Predicted Capture Rate Research Articles

Cosmic Spin and Mass Evolution of Black Holes and Its Impact

Abstract We build an evolution model of the central black hole that depends on the processes of gas accretion, the capture of stars, mergers, and electromagnetic torque. In the case of gas accretion in the presence of cooling sources, the flow is momentum driven, after which the black hole reaches a saturated mass; subsequently, it grows only by stellar capture and mergers. We model the evolution of the mass and spin with the initial seed mass and spin in ΛCDM cosmology. For stellar capture, we have assumed a power-law density profile for the stellar cusp in a framework of relativistic loss cone theory that includes the effects of black hole spin, Carter’s constant, loss cone angular momentum, and capture radius. Based on this, the predicted capture rates of 10−5 to 10−6 yr−1 are closer to the observed range. We have considered the merger activity to be effective for z ≲ 4, and we self-consistently include the Blandford–Znajek torque. We calculate these effects on the black hole growth individually and in combination, for deriving the evolution. Before saturation, accretion dominates the black hole growth (∼95% of the final mass), and subsequently stellar capture and mergers take over with roughly equal contributions. The simulations of the evolution of the M •–σ relation using these effects are consistent with available observations. We run our model backward in time and retrodict the parameters at formation. Our model will provide useful inputs for building demographics of the black holes and in formation scenarios involving stellar capture.

A Two Transition State Model for Radical−Molecule Reactions: Applications to Isomeric Branching in the OH−Isoprene Reaction

A two transition state model is applied to the prediction of the isomeric branching in the addition of hydroxyl radical to isoprene. The outer transition state is treated with phase space theory fitted to long-range transition state theory calculations on an electrostatic potential energy surface. High-level quantum chemical estimates are applied to the treatment of the inner transition state. A one-dimensional master equation based on an analytic reduction from two-dimensions for a particular statistical assumption about the rotational part of the energy transfer kernel is employed in the calculation of the pressure dependence of the addition process. We find that an accurate treatment of the two separate transition state regions, at the energy and angular momentum resolved level, is essential to the prediction of the temperature dependence of the addition rate. The transition from a dominant outer transition state to a dominant inner transition state is shown to occur at about 275 K, with significant effects from both transition states over the 30-500 K temperature range. Modest adjustments in the ab initio predicted inner saddle point energies yield predictions that are in quantitative agreement with the available high-pressure limit experimental observations and qualitative agreement with those in the falloff regime. The theoretically predicted capture rate is reproduced to within 10% by the expression [1.71 x 10(-10)(T/298)(-2.58) exp(-608.6/RT) + 5.47 x 10(-11)(T/298)-1.78 exp(-97.3/RT); with R = 1.987 and T in K] cm3 molecule(-1) s(-1) over the 30-500 K range. A 300 K branching ratio of 0.67:0.02:0.02:0.29 was determined for formation of the four possible OH-isoprene adduct isomers 1, 2, 3, and 4, respectively, and was found to be relatively insensitive to temperature. An Arrhenius activation energy of -0.77 kcal/mol was determined for the high-pressure addition rate constants around 300 K.

A Two Transition State Model for Radical−Molecule Reactions: A Case Study of the Addition of OH to C2H4

A two transition state model is applied to the study of the addition of hydroxyl radical to ethylene. This reaction serves as a prototypical example of a radical-molecule reaction with a negative activation energy in the high-pressure limit. The model incorporates variational treatments of both inner and outer transition states. The outer transition state is treated with a recently derived long-range transition state theory approach focusing on the longest-ranged term in the potential. High-level quantum chemical estimates are incorporated in a variational transition state theory treatment of the inner transition state. Anharmonic effects in the inner transition state region are explored with direct phase space integration. A two-dimensional master equation is employed in treating the pressure dependence of the addition process. An accurate treatment of the two separate transition state regions at the energy and angular momentum resolved level is essential to the prediction of the temperature dependence of the addition rate. The transition from a dominant outer transition state to a dominant inner transition state is predicted to occur at about 130 K, with significant effects from both transition states over the 10 to 400 K temperature range. Modest adjustment in the ab initio predicted inner saddle point energy yields theoretical predictions which are in quantitative agreement with the available experimental observations. The theoretically predicted capture rate is reproduced to within 10% by the expression [4.93 x 10(-12) (T/298)(-2.488) exp(-107.9/RT) + 3.33 x 10(-12) (T/298)(0.451) exp(117.6/RT); with R = 1.987 and T in K] cm3 molecules(-1) s(-1) over the 10-600 K range.

