Higher-order spin effects in the amplitude and phase of gravitational waveforms emitted by inspiraling compact binaries: Ready-to-use gravitational waveforms

We provide ready-to-use time-domain gravitational waveforms for spinning compact binaries with precession effects through 1.5PN order in amplitude and compute their mode decomposition using spin-weighted -2 spherical harmonics. In the presence of precession, the gravitational-wave modes (l,m) contain harmonics originating from combinations of the orbital frequency and precession frequencies. We find that the gravitational radiation from binary systems with large mass asymmetry and large inclination angle can be distributed among several modes. For example, during the last stages of inspiral, for some maximally spinning configurations, the amplitude of the (2,0) and (2,1) modes can be comparable to the amplitude of the (2,2) mode. If the mass ratio is not too extreme, the l=3 and l=4 modes are generally one or two orders of magnitude smaller than the l = 2 modes. Restricting ourselves to spinning, non-precessing compact binaries, we apply the stationary-phase approximation and derive the frequency-domain gravitational waveforms including spin-orbit and spin(1)- spin(2) effects through 1.5PN and 2PN order respectively in amplitude, and 2.5PN order in phase. Since spin effects in the amplitude through 2PN order affect only the first and second harmonics of the orbital phase, they do not extend the mass reach of gravitational-wave detectors. However, they can interfere with other harmonics and lower or raise the signal-to-noise ratio depending on the spin orientation. These ready-to-use waveforms could be employed in the data-analysis of the spinning, inspiraling binaries as well as in comparison studies at the interface between analytical and numerical relativity.Comment: 43 pages, 10 Postscript figures. submitted to Physical Review D. Includes corrections due to errat

Parameter estimation of coalescing supermassive black hole binaries with LISA

Laser Interferometer Space Antenna (LISA) will routinely observe coalescences of supermassive black hole (BH) binaries up to very high redshifts. LISA can measure mass parameters of such coalescences to a relative accuracy of $10^{-4}-10^{-6}$, for sources at a distance of 3 Gpc. The problem of parameter estimation of massive nonspinning binary black holes using post-Newtonian (PN) phasing formula is studied in the context of LISA. Specifically, the performance of the 3.5PN templates is contrasted against its 2PN counterpart using a waveform which is averaged over the LISA pattern functions. The improvement due to the higher order corrections to the phasing formula is examined by calculating the errors in the estimation of mass parameters at each order. The estimation of the mass parameters ${\cal M}$ and $\eta$ are significantly enhanced by using the 3.5PN waveform instead of the 2PN one. For an equal mass binary of $2\times10^6M_\odot$ at a luminosity distance of 3 Gpc, the improvement in chirp mass is $\sim 11$ and that of $\eta$ is $\sim 39$. Estimation of coalescence time $t_c$ worsens by 43%. The improvement is larger for the unequal mass binary mergers. These results are compared to the ones obtained using a non-pattern averaged waveform. The errors depend very much on the location and orientation of the source and general conclusions cannot be drawn without performing Monte Carlo simulations. Finally the effect of the choice of the lower frequency cut-off for LISA on the parameter estimation is studied.Comment: 12 pages, 5 figures (eps) significant revision, accepted for publication in Phys. Rev. D. Matches with the published versio

Using generalized PowerFlux methods to estimate the parameters of periodic gravitational waves

We investigate methods to estimate the parameters of the gravitational-wave signal from a spinning neutron star using Fourier transformed segments of the strain response from an interferometric detector. Estimating the parameters from the power, we find generalizations of the PowerFlux method. Using simulated elliptically polarized signals injected into Gaussian noise, we apply the generalized methods to estimate the squared amplitudes of the plus and cross polarizations (and, in the most general case, the polarization angle), and test the relative detection efficiencies of the various methods.Comment: 8 pages, presented at Amalid7, Sydney, Australia (July 2007), fixed minor typos and clarified discussion to match published CQG version; updated reference

Binary black hole detection rates in inspiral gravitational wave searches

The signal-to-noise ratios (SNRs) for quasi-circular binary black hole inspirals computed from restricted post-Newtonian waveforms are compared with those attained by more complete post-Newtonian signals, which are superpositions of amplitude-corrected harmonics of the orbital phase. It is shown that if one were to use the best available amplitude-corrected waveforms for detection templates, one should expect SNRs in actual searches to be significantly lower than those suggested by simulations based purely on restricted waveforms.Comment: 9 pages, 1 figur

