Wave dark matter ($\psi \rm{ DM}$) composed of extremely light bosons ($m_{ \psi} \sim 10^{ -22}\,\rm eV$), with quantum pressure suppressing structures below a kpc-scale de Broglie wavelength, has become a viable dark matter candidate. Compared to the conventional free-particle $\psi { \rm DM}$ (${ \rm FP} \psi { \rm DM}$), the extreme-axion $\psi \rm{ DM}$ model (${ \rm EA} \psi { \rm DM}$) proposed by Zhang & Chiueh (2017) features a larger cut-off wavenumber and a broad spectral bump in the matter transfer function. Here we conduct cosmological simulations to compare the halo abundances and assembly histories at $z=4-11$ between three different scenarios: ${ \rm FP} \psi { \rm DM}$, ${ \rm EA} \psi { \rm DM}$, and cold dark matter (CDM). We show that ${ \rm EA} \psi { \rm DM}$ produces significantly more abundant low-mass haloes than ${ \rm FP} \psi { \rm DM}$ with the same $m_{ \psi}$, and therefore could alleviate the tension in $m_{ \psi}$ required by the Ly$\alpha$ forest data and by the kpc-scale dwarf galaxy cores. We also find that, compared to the CDM counterparts, massive ${ \rm EA} \psi { \rm DM}$ haloes are on average $3-4$ times more massive at $z=10-11$ due to their earlier formation, undergo a slower mass accretion at $7 \lesssim z \lesssim 11$, and then show a rapidly rising major merger rate exceeding CDM by $\sim 50\%$ at $4 \lesssim z \lesssim 7$. This fact suggests that ${ \rm EA} \psi { \rm DM}$ haloes may exhibit more prominent starbursts at $z \lesssim 7$.
Categories: astro-ph.CO astro-ph.GA