The stochastic background: scaling laws and time to detection for pulsar timing arrays

We derive scaling laws for the signal-to-noise ratio of the optimal cross-correlation statistic, and show that the large power-law increase of the signal-to-noise ratio as a function of the observation time T that is usually assumed holds only at early times. After enough time has elapsed, pulsar timing arrays enter a new regime where the signal to noise only scales as . In addition, in this regime the quality of the pulsar timing data and the cadence become relatively unimportant. This occurs because the lowest frequencies of the pulsar timing residuals become gravitational-wave dominated. Pulsar timing arrays enter this regime more quickly than one might naively suspect. For T = 10 yr observations and typical stochastic background amplitudes, pulsars with residual root-mean-squares of less than about 1 μs are already in that regime. The best strategy to increase the detectability of the background in this regime is to increase the number of pulsars in the array. We also perform realistic simulations of the NANOGrav pulsar timing array, which through an aggressive pulsar survey campaign adds new millisecond pulsars regularly to its array, and show that a detection is possible within a decade, and could occur as early as 2016

Noise-marginalized optimal statistic: A robust hybrid frequentist-Bayesian statistic for the stochastic gravitational-wave background in pulsar timing arrays

Observations have revealed that nearly all galaxies contain supermassive black holes (SMBHs) at their centers. When galaxies merge, these SMBHs form SMBH binaries (SMBHBs) that emit low-frequency gravitational waves (GWs). The incoherent superposition of these sources produce a stochastic GW background (GWB) that can be observed by pulsar timing arrays (PTAs). The optimal statistic is a frequentist estimator of the amplitude of the GWB that specifically looks for the spatial correlations between pulsars induced by the GWB. In this paper, we introduce an improved method for computing the optimal statistic that marginalizes over the red noise in individual pulsars. We use simulations to demonstrate that this method more accurately determines the strength of the GWB, and we use the noise-marginalized optimal statistic to compare the significance of monopole, dipole, and Hellings-Downs (HD) spatial correlations and perform sky scrambles.Comment: 8 pages, 7 figures. Published in PR

Accelerated Bayesian model-selection and parameter-estimation in continuous gravitational-wave searches with pulsar-timing arrays

We describe several new techniques which accelerate Bayesian searches for continuous gravitational-wave emission from supermassive black-hole binaries using pulsar timing arrays. These techniques mitigate the problematic increase of search-dimensionality with the size of the pulsar array which arises from having to include an extra parameter per pulsar as the array is expanded. This extra parameter corresponds to searching over the phase of the gravitational-wave as it propagates past each pulsar so that we can coherently include the pulsar-term in our search strategies. Our techniques make the analysis tractable with powerful evidence-evaluation packages like MultiNest. We find good agreement of our techniques with the parameter-estimation and Bayes factor evaluation performed with full signal templates, and conclude that these techniques make excellent first-cut tools for detection and characterisation of continuous gravitational-wave signals with pulsar timing arrays. Crucially, at low to moderate signal-to-noise ratios the factor by which the analysis is sped up can be > 100, permitting rigorous programs of systematic injection and recovery of signals to establish robust detection criteria within a Bayesian formalism.Comment: 17 pages, 10 figures, 1 table. Minor changes to reflect published versio

The Local Nanohertz Gravitational-Wave Landscape From Supermassive Black Hole Binaries

Supermassive black hole binaries (SMBHBs) in the 10 million to 10 billion $M_\odot$ range form in galaxy mergers, and live in galactic nuclei with large and poorly constrained concentrations of gas and stars. There are currently no observations of merging SMBHBs--- it is in fact possible that they stall at their final parsec of separation and never merge. While LIGO has detected high frequency GWs, SMBHBs emit GWs in the nanohertz to millihertz band. This is inaccessible to ground-based interferometers, but possible with Pulsar Timing Arrays (PTAs). Using data from local galaxies in the 2 Micron All-Sky Survey, together with galaxy merger rates from Illustris, we find that there are on average $91\pm7$ sources emitting GWs in the PTA band, and $7\pm2$ binaries which will never merge. Local unresolved SMBHBs can contribute to GW background anisotropy at a level of $\sim20\%$, and if the GW background can be successfully isolated, GWs from at least one local SMBHB can be detected in 10 years.Comment: submitted to Nature Astronomy (reformatted for arXiv

