The Neutron-Star Equation of State and Gravitational Waves from Compact Binaries

The equation of state (EOS) of matter above nuclear density is currently uncertain by almost an order of magnitude. Fortunately, neutron stars (NS) provide an ideal laboratory for studying high density matter. In order to systematize the study of the EOS from NS observations, we introduce a parametrized high-density EOS that accurately fits theoretical candidate EOSs. We then determine the ability of several recent and near-future electromagnetic observations to constrain the parameter space of our EOS. Recent observations include measurements of masses, gravitational redshift, and spin period, and we find that high mass observations are the most useful at constraining the EOS. Reliable simultaneous mass--radius measurements or mass--moment of inertia measurements in the near future, on the other hand, would provide a dramatically stronger constraint by requiring the allowed parameters to lie on a hypersurface of the full parameter space. In addition to electromagnetic observations, binary neutron star (BNS) and black hole-neutron star (BHNS) coalescence events observed with gravitational-wave detectors offer the potential to dramatically improve our understanding of the EOS. Information about the EOS is encoded in the waveform through tidal interactions, and for BNS systems, the inspiral waveform depends on the EOS through a single parameter called the tidal deformability. Using recent numerical BHNS simulations we find that the entire BHNS inspiral-merger-ringdown waveform also depends on the EOS exclusively through the same tidal deformability parameter. Using these BNS and BHNS waveforms, we examine the ability of second generation detectors now in construction and planned third generation detectors to extract information about the EOS

Surrogate model for an aligned-spin effective one body waveform model of binary neutron star inspirals using Gaussian process regression

Fast and accurate waveform models are necessary for measuring the properties of inspiraling binary neutron star systems such as GW170817. We present a frequency-domain surrogate version of the aligned-spin binary neutron star waveform model using the effective one body formalism known as SEOBNRv4T. This model includes the quadrupolar and octopolar adiabatic and dynamical tides. The version presented here is improved by the inclusion of the spin-induced quadrupole moment effect, and completed by a prescription for tapering the end of the waveform to qualitatively reproduce numerical relativity simulations. The resulting model has 14 intrinsic parameters. We reduce its dimensionality by using universal relations that approximate all matter effects in terms of the leading quadrupolar tidal parameters. The implementation of the time-domain model can take up to an hour to evaluate using a starting frequency of 20Hz, and this is too slow for many parameter estimation codes that require $O(10^7)$ sequential waveform evaluations. We therefore construct a fast and faithful frequency-domain surrogate of this model using Gaussian process regression. The resulting surrogate has a maximum mismatch of $4.5\times 10^{-4}$ for the Advanced LIGO detector, and requires 0.13s to evaluate for a waveform with a starting frequency of 20Hz. Finally, we perform an end-to-end test of the surrogate with a set of parameter estimation runs, and find that the surrogate accurately recovers the parameters of injected waveforms.Comment: 19 pages, 10 figures, submitted to PR

Aligned spin neutron star-black hole mergers: a gravitational waveform amplitude model

The gravitational radiation emitted during the merger of a black hole with a neutron star is rather similar to the radiation from the merger of two black holes when the neutron star is not tidally disrupted. When tidal disruption occurs, gravitational waveforms can be broadly classified in two groups, depending on the spatial extent of the disrupted material. Extending previous work by some of us, here we present a phenomenological model for the gravitational waveform amplitude in the frequency domain encompassing the three possible outcomes of the merger: no tidal disruption, "mild" and "strong" tidal disruption. The model is calibrated to 134 general-relativistic numerical simulations of binaries where the black hole spin is either aligned or antialigned with the orbital angular momentum. All simulations were produced using the SACRA code and piecewise polytropic neutron star equations of state. The present model can be used to determine when black-hole binary waveforms are sufficient for gravitational-wave detection, to extract information on the equation of state from future gravitational-wave observations, to obtain more accurate estimates of black hole-neutron star merger event rates, and to determine the conditions under which these systems are plausible candidates as central engines of gamma-ray bursts, macronovae and kilonovae.Comment: 15 pages, 7 figures, 1 tabl

