Extreme & High Synchrotron Peak $\rm \gamma$-ray Blazars beyond 4FGL: The 2BIGB $\rm \gamma$-ray catalog

We present the results of a gamma-ray likelihood analysis over all the extreme and high synchrotron peak blazars (EHSP & HSP) from the 3HSP sample. We investigate 2013 multifrequency seed positions under the eyes of Fermi Large Area Telescope, integrating over 11 years of observations. We report on 1160 gamma-ray signatures detected down to the 3$\sigma$ threshold in the energy range between 500 MeV to 500 GeV. The detections include 235 additional sources concerning 4FGL, all confirmed via high-energy TS maps, and represent an improvement of ~25% for the number of EHSP & HSP currently described in gamma-rays. We build the gamma-ray spectral energy distribution for all the 1160 sources, delivering to the very high-energy community a dedicated spectral description of the entire 3HSP population. We plot the gamma-ray logN-logS for the 3HSP sample, and also for the EHSP & HSP subsamples. We measure the total contribution of HSP+EHSP to the extragalactic gamma-ray background, which reaches up to ~33% at 100 GeV. Also, we show how does the gamma-ray detectability improves according to the synchrotron peak flux as represented by the Figure of Merit (FOM) parameter. We highlight that the search for TeV peaked blazars may benefit from considering HSP and EHSP as a whole, instead of EHSPs only. We entitle this gamma-ray database as Second Brazil-ICRANet Gamma-ray Blazar catalog, with the acronym 2BIGB. All information will be available on public data repositories (Brazilian Science Data Center-BSDC, OpenUniverse, and GitHub at https://github.com/BrunoArsioli ), including the broadband models and the spectral energy distribution data points.