Measuring violations of General Relativity from single gravitational wave detection by non-spinning binary systems: higher-order asymptotic analysis

A frequentist asymptotic expansion method for error estimation is employed for a network of gravitational wave detectors to assess the amount of information that can be extracted from gravitational wave observations. Mathematically we derive lower bounds in the errors that any parameter estimator will have in the absence of prior knowledge to distinguish between the post-Einsteinian (ppE) description of coalescing binary systems and that of general relativity. When such errors are smaller than the parameter value, there is possibility to detect these violations from GR. A parameter space with inclusion of dominant dephasing ppE parameters $(\beta, b)$ is used for a study of first- and second-order (co)variance expansions, focusing on the inspiral stage of a nonspinning binary system of zero eccentricity detectible through Adv. LIGO and Adv. Virgo. Our procedure is an improvement of the Cram\'{e}r-Rao Lower Bound. When Bayesian errors are lower than our bound it means that they depend critically on the priors. The analysis indicates the possibility of constraining deviations from GR in inspiral SNR ($\rho \sim 15-17$) regimes that are achievable in upcoming scientific runs (GW150914 had an inspiral SNR $\sim 12$). The errors on $\beta$ also increase errors of other parameters such as the chirp mass $\mathcal{M}$ and symmetric mass ratio $\eta$. Application is done to existing alternative theories of gravity, which include modified dispersion relation of the waveform, non-spinning models of quadratic modified gravity, and dipole gravitational radiation (i.e., Brans-Dicke type) modifications.Comment: 15 pages, 9 figure

Induced Magnetic Dipole on Jupiter’s Moon Europa

Physics can have some of the most unique and extraordinary applications of basic principles applied on a larger scale. This paper will explore the properties of induced magnetic dipoles and will examine this phenomenon directly from Jupiter\u27s moon, Europa. These properties will be used to determine if there is liquid water beneath its icy surface and how this conclusion was verified. This will be accomplished using the concepts of magnetic dipoles and induced currents. Recent missions have also revealed estimates of the depth of Europa\u27s subsurface ocean. There have been many measurements taken of Europa\u27s magnetic field, and they are the most important variable in determining the depth of the Europan ocean depth. The relation between the magnetic dipole measurements and the ocean depth will be shown in figures

Core-Collapse Supernovae Overview with Swift Collaboration

The Core-Collapse supernovae (CCSNe) mark the dynamic and explosive end of the lives of massive stars. The mysterious mechanism, primarily focused with the shock revival phase, behind CCSNe explosions could be explained by detecting the corresponding gravitational wave (GW) emissions by the laser interferometer gravitational wave observatory, LIGO. GWs are extremely hard to detect because they are weak signals in a floor of instrument noise. Optical observations of CCSNe are already used in coincidence with LIGO data, as a hint of the times where to search for the emission of GWs. More of these hints would be very helpful. For the first time in history a Harvard group has observed X-ray transients in coincidence with optical CCSNe. This discovery has proven that even if a supernova had its light absorbed with dust, X-ray transients that are more penetrating, and thus could be used as a hint on where to search for GWs. The SWIFT satellite can monitor galaxies with an X-ray probe. The main goal of this project will be to quantify the benefits for LIGO by using the SWIFT satellite to monitor galaxies within 20 Mega parsecs from Earth

Asymptotic Accuracy of Geoacoustic Inversions

Criteria necessary to accurately estimate a set of unknown geoacoustic parameters from remote acoustic measurements are developed in order to aid the design of geoacoustic experiments. The approach is to have estimation error fall within a specified design threshold by adjusting controllable quantities such as experimental sample size or signal-to-noise ratio (SNR). This is done by computing conditions on sample size and SNR necessary for any estimate to have a variance that (1) asymptotically attains the Cramer–Rao lower bound (CRLB) and (2) has a CRLB that falls within the specified design error threshold. Applications to narrow band deterministic signals received with additive noise by vertical and horizontal arrays in typical continental shelf waveguides are explored. For typical low-frequency scenarios, necessary SNRs and samples sizes can often approach prohibitively large values when a few or more important geoacoustic parameters are unknown, making it difficult to attain practical design thresholds for allowable estimation error

Characterizing a supernova's Standing Accretion Shock Instability with neutrinos and gravitational waves

We perform a novel multi-messenger analysis for the identification and parameter estimation of the Standing Accretion Shock Instability (SASI) in a core collapse supernova with neutrino and gravitational wave (GW) signals. In the neutrino channel, this method performs a likelihood ratio test for the presence of SASI in the frequency domain. For gravitational wave signals we process an event with a modified constrained likelihood method. Using simulated supernova signals, the properties of the Hyper-Kamiokande neutrino detector, and O3 LIGO Interferometric data, we produce the two-dimensional probability density function (PDF) of the SASI activity indicator and calculate the probability of detection $P_\mathrm{D}$ as well as the false identification probability $P_\mathrm{FI}$. We discuss the probability to establish the presence of the SASI as a function of the source distance in each observational channel, as well as jointly. Compared to a single-messenger approach, the joint analysis results in $P_\mathrm{D}$ (at $P_\mathrm{FI}=0.1$) of SASI activities that is larger by up to $\approx~40\%$ for a distance to the supernova of 5 kpc. We also discuss how accurately the frequency and duration of the SASI activity can be estimated in each channel separately. Our methodology is suitable for implementation in a realistic data analysis and a multi-messenger setting.Comment: 24 pages, 15 figures, accepted by PR