CESAM Solar Models

AbstractSolar models have been computed using the code CESAM constructed at Nice (Morel, 1992), and the new opacities of Livermore for different mixtures. Their global characteristics, predicted capture rates of neutrinos for the chlorine and gallium experiments and their seismological properties are given.

Diving behaviour and diet of the blue-eyed shag at South Georgia

This paper describes a concurrent investigation of individual variation in diet, diving patterns and performance of blue-eyed shags Phalacrocorax atriceps breeding at South Georgia. Within one day individual shags exhibited one of three foraging strategies: short diving (4 birds, all dives 120 s) and mixed diving (15 birds, predominantly long but with a few short dives). The mean number of dives per day was significantly higher in shags that only made short dives (mean=172.0, SE=43.2) than birds with a mixed diving strategy (mean=40.5, SE=4.7) and birds that made only long dives (mean=30.8, SE=1.8). Diet was assessed using hard remains recovered from pellets regurgitated by the shags. Small nototheniid fish (c. 10 kJ per item) were by far the commonest prey but most pellets contained additional items. The frequency of pellets with additional items of higher energy value than nototheniid fish (10.c. 900 kJ per item), lower energy value (>1–10 kJ per item) and both higher and lower energy items was strikingly similar to the frequency of shags making long, short and both long and short dives respectively. Predicted aerobic dive limits suggested that during long dives, blue-eyed shags were probably sustained by anaerobic metabolism. Models of prey capture rates demonstrated that for both long and short diving, many items must be caught per dive when birds are feeding on prey at the lower end of the energy range. Predicted capture rates for the commonest recorded prey (small fish) differ markedly between the two diving strategies.

The solar neutrino problem

The observed capture rate for solar neutrinos in the 37Cl detector is lower than the predicted capture rate. This discrepancy between theory and observation is known as the ‘solar neutrino problem’. I review the basic elements in this problem: the detector efficiency, the theory of stellar (solar) evolution, the nuclear physics of energy generation, and the uncertainties in the predictions. I also answer the questions of: So What? and What Next?

Standard solar models and the uncertainties in predicted capture rates of solar neutrinos

The uncertainties that affect the prediction of solar neutrino fluxes are evaluated with the aid of standard solar models. The uncertainties are determined from available data for all measured quantities that are known to affect significantly the neutrino fluxes; these include nuclear reaction rates, the solar constant, and the primordial surface composition of the sun. Uncertainties in theoretical quantities (such as the stellar opacity, the equation of state, and the rate of the proton-proton reaction) are estimated from the range of values in published state-of-the-art calculations. The uncertainty in each neutrino flux that is caused by a specified uncertainty in any of the parameters is evaluated with the aid of a series of standard solar models that were constructed for this purpose; the results are expressed in terms of the logarithmic partial derivative of each flux with respect to each parameter. The effects on the neutrino fluxes of changing individual parameters by large amounts can usually be estimated to satisfactory accuracy by making use of the tabulated partial derivatives. An overall "effective $3\ensuremath{\sigma}$ level of uncertainty" is defined using the requirement that the true value should lie within the estimated range unless someone has made a mistake. Effective $3\ensuremath{\sigma}$ levels of uncertainty, as well as best estimates, are determined for the following possible detectors of solar neutrinos: $^{2}\mathrm{H}$, $^{7}\mathrm{Li}$, $^{37}\mathrm{Cl}$, $^{71}\mathrm{Ga}$, $^{79}\mathrm{Br}$, $^{81}\mathrm{Br}$, $^{97}\mathrm{Mo}$, $^{98}\mathrm{Mo}$, $^{115}\mathrm{In}$, and electron-neutrino scattering. The most important sources of uncertainty in the predicted capture rates are identified and discussed for each detector separately. For the $^{37}\mathrm{Cl}$ detector, the predicted capture rate is 7.6\ifmmode\pm\else\textpm\fi{}3.3 (effective $3\ensuremath{\sigma}$ errors) SNU. The measured production rate is (Cleveland, Davis, and Rowley, 1981) 2.1\ifmmode\pm\else\textpm\fi{}0.3 SNU ($1\ensuremath{\sigma}$ error). For a $^{71}\mathrm{Ga}$ detector, the expected capture rate is 106 (${1}_{\ensuremath{-}0.08}^{+0.12}$) SNU (also effective $3\ensuremath{\sigma}$ errors). The relatively small uncertainty quoted for the $^{71}\mathrm{Ga}$ detector is a direct result of the fact that $^{71}\mathrm{Ga}$ is primarily sensitive to neutrinos from the basic proton-proton reaction, the rate of which is determined largely by the observed solar luminosity. The Caltech and Munster measured values for the cross-section factor for the reaction $^{3}\mathrm{He}$($\ensuremath{\alpha}$,$\ensuremath{\gamma}$)$^{7}\mathrm{Be}$ are inconsistent with each other. The capture rates quoted above were obtained using the Caltech value for the cross-section factor. If the Munster value is used instead, then the predicted capture rate for the $^{37}\mathrm{Cl}$ experiment is 4.95\ifmmode\pm\else\textpm\fi{}2.1 SNU (effective $3\ensuremath{\sigma}$ errors) and, for the $^{71}\mathrm{Ga}$ experiment, 96.7 (${1}_{\ensuremath{-}0.08}^{+0.12}$) SNU (effective $3\ensuremath{\sigma}$ errors). In order for the best-estimate value to agree with the observation of Davis (1978) of 2 SNU for the $^{37}\mathrm{Cl}$ experiment, the cross-section factor ${S}_{34}(0)$ would have to be reduced by about $15\ensuremath{\sigma}$ to less than the Caltech value, i.e. to $7\ensuremath{\sigma}$ less than the Munster value. The characteristics of the standard solar model, constructed with the best available nuclear parameters, solar opacity, and equation of state, are presented in detail. The computational methods by which this and similar models were obtained are also described briefly. The primordial helium abundance inferred with the aid of standard solar models is $Y=0.25\ifmmode\pm\else\textpm\fi{}0.01$. The complementary relation between observations of solar neutrinos and of the normal modes of oscillation of the sun is examined. It is shown that the splitting of the observed large-$n$, small-$l$, $p$-mode (five minute) oscillations of the sun primarily originates in the outer ten percent of the solar mass, while the neutrinos from $^{8}\mathrm{B}$ beta decay originate primarily in the inner five percent of the solar mass. The solar luminosity, and the flux of neutrinos from the proton-proton reaction, come mostly from an intermediate region.

