The dynamics of precessing binary black holes using the post-Newtonian approximation

We investigate the (conservative) dynamics of binary black holes using the Hamiltonian formulation of the post-Newtonian (PN) equations of motion. The Hamiltonian we use includes spin-orbit coupling, spin-spin coupling, and mass monopole/spin-induced quadrupole interaction terms. In the case of both quasi-circular and eccentric orbits, we search for the presence of chaos (using the method of Lyapunov exponents) for a large variety of initial conditions. For quasi-circular orbits, we find no chaotic behavior for black holes with total mass 10 - 40 solar masses when initially at a separation corresponding to a Newtonian gravitational-wave frequency less than 150 Hz. Only for rather small initial radial distances, for which spin-spin induced oscillations in the radial separation are rather important, do we find chaotic solutions, and even then they are rare. Moreover, these chaotic quasi-circular orbits are of questionable astrophysical significance, since they originate from direct parametrization of the equations of motion rather than from widely separated binaries evolving to small separations under gravitational radiation reaction. In the case of highly eccentric orbits, which for ground-based interferometers are not astrophysically favored, we again find chaotic solutions, but only at pericenters so small that higher order PN corrections, especially higher spin PN corrections, should also be taken into account.Comment: 18 pages, 26 figure

Gravitational Waves from Compact Objects Accreting onto Active Galactic Nuclei

We consider a model in which massive stars form in a self-gravitating accretion disk around an active galactic nucleus. These stars may evolve and collapse to form compact objects on a time scale shorter than the accretion time, thus producing an important family of sources for LISA. Assuming the compact object formation/inspiral rate is proportional to the steady-state gas accretion rate, we use the observed extra-galactic X-ray luminosity function to estimate expected event rates and signal strengths. We find that these sources will produce a continuous low-frequency background detectable by LISA if more than >~ 1% of the accreted matter is in the form of compact objects. For compact objects with m >~ 10 Msun, the last stages of the inspiral events should be resolvable above a few mHz, at a rate of ~10-100 per year.Comment: 7 pages, to appear in Proceedings of Sixth International LISA Symposiu

RR Lyrae stars in four globular clusters in the Fornax dwarf galaxy

(Abridged) We have surveyed four globular clusters in the Fornax dwarf galaxy for RR Lyrae stars, using archival HST observations. We identify 197 new RR Lyrae stars in these four clusters. Despite the short observational baseline, we derive periods, light-curves, and photometric parameters for each. The Fornax clusters have exceptionally large RR Lyrae specific frequencies compared with the Galactic globular clusters. Furthermore, the Fornax cluster RR Lyrae stars are unusual in that their characteristics are intermediate between the two Galactic Oosterhoff groups. In this respect the Fornax clusters are similar to the field populations in several dwarf galaxies. We revise previous measurements of the HB morphology in each cluster. The Fornax clusters closely resemble the ``young'' Galactic halo population defined by Zinn. The existence of the second parameter effect among the Fornax clusters is also confirmed. Finally, we determine foreground reddening and distance estimates for each cluster. We find a mean distance modulus to Fornax of (m-M)_0 = 20.66 +/- 0.03 (random) +/- 0.15 (systematic). Our measurements are consistent with a line of sight depth of 8-10 kpc for this galaxy, matching its projected dimensions, and incompatible with tidal model explanations for the observed high velocity dispersions in many dSph galaxies. Dark matter dominance is suggested.Comment: 26 pages, 6 figures. Accepted for publication in MNRAS. Table 2 and Figure 2 will only be available in the electronic version. On-line data will soon be available at http://www.ast.cam.ac.uk/STELLARPOPS/Fornax_RRlyr

Deficit of temporal dynamics of detection of a moving object during egomotion in a stroke patient: a psychophysical and MEG study

