If the dark matter particles are axions, gravity can cause them to coalesce into axion stars, which are stable gravitationally bound systems of axions. In the previously known solutions for axion stars, gravity and the attractive force between pairs of axions are balanced by the kinetic pressure. The mass of these dilute axion stars cannot exceed a critical mass, which is about 10 −14 M if the axion mass is 10 −4 eV. We study axion stars using a simple approximation to the effective potential of the nonrelativistic effective field theory for axions. We find a new branch of dense axion stars in which gravity is balanced by the mean-field pressure of the axion Bose-Einstein condensate. The mass on this branch ranges from about 10 −20 M to about M . If a dilute axion star with the critical mass accretes additional axions and collapses, it could produce a bosenova, leaving a dense axion star as the remnant.

Axions can be described by a relativistic field theory with a real scalar field φ whose selfinteraction potential is a periodic function of φ. Low-energy axions, such as those produced in the early universe by the vacuum misalignment mechanism, can be described more simply by a nonrelativistic effective field theory with a complex scalar field ψ whose effective potential is a function of ψ * ψ. We determine the coefficients in the expansion of the effective potential to fifth order in ψ * ψ by matching low-energy axion scattering amplitudes. In order to describe a BoseEinstein condensate of axions that is too dense to truncate the expansion of the effective potential in powers of ψ * ψ, we develop a sequence of systematically improvable approximations to the effective potential that resum terms of all orders in ψ * ψ.

The number of nonrelativistic axions can be changed by inelastic reactions that produce photons or relativistic axions. Any odd number of axions can annihilate into two photons. Any even number of nonrelativistic axions can scatter into two relativistic axions. We calculate the rate at which axions are lost from axion stars from these inelastic reactions. In dilute systems of axions, the dominant inelastic reaction is axion decay into two photons. In sufficiently dense systems of axions, the dominant inelastic reaction is the scattering of four nonrelativistic axions into two relativistic axions. The scattering of odd numbers of axions into two photons produces monochromatic radiofrequency signals at odd-integer harmonics of the fundamental frequency set by the axion mass. This provides a unique signature for dense systems of axions, such as a dense axion star or a collapsing dilute axion star.

A classical nonrelativistic effective field theory for a real Lorentz-scalar field φ is most conveniently formulated in terms of a complex scalar field ψ. There have been two derivations of effective Lagrangians for the complex field ψ in which terms in the effective potential were determined to order (ψ * ψ) 4 . We point out an error in each of the effective Lagrangians. After correcting the errors, we demonstrate the equivalence of the two effective Lagrangians by verifying that they both reproduce T -matrix elements of the relativistic real scalar field theory and by also constructing a redefinition of the complex field ψ that transforms terms in one effective Lagrangian into the corresponding terms of the other.