Thermal tests on the LISA pathfinder engineering model

Report for the scientific sojourn carried out at Albert Einstein Institut in Germany, from April to July 2006.

Estudi de la configuració magnètica de l'experiment LTP (LISA Technology Package)

La Teoria de la Relativitat General preveu que quan un objecte massiu és sotmès a una certa acceleració en certes condicions ha d’emetre ones gravitacionals. Es tracta d’un tipus d’on altament energètica però que interacciona amb la matèria de manera molt feble i el seu punt d’emissió és força llunyà. Per la qual cosa la seva detecció és una tasca extraordinàriament complicada. Conseqüentment, la detecció d’aquestes ones es creu molt més factible utilitzant instruments situats a l’espai. Amb aquest objectiu, neis la missió LISA (Laser Interferometer Space Antenna). Es tracta aquesta d’una missió conjunta entre la NASA i l’ESA amb llançament previst per 2020-2025. Per reduir els riscs que comporta una primera utilització de tecnologia no testejada, unit a l’alt cost econòmic de la missió LISA. Aquesta missió contindrà instruments molt avançats: el LTP (LISA Technoplogy Package), desenvolupat per la Unió Europea, que provarà la tecnologia de LISA i el Drag Free flying system, que s’encarregarà de provar una sèrie de propulsors (thrusters) utilitzats per al control d’actitud i posició de satèl•lit amb precisió de nanòmetres. Particularment, el LTP, està composat per dues masses de prova separades per 35 centímetres, i d’un interferòmetre làser que mesura la variació de la distància relativa entre elles. D’aquesta manera, el LTP mesurarà les prestacions dels equips i les possibles interferències que afecten a la mesura. Entre les fonts de soroll es troben, entre d’altres, el vent i pressió de radiació solar, les càrregues electrostàtiques, el gradient tèrmic, les fluctuacions de voltatge o les forces internes. Una de les possibles causes de soroll és aquella que serà l’objecte d’estudi en aquest projecte de tesi doctoral: la presència dintre del LTP de camps magnètics, que exerceixen una força sobre les masses de prova, la seva estimació i el seu control, prenent en compte les caracterírstiques magnètiques de l’experiment i la dinàmica del satèl•lit.

Gravitational wave pulse and soliton wave collision

We study the collision of a gravitational wave pulse and a soliton wave on a spatially homogeneous background. This collision is described by an exact solution of Einsteins equations in a vacuum which is generated from a nondiagonal seed by means of a soliton transformation. The effect produced by the soliton on the amplitude and polarization of the wave is considered.

Gravitational wave pulse and soliton wave collision

We study the collision of a gravitational wave pulse and a soliton wave on a spatially homogeneous background. This collision is described by an exact solution of Einsteins equations in a vacuum which is generated from a nondiagonal seed by means of a soliton transformation. The effect produced by the soliton on the amplitude and polarization of the wave is considered.

What can we learn about gravitational wave physics with an elastic spherial antenna?

A general formalism is set up to analyze the response of an arbitrary solid elastic body to an arbitrary metric gravitational wave (GW) perturbation, which fully displays the details of the interaction antenna wave. The formalism is applied to the spherical detector, whose sensitivity parameters are thereby scrutinized. A multimode transfer function is defined to study the amplitude sensitivity, and absorption cross sections are calculated for a general metric theory of GW physics. Their scaling properties are shown to be independent of the underlying theory, with interesting consequences for future detector design. The GW incidence direction deconvolution problem is also discussed, always within the context of a general metric theory of the gravitational field.

Proposed gravitational wave observatory based on solid elastic spheres

Spherical gravitational wave (GW) detectors offer a wealth of so far unexplored possibilities to detect gravitational radiation. We find that a sphere can be used as a powerful testbed for any metric theory of gravity, not only general relativity as considered so far, by making use of a deconvolution procedure for all the electric components of the Riemann tensor. We also find that the spheres cross section is large at two frequencies, and advantageous at higher frequencies in the sense that a single antenna constitutes a real xylophone in its own. Proposed GW networks will greatly benefit from this. The main features of a two large sphere observatory are reported.

Hollow sphere as a detector of gravitational radiation

The most important features of the proposed spherical gravitational wave detectors are closely linked with their symmetry. Hollow spheres share this property with solid ones, considered in the literature so far, and constitute an interesting alternative for the realization of an omnidirectional gravitational wave detector. In this paper we address the problem of how a hollow elastic sphere interacts with an incoming gravitational wave and find an analytical solution for its normal mode spectrum and response, as well as for its energy absorption cross sections. It appears that this shape can be designed having relatively low resonance frequencies (~ 200 Hz) yet keeping a large cross section, so its frequency range overlaps with the projected large interferometers. We also apply the obtained results to discuss the performance of a hollow sphere as a detector for a variety of gravitational wave signals.

Cross section of a resonant-mass detector for scalar gravitational waves

Gravitationally coupled scalar fields, originally introduced by Jordan, Brans and Dicke to account for a non-constant gravitational coupling, are a prediction of many non-Einsteinian theories of gravity not excluding perturbative formulations of string theory. In this paper, we compute the cross sections for scattering and absorption of scalar and tensor gravitational waves by a resonant-mass detector in the framework of the Jordan-Brans-Dicke theory. The results are then specialized to the case of a detector of spherical shape and shown to reproduce those obtained in general relativity in a certain limit. Eventually we discuss the potential detectability of scalar waves emitted in a spherically symmetric gravitational collapse.

Detection of scalar gravitational waves with a hollow spherical antenna

We study the response and cross sections for the absorption of GW energy generated in a Jordan-Brans-Dicke theory by a resonant mass detector shaped as a hollow sphere. As a source of the GW we take a binary system in the Newtonian approximation. For masses of the stars of the order of the solar mass, the emitted GW sweeps a range of frequencies which include the first resonant mode of the detector.

Thermal and back-action noises in dual-sphere gravitational-wave detectors

We study the sensitivity limits of a broadband gravitational-wave detector based on dual resonators such as nested spheres. We determine both the thermal and back-action noises when the resonators displacements are read out with an optomechanical sensor. We analyze the contributions of all mechanical modes, using a new method to deal with the force-displacement transfer functions in the intermediate frequency domain between the two gravitational-wave sensitive modes associated with each resonator. This method gives an accurate estimate of the mechanical response, together with an evaluation of the estimate error. We show that very high sensitivities can be reached on a wide frequency band for realistic parameters in the case of a dual-sphere detector.

Dynamically tuned interferometers for the observation of gravitational waves from coalescing compact binaries

We propose a new method of operating laser interferometric gravitational-wave detectors when observing chirps of gravitational radiation from coalescing compact binary stars. This technique consists of the use of narrow-band dual recycling to increase the signal but with the tuning frequency of the detector arranged to follow the frequency of a chirp. We consider the response of such an instrument to chirps, including the effect of inevitable errors in tracking. Different possible tuning strategies are discussed. Both the final signal-to-noise ratio and timing accuracy are evaluated and are shown to be significantly improved by the use of dynamic tuning. This should allow an accurate and reliable measurement of Hubble's constant.

Estimation of the parameters of the gravitational-wage signal of a coalescing binary system

The statistical theory of signal detection and the estimation of its parameters are reviewed and applied to the case of detection of the gravitational-wave signal from a coalescing binary by a laser interferometer. The correlation integral and the covariance matrix for all possible static configurations are investigated numerically. Approximate analytic formulas are derived for the case of narrow band sensitivity configuration of the detector.