The Lyα halos around quasars provide valuable information how galaxies acquire the gas and supply it to the host galaxies and central super massive black holes (SMBHs). Previous studies have shown that, unlike z∼2−4, no correlation is found between the characteristics of Lyα halo and SMBH properties at z∼6. This is probably due to the bias of previous samples toward luminous quasars and that the Lyα photons are affected by resonance scattering, making it difficult to see the properties of the host galaxy. Therefore, larger sample containing low-luminosity quasars and better understanding of the host galaxies are needed. Also, measurements of the quasar proximity zone size have indicated that younger quasars do not have a Lyα halo. We propose deep FOCAS IFU observation of six faint quasars, whose host galaxy properties will be measured by JWST. Our main goals are (i) to study the relation between the Lyα halos and the properties of host galaxies and SMBHs, and find the primary driver of the Lyα halos (ii) to investigate quasar activity duration using the correlation between the proximity-zone size and the Lyα halo extension. Even if no correlation with host galaxies is found, it provides an important insight that the Lyα halos around quasars z∼6 is different from those of z∼3.
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