A new HW Vir binary from the Palomar Transient Factory: PTF1 J072455.75+125300.3 - An eclipsing subdwarf B binary with a M-star companion

We report the discovery of an eclipsing binary -- PTF1 J072456$+$125301-- composed of a subdwarf B (sdB) star ($g'=17.2^m$) with a faint companion. Subdwarf B stars are core helium-burning stars, which can be found on the extreme horizontal branch. About half of them reside in close binary systems, but few are known to be eclipsing, for which fundamental stellar parameters can be derived.\newline We conducted an analysis of photometric data and spectra from the Palomar 60'' and the 200" Hale telescope respectively. A quantitative spectral analysis found an effective temperature of $T_{\text{eff}}=33900\pm350$\,K, log g = $5.74\pm0.08$ and log($n_{\text{He}}/n_{\text{H}}) = -2.02 \pm0.07$, typical for an sdB star. The companion does not contribute to the optical light of the system, except through a distinct reflection effect. From the light curve an orbital period of 0.09980(25)\,d and a system inclination of 83.56\pm0.30\,^{\circ} were derived. The radial velocity curve yielded an orbital semi-amplitude of K_1=95.8\pm 8.1\,\text{km s^{-1}}. The mass for the M-type dwarf companion is $0.155\pm0.020\,M_{\odot}$. PTF1\,J072456$+$125301 has similar atmospheric parameters to those of pulsating sdB stars (V346 Hya stars). Therefore it could be a high-priority object for asteroseismology, if pulsations were detected such as in the enigmatic case of NY Vir.Comment: Accepted to A&A, 7pages, 4 figure

Application of approximation theory by nonlinear manifolds in Sturm-Liouville inverse problems

We give here some negative results in Sturm-Liouville inverse theory, meaning that we cannot approach any of the potentials with $m+1$ integrable derivatives on $\mathbb{R}^+$ by an $\omega$-parametric analytic family better than order of $(\omega\ln\omega)^{-(m+1)}$. Next, we prove an estimation of the eigenvalues and characteristic values of a Sturm-Liouville operator and some properties of the solution of a certain integral equation. This allows us to deduce from [Henkin-Novikova] some positive results about the best reconstruction formula by giving an almost optimal formula of order of $\omega^{-m}$.Comment: 40 page

Phase resolved spectroscopy and Kepler photometry of the ultracompact AM CVn binary SDSS J190817.07+394036.4

{\it Kepler} satellite photometry and phase-resolved spectroscopy of the ultracompact AM CVn type binary SDSS J190817.07+394036.4 are presented. The average spectra reveal a variety of weak metal lines of different species, including silicon, sulphur and magnesium as well as many lines of nitrogen, beside the strong absorption lines of neutral helium. The phase-folded spectra and the Doppler tomograms reveal an S-wave in emission in the core of the He I 4471 \AA\,absorption line at a period of $P_{\rm orb}=1085.7\pm2.8$\,sec identifying this as the orbital period of the system. The Si II, Mg II and the core of some He I lines show an S-wave in absorption with a phase offset of $170\pm15^\circ$ compared to the S-wave in emission. The N II, Si III and some helium lines do not show any phase variability at all. The spectroscopic orbital period is in excellent agreement with a period at $P_{\rm orb}=1085.108(9)$\,sec detected in the three year {\it Kepler} lightcurve. A Fourier analysis of the Q6 to Q17 short cadence data obtained by {\it Kepler} revealed a large number of frequencies above the noise level where the majority shows a large variability in frequency and amplitude. In an O-C analysis we measured a $\vert\dot{P}\vert\sim1.0\,$x$\,10^{-8}\,$s\,s$^{-1}$ for some of the strongest variations and set a limit for the orbital period to be $\vert\dot{P}\vert<10^{-10}$s\,s$^{-1}$. The shape of the phase folded lightcurve on the orbital period indicates the motion of the bright spot. Models of the system were constructed to see whether the phases of the radial velocity curves and the lightcurve variation can be combined to a coherent picture. However, from the measured phases neither the absorption nor the emission can be explained to originate in the bright spot.Comment: Accepted for publication in MNRAS, 15 pages, 14 figures, 5 table

