Tidal Love numbers and moment-Love relations of polytropic stars

摘要: The physical significance of tidal deformation in astronomical systems has long been known. recently discovered universal I-Love-Q relations, which connect moment inertia, quadrupole Love number, and spin-induced compact stars, also underscore the special role gravitational wave astronomy. Motivated by observation that such relations prevail Newtonian stars crucially depend on stiffness a star, we consider numbers polytropic whose is characterised index $n$. We first perturbatively solve Lane-Emden equation governing profile through application scaled delta expansion method then formulate perturbation series for multipolar number about two exactly solvable cases with $n=0$ $n=1$, respectively. Making use these to form two-point Pad\'e approximant, find an approximate expression error less than $2.5 \times 10^{-5}$ per cent (0.39 cent) $n\in[0,1]$ ($n\in[0,3]$). Similarly, determine mass moments accurately. Based findings, are able show general stationary incompressible limit irrespective state (EOS) star. Moreover, there secondary point near $n \approx 0.4444$, thus showing insensitivity $n$ $n\in[0,1]$. Our investigation clearly tracks universality from their validity stiff as neutron breakdown soft stars.