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Register a new userTidal invariants for compact binaries on quasi-circular orbits
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We extend the gravitational self-force approach to encompass `self-interaction tidal effects for a compact body of mass $mu$ on a quasi-circular orbit around a black hole of mass $M gg mu$. Specifically, we define and calculate at $O(mu)$ (conservative) shifts in the eigenvalues of the electric- and magnetic-type tidal tensors, and a (dissipative) shift in a scalar product between their eigenbases. This approach yields four gauge-invariant functions, from which one may construct other tidal quantities such as the curvature scalars and the speciality index. First, we analyze the general case of a geodesic in a regular perturbed vacuum spacetime admitting a helical Killing vector and a reflection symmetry. Next, we specialize to focus on circular orbits in the equatorial plane of Kerr spacetime at $O(mu)$. We present accurate numerical results for the Schwarzschild case for orbital radii up to the light-ring, calculated via independent implementations in Lorenz and Regge-Wheeler gauges. We show that our results are consistent with leading-order post-Newtonian expansions, and demonstrate the existence of additional structure in the strong-field regime. We anticipate that our strong-field results will inform (e.g.) effective one-body models for the gravitational two-body problem that are invaluable in the ongoing search for gravitational waves.
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We present a time domain waveform model that describes the inspiral-merger-ringdown (IMR) of compact binary systems whose components are non-spinning, and which evolve on orbits with low to moderate eccentricity. The inspiral evolution is described using third order post-Newtonian equations both for the equations of motion of the binary, and its far-zone radiation field. This latter component also includes instantaneous, tails and tails-of-tails contributions, and a contribution due to non-linear memory. This framework reduces to the post-Newtonian approximant TaylorT4 at third post-Newtonian order in the zero eccentricity limit. To improve phase accuracy, we incorporate higher-order post-Newtonian corrections for the energy flux of quasi-circular binaries and gravitational self-force corrections to the binding energy of compact binaries. This enhanced inspiral evolution prescription is combined with an analytical prescription for the merger-ringdown evolution using a catalog of numerical relativity simulations. This IMR waveform model reproduces effective-one-body waveforms for systems with mass-ratios between 1 to 15 in the zero eccentricity limit. Using a set of eccentric numerical relativity simulations, not used during calibration, we show that our eccentric model accurately reproduces the features of eccentric compact binary coalescence throughout the merger. Using this model we show that the gravitational wave transients GW150914 and GW151226 can be effectively recovered with template banks of quasi-circular, spin-aligned waveforms if the eccentricity $e_0$ of these systems when they enter the aLIGO band at a gravitational wave frequency of 14 Hz satisfies $e_0^{rm GW150914}leq0.15$ and $e_0^{rm GW151226}leq0.1$.
We investigate how stable circular orbits around a main compact object appear depending on the presence of a second one by using the Majumudar--Papapetrou dihole spacetime, which consists of the two extremal Reissner--Nordstr om black holes with different masses. While the parameter range of the separation of the two objects is divided due to the appearance of stable circular orbits, this division depends on its mass ratio. We show that the mass ratio range separates into four parts, and we find three critical values as the boundaries.
We combine different techniques to extract information about the logarithmic contributions to the two-body conservative dynamics within the post-Newtonian (PN) approximation of General Relativity. The logarithms come from the conservative part of non linear gravitational-wave tails and their iterations. Explicit, original expressions are found for conservative dynamics logarithmic tail terms up to 6PN order by adopting both traditional PN calculations and effective field theory (EFT) methods. We also determine all logarithmic terms at 7PN order, fixing a sub-leading logarithm from a tail-of-tail-of-tail process by comparison with self-force (SF) results. Moreover, we use renormalization group techniques to obtain the leading logarithmic terms to generic power $n$, appearing at $(3n+1)$PN order, and we resum the infinite series in a closed form. Half-integer PN orders enter the conservative dynamics starting at 5.5PN, but they do not generate logarithmic contributions up to next-to-next-to-leading order included. We nevertheless present their contribution at leading order in the small mass ratio limit.
We derive analytic expressions that provide Fourier domain gravitational wave (GW) response function for compact binaries inspiraling along moderately eccentric orbits. These expressions include amplitude corrections to the two GW polarization states that are accurate to the first post-Newtonian (PN) order. Additionally, our fully 3PN accurate GW phase evolution incorporates eccentricity effects up to sixth order at each PN order. Further, we develop a prescription to incorporate analytically the effects of 3PN accurate periastron advance in the GW phase evolution. This is how we provide a ready-to-use and efficient inspiral template family for compact binaries in moderately eccentric orbits. Preliminary GW data analysis explorations suggest that our template family should be required to construct analytic inspiral-merger-ringdown templates to model moderately eccentric compact binary coalescence.
We have performed a detailed analysis of orbital motion in the vicinity of a nearly extremal Kerr black hole. For very rapidly rotating black holes (spin a=J/M>0.9524M) we have found a class of very strong field eccentric orbits whose angular momentum L_z increases with the orbits inclination with respect to the equatorial plane, while keeping latus rectum and eccentricity fixed. This behavior is in contrast with Newtonian intuition, and is in fact opposite to the normal behavior of black hole orbits. Such behavior was noted previously for circular orbits; since it only applies to orbits very close to the black hole, they were named nearly horizon-skimming orbits. Our analysis generalizes this result, mapping out the full generic (inclined and eccentric) family of nearly horizon-skimming orbits. The earlier work on circular orbits reported that, under gravitational radiation emission, nearly horizon-skimming orbits tend to evolve to smaller orbit inclination, toward prograde equatorial configuration. Normal orbits, by contrast, always demonstrate slowly growing orbit inclination (orbits evolve toward the retrograde equatorial configuration). Using up-to-date Teukolsky-fluxes, we have concluded that the earlier result was incorrect: all circular orbits, including nearly horizon-skimming ones, exhibit growing orbit inclination. Using kludge fluxes based on a Post-Newtonian expansion corrected with fits to circular and to equatorial Teukolsky-fluxes, we argue that the inclination grows also for eccentric nearly horizon-skimming orbits. We also find that the inclination change is, in any case, very small. As such, we conclude that these orbits are not likely to have a clear and peculiar imprint on the gravitational waveforms expected to be measured by the space-based detector LISA.
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