Noise-marginalized optimal statistic: A robust hybrid frequentist-Bayesian statistic for the stochastic gravitational-wave background in pulsar timing arrays

Observations have revealed that nearly all galaxies contain supermassive black holes (SMBHs) at their centers. When galaxies merge, these SMBHs form SMBH binaries (SMBHBs) that emit low-frequency gravitational waves (GWs). The incoherent superposition of these sources produce a stochastic GW background (GWB) that can be observed by pulsar timing arrays. The optimal statistic is a frequentist estimator of the amplitude of the GWB that specifically looks for the spatial correlations between pulsars induced by the GWB. In this paper, we introduce an improved method for computing the optimal statistic that marginalizes over the red noise in individual pulsars. We use simulations to demonstrate that this method more accurately determines the strength of the GWB, and we use the noise-marginalized optimal statistic to compare the significance of monopole, dipole, and Hellings-Downs (HD) spatial correlations and perform sky scrambles

Potential determinants of health-care professionals’ use of survivorship care plans: a qualitative study using the theoretical domains framework

Abstract Background Survivorship care plans are intended to improve coordination of care for the nearly 14 million cancer survivors in the United States. Evidence suggests that survivorship care plans (SCPs) have positive outcomes for survivors, health-care professionals, and cancer programs, and several high-profile organizations now recommend SCP use. Nevertheless, SCP use remains limited among health-care professionals in United States cancer programs. Knowledge of barriers to SCP use is limited in part because extant studies have used anecdotal evidence to identify determinants. This study uses the theoretical domains framework to identify relevant constructs that are potential determinants of SCP use among United States health-care professionals. Methods We conducted semi-structured interviews to assess the relevance of 12 theoretical domains in predicting SCP use among 13 health-care professionals in 7 cancer programs throughout the United States with diverse characteristics. Relevant theoretical domains were identified through thematic coding of interview transcripts, identification of specific beliefs within coded text units, and mapping of specific beliefs onto theoretical constructs. Results We found the following theoretical domains (based on specific beliefs) to be potential determinants of SCP use: health-care professionals’ beliefs about the consequences of SCP use (benefit to survivors, health-care professionals, and the system as a whole); motivation and goals regarding SCP use (advocating SCP use; extent to which using SCPs competed for health-care professionals’ time); environmental context and resources (whether SCPs were delivered at a dedicated visit and whether a system, information technology, and funding facilitated SCP use); and social influences (whether using SCPs is an organizational priority, influential people support SCP use, and people who could assist with SCP use buy into using SCPs). Specific beliefs mapped onto the following psychological constructs: outcome expectancies, intrinsic motivation, goal priority, resources, leadership, and team working. Conclusions Previous studies have explored a limited range of determinants of SCP use. Our findings suggest a more comprehensive list of potential determinants that could be leveraged to promote SCP use. These results are particularly timely as cancer programs face impending SCP use requirements. Future work should develop instruments to measure the potential determinants and assess their relative influence on SCP use

High-precision 40Ar/39Ar dating of pleistocene tuffs and temporal anchoring of the Matuyama-Brunhes boundary

