[0812.4208] Influence of conservative corrections on parameter estimation for EMRIs

Authors: E A Huerta, Jonathan R Gair

Date: 22 Dec 2008

Abstract: We present an improved numerical kludge waveform model for circular, equatorial extreme-mass-ratio inspirals (EMRIs). The model is based on true Kerr geodesics, augmented by appropriate conservative and radiative self--force corrections from perturbative. We present a Monte Carlo analysis of parameter estimation errors from the Fisher Matrix and also assess the theoretical errors that would arise form omitting the conservative correction terms we include here. We present results for three different types of events, namely black holes, neutron stars or white dwarfs inspiralling into a supermassive black hole (SMBH). The analysis shows that for a typical source (a 10 solar mass compact object captured by a one million solar mass SMBH at signal to noise ratio of 30) we expect to determine the two masses to within a fractional error of ~0.0001, measure the spin parameter q to ~0.0003 and determine the location of the source on the sky and the spin orientation to within 0.001 steradians. We show that, for this kludge model, omitting the conservative corrections leads to a small error over much of the parameter space, i.e., the ratio r of the theoretical model error to the Fisher Matrix error is r<1 for all ten parameters in the model. For the few systems with larger errors typically r<3 and hence the conservative corrections can be marginally ignored. In addition, we use our model and first order self--force results for Schwarzschild black holes to estimate the error that arises from omitting the second-order radiative piece of the self-force. This indicates that it is not necessary to go beyond first order to obtain accurate parameter-error estimates.

abs pdf

Dec 22, 2008

0812.4208 (/preprints)
2008-12-22, 23:34 [edit]


[0812.3853] Gravitational lensing of stars orbiting the Massive Black Hole in the Galactic Center

Authors: Valerio Bozza, Luigi Mancini

Date: 19 Dec 2008

Abstract: The existence of a massive black hole in the center of the Milky Way, coinciding with the radio source Sgr A*, is being established on more and more solid ground. In principle, this black hole, acting as a gravitational lens, is able to bend the light emitted by stars moving within its neighborhood, eventually generating secondary images. Extending a previous analysis of the gravitational lensing phenomenology to a new set of 28 stars, whose orbits have been well determined by recent observations, we have calculated all the properties of their secondary images, including time and magnitude of their luminosity peaks and their angular distances from the central black hole. The best lensing candidate is represented by the star S6, since the magnitude of its secondary image at the peak reaches K=20.8, with an angular separation of 0.3 mas from the central black hole, that is just at the borders of the resolution limit in the K band of incoming astronomical instruments.

abs pdf

Dec 22, 2008

0812.3853 (/preprints)
2008-12-22, 23:34 [edit]


[0812.4149] Coherent detection method of gravitational wave bursts for spherical antennas

Authors: S. Foffa, R. Sturani

Date: 22 Dec 2008

Abstract: We provide a comprehensive theoretical framework and a quantitative test of the method we recently proposed for processing data from a spherical detector with five or six transducers. Our algorithm is a trigger event generator performing a coherent analysis of the sphere channels. In order to test our pipeline we first built a detailed numerical model of the detector, including deviations from the ideal case such as quadrupole modes splitting, and non-identical transducer readout chains. This model, coupled with a Gaussian noise generator, has then been used to produce six time series, corresponding to the outputs of the six transducers attached to the sphere. We finally injected gravitational wave burst signals into the data stream, as well as bursts of non-gravitational origin in order to mimic the presence of non-Gaussian noise, and then processed the mock data. We report quantitative results for the detection efficiency versus false alarm rate and for the affordability of the reconstruction of the direction of arrival. In particular, the combination of the two direction reconstruction methods can reduce by a factor of 10 the number false alarms due to the non-Gaussian noise.

abs pdf

Dec 22, 2008

0812.4149 (/preprints)
2008-12-22, 23:34 [edit]


