  Finite size effects in a neutron star merger are manifested, at leading
order, through the tidal deformabilities (Lambdas) of the stars. If strong
first-order phase transitions do not exist within neutron stars, both neutron
stars are described by the same equation of state, and their Lambdas are highly
correlated through their masses even if the equation of state is unknown. If,
however, a strong phase transition exists between the central densities of the
two stars, so that the more massive star has a phase transition and the least
massive star does not, this correlation will be weakened. In all cases, a
minimum Lambda for each neutron star mass is imposed by causality, and a less
conservative limit is imposed by the unitary gas constraint, both of which we
compute. In order to make the best use of gravitational wave data from mergers,
it is important to include the correlations relating the Lambdas and the masses
as well as lower limits to the Lambdas as a function of mass. Focusing on the
case without strong phase transitions, and for mergers where the chirp mass
M_chirp<1.4M_sun, which is the case for all observed double neutron star
systems where a total mass has been accurately measured, we show that the
dimensionless Lambdas satisfy Lambda_1/Lambda_2= q^6, where q=M_2/M_1 is the
binary mass ratio; $M$ is mass of each star, respectively. Moreover, they are
bounded by q^{n_-}>Lambda_1/Lambda_2> q^{n_{0+}+qn_{1+}}, where
n_-<n_{0+}+qn_{1+}; the parameters depend only on M_chirp, which is accurately
determined from the gravitational-wave signal. We also provide analytic
expressions for the wider bounds that exist in the case of a strong phase
transition. We argue that bounded ranges for Lambda_1/Lambda_2, tuned to
M_chirp, together with lower bounds to Lambda(M), will be more useful in
gravitational waveform modeling than other suggested approaches.
