Subaru High-$z$ Exploration of Low-Luminosity Quasars (SHELLQs). XXIII. The powering mechanisms of the Ly$α$ haloes around high-$z$ quasars probed by slit spectroscopy

We present the analysis of Ly$α$ haloes around faint quasars at $z\sim4$ and $z\sim6$. We use 20 and 162 quasars at $z\sim4$ and $z\sim6$, taken by slit spectroscopy, and detect Ly$α$ haloes around 12 and 26 of these quasars, respectively. The average absolute magnitudes of the detected quasars are $\langle M_{1450} \rangle = -23.84$ mag at $z\sim4$ and $\langle M_{1450} \rangle = -23.68$ mag at $z\sim6$, which are comparable at $z\sim4$ and 3 mag fainter at $z\sim6$ than those of previous studies. The median surface brightness profiles are found to be consistent with an exponential curve, showing a hint of flattening within a radius of 5 kpc. The Ly$α$ haloes around these faint quasars are systematically fainter than those around bright quasars in the previous studies. We confirm the previous results that the Ly$α$ halo luminosity depends on both the ionizing and Ly$α$ peak luminosities of quasars at $z\sim4$, and also find that a similar correlation holds even at $z\sim6$. While the observed Ly$α$ halo luminosity is overall attributed to recombination emission from the optically thin gas clouds in the CGM, its luminosity dependences can be consistently explained by the partial contributions of recombination radiation from the optically thick clouds, which is thought to originate from the CGM centre, and the scattered Ly$α$ photons, which is resonantly trapped at the CGM centre and escaping outside of the haloes.