[0812.3936] Mass, inertia and gravitation

Authors: Marc-Thierry Jaekel, Serge Reynaud

Date: 22 Dec 2008

Abstract: We discuss some effects induced by quantum field fluctuations on mass, inertia and gravitation. Recalling the problem raised by vacuum field fluctuations with respect to inertia and gravitation, we show that vacuum energy differences, such as Casimir energy, do contribute to inertia. Mass behaves as a quantum observable and in particular possesses quantum fluctuations. We show that the compatibility of the quantum nature of mass with gravitation can be ensured by conformal symmetries, which allow one to formulate a quantum version of the equivalence principle. Finally, we consider some corrections to the coupling between metric fields and energy-momentum tensors induced by radiative corrections. Newton gravitation constant is replaced by two different running coupling constants in the sectors of traceless and traced tensors. There result metric extensions of general relativity, which can be characterized by modified Ricci curvatures or by two gravitation potentials. The corresponding phenomenological framework extends the usual Parametrized Post-Newtonian one, with the ability to remain compatible with classical tests of gravity while accounting for new features, such as Pioneer like anomalies or anomalous light deflection.

abs pdf

Dec 22, 2008

0812.3936 (/preprints)
2008-12-22, 23:34 [edit]


[gr-qc/0610105] The Hole Argument. Physical Events and the Superspace

Authors: Mihaela D. Iftime

Date: 21 Oct 2006

Abstract: The 'hole argument'(the English translation of German 'Lochbetrachtung') was formulated by Albert Einstein in 1913 in his search for a relativistic theory of gravitation. The hole argument was deemed to be based on a trivial error of Einstein, until 1980 when John Stachel (Talk on Einsteins Search for General Covariance, 1912-1915 at the GRG meeting in Jena 1980) recognized its highly non-trivial character. Since then the argument has been intensively discussed by many physicists and philosophers of science. (See e.g., Earman & Norton (1987), Gaul & Rovelli (1999), Stachel & Iftime(2005}, and Iftime & Stachel(2006).)
I shall provide here a coordinate-free formulation of the argument using the language of categories and bundles, and generalize the argument for arbitrary covariant and permutable theories (see Iftime & Stachel(2006). In conclusion I shall point out a way of avoiding the hole argument, by looking at the structure of the space of solutions of Einstein's equations on a space-time manifold. This superspace Q(M) is defined as the orbit space of space-time solutions on M under the action of the diffeomorphisms of M, and it plays an important role in the study of the gravitational field and attempts to find a theory of quantum gravity (QG).

abs pdf

Dec 17, 2008

0610105 (/preprints/gr-qc)
2008-12-17, 08:41 [edit]


[0812.2245] Relativistic Simulations of Black Hole-Neutron Star Mergers: Effects of black-hole spin

Authors: Zachariah B. Etienne, Yuk Tung Liu, Stuart L. Shapiro, Thomas W. Baumgarte

Date: 11 Dec 2008

Abstract: Black hole-neutron star (BHNS) binary mergers are candidate engines for generating both short-hard gamma-ray bursts (SGRBs) and detectable gravitational waves. Using our most recent conformal thin-sandwich BHNS initial data and our fully general relativistic hydrodynamics code, which is now AMR-capable, we are able to efficiently and accurately simulate these binaries from large separations through inspiral, merger, and ringdown. We evolve the metric using the BSSN formulation with the standard moving puncture gauge conditions and handle the hydrodynamics with a high-resolution shock-capturing scheme. We explore the effects of BH spin (aligned and anti-aligned with the orbital angular momentum) by evolving three sets of initial data with BH:NS mass ratio q=3: the data sets are nearly identical, except the BH spin is varied between a/M = -0.5 (anti-aligned), 0.0, and 0.75. The number of orbits before merger increases with a/M, as expected. We also study the nonspinning BH case in more detail, varying q between 1, 3, and 5. We calculate gravitational waveforms for the cases we simulate and compare them to binary black-hole waveforms. Only a small disk (< 0.01 M_sun) forms for the anti-aligned spin case (a/M = -0.5) and for the most extreme mass ratio case (q=5). By contrast, a massive (M_disk is about 0.2 M_sun), hot disk forms in the rapidly spinning (a/M = 0.75) aligned BH case. Such a disk could drive a SGRB,possibly by, e.g., producing a copious flux of neutrino-antineutino pairs.

abs pdf

Dec 16, 2008

0812.2245 (/preprints)
2008-12-16, 11:43 [edit]


[0812.2581] Improved spacecraft radio science using an on-board atomic clock: application to gravitational wave searches