Neutrinos from a standard solar model

view Abstract Citations (26) References (34) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Neutrinos from a standard solar model Filippone, B. W. ; Schramm, D. N. Abstract Solar model calculations are performed, as both (1) an independent check of the new value for the Cl-37 capture rate, and (2) an extension of the input parameters of a standard model to the extremes of experimental and theoretical limits with a view to implications for stellar evolution or neutrino physics. Capture rates are calculated for the on-line Cl-37 experiment and the proposed experiment employing Ga-71 as an example of a detector sensitive to the high-flux, lower-energy p-p neutrinos. The effects of uncertainties in the input parameters on the predicted capture rate in the two detectors are examined by: (1) calculating the effect of individual uncertainties on the mean standard model and summing these errors in quadrature; (2) simultaneously varying several key parameters to yield upper and lower limits; and (3) by generating a set of models whose parameters are determined by a Monte Carlo method. Publication: The Astrophysical Journal Pub Date: February 1982 DOI: 10.1086/159643 Bibcode: 1982ApJ...253..393F Keywords: Particle Flux Density; Solar Flux; Solar Neutrinos; Stellar Models; Stellar Structure; Abundance; Capture Effect; Chlorine; Gallium Isotopes; Monte Carlo Method; Nuclear Fusion; Standard Deviation; Stellar Evolution; Stellar Luminosity; Solar Physics full text sources ADS |

New Solar-Neutrino Flux Calculations and Implications Regarding Neutrino Oscillations

The results of new calculations of solar-neutrino fluxes are presented; the fluxes are obtained from detailed solar models that make use of improved opacities and nuclear-physics cross sections. By evaluating known uncertainties in the predicted capture rate for the $^{37}\mathrm{Cl}$ solar-neutrino experiment, we find that the ratio of theoretical to (best-estimate) observed capture rate lies in the range 4.0 to 2.6. These results constitute a strong constraint on models of neutrino oscillations if the entire discrepancy is ascribed to neutrino oscillations.

Solar Neutrinos.IV. Effect of Radiative Opacities on Calculated Neutrino Fluxes

The effect of radiativc opacities on the predicted capture rate for the / sup 37/Cl solar neutrino experiment is investigated with the aid of new opacities obtained from an improved Los Alamos code. (auth)

Solar Neutrinos

The predicted capture rate in the ${\mathrm{Cl}}^{37}$ experiment for detecting solar neutrinos is calculated using the results of recent nuclear experiments and solar-model investigations. It is shown that additional experiments (e.g., with ${\mathrm{H}}^{2}$, ${\mathrm{Li}}^{7}$, ${\mathrm{B}}^{11}$, or $\ensuremath{\nu}\ensuremath{-}e$ scattering) are necessary to establish the relative contributions of the proton-proton chain and the CNO cycle to solar energy generation.