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Roles of the kinetic and dynamic mechanisms in the $L_p - E_p$ relation

The $L_p - E_p$ relation is a well-known relation in gamma-ray bursts. Its implication remains unclear. We propose to investigate the underlying mechanisms of this relation by considering the corresponding kinetic and dynamic mechanisms separately. In this way, one can tell how much the kinetic or dynamic mechanism contributes to the index of the relationship. Our analysis gives rise to several conclusions. (1) The index of the kinetic effect in the $L_p - E_p$ relation can simply be derived from the theory of special relativity, which is generally larger than 2, depending on the situation concerned. (2) The index of the dynamic effect in the relation can be deduced from observation once a model of jets is adopted. According to current GRB data, we find: the dynamic effect alone tends to make an anti-correlation between $L_p$ and $E_p$; in terms of statistics, the dynamic effect is obviously smaller than the kinetic effect; in the situation of jets with moving discrete radio clouds which moves directly towards the observer, the index of the dynamic effect is currently constrained within $(-1.6, -1)$, while in other situations of jets, the constrains are different; both internal and external shocks can account for the current data.