Authors: Massimo Tinto, George J. Dick, John D. Prestage, J.W. Armstrong

Date: 13 Dec 2008

Abstract: Recent advances in space-qualified atomic clocks (low-mass, low power-consumption, frequency stability comparable to that of ground-based clocks) can enable interplanetary spacecraft radio science experiments at unprecedented Doppler sensitivities. The addition of an on-board digital receiver would allow the up- and down-link Doppler frequencies to be measured separately. Such separate, high-quality measurements allow optimal data combinations that suppress the currently-leading noise sources: phase scintillation noise from the Earth's atmosphere and Doppler noise caused by mechanical vibrations of the ground antenna. Here we provide a general expression for the optimal combination of ground and on-board Doppler data and compute the sensitivity such a system would have to low-frequency gravitational waves (GWs). Assuming a plasma scintillation noise calibration comparable to that already demonstrated with the multi-link CASSINI radio system, the space-clock/digital-receiver instrumentation enhancements would give GW strain sensitivity of $2.0 \times 10ˆ{-17}$ for randomly polarized, monochromatic GW signals over a two-decade ($\sim0.0001-0.01$ Hz) region of the low-frequency band. This is about an order of magnitude better than currently achieved with traditional two-way coherent Doppler experiments. The utility of optimally combining simultaneous up- and down-link observations is not limited to GW searches. The Doppler tracking technique discussed here could be performed at minimal incremental cost to also improve other radio science experiments (i.e. tests of relativistic gravity, planetary and satellite gravity field measurements, atmospheric and ring occultations) on future interplanetary missions.

abs pdf

Dec 16, 2008

0812.2581 (/preprints)
2008-12-16, 11:43 [edit]


[0812.1806] Geodesic stability, Lyapunov exponents and quasinormal modes

Authors: Vitor Cardoso, Alex S. Miranda, Emanuele Berti, Helvi Witek, Vilson T. Zanchin

Date: 9 Dec 2008

Abstract: Geodesic motion determines important features of spacetimes. Null unstable geodesics are closely related to the appearance of compact objects to external observers and have been associated with the characteristic modes of black holes. By computing the Lyapunov exponent, which is the inverse of the instability timescale associated with this geodesic motion, we show that, in the eikonal limit, quasinormal modes of black holes in any dimensions are determined by the parameters of the circular null geodesics. This result is independent of the field equations and only assumes a stationary, spherically symmetric and asymptotically flat line element, but it does not seem to be easily extendable to anti-de Sitter spacetimes. We further show that (i) in spacetime dimensions greater than four, equatorial circular timelike geodesics in a Myers-Perry black hole background are unstable, and (ii) the instability timescale of equatorial null geodesics in Myers-Perry spacetimes has a local minimum for spacetimes of dimension d > 5.

abs pdf

Dec 15, 2008

0812.1806 (/preprints)
2008-12-15, 07:23 [edit]


[0812.1590] Characterizing the Gravitational Wave Signature from Cosmic String Cusps

Authors: Joey Shapiro Key, Neil J. Cornish

Date: 8 Dec 2008

Abstract: Cosmic strings are predicted to form kinks and cusps that travel along the string at close to the speed of light. These disturbances are radiated away as highly beamed gravitational waves that produce a burst like pulse as the cone of emission sweeps past an observer. Gravitational wave detectors such as the Laser Interferometer Space Antenna (LISA) and the Laser Interferometer Gravitational wave Observatory (LIGO) will be capable of detecting these bursts for a wide class of string models. Such a detection would illuminate the fields of string theory, cosmology, and relativity. Here we develop template based Markov Chain Monte Carlo (MCMC) techniques that can efficiently detect and characterize the signals from cosmic string cusps. We estimate how well the signal parameters can be recovered by the advanced LIGO-Virgo network and the LISA detector using a combination of MCMC and Fisher matrix techniques. We also consider joint detections by the ground and space based instruments. We show that a parallel tempered MCMC approach can detect and characterize the signals from cosmic string cusps, and we demonstrate the utility of this approach on simulated data from the third round of Mock LISA Data Challenges (MLDCs).

abs pdf

Dec 15, 2008

0812.1590 (/preprints)
2008-12-15, 07:23 [edit]


