Wave Cold Dark Matter Can Reproduce the Radial Acceleration Relation in X-ray Elliptical Galaxies
Abstract
Wave cold dark matter (wave CDM) is a well-motivated variant within the collisionless CDM paradigm, in which the de~Broglie wavelengths of ultralight bosons become relevant on galactic scales. While many of the previous tests of wave CDM have focused on small-scale tensions involving solitonic cores and certain soliton--halo relations in galaxies, the radial acceleration relation (RAR) provides a complementary test: for a given baryonic mass distribution, it probes whether the DM halo can reproduce the observed total gravitational field. In this work we test wave CDM against the RAR using eight X-ray elliptical galaxies from the compilation of Lelli~et~al. We perform a suite of three-dimensional Schrodinger--Poisson simulations and evolve the wave-CDM halos to virialized quasi-stationary states. For each galaxy and each adopted boson mass, we select the realization whose final snapshot most closely matches the empirical RAR. We find that the selected wave-CDM realizations for these elliptical galaxies can reproduce the RAR without including baryonic feedback or dark-matter self-interactions. At the boson mass $m_a=10^{-23} eV$, the combined fit to the eight galaxies gives $a_0=1.19 x 10^{-10} m/s^2$, consistent with the canonical value inferred from disk galaxies. When the boson mass is varied over $3 x 10^{-24} eV < m_a < 2 x 10^{-23} eV$, the best-fit value of $a_0$ changes only by ~11$, and this variation shows no systematic trend with $m_a$. This insensitivity to boson mass arises because, over the radial range relevant for the RAR, the virialized halos are supported mainly by their velocity field, whereas the boson-mass-dependent quantum-pressure term is dynamically subdominant. Consequently, different boson masses can yield similar acceleration relations despite producing different central solitonic structures. These results show that wave CDM can reproduce the RAR in elliptical galaxies, and provide a new galactic-scale test of the model beyond the previous focus on solitonic cores.