Three Subclasses of the Intensity-tracking Pattern in Gamma-Ray Burst Spectral Evolution

The properties of the spectral evolution during the prompt emission phase of gamma-ray bursts (GRBs), which are closely related to the radiation mechanism (synchrotron or photosphere), are still a subject of debate. Two spectral evolution patterns (``hard-to-soft'' and ``intensity-tracking'') have been commonly observed in GRB prompt emission spectra. Here we present a well-defined sample of 20 single-pulse GRBs detected by \emph{Fermi} whose prompt emission spectra exhibit the intensity-tracking pattern. By performing a time-resolved spectral analysis, we derive $E_{\rm p}$ and the energy flux $F$ from the same time bins and introduce a matched-bin lag, $t_{\rm lag}^{\rm F} \equiv t_{\rm p}(E_{\rm p})-t_{\rm p}(F)$, where $t_{\rm p}$ denotes the time at which each quantity reaches its maximum. We find that the intensity-tracking pattern subdivides into three distinct subclasses: Type I (5/20), with aligned $E_{\rm p}$ and flux peaks; Type II (13/20), with $E_{\rm p}$ peaking before the flux; and Type III (2/20), with $E_{\rm p}$ peaking after the flux. The early-peaking Type~II subclass dominates the sample. The subclasses also exhibit systematic differences in their spectral and temporal properties. Type II bursts are systematically harder than Type I, show broader flux pulses, and more often display asymmetric rising and decaying $E_{\rm p}$-$F$ branches. Type I is consistent with tightly coupled spectral and power evolution, whereas Type II is more naturally explained by nonthermal or hybrid prompt-emission scenarios in which spectral hardening precedes the peak radiative output. Type III appears to form a rare positive-lag tail whose physical origin remains uncertain.