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In this paper we study how a Yukawa coupling of the Standard Model fermionsto a light scalar field effects the stellar structure of cold stellar remnantssuch as neutron stars. We elucidate the stellar structure phenomenology using asimple model of a massive scalar coupled to a single dominant fermion with noother interactions. For a broad scalar mass range ($10^{-10}\,\mathrm{eV}\llm_\phi\ll10^3\,\mathrm{eV}$ for neutron stars) we show that theequation-of-state and stellar structure depends only the effective coupling$\mathfrak{g}=\frac{g_f\,m_f}{m_\phi}$, where $g_f$ is the Yukawa coupling,$m_f$ the fermion mass and $m_\phi$ is the scalar kinematic mass at nucleardensities. If $\mathfrak{g}>\mathcal{O}(1)$ the Yukawa coupled matter exhibitsvarious anomalous behaviors including hydrodynamic instability, negativepressure, distinct phases (soft and hard) of matter with sharp phase boundariesbetween them and with vacuum. These anomalies can lead to stars consisting ofonly soft, only hard or hybrid of soft and hard matter. These stars can havevarying signs of the slope of the mass-radius relation, anomalously large andsmall masses, gaps in allowed radii, multiple radii for the same mass, verythin crusts and radiate anomalously large amounts of energy when they form (inthe form of neutrinos for neutron stars). To the extent that these anomalieshave not and/or will not be observed limits the effective coupling to$\mathfrak{g}<\mathcal{O}(1)$. We argue this phenomenology is generic torealistic models of stars with Yukawa coupled matter.

Structure of Stellar Remnants with Coupling to a Light Scalar