes identical with the entropy of the black hole, which corresponds to “no information loss”.     

Variability in GRB afterglows and GRB 021004

We present general analytic expressions for GRB afterglow light curves arising from a variable external density profile and/or a variable energy in the blast wave. The former could arise from a clumpy ISM or a variable stellar wind; The latter could arise from refreshed shocks or from an angular dependent jet structure (patchy shell). Both scenarios would lead to a variable light curve. Our formalism enables us to invert the observed light curve and obtain possible density or energy profiles. The optical afterglow of GRB 021004 was detected 537 s AB (after the burst) [GCN (2002) 1564]. Extensive follow up observations revealed a significant temporal variability. We apply our formalism to the R-band light curve of GRB 021004 and we find that several models provide a good fit to the data. We consider the patchy shell model with p=2.2 as the most likely explanation. According to this model our line of sight was towards a ‘cold spot’ that has lead to a relativity low γ-ray flux and an initially weak afterglow (while the X-ray afterglow flux after a day was above average). Observations above the cooling frequency, ν_c, could provide the best way to distinguish between our different models.     

Analytical predictions of non-Gaussian distribution parameters for stellar plasmas

Stimulated by the recent debate on the physical relevance and on the predictivity of q-Gaussian formalism, we present specific analytical expressions for the parameters characterizing non-Gaussian distributions, such as the nonextensive parameter q, expressions that we have proposed for different physical systems, an important example being plasmas in the stellar cores.     

Bivariate least squares linear regression: Towards a unified analytic formalism. I. Functional models

Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts (York, 1966, York, 1969) is reviewed using a new formalism in terms of deviation (matrix) traces which, for unweighted data, reduce to usual quantities leaving aside an unessential (but dimensional) multiplicative factor. Within the framework of classical error models, the dependent variable relates to the independent variable according to the usual additive model. The classes of linear models considered are regression lines in the general case of correlated errors in X and in Y for weighted data, and in the opposite limiting situations of (i) uncorrelated errors in X and in Y, and (ii) completely correlated errors in X and in Y. The special case of (C) generalized orthogonal regression is considered in detail together with well known subcases, namely: (Y) errors in X negligible (ideally null) with respect to errors in Y; (X) errors in Y negligible (ideally null) with respect to errors in X; (O) genuine orthogonal regression; (R) reduced major-axis regression. In the limit of unweighted data, the results determined for functional models are compared with their counterparts related to extreme structural models i.e. the instrumental scatter is negligible (ideally null) with respect to the intrinsic scatter (Isobe et al., 1990, Feigelson and Babu, 1992). While regression line slope and intercept estimators for functional and structural models necessarily coincide, the contrary holds for related variance estimators even if the residuals obey a Gaussian distribution, with the exception of Y models. An example of astronomical application is considered, concerning the [O/H]–[Fe/H] empirical relations deduced from five samples related to different stars and/or different methods of oxygen abundance determination. For selected samples and assigned methods, different regression models yield consistent results within the errors (?σ) for both heteroscedastic and homoscedastic data. Conversely, samples related to different methods produce discrepant results, due to the presence of (still undetected) systematic errors, which implies no definitive statement can be made at present. A comparison is also made between different expressions of regression line slope and intercept variance estimators, where fractional discrepancies are found to be not exceeding a few percent, which grows up to about 20% in the presence of large dispersion data. An extension of the formalism to structural models is left to a forthcoming paper.     

Relaxational dissipation in atmospheric waves—I. Basic formulation

Relaxation of molecular thermal energy between translational and internal degrees of freedom, which occurs in the course of molecular collisions, acts to dissipate dynamical energy of the atmosphere and so produces attenuation of atmospheric waves. This paper establishes a basic formalism by means of which the effects may be incorporated readily into dynamical studies. It does so with the aid of a frequency-dependent complex thermal capacitance, c_ω, for which general formulae are developed. These formulae are extended to include the effects of radiative relaxation as well, and the imaginary part of c_ω is recast in a generalized form of Newtonian cooling coefficient; the relative importance of collisional relaxation and radiative relaxation in the dissipation of dynamical energy may be assessed readily with the aid of either parameter.The ‘volume viscosity’ that is sometimes attributed to the atmosphere is shown to have its origins in the same relaxation processes and to be nothing other than an alternative to C_ω, for expressing their effects, an alternative that is inferior and even illegitimate in some circumstances and therefore one that should be abandoned in favour of c_ω.Though the paper is largely tutorial in nature, it establishes generalizations and limitations that appear to be absent from other work. Its formal results are applied to waves in the Earth's upper atmosphere in a companion paper.     

