  The density distribution of flare loops and the mechanisms of their emission
in the continuum are still open questions. On September 10, 2017 a prominent
loop system appeared during the gradual phase of an X8.2 flare (SOL2017-09-10),
visible in all passbands of SDO/AIA and in the white-light continuum of
SDO/HMI. We investigate its electron density by taking into account all
radiation processes in the flare loops, i.e. the Thomson continuum, hydrogen
Paschen and Brackett recombination continua, as well as free-free continuum
emission. We derive a quadratic function of the electron density for a given
temperature and effective loop thickness. By absolutely calibrating SDO/HMI
intensities, we convert the measured intensities into electron density at each
pixel in the loops. For a grid of plausible temperatures between cool (6000 K)
and hot (10^6 K) structures, the electron density is computed for
representative effective thicknesses between 200 and 20 000 km. We obtain a
relatively high maximum electron density, about 10^13 cm^-3. At such high
electron densities, the Thomson continuum is negligible and therefore one would
not expect a significant polarization degree in dense loops. We conclude that
the Paschen and Brackett recombination continua are dominant in cool flare
loops, while the free-free continuum emission is dominant for warmer and hot
loops.
