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Observations of local star‐forming galaxies have revealed a correlation between the rate at which galaxies form stars and their X‐ray luminosity. We combine this correlation with the most recent observational constraints on the integrated star formation rate (SFR) density and find that star‐forming galaxies account for 5–20 per cent of the total soft and hard X‐ray backgrounds, where the precise number depends on the energy band and the assumed average X‐ray spectral energy distribution of the galaxies below ∼20 keV. If we combine the  L  X –SFR relation with recently derived SFR function, then we find that star‐forming galaxies whose X‐ray flux falls well (more than a factor of 10) below the detection thresholds of the  Chandra Deep Fields  can fully account for the unresolved soft X‐ray background, which corresponds to ∼6 per cent of its total. Motivated by this result, we put limits on the allowed redshift evolution of the parameter  c  X ≡ L  X /SFR and/or its evolution towards lower and higher SFRs. If we parametrize the redshift evolution of  c  X  ∝ (1 + z )  b  , then we find that  b ≤ 1.3 (95 per cent confidence level). On the other hand, the observed X‐ray luminosity functions of star‐forming galaxies indicate that  c  X  may be increasing towards higher redshifts and/or higher SFRs at levels that are consistent with the X‐ray background, but possibly at odds with the locally observed  L  X –SFR relation.

Constraints on the redshift evolution of the L X –SFR relation from the cosmic X‐ray backgrounds