Asteroid rotation: IV. 1979 observations

Results of photoelectric lightcurve observations made during 1979 are reported. Of a total of 53 asteroids observed, reliable rotation periods are reported for 22 asteroids for which no previous values are known, 7 periods are reported which are revisions of previously reported values, and for 12 other asteroids periods are suggested which are admittedly of low reliability and those objects should be reobserved. In addition, phase relations are presented for many of the asteroids, fitted to the theoretical phase function of Lumme and Bowell (Astron. J., 86, 1705, 1981). Adopting their formalism, mean absolute magnitudes at zero phase angle, $\text{V}\text{(0°)}$, for 52 asteroids, and values of the multiple scattering parameter, Q, for 22 asteroids are reported. For comparison purposes, the absolute magnitude, V(1,0) and the linear phase coefficient, βv, in the traditional system are computed. In the appendixes (1) the methods of observation and data reduction are discussed, which are recommended to other lightcurve observers in the hope of standardizing reporting practices as much as possible; and (2) a cumulative index of all asteroid rotation data of which the authors are aware is presented.     

Charged-particle induced thermonuclear reaction rates of 3He(3He,2p)4He, 3He(4He,γ)7Be and 7Be(p,γ)8B by using the exact tunneling probability

The astrophysical S-factor of the experimental cross section data of the main reactions in the proton–proton chain, i.e. ³He(³He,2p)⁴He, ³He(⁴He,γ)⁷Be and ⁷Be(p,γ)⁸B, are reanalyzed by using the exact tunneling probability in nuclear reactions. Our goal is to test this treatment in finding the reaction rate per pair for non-resonant reactions. At low temperatures, the exact treatment is identical to the standard formalism but diverges at higher temperatures.     

The radiation of energy by a current in a plasma

The derivation of the differential power emitted in any given direction by a current J in a linear, homogeneous and non-absorbing plasma is reviewed in detail. The conventional derivation is shown to give the poweremitted; a formalism for the powerreceived is established by evaluating the Poynting vector in terms of the far field. It is pointed out that the two power expressions differ because the same energy dE is emitted in a time dt _e but received over a different time dt _r . Moreover, a careful scrutiny of both the formalism for the power emission and for the power reception exposes implicit assumptions which do not hold if the plasma is anisotropic. The necessary steps for establishing a valid formalism for anisotropic media are briefly sketched.     

Integrable approximation of J 2-perturbed relative orbits

Most existing satellite relative motion theories utilize mean elements, and therefore cannot be used for calculating long-term bounded perturbed relative orbits. The goal of the current paper is to find an integrable approximation for the relative motion problem under the J ₂ perturbation, which is adequate for long-term prediction of bounded relative orbits with arbitrary inclinations. To that end, a radial intermediary Hamiltonian is utilized. The intermediary Hamiltonian retains the original structure of the full J ₂ Hamiltonian, excluding the latitude dependence. This formalism provides integrability via separation, a fact that is utilized for finding periodic relative orbits in a local-vertical local-horizontal frame and determine an initialization scheme that yields long-term boundedness of the relative distance. Numerical experiments show that the intermediary-based computation of orbits provides long-term bounded orbits in the full J ₂ problem for various inclinations. In addition, a test case is shown in which the radial intermediary-based initial conditions of the chief and deputy satellites yield bounded relative distance in a high-precision orbit propagator.     

Dynamics of charged shell with a cosmological constant

Using the Darmois–Israel formalism technique, charged thin shell in the presence of a cosmological constant is constructed. An equation governing the behavior of the radial pressure across the junction surface is deduced. The cosmological constant term and the charge term slows down the collapse of matter.The spherical N-shell model with an appropriate initial condition imitates quite well the FRW universe with Λ ≠ 0.     