[0812.2325] Modelling the final state from binary black-hole coalescences

Authors: Luciano Rezzolla

Date: 12 Dec 2008

Abstract: Over the last few years enormous progress has been made in the numerical description of the inspiral and merger of binary black holes. A particular effort has gone into the modelling of the physical properties of the final black hole, namely its spin and recoil velocity, as these quantities have direct impact in astrophysics, cosmology and, of course, general relativity. As numerical-relativity calculations still remain computationally very expensive and cannot be used to investigate the complete space of possible parameters, semi-analytic approaches have been developed and shown to reproduce with very high precision the numerical results. I here collect and review these efforts, pointing out the relative strengths and weaknesses, and discuss which directions are more promising to further improve them.

abs pdf

Dec 15, 2008

0812.2325 (/preprints)
2008-12-15, 07:22 [edit]


[0812.0751] A LISA Data-Analysis Primer

Authors: Michele Vallisneri

Date: 3 Dec 2008

Abstract: This article is an introduction for the nonpractitioner to the ideas and issues of LISA data analysis, as reflected in the explorations and experiments of the participants in the Mock LISA Data Challenges. In particular, I discuss the methods and codes that have been developed for the detection and parameter estimation of supermassive black-hole binaries, extreme mass-ratio inspirals, and Galactic binaries.

abs pdf

Dec 09, 2008

0812.0751 (/preprints)
2008-12-09, 08:48 [edit]


[0812.0549] On the ability of various circular inspiral templates to capture inspiral gravitational waves from compact binaries having tiny orbital eccentricities

Authors: Manuel Tessmer, Achamveedu Gopakumar

Date: 2 Dec 2008

Abstract: We probe the ability of various types of post-Newtonian(PN)-accurate circular templates to capture inspiral gravitational-wave (GW) signals from compact binaries having tiny orbital eccentricities. The GW signals are constructed by adapting the phasing formalism, available in T. Damour, A. Gopakumar, and B. R. Iyer, [Phys. Rev. D 70, 064028 (2004)], employing the orbital energy and the time-eccentricity to describe the orbital evolution. Using the fitting factor estimates, relevant for the initial LIGO, we show that circular templates, based on the adiabatic TaylorT1, complete adiabatic TaylorT1 and TaylorT4 approximants are unable to capture our GW signals from compact binaries having tiny residual orbital eccentricities. However, the 2PN-order circular inspiral templates based on the recently introduced TaylorEt approximant are found to be both effectual and faithful in capturing GWs from inspiralling compact binaries having moderate eccentricities and we provide physical explanations for our observations.

abs pdf

Dec 09, 2008

0812.0549 (/preprints)
2008-12-09, 08:48 [edit]


[0812.0809] Constraints on the Size of Extra Dimensions from the Orbital Evolution of the Black-Hole X-Ray Binary XTE J1118 480

Authors: Tim Johannsen (Arizona)

Date: 3 Dec 2008

Abstract: In a universe of the Randall-Sundrum type, black holes are unstable and emit gravitational modes in the extra dimension. This leads to dramatically shortened lifetimes of astrophysical black holes and to an observable change of the orbital period of black-hole binaries. I obtain an upper limit on the rate of change of the orbital period of the binary XTE J1118+480 and constrain the asymptotic curvature radius of the extra dimension to a value that is of the same order as the constraints from other astrophysical sources. A unique property of XTE J1118+480 is that the expected rate of change of the orbital period due to magnetic braking alone is so large that only one additional measurement of the orbital period would lead to the first detection of orbital evolution of a black-hole binary and impose the tightest constraint to date on the size of one extra dimension of the order of 35 microns.

abs pdf

Dec 09, 2008

0812.0809 (/preprints)
2008-12-09, 08:46 [edit]


[0812.0887] Super-ASTROD: Probing primordial gravitational waves and mapping the outer solar system

Authors: Wei-Tou Ni

Date: 4 Dec 2008

Abstract: Super-ASTROD (Super Astrodynamical Space Test of Relativity using Optical Devices or ASTROD III) is a mission concept with 3-5 spacecraft in 5 AU orbits together with an Earth-Sun L1/L2 spacecraft ranging optically with one another to probe primordial gravitational-waves with frequencies 0.1 microHz - 1 mHz, to test fundamental laws of spacetime and to map the outer solar system. In this paper we address to its scientific goals, orbit and payload selection, and sensitivity to gravitational waves.

abs pdf

Dec 09, 2008

0812.0887 (/preprints)
2008-12-09, 08:46 [edit]


