We numerically studied the formation of giant planet (GP) and brown dwarf (BD) embryos in gravitationally unstable protostellar disks and compared our findings with the directly imaged, wide-orbit (≳50 AU) companions that are known to-date. The viability of the disk fragmentation scenario for the formation of wide-orbit companions in protostellar disks around (sub-)solar mass stars was investigated. We focused on the likelihood of survival of GP/BD embryos formed via disk gravitational fragmentation.

We used numerical hydrodynamics simulations of disk formation and evolution with an accurate treatment of disk thermodynamics. Using the thin-disk limit allowed us to probe the long-term evolution of protostellar disks, starting from the gravitational collapse of a pre-stellar core and ending in the T Tauri phase after at least 1.0 Myr of disk evolution. We focused on models that produced wide-orbit GP/BD embryos that opened a gap in the disk and showed radial migration timescales similar to or longer than the typical disk lifetime.

While most models showed disk fragmentation, only 6 models out of 60 revealed the formation of quasi-stable, wide-orbit GP/BD embryos. The low probability for the fragment survival is caused by efficient inward migration/ejection/dispersal mechanisms that operate in the embedded phase of star formation. We found that only massive and extended protostellar disks (≳0.2   M_⊙), which experience gravitational fragmentation not only in the embedded but also in the T Tauri phases of star formation, can form wide-orbit companions. Disk fragmentation 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 modeling failed to produce embryos on orbital distances  ≲170 AU, whereas several directly imaged companions were found at smaller orbits down to a few AU. Disk fragmentation also failed to produce wide-orbit companions around stars with mass  ≲0.7   M_⊙, in disagreement with observations.

Disk fragmentation is unlikely to explain the whole observed spectrum of wide-orbit companions to (sub-)solar-mass stars and other formation mechanisms, for instance, dynamical scattering of closely packed companions onto wide orbits, should be invoked to account for companions at orbital distance from a few tens to  ≈150 AU and wide-orbit companions with masses of the host star  ≤ 0.7 M_⊙. Definite measurements of orbit eccentricities and a wider sample of numerical models are needed to distinguish between the formation scenarios of GP/BD on wide orbits.