Meridian circulation in differentially rotating stars

We formulate the first order theory of meridian circulation in radiative zones of approximate chemical homogeneity so as to allow calculation of circulation velocities in a star subject to an arbitrary axially symmetric angular velocity ω(r, θ). The calculation includes circulation due to perturbations in the nuclear burning rate. The formalism agrees with previous calculations relevant to special cases, and assumes maximum simplicity for rotation on cylinders. We find two types of steady state configurations: (1) rotation according to a special class of distributions ω(r, θ) which drive no currents, and (2) rotation according to arbitrary ω(r, θ), but with a correction to the molecular weight μ such that the net circulation velocity is zero. We find that a small μ gradient can quench the circulation in many cases. In particular, we conclude that a large differential rotation in the Sun might have escaped disruption by meridian currents, for a μ stratification of a few parts in 10³.     

Reconstruction of f(R,T) gravity in anisotropic cosmological models of accelerating universe

In this paper, we search the existence of Bianchi type I cosmological model in f(R,T) gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the trace of the stress-energy tensor T. We obtain the gravitational field equations in the metric formalism, and reconstruct the corresponding f(R,T) functions. Attention is attached to the special case, f(R,T)=f ₁(R)+f ₂(T) and two examples are assumed for this model. In the first example, we consider the unification of matter dominated and accelerated phases with f(R) gravity in anisotropic universe, and in the second instance, model of f(R,T) gravity with transition of matter dominated phase to the acceleration phase is obtained. In both cases, f(R,T) is proportional to a power of R with exponents depending on the input parameters.     

Nonextensive Statistical Mechanics: Some Links with Astronomical Phenomena

A variety of astronomical phenomena appear to not satisfy the ergodic hypothesis in the relevant stationary state, if any. As such, there is no reason for expecting the applicability of Boltzmann–Gibbs (BG) statistical mechanics. Some of these phenomena appear to follow, instead, nonextensive statistical mechanics. In the same manner that the BG formalism is based on the entropy S _BG=?k∑ _i p _i ln p _i, the nonextensive one is based on the form S _q=k(1 ?∑ _i p _i ^q)/(q? 1) (with S ₁=S _BG). The stationary states of the former are characterized by an exponential dependence on the energy, whereas those of the latter are characterized by an (asymptotic) power law. A brief review of this theory is given here, as well as of some of its applications, such as the solar neutrino problem, polytropic self-gravitating systems, galactic peculiar velocities, cosmic rays and some cosmological aspects. In addition to these, an analogy with the Keplerian elliptic orbits versus the Ptolemaic epicycles is developed, where we show that optimizing S _q with a few constraints is equivalent to optimizing S _BG with an infinite number of constraints.     

Thermal relic abundance and anisotropy due to modified gravity

Alternative cosmologies, based on extensions of General Relativity, predict modified thermal histories in the early universe during the pre Big Bang Nucleosynthesis (BBN) era. When the expansion rate is enhanced with respect to the standard case, thermal relics typically decouple with larger relic abundances. In this paper, we study the dynamical evolution of an f(R) model of gravity in a homogeneous and anisotropic background which is given by a Bianchi type-I model of the universe filled with dark matter, which is described by a perfect fluid with a barotropic equation of state. As an example of a consistent analysis of modified gravity, we apply the formalism to a simple background solution of R+βR ⁿ gravity. Our analysis shows that f(R) cosmology allows dark matter masses lesser than 100 GeV, in the regime ρ ^c ?ρ ^m . We finally discuss how these limits apply to some specific realizations of standard cosmologies: an f(R) gravity model, Einstein frame model.     

FRB Event Rate Predictions for the Ooty Wide Field Array

We developed a generic formalism to estimate the event rate and the redshift distribution of Fast Radio Bursts (FRBs) in our previous publication (Bera et al. 2016), considering FRBs are of an extragalactic origin. In this paper, we present (a) the predicted pulse widths of FRBs by considering two different scattering models, (b) the minimum total energy required to detect events, (c) the redshift distribution and (d) the detection rates of FRBs for the Ooty Wide Field Array (OWFA). The energy spectrum of FRBs is modelled as a power law with an exponent ?α and our analysis spans a range ?3≤α≤5. We find that OWFA will be capable of detecting FRBs with α≥0. The redshift distribution and the event rates of FRBs are estimated by assuming two different energy distribution functions; a Delta function and a Schechter luminosity function with an exponent ?2≤γ≤2. We consider an empirical scattering model based on pulsar observations (model I) as well as a theoretical model (model II) expected for the intergalactic medium. The redshift distributions peak at a particular redshift z _p for a fixed value of α, which lie in the range 0.3≤z _p ≤1 for the scattering model I and remain flat and extend up to high redshifts (z?5) for the scattering model II.     

