Observing mergers of non-spinning black-hole binaries

Advances in the field of numerical relativity now make it possible to calculate the final, most powerful merger phase of binary black-hole coalescence for generic binaries. The state of the art has advanced well beyond the equal-mass case into the unequal-mass and spinning regions of parameter space. We present a study of the nonspinning portion of parameter space, primarily using an analytic waveform model tuned to available numerical data, with an emphasis on observational implications. We investigate the impact of varied mass ratio on merger signal-to-noise ratios (SNRs) for several detectors, and compare our results with expectations from the test-mass limit. We note a striking similarity of the waveform phasing of the merger waveform across the available mass ratios. Motivated by this, we calculate the match between our 1:1 (equal mass) and 4:1 mass-ratio waveforms during the merger as a function of location on the source sky, using a new formalism for the match that accounts for higher harmonics. This is an indicator of the amount of degeneracy in mass ratio for mergers of moderate-mass-ratio systems.Comment: 13 pages, 11 figures, submitted to Phys. Rev.

Consistency of post-Newtonian waveforms with numerical relativity

General relativity predicts the gravitational wave signatures of coalescing binary black holes. Explicit waveform predictions for such systems, required for optimal analysis of observational data, have so far been achieved using the post-Newtonian (PN) approximation. The quality of this treatment is unclear, however, for the important late-inspiral portion. We derive late-inspiral waveforms via a complementary approach, direct numerical simulation of Einstein's equations. We compare waveform phasing from simulations of the last $\sim 14$ cycles of gravitational radiation from equal-mass, nonspinning black holes with the corresponding 2.5PN, 3PN, and 3.5PN orbital phasing. We find phasing agreement consistent with internal error estimates based on either approach, suggesting that PN waveforms for this system are effective until the last orbit prior to final merger.Comment: Replaced with published version -- one figure removed, text and other figures updated for clarity of discussio

Toward faithful templates for non-spinning binary black holes using the effective-one-body approach

We present an accurate approximation of the full gravitational radiation waveforms generated in the merger of non-eccentric systems of two non-spinning black holes. Utilizing information from recent numerical relativity simulations and the natural flexibility of the effective-one-body (EOB) model, we extend the latter so that it can successfully match the numerical relativity waveforms during the last stages of inspiral, merger and ringdown. By ``successfully'' here, we mean with phase differences < 8% of a gravitational-wave cycle accumulated by the end of the ringdown phase, maximizing only over time of arrival and initial phase. We obtain this result by simply adding a 4-post-Newtonian order correction in the EOB radial potential and determining the (constant) coefficient by imposing high-matching performances with numerical waveforms of mass ratios m1/m2 = 1, 3/2, 2 and 4, m1 and m2 being the individual black-hole masses. The final black-hole mass and spin predicted by the numerical simulations are used to determine the ringdown frequency and decay time of three quasi-normal-mode damped sinusoids that are attached to the EOB inspiral-(plunge) waveform at the EOB light-ring. The EOB waveforms might be tested and further improved in the future by comparison with extremely long and accurate inspiral numerical-relativity waveforms. They may already be employed for coherent searches and parameter estimation of gravitational waves emitted by non-spinning coalescing binary black holes with ground-based laser-interferometer detectors.Comment: 15 pages, 9 figure

Binary black hole late inspiral: Simulations for gravitational wave observations

Coalescing binary black hole mergers are expected to be the strongest gravitational wave sources for ground-based interferometers, such as the LIGO, VIRGO, and GEO600, as well as the space-based interferometer LISA. Until recently it has been impossible to reliably derive the predictions of General Relativity for the final merger stage, which takes place in the strong-field regime. Recent progress in numerical relativity simulations is, however, revolutionizing our understanding of these systems. We examine here the specific case of merging equal-mass Schwarzschild black holes in detail, presenting new simulations in which the black holes start in the late inspiral stage on orbits with very low eccentricity and evolve for ~1200M through ~7 orbits before merging. We study the accuracy and consistency of our simulations and the resulting gravitational waveforms, which encompass ~14 cycles before merger, and highlight the importance of using frequency (rather than time) to set the physical reference when comparing models. Matching our results to PN calculations for the earlier parts of the inspiral provides a combined waveform with less than half a cycle of accumulated phase error through the entire coalescence. Using this waveform, we calculate signal-to-noise ratios (SNRs) for iLIGO, adLIGO, and LISA, highlighting the contributions from the late-inspiral and merger-ringdown parts of the waveform which can now be simulated numerically. Contour plots of SNR as a function of z and M show that adLIGO can achieve SNR >~ 10 for some intermediate-mass binary black holes (IMBBHs) out to z ~ 1, and that LISA can see massive binary black holes (MBBHs) in the range 3x10^4 100 out to the earliest epochs of structure formation at z > 15.Comment: 17 pages, 20 figures. Final published versio