Infinite Kinematic Self-Similarity and Perfect Fluid Spacetimes

Perfect fluid spacetimes admitting a kinematic self-similarity of infinite type are investigated. In the case of plane, spherically or hyperbolically symmetric space-times the field equations reduce to a system of autonomous ordinary differential equations. The qualitative properties of solutions of this system of equations, and in particular their asymptotic behavior, are studied. Special cases, including some of the invariant sets and the geodesic case, are examined in detail and the exact solutions are provided. The class of solutions exhibiting physical self-similarity are found to play an important role in describing the asymptotic behavior of the infinite kinematic self-similar models.Comment: 38 pages, 6 figures. Accepted for publication in General Relativity & Gravitatio

Self-similar static solutions admitting a two-space of constant curvature

A recent result by Haggag and Hajj-Boutros is reviewed within the framework of self-similar space-times, extending, in some sense, their results and presenting a family of metrics consisting of all the static spherically symmetric perfect fluid solutions admitting a homothety.Comment: 6 page

Large-scale distribution of microbial and viral populations in the South Atlantic Ocean

Viruses are abundant, diverse and dynamic compo-nents of the marine environments and play a signi?-cant role in the ocean biogeochemical cycles. Toassess potential variations in the relation betweenviruses and microbes in different geographic regionsand depths, viral and microbial abundance and pro-duction were determined throughout the watercolumn along a latitudinal transect in the South Atlan-tic Ocean. Path analysis was used to examine therelationships between several abiotic and bioticparameters and the different microbial and viral popu-lations distinguished by ?ow cytometry.The depth-integrated contribution of microbial andviral abundance to the total microbial and viralbiomass differed signi?cantly among the differentprovinces. Additionally, the virus-to-microbe ratioincreased with depth and decreased laterally towardsthe more productive regions. Our data revealed thatthe abundance of phytoplankton and microbes is themain controlling factor of the viral populations in theeuphotic and mesopelagic layers, whereas in thebathypelagic realm, viral abundance was only weaklyrelated to the biotic and abiotic variables. The relativecontribution of the three viral populations distin-guished by ?ow cytometry showed a clear geographi-cal pattern throughout the water column, suggestingthat these populations are composed of distinct tax

Parameter estimation of compact binaries using the inspiral and ringdown waveforms

We analyze the problem of parameter estimation for compact binary systems that could be detected by ground-based gravitational wave detectors. So far this problem has only been dealt with for the inspiral and the ringdown phases separately. In this paper, we combine the information from both signals, and we study the improvement in parameter estimation, at a fixed signal-to-noise ratio, by including the ringdown signal without making any assumption on the merger phase. The study is performed for both initial and advanced LIGO and VIRGO detectors.Comment: matching cqg versio

Removing non-stationary, non-harmonic external interference from gravitational wave interferometer data

We describe a procedure to identify and remove a class of non-stationary and non-harmonic interference lines from gravitational wave interferometer data. These lines appear to be associated with the external electricity main supply, but their amplitudes are non-stationary and they do not appear at harmonics of the fundamental supply frequency. We find an empirical model able to represent coherently all the non-harmonic lines we have found in the power spectrum, in terms of an assumed reference signal of the primary supply input signal. If this signal is not available then it can be reconstructed from the same data by making use of the coherent line removal algorithm that we have described elsewhere. All these lines are broadened by frequency changes of the supply signal, and they corrupt significant frequency ranges of the power spectrum. The physical process that generates this interference is so far unknown, but it is highly non-linear and non-stationary. Using our model, we cancel the interference in the time domain by an adaptive procedure that should work regardless of the source of the primary interference. We have applied the method to laser interferometer data from the Glasgow prototype detector, where all the features we describe in this paper were observed. The algorithm has been tuned in such a way that the entire series of wide lines corresponding to the electrical interference are removed, leaving the spectrum clean enough to detect signals previously masked by them. Single-line signals buried in the interference can be recovered with at least 75 % of their original signal amplitude.Comment: 14 pages, 5 figures, Revtex, psfi