Abstract
The attempt has been taken to calculate the density of stars possessing quark matter core using sphere packing concept of crystallography. The quark matter has been taken as solid in nature as predicted in references 36 and 37, and due to immense gravitational pressure at the core of the star the densest packing of quarks as spheres has been assumed to calculate the packing fraction Φ, thus the density ρ of the matter. Three possible types of pickings—mono-sized sphere packing, binary sphere packing and ternary sphere packing, have been worked out using three possible types of quark matter. It has been concluded that no value about the ρ of quark matter can be calculated using binary and ternary packing conditions and for mono-sized packing condition different flavor quark matters of different values in the density have been calculated using results from the experiments done by HI, ZEUS, L3 and CDF Collaborations about the radius limit of quark. For example, for u quark matter ρ ranges from 4.0587 × 1048 - 7.40038 × 1048 MeV/c2 cm3 using results of L3 Collaboration, for s quark matter 15.91794 × 1048 - 17.6866 × 1048 MeV/c2 cm3, etc.
Highlights
Neutron stars are one of the densest stars known in the cosmos
There is a limit for neutron star above which the stars are said to form black hole [3] [4] which is a region of space time from which nothing can escape to infinity as predicted by General theory of relativity [5]
Since we have not been able to calculate the density by considering the quark matter inside the core of the neutron star as a binary sphere packing and ternary sphere packing, we can consider the problem as mono sized spherical quark problem which is the only option for us at this time to imagine the density of the matter in the core of neutron star
Summary
Neutron stars are one of the densest stars known in the cosmos. They are formed by the gravitational collapse of some massive stars having inner core mass above Chandrasekhar limit—1.4 Mo [1], but with mass lesser than the mass required to overcome neutron degeneracy pressure. FCC (face centered cubic) or CCP (cubic close packing) and HCP (hexagonal close packing) are the two unit structures known possible in the close packing of spherically symmetrical and mono sized particles These two structures have the highest packing density as proved by Gauss in 1831 and originally proposed by Johannes Kepler in 1611 in his so called Kepler’s conjecture theorem [16] [17]. The highest average atomic packing function (APF) Φ possible due to Keplers’ Conjecture theorem is 0.74048048 [4] [18] This value validates only to mono sized sphere packing. In the previous paper neutrons where taken as spheres and here quarks We can say this is the second work done on the technique, that is, use of sphere packing in astronomy to derive density of stars
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