A detector of small harmonic displacements based on two coupled microwave cavities

The design and test of a detector of small harmonic displacements is presented. The detector is based on the principle of the parametric conversion of power between the resonant modes of two superconducting coupled microwave cavities. The work is based on the original ideas of Bernard, Pegoraro, Picasso and Radicati, who, in 1978, suggested that superconducting coupled cavities could be used as sensitive detectors of gravitational waves, and on the work of Reece, Reiner and Melissinos, who, {in 1984}, built a detector of this kind. They showed that an harmonic modulation of the cavity length l produced an energy transfer between two modes of the cavity, provided that the frequency of the modulation was equal to the frequency difference of the two modes. They achieved a sensitivity to fractional deformations of dl/l~10^{-17} Hz^{-1/2}. We repeated the Reece, Reiner and Melissinos experiment, and with an improved experimental configuration and better cavity quality, increased the sensitivity to dl/l~10^{-20} Hz^{-1/2}. In this paper the basic principles of the device are discussed and the experimental technique is explained in detail. Possible future developments, aiming at gravitational waves detection, are also outlined.Comment: 28 pages, 12 eps figures, ReVteX. \tightenlines command added to reduce number of pages. The following article has been accepted by Review of Scientific Instruments. After it is published, it will be found at http://link.aip.org/link/?rs

Pairing gaps in Hartree-Fock Bogoliubov theory with the Gogny D1S interaction

As part of a program to study odd-A nuclei in the Hartree-Fock-Bogoliubov (HFB) theory, we have developed a new calculational tool to find the HFB minima of odd-A nuclei based on the gradient method and using interactions of Gogny's form. The HFB minimization includes both time-even and time-odd fields in the energy functional, avoiding the commonly used "filling approximation". Here we apply the method to calculate neutron pairing gaps in some representative isotope chains of spherical and deformed nuclei, namely the Z=8,50 and 82 spherical chains and the Z=62 and 92 deformed chains. We find that the gradient method is quite robust, permitting us to carry out systematic surveys involving many nuclei. We find that the time-odd field does not have large effect on the pairing gaps calculated with the Gogny D1S interaction. Typically, adding the T-odd field as a perturbation increases the pairing gap by ~100 keV, but the re-minimization brings the gap back down. This outcome is very similar to results reported for the Skyrme family of nuclear energy density functionals. Comparing the calculated gaps with the experimental ones, we find that the theoretical errors have both signs implying that the D1S interaction has a reasonable overall strength. However, we find some systematic deficiencies comparing spherical and deformed chains and comparing the lighter chains with the heavier ones. The gaps for heavy spherical nuclei are too high, while those for deformed nuclei tend to be too low. The calculated gaps of spherical nuclei show hardly any A-dependence, contrary to the data. Inclusion of the T-odd component of the interaction does not change these qualitative findings

Novel analysis of chiral loop effects in the generalized Gerasimov-Drell-Hearn sum rule

We study the chiral loop corrections to the generalized Gerasimov-Drell-Hearn sum rule of the nucleon for finite photon virtuality in the framework of a Lorentz-invariant formulation of baryon chiral perturbation theory. We perform a complete one-loop calculation and obtain significant differences to previously found results based on the heavy baryon approach for the proton and neutron spin-dependent forward Compton amplitudes.Comment: 7 pp, 3 figs, published version, extended discussion, minor revision

Mixed Meson Masses with Domain-Wall Valence and Staggered Sea Fermions

Mixed action lattice calculations allow for an additive lattice spacing dependent mass renormalization of mesons composed of one sea and one valence quark, regardless of the type of fermion discretization methods used in the valence and sea sectors. The value of the mass renormalization depends upon the lattice actions used. This mixed meson mass shift is an important lattice artifact to determine for mixed action calculations; because it modifies the pion mass, it plays a central role in the low energy dynamics of all hadronic correlation functions. We determine the leading order, $\mathcal{O}(a^2)$, and next to leading order, $\mathcal{O}(a^2 m_\pi^2)$, additive mass shift of \textit{valence-sea} mesons for a mixed lattice action with domain-wall valence fermions and rooted staggered sea fermions, relevant to the majority of current large scale mixed action lattice efforts. We find that on the asqtad improved coarse MILC lattices, this additive mass shift is well parameterized in lattice units by $\Delta(am)^2 = 0.034(2) -0.06(2) (a m_\pi)^2$, which in physical units, using $a=0.125$ fm, corresponds to $\Delta(m)^2 = (291\pm 8 \textrm{MeV})^2 -0.06(2) m_\pi^2$. In terms of the mixed action effective field theory parameters, the corresponding mass shift is given by $a^2 \Delta_\mathrm{Mix} = (316 \pm 4 \textrm{MeV})^2$ at leading order plus next-to-leading order corrections including the necessary chiral logarithms for this mixed action calculation, determined in this work. Within the precision of our calculation, one can not distinguish between the full next-to-leading order effective field theory analysis of this additive mixed meson mass shift and the parameterization given above.Comment: 28 pages, 3 figures, 5 table

