arXiv subjects

Will M. Farr

Publications and source records attributed to Will M. Farr.

At least 91 records · Page 5Linked to original sources

arXiv2018

Hidden Planetary Friends: On the Stability Of 2-Planet Systems in the Presence of a Distant, Inclined Companion

Recent observational campaigns have shown that multi-planet systems seem to be abundant in our Galaxy. Moreover, it seems that these systems might have distant companions, either planets, brown-dwarfs or other stellar objects. These companions might be inclined with respect to the inner planets, and could potentially excite the eccentricities of the inner planets through the Eccentric Kozai-Lidov mechanism. These eccentricity excitations could perhaps cause the inner orbits to cross, disrupting the inner system. We study the stability of two-planet systems in the presence of a distant, inclined, giant planet. Specifically, we derive a stability criterion, which depends on the companion's separation and eccentricity. We show that our analytic criterion agrees with the results obtained from numerically integrating an ensemble of systems. Finally, as a potential proof-of-concept, we provide a set of predictions for the parameter space that allows the existence of planetary companions for the Kepler-419, Kepler-56, Kepler-448, Kepler-88, Kepler-109, and Kepler-36 systems.

astro-ph.EP↗

arXiv2018

What if LIGO's gravitational wave detections are strongly lensed by massive galaxy clusters?

Motivated by the preponderance of so-called "heavy black holes" in the binary black hole (BBH) gravitational wave (GW) detections to date, and the role that gravitational lensing continues to play in discovering new galaxy populations, we explore the possibility that the GWs are strongly-lensed by massive galaxy clusters. For example, if one of the GW sources were actually located at $z=1$, then the rest-frame mass of the associated BHs would be reduced by a factor $\sim2$. Based on the known populations of BBH GW sources and strong-lensing clusters, we estimate a conservative lower limit on the number of BBH mergers detected per detector year at LIGO/Virgo's current sensitivity that are multiply-imaged, of $R_{\rm detect}\simeq10^{-5}{\rm yr}^{-1}$. This is equivalent to rejecting the hypothesis that one of the BBH GWs detected to date was multiply-imaged at $<\sim4σ$. It is therefore unlikely but not impossible that one of the GWs is multiply-imaged. We identify three spectroscopically confirmed strong-lensing clusters with well constrained mass models within the $90\%$ credible sky localisations of the BBH GWs from LIGO's first observing run. In the event that one of these clusters multiply-imaged one of the BBH GWs, we predict that $20-60\%$ of the putative next appearances of the GWs would be detectable by LIGO, and that they would arrive at Earth within three years of first detection.

astro-ph.HE↗

arXiv2017

Using spin to understand the formation of LIGO's black holes

With the detection of four candidate binary black hole (BBH) mergers by the Advanced LIGO detectors thus far, it is becoming possible to constrain the properties of the BBH merger population in order to better understand the formation of these systems. Black hole (BH) spin orientations are one of the cleanest discriminators of formation history, with BHs in dynamically formed binaries in dense stellar environments expected to have spins distributed isotropically, in contrast to isolated populations where stellar evolution is expected to induce BH spins preferentially aligned with the orbital angular momentum. In this work we propose a simple, model-agnostic approach to characterizing the spin properties of LIGO's BBH population. Using measurements of the effective spin of the binaries, which is LIGO's best constrained spin parameter, we introduce a simple parameter to quantify the fraction of the population that is isotropically distributed, regardless of the spin magnitude distribution of the population. Once the orientation characteristics of the population have been determined, we show how measurements of effective spin can be used to directly constrain the underlying BH spin magnitude distribution. Although we find that the majority of the current effective spin measurements are too small to be informative, with LIGO's four BBH candidates we find a slight preference for an underlying population with aligned spins over one with isotropic spins (with an odds ratio of 1.1). We argue that it will be possible to distinguish symmetric and anti-symmetric populations at high confidence with tens of additional detections, although mixed populations may take significantly more detections to disentangle. We also derive preliminary spin magnitude distributions for LIGO's black holes, under the assumption of aligned or isotropic populations.

