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Register a new userMapping the Gravitational-wave Sky with LISA: A Bayesian Spherical Harmonic Approach
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The millihertz gravitational-wave frequency band is expected to contain a rich symphony of signals with sources ranging from galactic white dwarf binaries to extreme mass ratio inspirals. Many of these gravitational-wave signals will not be individually resolvable. Instead, they will incoherently add to produce stochastic gravitational-wave confusion noise whose frequency content will be governed by the dynamics of the sources. The angular structure of the power of the confusion noise will be modulated by the distribution of the sources across the sky. Measurement of this structure can yield important information about the distribution of sources on galactic and extra-galactic scales, their astrophysics and their evolution over cosmic timescales. Moreover, since the confusion noise is part of the noise budget of LISA, mapping it will also be essential for studying resolvable signals. In this paper, we present a Bayesian algorithm to probe the angular distribution of the stochastic gravitational-wave confusion noise with LISA using a spherical harmonic basis. We develop a technique based on Clebsch-Gordan coefficients to mathematically constrain the spherical harmonics to yield a non-negative distribution, making them optimal for expanding the gravitational-wave power and amenable to Bayesian inference. We demonstrate these techniques using a series of simulations and analyses, including recovery of simulated distributed and localized sources of gravitational-wave power. We also apply this method to map the gravitational-wave foreground from galactic white-dwarfs using a simplified model of the galactic white dwarf distribution.
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I present an exact and explicit solution to the scalar (Stokes flux intensity) radio interferometer imaging equation on a spherical surface which is valid also for non-coplanar interferometer configurations. This imaging equation is comparable to $w$-term imaging algorithms, but by using a spherical rather than a Cartesian formulation this term has no special significance. The solution presented also allows direct identification of the scalar (spin 0 weighted) spherical harmonics on the sky. The method should be of interest for future multi-spacecraft interferometers, wide-field imaging with non-coplanar arrays, and CMB spherical harmonic measurements using interferometers.
The Laser Interferometer Space Antenna will be the first Gravitational Wave observatory in space. It is scheduled to fly in the early 2030s. LISA design predicts sensitivity levels that enable the detection a Stochastic Gravitational Wave Background signal. This stochastic type of signal is a superposition of signatures from sources that cannot be resolved individually and which are of various types, each one contributing with a different spectral shape. In this work we present a fast methodology to assess the detectability of a stationary, Gaussian, and isotropic stochastic signal in a set of frequency bins, combining information from the available data channels. We derive an analytic expression of the Bayes Factor between the instrumental noise-only and the signal plus instrumental noise models, that allows us to compute the detectability bounds of a given signal, as a function of frequency and prior knowledge on the instrumental noise spectrum.
To date weak gravitational lensing surveys have typically been restricted to small fields of view, such that the $textit{flat-sky approximation}$ has been sufficiently satisfied. However, with Stage IV surveys ($textit{e.g. LSST}$ and $textit{Euclid}$) imminent, extending mass-mapping techniques to the sphere is a fundamental necessity. As such, we extend the sparse hierarchical Bayesian mass-mapping formalism presented in previous work to the spherical sky. For the first time, this allows us to construct $textit{maximum a posteriori}$ spherical weak lensing dark-matter mass-maps, with principled Bayesian uncertainties, without imposing or assuming Gaussianty. We solve the spherical mass-mapping inverse problem in the analysis setting adopting a sparsity promoting Laplace-type wavelet prior, though this theoretical framework supports all log-concave posteriors. Our spherical mass-mapping formalism facilitates principled statistical interpretation of reconstructions. We apply our framework to convergence reconstruction on high resolution N-body simulations with pseudo-Euclid masking, polluted with a variety of realistic noise levels, and show a significant increase in reconstruction fidelity compared to standard approaches. Furthermore we perform the largest joint reconstruction to date of the majority of publicly available shear observational datasets (combining DESY1, KiDS450 and CFHTLens) and find that our formalism recovers a convergence map with significantly enhanced small-scale detail. Within our Bayesian framework we validate, in a statistically rigorous manner, the communitys intuition regarding the need to smooth spherical Kaiser-Squires estimates to provide physically meaningful convergence maps. Such approaches cannot reveal the small-scale physical structures that we recover within our framework.
Space-based gravitational wave detectors based on the Laser Interferometer Space Antenna (LISA) design operate by synthesizing one or more interferometers from fringe velocity measurements generated by changes in the light travel time between three spacecraft in a special set of drag-free heliocentric orbits. These orbits determine the inclination of the synthesized interferometer with respect to the ecliptic plane. Once these spacecraft are placed in their orbits, the orientation of the interferometers at any future time is fixed by Keplers Laws based on the initial orientation of the spacecraft constellation, which may be freely chosen. Over the course of a full solar orbit, the initial orientation determines a set of locations on the sky were the detector has greatest sensitivity to gravitational waves as well as a set of locations where nulls in the detector response fall. By artful choice of the initial orientation, we can choose to optimize or suppress the antennas sensitivity to sources whose location may be known in advance (e.g., the Galactic Center or globular clusters).
The Laser Interferometer Space Antenna (LISA) will open three decades of gravitational wave (GW) spectrum between 0.1 and 100 mHz, the mHz band. This band is expected to be the richest part of the GW spectrum, in types of sources, numbers of sources, signal-to-noise ratios and discovery potential. When LISA opens the low-frequency window of the gravitational wave spectrum, around 2034, the surge of gravitational-wave astronomy will strongly compel a subsequent mission to further explore the frequency bands of the GW spectrum that can only be accessed from space. The 2020s is the time to start developing technology and studying mission concepts for a large-scale mission to be launched in the 2040s. The mission concept would then be proposed to Astro2030. Only space based missions can access the GW spectrum between 10 nHz and 1 Hz because of the Earths seismic noise. This white paper surveys the science in this band and mission concepts that could accomplish that science. The proposed small scale activity is a technology development program that would support a range of concepts and a mission concept study to choose a specific mission concept for Astro2030. In this white paper, we will refer to a generic GW mission beyond LISA as bLISA.
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