X-rays from binaries in small , metal-deficient galaxies may have contributed significantly to the heating and reionization of the early universe .
We investigate this claim by studying blue compact dwarfs ( BCDs ) as local analogues to these early galaxies .
We constrain the relation of the X-ray luminosity function ( XLF ) to the star-formation rate ( SFR ) using a Bayesian approach applied to a sample of 25 BCDs .
The functional form of the XLF is fixed to that found for near-solar metallicity galaxies and is used to find the probability distribution of the normalisation that relates X-ray luminosity to SFR .
Our results suggest that the XLF normalisation for low metallicity BCDs ( 12+log ( O/H ) < 7.7 ) is not consistent with the XLF normalisation for galaxies with near solar metallicities , at a confidence level 1 - 5 \times 10 ^ { -6 } .
The XLF normalisation for the BCDs is found to be 14.5 \pm 4.8 ( M _ { \odot } ^ { -1 } \text { yr } ) , a factor of 9.7 \pm 3.2 higher than for near solar metallicity galaxies .
Simultaneous determination of the XLF normalisation and power law index result in estimates of q = 21.2 ^ { +12.2 } _ { -8.8 } ( M _ { \odot } ^ { -1 } \text { yr } ) and \alpha = 1.89 ^ { +0.41 } _ { -0.30 } , respectively .
Our results suggest a significant enhancement in the population of high-mass X-ray binaries in BCDs compared to the near-solar metallicity galaxies .
This suggests that X-ray binaries could have been a significant source of heating in the early universe .