astro-ph.HE↗

arXiv2017

Distinguishing Spin-Aligned and Isotropic Black Hole Populations With Gravitational Waves

The first direct detections of gravitational waves from merging binary black holes open a unique window into the binary black hole formation environment. One promising environmental signature is the angular distribution of the black hole spins; systems formed through dynamical interactions among already-compact objects are expected to have isotropic spin orientations whereas binaries formed from pairs of stars born together are more likely to have spins preferentially aligned with the binary orbital angular momentum. We consider existing gravitational wave measurements of the binary effective spin, the best-measured combination of spin parameters, in the four likely binary black hole detections GW150914, LVT151012, GW151226, and GW170104. If binary black hole spin magnitudes extend to high values we show that the data exhibit a $2.4σ$ ($0.015$ odds ratio) preference for an isotropic angular distribution over an aligned one. By considering the effect of 10 additional detections, we show that such an augmented data set would enable in most cases a preference stronger than $5σ$ ($2.9 \times 10^{-7}$ odds ratio). The existing preference for either an isotropic spin distribution or low spin magnitudes for the observed systems will be confirmed (or overturned) confidently in the near future.

astro-ph.HE↗

arXiv2017

Hierarchical inference of the relationship between Concentration and Mass in Galaxy Groups and Clusters

Mass is a fundamental property of galaxy groups and clusters. In theory weak gravitational lensing will enable an approximately unbiased measurement of mass, but parametric methods for extracting cluster masses from data require the additional knowledge of concentration. Measurements of both mass and concentration are limited by the degeneracy between the two parameters, particularly in low mass, high redshift systems where the signal-to-noise is low. In this paper we develop a hierarchical model of mass and concentration for mass inference we test our method on toy data and then apply it to a sample of galaxy groups and poor clusters down to masses of $\sim$ 1e13 M$_\odot$. Our fit and model gives a relationship among masses, concentrations and redshift that allow prediction of these parameters from incomplete and noisy future measurements. Additionally the underlying population can be used to infer an observationally based concentration-mass relation. Our method is equivalent to a quasi- stacking approach with the degree of stacking set by the data. We also demonstrate that mass and concentration derived from pure stacking can be offset from the population mean with differing values depending on the method of stacking.

astro-ph.CO↗

arXiv2016

Model-independent inference on compact-binary observations

The recent advanced LIGO detections of gravitational waves from merging binary black holes enhance the prospect of exploring binary evolution via gravitational-wave observations of a population of compact-object binaries. In the face of uncertainty about binary formation models, model-independent inference provides an appealing alternative to comparisons between observed and modelled populations. We describe a procedure for clustering in the multi-dimensional parameter space of observations that are subject to significant measurement errors. We apply this procedure to a mock data set of population-synthesis predictions for the masses of merging compact binaries convolved with realistic measurement uncertainties, and demonstrate that we can accurately distinguish subpopulations of binary neutron stars, binary black holes, and mixed neutron star -- black hole binaries with tens of observations.

astro-ph.HE↗

arXiv2016

A simple model to describe intrinsic stellar noise for exoplanet detection around red giants

In spite of the huge advances in exoplanet research provided by the NASA Kepler Mission, there remain only a small number of transit detections around evolved stars. Here we present a reformulation of the noise properties of red-giant stars, where the intrinsic stellar granulation, and the stellar oscillations described by asteroseismology play a key role. The new noise model is a significant improvement on the current Kepler results for evolved stars. Our noise model may be used to help understand planet detection thresholds for the ongoing K2 and upcoming TESS missions, and serve as a predictor of stellar noise for these missions. As an application of our noise model, we explore the minimum detectable planet radii for red giant stars, and find that Neptune sized planets should be detectable around low luminosity red giant branch stars.

