Interaction of massive black hole binaries with their stellar environment: II. Loss-cone depletion and binary orbital decay

We study the long-term evolution of massive black hole binaries (MBHBs) at the centers of galaxies using detailed scattering experiments to solve the full three-body problem. Ambient stars drawn from a isotropic Maxwellian distribution unbound to the binary are ejected by the gravitational slingshot. We construct a minimal, hybrid model for the depletion of the loss cone and the orbital decay of the binary, and show that secondary slingshots - stars returning on small impact parameter orbits to have a second super-elastic scattering with the MBHB - may considerably help the shrinking of the pair in the case of large binary mass ratios. In the absence of loss-cone refilling by two-body relaxation or other processes, the mass ejected before the stalling of a MBHB is half the binary reduced mass. About 50% of the ejected stars are expelled ejected in a "burst" lasting ~1E4 yrs M_6^1/4, where M_6 is the binary mass in units of 1E6 Msun. The loss cone is completely emptied in a few bulge crossing timescales, 1E7 yrs M_6^1/4. Even in the absence of two-body relaxation or gas dynamical processes, unequal mass and/or eccentric binaries with M_6 >0.1 can shrink to the gravitational wave emission regime in less than a Hubble time, and are therefore "safe" targets for the planned Laser Interferometer Space Antenna (LISA).Comment: Minor revision. 10 pages, 7 figures, ApJ in pres

Low-frequency gravitational radiation from coalescing massive black hole binaries in hierarchical cosmologies

We compute the expected gravitational wave signal from coalescing massive black hole (MBH) binaries at the center of galaxies in a hierarchical structure formation scenario in which seed holes of intermediate mass form far up in the dark halo merger tree. The merger history of DM halos and MBHs is followed from z=20 to the present in a LCDM cosmology. MBHs get incorporated through halo mergers into larger and larger structures, sink to the center owing to dynamical friction against the DM background, accrete cold material in the merger remnant, and form MBH binary systems. Stellar dynamical interactions cause the hardening of the binary at large separations, while gravitational wave emission takes over at small radii and leads to the final coalescence of the pair. The integrated emission from inspiraling MBH binaries results in a gravitational wave background (GWB). The characteristic strain spectrum has the standard h_c(f)\propto f^{-2/3} behavior only in the range 1E-9<f<1E-6 Hz. At lower frequencies the orbital decay of MBH binaries is driven by the ejection of background stars, and h_c(f) \propto f. At higher frequencies, f>1E-6 Hz, the strain amplitude is shaped by the convolution of last stable circular orbit emission. We discuss the observability of inspiraling MBH binaries by the planned LISA. Over a 3-year observing period LISA should resolve this GWB into discrete sources, detecting ~60 (~250) individual events above a S/N=5 (S/N=1) confidence level. (Abridged)Comment: 11 pages, 8 figues. Revised version accepted to be published in ApJ Discussion on number counts corrected and expande

Fundamental physics and cosmology with LISA

In this article we give a brief review of the fundamental physics that can be done with the future space-based gravitational wave detector LISA. This includes detection of gravitational wave bursts coming from cosmic strings, measuring a stochastic gravitational wave background, mapping spacetime around massive compact objects in galactic nuclei with extreme-mass-ratio inspirals and testing the predictions of General Relativity for the strong dynamical fields of inspiralling binaries. We give particular attention to new results which show the capability of LISA to constrain cosmological parameters using observations of coalescing massive Black Hole binaries

Optimizing Pulsar Timing Arrays to Maximize Gravitational Wave Single Source Detection: a First Cut

