Thermal Components in Gamma-ray Bursts. II. Constraining the Hybrid Jet Model

A more general picture in explaining the origin of the jet composition of gamma-ray bursts (GRBs), namely, the hybrid jet model (introduced another magnetization parameter $\sigma_{0}$ on the basis of the traditional fireball model), has been well studied in \cite{2015ApJ...801..103G}, but still has not applied to a large GRB sample. Here, we first employ the "top-down" approach in \cite{2015ApJ...801..103G} to diagnose the properties at central engine to see how the hybrid model can account for the observed data as well, using a full {\it Fermi} GRB sample (8 bursts) with the detected photosphere component, as presented in \cite{2019arXiv190502340L} (our Paper I). We derive all physical parameters for a hybrid problem with three typical $r_{0}$ values ($r_{0}$=10$^{7}$ cm, 10$^{8}$ cm, and 10$^{9}$ cm). We find the dimensionless entropy $\eta \gg$ 1 for all the cases while (1+$\sigma_{0}$) $>$1 for 5 bursts (GRB 081224, GRB 110721A, GRB 090719, GRB 100707, and GRB 100724), which indicate that in addition to a hot fireball component, another a cold Poynting-flux component may also play an important role. Other 3 bursts (GRB 190114C, GRB 090902B, and GRB 160107) for (1+$\sigma_{0}$) $>$1 show $r_{0}$-dependent behavior. Our analysis also shows that a few time bins for all $r_{0}$ in GRB 081224 and GRB 110721A, the magnetization parameter at $\sim$10$^{15}$cm (1+$\sigma_{\rm r15}$) greater than unity, which indicates non-thermal radiation mechanism for these bursts may be ICMART event rather than internal shocks. Other GRBs either exhibit $r_{0}$-dependent characteristic (GRB 090719, GRB 100707, GRB 100724B, and GRB 160107), or no time bin (GRB 190114C and GRB 090902B) satisfy (1+$\sigma_{\rm r15}$) $>$1. We conclude that a majority of bursts (probably all) can be well interpreted by the hybrid jet problem, and our analysis opens up a new window to understand the jet composition of GRBs.