Spitzer-selected z > 1.3 protocluster candidates in the LSST Deep Drilling Fields

We have identified 189 candidate z > 1.3 protoclusters and clusters in the LSST Deep Drilling Fields. This sample will enable the measurement of the metal enrichment and star formation history of clusters during their early assembly period through the direct measurement of the rate of supernovae identified through the LSST. The protocluster sample was selected from galaxy overdensities in a Spitzer/IRAC colour-selected sample using criteria that were optimized for protocluster purity using a realistic light-cone. Our tests reveal that $60\!-\!80~{{\ \rm per\ cent}}$ of the identified candidates are likely to be genuine protoclusters or clusters, which is corroborated by a ~4σ stacked X-ray signal from these structures. We provide photometric redshift estimates for 47 candidates which exhibit strong peaks in the photo-z distribution of their candidate members. However, the lack of a photo-z peak does not mean a candidate is not genuine, since we find a stacked X-ray signal of similar significance from both the candidates that exhibit photo-z peaks and those that do not. Tests on the light-cone reveal that our pursuit of a pure sample of protoclusters results in that sample being highly incomplete ($\sim 4~{{\ \rm per\ cent}}$) and heavily biased towards larger, richer, more massive, and more centrally concentrated protoclusters than the total protocluster population. Most ($\sim 75~{{\ \rm per\ cent}}$) of the selected protoclusters are likely to have a maximum collapsed halo mass of between 10¹³ and 10¹⁴ M_⊙, with only $\sim 25~{{\ \rm per\ cent}}$ likely to be collapsed clusters above 10¹⁴ M_⊙. However, the aforementioned bias ensures our sample is $\sim 50~{{\ \rm per\ cent}}$ complete for structures that have already collapsed into clusters more massive than 10¹⁴ M_⊙.