Inferring Compton-thick AGN candidates at z>2 with Chandra using the >8 keV restframe spectral curvature

To fully understand cosmic black hole growth we need to constrain the population of heavily obscured active galactic nuclei (AGN) at the peak of cosmic black hole growth ($z\sim$1-3). Sources with obscuring column densities higher than $\mathrm{10^{24}}$ atoms $\mathrm{cm^{-2}}$, called Compton-thick (CT) AGN, can be identified by excess X-ray emission at $\sim$20-30 keV, called the "Compton hump". We apply the recently developed Spectral Curvature (SC) method to high-redshift AGN (2<z<5) detected with Chandra. This method parametrizes the characteristic "Compton hump" feature cosmologically redshifted into the X-ray band at observed energies <10 keV. We find good agreement in CT AGN found using the SC method and bright sources fit using their full spectrum with X-ray spectroscopy. In the Chandra deep field south, we measure a CT fraction of $\mathrm{17^{+19}_{-11}\%}$ (3/17) for sources with observed luminosity $\mathrm{>5\times 10^{43}}$ erg $\mathrm{s^{-1}}$. In the Cosmological evolution survey (COSMOS), we find an observed CT fraction of $\mathrm{15^{+4}_{-3}\%}$ (40/272) or $\mathrm{32\pm11 \%}$ when corrected for the survey sensitivity. When comparing to low redshift AGN with similar X-ray luminosities, our results imply the CT AGN fraction is consistent with having no redshift evolution. Finally, we provide SC equations that can be used to find high-redshift CT AGN (z>1) for current (XMM-Newton) and future (eROSITA and ATHENA) X-ray missions.