Peak energy of the prompt emission of long gamma-ray bursts versus their fluence and peak flux

The spectral-energy (and luminosity) correlations in long gamma-ray bursts are being hotly debated to establish, first of all, their reality against possible selection effects. These are best studied in the observer planes, namely the peak energy E-peak(obs) versus the fluence F or the peak flux P. In a recent paper, we have started to investigate this problem considering all bursts with known redshift and spectral properties. Here, we consider instead all bursts with known E-peak(obs), irrespective of redshift, adding to those a sample of 100 faint BATSE bursts representative of a larger population of 1000 objects. This allows us to construct a complete, fluence-limited, sample, tailored to study the selection/instrumental effects we consider. We found that the fainter BATSE bursts have smaller E-peak(obs) than those of bright events. As a consequence, the E-peak(obs) of these bursts is correlated with the fluence, though with a slope flatter than that defined by bursts with z. Selection effects, which are present, are shown not to be responsible for the existence of such a correlation. About six per cent of these bursts are surely outliers of the E-peak-E-iso correlation (updated in this paper to include 83 bursts), since they are inconsistent with it for any redshift. E-peak(obs) also correlates with the peak flux, with a slope similar to the E-peak-L-iso correlation. In this case, there is only one sure outlier. The scatter of the E-peak(obs) P correlation defined by the BATSE bursts of our sample is significantly smaller than the E-peak(obs)-F correlation of the same bursts, while for the bursts with known redshift the E-peak-E-iso correlation is tighter than the E-peak-L-iso one. Once a very large number of bursts with E-peak(obs) and redshift will be available, we thus expect that the E-peak-L-iso correlation will be similar to that currently found, whereas it is very likely that the E-peak-E-iso correlation will become flatter and with a larger scatter.