Report on the first round of the Mock LISA Data Challenges

The Mock LISA Data Challenges (MLDCs) have the dual purpose of fostering the development of LISA data analysis tools and capabilities, and demonstrating the technical readiness already achieved by the gravitational-wave community in distilling a rich science payoff from the LISA data output. The first round of MLDCs has just been completed: nine challenges consisting of data sets containing simulated gravitational-wave signals produced either by galactic binaries or massive black hole binaries embedded in simulated LISA instrumental noise were released in June 2006 with deadline for submission of results at the beginning of December 2006. Ten groups have participated in this first round of challenges. All of the challenges had at least one entry which successfully characterized the signal to better than 95% when assessed via a correlation with phasing ambiguities accounted for. Here, we describe the challenges, summarize the results and provide a first critical assessment of the entries

Angular Resolution of the LISA Gravitational Wave Detector

We calculate the angular resolution of the planned LISA detector, a space-based laser interferometer for measuring low-frequency gravitational waves from galactic and extragalactic sources. LISA is not a pointed instrument; it is an all-sky monitor with a quadrupolar beam pattern. LISA will measure simultaneously both polarization components of incoming gravitational waves, so the data will consist of two time series. All physical properties of the source, including its position, must be extracted from these time series. LISA's angular resolution is therefore not a fixed quantity, but rather depends on the type of signal and on how much other information must be extracted. Information about the source position will be encoded in the measured signal in three ways: 1) through the relative amplitudes and phases of the two polarization components, 2) through the periodic Doppler shift imposed on the signal by the detector's motion around the Sun, and 3) through the further modulation of the signal caused by the detector's time-varying orientation. We derive the basic formulae required to calculate the LISA's angular resolution $\Delta \Omega_S$ for a given source. We then evaluate $\Delta \Omega_S$ for two sources of particular interest: monchromatic sources and mergers of supermassive black holes. For these two types of sources, we calculate (in the high signal-to-noise approximation) the full variance-covariance matrix, which gives the accuracy to which all source parameters can be measured. Since our results on LISA's angular resolution depend mainly on gross features of the detector geometry, orbit, and noise curve, we expect these results to be fairly insensitive to modest changes in detector design that may occur between now and launch. We also expect that our calculations could be easily modified to apply to a modified design.Comment: 15 pages, 5 figures, RevTex 3.0 fil

Plagioclase‐Saturated Melt Hygrothermobarometry and Plagioclase‐Melt Equilibria Using Machine Learning

Compositions of plagioclase‐melt pairs are commonly used to constrain temperatures (T), dissolved water contents (H2O) and pressures (P) of pre‐eruptive magma storage and transport. However, previous plagioclase‐based thermometers, hygrometers, and barometers can have significant errors, leading to imprecise reconstructions of conditions during plagioclase growth. Here, we explore whether we can refine existing plagioclase‐based hygrothermobarometers with either plagioclase‐melt or melt‐only chemistry (±T/H2O), calibrated using random forest machine learning on experimental petrology data (n = 1,152). We find that both the plagioclase‐melt and melt‐only models return similar cross‐validation root‐mean‐square errors (RMSEs), as the melt holds most of the P‐T‐H2O information rather than the plagioclase. T/H2O‐dependent melt models have test set RMSEs of 25°C, 0.70 wt.% and 76 MPa for temperature, H2O content and pressure, respectively, while T/H2O‐independent models have RMSEs of 38°C, 0.97 wt.% and 91 MPa. The melt thermometer and hygrometer are applicable to a wide range of plagioclase‐bearing melts at temperatures between 664 and 1355°C, and with H2O concentrations up to 11.2 wt.%, while the melt barometer is suitable for pressures of ≤500 MPa. An updated plagioclase‐melt equilibrium model has also been calibrated, allowing the equilibrium anorthite content to be predicted with an error of 5.8 mol%. The new P‐T‐H2O‐An models were applied to matrix glasses and melt inclusions from the 1980 Mount St Helens (USA) and 2014–2015 Holuhraun (Iceland) eruptions, corroborating previous independent estimates and observations. Models are available at https://github.com/kyra‐cutler/Plag‐saturated‐melt‐P‐T‐H2O‐An, enabling assessment of plagioclase‐melt equilibrium and characterization of last‐equilibrated P‐T‐H2O conditions of plagioclase‐saturated magmas

