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Authors: Ryan N. Lang, Scott A. Hughes

Date: 19 Oct 2007

Abstract: Massive black hole binary coalescences are prime targets for space-based gravitational-wave (GW) observatories. GW measurements can localize the position of a coalescing binary on the sky to an ellipse with major axis ${a few} \times 10$ arcminutes to a few degrees, depending on source redshift, and a minor axis which is $2 - 4$ times smaller. Neglecting weak gravitational lensing, GWs would also determine the source's luminosity distance to better than percent accuracy for close sources, degrading to several percent for more distant sources. Assuming a well-measured cosmology, the source's redshift could be inferred with similar accuracy. GWs alone can thus pinpoint a binary to a 3-dimensional ‘pixel,’ guiding searches for the hosts of these events. We examine the time evolution of this pixel, studying it at merger and at several intervals before merger. One day before merger, the major axis of the error ellipse is typically larger than its final value by a factor $\sim 1.5-6$. The minor axis is larger by $\sim 2-9$, and the error in the luminosity distance is larger by a factor $\sim 1.5-7$. This large change over short time is due to spin-induced precession, which is strongest in the final days before merger. The evolution is slower as we go back further in time. For $z = 1$, we find that GWs will localize a binary to within $\sim 10$ square degrees as early as a month prior to merger and determine distance (and hence redshift) to several percent. [Abridged]

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