Comparison of LISA and Atom Interferometry for Gravitational Wave Astronomy in Space

One of the atom interferometer gravitational wave missions proposed by Dimopoulos et al.1 in 2008 was called AGIS-Sat. 2. It had a suggested gravitational wave sensitivity set by the atom state detection shot noise level that started at 1 mHz, was comparable to LISA sensitivity from 1 to about 20 mHz, and had better sensitivity from 20 to 500 mHz. The separation between the spacecraft was 1,000 km, with atom interferometers 200 m long and shades from sunlight used at each end. A careful analysis of many error sources was included, but requirements on the time-stability of both the laser wavefront aberrations and the atom temperatures in the atom clouds were not investigated. After including these considerations, the laser wavefront aberration stability requirement to meet the quoted sensitivity level is about 1\times10-8 wavelengths, and is far tighter than for LISA. Also, the temperature fluctuations between atom clouds have to be less than 1 pK. An alternate atom interferometer GW mission in Earth orbit called AGIS-LEO with 30 km satellite separation has been suggested recently. The reduction of wavefront aberration noise by sending the laser beam through a high-finesse mode-scrubbing optical cavity is discussed briefly, but the requirements on such a cavity are not given. Unfortunately, such an Earth-orbiting mission seems to be considerably more difficult to design than a non-geocentric mission and does not appear to have comparably attractive scientific goals.Comment: Submitted to Proc. 46th Rencontres de Moriond: Gravitational Waves and Experimental Gravity, March 20 - 27, 2011, La Thuile, Ital

Noise characterization for LISA

We consider the general problem of estimating the inflight LISA noise power spectra and cross-spectra, which are needed for detecting and estimating the gravitational wave signals present in the LISA data. For the LISA baseline design and in the long wavelength limit, we bound the error on all spectrum estimators that rely on the use of the fully symmetric Sagnac combination ($\zeta$). This procedure avoids biases in the estimation that would otherwise be introduced by the presence of a strong galactic background in the LISA data. We specialize our discussion to the detection and study of the galactic white dwarf-white dwarf binary stochastic signal.Comment: 9 figure

Effects of finite arm-length of LISA on analysis of gravitational waves from MBH binaries

Response of an interferometer becomes complicated for gravitational wave shorter than the arm-length of the detector, as nature of wave appears strongly. We have studied how parameter estimation for merging massive black hole binaries are affected by this complicated effect in the case of LISA. It is shown that three dimensional positions of some binaries might be determined much better than the past estimations that use the long wave approximation. For equal mass binaries this improvement is most prominent at \sim 10^5\sol.Comment: 10 pages, 3 figures, to appear in Phys.Rev.

Algebraic approach to time-delay data analysis for LISA

Cancellation of laser frequency noise in interferometers is crucial for attaining the requisite sensitivity of the triangular 3-spacecraft LISA configuration. Raw laser noise is several orders of magnitude above the other noises and thus it is essential to bring it down to the level of other noises such as shot, acceleration, etc. Since it is impossible to maintain equal distances between spacecrafts, laser noise cancellation must be achieved by appropriately combining the six beams with appropriate time-delays. It has been shown in several recent papers that such combinations are possible. In this paper, we present a rigorous and systematic formalism based on algebraic geometrical methods involving computational commutative algebra, which generates in principle {\it all} the data combinations cancelling the laser frequency noise. The relevant data combinations form the first module of syzygies, as it is called in the literature of algebraic geometry. The module is over a polynomial ring in three variables, the three variables corresponding to the three time-delays around the LISA triangle. Specifically, we list several sets of generators for the module whose linear combinations with polynomial coefficients generate the entire module. We find that this formalism can also be extended in a straight forward way to cancel Doppler shifts due to optical bench motions. The two modules are infact isomorphic. We use our formalism to obtain the transfer functions for the six beams and for the generators. We specifically investigate monochromatic gravitational wave sources in the LISA band and carry out the maximisiation over linear combinations of the generators of the signal-to-noise ratios with the frequency and source direction angles as parameters.Comment: 27 Pages, 6 figure

Annual modulation of the Galactic binary confusion noise bakground and LISA data analysis

We study the anisotropies of the Galactic confusion noise background and its effects on LISA data analysis. LISA has two data streams of the gravitational waves signals relevant for low frequency regime. Due to the anisotropies of the background, the matrix for their confusion noises has off-diagonal components and depends strongly on the orientation of the detector plane. We find that the sky-averaged confusion noise level $\sqrt {S(f)}$ could change by a factor of 2 in three months, and would be minimum when the orbital position of LISA is either around the spring or autumn equinox.Comment: 13 pages, 6 figure

