Gravitomagnetism and the Earth-Mercury range

We numerically work out the impact of the general relativistic Lense-Thirring effect on the Earth-Mercury range caused by the gravitomagnetic field of the rotating Sun. The peak-to peak nominal amplitude of the resulting time-varying signal amounts to 1.75 10^1 m over a temporal interval 2 yr. Future interplanetary laser ranging facilities should reach a cm-level in ranging to Mercury over comparable timescales; for example, the BepiColombo mission, to be launched in 2014, should reach a 4.5 - 10 cm level over 1 - 8 yr. We looked also at other Newtonian (solar quadrupole mass moment, ring of the minor asteroids, Ceres, Pallas, Vesta, Trans-Neptunian Objects) and post-Newtonian (gravitoelectric Schwarzschild solar field) dynamical effects on the Earth-Mercury range. They act as sources of systematic errors for the Lense-Thirring signal which, in turn, if not properly modeled, may bias the recovery of some key parameters of such other dynamical features of motion. Their nominal peak-to-peak amplitudes are as large as 4 10^5 m (Schwarzschild), 3 10^2 m (Sun's quadrupole), 8 10^1 m (Ceres, Pallas, Vesta), 4 m (ring of minor asteroids), 8 10^-1 m (Trans-Neptunian Objects). Their temporal patterns are different with respect to that of the gravitomagnetic signal.Comment: LaTex2e, 19 pages, 2 tables, 6 figures. Small typo in pag. 1406 of the published version fixe

Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. In particular, when the involved kernel is analytic in the sampling parameter it can be stated in an abstract setting of reproducing kernel Hilbert spaces of entire functions which includes as a particular case the classical Shannon sampling theory. This abstract setting allows us to obtain a sort of converse result and to characterize when the sampling formula associated with an analytic Kramer kernel can be expressed as a Lagrange-type interpolation series. On the other hand, the de Branges spaces of entire functions satisfy orthogonal sampling formulas which can be written as Lagrange-type interpolation series. In this work some links between all these ideas are established

The Zero-Removing Property and Lagrange-Type Interpolation Series

The classical Kramer sampling theorem, which provides a method for obtaining orthogonal sampling formulas, can be formulated in a more general nonorthogonal setting. In this setting, a challenging problem is to characterize the situations when the obtained nonorthogonal sampling formulas can be expressed as Lagrange-type interpolation series. In this article a necessary and sufficient condition is given in terms of the zero removing property. Roughly speaking, this property concerns the stability of the sampled functions on removing a finite number of their zeros

First preliminary tests of the general relativistic gravitomagnetic field of the Sun and new constraints on a Yukawa-like fifth force from planetary data

The general relativistic Lense-Thirring precessions of the perihelia of the inner planets of the Solar System are about 10^-3 arcseconds per century. Recent improvements in planetary orbit determination may yield the first observational evidence of such a tiny effect. Indeed, corrections to the known perihelion rates of -0.0036 +/- 0.0050, -0.0002 +/- 0.0004 and 0.0001 +/- 0.0005 arcseconds per century were recently estimated by E.V. Pitjeva for Mercury, the Earth and Mars, respectively, on the basis of the EPM2004 ephemerides and a set of more than 317,000 observations of various kinds. The predicted relativistic Lense-Thirring precessions for these planets are -0.0020, -0.0001 and -3 10^-5 arcseconds per century, respectively and are compatible with the determined perihelia corrections. The relativistic predictions fit better than the zero-effect hypothesis, especially if a suitable linear combination of the perihelia of Mercury and the Earth, which a priori cancels out any possible bias due to the solar quadrupole mass moment, is considered. However, the experimental errors are still large. Also the latest data for Mercury processed independently by Fienga et al. with the INPOP ephemerides yield preliminary insights about the existence of the solar Lense-Thirring effect. The data from the forthcoming planetary mission BepiColombo will improve our knowledge of the orbital motion of this planet and, consequently, the precision of the measurement of the Lense-Thirring effect. As a by-product of the present analysis, it is also possible to constrain the strength of a Yukawa-like fifth force to a 10^-12-10^-13 level at scales of about one Astronomical Unit (10^11 m).Comment: LaTex, 22 pages, 1 figure, 5 tables, 62 references. To appear in Planetary and Space Scienc

Gravitomagnetic Accelerators

We study a simple class of time-dependent rotating Ricci-flat cylindrically symmetric spacetime manifolds whose geodesics admit gravitomagnetic jets. The helical paths of free test particles in these jets up and down parallel to the rotation axis are analogous to those of charged particles in a magnetic field. The jets are attractors. The jet speed asymptotically approaches the speed of light. In effect, such source-free spacetime regions act as "gravitomagnetic accelerators".Comment: 4 pages, 2 figures; v2: reference added; v3: slightly expanded version accepted for publication in Phys. Lett.

Regular singular Sturm-Liouville operators and their zeta-determinants

We consider Sturm-Liouville operators on the line segment [0, 1] with general regular singular potentials and separated boundary conditions. We establish existence and a formula for the associated zeta-determinant in terms of the Wronski- determinant of a fundamental system of solutions adapted to the boundary conditions. This generalizes the earlier work of the first author, treating general regular singular potentials but only the Dirichlet boundary conditions at the singular end, and the recent results by Kirsten-Loya-Park for general separated boundary conditions but only special regular singular potentials.Comment: 38 pages, 2 figures; Completely revised according to the referees comprehensive suggestions; v3: minor corrections, accepted for publication in Journal of Functional Analysi

Search for blue compact dwarf galaxies during quiescence II: metallicities of gas and stars, ages, and star-formation rates

We examine the metallicity and age of a large set of SDSS/DR6 galaxies that may be Blue Compact Dwarf (BCD) galaxies during quiescence (QBCDs).The individual spectra are first classified and then averaged to reduce noise. The metallicity inferred from emission lines (tracing ionized gas) exceeds by ~0.35 dex the metallicity inferred from absorption lines (tracing stars). Such a small difference is significant according to our error budget estimate. The same procedure was applied to a reference sample of BCDs, and in this case the two metallicities agree, being also consistent with the stellar metallicity in QBCDs. Chemical evolution models indicate that the gas metallicity of QBCDs is too high to be representative of the galaxy as a whole, but it can represent a small fraction of the galactic gas, self enriched by previous starbursts. The luminosity weighted stellar age of QBCDs spans the whole range between 1 and 10 Gyr, whereas it is always smaller than 1 Gyr for BCDs. Our stellar ages and metallicities rely on a single stellar population spectrum fitting procedure, which we have specifically developed for this work using the stellar library MILES.Comment: Accepted for publication in ApJ. 20 pages. 16 figures (corrected typos