Reference-State One-Particle Density-Matrix Theory

A density-matrix formalism is developed based on the one-particle density-matrix of a single-determinantal reference-state. The v-representable problem does not appear in the proposed method, nor the need to introduce functionals defined by a constrained search. The correlation-energy functionals are not universal; they depend on the external potential. Nevertheless, model systems can still be used to derive universal energy-functionals. In addition, the correlation-energy functionals can be partitioned into individual terms that are -- to a varying degree -- universal; yielding, for example, an electron gas approximation. Variational and non-variational energy functionals are introduced that yield the target-state energy when the reference state -- or its corresponding one-particle density matrix -- is constructed from Brueckner orbitals. Using many-body perturbation theory, diagrammatic expansions are given for the non-variational energy-functionals, where the individual diagrams explicitly depend on the one-particle density-matrix. Non-variational energy-functionals yield generalized Hartree--Fock equations involving a non-local correlation-potential and the Hartree--Fock exchange; these equations are obtained by imposing the Brillouin--Brueckner condition. The same equations -- for the most part -- are obtained from variational energy-functionals using functional minimizations, yielding the (kernel of) correlation potential as the functional derivative of correlation-energy functionals. Approximations for the correlation-energy functions are introduced, including a one-particle-density-matrix variant of the local-density approximation (LDA) and a variant of the Lee--Yang--Parr (LYP) functional.Comment: 68 Page, 0 Figures, RevTeX 4, Submitted to Phys.Rev.A (on April 28 2003

The Effect of Combined Magnetic Geometries on Thermally Driven Winds I: Interaction of Dipolar and Quadrupolar Fields

Cool stars with outer convective envelopes are observed to have magnetic fields with a variety of geometries, which on large scales are dominated by a combination of the lowest order fields such as the dipole, quadrupole and octupole modes. Magnetised stellar wind outflows are primarily responsible for the loss of angular momentum from these objects during the main sequence. Previous works have shown the reduced effectiveness of the stellar wind braking mechanism with increasingly complex, but singular, magnetic field geometries. In this paper, we quantify the impact of mixed dipolar and quadrupolar fields on the spin-down torque using 50 MHD simulations with mixed field, along with 10 of each pure geometries. The simulated winds include a wide range of magnetic field strength and reside in the slow-rotator regime. We find that the stellar wind braking torque from our combined geometry cases are well described by a broken power law behaviour, where the torque scaling with field strength can be predicted by the dipole component alone or the quadrupolar scaling utilising the total field strength. The simulation results can be scaled and apply to all main-sequence cool stars. For Solar parameters, the lowest order component of the field (dipole in this paper) is the most significant in determining the angular momentum loss.Comment: 15 pages + 9 figures (main), 3 pages + 1 figure (appendix), accepted for publication to Ap

The Effect of Magnetic Variability on Stellar Angular Momentum Loss II: The Sun, 61 Cygni A, ϵ\epsilon Eridani, ξ\xi Bootis A and τ\tau Bootis A

The magnetic fields of low-mass stars are observed to be variable on decadal timescales, ranging in behaviour from cyclic to stochastic. The changing strength and geometry of the magnetic field should modify the efficiency of angular momentum loss by stellar winds, but this has not been well quantified. In Finley et al. (2018) we investigated the variability of the Sun, and calculated the time-varying angular momentum loss rate in the solar wind. In this work, we focus on four low-mass stars that have all had their surface magnetic fields mapped for multiple epochs. Using mass loss rates determined from astrospheric Lyman-$\alpha$ absorption, in conjunction with scaling relations from the MHD simulations of Finley & Matt (2018), we calculate the torque applied to each star by their magnetised stellar winds. The variability of the braking torque can be significant. For example, the largest torque for $\epsilon$ Eri is twice its decadal averaged value. This variation is comparable to that observed in the solar wind, when sparsely sampled. On average, the torques in our sample range from 0.5-1.5 times their average value. We compare these results to the torques of Matt et al. (2015), which use observed stellar rotation rates to infer the long-time averaged torque on stars. We find that our stellar wind torques are systematically lower than the long-time average values, by a factor of ~3-30. Stellar wind variability appears unable to resolve this discrepancy, implying that there remain some problems with observed wind parameters, stellar wind models, or the long-term evolution models, which have yet to be understood.Comment: 15 pages + 8 figures, accepted for publication to Ap

The TeV Energy Spectrum of Mrk 421 Measured in A High Flaring State

The BL Lac object (blazar) Mrk 421 was observed during its outburst in April 2004 with the Whipple 10 m telescope for a total of about 24.5 hours. The measured gamma-ray rate varied substantially over the range from 4 to 10 gamma's/min and eventually exceeded the steady gamma-ray rate of the Crab Nebula (standard candle) by a factor of 3. The overall significance of the gamma-ray signal exceeded 70 sigma and the total number of excess events was more than 10,000. The signal light curve does not show any particular variability pattern. This unique Mrk 421 outburst enabled the measurement of a high quality spectrum of very high-energy gamma rays in a high state of emission. This spectrum is a power-law and it extends beyond 10 TeV.Comment: 4 pages, 5 figures, Proc. 30th International Cosmic Ray Conference, Merida, Mexico, 200

Letter from William P. Finley & Jenny Finley to James B. Finley

James\u27 brother William writes to express his affection for James and Hannah. He announces the birth of a son -- Robert Patterson Finley. William tells James that their brother John has gone to to Xenia to teach school. William fears that John has lost religion. Abstract Number - 916https://digitalcommons.owu.edu/finley-letters/1402/thumbnail.jp

Letter from William P. Finley & Jenny Finley to James B. Finley

This letter is full of expressions of hope for Heaven. William tells of some financial trouble he has had about a mare. William asks to borrow $10 from James. A girl has been born into the family and named Rebecca. Abstract Number - 920https://digitalcommons.owu.edu/finley-letters/1201/thumbnail.jp