Effective-one-body waveforms for binary neutron stars using surrogate models

Gravitational-wave observations of binary neutron star systems can provide information about the masses, spins, and structure of neutron stars. However, this requires accurate and computationally efficient waveform models that take <1s to evaluate for use in Bayesian parameter estimation codes that perform 10^7 - 10^8 waveform evaluations. We present a surrogate model of a nonspinning effective-one-body waveform model with l = 2, 3, and 4 tidal multipole moments that reproduces waveforms of binary neutron star numerical simulations up to merger. The surrogate is built from compact sets of effective-one-body waveform amplitude and phase data that each form a reduced basis. We find that 12 amplitude and 7 phase basis elements are sufficient to reconstruct any binary neutron star waveform with a starting frequency of 10Hz. The surrogate has maximum errors of 3.8% in amplitude (0.04% excluding the last 100M before merger) and 0.043 radians in phase. The version implemented in the LIGO Algorithm Library takes ~0.07s to evaluate for a starting frequency of 30Hz and ~0.8s for a starting frequency of 10Hz, resulting in a speed-up factor of ~10^3 - 10^4 relative to the original Matlab code. This allows parameter estimation codes to run in days to weeks rather than years, and we demonstrate this with a Nested Sampling run that recovers the masses and tidal parameters of a simulated binary neutron star system.Comment: 17 pages, 11 figures, submitted to PR

Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral

The early part of the gravitational wave signal of binary neutron star inspirals can potentially yield robust information on the nuclear equation of state. The influence of a star's internal structure on the waveform is characterized by a single parameter: the tidal deformability lambda, which measures the star's quadrupole deformation in response to the companion's perturbing tidal field. We calculate lambda for a wide range of equations of state and find that the value of lambda spans an order of magnitude for the range of equation of state models considered. An analysis of the feasibility of discriminating between neutron star equations of state with gravitational wave observations of the early part of the inspiral reveals that the measurement error in lambda increases steeply with the total mass of the binary. Comparing the errors with the expected range of lambda, we find that Advanced LIGO observations of binaries at a distance of 100 Mpc will probe only unusually stiff equations of state, while the proposed Einstein Telescope is likely to see a clean tidal signature.Comment: 12 pages, submitted to PR

Systematic and statistical errors in a Bayesian approach to the estimation of the neutron-star equation of state using advanced gravitational wave detectors

Advanced ground-based gravitational-wave detectors are capable of measuring tidal influences in binary neutron-star systems. In this work, we report on the statistical uncertainties in measuring tidal deformability with a full Bayesian parameter estimation implementation. We show how simultaneous measurements of chirp mass and tidal deformability can be used to constrain the neutron-star equation of state. We also study the effects of waveform modeling bias and individual instances of detector noise on these measurements. We notably find that systematic error between post-Newtonian waveform families can significantly bias the estimation of tidal parameters, thus motivating the continued development of waveform models that are more reliable at high frequencies

Intrusive History and Petrogenesis of the Ash Mountain Complex, Sierra Nevada Batholith, California (USA)

The Ash Mountain Complex (AMC) in the western Sierra Nevada batholith (SNB; California, USA) is an exposure of six compositionally diverse intrusive lithologies with clear crosscutting relationships that permit a focused investigation of magma source characteristics and the relative roles of petrogenetic processes on the evolution of the system. We use new field observations, zircon U-Pb dates, major and trace element data, and Sr-Nd-Pb isotopic data to develop a model that can be applied to similar SNB intrusive suites. Stage 1 units, emplaced ca. 105 Ma, consist of two gabbros, a gabbrodiorite, and a granite. Stage 2 and stage 3 units were emplaced ca. 104 Ma and ca. 103 Ma, respectively, and are granites. We suggest that stage 1 gabbroids were derived by partial melting of lithospheric mantle, whereas coeval felsic magmas were derived by partial melting of a mafic, juvenile crustal source. Stage 2 and stage 3 granitoids were derived from similar sources that generated stage 1 granitoids, but there was greater input from evolved crust. Fractionation and/or assimilation played only a minor role in system evolution. Past studies of SNB magmas have come to conflicting conclusions about the petrogenesis of intermediate magmas that dominate the batholith; we hypothesize that mafic and felsic end members of the AMC could represent end members in mixing processes that generate these magmas. The timing of emplacement of the AMC coincides with a transition of magmatic style in the SNB, from smaller volume magmatic suites with mixed mantle and crustal sources to larger volume magmatic suites derived from greater proportions of crust