Testing Alternative Theories of Gravity using LISA

We investigate the possible bounds which could be placed on alternative theories of gravity using gravitational wave detection from inspiralling compact binaries with the proposed LISA space interferometer. Specifically, we estimate lower bounds on the coupling parameter \omega of scalar-tensor theories of the Brans-Dicke type and on the Compton wavelength of the graviton \lambda_g in hypothetical massive graviton theories. In these theories, modifications of the gravitational radiation damping formulae or of the propagation of the waves translate into a change in the phase evolution of the observed gravitational waveform. We obtain the bounds through the technique of matched filtering, employing the LISA Sensitivity Curve Generator (SCG), available online. For a neutron star inspiralling into a 10^3 M_sun black hole in the Virgo Cluster, in a two-year integration, we find a lower bound \omega > 3 * 10^5. For lower-mass black holes, the bound could be as large as 2 * 10^6. The bound is independent of LISA arm length, but is inversely proportional to the LISA position noise error. Lower bounds on the graviton Compton wavelength ranging from 10^15 km to 5 * 10^16 km can be obtained from one-year observations of massive binary black hole inspirals at cosmological distances (3 Gpc), for masses ranging from 10^4 to 10^7 M_sun. For the highest-mass systems (10^7 M_sun), the bound is proportional to (LISA arm length)^{1/2} and to (LISA acceleration noise)^{-1/2}. For the others, the bound is independent of these parameters because of the dominance of white-dwarf confusion noise in the relevant part of the frequency spectrum. These bounds improve and extend earlier work which used analytic formulae for the noise curves.Comment: 16 pages, 9 figures, submitted to Classical & Quantum Gravit

LISA detections of massive black hole inspirals: parameter extraction errors due to inaccurate template waveforms

The planned Laser Interferometer Space Antenna (LISA) is expected to detect the inspiral and merger of massive black hole binaries (MBHBs) at z <~ 5 with signal-to-noise ratios (SNRs) of hundreds to thousands. Because of these high SNRs, and because these SNRs accrete over periods of weeks to months, it should be possible to extract the physical parameters of these systems with high accuracy; for instance, for a ~ 10^6 Msun MBHBs at z = 1 it should be possible to determine the two masses to ~ 0.1% and the sky location to ~ 1 degree. However, those are just the errors due to noise: there will be additional "theoretical" errors due to inaccuracies in our best model waveforms, which are still only approximate. The goal of this paper is to estimate the typical magnitude of these theoretical errors. We develop mathematical tools for this purpose, and apply them to a somewhat simplified version of the MBHB problem, in which we consider just the inspiral part of the waveform and neglect spin-induced precession, eccentricity, and PN amplitude corrections. For this simplified version, we estimate that theoretical uncertainties in sky position will typically be ~ 1 degree, i.e., comparable to the statistical uncertainty. For the mass and spin parameters, our results suggest that while theoretical errors will be rather small absolutely, they could still dominate over statistical errors (by roughly an order of magnitude) for the strongest sources. The tools developed here should be useful for estimating the magnitude of theoretical errors in many other problems in gravitational-wave astronomy.Comment: RevTeX4, 16 pages, 2 EPS figures. Corrected typos, clarified statement

RHIC Physics with the Parton Cascade Model

We present an analysis of the net-baryon number rapidity distribution and of direct photon emission in the framework of the Parton Cascade Model.Comment: 4 pages 4 figures included, proceedings of QM 200

LISA data analysis I: Doppler demodulation

The orbital motion of the Laser Interferometer Space Antenna (LISA) produces amplitude, phase and frequency modulation of a gravitational wave signal. The modulations have the effect of spreading a monochromatic gravitational wave signal across a range of frequencies. The modulations encode useful information about the source location and orientation, but they also have the deleterious affect of spreading a signal across a wide bandwidth, thereby reducing the strength of the signal relative to the instrument noise. We describe a simple method for removing the dominant, Doppler, component of the signal modulation. The demodulation reassembles the power from a monochromatic source into a narrow spike, and provides a quick way to determine the sky locations and frequencies of the brightest gravitational wave sources.Comment: 5 pages, 7 figures. References and new comments adde

Estimating the detectable rate of capture of stellar mass black holes by massive central black holes in normal galaxies

The capture and subsequent inspiral of stellar mass black holes on eccentric orbits by central massive black holes, is one of the more interesting likely sources of gravitational radiation detectable by LISA. We estimate the rate of observable events and the associated uncertainties. A moderately favourable mass function could provide many detectable bursts each year, and a detection of at least one burst per year is very likely given our current understanding of the populations in cores of normal spiral galaxies.Comment: 3 pages 2-column revtex Latex macro. No figures. Classical and Quantum Gravity, accepte

Hurst Coefficient in long time series of population size: Model for two plant populations with different reproductive strategies

Can the fractal dimension of fluctuations in population size be used to estimate extinction risk? The problem with estimating this fractal dimension is that the lengths of the time series are usually too short for conclusive results. This study answered this question with long time series data obtained from an iterative competition model. This model produces competitive extinction at different perturbation intensities for two different germination strategies: germination of all seeds vs. dormancy in half the seeds. This provided long time series of 900 years and different extinction risks. The results support the hypothesis for the effectiveness of the Hurst coefficient for estimating extinction risk

Orbital evolution of a test particle around a black hole: higher-order corrections

We study the orbital evolution of a radiation-damped binary in the extreme mass ratio limit, and the resulting waveforms, to one order beyond what can be obtained using the conservation laws approach. The equations of motion are solved perturbatively in the mass ratio (or the corresponding parameter in the scalar field toy model), using the self force, for quasi-circular orbits around a Schwarzschild black hole. This approach is applied for the scalar model. Higher-order corrections yield a phase shift which, if included, may make gravitational-wave astronomy potentially highly accurate.Comment: 4 pages, 3 Encapsulated PostScript figure