Seeking the growth of the first black hole seeds with JWST

In this paper we provide predictions for the BH population that would be observable with planned JWST surveys at $5 \le z \le 15$. We base our study on the recently developed Cosmic Archaeology Tool (CAT), which allows us to model BH seeds formation and growth, while being consistent with the general population of AGNs and galaxies observed at $4 \le z \le 7$. We find that JWST planned surveys will provide a complementary view on active BHs at $z > 5$, with JADES-Medium/-Deep being capable of detecting the numerous BHs that populate the faint-end of the distribution, COSMOS-Web sampling a large enough area to detect the rarest brightest systems, and CEERS/PRIMER bridging the gap between these two regimes. The relatively small field of view of the above surveys preferentially selects BHs with masses $6 \leq {\rm Log} (M_{\rm BH}/M_\odot) < 8$ at $7 \le z < 10$, residing in relatively metal poor (${\rm Log} (Z/Z_\odot) \ge -2$) and massive ($8\leq {\rm Log} (M_*/M_\odot) < 10$) galaxies. At $z \ge 10$, only JADES-Deep will have the sensitivity to detect growing BHs with masses $4 \leq {\rm Log} (M_{\rm BH}/M_\odot) < 6$, hosted by more metal poor ($-3 \leq {\rm Log} (Z/Z_\odot) < -2$) and less massive ($6 \leq {\rm Log} (M_*/M_\odot) < 8$) galaxies. In our model, the latter population corresponds to heavy BH seeds formed by the direct collapse of super-massive stars in their earliest phases of mass growth. Detecting these systems would provide invaluable insights on the nature and early growth of the first BH seeds.