The system of four planets around HR8799 offers a unique opportunity to probe the physics and chemistry at play in the atmospheres of self-luminous young (~30 Myr) planets. We recently obtained new photometry of the four planets and low-resolution (R~30) spectra of HR8799 d and e with the SPHERE instrument (paper III). In this paper (paper IV), we compare the available spectra and photometry of the planets to known objects and atmospheric models (BT-SETTL14, Cloud-AE60, Exo-REM) to characterize the atmospheric properties of the planets. We find that HR8799d and e properties are well reproduced by those of L6-L8 dusty dwarfs discovered in the field, among which some are candidate members of young nearby associations. No known object reproduces well the properties of planets b and c. Nevertheless, we find that the spectra and WISE photometry of peculiar and/or young early-T dwarfs reddened by submicron grains made of corundum, iron, enstatite, or forsterite successfully reproduce the SED of these two planets. Our analysis confirms that only the Exo-REM models with thick clouds fit (within 2{sigma}) the whole set of spectrophotometric datapoints available for HR8799 d and e for Teff = 1200 K, log g in the range 3.0-4.5, and M/H=+0.5. The models still fail to reproduce the SED of HR8799c and b. The determination of the metallicity, log g, and cloud thickness are degenerate. We conclude that an enhanced content in dust and decreased CIA of H2 is certainly responsible for the deviation of the properties of the planet with respect to field dwarfs. The analysis suggests in addition that HR8799c and b have later spectral types than the two other planets, and therefore could both have lower masses.
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