Limits on Population III star formation in minihaloes implied by Planck

Recently, Planck measured a value of the cosmic microwave background (CMB) optical depth due to electron scattering of $\tau=0.066 \pm 0.016$. Here we show that this low value leaves essentially no room for an early partial reionisation of the intergalactic medium (IGM) by high-redshift Population III (Pop III) stars, expected to have formed in low-mass minihaloes. We perform semi-analytic calculations of reionisation which include the contribution from Pop II stars in atomic cooling haloes, calibrated with high-redshift galaxy observations, and Pop III stars in minihaloes with feedback due to Lyman-Werner (LW) radiation and metal enrichment. We find that without LW feedback or prompt metal enrichment (and assuming a minihalo escape fraction of 0.5) the Pop III star formation efficiency cannot exceed $\sim{\rm a~few}\times 10^{-4}$, without violating the constraints set by Planck data. This excludes massive Pop III star formation in typical $10^6 M_\odot$ minihaloes. Including LW feedback and metal enrichment alleviates this tension, allowing large Pop III stars to form early on before they are quenched by feedback. We find that the total density of Pop III stars formed across cosmic time is $\lesssim 10^{4-5}~M_\odot~{\rm Mpc^{-3}}$ and does not depend strongly on the feedback prescription adopted. Additionally, we perform a simple estimate of the possible impact on reionisation of X-rays produced by accretion onto black hole remnants of Pop III stars. We find that unless the accretion duty cycle is very low ($\lesssim 0.01$), this could lead to an optical depth inconsistent with Planck.