A Global View of QCD Axion Stars. (arXiv:1905.00981v1 [hep-ph])
<a href="http://arxiv.org/find/hep-ph/1/au:+Eby_J/0/1/0/all/0/1">Joshua Eby</a>, <a href="http://arxiv.org/find/hep-ph/1/au:+Leembruggen_M/0/1/0/all/0/1">Madelyn Leembruggen</a>, <a href="http://arxiv.org/find/hep-ph/1/au:+Street_L/0/1/0/all/0/1">Lauren Street</a>, <a href="http://arxiv.org/find/hep-ph/1/au:+Suranyi_P/0/1/0/all/0/1">Peter Suranyi</a>, <a href="http://arxiv.org/find/hep-ph/1/au:+Wijewardhana_L/0/1/0/all/0/1">L.C.R. Wijewardhana</a>
Taking a comprehensive view, including a full range of boundary conditions, Taking a comprehensive view, including a full range of boundary conditions, http://arxiv.org/icons/sfx.gif
we reexamine QCD axion star solutions based on the relativistic Klein-Gordon
equation (using the Ruffini-Bonazzola approach) and its non-relativistic limit,
the Gross-Pit”aevskii equation. A single free parameter, conveniently chosen
as the central value of the wave function with range $0 < Z(0)< infty$, or
alternatively the chemical potential with range $-m
we reexamine QCD axion star solutions based on the relativistic Klein-Gordon
equation (using the Ruffini-Bonazzola approach) and its non-relativistic limit,
the Gross-Pit”aevskii equation. A single free parameter, conveniently chosen
as the central value of the wave function with range $0 < Z(0)< infty$, or
alternatively the chemical potential with range $-m<mu< 0$ (where $m$ is the
axion mass), uniquely determines a spherically-symmetric ground state solution,
the axion condensate. We clarify how the interplay of various terms of the
Klein-Gordon equation determines the properties of solutions in three separate
regions: the structurally stable dilute and dense regions, and the
intermediate, structurally unstable transition region. From the Klein-Gordon
equation, one can derive alternative equations of motion including the
Gross-Pit”aevskii and Sine-Gordon equations, which have been used previously
to describe axion stars in the dense region. In this work, we clarify precisely
how and why such methods break down as the binding energy increases,
emphasizing the necessity of using the full relativistic Klein-Gordon approach.
Finally, we point out that, even after including perturbative axion number
violating corrections, solutions to the equations of motion, which assume
approximate conservation of axion number, break down completely in the strong
coupling regime where the magnitude of the chemical potential approaches the
axion mass.
