F. Santucci | Searcharxiv

arXiv2026

Low-Frequency Stochastic Gravitational-Wave Background in Gaia DR3 catalog

We investigate the potential to detect low-frequency gravitational waves (GWs) through their imprints on the proper motions of distant quasars observed by the Gaia mission. Using astrometric data from Gaia DR3, we simulate the effect of GWs on the proper motions of quasars, incorporating their actual sky positions and measurement uncertainties. We investigate two closely related data analysis techniques for the extraction and characterization of GW signals from quasar proper motions: Vector Spherical Harmonics (VSH) and angular correlation functions, commonly referred to as Hellings-Downs curves (HDC). Using realistic simulated data, we forecast their sensitivity and accuracy to GWs, and evaluate the impact of systematic errors. From these simulations, we derive an upper limit on the amplitude of a stochastic GW background, constrained by the observational timespan, astrometric precision, and the sky distribution of quasars. VSH decomposition appears less sensitive to uneven sky sampling and anisotropic noise. The HDC approach retains a larger fraction of the pairwise correlation information and therefore exhibits higher raw statistical sensitivity under idealized conditions. We find that, with Gaia DR3 proper motion errors, the lower limit for a detectable GW strain is of 10^{-11}, with possible improvements to about 3 x 10^{-12} for the next Gaia Data Release 4 (for the same number of quasars). This limit holds for a stochastic GW spectrum integrated over all frequencies less than half the inverse of the 34-month observational timespan of Gaia DR3, corresponding to approximately 5.6 nHz. We also investigate how different data-restriction and weighting schemes influence the final estimate of the gravitational wave strain.

astro-ph.CO↗

arXiv2015

On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and discontinuous shocks

We study the generalization of the dispersionless Kadomtsev - Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one dimensional waves in the absence of dispersion and dissipation, and arising in several physical contexts, like acoustics, plasma physics, hydrodynamics and nonlinear optics. In 2+1 dimensions and with quadratic nonlinearity, this equation is integrable through a novel IST, and it has been recently shown to be a prototype model equation in the description of the two dimensional wave breaking of localized initial data. In higher dimensions and with higher nonlinearity, the generalized dKP equations are not integrable, but their invariance under motions on the paraboloid allows one to construct in this paper a family of exact solutions describing waves constant on their paraboloidal wave front and breaking simultaneously in all points of it, developing after breaking either multivaluedness or single valued discontinuous shocks. Then such exact solutions are used to build the longtime behavior of the solutions of the Cauchy problem, for small and localized initial data, showing that wave breaking of small initial data takes place in the longtime regime if and only if $m(n-1)\le 2$. At last, the analytic aspects of such a wave breaking are investigated in detail in terms of the small initial data, in both cases in which the solution becomes multivalued after breaking or it develops a discontinuous shock. These results, contained in the 2012 master thesis of one of the authors (FS), generalize those obtained by one of the authors (PMS) and S.V.Manakov for the dKP equation in n+1 dimensions with quadratic nonlinearity, and are obtained following the same strategy.

nlin.SI↗