Modeling kicks from the merger of generic black-hole binaries

Recent numerical relativistic results demonstrate that the merger of comparable-mass spinning black holes has a maximum ``recoil kick'' of up to \sim 4000 \kms. However the scaling of these recoil velocities with mass ratio is poorly understood. We present new runs showing that the maximum possible kick perpendicular to the orbital plane does not scale as $\sim\eta^2$ (where $\eta$ is the symmetric mass ratio), as previously proposed, but is more consistent with $\sim\eta^3$, at least for systems with low orbital precession. We discuss the effect of this dependence on galactic ejection scenarios and retention of intermediate-mass black holes in globular clusters.Comment: 5 pages, 1 figure, 3 tables. Version published in Astrophys. J. Let

Complex CatSper-dependent and independent [Ca2⁺]i signalling in human spermatozoa induced by follicular fluid

STUDY QUESTION: Does progesterone in human follicular fluid (hFF) activate CatSper and do other components of hFF modulate this effect and/or contribute separately to hFF-induced Ca2+ signaling?SUMMARY ANSWER: hFF potently stimulates CatSper and increases [Ca2+]i, primarily due to high concentrations of progesterone, however,other components of hFF also contribute to [Ca2+]i signaling, including modulation of CatSper channel activity and inhibition of [Ca2+]i oscillations.WHAT IS KNOWN ALREADY: CatSper, the principal Ca2+ channel in spermatozoa, is progesterone-sensitive and essential for fertility. Both hFF and progesterone, which is present in hFF, influence sperm function and increase their [Ca2+]i.STUDY DESIGN, SIZE, DURATION: This basic medical research study used semen samples from &gt;40 donors and hFF from &gt;50 patients who were undergoing surgical oocyte retrieval for IVF/ICSI.PARTICIPANTS/MATERIALS, SETTING, METHODS: Semen donors and patients were recruited in accordance with local ethics approval (13/ES/0091) from the East of Scotland Research Ethics Service REC1. Activities of CatSper and KSper were assessed by patch clamp electrophysiology. Sperm [Ca2+]i responses were examined in sperm populations and single cells. Computer-assisted sperm analysis (CASA) parameters and penetration into viscous media were used to assess functional effects.MAIN RESULTS AND THE ROLE OF CHANCE: hFF and progesterone significantly potentiated CatSper currents. Under quasiphysiologicalconditions, hFF (up to 50%) failed to alter membrane K+ conductance or current reversal potential. hFF and progesterone (at an equivalent concentration) stimulated similar biphasic [Ca2+]i signals both in sperm populations and single cells. At a high hFF concentration (10%), the sustained (plateau) component of the [Ca2+]i signal was consistently greater than that induced by progesterone alone. In single cell recordings, 1% hFF-induced [Ca2+]i oscillations similarly to progesterone but with 10% hFF generation of [Ca2+]i oscillations was suppressed. After treatment to ‘strip’ lipid-derived mediators, hFF failed to significantly stimulate CatSper currents but induced small [Ca2+]i responsesthat were greater than those induced by the equivalent concentration of progesterone after stripping. Similar [Ca2+]i responses were observed when sperm pretreated with 3 μM progesterone (to desensitize progesterone responses) were stimulated with hFF or stripped hFF. hFF stimulated viscous media penetration and was more effective than the equivalent does of progesterone.LARGE SCALE DATA: N/A.LIMITATIONS, REASONS FOR CAUTION: This was an in vitro study. Caution must be taken when extrapolating these results in vivo.WIDER IMPLICATIONS OF THE FINDINGS: This study directly demonstrates that hFF activates CatSper and establishes that the biologically important effects of hFF reflect, at least in part, action on this channel, primarily via progesterone. However, these experiments also demonstrate that other components of hFF both contribute to the [Ca2+]i signal and modulate the activation of CatSper. Simple in vitro experiments performed out of the context of the complex in vivo environment need to be interpreted with caution