To investigate the temporal dynamics underlying object motion detection during egomotion, we used psychophysics and MEG with a motion discrimination task. The display contained nine spheres moving for 1 second, eight moved consistent with forward observer translation, and one (the target) with independent motion within the scene (approaching or receding). Observers's task was to detect the target. Seven healthy subjects (7HS) and patient PF with an infarct involving the left occipital-temporal cortex participated in both the psychophysical and MEG study. Psychophysical results showed that PF was severely impaired on this task. He was also impaired on the discrimination of radial motion (with even poorer performance on contraction) and 2D direction as well as on detecting motion discontinuity. We used anatomically constrained MEG and dynamic Granger causality to investigate the direction and dynamics of connectivity between the functional areas involved in the object-motion task and compared the results of 7HS and PF. The dynamics of the causal connections among the motion responsive cortical areas (MT, STS, IPS) during the first 200 ms of the stimulus was similar in all subjects. However, in the later part of the stimulus (>200 ms) PF did not show significant causal connections among these areas. Also the 7HS had a strong, probably attention modulatory connection, between MPFC and MT, which was completely absent in PF. In PF and the 7HS, analysis of onset latencies revealed two stages of activations: early after motion onset (200–400 ms) bilateral activations in MT, IPS, and STS, followed (>500 ms) by activity in the postcentral sulcus and middle prefrontal cortex (MPFC). We suggest that the interaction of these early and late onset areas is critical to object motion detection during self-motion, and disrupted connections among late onset areas may have contributed to the perceptual deficits of patient PF.Published versio

New Photodetection Method Using Unbalanced Sidebands for Squeezed Quantum Noise in Gravitational Wave Interferometer

Homodyne detection is one of the ways to circumvent the standard quantum limit for a gravitational wave detector. In this paper it will be shown that the same quantum-non-demolition effect using homodyne detection can be realized by heterodyne detection with unbalanced RF sidebands. Furthermore, a broadband quantum-non-demolition readout scheme can also be realized by the unbalanced sideband detection.Comment: 9 pages, 5 figure

Is mass loss along the red giant branch of globular clusters sharply peaked? The case of M3

There is a growing evidence that several globular clusters must contain multiple stellar generations, differing in helium content. This hypothesis has helped to interpret peculiar unexplained features in their horizontal branches. In this framework we model the peaked distribution of the RR Lyr periods in M3, that has defied explanation until now. At the same time, we try to reproduce the colour distribution of M3 horizontal branch stars. We find that only a very small dispersion in mass loss along the red giant branch reproduces with good accuracy the observational data. The enhanced and variable helium content among cluster stars is at the origin of the extension in colour of the horizontal branch, while the sharply peaked mass loss is necessary to reproduce the sharply peaked period distribution of RR Lyr variables. The dispersion in mass loss has to be <~ 0.003 Msun, to be compared with the usually assumed values of ~0.02 Msun. This requirement represents a substantial change in the interpretation of the physical mechanisms regulating the evolution of globular cluster stars.Comment: Accepted for publication in The Astrophysical Journa

Anatomy of the binary black hole recoil: A multipolar analysis

We present a multipolar analysis of the gravitational recoil computed in recent numerical simulations of binary black hole (BH) coalescence, for both unequal masses and non-zero, non-precessing spins. We show that multipole moments up to and including l=4 are sufficient to accurately reproduce the final recoil velocity (within ~2%) and that only a few dominant modes contribute significantly to it (within ~5%). We describe how the relative amplitudes, and more importantly, the relative phases, of these few modes control the way in which the recoil builds up throughout the inspiral, merger, and ringdown phases. We also find that the numerical results can be reproduced by an ``effective Newtonian'' formula for the multipole moments obtained by replacing the radial separation in the Newtonian formulae with an effective radius computed from the numerical data. Beyond the merger, the numerical results are reproduced by a superposition of three Kerr quasi-normal modes (QNMs). Analytic formulae, obtained by expressing the multipole moments in terms of the fundamental QNMs of a Kerr BH, are able to explain the onset and amount of ``anti-kick'' for each of the simulations. Lastly, we apply this multipolar analysis to help explain the remarkable difference between the amplitudes of planar and non-planar kicks for equal-mass spinning black holes.Comment: 28 pages, 20 figures, submitted to PRD; v2: minor revisions from referee repor