Testing Scalar-Tensor Gravity Using Space Gravitational-Wave Interferometers

We calculate the bounds which could be placed on scalar-tensor theories of gravity of the Jordan, Fierz, Brans and Dicke type by measurements of gravitational waveforms from neutron stars (NS) spiralling into massive black holes (MBH) using LISA, the proposed space laser interferometric observatory. Such observations may yield significantly more stringent bounds on the Brans-Dicke coupling parameter \omega than are achievable from solar system or binary pulsar measurements. For NS-MBH inspirals, dipole gravitational radiation modifies the inspiral and generates an additional contribution to the phase evolution of the emitted gravitational waveform. Bounds on \omega can therefore be found by using the technique of matched filtering. We compute the Fisher information matrix for a waveform accurate to second post-Newtonian order, including the effect of dipole radiation, filtered using a currently modeled noise curve for LISA, and determine the bounds on \omega for several different NS-MBH canonical systems. For example, observations of a 1.4 solar mass NS inspiralling to a 1000 solar mass MBH with a signal-to-noise ratio of 10 could yield a bound of \omega > 240,000, substantially greater than the current experimental bound of \omega > 3000.Comment: 18 pages, 4 figures, 1 table; to be submitted to Phys. Rev.

On the topological classification of binary trees using the Horton-Strahler index

The Horton-Strahler (HS) index $r=\max{(i,j)}+\delta_{i,j}$ has been shown to be relevant to a number of physical (such at diffusion limited aggregation) geological (river networks), biological (pulmonary arteries, blood vessels, various species of trees) and computational (use of registers) applications. Here we revisit the enumeration problem of the HS index on the rooted, unlabeled, plane binary set of trees, and enumerate the same index on the ambilateral set of rooted, plane binary set of trees of $n$ leaves. The ambilateral set is a set of trees whose elements cannot be obtained from each other via an arbitrary number of reflections with respect to vertical axes passing through any of the nodes on the tree. For the unlabeled set we give an alternate derivation to the existing exact solution. Extending this technique for the ambilateral set, which is described by an infinite series of non-linear functional equations, we are able to give a double-exponentially converging approximant to the generating functions in a neighborhood of their convergence circle, and derive an explicit asymptotic form for the number of such trees.Comment: 14 pages, 7 embedded postscript figures, some minor changes and typos correcte

Non-adiabatic quantum effects from a Standard Model time-dependent Higgs vev

We consider the time-dependence of the Higgs vacuum expectation value (vev) given by the dynamics of the Standard Model and study the non-adiabatic production of both bosons and fermions, which is intrinsically non-perturbative. In the Hartree approximation, we analyse the general expressions that describe the dissipative dynamics due to the back-reaction of the produced particles. In particular, we solve numerically some relevant cases for the Standard Model phenomenology in the regime of relatively small oscillations of the Higgs vev.Comment: 35 pages, 15 figures and 2 table

Orbital Tests of Relativistic Gravity using Artificial Satellites

We reexamine non-Einsteinian effects observable in the orbital motion of low-orbit artificial Earth satellites. The motivations for doing so are twofold: (i) recent theoretical studies suggest that the correct theory of gravity might contain a scalar contribution which has been reduced to a small value by the effect of the cosmological expansion; (ii) presently developed space technologies should soon give access to a new generation of satellites endowed with drag-free systems and tracked in three dimensions at the centimeter level. Our analysis suggests that such data could measure two independent combinations of the Eddington parameters (beta - 1) and (gamma - 1) at the 10^-4 level and probe the time variability of Newton's "constant" at the d(ln G)/dt ~ 10^-13 yr^-1 level. These tests would provide well-needed complements to the results of the Lunar Laser Ranging experiment, and of the presently planned experiments aiming at measuring (gamma -1). In view of the strong demands they make on the level of non- gravitational perturbations, these tests might require a dedicated mission consisting of an optimized passive drag-free satellite.Comment: 17 pages, IHES/P/94/22 and CPT-94/P.E.302

Correlations in Scale-Free Networks: Tomography and Percolation

We discuss three related models of scale-free networks with the same degree distribution but different correlation properties. Starting from the Barabasi-Albert construction based on growth and preferential attachment we discuss two other networks emerging when randomizing it with respect to links or nodes. We point out that the Barabasi-Albert model displays dissortative behavior with respect to the nodes' degrees, while the node-randomized network shows assortative mixing. These kinds of correlations are visualized by discussig the shell structure of the networks around their arbitrary node. In spite of different correlation behavior, all three constructions exhibit similar percolation properties.Comment: 6 pages, 2 figures; added reference