Coating thermal noise for arbitrary shaped beams

Advanced LIGO's sensitivity will be limited by coating noise. Though this noise depends on beam shape, and though nongaussian beams are being seriously considered for advanced LIGO, no published analysis exists to compare the quantitative thermal noise improvement alternate beams offer. In this paper, we derive and discuss a simple integral which completely characterizes the dependence of coating thermal noise on shape. The derivation used applies equally well, with minor modifications, to all other forms of thermal noise in the low-frequency limit.Comment: 3 pages. Originally performed in August 2004. Submitted to CQG. (v2) : Corrections from referee and other

Bounds on Expected Black Hole Spins in Inspiraling Binaries

As a first step towards understanding the angular momentum evolution history of black holes in merging black-hole/neutron-star binaries, we perform population synthesis calculations to track the distribution of accretion histories of compact objects in such binaries. We find that there are three distinct processes which can possibly contribute to the black-hole spin magnitude: a birth spin for the black hole, imparted at either (i) the collapse of a massive progenitor star to a black hole or (ii) the accretion-induced collapse of a neutron star to a black hole; and (iii) an accretion spin-up when the already formed black hole [via (i) or (ii)] goes through an accretion episode (through an accretion disk or a common-envelope phase). Our results show that, with regard to accretion-induced spinup in merging BH-NS binaries [method (iii) above], only {\em accretion episodes associated with common-envelope phases and hypercritical accretion rates} occur in the formation history of merging black hole/neutron star binaries. Lacking unambiguous experimental information about BH birth spins [i.e., regarding the results of processes (i) and (ii)], we choose two fiducial values for the BH birth angular momentum parameter a=J/M^2, consistent with observations of (i) NS birth spins (a roughly 0) and (ii) X-ray binaries (a=0.5). Using these two fiducial values and a conservative upper bound on the specific angular momentum of accreted matter, we discuss the expected range of black hole spins in the binaries of interest. We conclude with comments on the significance of these results for ground-based gravitational-wave searches of inspiral signals from black hole binaries.Comment: Submitted to ApJ. (v1) Uses emulateapj.cls. 5 figures. (v2): corrected reference list and uses smaller figures (v3): Includes changes in response to referee comments, including new discussion of XRBs. Figures merged, so only 3 figures (v4) Minor typo correction, plus updated abstract posted onlin

Precession during merger 1: Strong polarization changes are observationally accessible features of strong-field gravity during binary black hole merger

The short gravitational wave signal from the merger of compact binaries encodes a surprising amount of information about the strong-field dynamics of merger into frequencies accessible to ground-based interferometers. In this paper we describe a previously-unknown "precession" of the peak emission direction with time, both before and after the merger, about the total angular momentum direction. We demonstrate the gravitational wave polarization encodes the orientation of this direction to the line of sight. We argue the effects of polarization can be estimated nonparametrically, directly from the gravitational wave signal as seen along one line of sight, as a slowly-varying feature on top of a rapidly-varying carrier. After merger, our results can be interpreted as a coherent excitation of quasinormal modes of different angular orders, a superposition which naturally "precesses" and modulates the line-of-sight amplitude. Recent analytic calculations have arrived at a similar geometric interpretation. We suspect the line-of-sight polarization content will be a convenient observable with which to define new high-precision tests of general relativity using gravitational waves. Additionally, as the nonlinear merger process seeds the initial coherent perturbation, we speculate the amplitude of this effect provides a new probe of the strong-field dynamics during merger. To demonstrate the ubiquity of the effects we describe, we summarize the post-merger evolution of 104 generic precessing binary mergers. Finally, we provide estimates for the detectable impacts of precession on the waveforms from high-mass sources. These expressions may identify new precessing binary parameters whose waveforms are dissimilar from the existing sample.Comment: 11 figures; v2 includes response to referee suggestion

Blindly detecting orbital modulations of jets from merging supermassive black holes