Single-cell analysis of [Ca²⁺]i signalling in sub-fertile men:characteristics and relation to fertilization outcome

STUDY QUESTIONWhat are the characteristics of progesterone-induced (CatSper-mediated) single cell [Ca2+]i signals in spermatozoa from sub-fertile men and how do they relate to fertilizing ability?SUMMARY ANSWERSingle cell analysis of progesterone-induced (CatSper-mediated) [Ca2+]i showed that reduced progesterone-sensitivity is a common feature of sperm from sub-fertile patients and is correlated with fertilization rate.WHAT IS KNOWN ALREADYStimulation with progesterone is a widely used method for assessing [Ca2+]i mobilization by activation of CatSper in human spermatozoa. Although data are limited, sperm population studies have indicated an association of poor [Ca2+]i response to progesterone with reduced fertilization ability.STUDY DESIGN, SIZE, DURATIONThis was a cohort study using semen samples from 21 donors and 101 patients attending the assisted conception unit at Ninewells Hospital Dundee who were undergoing ART treatment. Patients were recruited from January 2016 to June 2017.PARTICIPANTS/MATERIALS, SETTING, METHODSSemen donors and patients were recruited in accordance with local ethics approval (13/ES/0091) from the East of Scotland Research Ethics Service (EoSRES) REC1. [Ca2+]i responses were examined by single cell imaging and motility parameters assessed by computer-assisted sperm analysis (CASA).MAIN RESULTS AND THE ROLE OF CHANCEFor analysis, patient samples were divided into three groups IVF(+ve) (successful fertilization; 62 samples), IVF-FF (failed fertilization; eight samples) and ICSI (21 samples). A further 10 IVF samples showed large, spontaneous [Ca2+]i oscillations and responses to progesterone could not be analysed. All patient samples loaded with the [Ca2+]i-indicator fluo4 responded to progesterone stimulation with a biphasic increase in fluorescence (transient followed by plateau) which resembled that seen in progesterone-stimulated donor samples. The mean normalized response (progesterone-induced increase in fluorescence normalized to resting level) was significantly smaller in IVF-FF and ICSI patient groups than in donors. All samples were further analysed by plotting, for each cell, the relationship between resting fluorescence intensity and the progesterone-induced fluorescence increment. In donor samples these plots overlaid closely and had a gradient of ≈ 2 and plots for most IVF(+ve) samples closely resembled the donor distribution. However, in a subset (≈ 10%) of IVF(+ve) samples, 3/8 IVF-FF samples and one-third of ICSI samples the gradient of the plot was significantly lower, indicating that the response to progesterone of the cells in these samples was abnormally small. Examination of the relationship between gradient (regression coefficient of the plot) in IVF samples and fertilization rate showed a positive correlation. In IVF-FF and ICSI groups, the proportion of cells in which a response to progesterone could be detected was significantly lower than in donors and IVF (+ve) patients. Approximately 20% of cells in donor, IVF(+ve) and ICSI samples generated [Ca2+]i oscillations when challenged with progesterone but in IVF-FF samples only ≈ 10% of cells generated oscillations and there was a significantly greater proportion of samples where no oscillations were observed. Levels of hyperactivated motility were lower in IVF(+ve) and IVF-FF groups compared to controls, IVF-FF also having lower levels than IVF(+ve).LIMITATIONS, REASONS FOR CAUTIONThis is an in vitro study and caution must be taken when extrapolating these results in vivo.WIDER IMPLICATIONS OF THE FINDINGSThis study reveals important details of impaired [Ca2+]i signalling in sperm from sub-fertile men that cannot be detected in population studies