An Analytical Toy Equation of State for Neutron Stars Consistent with Current Observations

Fast analytic and semi-analytic studies of neutron stars often require an equation of state that is convenient to evaluate while producing relativistic stellar sequences compatible with current multimessenger constraints. We construct such a benchmark by scanning a smooth double polytropic relation for the energy density as a function of pressure, $\hat\epsilon (\hat p)=a_1\hat p^{\Gamma_1}+a_2\hat p^{\Gamma_2}$. The parameters are selected with filters based on massive pulsars, tidal deformability from the binary-neutron-star event GW170817, and NICER mass-radius measurements. A single polytropic baseline scan finds no model passing all filters, whereas a double-polytrope scan identifies a viable region. A curve-integral score, evaluated against public NICER and GW170817 posterior data sets, is then used to choose benchmark equations of state within this region. The selected representatives support $M_{\max}=2.44$--$2.49\,M_\odot$, with $R_{1.4}\simeq 11.3$ km and $\Lambda_{1.4}=485$--$512$, and remain causal on the stable branch. This compact analytic family provides reference cases for relativistic stellar-structure tests at current observational scales.