Observing the Galaxy's massive black hole with gravitational wave bursts

An extreme-mass-ratio burst (EMRB) is a gravitational wave signal emitted when a compact object passes through periapsis on a highly eccentric orbit about a much more massive object, in our case a stellar mass object about a 10^6 M_sol black hole. EMRBs are a relatively unexplored means of probing the spacetime of massive black holes (MBHs). We conduct an investigation of the properties of EMRBs and how they could allow us to constrain the parameters, such as spin, of the Galaxy's MBH. We find that if an EMRB event occurs in the Galaxy, it should be detectable for periapse distances r_p < 65 r_g for a \mu = 10 M_sol orbiting object, where r_g = GM/c^2 is the gravitational radius. The signal-to-noise ratio scales as \rho ~ -2.7 log(r_p/r_g) + log(\mu/M_sol) + 4.9. For periapses r_p < 10 r_g, EMRBs can be informative, and provide good constraints on both the MBH's mass and spin. Closer orbits provide better constraints, with the best giving accuracies of better than one part in 10^4 for both the mass and spin parameter.Comment: 25 pages, 17 figures, 1 appendix. One more typo fixe

Expectations for extreme-mass-ratio bursts from the Galactic Centre

When a compact object on a highly eccentric orbit about a much more massive body passes through periapsis it emits a short gravitational wave signal known as an extreme-mass-ratio burst (EMRB). We consider stellar mass objects orbiting the massive black hole (MBH) found in the Galactic Centre. EMRBs provide a novel means of extracting information about the MBH; an EMRB from the Galactic MBH could be highly informative regarding the MBH's mass and spin if the orbital periapsis is small enough. However, to be a useful astronomical tool EMRBs must be both informative and sufficiently common to be detectable with a space-based interferometer. We construct a simple model to predict the event rate for Galactic EMRBs. We estimate there could be on average ~2 bursts in a two year mission lifetime for LISA. Stellar mass black holes dominate the event rate. Creating a sample of 100 mission realisations, we calculate what we could learn about the MBH. On average, we expect to be able to determine the MBH mass to ~1% and the spin to ~0.1 using EMRBs.Comment: 22 pages, 5 figures, 2 appendices. Minor changes to reflect published versio

How Hot Is Radiation?

A self-consistent approach to nonequilibrium radiation temperature is introduced using the distribution of the energy over states. We begin rigorously with ensembles of Hilbert spaces and end with practical examples based mainly on the far from equilibrium radiation of lasers. We show that very high, but not infinite, laser radiation temperatures depend on intensity and frequency. Heuristic "temperatures" derived from a misapplication of equilibrium arguments are shown to be incorrect. More general conditions for the validity of nonequilibrium temperatures are also established.Comment: 26 pages, revised, LaTeX, 3 encapsulated PostScript figure

Equivalence between two-mode spin squeezed states and pure entangled states with equal spin

We prove that a pure entangled state of two subsystems with equal spin is equivalent to a two-mode spin-squeezed state under local operations except for a set of bipartite states with measure zero, and we provide a counterexample to the generalization of this result to two subsystems of unequal spin.Comment: 6 pages, no figure

Geometric phases and anholonomy for a class of chaotic classical systems

Berry's phase may be viewed as arising from the parallel transport of a quantal state around a loop in parameter space. In this Letter, the classical limit of this transport is obtained for a particular class of chaotic systems. It is shown that this ``classical parallel transport'' is anholonomic --- transport around a closed curve in parameter space does not bring a point in phase space back to itself --- and is intimately related to the Robbins-Berry classical two-form.Comment: Revtex, 11 pages, no figures

Quantum Charged Spinning Particles in a Strong Magnetic Field (a Quantal Guiding Center Theory)