Pulsar Timing Arrays (PTAs) use high accuracy timing of a collection of low timing noise pulsars to search for gravitational waves in the microhertz to nanohertz frequency band. The sensitivity of such a PTA depends on (a) the direction of the gravitational wave source, (b) the timing accuracy of the pulsars in the array and (c) how the available observing time is allocated among those pulsars. Here, we present a simple way to calculate the sensitivity of the PTA as a function of direction of a single GW source, based only on the location and root-mean-square residual of the pulsars in the array. We use this calculation to suggest future strategies for the current North American Nanohertz Observatory for Gravitational Waves (NANOGrav) PTA in its goal of detecting single GW sources. We also investigate the affects of an additional pulsar on the array sensitivity, with the goal of suggesting where PTA pulsar searches might be best directed. We demonstrate that, in the case of single GW sources, if we are interested in maximizing the volume of space to which PTAs are sensitive, there exists a slight advantage to finding a new pulsar near where the array is already most sensitive. Further, the study suggests that more observing time should be dedicated to the already low noise pulsars in order to have the greatest positive effect on the PTA sensitivity. We have made a web-based sensitivity mapping tool available at http://gwastro.psu.edu/ptasm.Comment: 14 pages, 3 figures, accepted by Ap

Resolving multiple supermassive black hole binaries with pulsar timing arrays II: genetic algorithm implementation

Pulsar timing arrays (PTAs) might detect gravitational waves (GWs) from massive black hole (MBH) binaries within this decade. The signal is expected to be an incoherent superposition of several nearly-monochromatic waves of different strength. The brightest sources might be individually resolved, and the overall deconvolved, at least partially, in its individual components. In this paper we extend the maximum-likelihood based method developed in Babak & Sesana 2012, to search for individual MBH binaries in PTA data. We model the signal as a collection of circular monochromatic binaries, each characterized by three free parameters: two angles defining the sky location, and the frequency. We marginalize over all other source parameters and we apply an efficient multi-search genetic algorithm to maximize the likelihood function and look for sources in synthetic datasets. On datasets characterized by white Gaussian noise plus few injected sources with signal-to-noise ratio (SNR) in the range 10-60, our search algorithm performs well, recovering all the injections with no false positives. Individual source SNRs are estimated within few % of the injected values, sky locations are recovered within few degrees, and frequencies are determined with sub-Fourier bin precision

Reconstructing the massive black hole cosmic history through gravitational waves

The massive black holes we observe in galaxies today are the natural end-product of a complex evolutionary path, in which black holes seeded in proto-galaxies at high redshift grow through cosmic history via a sequence of mergers and accretion episodes. Electromagnetic observations probe a small subset of the population of massive black holes (namely, those that are active or those that are very close to us), but planned space-based gravitational-wave observatories such as the Laser Interferometer Space Antenna (LISA) can measure the parameters of ``electromagnetically invisible'' massive black holes out to high redshift. In this paper we introduce a Bayesian framework to analyze the information that can be gathered from a set of such measurements. Our goal is to connect a set of massive black hole binary merger observations to the underlying model of massive black hole formation. In other words, given a set of observed massive black hole coalescences, we assess what information can be extracted about the underlying massive black hole population model. For concreteness we consider ten specific models of massive black hole formation, chosen to probe four important (and largely unconstrained) aspects of the input physics used in structure formation simulations: seed formation, metallicity ``feedback'', accretion efficiency and accretion geometry. For the first time we allow for the possibility of ``model mixing'', by drawing the observed population from some combination of the ``pure'' models that have been simulated. A Bayesian analysis allows us to recover a posterior probability distribution for the ``mixing parameters'' that characterize the fractions of each model represented in the observed distribution. Our work shows that LISA has enormous potential to probe the underlying physics of structure formation.Comment: 24 pages, 16 figures, submitted to Phys. Rev.

Ozone in Lombardy: Years 1998-1999

Photochemical pollutants, especially ozone, have reached very high levels in Lombardy in recent years, with peaks of up to 150 ppb in late spring and summer. Lombardy, lying on the Po Plain, supports a large number of cities and industries and these, along with heavy traffic, produce copious amounts of primary pollutants such as nitrogen oxides and numerous volatile organic compounds. Furthermore, the peculiar orography of this region fosters the stagnation of air masses on a basin-scale and the presence of diurnal breezes towards northern areas, along with the evolution of the Mixing Layer, spread the polluted air masses over a large territory. Numerous stations in Lombardy give the concentrations of ozone and of nitrogen oxides. In this paper, ozone measurements carried out at the plain area around Milan and at pre-alpine sites in the spring and summer 1998 and 1999 will be shown and discussed, focusing on the months of May and July. The study of temporal and spatial behaviour of ozone goes hand in hand with the analysis of the Boundary Layer’s evolution. A number of radon stations were operating in Milan and in other sites in Lombardy. Measurements of atmospheric concentrations of radon yield an index of atmospheric stability, of the formation of thermal inversion, of convective turbulence, and of the movement of air masses, and hence they are very relevant to the understanding of the conditions of atmospheric pollutants

