  Core level binding energies and absorption edges are at the heart of many
experimental techniques concerned with element-specific structure, electronic
structure, chemical reactivity, elementary excitations and magnetism. X-ray
photoemission spectroscopy (XPS) in particular, can provide information about
the electronic and vibrational many-body interactions in a solid as these are
reflected in the detailed energy distribution of the photoelectrons. Ultrafast
pump-probe techniques add a new dimension to such studies, introducing the
ability to probe a transient state of the many-body system. Here we use a free
electron laser to investigate the effect of a transiently excited electron gas
on the core level spectrum of graphene, showing that it leads to a large
broadening of the C 1s peak. Confirming a decade-old prediction, the broadening
is found to be caused by an exchange of energy and momentum between the
photoemitted core electron and the hot electron system, rather than by
vibrational excitations. This interpretation is supported by a line shape
analysis that accounts for the presence of the excited electrons. Fitting the
spectra to this model directly yields the electronic temperature of the system,
in agreement with electronic temperature values obtained from valence band
data. Furthermore, making use of time- and momentum-resolved C 1s spectra, we
illustrate how the momentum change of the outgoing core electrons leads to a
small but detectable change in the time-resolved photoelectron diffraction
pattern and to a nearly complete elimination of the core level binding energy
variation associated with the narrow $\sigma$-band in the C 1s state. The
results demonstrate that the XPS line shape can be used as an element-specific
and local probe of the excited electron system and that X-ray photoelectron
diffraction investigations remain feasible at very high electronic
temperatures.