Fast post-adiabatic waveforms in the time domain: Applications to compact binary coalescences in LIGO and Virgo

We present a computationally efficient (time-domain) multipolar waveform model for quasi-circular spin-aligned compact binary coalescences. The model combines the advantages of the numerical-relativity informed, effective-one-body (EOB) family of models with a post-adiabatic solution of the equations of motion for the inspiral part of the two-body dynamics. We benchmark this model against other state-of-the-art waveforms in terms of efficiency and accuracy. We find a speed-up of one to two orders of magnitude compared to the underlying time-domain EOB model for the total mass range $2 - 100 M_{\odot}$. More specifically, for a low total-mass system, such as a binary neutron star with equal masses of $1.4 M_{\odot}$, like GW170817, the computational speedup is around 100 times; for an event with total mass $\sim 40 M_\odot$ and mass ratio $\sim 3$, like GW190412, the speedup is by a factor of $\sim 20$, while for a binary system of comparable masses and total mass of $\sim 70 M_{\odot}$, like GW150914, it is by a factor of $\sim 10$. We demonstrate that the new model is extremely faithful to the underlying EOB model with unfaithfulness less than $0.01\%$ across the entire applicable region of parameter space. Finally, we present successful applications of this new waveform model to parameter estimation studies and tests of general relativity

Transition from inspiral to plunge for eccentric equatorial Kerr orbits

Ori and Thorne have discussed the duration and observability (with LISA) of the transition from circular, equatorial inspiral to plunge for stellar-mass objects into supermassive ($10^{5}-10^{8}M_{\odot}$) Kerr black holes. We extend their computation to eccentric Kerr equatorial orbits. Even with orbital parameters near-exactly determined, we find that there is no universal length for the transition; rather, the length of the transition depends sensitively -- essentially randomly -- on initial conditions. Still, Ori and Thorne's zero-eccentricity results are essentially an upper bound on the length of eccentric transitions involving similar bodies (e.g., $a$ fixed). Hence the implications for observations are no better: if the massive body is $M=10^{6}M_{\odot}$, the captured body has mass $m$, and the process occurs at distance $d$ from LISA, then $S/N \lesssim (m/10 M_{\odot})(1\text{Gpc}/d)\times O(1)$, with the precise constant depending on the black hole spin. For low-mass bodies ($m \lesssim 7 M_\odot$) for which the event rate is at least vaguely understood, we expect little chance (probably [much] less than 10%, depending strongly on the astrophysical assumptions) of LISA detecting a transition event with $S/N>5$ during its run; however, even a small infusion of higher-mass bodies or a slight improvement in LISA's noise curve could potentially produce $S/N>5$ transition events during LISA's lifetime.Comment: Submitted to PR

The giant, horizontal and asymptotic branches of galactic globular clusters. I. The catalog, photometric observables and features

A catalog including a set of the most recent Color Magnitude Diagrams (CMDs) is presented for a sample of 61 Galactic Globular Clusters (GGCs). We used this data-base to perform an homogeneous systematic analysis of the evolved sequences (namely, Red Giant Branch (RGB), Horizontal Branch (HB) and Asymptotic Giant Branch (AGB)). Based on this analysis, we present: (1) a new procedure to measure the level of the ZAHB (V_ZAHB) and an homogeneous set of distance moduli obtained adopting the HB as standard candle; (2) an independent estimate for RGB metallicity indicators and new calibrations of these parameters in terms of both spectroscopic ([Fe/H]_CG97) and global metallicity ([M/H], including also the alpha-elements enhancement). The set of equations presented can be used to simultaneously derive a photometric estimate of the metal abundance and the reddening from the morphology and the location of the RGB in the (V,B-V)-CMD. (3) the location of the RGB-Bump (in 47 GGCs) and the AGB-Bump (in 9 GGCs). The dependence of these features on the metallicity is discussed. We find that by using the latest theoretical models and the new metallicity scales the earlier discrepancy between theory and observations (~0.4 mag) completely disappears.Comment: 51 pages, 23 figures, AAS Latex, macro rtrpp4.sty included, accepted by A