A quantal guiding center theory allowing to systematically study the separation of the different time scale behaviours of a quantum charged spinning particle moving in an external inhomogeneous magnetic filed is presented. A suitable set of operators adapting to the canonical structure of the problem and generalizing the kinematical momenta and guiding center operators of a particle coupled to a homogenous magnetic filed is constructed. The Pauli Hamiltonian rewrites in this way as a power series in the magnetic length $l_B= \sqrt{\hbar c/eB}$ making the problem amenable to a perturbative analysis. The first two terms of the series are explicitly constructed. The effective adiabatic dynamics turns to be in coupling with a gauge filed and a scalar potential. The mechanism producing such magnetic-induced geometric-magnetism is investigated in some detail.Comment: LaTeX (epsfig macros), 27 pages, 2 figures include

Genome-wide association study for calving performance using high-density genotypes in dairy and beef cattle

peer-reviewedBackground Calving difficulty and perinatal mortality are prevalent in modern-day cattle production systems. It is well-established that there is a genetic component to both traits, yet little is known about their underlying genomic architecture, particularly in beef breeds. Therefore, we performed a genome-wide association study using high-density genotypes to elucidate the genomic architecture of these traits and to identify regions of the bovine genome associated with them. Results Genomic regions associated with calving difficulty (direct and maternal) and perinatal mortality were detected using two statistical approaches: (1) single-SNP (single nucleotide polymorphism) regression and (2) a Bayesian approach. Data included high-density genotypes on 770 Holstein-Friesian, 927 Charolais and 963 Limousin bulls. Several novel or previously identified genomic regions were detected but associations differed by breed. For example, two genomic associations, one each on chromosomes 18 and 2 explained 2.49 % and 3.13 % of the genetic variance in direct calving difficulty in the Holstein-Friesian and Charolais populations, respectively. Imputed Holstein-Friesian sequence data was used to refine the genomic regions responsible for significant associations. Several candidate genes on chromosome 18 were identified and four highly significant missense variants were detected within three of these genes (SIGLEC12, CTU1, and ZNF615). Nevertheless, only CTU1 contained a missense variant with a putative impact on direct calving difficulty based on SIFT (0.06) and Polyphen (0.95) scores. Using imputed sequence data, we refined a genomic region on chromosome 4 associated with maternal calving difficulty in the Holstein-Friesian population and found the strongest association with an intronic variant in the PCLO gene. A meta-analysis was performed across the three breeds for each calving performance trait to identify common variants associated with these traits in the three breeds. Our results suggest that a portion of the genetic variation in calving performance is common to all three breeds. Conclusion The genomic architecture of calving performance is complex and mainly influenced by many polymorphisms of small effect. We identified several associations of moderate effect size but the majority were breed-specific, indicating that breed-specific alleles exist for calving performance or that the linkage phase between genotyped allele and causal mutation varies between breeds

Dynamical diffraction in sinusoidal potentials: uniform approximations for Mathieu functions

Eigenvalues and eigenfunctions of Mathieu's equation are found in the short wavelength limit using a uniform approximation (method of comparison with a `known' equation having the same classical turning point structure) applied in Fourier space. The uniform approximation used here relies upon the fact that by passing into Fourier space the Mathieu equation can be mapped onto the simpler problem of a double well potential. The resulting eigenfunctions (Bloch waves), which are uniformly valid for all angles, are then used to describe the semiclassical scattering of waves by potentials varying sinusoidally in one direction. In such situations, for instance in the diffraction of atoms by gratings made of light, it is common to make the Raman-Nath approximation which ignores the motion of the atoms inside the grating. When using the eigenfunctions no such approximation is made so that the dynamical diffraction regime (long interaction time) can be explored.Comment: 36 pages, 16 figures. This updated version includes important references to existing work on uniform approximations, such as Olver's method applied to the modified Mathieu equation. It is emphasised that the paper presented here pertains to Fourier space uniform approximation

Thermalization of a Brownian particle via coupling to low-dimensional chaos

It is shown that a paradigm of classical statistical mechanics --- the thermalization of a Brownian particle --- has a low-dimensional, deterministic analogue: when a heavy, slow system is coupled to fast deterministic chaos, the resultant forces drive the slow degrees of freedom toward a state of statistical equilibrium with the fast degrees. This illustrates how concepts useful in statistical mechanics may apply in situations where low-dimensional chaos exists.Comment: Revtex, 11 pages, no figures