Constraints on ultralight axions from compact binary systems

Ultralight particles (mₐ~10^-21--10^-22 eV) with axionlike couplings to other particles can be candidates for fuzzy dark matter (FDM) if the axion decay constant fₐ~10¹⁷ GeV. If a compact star is immersed in such a low-mass axionic potential, it develops a long-range field outside the star. This axionic field is radiated away when the star is in a binary orbit. The orbital period of a compact binary decays mainly due to the gravitational wave radiation, which was confirmed first in the Hulse-Taylor binary pulsar. The orbital period can also decay by radiation of other light particles like axions and axionlike particles (ALPs). For axionic radiation to take place, the orbital frequency of the periodic motion of the binary system should be greater than the mass of the scalar particle which can be radiated. This implies that, for most of the observed binaries, particles with mass mₐ<10^-19 eV can be radiated, which includes FDM particles. In this paper, we consider four compact binary systems---PSR J0348+0432, PSR J0737-3039, PSR J1738+0333, and PSR B1913+16 (Hulse-Taylor binary)---and show that the observations of the decay in orbital period set a bound on the axion decay constant of fₐO(10¹¹ GeV). This implies that fuzzy dark matter cannot couple to gluons.