  Ultralight-axion (ULA) dark matter is one of the possible solutions to
resolve small-scale problems, especially the core-cusp problem. This is because
ULA dark matter can create a central soliton core in all dark matter haloes
stemmed from the quantum pressure against gravity below the de Broglie
wavelength, which becomes manifest on astrophysical scales with axion mass
range $\sim10^{-22}$ eV. In this work, we apply our non-spherical dynamical
models to the kinematic data of eight classical dwarf spheroidals (dSphs) to
obtain more reliable and realistic limits on ULA particle mass. This is
motivated by the reasons that the light distributions of the dSphs are not
spherical, nor are the shapes of dark matter haloes predicted by ULA dark
matter simulations. Compared with the previous studies on ULA dark matter
assuming spherical mass models, our result is less stringent than those
constraints due to the uncertainties on non-sphericity. On the other hand,
remarkably, we find that the dSphs would prefer to have a flattened dark matter
halo rather than a spherical one, especially Draco favours a strongly elongated
dark matter halo caused naively by the assumption of a soliton-core profile.
Moreover, our consequent non-spherical core profiles are much more flattened
than numerical predictions based on ULA dark matter, even though there are
still uncertainties on the estimation of dark matter halo structure. To
alleviate this discrepancy, further understanding of baryonic and/or ULA dark
matter physics on small mass scales might be needed.