astro-ph.SR↗

arXiv2016

Circumstellar Debris Disks: Diagnosing the Unseen Perturber

The first indication of the presence of a circumstellar debris disk is usually the detection of excess infrared emission from the population of small dust grains orbiting the star. This dust is short-lived, requiring continual replenishment, and indicating that the disk must be excited by an unseen perturber. Previous theoretical studies have demonstrated that an eccentric planet orbiting interior to the disk will stir the larger bodies in the belt and produce dust via interparticle collisions. However, motivated by recent observations, we explore another possible mechanism for heating a debris disk: a stellar-mass perturber orbiting exterior to and inclined to the disk and exciting the disk particles' eccentricities and inclinations via the Kozai-Lidov mechanism. We explore the consequences of an exterior perturber on the evolution of a debris disk using secular analysis and collisional N-body simulations. We demonstrate that a Kozai-Lidov excited disk can generate a dust disk via collisions and we compare the results of the Kozai-Lidov excited disk with a simulated disk perturbed by an interior eccentric planet. Finally, we propose two observational tests of a dust disk that can distinguish whether the dust was produced by an exterior brown dwarf or stellar companion or an interior eccentric planet.

astro-ph.EP↗

arXiv2016

Dynamic temperature selection for parallel-tempering in Markov chain Monte Carlo simulations

Modern problems in astronomical Bayesian inference require efficient methods for sampling from complex, high-dimensional, often multi-modal probability distributions. Most popular methods, such as Markov chain Monte Carlo sampling, perform poorly on strongly multi-modal probability distributions, rarely jumping between modes or settling on just one mode without finding others. Parallel tempering addresses this problem by sampling simultaneously with separate Markov chains from tempered versions of the target distribution with reduced contrast levels. Gaps between modes can be traversed at higher temperatures, while individual modes can be efficiently explored at lower temperatures. In this paper, we investigate how one might choose the ladder of temperatures to achieve more efficient sampling, as measured by the autocorrelation time of the sampler. In particular, we present a simple, easily-implemented algorithm for dynamically adapting the temperature configuration of a sampler while sampling. This algorithm dynamically adjusts the temperature spacing to achieve a uniform rate of exchanges between chains at neighbouring temperatures. We compare the algorithm to conventional geometric temperature configurations on a number of test distributions and on an astrophysical inference problem, reporting efficiency gains by a factor of 1.2-2.5 over a well-chosen geometric temperature configuration and by a factor of 1.5-5 over a poorly chosen configuration. On all of these problems a sampler using the dynamical adaptations to achieve uniform acceptance ratios between neighbouring chains outperforms one that does not.

astro-ph.IM↗

arXiv2016

Parameter estimation on gravitational waves from neutron-star binaries with spinning components

Inspiraling binary neutron stars are expected to be one of the most significant sources of gravitational-wave signals for the new generation of advanced ground-based detectors. We investigate how well we could hope to measure properties of these binaries using the Advanced LIGO detectors, which began operation in September 2015. We study an astrophysically motivated population of sources (binary components with masses $1.2~\mathrm{M}_\odot$--$1.6~\mathrm{M}_\odot$ and spins of less than $0.05$) using the full LIGO analysis pipeline. While this simulated population covers the observed range of potential binary neutron-star sources, we do not exclude the possibility of sources with parameters outside these ranges; given the existing uncertainty in distributions of mass and spin, it is critical that analyses account for the full range of possible mass and spin configurations. We find that conservative prior assumptions on neutron-star mass and spin lead to average fractional uncertainties in component masses of $\sim 16\%$, with little constraint on spins (the median $90\%$ upper limit on the spin of the more massive component is $\sim 0.7$). Stronger prior constraints on neutron-star spins can further constrain mass estimates, but only marginally. However, we find that the sky position and luminosity distance for these sources are not influenced by the inclusion of spin; therefore, if LIGO detects a low-spin population of BNS sources, less computationally expensive results calculated neglecting spin will be sufficient for guiding electromagnetic follow-up.