Small-Energy Analysis for the Selfadjoint Matrix Schroedinger Operator on the Half Line

The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the most general selfadjoint boundary condition at the origin. When the matrix potential is integrable and has a first moment, it is shown that the corresponding scattering matrix is continuous at zero energy. An explicit formula is provided for the scattering matrix at zero energy. The small-energy asymptotics are established also for the corresponding Jost matrix, its inverse, and various other quantities relevant to the corresponding direct and inverse scattering problems.Comment: This published version has been edited to improve the presentation of the result

Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation

The Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral measure for that boundary condition, and a subset of the discrete eigenvalues for a different boundary condition. This result extends the celebrated two-spectrum uniqueness theorem of Borg and Marchenko to the case where there is also a continuous spectru

Whittaker-Hill equation and semifinite-gap Schroedinger operators

A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by applying Darboux transformations to the Whittaker-Hill equation. We give a criterion of the regularity of the corresponding potentials and investigate the spectral properties of the new operators.Comment: Revised versio

The inverse scattering problem at fixed energy based on the Marchenko equation for an auxiliary Sturm-Liouville operator

A new approach is proposed to the solution of the quantum mechanical inverse scattering problem at fixed energy. The method relates the fixed energy phase shifts to those arising in an auxiliary Sturm-Liouville problem via the interpolation theory of the Weyl-Titchmarsh m-function. Then a Marchenko equation is solved to obtain the potential.Comment: 6 pages, 8 eps figure

Genuine converging solution of self-consistent field equations for extended many-electron systems

Calculations of the ground state of inhomogeneous many-electron systems involve a solving of the Poisson equation for Coulomb potential and the Schroedinger equation for single-particle orbitals. Due to nonlinearity and complexity this set of equations, one believes in the iterative method for the solution that should consist in consecutive improvement of the potential and the electron density until the self-consistency is attained. Though this approach exists for a long time there are two grave problems accompanying its implementation to infinitely extended systems. The first of them is related with the Poisson equation and lies in possible incompatibility of the boundary conditions for the potential with the electron density distribution. The analysis of this difficulty and suggested resolution are presented for both infinite conducting systems in jellium approximation and periodic solids. It provides the existence of self-consistent solution for the potential at every iteration step due to realization of a screening effect. The second problem results from the existence of continuous spectrum of Hamiltonian eigenvalues for unbounded systems. It needs to have a definition of Hilbert space basis with eigenfunctions of continuous spectrum as elements, which would be convenient in numerical applications. The definition of scalar product specifying the Hilbert space is proposed that incorporates a limiting transition. It provides self-adjointness of Hamiltonian and, respectively, the orthogonality of eigenfunctions corresponding to the different eigenvalues. In addition, it allows to normalize them effectively to delta-function and to prove in the general case the orthogonality of the 'right' and 'left' eigenfunctions belonging to twofold degenerate eigenvalues.Comment: 12 pages. Reported on Interdisciplinary Workshop "Nonequilibrium Green's Functions III", August 22 - 26, 2005, University Kiel, Germany. To be published in Journal of Physics: Conference Series, 2006; Typos in Eqs. (37), (53) and (54) are corrected. The content of the footnote is changed. Published version available free online at http://www.iop.org/EJ/abstract/1742-6596/35/1/01

Late pleistocene sedimentation history of the Shirshov Ridge, Bering Sea

The analysis of the lithology, grain-size distribution, clay minerals, and geochemistry of Upper Pleistocene sediments from the submarine Shirshov Ridge (Bering Sea) showed that the main source area was the Yukon–Tanana terrane of Central Alaska. The sedimentary materials were transported by the Yukon River through Beringia up to the shelf break, where they were entrained by a strong northwestward-flowing sea current. The lithological data revealed several pulses of ice-rafted debris deposition, roughly synchronous with Heinrich events, and periods of weaker bottom-current intensity. Based on the geochemical results, we distinguished intervals of an increase in paleoproductivity and extension of the oxygen minimum zone. The results suggest that there were three stages of deposition driven by glacioeustatic sea-level fluctuations and glacial cycles in Alaska