  Knowledge of the electron density distribution in the solar corona put
constraints on the magnetic field configurations for coronal modeling and on
initial conditions for solar wind modeling. We work with polarized
SOHO/LASCO-C2 images from the last two recent minima of solar activity
(1996-1997 and 2008-2010), devoid of coronal mass ejections. The goals are to
derive the 4D electron density distributions in the corona by applying a newly
developed time-dependent tomographic reconstruction method and to compare the
results between the two solar minima and with two magnetohydrodynamic models.
First, we confirm that the values of the density distribution in thermodynamic
models are more realistic than in polytropic ones. The tomography provides more
accurate distributions in the polar regions, and we find that the density in
tomographic and thermodynamic solutions varies with the solar cycle in both
polar and equatorial regions. Second, we find that the highest-density
structures do not always correspond to the predicted large-scale heliospheric
current sheet or its helmet streamer but can follow the locations of
pseudo-streamers. We deduce that tomography offers reliable density
distributions in the corona, reproducing the slow time evolution of coronal
structures, without prior knowledge of the coronal magnetic field over a full
rotation. Finally, we suggest that the highest-density structures show a
differential rotation well above the surface depending on how they are
magnetically connected to the surface. Such valuable information on the
rotation of large-scale structures could help to connect the sources of the
solar wind to their in situ counterparts in future missions such as Solar
Orbiter and Solar Probe Plus.
