Gravitational waves from the coalescence of two neutron stars were recently
detected for the first time by the LIGO-Virgo collaboration, in event GW170817.
This detection placed an upper limit on the effective tidal deformability of
the two neutron stars and tightly constrained the chirp mass of the system. We
report here on a new simplification that arises in the effective tidal
deformability of the binary, when the chirp mass is specified. We find that, in
this case, the effective tidal deformability of the binary is surprisingly
independent of the component masses of the individual neutron stars, and
instead depends primarily on the ratio of the chirp mass to the neutron star
radius. Thus, a measurement of the effective tidal deformability can be used to
directly measure the neutron star radius. We find that the upper limit on the
effective tidal deformability from GW170817 implies that the radius cannot be
larger than ~13km, at the 90% level, independent of the assumed masses for the
component stars. The result can be applied generally, to probe the stellar
radii in any neutron star-neutron star merger with a measured chirp mass. The
approximate mass-independence disappears for neutron star-black hole mergers.
Finally, we discuss a Bayesian inference of the equation of state that uses the
measured chirp mass and tidal deformability from GW170817 combined with nuclear
and astrophysical priors and discuss possible statistical biases in this
inference.Comment: Submitted to ApJ Letter
