Search for: All records

This paper shows analytically and numerically that a vortex plate coupled to a neutral density filter can deliver a true optical spatial derivative when placed at the focal plane of a 2flens pair. This technique turns any intensity or phase variations of coherent light into an intensity that is proportional to the square of the norm of the initial variation gradient. Since the optical derivative removes the uniform background, it is possible to measure the mode numbers of spatial phase gradients or fluctuations optically, without using any interferometer. 

Radial basis functions are typically used when discretization schemes require inhomogeneous node distributions. While spawning from a desire to interpolate functions on a random set of nodes, they have found successful applications in solving many types of differential equations. However, the weights of the interpolated solution, used in the linear superposition of basis functions to interpolate the solution, and the actual value of the solution are completely different. In fact, these weights mix the value of the solution with the geometrical location of the nodes used to discretize the equation. In this paper, we used nodal radial basis functions, which are interpolants of the impulse function at each node inside the domain. This transformation allows to solve a linear hyperbolic partial differential equation using series expansion rather than the explicit computation of a matrix inverse. This transformation effectively yields an implicit solver which only requires the multiplication of vectors with matrices. Because the solver requires neither matrix inverse nor matrix-matrix products, this approach is numerically more stable and reduces the error by at least two orders of magnitude, compared to solvers using radial basis functions directly. Further, boundary conditions are integrated directly inside the solver, at no extra cost. The method is locally conservative, keeping the error virtually constant throughout the computation. 

Abstract Rotating nonaxisymmetric neutron stars (NSs) are promising sources for continuous gravitational waves (CWs). CWs may, if detected, inform us about the internal structure and equation of state of NSs. Here, we present a narrowband search for CWs from known pulsars, for which a matched-filter search can be applied. Narrowband searches are robust to mismatches between electromagnetic (EM) and gravitational emissions, in contrast to fully targeted searches where they are assumed to be phase-locked. In this work, we search for the CW counterparts emitted by 34 pulsars using data from the first and second parts of the fourth LIGO–Virgo–KAGRA observing run. We use the 5n-vector narrowband pipeline, which applies frequency-domain matched filtering. In previous searches, it covered a narrow range in the frequency—frequency time derivative (f— $\dot{f}$ ) space. Here, we also explore a range in the second time derivative of the frequency $\ddot{f}$ around the EM observations. Additionally, for the first time, we target sources in a binary system with this kind of search. We find no evidence for CWs and therefore set upper limits on the strain amplitude emitted by each pulsar. For 20 analyses, we report an upper limit below the theoretical spin-down limit. The tightest constraint is for pulsar PSR J0534+2200 (the Crab pulsar), for which our strain upper limit on the CW amplitude corresponds to ≤0.04% of the spin-down power being radiated in the CW channel. 

Abstract We detail the population properties of binary neutron star, neutron star–black hole binary, and binary black hole mergers using 158 events from the cumulative Gravitational-Wave Transient Catalog 4.0. The black hole primary mass distribution consists of a power-law-like continuum that steepens above 35M_⊙with overdensities at 10M_⊙and 35M_⊙. Binary black holes with primary masses near 10M_⊙are more likely to have less massive secondaries, with a mass ratio distribution peaking at $q=0.71_{-0.11}^{+0.12}$ , potentially a signature of stable mass transfer during binary evolution. Black hole spins are inferred to be nonextremal, with 90% of black holes havingχ < 0.6, and preferentially aligned with binary orbits, implying many merging binaries form in isolation. However, we find that a significant fraction, 0.23–0.41, of binaries have negative effective inspiral spins, suggesting many could be formed dynamically in gas-free environments. We find evidence for correlation between effective inspiral spin and mass ratio, driven either by variation in the mode of the distribution or the width. The binary black hole merger rate increases with redshift, consistent with the cosmic star formation density. While there is no evidence of the mass spectrum evolving with redshift, the distribution of effective inspiral spin is found to broaden as redshift increases out toz ≈ 1. We infer the local merger rates (atz= 0) to be 8.8–250 Gpc⁻³yr⁻¹for binary neutron stars, 9.3–86 Gpc⁻³yr⁻¹for neutron star–black hole binaries, and 13–26 Gpc⁻³yr⁻¹for binary black holes; all values reflect central 90% credible intervals. 

We present a search for gravitational waves from inspiraling, planetary-mass ultracompact binaries using data from the first part of the fourth observing run of LIGO, Virgo, and KAGRA. Finding no evidence of such systems, we determine the maximum distance reach for such objects and their merger rate densities. Then, we identify classes of primordial black hole mass distributions for which these rate limits can be translated into relevant constraints on the mass distribution of primordial black holes, assuming that they are all composed of dark matter, in the mass range $[{10}^{-6},{10}^{-3}]M_{\odot }$ . Our constraints for the class of primordial black hole mass distribution functions $f\left(m\right)$ we consider reach down to $f\left(m\right)\sim 0.1$ . They are consistent with existing microlensing results in the planetary-mass range, provide a complementary probe to subsolar mass objects, and are publicly available [1].