tokens: i.e. brighter quasars may live in a region of higher overdensities (e.g. see Guimarães et al. 2007 , and references therein). In order to check this effect, we devised a subsample of low and high luminosity. In the low- and high-luminosity bins, we have taken 25 lowest and 25 highest (∼29 per cent of the total sample) luminosity quasars of our sample. As can be seen from Fig. 7 , the excess pixel optical depth ratio is more pronounced for the subsample of higher luminosity with log L 912 > = 31.85 ergs s −1 Hz −1 as compared to the subsample of lower luminosity with log L 912 > = 31.12 ergs s −1 Hz −1 . The integrated value under the curve (e.g. see Fig. 7 ) between −6 ≤ r ≤ 0 Mpc is found to be higher by a factor of 3.70 ± 0.22 and 1.62 ± 0.15 w.r.t. the corresponding integrated value of curve for high- and low-luminosity subsamples, respectively. However, we do notice that higher luminosity bin has a higher median redshift of z em > = 4.06 in comparison to z em > = 3.85 for the lower luminosity bin (e.g. see grey shade). However, the above R τ ( r ) difference, especially in the −2 ≤ r ≤ 0 Mpc bins, cannot be merely explained by the redshift difference in these two subsamples. Figure 7. Left-hand panel : Same as right-hand panel of Fig. 6 , but for the extreme 25 low- and 25 high-luminosity quasars in our sample (e.g. see text in Section 4 ). The Lyman continuum luminosity was calculated using V -band magnitude (e.g. see Section 2.1 .) Right-hand panel : The plot shows radius versus flux (similar to Fig. 4 ) for the transmitted flux of the subsample of extreme 25 low- and 25 high-luminosity quasars. The transmitted flux of the control sample of IGM for the higher luminosity and lower luminosity quasars is shown in red-dashed and blue dot–dashed lines, respectively. Additionally, we also used our sample to check for any difference of density profile among radio-loud (RL) and radio-quiet (RQ) quasars (e.g. see Sopp Alexander 1991 ; Dunlop et al. 2003 ; Gopal-Krishna, Mangalam Wiita 2008 ; Retana-Montenegro Röttgering 2017 ) where the former is generally associated with the presence of jets. Such bimodality is quantified by a radio-loudness parameter ( i.e. ) defined as a ratio between the rest-frame flux densities at 5 GHz and 2500 Å (see also Ivezić et al. 2002 ; Kellermann et al. 2016 , and references therein), with its value ≥ 23 for RL sources as adopted by Ganguly et al. ( 2013 ). Out of the 85 quasars in our sample, 62 have information about its radio-loudness parameter with 12 being RL (i.e. 23) quasars and 50 being RQ (i.e. ) quasars (e.g. see Perrotta et al. 2016 ). We plot R τ ( r ) for these two sub-samples (i.e. RL and RQ quasars) as shown in Fig. 8 . From this figure, it is evident that their R τ ( r ) profile is quite similar in both sub-samples, though the sample size of RL quasars is small here (12 quasars). Here, we also note that the typical luminosity (median) among these two sub-samples is almost similar being 2.23 × 10 31
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