## Abstract

The recent discovery of the gravitational wave source GW150914 has revealed a coalescing binary black hole (BBH) with masses of ∼30 M. Previous proposals for the origin of such a massive binary include Population III (PopIII) stars. PopIII stars are efficient producers of BBHs and of a gravitational wave background (GWB) in the 10–100 Hz band, and also of ionizing radiation in the early Universe. We quantify the relation between the amplitude of the GWB (Ωgw) and the electron scattering optical depth (τe), produced by PopIII stars, assuming that fesc ≈ 10 per cent of their ionizing radiation escapes into the intergalactic medium. We find that PopIII stars would produce a GWB that is detectable by the future O5 LIGO/Virgo if τe ≳ 0.07, consistent with the recent Planck measurement of τe = 0.055 ± 0.09. Moreover, the spectral index of the background from PopIII BBHs becomes as small as dln Ωgw/dln f ≲ 0.3 at f ≳ 30 Hz, which is significantly flatter than the value ∼2/3 generically produced by lower redshift and less-massive BBHs. A detection of the unique flattening at such low frequencies by the O5 LIGO/Virgo will indicate the existence of a high-chirp mass, high-redshift BBH population, which is consistent with the PopIII origin. A precise characterization of the spectral shape near 30–50 Hz by the Einstein Telescope could also constrain the PopIII initial mass function and star formation rate.