Abstract Details
| Name: SAFIQUL ISLAM Affiliation: PDF, Harish Chandra Research Institute, Allahabad Conference ID: ASI2018_1209 Title : A parametric model to study the mass radius relationship of stars Authors and Co-Authors : SATADAL DATTA*, Prof. Tapas Das*. *Harish-Chandra research Institute, Chhatnag Road, Jhunsi, Allahabad-211019, India Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai - 400094, India Abstract Type : Poster Abstract Category : General Relativity and Cosmology Abstract : For relativistic charged fluid with the signature of pressure anisotropy, where the anisotropy is defined by the finite non zero difference between the radial and the tangential fluid pressure, the Einstein Maxwell field equations are solved for static spherically symmetric spacetime. Certain functional form of the electric field as well as the effective gravitational potential have been introduced in our model, where such field and potential are characterized by two free parameters a and b, with certain relationships defined between these two parameters, where such relationships are obtained using a particular form of stability criteria. The charge and the mass energy density have been expressed (as a consequence of the interior solution) as a function of the radial distance. From there, we obtain the mass-radius relationship for the interior solution. Once such mass-radius relationship is integrated for a particular limit defined by the radius of the star, one can obtain what will be the mass of the charged fluid considered in our model, embedded within a sphere of radius R. Hence our model here provides the mass M(R) of star of radius R. M(R) in our calculations, however, is characterized by (a,b), and there remains a specific relationship between a and b, which are obtained by using some predefined stability criterion. Various values of a and b provides various [M(R)-R] measurements. For different values of a and b, one can find M(R) for different values of R, and hence using our model, we can study the mass radius relation for different categories of stellar objects located at various regions of the Hertzsprung-Russel diagram. We find that the mass and radius of the considered stars in sub-giants class and blue-giant class are of the same order and that is reflected in a-b parameter space too. Obviously, among the considered stars, this model does not distinguish sub-giants and blue giants. Nevertheless, this difference is prominent and clear for the other classes of the considered stars. The compactness of the star and permissible region in a-b parameter space for the star closely matches with the red dwarf category. Our model clearly distinguishes this brown dwarf from the other stars. Actually, this model is good in categorising the stars depending on their mass and radius. This model clearly classifies stars into two categories, i.e; 0 < n < 0.5 and 0.5 ≤ n < 1. Given compactness of a star, one of the two above categories for the star is determined. Now one needs an additional input about the star (radius or mass of the star) to determine on which subcategories, i.e; on which type the star fits in if n < 0.5 (because all of the stars in H-R diagram have n < 0.5). |