tokens: to contextualize this nebula, we measured the SB Ly α profile through the standard NB images, similar to previous works ( B16 , A19 ). We computed the circularly averaged profile from the pseudo-NB image obtained by collapsing the MUSE data cube using the maximum spectral size of the 3D mask as the width, which in the case of our Ly α emission is 30 Å. We then performed an exponential fit and a power-law fit above the 2 σ noise limit, i.e., SB of ≈0.5 × 10 −18 erg s −1 cm −2 arcsec −2 , that returns a normalization parameter (at a radius of 10 pkpc) of log 10 ( C p , r 10 ) = −15.8 and a slope α of −2.4, compatible with other Ly α SB profiles obtained with MUSE. More details on the fitting process are provided in Appendix B of B16 . The red line in Figure 7 shows the circularly averaged values computed in units of SB × ((1 + z )/4) 4 with an extent of more than 100 pkpc from the QSO. We chose these units because we wanted to perform a consistent comparison of the J0952+0114 SB profile with the other Ly α systems in the literature and therefore avoid any redshift dependence and cosmological dimming effects. Figure 7 also shows the comparison with previous works as the median profile of the MUSE QSO nebulae we published in Borisova et al. 2016 (purple line, see also Appendix C ) and the best exponential fit to the QSO MUSEUM sample ( A19 , blue line). As discussed later in Section 5 , the outer parts (beyond 10 pkpc) of the J0952+0114 SB profile are very similar to what we found in other giant fluorescent nebulae around QSOs at z ≈ 3. The innermost regions are brighter due to the presence of the PDLA; however, this could reflect the difficulty of tracing the nebula into the center of typical objects (without PDLAs). Figure 7. Ly α surface brightness (SB) profile of the J0952+0114 nebula as a function of the projected physical distance from the QSO. The circularly averaged profile is plotted with the red solid line. Other Ly α SB profiles are also plotted for comparison. In particular, the median SB profile of the MUSE Ly α nebulae from B16 is shown in purple with the dashed lines marking the 10th and 90th percentiles. This median profile has been rescaled to z = 3. The best exponential fit (and its dispersion) of the SB profiles from the QSO MUSEUM is plotted with the solid blue line (light blue area, Arrigoni Battaia et al. 2019 ). 4.4. He <sc>ii</sc>/Ly<italic>α</italic> and C <sc>iv</sc>/Ly<italic>α</italic> Map Ratios Ly α λ 1216, C iv λ 1550, and He ii λ 1640 are some of the brightest rest-frame UV lines employed to better constrain the nature of ionized gas in emission. In particular, the ratios of these lines, i.e., He ii /Ly α and C iv /Ly α , are particularly useful for insights into the physical properties of the emitting gas, such as the ionization parameter, density, and metallicity (Villar-Martin et al. 1997 ; Arrigoni Battaia et al. 2015 ; Prescott et al. 2015 ; C19 and references therein). Differently from previous works, in
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