astro-ph.HE↗

arXiv2015

Astrophysical constraints on massive black hole binary evolution from Pulsar Timing Arrays

We consider the information that can be derived about massive black-hole binary populations and their formation history solely from current and possible future pulsar timing array (PTA) results. We use models of the stochastic gravitational-wave background from circular massive black hole binaries with chirp mass in the range $10^6 - 10^{11} M_\odot$ evolving solely due to radiation reaction. Our parameterised models for the black hole merger history make only weak assumptions about the properties of the black holes merging over cosmic time. We show that current PTA results place an upper limit on the black hole merger density which does not depend on the choice of a particular merger history model, however they provide no information about the redshift or mass distribution. We show that even in the case of a detection resulting from a factor of 10 increase in amplitude sensitivity, PTAs will only put weak constraints on the source merger density as a function of mass, and will not provide any additional information on the redshift distribution. Without additional assumptions or information from other observations, a detection cannot meaningfully bound the massive black hole merger rate above zero or any particular mass.

astro-ph.CO↗

arXiv2015

An Efficient Interpolation Technique for Jump Proposals in Reversible-Jump Markov Chain Monte Carlo Calculations

Selection among alternative theoretical models given an observed data set is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty: it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the MCMC algorithm and convergence is correspondingly slow. Here we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose inter-model jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient "global" proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher-dimensional spaces efficiently.

astro-ph.IM↗

arXiv2015

Parameter estimation for binary neutron-star coalescences with realistic noise during the Advanced LIGO era

Advanced ground-based gravitational-wave (GW) detectors begin operation imminently. Their intended goal is not only to make the first direct detection of GWs, but also to make inferences about the source systems. Binary neutron-star mergers are among the most promising sources. We investigate the performance of the parameter-estimation \edit{(PE)} pipeline that will be used during the first observing run of the Advanced Laser Interferometer Gravitational-wave Observatory (aLIGO) in 2015: we concentrate on the ability to reconstruct the source location on the sky, but also consider the ability to measure masses and the distance. Accurate, rapid sky-localization is necessary to alert electromagnetic (EM) observatories so that they can perform follow-up searches for counterpart transient events. We consider PE accuracy in the presence of \edit{non-stationary}, non-Gaussian noise. We find that the character of the noise makes negligible difference to the PE performance \edit{at a given signal-to-noise ratio}. The source luminosity distance can only be poorly constrained, the median $90\%$ ($50\%$) credible interval scaled with respect to the true distance is $0.85$ ($0.38$). However, the chirp mass is well measured. Our chirp-mass estimates are subject to systematic error because we used gravitational-waveform templates without component spin to carry out inference on signals with moderate spins, but the total error is typically less than $10^{-3} M_\odot$. The median $90\%$ ($50\%$) credible region for sky localization is $\sim600~\mathrm{deg^{2}}$ ($\sim150~\mathrm{deg^{2}}$), with $3\%$ ($30\%$) of detected events localized within $100~\mathrm{deg^{2}}$. Early aLIGO, with only two detectors, will have a sky-localization accuracy for binary neutron stars of hundreds of square degrees; this makes EM follow-up challenging, but not impossible.

astro-ph.HE↗

arXiv2015

Evolutionary Channels for the Formation of Double Neutron Stars

We analyze binary population models of double-neutron stars and compare results to the accurately measured orbital periods and eccentricities of the eight known such systems in our Galaxy. In contrast to past similar studies, we especially focus on the dominant evolutionary channels (we identify three); for the first time, we use a detailed understanding of the evolutionary history of three double neutron stars as actual constraints on the population models. We find that the evolutionary constraints derived from the double pulsar are particularly tight, and less than half of the examined models survive the full set of constraints. The top-likelihood surviving models yield constraints on the key binary evolution parameters, but most interestingly reveal (i) the need for electron-capture supernovae from relatively low-mass degenerate, progenitor cores, and (ii) the most likely evolutionary paths for the rest of the known double neutron stars. In particular, we find that J1913+16 likely went through a phase of Case BB mass transfer, and J1906+0746 and J1756-2251 are consistent with having been formed in electron-capture supernovae.

