  The properties of pre-eruptive structures and coronal mass ejections (CMEs)
are characterized by those of their footpoints, the latter of which thus
attract great interest. However, how to identify the footpoints of pre-eruptive
structures and how to identify the footpoints with ground-based instruments,
still remain elusive. In this work, we study an arc-shaped structure intruding
in the sunspot umbra. It is located close to the (pre-)eruptive flux rope
footpoint and is thus expected to help identify the footpoint. We analyse this
arc-shaped structure, which we name as "sunspot scar", in a CME event on 2012
July 12 and in two CME events in observationally-inspired MHD simulations
performed by OHM and MPI-AMRVAC. The sunspot scar has a more inclined magnetic
field with a weaker vertical component and a stronger horizontal component
relative to that in the surrounding umbra and manifests as a light bridge in
the white light passband. The hot field lines anchored in the sunspot scar are
spatially at the transition between the flux rope and the background coronal
loops, and temporally in the process of the slipping reconnection which builds
up the flux rope. The sunspot scar and its related light bridge mark the edge
of the CME flux rope footpoint, and especially, the edge of the pre-eruptive
flux rope footpoint in the framework of "pre-eruptive structures being flux
ropes". Therefore, they provide a new perspective for the identification of
pre-eruptive and CME flux rope footpoints, and also new methods for studying
the properties and evolution of pre-eruptive structures and CMEs with
photospheric observations only.
