Stable ultracompact objects and an upper bound on neutron star masses

We have proposed a core-envelope model with stiffest equation of state [spe ed of sound equal to that of light] in the core and a polytropic equation w ith constant adiabatic index Gamma(1) = [dlnP/dln rho] in the envelope and obtained a stable configuration with a maximum value of u congruent to 0.35 74 when the ratio of pressure to density at the core-envelope boundary reac hes about 0.014. The maximum mass of neutron star based upon this model com es out to be 7.944M., if the (average) density of the configuration is cons trained by fastest rotating pulsar, with rotation period, P-rot congruent t o 1.558 ms, known to date. The average density of the configuration turns o ut to be 1.072 x 10(14) g cm(-3). The model gives dynamically stable config urations with compaction parameter u [= (M/R),where M = mass and R = radius of the structure] > (1/3) which are important to study Ultra-Compact Objec ts [UCOs]. The theoretically obtained maximum value of u is also important regarding millisecond oscillations seen during X-Ray burst (if they are pro duced due to spin modulation) from a rotating neutron star, because the max imum modulation amplitude depends only upon the compaction parameter and th e observed value of this amplitude provides a tool for testing theoretical models of neutron stars. The M(envelope)/M(star) ratio corresponds to a val ue similar to 10(-2) which may be relevant in explaining the rotational irr egularities in pulsars known as the timing noise and glitches.