In the last few years before merger, supermassive black hole binaries will rapidly inspiral and precess in a magnetic field imposed by a surrounding circumbinary disk. Multiple simulations suggest this relative motion will convert some of the local energy to a Poynting-dominated outflow, with a luminosity 10^{43} erg/s * (B/10^4 G)^2(M/10^8 Msun)^2 (v/0.4 c)^2, some of which may emerge as synchrotron emission at frequencies near 1 GHz where current and planned wide-field radio surveys will operate. On top of a secular increase in power on the gravitational wave inspiral timescale, orbital motion will produce significant, detectable modulations, both on orbital periods and (if black hole spins are not aligned with the binary's total angular momenta) spin-orbit precession timescales. Because the gravitational wave merger time increases rapidly with separation, we find vast numbers of these transients are ubiquitously predicted, unless explicitly ruled out (by low efficiency $\epsilon$) or obscured (by accretion geometry f_{geo}). If the fraction of Poynting flux converted to radio emission times the fraction of lines of sight accessible $f_{geo}$ is sufficiently large (f_{geo} \epsilon > 2\times 10^{-4} for a 1 year orbital period), at least one event is accessible to future blind surveys at a nominal 10^4 {deg}^2 with 0.5 mJy sensitivity. Our procedure generalizes to other flux-limited surveys designed to investigate EM signatures associated with many modulations produced by merging SMBH binaries.Comment: Submitted to ApJ. v1 original submission; v2 minor changes in response to refere

The dependence of test-mass thermal noises on beam shape in gravitational-wave interferometers

In second-generation, ground-based interferometric gravitational-wave detectors such as Advanced LIGO, the dominant noise at frequencies $f \sim 40$ Hz to $\sim 200$ Hz is expected to be due to thermal fluctuations in the mirrors' substrates and coatings which induce random fluctuations in the shape of the mirror face. The laser-light beam averages over these fluctuations; the larger the beam and the flatter its light-power distribution, the better the averaging and the lower the resulting thermal noise. In semi-infinite mirrors, scaling laws for the influence of beam shape on the four dominant types of thermal noise (coating Brownian, coating thermoelastic, substrate Brownian, and substrate thermoelastic) have been suggested by various researchers and derived with varying degrees of rigour. Because these scaling laws are important tools for current research on optimizing the beam shape, it is important to firm up our understanding of them. This paper (1) gives a summary of the prior work and of gaps in the prior analyses, (2) gives a unified and rigorous derivation of all four scaling laws, and (3) explores, relying on work by J. Agresti, deviations from the scaling laws due to finite mirror size.Comment: 25 pages, 10 figures, submitted to Class. Quantum Gra

Binary compact object coalescence rates: The role of elliptical galaxies

We estimate binary compact object merger detection rates for LIGO, including the binaries formed in ellipticals long ago. Specifically, we convolve hundreds of model realizations of elliptical- and spiral-galaxy population syntheses with a model for elliptical- and spiral-galaxy star formation history as a function of redshift. Our results favor local merger rate densities of 4\times 10^{-3} {Mpc}^{-3}{Myr}^{-1} for binary black holes (BH), 3\times 10^{-2} {Mpc}^{-3}{Myr}^{-1} for binary neutron stars (NS), and 10^{-2} {Mpc}^{-3}{Myr}^{-1} for BH-NS binaries. Mergers in elliptical galaxies are a significant fraction of our total estimate for BH-BH and BH-NS detection rates; NS-NS detection rates are dominated by the contribution from spiral galaxies. Using only models that reproduce current observations of Galactic NS-NS binaries, we find slightly higher rates for NS-NS and largely similar ranges for BH-NS and BH-BH binaries. Assuming a detection signal-to-noise ratio threshold of 8 for a single detector (as part of a network), corresponding to radii \Cv of the effective volume inside of which a single LIGO detector could observe the inspiral of two 1.4 M_\sun neutron stars of 14 Mpc and 197 Mpc, for initial and advanced LIGO, we find event rates of any merger type of 2.9* 10^{-2} -- 0.46 and 25-400 per year (at 90% confidence level), respectively. We also find that the probability P_{detect} of detecting one or more mergers with this single detector can be approximated by (i) P_{detect}\simeq 0.4+0.5\log (T/0.01{yr}), assuming \Cv=197 {Mpc} and it operates for T years, for T between 2 days and 0.1 {yr}); or by (ii) P_{detect}\simeq 0.5 + 1.5 \log \Cv/32{Mpc}, for one year of operation and for \Cv between 20 and 70 Mpc. [ABRIDGED]Comment: 22 pages, 11 figures. Accepted by ApJ. v2 adds several figures, an electronic-only table of all intermediate binary evolution simulations (tab1.txt here), and new subsections outlining broader significance (e.g., 5.4; 4.6; 6.1