tokens: so rapidly that it becomes useless. This means that simultaneous operations of LISA and radio instruments such as SKA are beneficial for making full use of our multimessenger strategy. Following consideration of the dispersion measure, we determine the steps of trial values for the amplitude and phase of the modulation by requiring that the pulse arrival time changes by the sampling time. The number of required trials for the modulation amplitude is given by and that for the modulation phase is given by Additionally, the uncertainty in the eccentricity of Δ e ≈ 0.003 could change the arrival time by t mod Δ e , and this will require trials of for our fiducial parameters. We expect that extension to a slightly eccentric orbit will be straightforward. We should remark on the spin precession. Its period will be for our fiducial parameters (Barker O’Connell 1975 ), and we expect its effect to be marginal. We leave the careful assessment for future work, and information from LISA will prove useful even when the precession must be corrected for. 3.3 Comparison with an all-sky survey To elucidate usefulness of the multimessenger observation with LISA , we compare its performance with an all-sky survey of radio instruments. To keep the sensitivity fixed, we assume that the integration time per pointing is the same for both observation strategies. We also fix the sampling time. A comparison with an all-sky survey based on the phase-modulation search, with which the sensitivity is not maximal, is briefly made in the end of this section. First, the all-sky survey trivially requires a large number of pointings, and thus the integration time must actually be shortened. If we do not restrict the search to a limited portion of the sky, e.g. the Galactic plane, equation ( 17 ) suggests that O (10 4 ) pointings in terms of a single-dish beam are required to find a limited number of targets. Even if instruments with a large field-of-view are available (Smits et al. 2009 ), the number of pointings may not be reduced below O (10 2 ). If we evaluate the number of pointings in terms of tied-array beams, the all-sky survey requires O (10 8 ) pointings, which is larger by O (10 6 ) compared to the multimessenger observation with LISA , equation ( 20 ). However, results of the all-sky survey can be used for various applications including standard pulsar searches, and thus this comparison is valid only when we focus on detections of pulsars in the shortest period class of binary neutron stars. Next, the coherent integration becomes significantly costly because of brute-force corrections for the orbital modulation. We have to search over a large parameter space of not only the modulation amplitude and phase but also the orbital frequency. By requiring that the phase error caused by the frequency mismatch accumulated during the integration time does not induce a timing error larger than the sampling time, particularly for the harmonic summing to be successful, the step in
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