Constraining properties of neutron stars with heavy-ion reactions

Nuclear reactions induced by stable and/or radioactive neutron- rich nuclei provide the opportunity to pin down the equation of state of neutron-rich matter, especially the density ($\rho$) dependence of its isospin-dependent part, i.e., the nuclear symmetry energy $E_{\rm sym}$. A conservative constraint, $32 (\rho /\rho_{0})^{0.7} < E_{\rm sym}(\rho ) < 32(\rho /\rho _ {0})^{1.1}$, around the nuclear matter saturation density $\rho_0$ has recently been obtained from the isospin diffusion data in intermediate energy heavy-ion collisions. We review this exciting result and discuss its consequences and implications on nuclear effective interactions, radii and cooling mechanisms of neutron stars.