We explore X-ray emission from a sample of 18 He II 1640 emitting star-forming galaxies at z ~ 2.3-3.6 from the VANDELS survey in the Chandra Deep Field South, to set constraints on the role of X-ray sources in powering the He II emission. We find that 4 He II emitters have tentative detections with S/N ~ 2 and have X-ray luminosities, L_X = 1.5-4.9 x 10^41 erg/s. The stacked luminosity of all 18 He II emitters is 2.6 x 10^41 erg/s, and that of a subset of 13 narrow He II emitters (FHWM(He II) < 1000 km/s) is 3.1 x 10^41 erg/s. We also measure stacked L_X for non-He II emitters through bootstrapping of matched samples, and find L_X = 2.5 x 10^41 erg/s, which is not significantly different from L_X measured for He II emitters. The L_X per star-formation rate for He II emitters (log (L_X/SFR) ~ 40.0) and non-emitters (log (L_X/SFR) ~ 39.9) are also comparable and in line with the redshift evolution and metallicity dependence predicted by models. Due to the non-significant difference between the X-ray emission from galaxies with and without He II, we conclude that X-ray binaries or weak or obscured AGNs are unlikely to be the dominant producers of He II ionising photons in VANDELS star-forming galaxies at z ~ 3. Given the comparable physical properties of both He II emitters and non-emitters reported previously, alternative He II ionising mechanisms such as localised low-metallicity stellar populations, Pop-III stars, etc. may need to be explored.
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