Observing gravitational wave bursts in pulsar timing measurements

We propose a novel method for observing the gravitational wave signature of super-massive black hole (SMBH) mergers. This method is based on detection of a specific type of gravitational waves, namely gravitational wave burst with memory (BWM), using pulsar timing. We study the unique signature produced by BWM in anomalous pulsar timing residuals. We show that the present day pulsar timing precision allows one to detect BWM due to SMBH mergers from distances up to 1 Gpc (for case of equal mass 10^8 Msun SMBH). Improvements in precision of pulsar timing together with the increase in number of observed pulsars should eventually lead to detection of a BWM signal due to SMBH merger, thereby making the proposed technique complementary to the capabilities of the planned LISA mission.Comment: 9 pages, 1 figure, generally matches the MNRAS versio

Quality over Quantity: Optimizing pulsar timing array analysis for stochastic and continuous gravitational wave signals

The search for gravitational waves using Pulsar Timing Arrays (PTAs) is acomputationally expensive complex analysis that involves source-specific noisestudies. As more pulsars are added to the arrays, this stage of PTA analysiswill become increasingly challenging. Therefore, optimizing the number ofincluded pulsars is crucial to reduce the computational burden of dataanalysis. Here, we present a suite of methods to rank pulsars for use withinthe scope of PTA analysis. First, we use the maximization of thesignal-to-noise ratio as a proxy to select pulsars. With this method, we targetthe detection of stochastic and continuous gravitational wave signals. Next, wepresent a ranking that minimizes the coupling between spatial correlationsignatures, namely monopolar, dipolar, and Hellings & Downs correlations.Finally, we also explore how to combine these two methods. We test theseapproaches against mock data using frequentist and Bayesian hypothesis testing.For equal-noise pulsars, we find that an optimal selection leads to an increasein the log-Bayes factor two times steeper than a random selection for thehypothesis test of a gravitational wave background versus a common uncorrelatedred noise process. For the same test but for a realistic EPTA dataset, a subsetof 25 pulsars selected out of 40 can provide a log-likelihood ratio that is$89\%$ of the total, implying that an optimally selected subset of pulsars canyield results comparable to those obtained from the whole array. We expectthese selection methods to play a crucial role in future PTA data combinations.<br

Probing seed black holes using future gravitational-wave detectors

Identifying the properties of the first generation of seeds of massive black holes is key to understanding the merger history and growth of galaxies. Mergers between ~100 solar mass seed black holes generate gravitational waves in the 0.1-10Hz band that lies between the sensitivity bands of existing ground-based detectors and the planned space-based gravitational wave detector, the Laser Interferometer Space Antenna (LISA). However, there are proposals for more advanced detectors that will bridge this gap, including the third generation ground-based Einstein Telescope and the space-based detector DECIGO. In this paper we demonstrate that such future detectors should be able to detect gravitational waves produced by the coalescence of the first generation of light seed black-hole binaries and provide information on the evolution of structure in that era. These observations will be complementary to those that LISA will make of subsequent mergers between more massive black holes. We compute the sensitivity of various future detectors to seed black-hole mergers, and use this to explore the number and properties of the events that each detector might see in three years of observation. For this calculation, we make use of galaxy merger trees and two different seed black hole mass distributions in order to construct the astrophysical population of events. We also consider the accuracy with which networks of future ground-based detectors will be able to measure the parameters of seed black hole mergers, in particular the luminosity distance to the source. We show that distance precisions of ~30% are achievable, which should be sufficient for us to say with confidence that the sources are at high redshift.Comment: 14 pages, 6 figures, 2 tables, accepted for proceedings of 13th GWDAW meetin