A large fraction of brown dwarfs and low-mass hydrogen-burning stars may form by gravitational fragmentation of protostellar discs .
We explore the conditions for disc fragmentation and we find that they are satisfied when a disc is large enough ( \stackrel { > } { { } _ { \sim } } 100 Â AU ) so that its outer regions can cool efficiently , and it has enough mass to be gravitationally unstable , at such radii .
We perform radiative hydrodynamic simulations and show that even a disc with mass 0.25 ~ { } { M _ { \sun } } and size 100Â AU fragments .
The disc mass , radius , and the ratio of disc-to-star mass ( M _ { D } / M _ { \star } \approx 0.36 ) are smaller than in previous studies ( Stamatellos & Whitworth 2009a ) .
We find that fragmenting discs drastically decrease in mass and size within a few 10 ^ { 4 } yr of their formation , since a fraction of their mass , especially outside \sim 100 Â AU is consumed by the new stars and brown dwarfs that form .
Fragmenting discs end up with masses \sim 0.001 - 0.1 { M } _ { \sun } , and sizes \sim 20 - 100 Â AU .
On the other hand , discs that are marginally stable evolve on a viscous timescale , thus living longer ( \sim 1 - 10 Myr ) .
We produce simulated images of fragmenting discs and find that observing discs that are undergoing fragmentation is possible using current ( e.g .
IRAM-PdBI ) and future ( e.g .
ALMA ) interferometers , but highly improbable due to the short duration of this process .
Comparison with observations shows that many observed discs may be remnants of discs that have fragmented at an earlier stage .
However , there are only a few candidates that are possibly massive and large enough to currently be gravitationally unstable .
The rarity of massive ( \stackrel { > } { { } _ { \sim } } 0.2 { M } _ { \sun } ) , extended ( \stackrel { > } { { } _ { \sim } } 100 Â AU ) discs indicates either that such discs are highly transient ( i.e .
form , increase in mass becoming gravitationally unstable due to infall of material from the surrounding envelope , and quickly fragment ) , or that their formation is suppressed ( e.g .
by magnetic fields ) .
We conclude that current observations of early-stage discs can not exclude the mechanism of disc fragmentation .