Signed Sound-Speed Deformations of BSk24-Anchored Barotropes: Neutron-Star Response
Background: Localized structure in the equilibrium squared sound speed can affect neutron-star observables, but modifying $dP/d\epsilon$ requires thermodynamically consistent reconstruction and assessment over the complete declared domain. Purpose: We quantify the response to positive and negative localized sound-speed changes around a unified BSk24 baseline while keeping the deformation geometry, admission criteria, reconstruction, and fixed-mass comparison protocol fixed. Method: A Gaussian profile with quintic smootherstep activation is added to $c_{\rm s}^2$. Proposals violating $P>0$ or $0<c_{\rm s}^2\leq1$ anywhere in the retained domain are rejected before reconstruction. Passing cases are reconstructed as effective cold one-fluid barotropes and evolved with the Tolman-Oppenheimer-Volkoff and tidal equations. Results: The $A=0$ case reproduces the undeformed control exactly. A localized change produces a persistent pressure offset, relocates the fixed-mass central state, and yields a mass-dependent, nonlinear, sign-asymmetric response. For $A=-0.8$ and $+0.8$, respectively, $\Delta\Lambda/\Lambda_0=(-46.02\%,+35.33\%)$ at $1.4\,M_\odot$ and $(-63.52\%,+87.17\%)$ at $2.0\,M_\odot$. The reached stiffened feature remains core connected at the reporting endpoints, whereas the softened feature becomes an off-center shell at high mass. Conclusions: These phenomenological BSk24-anchored effective barotropes illustrate how a local sound-speed intervention propagates through thermodynamic reconstruction and stellar structure. They are not BSk24 predictions or evidence for a microscopic composition or phase transition.