A broken "$\alpha$-intensity" relation caused by the evolving photosphere emission and the nature of the extraordinarily bright GRB 230307A

GRB 230307A is one of the brightest gamma-ray bursts detected so far. With the excellent observation of GRB 230307A by Fermi-GBM, we can reveal the details of prompt emission evolution. As found in high-time-resolution spectral analysis, the early low-energy spectral indices ($\alpha$) of this burst exceed the limit of synchrotron radiation ($\alpha =-2\mathrm{/}3$), and gradually decreases with the energy flux ($F$). A tight $E_{\mathrm{p}}\propto F^{0.54}$ correlation anyhow holds within the whole duration of the burst, where $E_{\mathrm{p}}$ is the spectral peak energy. Such evolution pattern of $\alpha$ and $E_{\mathrm{p}}$ with intensity is called double tracking". For the $α-F$ relation, we find a log Bayes factor $\sim$ 210 in favor of a smoothly broken power-law function over a linear function in log-linear space. We call this particular $α-F$ relation as broken $\alpha$-intensity", and interpret it as the evolution of the ratio of thermal and non-thermal components, which is also the evolution of the photosphere. GRB 230307A with a duration of $\sim 35\mathrm{s}$, if indeed at a redshift of $z=0.065$, is likely a neutron star merger event (i.e., it is intrinsically ``short"). Intriguingly, different from GRB 060614 and GRB 211211A, this long event is not composed of a hard spike followed by a soft tail, suggesting that the properties of the prompt emission light curves are not a good tracer of the astrophysical origins of the bursts. The other possibility of $z=3.87$ would point toward very peculiar nature of both GRB 230307A and its late time thermal-like emission.