One can distinguish three broad classes of coordinated observations: triggered gravitational-wave searches, follow-up electromagnetic observations, and parameter refinement.
Finding electromagnetic counterparts to gravitational wave observations is important, of course, for learning about the nature of the events. But it has a more subtle benefit: it generally improves significantly the accuracy with which parameters can be estimated from the gravitational wave observation. The reason is that one of the biggest sources of parameter uncertainty is the sky location of a gravitational wave source. Interferometers have broad antenna patterns, which is helpful in that they can monitor essentially the entire sky continuously, but which means that directional information for transient events can come only from time delay information among different detectors. The simple Rayleigh limit for ground-based interferometers gives angular accuracies on the order of several degrees, divided by the amplitude SNR (never smaller than 5 for any reasonable detection). The covariance of angular errors with uncertainties in other parameters (distance, polarization, stellar masses, etc) is usually significant. Therefore, if a follow-up electromagnetic observation can provide a more accurate position, this can also improve the determination of all the other parameters measured gravitationally.
Triggered searches are already being performed by the LSC for gravitational waves associated with gamma-ray bursts . The nondetection of any gravitational waves associated with the gamma-ray burst GRB 070201 showed that it was not created by the merger of neutron stars in the nearby galaxy M31, despite its positional coincidence on the sky . In addition, the gravitational wave detectors are monitoring the triggers provided by both high-energy and low-energy neutrino detectors in order to get instant warning of a supernova in our galaxy or of some more exotic event further away. As we have noted above, X-ray flares from neutron stars may signal normal-mode radiation from acoustic vibrations.
Triggers may also allow the first detection of gravitational waves from the normal modes of neutron stars, which as mentioned in Section 7.3.3, would provide our first “view” inside these exotic objects. These triggers could be radio-pulsar glitches, X-ray flares, or even the formation and subsequent ringdown of a neutron star.
Follow-up observations of neutron-star–binary coalescence events are likely to be particularly informative. It is possible that these events are associated with short gamma-ray bursts, in which case most events are missed because of the narrow beaming of the gamma rays. Gravitational waves, by contrast, are emitted nearly isotropically, so that they will pick out essentially all such events within the range of the detectors, and astronomers can subsequently search for afterglows and prompt X- and gamma-ray emission. The ability to study such events from all aspect angles will help model them reliably. Even if coalescences are not associated with gamma-ray bursts, it is difficult to imagine that they will not produce visible afterglows or other transient electromagnetic events that would presumably not have been recognized before. The same considerations apply to coalescences of neutron stars and black holes.
Gravitational wave events may also provide our first notice of a gravitational collapse event, if the event is a strong radiator and is too far away for neutrino detectors to see it. While supernova simulations generally suggest that the amplitude of emitted gravitational waves is small , numerical simulations of the aftermath of neutron-star coalescence suggest the possibility of very powerful gravitational-wave emission . While this event seems to lead inevitably to a black hole, because the total mass is too large for a single neutron star, neutron stars might occasionally be formed in this way by mergers of white dwarfs, again with strong rotation and the possibility of the emission of strong gravitational radiation. In this connection the suggestion of Arons  that at least some magnetars are formed in events of some kind that involve strong magnetic field braking but also strong gravitational wave emission, and that these events are the source of the ultra-high–energy cosmic rays whose source, is so far unexplained .
LISA offers particularly interesting opportunities for follow-up observations with electromagnetic waves, beyond the direct monitoring of the merger events for SMBHs mentioned above. Because SMBHs often carry accretion disks, the merger event may be followed by the turning on of accretion after a delay of, perhaps, a year or so . The merger may also cause a prompt shock in surrounding gas, due to the essentially instantaneous loss of several percent of the gravity of the central mass. These or similar effects may make it possible to identify the galaxies that host LISA mergers, which in turn will allow one to associate a redshift with the luminosity distance that the gravitational wave event provides. This will be important for LISA’s cosmographic capabilities (next section).
LISA will look for close white-dwarf binaries in our galaxy and will probably see thousands of them. White-dwarf binaries never reach the last stable orbit, which would occur at roughly 1.5 kHz for these masses. Instead they undergo a tidal interaction and can either disrupt at much lower frequency or end up as AM CVns (see, for instance, [344, 271]). In the latter case, we have a close white-dwarf binary with orbital periods of minutes or hours, wherein the smaller of the two stars transfers mass to the more massive one. This mass loss leads to an increase in the orbital period as a result of redistribution of the angular momentum. So far only a handful of AM CVn systems are known. LISA could potential discover a lot more of these as their orbital periods are right in the heart of LISA’s sensitivity band and simultaneous observation of these systems in the gravitational and electromagnetic window has huge impacts on the science we can learn about these end products of stellar evolution and their eventual fate.
For each resolved white-dwarf binary LISA can determine the orbital period and the spatial orientation of the orbit, and it can give a relatively crude position. If the orbit is seen to decay during the observation, LISA can determine the distance to the binary. If the binary is known from optical or X-ray observations, then this can be very valuable additional information about the system, again complementary to that which is normally available from the electromagnetic observation. Even for systems that have not been identified, LISA’s census of white-dwarf binaries will provide important statistics (on the mass function, distribution of separations, etc) that should lead to a better understanding of white-dwarf and binary evolution.
In the near term, one of the most practical applications of multimessenger astronomy is to use electromagnetic observations to refine the values of key search parameters for the gravitational wave data analysis. This has been extensively discussed for possible observations of low-mass X-ray binaries, as described in Section 7.3.5. Watts et al.  surveyed the known ranges of parameters, such as spin rates and orbital parameters, and concluded that they need to be narrowed considerably if a practical search were to be possible, not just because of the computer power required, but more importantly because of the loss of significance if too large a parameter space has to be searched.
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