Electron capture strength on odd-A nucleus 59Co in explosive astrophysical environment

The Gamow-Teller (GT) transitions within massive stars play sumptuous role in the dynamics of core collapse supernovae. GT strength distributions and electron capture rates have been calculated for odd-A nucleus ⁵⁹Co within the proton-neutron quasiparticles random phase approximation (pn-QRPA) formalism. The pn-QRPA results are compared with other model calculations and (n,p) reaction experiment carried out at TRIUMF charge-exchange facility. The pn-QRPA calculated a total B(GT ₊) strength of 3.3 for ⁵⁹Co to be compared with the shell model value of 2.5 and the 1.9±0.1 in the (n,p) charge-exchange reaction. Aufderheide et al. (1993) extracted total strength equaling 2.4±0.3. The placement of GT centroid at 5.6 MeV by the pn-QRPA model is in reasonable agreement with the shell model centroid at 5.1 MeV whereas the measured GT centroid was placed at 4.4±0.3 MeV in the (n,p) experiment. Fuller, Fowler and Newman (FFN) (1980, 1982a, 1982b), placed the GT centroid at too low excitation energy of 2.0 MeV in the daughter nucleus ⁵⁹Fe, and this misplacement led to the enhancement of FFN rates. The suppressed pn-QRPA and shell model electron capture rates are in good agreement with each other. The rates are suggestive of higher value of Y _e (electron-to-baryon ratio) and may contribute to a more massive homologously collapsing core resulting in a more energetic shock. It might be interesting for the simulators to check the effect of these suppressed rates on the fine-tuning of the time rate of Y _e , the concomitant heavy element nucleosynthesis, and, on the energetics of the subsequent shock wave.     

High-energy cosmology

Our knowledge of the high-energy universe is undergoing a period of rapid change as new astronomical detectors of high-energy radiation start to operate at their design sensitivities. Now is a boomtime for high-energy astrophysics, with new discoveries from Swift and HESS, results from MAGIC and VERITAS starting to be reported, the upcoming launches of the γ-ray space telescopes GLAST and AGILE, and anticipated data releases from IceCube and Auger. A formalism for calculating statistical properties of cosmological γ-ray sources is presented. Application is made to model calculations of the statistical distributions of γ-ray and neutrino emission from (i) beamed sources, specifically, long-duration GRBs, blazars, and extragalactic microquasars, and (ii) unbeamed sources, including normal galaxies, starburst galaxies and clusters. Expressions for the integrated intensities of faint beamed and unbeamed high-energy radiation sources are also derived. A toy model for the background intensity of radiation from dark-matter annihilation taking place in the early universe is constructed. Estimates for the γ-ray fluxes of local group galaxies, starburst, and infrared luminous galaxies are briefly reviewed. Because the brightest extragalactic γ-ray sources are flaring sources, and these are the best targets for sources of PeV–EeV neutrinos and ultra-high energy cosmic rays, rapidly slewing all-sky telescopes like MAGIC and an all-sky γ-ray observatory beyond Milagro will be crucial for optimal science return in the multi-messenger age.     

Bidirectional reflectance spectroscopy: 3. Correction for macroscopic roughness

A mathematically rigorous formalism is derived by which an arbitrary photometric function for the bidirectional reflectance of a smooth surface may be corrected to include effects of general macroscopic roughness. The correction involves only one arbitrary parameter, the mean slope angle $\text{θ}$, and is applicable to surfaces of any albedo. Using physically reasonable assumptions and mathematical approximations the correction expressions are evaluated analytically to second order in $\text{θ}$. The correction is applied to the bidirectional reflectance function of B. Hapke (1981, J. Geophys. Res.86, 3039–3054). Expressions for both the differential and integral brightnesses are obtained. Photometric profiles on hypothetical smooth and rough planets of low and high albedo are shown to illustrate the effects of macroscopic roughness. The theory is applied to observations of Mercury and predicts the integral phase function, the apparent polar darkening, and the lack of limb brightness surge on the planet. The roughness-corrected bidirectional reflectance function is sufficiently simple that it can be conveniently evaluated on a programmable hand-held calculator.