Jeans Analysis for Dwarf Spheroidal Galaxies in Wave Dark Matter

Although still under debate, observations generally suggest that dwarf spheroidal (dSph) galaxies exhibit large constant-density cores in the centers, which can hardly be explained by dissipationless cold dark matter simulations without baryonic feedback. Wave dark matter (${\psi {\rm DM}}$), characterized by a single parameter, the dark matter particle mass $m_{\psi}$, predicts a central soliton core in every galaxy arising from quantum pressure against gravity. Here we apply Jeans analysis assuming a soliton core profile to the kinematic data of eight classical dSphs so as to constrain $m_{\psi}$, and obtain $m_{\psi}=1.18_{-0.24}^{+0.28}\times10^{-22}{\,\rm eV}$ and $m_{\psi}=1.79_{-0.33}^{+0.35}\times10^{-22}{\,\rm eV}~(2\sigma)$ using the observational data sets of Walker et al. (2007) and Walker et al. (2009b), respectively. We show that the estimate of $m_{\psi}$ is sensitive to the dSphs kinematic data sets and is robust to various models of stellar density profile. We also consider multiple stellar subpopulations in dSphs and find consistent results. This mass range of $m_{\psi}$ is in good agreement with other independent estimates, such as the high-redshift luminosity functions, the reionization history, and the Thomson optical depth to the cosmic microwave background.