Using a simple model of a neutron star with a perfectly rigid crust constructed with a set of crust and core equations of state that span the range of nuclear experimental uncertainty in the symmetry energy , we calculate the instability window for the onset of the Chandrasekhar-Friedmann-Schutz ( CFS ) instability in r-mode oscillations for canonical neutron stars ( 1.4 M _ { \odot } ) and massive neutron stars ( 2.0 M _ { \odot } ) .
In these models the crust-core transition density , and thus crustal thickness , is calculated consistently with the core equation of state ( EOS ) .
The EOSs are calculated using a simple model for the energy density of nuclear matter and probe the dependence on the symmetry energy by varying the slope of the symmetry energy at saturation density L from 25 MeV ( soft symmetry energy and EOS ) to 115 MeV ( stiff symmetry energy and EOS ) while keeping the EOS of symmetric nuclear matter fixed .
For the canonical neutron star , the lower bound of the r-mode instability window is reduced in frequency by \approx 150 Hz from the softest to the stiffest symmetry energy used , independent of mass and temperature .
The instability window also drops by \approx 100 Hz independent of EOS when the mass is raised from 1.4 M _ { \odot } to 2.0 M _ { \odot } .
Where temperature estimates are available , the observed neutron stars in low mass X-ray binaries ( LMXBs ) have frequencies below the instability window for the 1.4 M _ { \odot } models , while some LMXBs fall within the instability window for 2.0 M _ { \odot } stars if the symmetry energy is relatively stiff , indicating that a softer symmetry energy is more consistent with observations within this model .
Thus we conclude that smaller values of L help stabilize neutron stars against runaway r-mode oscillations .
The critical temperature , below which no star can reach the instability window without exceeding its Kepler frequency , varies by nearly an order of magnitude from soft to stiff symmetry energies .
When the crust thickness and core EOS are treated consistently , a thicker crust corresponds to a lower critical temperature , the opposite result to previous studies in which the transition density was independent of the core EOS .