Topics in Physics and Astrophysics of LIGO

Citation

Levin, Yuri (1999) Topics in Physics and Astrophysics of LIGO. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ped8-ec41. https://resolver.caltech.edu/CaltechTHESIS:08292017-115000442

Abstract

This thesis deals with three topics, all of which are related to the generation or detection of gravitational waves:

(I) The Standard Quantum Limit (SQL) for LIGO and Quantum Non­ demolition (QND) measurements, which allow one to overcome the SQL. Two particular QND measurement schemes are considered: (i) a Speed Meter, in which a small Fabry-Perot cavity attached to a LIGO test mass produces a phase shift proportional to the test mass's speed; and (ii) the Braginsky-Khalili nonlinear meter (BK-meter), in which a gravity-wave-induced motion of the nodes of the light beam inside a LIGO optical cavity is read out using a nonlinear medium which couples light to a microwave readout device. Our analysis shows that

(a) Using the Speed Meter one can perform naturally a broad-band QND mea­surement of a force acting on the test mass; however, this requires circulating light power which is unrealistically high for LIGO.

(b) The BK-meter can provide a natural way to perform a narrow-band QND measurement of a force acting on the mirrors of the optical cavity.

While neither of these QND measurement schemes can be immediately imple­ mented for LIGO, they might provide conceptual steps towards the design of a prac­tical QND interferometer.

(II) Mechanical thermal noise in LIGO. We develop a new method of calcu­ lating thermal noise in mechanical systems, which is based on a direct application of the Fluctuation-Dissipation theorem. This method is capable of handling mechanical systems with inhomogeneous dissipation, by contrast with previous met hods (based on decomposing motion of the system into normal modes), which give incorrect results when the dissipation is inhomogeneous.

We apply our direct method to an internal thermal noise in LIGO test masses. We find that:

(a) The test-mass surface defects will make a larger contribution to thermal noise than was previously inferred by combining the (incorrect) mode-sum met hod with measurements of the Q's of the test masses' modes.

(b)Our direct met hod is more precise and computationally less expensive for small beam sizes than the previous mode-sum method.

We also apply our direct method of analysis to suspension thermal noise in LIGO. We find that by careful positioning the laser beam spot on the mirror face and by monitoring independently the motion of the suspension wires, it may be possible to reduce the suspension thermal noise by a factor ~ 100 in spectral density.

(III) R-modes in Neutron Stars (NS) in Low-Mass X-ray Binaries (LMXBs). We study the suggestion that the accretion of gas onto a neutron star in an LMXB triggers an instability in which the star's r-modes are amplified by gravitational-wave emission. We find that if this is the case, then the subsequent neutron-star evolution depends critically on whether the neutron-star viscosity decreases with temperature, or is temperature-independent.

In the former case, the Neutron Star goes through runaway cycles of rapid (~ 1 month) heating-rapid (~ 1 month) spindown-slow (~ 10⁵ years) cooling-slow (~ 10⁶ years) spin-up. In this scenario the duration of the gravitational radiation from the unstable r-modes is so short that even LIGO-III interferometers are unlikely to be able to catch a single LMXB in the throes of its gravitational-wave emission.

In the latter (temperature-independent) case, however, the Neutron Star probably settles down into an equilibrium state with constant spin rate and temperature, and becomes a steady emitter of gravitational waves, which might be detectible by LIGO­ II interferometers.

All the capters in this thesis, except the introductory chapter I, have been published or are in press.

Thesis Files