Some of the first calculations of the growth and overlap of cosmological H ii regions originating from quasars concluded that they could not fully account for reionization. Other radiation sources must have contributed to the photon budget . Later with z > 4 galaxy observations, it was clear that low-luminosity galaxies were the primary source of ionizing photons (e.g. [12, 23, 59]). However, Population III preceded galaxy formation, and they were the first sources of ionizing radiation, starting cosmic reionization. They are thought to have a top-heavy IMF, as discussed in the previous section, and zero-metallicity stellar models were constructed to estimate their luminosities, lifetimes, and spectra as a function of mass [64, 15, 53]. One key feature is mass-independent surface temperature of 105 K above 40 M, caused by a lack of opacity from metal lines. Thus, Population III are copious producers of ionizing photons with an average photon energy ~ 30 eV and also H2 dissociating radiation, which is < 13.6 eV where the neutral universe is optically-thin. Because the formation of Population III stars is primarily dependent on H2 formation, any H2 dissociating radiation can suppress Population III star formation from large distances [22, 38, 34, 69, 46].
3.1. H ii regions from Population III stars
Combining the main sequence properties of Population III stars and the endpoints of cosmological simulations, one-dimensional radiation hydrodynamics simulations followed the growth of an H ii region from Population III stars with masses ranging from 25 to 500 M [36, 66]. The ionization front drives a 30 km s-1 shock wave. Because the escape velocity of 106 M halos is only ~ 3 km s-1, approximately 90% of the gas is expelled from the DM halo, leaving behind a warm (T ~ 3 × 104 K) and diffuse ( ~ 0.1 cm-3) medium. At the end of the star's lifetime, a 100 M star creates an H ii region with a radius ~ 3 kpc.
Shortly afterward, it became feasible to include radiative transfer in cosmological simulations, either through moment methods or ray tracing. In three dimensions, it is possible to investigate the ionization of a clumpy and inhomogeneous medium and any ionization front instabilities  that might arise.  found that between 70% and 90% of the ionizing photons escaped into the IGM, using ionization front tracking and an approximate method to calculate the thermodynamic state behind the front. This calculation also showed that some nearby halos are not fully photo-evaporated, leaving behind a neutral core. Furthermore, nearby filamentary structure is slower to ionize, and the ionization front grows faster in the voids, creating a "butterfly" shape . The first three-dimensional radiation hydrodynamics simulations uncovered multi-fold complexities that were not seen in previous simulations, such as cometary structures and elephant trunks seen in nearby star forming regions . Figure 1 shows the growth of the H ii region emanating from the host minihalo. The density structures in the nearby filaments were largely unaffected by the radiation because they are self-shielded. The 30 km s-1 shock wave collects 105 M of gas into a shell over the lifetime of the star, which is Jeans stable and is dispersed after the star's death.
Figure 1. The formation of a H ii region from a Population III star, shown with projections of gas density (top) and temperature (bottom) of a ~ 3 proper kpc region, centered on the first star at z = 20. From left to right, the depicted times correspond to 0, 1, 2.7, and 8 Myr after the star formed. The insets correspond to the same times, have the same color scale, and show the central 150 pc. From .
As the H ii region grows up to 3 kpc in radius, nearby halos become engulfed in a sea of ionized gas. Because free electrons are the catalyst for H2 formation, a boosted electron fraction promotes more efficient cooling; furthermore, HD cooling becomes relevant in the collapse of these halos in relic H ii regions [44, 75, 76, 41]. Instead being limited to a 300 K temperature floor, this gas cools to ~ 50 K, resulting in a Jeans mass a factor of ~ 5/2 lower. Thus, it is expected that these Population III stars will have a lower characteristic mass in the approximate range of 5-60 M. After this discovery, it was felt that these two different population needed to be separated, where metal-free stars forming in an unaffected region are termed "Population III.1", and metal-free stars forming in ionized gas were coined "Population III.2" .
3.2. Contribution to reionization
The H ii regions from metal-free stars are much larger than present-day H ii regions and can have a sizable impact on the reionization history.  found that Population III stars can ionize up to 25% of the local IGM in a biased region, surrounding a rare 3- overdensity. Because Population III stars are short lived (~ 3 Myr), the H ii regions are fully ionized only for a short time and then quickly recombines over the next ~ 50 Myr. Within a local cosmological region, there are many relic H ii regions but only a handful of active H ii regions with T > 104 K. Once the H ii regions start to overlap, each star can ionize a larger volume as the neutral hydrogen column density decreases. At the end of the simulation, one in ten ionizing photons results in a sustained ionization in the intergalactic medium (IGM). In addition to ionizing the IGM, the photo-heating of the host halo and IGM delays further local star formation by smoothing out gas overdensities in nearby minihalos and IGM, which is depicted in Figure 2. Reducing the IGM clumpiness reduces the recombination rate, which is measured by the clumping factor C = < >2 / < 2 >, by 50% .
Figure 2. The effects of radiative feedback from the first stars, shown in projections of gas density (left) and temperature (right) in a field of view of 8.5 proper kpc in a region heated and ionized by tens of Population III stars at z = 16. Notice how most of the nearby substructures are photo-evaporated. From .
This simulation only considered a small region (1 comoving Mpc3) and cannot make predictions for global reionization history. To address cosmic reionization, simulations with sizes ~ 100 Mpc are necessary. Here the small-scale clumpiness cannot be resolved, and clumping factor plays a key role in subgrid models. In general, H ii regions from Population III stars generate more small-scale power, and at late times, they are quickly overrun by nearby H ii regions produced by larger galaxies . In addition, Population III H ii regions start reionization earlier and prolongs reionization .