Isolated pulsars are rotating neutron stars with accurately measured angular velocities \Omega , and their time derivatives that show unambiguously that the pulsars are slowing down .
Although the exact mechanism of the spin-down is a question of detailed debate , the commonly accepted view is that it arises through emission of magnetic dipole radiation ( MDR ) from a rotating magnetized body .
Other processes , including the emission of gravitational radiation , and of relativistic particles ( pulsar wind ) , are also being considered .
The calculated energy loss by a rotating pulsar with a constant moment of inertia is assumed proportional to a model dependent power of \Omega .
This relation leads to the power law \dot { \Omega } = -K \Omega ^ { n } where n is called the braking index .
The MDR model predicts n exactly equal to 3 .
Selected observations of isolated pulsars provide rather precise values of n , individually accurate to a few percent or better , in the range 1 < n < 2.8 , which is consistently less than the predictions of the MDR model .
In spite of an extensive investigation of various modifications of the MDR model , no satisfactory explanation of observation has been found yet .

The aim of this work is to determine the deviation of the value of n from the canonical n = 3 for a star with a frequency dependent moment of inertia in the region of frequencies from zero ( static spherical star ) to the Kepler velocity ( onset of mass shedding by a rotating deformed star ) , in the macroscopic MDR model .
For the first time , we use microscopic realistic equations of state ( EoS ) of the star to determine its behavior and structure .
In addition , we examine the effects of the baryonic mass M _ { B } of the star , and possible core superfluidity , on the value of the braking index within the MDR model .

Four microscopic equations of state are employed as input to two different computational codes that solve Einstein ’ s equations numerically , either exactly or using the perturbative Hartle-Thorne method , to calculate the moment of inertia and other macroscopic properties of rotating neutron stars .
The calculations are performed for fixed values of M _ { B } ( as masses of isolated pulsars are not known ) ranging from 1.0 - 2.2 M _ { \odot } , and fixed magnetic dipole moment and inclination angle between the rotational and magnetic field axes .
The results are used to solve for the value of the braking index as a function of frequency , and find the effect of the choice of the EoS , M _ { B } .
The density profile of a star with a given M _ { B } is calculated to determine the transition between the crust and the core and used in estimation of the effect of core superfluidity on the braking index .

Our results show conclusively that , within the model used in this work , any significant deviation of the braking index away from the value n = 3 occurs at frequencies higher than about ten times the frequency of the slow rotating isolated pulsars most accurately measured to date .
The rate of change of n with frequency is related to the softness of the EoS and the M _ { B } of the star as this controls the degree of departure from sphericity .
Change in the moment of inertia in the MDR model alone , even with the more realistic features considered here , can not explain the observational data on the braking index and other mechanisms have to be sought .