DFM thanks NERC for continued funding of the Argon Isotope Facility at SUERC and NERC Faciltiies grant IP/1626/0516. PRR thanks the Ann and Gordon Getty Foundation and the U.S. National Science Foundation (grant BCS-0715465) for support of his work. LM was funded by the Marie Curie FP7 Intra-European Fellowship Program for the duration of this project. VCS acknowledges support from the John Fell Fund, University of Oxford.High-precision 40Ar/39Ar ages for a series of proximal tuffs from the Toba super-volcano in Indonesia, and the Bishop Tuff and Lava Creek Tuff B in North America have been obtained. Core from Ocean Drilling Project Site 758 in the eastern equatorial Indian Ocean contains discrete tephra layers that we have geochemically correlated to the Young Toba Tuff (73.7 ± 0.3 ka), Middle Toba Tuff (502 ± 0.7 ka) and two eruptions (OTTA and OTTB) related to the Old Toba Tuff (792.4 ± 0.5 and 785.6 ± 0.7 ka, respectively) (40Ar/39Ar data reported as full external precision, 1 sigma). Within ODP 758 Termination IX is coincident with OTTB and hence this age tightly constrains the transition from Marine Isotope Stage 19–20 for the Indian Ocean. The core also preserves the location of the Australasian tektites, and the Matuyama-Brunhes boundary with Bayesian age-depth models used to determine the ages of these events, c. 784 ka and c. 786 ka, respectively. In North America, the Bishop Tuff (766.6 ± 0.4 ka) and Lava Creek Tuff B (627.0 ± 1.5 ka) have quantifiable stratigraphic relationships to the Matuyama-Brunhes boundary. Linear age-depth extrapolation, allowing for uncertainties associated with potential hiatuses in five different terrestrial sections, defines a geomagnetic reversal age of 789 ± 6 ka. Considering our data with respect to the previously published age data for the Matuyama-Brunhes boundary of Sagnotti et al. (2014), we suggest at the level of temporal resolution currently attainable using radioisotopic dating the last reversal of Earths geomagnetic field was isochronous. An overall Matuyama-Brunhes reversal age of 783.4 ± 0.6 ka is calculated, which allowing for inherent uncertainties in the astronomical dating approach, is indistinguishable from the LR04 stack age (780 ± 5 ka) for the geomagnetic boundary. Our high-precision age is 10 ± 2 ka older than the Matuyama-Brunhes boundary age of 773 ± 1 ka, as reported previously by Channell et al. (2010) for Atlantic Ocean records. As ODP 758 features in the LR04 marine stack, the high-precision 40Ar/39Ar ages determined here, as well as the Matuyama-Brunhes boundary age, can be used as temporally accurate and precise anchors for the Pleistocene time scale.Publisher PDFPeer reviewe

Weak Lensing from Space III: Cosmological Parameters

Weak gravitational lensing provides a unique method to directly map the dark matter in the universe and measure cosmological parameters. Current weak lensing surveys are limited by the atmospheric seeing from the ground and by the small field of view of existing space telescopes. We study how a future wide-field space telescope can measure the lensing power spectrum and skewness, and set constraints on cosmological parameters. The lensing sensitivity was calculated using detailed image simulations and instrumental specifications studied in earlier papers in this series. For instance, the planned SuperNova/Acceleration Probe (SNAP) mission will be able to measure the matter density parameter Omega_m and the dark energy equation of state parameter w with precisions comparable and nearly orthogonal to those derived with SNAP from supernovae. The constraints degrade by a factor of about 2 if redshift tomography is not used, but are little affected if the skewness only is dropped. We also study how the constraints on these parameters depend upon the survey geometry and define an optimal observing strategy.Comment: 12 pages, 11 figures. Accepted versio

Plane waves with weak singularities

We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of divergence is such that the distortion suffered by a freely falling observer remains finite. Among such weak singular plane waves there is a sub-class which do not exhibit large back reaction in the presence of test scalar probes. String propagation in these backgrounds is smooth and there is a natural way to continue the metric beyond the singularity. This continued metric admits string propagation without the string becoming infinitely excited. We construct a one parameter family of smooth metrics which are at a finite distance in the space of metrics from the extended metric and a well defined operator in the string sigma model which resolves the singularity.Comment: 22 pages, Added references and clarifying comment