astro-ph.SR↗

arXiv2015

Efficient method for measuring the parameters encoded in a gravitational-wave signal

Once upon a time, predictions for the accuracy of inference on gravitational-wave signals relied on computationally inexpensive but often inaccurate techniques. Recently, the approach has shifted to actual inference on noisy signals with complex stochastic Bayesian methods, at the expense of significant computational cost. Here, we argue that it is often possible to have the best of both worlds: a Bayesian approach that incorporates prior information and correctly marginalizes over uninteresting parameters, providing accurate posterior probability distribution functions, but carried out on a simple grid at a low computational cost, comparable to the inexpensive predictive techniques.

astro-ph.IM↗

arXiv2015

Robust parameter estimation for compact binaries with ground-based gravitational-wave observations using the LALInference software library

The Advanced LIGO and Advanced Virgo gravitational wave (GW) detectors will begin operation in the coming years, with compact binary coalescence events a likely source for the first detections. The gravitational waveforms emitted directly encode information about the sources, including the masses and spins of the compact objects. Recovering the physical parameters of the sources from the GW observations is a key analysis task. This work describes the LALInference software library for Bayesian parameter estimation of compact binary signals, which builds on several previous methods to provide a well-tested toolkit which has already been used for several studies. We show that our implementation is able to correctly recover the parameters of compact binary signals from simulated data from the advanced GW detectors. We demonstrate this with a detailed comparison on three compact binary systems: a binary neutron star, a neutron star black hole binary and a binary black hole, where we show a cross-comparison of results obtained using three independent sampling algorithms. These systems were analysed with non-spinning, aligned spin and generic spin configurations respectively, showing that consistent results can be obtained even with the full 15-dimensional parameter space of the generic spin configurations. We also demonstrate statistically that the Bayesian credible intervals we recover correspond to frequentist confidence intervals under correct prior assumptions by analysing a set of 100 signals drawn from the prior. We discuss the computational cost of these algorithms, and describe the general and problem-specific sampling techniques we have used to improve the efficiency of sampling the compact binary coalescence parameter space.

gr-qc↗

arXiv2014

The Occurrence of Earth-Like Planets Around Other Stars

The quantity $η_\oplus$, the number density of planets per star per logarithmic planetary radius per logarithmic orbital period at one Earth radius and one year period, describes the occurrence of Earth-like extrasolar planets. Here we present a measurement of $η_\oplus$ from a parameterised forward model of the (correlated) period-radius distribution and the observational selection function in the most recent (Q17) data release from the Kepler satellite. We find $η_\oplus = 3.9_{-1.6}^{+2.2}\%$ (90% CL). We conclude that each star hosts $3.83_{-0.62}^{+0.76}$ planets with $P \lesssim 3 \mathrm{yr}$ and $R \gtrsim 0.2 R_\oplus$. Our empirical model for false-positive contamination is consistent with the dominant source being background eclipsing binary stars. The distribution of planets we infer is consistent with a highly-stochastic planet formation process producing many correlated, fractional changes in planet sizes and orbits.

astro-ph.EP↗

arXiv2014

Counting And Confusion: Bayesian Rate Estimation With Multiple Populations

We show how to obtain a Bayesian estimate of the rates or numbers of signal and background events from a set of events when the shapes of the signal and background distributions are known, can be estimated, or approximated; our method works well even if the foreground and background event distributions overlap significantly and the nature of any individual event cannot be determined with any certainty. We give examples of determining the rates of gravitational-wave events in the presence of background triggers from a template bank when noise parameters are known and/or can be fit from the trigger data. We also give an example of determining globular-cluster shape, location, and density from an observation of a stellar field that contains a non-uniform background density of stars superimposed on the cluster stars.

astro-ph.IM↗