2025ApJ...988..117L

The E_p,i-L_iso correlation of long gamma-ray bursts (LGRBs) is regarded as a fundamental correlation for standardizing LGRBs to probe cosmology and constrain LGRB physics. However, this correlation may be affected by potential selection effects, which are likely overlooked in the current small LGRB redshift sample. In this work, we simulate a large LGRB sample that reflects the observed situation, aiming to study the impact of peak flux P on the observed LGRB E_p,i-L_iso correlation. We find that the overall E_p,i and L_iso distribution, which will directly affect the best-fit result of the correlation, is significantly dependent on the value of P. This indicates that the impact of peak flux selection should be carefully considered in the studies and applications of the E_p,i-L_iso correlation. Notably, we show that our simulated data can reproduce the observed P distribution only if some dependence between E_p,i and L_iso is included in the simulation. This is an indication that the E_p,i-L_iso connection is a crucial property of LGRBs. We also find that GRBs with high peak flux in the low-E_p,i and L_iso region are not the straightforward extrapolation of the GRB population in the higher-E_p,i and L_iso region. Selecting four bursts with L_iso ≤ 10⁵⁰ erg s^–1, E_p,i ≤ 10^2.5 keV, and P ≥ 10^0.5 ph cm^–2 s^–1, we find two bursts, GRB 060614 and GRB 191019A, which may not be associated with the theoretical massive-star origin of LGRBs. This suggests that combining P with the position in the E_p,i-L_iso diagram may be used to indicate alternative LGRB origins.