Probing neutron stars with gravitational waves

Within the next decade gravitational-wave (GW) observations by Advanced LIGO [1] in the United States, Advanced Virgo [2] and GEO HF [32] in Europe, and possibly other ground-based instruments will provide unprecedented opportunities to look directly into the dense interiors of neutron stars which are opaque to all forms of electromagnetic (EM) radiation. The 10-10 4 Hz frequency band available to these ground-based interferometers is inhabited by many neutron star mode frequencies, spin frequencies, and inverse dynamical timescales. GWs can provide information on bulk properties of neutron stars (masses, radii, locations. . . ) as well as microphysics of their substance (crystalline structure, viscosity, composition. . . ), some of which is difficult or impossible to obtain by EM observations alone. The former will tell us about the astrophysics of neutron stars, and the latter will illuminate fundamental issues in nuclear and particle physics and the physics of extremely condensed matter. Although GW searches can be done "blind," they become richer and more informative with input from EM observations; and thus the combination of the two is crucial for learning the most we can about neutron stars. Healthy GW and EM observational programs must be accompanied by vigorous theoretical research on the interface of astrophysics, gravitational physics, nuclear and particle physics in order to extract the most from the observations. Advanced LIGO has been funded and it and its international partners will not be ranked as part of the decadal review. Our purpose here is rather to describe the neutron-star aspect of GW science and point out observational and theory issues in EM astronomy and astrophysics which connect to it, and thus are important to maximizing the scientific output of the advanced detectors (LIGO, Virgo, and GEO HF) and the future underground GW detectors now in planning.

Opportunities to learn about neutron stars through GW and and GW/EM observations naturally divide into four categories: supernovae, binary mergers, starquakes, and continuous waves. The first is addressed in another white paper [13]; here we address the other three.

Advanced LIGO is likely to observe mergers of double neutron star (NS/NS) binaries at a rate of a few to a few hundred per year; and black-hole/neutron-star (BH/NS) binaries perhaps in a comparable range of rates [18]. If the observed rates are at either extreme of the range, they would reflect on extremes of compact binary populations and aspects of their formation such as the properties of a common envelope phase and the distribution of neutron-star birth kicks, both of which can prematurely merge or disrupt binaries before the second neutron star or the black hole is formed.

Individual merger signals can reveal aspects of neutron star structure: For BH/NS mergers the tidal disruption of the neutron star can take place at frequencies where groundbased GW detectors are most sensitive. The latest, fully relativistic, numerical simulations of merger [15] confirm the earlier Newtonian intuition that the “break frequency” of the merger signal, the frequency at which much of the neutron star is swallowed by the black hole and the signal becomes very faint, is strongly correlated with the neutron star radius and therefore can serve as a good measurement of it. Beyond Advanced LIGO, or with a very lucky event during the time of Advanced LIGO, a neutron star’s mass can be measured to as well as 20% from the precessional modulation of the signal if the companion is a rapidly rotating black hole [27]; and a high neutron star mass would significantly constrain the star’s composition. Recent analytical [16] and numerical estimates [24] of the effects of tidal deformations on NS/NS orbits (and thus the phase evolution of merger signals) indicate that the strongest signals observed by Advanced LIGO might yield measurements of stellar radii to a precision as good as 1 km, even better than the break frequency. Such a radius measurement constrains to order 10% the pressure around twice nuclear density, a number unattainable in terrestrial laboratories which is correlated with properties such as the incompressibility and isospin asymmetry energy of nuclear matter.

GW and EM observations of mergers are important to each other as described in the transient white paper [13]: The availability of EM triggers localized in time and sky position increases the sensitivity of GW searches, and comparison of GW and EM observations can constrain properties of the merger and gamma-ray burst (if any). EM observations are important to GW mergers in another respect: While there are several observed NS/NS systems on which to empirically base merger rates, and eventually make population statements by comparing to observed GW merger rates, the BH/NS event rates are estimated purely based on theoretical population synthesis codes which contain many poorly known factors. If a pulsar survey, performed for

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