Recent observations by the Chandra observatory suggest that some neutron stars may cool rapidly, perhaps by the direct URCA process which requires a high proton fraction. The proton fraction is determined by the nuclear symmetry energy whose density dependence may be constrained by measuring the neutron radius of a heavy nucleus, such as ${}^{208}\mathrm{Pb}.$ Such a measurement is necessary for a reliable extrapolation of the proton fraction to the higher densities present in a neutron star. A large neutron radius in ${}^{208}\mathrm{Pb}$ implies a stiff symmetry energy that grows rapidly with density, thereby favoring a high proton fraction and allowing direct URCA cooling. Predictions for the neutron radius in ${}^{208}\mathrm{Pb}$ are correlated to the proton fraction in dense matter by using a variety of relativistic effective field-theory models. Models that predict a neutron ${(R}_n)$ minus proton ${(R}_p)$ root-mean-square radius in ${}^{208}\mathrm{Pb}$ to be $R_n-R_p\lesssim 0.20\mathrm{fm}$ have proton fractions too small to allow the direct URCA cooling of ${1.4M}_{\odot }$ neutron stars. Conversely, if $R_n-R_p\gtrsim 0.25\mathrm{fm},$ the direct URCA process is allowed (by all models) to cool down a ${1.4M}_{\odot }$ neutron star. The Parity Radius Experiment at Jefferson Laboratory aims to measure the neutron radius in ${}^{208}\mathrm{Pb}$ accurately and model independently via parity-violating electron scattering. Such a measurement would greatly enhance our ability to either confirm or dismiss the direct URCA cooling of neutron stars.

• Received 24 July 2002

DOI:https://doi.org/10.1103/PhysRevC.66.055803