  Experimental and theoretical results are presented for double, triple, and
quadruple photoionization of Si$^+$ and Si$^{2+}$ ions and for double
photoionization of Si$^{3+}$ ions by a single photon. The experiments employed
the photon-ion merged-beams technique at a synchrotron light source. The
experimental photon-energy range 1835--1900 eV comprises resonances associated
with the excitation of a $1s$ electron to higher subshells and subsequent
autoionization. Energies, widths, and strengths of these resonances are
extracted from high-resolution photoionization measurements, and the core-hole
lifetime of K-shell ionized neutral silicon is inferred. In addition,
theoretical cross sections for photoabsorption and multiple photoionization
were obtained from large-scale Multi-Configuration Dirac-Hartree-Fock (MCDHF)
calculations. The present calculations agree with the experiment much better
than previously published theoretical results. The importance of an accurate
energy calibration of laboratory data is pointed out. The present benchmark
results are particularly useful for discriminating between silicon absorption
in the gaseous and in the solid component (dust grains) of the interstellar
medium.
