Gravitational wave background from Population III binary black holes consistent with cosmic reionization

The recent discovery of the gravitational wave source GW150914 has revealed a coalescing binary black hole (BBH) with masses of similar to 30 M-circle dot. 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 (Omega(gw)) and the electron scattering optical depth (tau(e)), produced by PopIII stars, assuming that f(esc) approximate to 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 tau(e) greater than or similar to 0.07, consistent with the recent Planck measurement of tau(e) = 0.055 +/- 0.09. Moreover, the spectral index of the background from PopIII BBHs becomes as small as d ln Omega(gw)/d ln f less than or similar to 0.3 at f greater than or similar to 30 Hz, which is significantly flatter than the value similar to 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.