[0806.2316] Resource Letter BH-2: Black Holes

Authors: Elena Gallo (MIT), Don Marolf (UCSB)

Date: 13 Jun 2008

Abstract: This resource letter is designed to guide students, educators, and researchers through (some of) the literature on black holes. Both the physics and astrophysics of black holes are discussed. Breadth has been emphasized over depth, and review articles over primary sources. We include resources ranging from non-technical discussions appropriate for broad audiences to technical reviews of current research. Topics addressed include classification of stationary solutions, perturbations and stability of black holes, numerical simulations, collisions, the production of gravity waves, black hole thermodynamics and Hawking radiation, quantum treatments of black holes, black holes in both higher and lower dimensions, and connections to nuclear and condensed matter physics. On the astronomical end, we also cover the physics of gas accretion onto black holes, relativistic jets, gravitationally red-shifted emission lines, evidence for stellar-mass black holes in binary systems and super-massive black holes at the centers of galaxies, the quest for intermediate mass black holes, the assembly and merging history of super-massive black holes through cosmic time, and their affects on the evolution of galaxies.

abs pdf

Dec 09, 2008

0806.2316 (/preprints)
2008-12-09, 08:45 [edit]


[0812.0110] Carter-like constants of the motion in Newtonian gravity and electrodynamics

Authors: Clifford M. Will

Date: 29 Nov 2008

Abstract: For a test body orbiting an axisymmetric body in Newtonian gravitational theory with multipole moments Q_L, (and for a charge in a non-relativistic orbit about a charge distribution with the same multipole moments) we show that there exists, in addition to the energy and angular momentum component along the symmetry axis, a conserved quantity analogous to the Carter constant of Kerr spacetimes in general relativity, if the odd-L moments vanish, and the even-L moments satisfy Q_2L = m (Q_2/m)ˆL. Strangely, this is precisely the relation among mass moments enforced by the no-hair theorems of rotating black holes. By contrast, if Newtonian gravity is supplemented by a multipolar gravitomagnetic field, whose leading term represents frame-dragging (or if the electrostatic field is supplemented by a multipolar magnetic field), we are unable to find an analogous Carter-like constant. This further highlights the very special nature of the Kerr geometry of general relativity.

abs pdf

Dec 02, 2008

0812.0110 (/preprints)
2008-12-02, 08:38 [edit]


[0812.0069] Post-Newtonian corrections to the gravitational-wave memory for quasi-circular, inspiralling compact binaries

Authors: Marc Favata (KITP)

Date: 30 Nov 2008

Abstract: The Christodoulou memory is a nonlinear contribution to the gravitational-wave field that is sourced by the gravitational-wave stress-energy tensor. For quasi-circular, inspiralling binaries, the Christodoulou memory produces a growing, non-oscillatory change in the gravitational-wave "plus" polarization, resulting in the permanent displacement of a pair of freely-falling test masses after the wave has passed. In addition to its non-oscillatory behavior, the Christodoulou memory is interesting because even though it originates from 2.5 post-Newtonian (PN) order multipole interactions, it affects the waveform at leading-(Newtonian)-order. The memory is also potentially detectable in binary black hole mergers. While the oscillatory pieces of the gravitational-wave polarizations for quasi-circular, inspiralling compact binaries have been computed to 3PN order, the memory contribution to the polarizations has only been calculated to leading-order (the next-to-leading order 0.5PN term has previously been shown to vanish). Here the calculation of the memory for quasi-circular, inspiralling binaries is extended to 3PN order. While the angular dependence of the memory is essentially unchanged, the PN correction terms tend to reduce the memory's magnitude. Explicit expressions are given for the memory contributions to the polarizations and the spin-weighted spherical-harmonic modes of the metric and curvature perturbations. Combined with the results of Blanchet et al. (2008), this completes the waveform to 3PN order. This paper also discusses: (i) difficulties in extracting the memory from numerical simulations, (ii) other non-oscillatory effects that enter the waveform at high PN orders, and (iii) issues concerning the observability of the memory.

abs pdf

Dec 02, 2008

0812.0069 (/preprints)
2008-12-02, 08:38 [edit]


