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We present the results obtained from follow-up observations of the MUSE UltraDeep Field (MUDF) at X-ray energies with XMM-Newton. The MUDF is centred on aunique field with two bright, physically associated quasars at $z\simeq3.23$,separated by $\sim$500 kpc in projection. Both quasars are embedded withinextended Ly$\alpha$ nebulae ($\gtrsim 100~\rm kpc$ at a surface brightness fluxlevel of $\approx 6\times 10^{-19} \rm erg~s^{-1}~cm^{-2}~arcsec^{-2}$), whoseelongated morphology is suggestive of an extended filament connecting thequasar haloes. The new X-ray observations presented here allow us tocharacterise the physical properties (e.g. X-ray slope, luminosities, gascolumn densities) in the innermost region of the MUDF quasars. We find thatboth quasars are X-ray underluminous compared to objects at similar ultravioletluminosities. Based on our X-ray spectral analysis, absorbing columns of$N_H(z)\gtrsim$ 10$^{23}$ cm$^{-2}$ appear unlikely, therefore such a weaknessis possibly intrinsic. When also including literature data, we do not observeany detectable trend between the area of the nebulae and nuclear luminositiesat both the rest-frame 2 keV and 2500 $\rm \mathring{A}$. The area is also notcorrelated with the X-ray photon index nor with the integrated band flux in thehard band (2$-$10 keV). We also do not find any trend between the extendedLy$\alpha$ emission of the nebulae and the nuclear X-ray luminosity. Finally,the properties of the MUDF quasars' nebulae are consistent with the observedrelation between the Ly$\alpha$ integrated luminosity of the nebulae and theirarea. Our results suggest that the quasar ionization power is not a strongdriver of the morphology and size of the nebulae.

The MUSE Ultra Deep Field (MUDF). IV. A pair of X-ray weak quasars at the heart of two extended Ly{\alpha} nebulae