  About 2100 star-forming galaxy protocluster candidates at z=1-4 were
identified at sub-mm wavelengths in the Planck all sky survey. Follow-up
spectroscopic observations of a few candidates have confirmed the presence of
actual galaxy overdensities with large star-formation rates. In this work, we
use state-of-the-art hydrodynamical simulations to investigate whether the
Planck high-z sub-mm sources are progenitors of massive clusters at z=0. To
match the PHz sources with simulated halos, we select the most star-forming
halos from z = 3 to z =1.3 in the TNG300 simulation. The total star formation
rate (SFR) of the simulated protocluster candidates is computed from the SFR of
all the galaxies within an aperture corresponding to the Planck beam size,
including those along the line-of-sight. The simulations reproduce the Planck
derived SFRs as the sum of both, the SFR of at least one of the most SF high-z
halo, and the average contribution from SF sources along the line-of-sight.
Focusing on the spectroscopically confirmed PHz protoclusters, we compare the
observed properties of their galaxy members with those in the most SF simulated
halos. We find a good agreement in the stellar mass and SFR distributions, and
in the galaxy number counts, but the SFR-stellar mass relation of the simulated
galaxies tends to be shifted to lower SFRs with respect to the observed one.
Based on the estimated final masses of the simulated halos, we infer that
between 63% and 72% of the Planck selected protoclusters will evolve into
massive galaxy clusters at z=0. Despite contamination from star-forming
galaxies along the line of sight, we confirm the efficiency of Planck to select
star-forming protoclusters at Cosmic Noon with the simulations, and provide a
new criterion for selecting the most massive cluster progenitors at high-z,
using observables like the number of galaxy members and their SFR distribution.