[0812.0170] Dark energy towards observational tests and data

Authors: S. Capozziello

Date: 30 Nov 2008

Abstract: A huge amount of good quality data converges towards the picture of a spatially flat universe undergoing the today observed phase of accelerated expansion. This new observational trend is commonly addressed as Precision Cosmology. Despite of the excellent surveys, the nature of dark energy, dominating the matter-energy content of the universe, is still unknown and a lot of different scenarios are viable candidates to explain cosmic acceleration. Methods to test these cosmological models are based on distance measurements and lookback time toward astronomical objects used as standard candles. The related degeneracy problem is the signal that more data at low 0<z<1, medium 1<z<10 and high 10 <z< 1000 redshift are needed to definitively select realistic models.

abs pdf

Dec 02, 2008

0812.0170 (/preprints)
2008-12-02, 08:38 [edit]


[0812.0012] The n-body problem in General Relativity up to the second post-Newtonian order from perturbative field theory

Authors: Yi-Zen Chu

Date: 29 Nov 2008

Abstract: Motivated by experimental probes of general relativity, we adopt methods from perturbative (quantum) field theory to compute, up to certain integrals, the effective lagrangian for its n-body problem. Perturbation theory is performed about a background Minkowski spacetime to O[(v/c)ˆ4] beyond Newtonian gravity, where v is the typical speed of these n particles in their center of energy frame. For the specific case of the 2 body problem, the major efforts underway to measure gravitational waves produced by in-spiraling compact astrophysical binaries require their gravitational interactions to be computed beyond the currently known O[(v/c)ˆ7]. We argue that such higher order post-Newtonian calculations must be automated for these field theoretic methods to be applied successfully to achieve this goal. In view of this, we outline an algorithm that would in principle generate the relevant Feynman diagrams to an arbitrary order in v/c and take steps to develop the necessary software. The Feynman diagrams contributing to the n-body effective action at O[(v/c)ˆ6] beyond Newton are derived.

abs pdf

Dec 02, 2008

0812.0012 (/preprints)
2008-12-02, 08:37 [edit]


[0811.0684] Short Gamma-Ray Bursts and Gravitational Waves from Dynamically Formed Merging Binaries

Authors: Dafne Guetta, Luigi Stella

Date: 5 Nov 2008

Abstract: Merging binary systems consisting of two collapsed objects are among the most promising sources of high frequency gravitational wave, GW, signals for ground based interferometers. Double neutron star or black hole/neutron star mergers are also believed to give rise to short hard bursts, SHBs, a subclass of gamma ray bursts. SHBs might thus provide a powerful way to infer the merger rate of two-collapsed object binaries. Under the hypothesis that most SHBs originate from double neutron star or black hole/neutron star mergers, we outline here a method to estimate the incidence of merging events from dynamically formed binaries in globular clusters and infer the corresponding GW event rate that can be detected with Advanced LIGO/Virgo. In particular a sizeable fraction of detectable GW events is expected to be coincident with SHBs. The beaming and redshift distribution of SHBs are reassessed and their luminosity function constrained by using the results from recent SHBs observations. We confirm that a substantial fraction of SHBs goes off at low redshifts, where the merging of systems formed in globular clusters through dynamical interactions is expected.

abs pdf

Dec 01, 2008

0811.0684 (/preprints)
2008-12-01, 08:18 [edit]


[0811.4711] Local dark matter searches with LISA

Authors: M. Cerdonio, R. De Pietri, Ph. Jetzer, M. Sereno

Date: 28 Nov 2008

Abstract: The drag-free satellites of LISA will maintain the test masses in geodesic motion over many years with residual accelerations at unprecedented small levels and time delay interferometry (TDI) will keep track of their differential positions at level of picometers. This may allow investigations of fine details of the gravitational field in the Solar System previously inaccessible. In this spirit, we present the concept of a method to measure directly the gravitational effect of the density of diffuse Local Dark Matter (LDM) with a constellation of a few drag-free satellites, by exploiting how peculiarly it would affect their relative motion. Using as test bed an idealized LISA with rigid arms, we find that the separation in time between the test masses is uniquely perturbed by the LDM, so that they acquire a differential breathing mode. Such a LDM signal is related to the LDM density within the orbits and has characteristic spectral components, with amplitudes increasing in time, at various frequencies of the dynamics of the constellation. This is the relevant result, in that the LDM signal is brought to non-zero frequencies.

abs pdf

Dec 01, 2008

0811.4711 (/preprints)
2008-12-01, 08:17 [edit]


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