Recent experiments have introduced a new concept for analyzing the photoemi
ssion spectra of correlated electrons-the remnant Fermi surface (rFs), whic
h can be measured even in systems which lack a conventional Fermi surface.
Here, we analyze the rFs in a number of interacting electron models, and fi
nd that the results fall into two classes. For systems with particle-partic
le (pairing) instabilities, the rFs is an accurate replica of the true Ferm
i surface. In the presence of particle-hole (nesting) instabilities, the rF
s is a map of the resulting superlattice Brillouin zone. The results sugges
t that the gap in Ca2CuO2Cl2 is of particle-hole origin.