The rf control and detection system for PACO the parametric converter detector

In this technical note the rf control and detection system for a detector of small harmonic displacements based on two coupled microwave cavities (PACO) is presented. The basic idea underlying this detector is the principle of parametric power conversion between two resonant modes of the system, stimulated by the (small) harmonic modulation of one system parameter. In this experiment we change the cavity length applying an harmonic voltage to a piezo-electric crystal. The system can achieve a great sensitivity to small harmonic displacements and can be an interesting candidate for the detection of small, mechanically coupled, interactions (e.g. high frequency gravitational waves).Comment: 13 pages, 4 postscript figure

The Final Merger of Black-Hole Binaries

Recent breakthroughs in the field of numerical relativity have led to dramatic progress in understanding the predictions of General Relativity for the dynamical interactions of two black holes in the regime of very strong gravitational fields. Such black-hole binaries are important astrophysical systems and are a key target of current and developing gravitational-wave detectors. The waveform signature of strong gravitational radiation emitted as the black holes fall together and merge provides a clear observable record of the process. After decades of slow progress, these mergers and the gravitational-wave signals they generate can now be routinely calculated using the methods of numerical relativity. We review recent advances in understanding the predicted physics of events and the consequent radiation, and discuss some of the impacts this new knowledge is having in various areas of astrophysics.Comment: 57 pages; 9 figures. Updated references & fixed typos. Published version is at http://www.annualreviews.org/doi/abs/10.1146/annurev.nucl.010909.08324

Black-hole binaries, gravitational waves, and numerical relativity

Understanding the predictions of general relativity for the dynamical interactions of two black holes has been a long-standing unsolved problem in theoretical physics. Black-hole mergers are monumental astrophysical events, releasing tremendous amounts of energy in the form of gravitational radiation, and are key sources for both ground- and space-based gravitational-wave detectors. The black-hole merger dynamics and the resulting gravitational waveforms can only be calculated through numerical simulations of Einstein's equations of general relativity. For many years, numerical relativists attempting to model these mergers encountered a host of problems, causing their codes to crash after just a fraction of a binary orbit could be simulated. Recently, however, a series of dramatic advances in numerical relativity has allowed stable, robust black-hole merger simulations. This remarkable progress in the rapidly maturing field of numerical relativity, and the new understanding of black-hole binary dynamics that is emerging is chronicled. Important applications of these fundamental physics results to astrophysics, to gravitational-wave astronomy, and in other areas are also discussed.Comment: 54 pages, 42 figures. Some typos corrected & references updated. Essentially final published versio

Neon, sulphur and argon abundances of planetary nebulae in the sub-solar metallicity Galactic anti-centre

Context: Spectra of planetary nebulae show numerous fine structure emission lines from ionic species, enabling us to study the overall abundances of the nebular material that is ejected into the interstellar medium. The abundances derived from planetary nebula emission show the presence of a metallicity gradient within the disk of the Milky Way up to Galactocentric distances of ∼ 10 kpc, which are consistent with findings from studies of different types of sources, including H II regions and young B-type stars. The radial dependence of these abundances further from the Galactic centre is in dispute. Aims: We aim to derive the abundances of neon, sulphur and argon from a sample of planetary nebulae towards the Galactic anti- centre, which represent the abundances of the clouds from which they were formed, as they remain unchanged throughout the course of stellar evolution. We then aim to compare these values with similarly analysed data from elsewhere in the Milky Way in order to observe whether the abundance gradient continues in the outskirts of our Galaxy. Methods: We have observed 23 planetary nebulae at Galactocentric distances of 8–21 kpc with Spitzer IRS. The abundances were calculated from infrared emission lines, for which we observed the main ionisation states of neon, sulphur, and argon, which are little affected by extinction and uncertainties in temperature measurements or fluctuations within the planetary nebula. We have complemented these observations with others from optical studies in the literature, in order to reduce or avoid the need for ionisation correction factors in abundance calculations. Results: The overall abundances of our sample of planetary nebulae in the Galactic anti-centre are lower than those in the solar neighbourhood. The abundances of neon, sulphur, and argon from these stars are consistent with a metallicity gradient from the solar neighbourhood up to Galactocentric distances of ∼ 20 kpc, albeit with varying degrees of dispersion within the data

Parametric gravity wave detector

Since 1978 superconducting coupled cavities have been proposed as a sensitive detector of gravitational waves. The interaction of the gravitational wave with the cavity walls, and the esulting motion, induces the transition of some energy from an initially excited cavity mode to an empty one. The energy transfer is maximum when the frequency of the wave is equal to the frequency difference of the two cavity modes. In 1984 Reece, Reiner and Melissinos built a detector of the type proposed, and used it as a transducer of harmonic mechanical motion, achieving a sensitivity to fractional deformations of the order dx/x ~ 10^(-18). In this paper the working principles of the detector are discussed and the last experimental results summarized. New ideas for the development of a realistic gravitational waves detector are considered; the outline of a possible detector design and its expected sensitivity are also shown.Comment: 9 pages, 6 figures. Talk given at the Workshop on Electromagnetic Probes of Fundamentals Physics, Erice (Italy), October 200