Colloquium: Multimessenger astronomy with continuous gravitational waves and future detectors

Continuous gravitational waves from rapidly rotating neutron stars are on the new frontiers of gravitational wave astrophysics and have strong connections to electromagnetic astronomy, nuclear astrophysics, and condensed matter physics. In this Colloquium I survey prospects for detection of continuous gravitational waves from various neutron star populations, especially aided by electromagnetic observations. Although there are caveats, current theories and observations suggest that the first detections are likely within a few years, and that many are likely in the era of next generation detectors such as Cosmic Explorer and the Einstein Telescope. I also survey what can be learned from these signals, each one of which will contain more cycles than all the compact binary mergers ever detected. Since continuous gravitational wave emission mechanisms depend on aspects of neutron star physics, such as crustal elasticity, which are not well constrained by current astronomical observations and physical experiments, their detection can tell us a great deal that is new about extreme matter. Even more can be learned by combining gravitational wave observations with data from the Square Kilometre Array, the Next Generation Very Large Array, FAST, and other electromagnetic detectors operating in the next generation era.