Structure of stellar remnants with coupling to a light scalar

In this paper, we study how a Yukawa coupling of the Standard Model fermions to a light scalar field affects the stellar structure of cold stellar remnants such as neutron stars. We elucidate the stellar structure phenomenology using a simple model of a massive scalar coupled to a single dominant fermion with no other interactions. For a broad scalar mass range (10(-10) eV << m(phi) << 10(3) eV for neutron stars) we show that the equation-of-state and stellar structure depends on the effective coupling g = g(f) m(f)/m(phi) , where gf is the Yukawa coupling, m(f) is the fermion mass, and m(phi) is the scalar kinematic mass at nuclear densities. If g > O(1) the Yukawa coupled matter exhibits various anomalous behaviors including hydrodynamic instability, negative pressure, distinct phases (soft and hard) of matter with sharp phase boundaries between them and with the vacuum. These anomalies can lead to stars consisting of only soft, only hard, or a hybrid of soft and hard matter. These stars can have either sign for the slope of the mass-radius relation, anomalously large and small masses, gaps in allowed radii, multiple radii for the same mass, thin crusts and radiate anomalously large amounts of energy when they form (in the form of neutrinos for neutron stars). To the extent that these anomalies have not and/or will not be observed limits the effective coupling to g < O(1). We argue this phenomenology is generic to stars with Yukawa coupled matter.