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Context: We studied numerically the formation of giant planet (GP) and browndwarf (BD) embryos in gravitationally unstable protostellar disks and comparedour findings with directly-imaged, wide-orbit (>= 50 AU) companions knownto-date. The viability of the disk fragmentation scenario for the formation ofwide-orbit companions in protostellar disks around (sub-)solar mass stars wasinvestigated. Methods: We used numerical hydrodynamics simulations of diskformation and evolution with an accurate treatment of disk thermodynamics. Theuse of the thin-disk limit allowed us to probe the long-term evolution ofprotostellar disks. We focused on models that produced wide-orbit GP/BDembryos, which opened a gap in the disk and showed radial migration timescalessimilar to or longer than the typical disk lifetime. Results: While diskfragmentation was seen in the majority of our models, only 6 models out of 60revealed the formation of quasi-stable, wide-orbit GP/BD embryos. Diskfragmentation produced GP/BD embryos with masses in the 3.5-43 M_J range,covering the whole mass spectrum of directly-imaged, wide-orbit companions to(sub-)solar mass stars. On the other hand, our modelling failed to produceembryos on orbital distances <= 170 AU, whereas several directly-imagedcompanions were found at smaller orbits down to a few AU. Disk fragmentationalso failed to produce wide-orbit companions around stars with mass <= 0.7Msun, in disagreement with observations. Conclusions: Disk fragmentation isunlikely to explain the whole observed spectrum of wide-orbit companions to(sub-)solar-mass stars and other formation mechanisms, e.g., dynamicalscattering of closely-packed companions onto wide orbits, should be invoked toaccount for companions at orbital distance from a few tens to \approx 150 AUand wide-orbit companions with masses of the host star <= 0.7 Msun. (abridged)

Formation of giant planets and brown dwarfs on wide orbits