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A Study of Possible Applications of the Half-Projected Hartree-Fock Method for Determining Singlet Excited States

The Half-Projected Hartree-Fock model (HPHF) is proposed for determining open shell singlet states. Some properties of the HPHF wave function are reviewed in order to discuss its application to determining excited states of medium size molecules. A calculation procedure similar to that of the UHF method is described. Some results for the methylene biradical and formic acid are presented. The HPHF model is found to be useful for determining the lowest excited states

The r-mode instability: Analytical solution with gravitational radiation reaction

Analytical r-mode solutions are investigated within the linearized theory in the case of a slowly rotating, Newtonian, barotropic, non-magnetized, perfect-fluid star in which the gravitational radiation (GR) reaction force is present. For the GR reaction term we use the 3.5 post-Newtonian order expansion of the GR force, in order to include the contribution of the current quadrupole moment. We find the explicit expression for the r-mode velocity perturbations and we conclude that they are sinusoidal with the same frequency as the well-known GR force-free linear r-mode solution, and that the GR force drives the r-modes unstable with a growth timescale that agrees with the expression first found by Lindblom, Owen and Morsink. We also show that the amplitude of these velocity perturbations is corrected, relatively to the GR force-free case, by a term of order W^6, where W is the angular velocity of the star.Comment: 11 pages, RevTeX4. Discussion on the nonlinear theory removed. Published versio

Theory of Stellar Oscillations

In recent years, astronomers have witnessed major progresses in the field of stellar physics. This was made possible thanks to the combination of a solid theoretical understanding of the phenomena of stellar pulsations and the availability of a tremendous amount of exquisite space-based asteroseismic data. In this context, this chapter reviews the basic theory of stellar pulsations, considering small, adiabatic perturbations to a static, spherically symmetric equilibrium. It starts with a brief discussion of the solar oscillation spectrum, followed by the setting of the theoretical problem, including the presentation of the equations of hydrodynamics, their perturbation, and a discussion of the functional form of the solutions. Emphasis is put on the physical properties of the different types of modes, in particular acoustic (p-) and gravity (g-) modes and their propagation cavities. The surface (f-) mode solutions are also discussed. While not attempting to be comprehensive, it is hoped that the summary presented in this chapter addresses the most important theoretical aspects that are required for a solid start in stellar pulsations research.Comment: Lecture presented at the IVth Azores International Advanced School in Space Sciences on "Asteroseismology and Exoplanets: Listening to the Stars and Searching for New Worlds" (arXiv:1709.00645), which took place in Horta, Azores Islands, Portugal in July 201

CCSD(T) Study of CD3-O-CD3 and CH3-O-CD3 Far-Infrared Spectra

From a vibrationally corrected 3D potential energy surface determined with highly correlated ab initio calculations (CCSD(T)), the lowest vibrational energies of two dimethyl-ether isotopologues, 12CH3–16O–12CD3 (DME-d3) and 12CD3–16O–12CD3 (DME-d6), are computed variationally. The levels that can be populated at very low temperatures correspond to the COC-bending and the two methyl torsional modes. Molecular symmetry groups are used for the classification of levels and torsional splittings. DME-d6 belongs to the G36 group, as the most abundant isotopologue 12CH3–16O–12CH3 (DME-h6), while DME-d3 is a G18 species. Previous assignments of experimental Raman and far-infrared spectra are discussed from an effective Hamiltonian obtained after refining the ab initio parameters. Because a good agreement between calculated and experimental transition frequencies is reached, new assignments are proposed for various combination bands corresponding to the two deuterated isotopologues and for the 020 → 030 transition of DME-d6. Vibrationally corrected potential energy barriers, structural parameters, and anharmonic spectroscopic parameters are provided. For the 3N – 9 neglected vibrational modes, harmonic and anharmonic fundamental frequencies are obtained using second-order perturbation theory by means of CCSD and MP2 force fields. Fermi resonances between the COC-bending and the torsional modes modify DME-d3 intensities and the band positions of the torsional overtones

