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Register a new userOscillatory path integrals for radio astronomy
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We introduce a new method for evaluating the oscillatory integrals which describe natural interference patterns. As an illustrative example of contemporary interest, we consider astrophysical plasma lensing of coherent sources like pulsars and fast radio bursts in radioastronomy. Plasma lenses are known to occur near the source, in the interstellar medium, as well as in the solar wind and the earths ionosphere. Such lensing is strongest at long wavelengths hence it is generally important to go beyond geometric optics and into the full wave optics regime. Our computational method is a spinoff of new techniques two of us, and our collaborators, have developed for defining and performing Lorentzian path integrals. Cauchys theorem allows one to transform a computationally fragile and expensive, highly oscillatory integral into an exactly equivalent sum of absolutely and rapidly convergent integrals which can be evaluated in polynomial time. We require only that it is possible to analytically continue the lensing phase, expressed in the integrated coordinates, into the complex domain. We give a first-principles derivation of the Fresnel-Kirchhoff integral, starting from Feynmans path integral for a massless particle in a refractive medium. We then demonstrate the effectiveness of our method by computing the interference patterns of Thoms caustic catastrophes, both in their normal forms and within a variety of more realistic, local lens models, over all wavelengths. Our numerical method, implemented in a freely downloadable code, provides a fast, accurate tool for modeling interference patterns in radioastronomy and other fields of physics.
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At supranuclear densities, explored in the core of neutron stars, a strong phase transition from hadronic matter to more exotic forms of matter might be present. To test this hypothesis, binary neutron-star mergers offer a unique possibility to probe matter at densities that we can not create in any existing terrestrial experiment. In this work, we show that, if present, strong phase transitions can have a measurable imprint on the binary neutron-star coalescence and the emitted gravitational-wave signal. We construct a new parameterization of the supranuclear equation of state that allows us to test for the existence of a strong phase transition and extract its characteristic properties purely from the gravitational-wave signal of the inspiraling neutron stars. We test our approach using a Bayesian inference study simulating 600 signals with three different equations of state and find that for current gravitational-wave detector networks already twelve events might be sufficient to verify the presence of a strong phase transition. Finally, we use our methodology to analyze GW170817 and GW190425, but do not find any indication that a strong phase transition is present at densities probed during the inspiral.
We explore opportunities for multi-messenger astronomy using gravitational waves (GWs) and prompt, transient low-frequency radio emission to study highly energetic astrophysical events. We review the literature on possible sources of correlated emission of gravitational waves and radio transients, highlighting proposed mechanisms that lead to a short-duration, high-flux radio pulse originating from the merger of two neutron stars or from a superconducting cosmic string cusp. We discuss the detection prospects for each of these mechanisms by low-frequency dipole array instruments such as LWA1, LOFAR and MWA. We find that a broad range of models may be tested by searching for radio pulses that, when de-dispersed, are temporally and spatially coincident with a LIGO/Virgo GW trigger within a $usim 30$ second time window and $usim 200 mendash 500 punits{deg}^{2}$ sky region. We consider various possible observing strategies and discuss their advantages and disadvantages. Uniquely, for low-frequency radio arrays, dispersion can delay the radio pulse until after low-latency GW data analysis has identified and reported an event candidate, enabling a emph{prompt} radio signal to be captured by a deliberately targeted beam. If neutron star mergers do have detectable prompt radio emissions, a coincident search with the GW detector network and low-frequency radio arrays could increase the LIGO/Virgo effective search volume by up to a factor of $usim 2$. For some models, we also map the parameter space that may be constrained by non-detections.
We develop two classes of composite moment-free numerical quadratures for computing highly oscillatory integrals having integrable singularities and stationary points. The first class of the quadrature rules has a polynomial order of convergence and the second class has an exponential order of convergence. We first modify the moment-free Filon-type method for the oscillatory integrals without a singularity or a stationary point to accelerate their convergence. We then consider the oscillatory integrals without a singularity or a stationary point and then those with singularities and stationary points. The composite quadrature rules are developed based on partitioning the integration domain according to the wave number and the singularity of the integrand. The integral defined on a subinterval has either a weak singularity without rapid oscillation or oscillation without a singularity. The classical quadrature rules for weakly singular integrals using graded points are employed for the singular integral without rapid oscillation and the modified moment-free Filon-type method is used for the oscillatory integrals without a singularity. Unlike the existing methods, the proposed methods do not have to compute the inverse of the oscillator. Numerical experiments are presented to demonstrate the approximation accuracy and the computational efficiency of the proposed methods. Numerical results show that the proposed methods outperform methods published most recently.
The gravitational-wave (GW) detection of GW190521 has provided new insights on the mass distribution of black holes and new constraints for astrophysical formation channels. With independent claims of GW190521 having significant pre-merger eccentricity, we investigate what this implies for GW190521-like binaries that form dynamically. The Laser Interferometer Space Antenna (LISA) will also be sensitive to GW190521-like binaries if they are circular from an isolated formation channel. We show, however, that GW190521-like binaries that form dynamically may skip the LISA band entirely. To this end, we simulate GW190521 analogues that dynamically form via post-Newtonian binary-single scattering. From these scattering experiments, we find that GW190521-like binaries may enter the LIGO-Virgo band with significant eccentricity as suggested by recent studies, though well below an eccentricity of $e_{rm 10Hz} lesssim 0.7$. Eccentric GW190521-like binaries further motivate the astrophysical science case for a decihertz GW observatory, such as the kilometer-scale version of the Midband Atomic Gravitational-wave Interferometric Sensor (MAGIS). Pre-merger observations of GW190521-like binaries with such a decihertz GW detector would be able to constrain the eccentricity of GW190521-like binaries to greater precision than with just LIGO-Virgo alone. These eccentricity constraints would also provide additional insights into the possible environments that GW190521-like binaries form in.
A space-based interferometer operating in the previously unexplored mHz gravitational band has tremendous discovery potential. If history is any guide, the opening of a new spectral band will lead to the discovery of entirely new sources and phenomena. The mHz band is ideally suited to exploring beyond standard model processes in the early universe, and with the sensitivities that can be reached with current technologies, the discovery space for exotic astrophysical systems is vast.
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