The Density Profile of a Neutron Star

The problem posed in this study is to determine the density distribution within an ideal spherically symmetric neutron star based on only two constraints: the volumetrically averaged density and a moment of inertia factor, <i>f</i>. In order to deal with the above, it is recognized that space within these objects is heavily curved, and thus lengths, densities, and the moment of inertia have to be adjusted for relativistic effects. For the first time, the minimum relative entropy methodology (MRE) is used to find the expected value of a series of effective densities within a neutron star. In numerical experiments, we use the data from the star PSR J0737-3039A, which has a mass of 2.6×1030 kg and a radius of 13.75 km. Here, the factor <i>f</i> is based on a range of values of moments of inertia (MOI): 1.30-1.63 ×1045 g cm². For f=0.324, at no time do densities cross over 1×1015 gm/cc. For the most part, densities > 6×1014 gm/cc are shown at radial dimensions of less than about 4 km. When f=0.258, densities closer to the core are pushed higher, as one might expect, and peak at slightly over 4×1015 gm/cc. If recent values of MOI are more appropriate at 1.15×1045 g cm², this then suggests core densities greater than 4×1015 gm/cc. These various density models lead to quantitative statements about qualitative interpretations, and as time goes on, any internal density models should satisfy the two constraints posed. Also, since the model presented here is probabilistic, it can be established that density at a certain depth is constrained within a certain confidence limit. The expected values of densities for PSR J0737-3039A are in reasonable agreement with current conceptual neutron star models but are highly sensitive to assumed MOI values. It is emphasized that the probabilities and the mean values of density obtained are conditional on the imposed moments, namely, M and <i>f</i>, and also the radius R.