Age determination of the HR8799 planetary system using asteroseismology

Discovery of the first planetary system by direct imaging around HR8799 has made the age determination of the host star a very important task. This determination is the key to derive accurate masses of the planets and to study the dynamical stability of the system. The age of this star has been estimated using different procedures. In this work we show that some of these procedures have problems and large uncertainties, and the real age of this star is still unknown, needing more observational constraints. Therefore, we have developed a comprehensive modeling of HR8799, and taking advantage of its gamma Doradus-type pulsations, we have estimated the age of the star using asteroseismology. The accuracy in the age determination depends on the rotation velocity of the star, and therefore an accurate value of the inclination angle is required to solve the problem. Nevertheless, we find that the age estimate for this star previously published in the literature ([30,160] Myr) is unlikely, and a more accurate value might be closer to the Gyr. This determination has deep implications on the value of the mass of the objects orbiting HR8799. An age around $\approx$ 1 Gyr implies that these objects are brown dwarfs.Comment: 5 pages, 3 figures, accepted in MNRAS Letter

Second-order rotational effects on the r-modes of neutron stars

Techniques are developed here for evaluating the r-modes of rotating neutron stars through second order in the angular velocity of the star. Second-order corrections to the frequencies and eigenfunctions for these modes are evaluated for neutron star models. The second-order eigenfunctions for these modes are determined here by solving an unusual inhomogeneous hyperbolic boundary-value problem. The numerical techniques developed to solve this unusual problem are somewhat non-standard and may well be of interest beyond the particular application here. The bulk-viscosity coupling to the r-modes, which appears first at second order, is evaluated. The bulk-viscosity timescales are found here to be longer than previous estimates for normal neutron stars, but shorter than previous estimates for strange stars. These new timescales do not substantially affect the current picture of the gravitational radiation driven instability of the r-modes either for neutron stars or for strange stars.Comment: 13 pages, 5 figures, revte

On a mechanism for enhancing magnetic activity in tidally interacting binaries

We suggest a mechanism for enhancing magnetic activity in tidally interacting binaries. We suppose that the deviation of the primary star from spherical symmetry due to the tidal influence of the companion leads to stellar pulsation in its fundamental mode. It is shown that stellar radial pulsation amplifies torsional Alfv{\'e}n waves in a dipole-like magnetic field, buried in the interior, according to the recently proposed swing wave-wave interaction (Zaqarashvili 2001). Then amplified Alfv{\'e}n waves lead to the onset of large-scale torsional oscillations, and magnetic flux tubes arising towards the surface owing to magnetic buoyancy diffuse into the atmosphere producing enhanced chromospheric and coronal emission.Comment: Accepted in Ap

First Kepler results on compact pulsators VIII: Mode identifications via period spacings in g−g-mode pulsating Subdwarf B stars

We investigate the possibility of nearly-equally spaced periods in 13 hot subdwarf B (sdB) stars observed with the Kepler spacecraft and one observed with CoRoT. Asymptotic limits for gravity (g-)mode pulsations provide relationships between equal period spacings of modes with differing degrees and relationships between periods of the same radial order but differing degrees. Period transforms, Kolmogorov-Smirnov tests, and linear least-squares fits have been used to detect and determine the significance of equal period spacings. We have also used Monte Carlo simulations to estimate the likelihood that the detected spacings could be produced randomly. Period transforms for nine of the Kepler stars indicate ell=1 period spacings, with five also showing peaks for ell=2 modes. 12 stars indicate ell=1 modes using the Kolmogorov-Smirnov test while another shows solely ell=2 modes. Monte Carlo results indicate that equal period spacings are significant in 10 stars above 99% confidence and 13 of the 14 are above 94% confidence. For 12 stars, the various methods find consistent regular period spacing values to within the errors, two others show some inconsistencies, likely caused by binarity, and the last has significant detections but the mode assignment disagrees between methods. We find a common ell=1 period spacing spanning a range from 231 to 272 s allowing us to correlate pulsation modes with 222 periodicities and that the ell=2 period spacings are related to the ell=1 spacings by the asymptotic relationship $1/\sqrt{3}$. We briefly discuss the impact of equal period spacings which indicate low-degree modes with a lack of significant mode trappings.Comment: 27 pages, 4 figures, 17 tables. Accepted for publication in Monthly Notices of the Royal Astronomical Societ