Sensitive dependence of isotope and isobar distribution of limiting temperatures on symmetry energy

The mass, isotope, and isobar distributions of limiting temperatures for finite nuclei are investigated by using a thermodynamics approach together with the Skyrme energy density functional. The relationship between the width of the isotope (isobar) distribution of limiting temperatures and the stiffness of the density dependence of the symmetry energy clearly is observed. The nuclear symmetry energy with smaller slope parameter $L_{rm{sym}}$ causes a wider the isotope (isobar) distribution of limiting temperatures. The widths of the isotope (isobar) distributions of limiting temperatures could be useful observables for exploring the information of the density dependence of the nuclear symmetry energy at finite temperatures.