  Exploring nucleon drip lines and astrophysical rapid neutron capture process
(r-process) paths in the nuclear landscape is extremely challenging in nuclear
physics and astrophysics. While various models predict similar proton drip
line, their predictions for neutron drip line and the r-process paths involving
heavy neutron-rich nuclei exhibit a significant variation which hampers our
accurate understanding of the r-process nucleosynthesis mechanism. Using
microscopic density functional theory with a representative set of
non-relativistic and relativistic interactions, we demonstrate for the first
time that this variation is mainly due to the uncertainty of nuclear matter
symmetry energy $E_{\rm{sym}}(\rho_{\rm{sc}})$ at the subsaturation cross
density $\rho_{\rm{sc}}=0.11/0.16\times\rho_0$ ($\rho_0$ is saturation
density), which reflects the symmetry energy of heavy nuclei. Using the recent
accurate constraint on $E_{\rm{sym}}(\rho_{\rm{sc}})$ from the binding energy
difference of heavy isotope pairs, we obtain quite precise predictions for the
location of the neutron drip line, the r-process paths and the number of bound
nuclei in the nuclear landscape. Our results have important implications on
extrapolating the properties of unknown neutron-rich rare isotopes from the
data on known nuclei.
