The equation of state of the nuclear matter inside a neutron star is still poorly understood, and it is very hard to obtain relevant information by way of conventional (electromagnetic) astronomy. Kip Thorne has conjectured that we could get a handle on the equation of state by detecting and analyzing the gravitational waves emitted by tidally disrupting neutron stars in neutron-star/black-hole inspiraling binaries (the neutron stars disrupt because at close separations the differential pull of the black hole on the various parts of the stars is stronger than their self gravitation).
I studied a simple model where the neutron star is a tidally distorted Newtonian ellipsoid on a circular, equatorial geodesic around a Kerr black hole. I take the radius of the neutron star, for a fixed mass, as a representative of the uncertainty in the equation of state. I find that LIGO-II (circa 2006-2008) should be able to determine the radius with an error of 15 percent, for binary inspirals happening at a distance that yields about one coalescence per year (under current estimates, which are subject to many uncertainties). LIGO-I will not be sensitive enough for these observations, unless a suitable disruption event happens very close to our galaxy.
My results suggest that second-generation gravitational interferometers could extract valuable information about the neutron-star equation of state from tidal-disruption gravitational waves.
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