Dynamical stability of the modified Tolman VII solution

Studies of neutron stars are at their peak after the multimessenger observation binary merger event GW170817, which strongly constrains stellar parameters like tidal deformability, masses, and radii. Although current future observations will provide stronger limits on parameters, knowledge explicit interior solutions to Einstein's equations, connect observed with internal structure, crucial have a satisfactory description these compact objects. A well-known exact solution, has shown relatively good approximation star, is Tolman VII solution. In order better fitting for energy density profile, realistic equations state stars, recently, Jiang Yagi proposed modified version this model, introduces an additional parameter $\ensuremath{\alpha}$, reflecting interplay quadratic newly added quartic term in profile. Here we study dynamical stability solution using theory infinitesimal adiabatic radial oscillations developed by Chandrasekhar. For purpose, determine values critical index, onset instability, considering configurations varying compactness $\ensuremath{\alpha}$. We found that new models stable against considerable range thus supporting applicability as physically plausible stars.