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Ultralight axion like particles (ALPs) of mass $m_a\in(10^{-21}\rm{eV}-10^{-22}\rm{eV})$ with axion decay constant $f_a\sim10^{17}\rm{GeV}$ can be candidates for fuzzy dark matter (FDM). If celestialbodies like Earth and Sun are immersed in a low mass axionic FDM potential andif the ALPs have coupling with nucleons then the coherent oscillation of theaxionic field results a long range axion hair outside of the celestial bodies.The range of the axion mediated Yukawa type fifth force is determined by thedistance between the Earth and the Sun which fixes the upper bound of the massof axion as $m_a\lesssim10^{-18}\rm{eV}$. The long range axionic Yukawapotential between the Earth and Sun changes the gravitational potential betweenthem and contribute to the light bending and the Shapiro time delay. From theobservational uncertainties of those experiments, we put an upper bound on theaxion decay constant as $f_a\lesssim 9.85\times 10^{6}\rm{GeV}$, which is thestronger bound obtained from Shapiro time delay. This implies if ALPs are FDM,then they do not couple to nucleons.

Constraints on axionic fuzzy dark matter from light bending and Shapiro time delay