Direct imaging searches have revealed many very low-mass objects, including a small number of planetary mass objects, as wide-orbit companions to young stars. The formation mechanism of these objects remains uncertain. In this paper we present the pr
edictions of the disc fragmentation model regarding the properties of the discs around such low-mass objects. We find that the discs around objects that have formed by fragmentation in discs hosted by Sun-like stars (referred to as parent discs and parent stars) are more massive than expected from the ${M}_{rm disc}-M_*$ relation (which is derived for stars with masses $M_*>0.2 {rm M}_{odot}$). Accordingly, the accretion rates onto these objects are also higher than expected from the $dot{M}_*-M_*$ relation. Moreover there is no significant correlation between the mass of the brown dwarf or planet with the mass of its disc nor with the accretion rate from the disc onto it. The discs around objects that form by disc fragmentation have larger than expected masses as they accrete gas from the disc of their parent star during the first few kyr after they form. The amount of gas that they accrete and therefore their mass depend on how they move in their parent disc and how they interact with it. Observations of disc masses and accretion rates onto very low-mass objects are consistent with the predictions of the disc fragmentation model. Future observations (e.g. by ALMA) of disc masses and accretion rates onto substellar objects that have even lower masses (young planets and young, low-mass brown dwarfs), where the scaling relations predicted by the disc fragmentation model diverge significantly from the corresponding relations established for higher-mass stars, will test the predictions of this model.
I discuss the role that disc fragmentation plays in the formation of gas giant and terrestrial planets, and how this relates to the formation of brown dwarfs and low-mass stars, and ultimately to the process of star formation. Protostellar discs may
fragment, if they are massive enough and can cool fast enough, but most of the objects that form by fragmentation are brown dwarfs. It may be possible that planets also form, if the mass growth of a proto-fragment is stopped (e.g. if this fragment is ejected from the disc), or suppressed and even reversed (e.g by tidal stripping). I will discuss if it is possible to distinguish whether a planet has formed by disc fragmentation or core accretion, and mention of a few examples of observed exoplanets that are suggestive of formation by disc fragmentation .
It is estimated that ~60% of all stars (including brown dwarfs) have masses below 0.2Msun. Currently, there is no consensus on how these objects form. I will briefly review the four main theories for the formation of low-mass objects: turbulent fragm
entation, ejection of protostellar embryos, disc fragmentation, and photo-erosion of prestellar cores. I will focus on the disc fragmentation theory and discuss how it addresses critical observational constraints, i.e. the low-mass initial mass function, the brown dwarf desert, and the binary statistics of low-mass stars and brown dwarfs. I will examine whether observations may be used to distinguish between different formation mechanisms, and give a few examples of systems that strongly favour a specific formation scenario. Finally, I will argue that it is likely that all mechanisms may play a role in low-mass star and brown dwarf formation.
Protostars grow in mass by accreting material through their discs, and this accretion is initially their main source of luminosity. The resulting radiative feedback heats the environments of young protostars, and may thereby suppress further fragment
ation and star formation. There is growing evidence that the accretion of material onto protostars is episodic rather than continuous; most of it happens in short bursts that last up to a few hundred years, whereas the intervals between these outbursts of accretion could be thousands of years. We have developed a model to include the effects of episodic accretion in simulations of star formation. Episodic accretion results in episodic radiative feedback, which heats and temporarily stabilises the disc, suppressing the growth of gravitational instabilities. However, once an outburst has been terminated, the luminosity of the protostar is low, and the disc cools rapidly. Provided that there is enough time between successive outbursts, the disc may become gravitationally unstable and fragment. The model suggests that episodic accretion may allow disc fragmentation if (i) the time between successive outbursts is longer than the dynamical timescale for the growth of gravitational instabilities (a few kyr), and (ii) the quiescent accretion rate onto the protostar is sufficiently low (at most a few times 1e-7 Msun/yr). We also find that after a few protostars form in the disc, their own episodic accretion events shorten the intervals between successive outbursts, and sup- press further fragmentation, thus limiting the number of objects forming in the disc. We conclude that episodic accretion moderates the effect of radiative feedback from young protostars on their environments, and, under certain conditions, allows the formation of low-mass stars, brown dwarfs, and planetary-mass objects by fragmentation of protostellar discs.
It is speculated that the accretion of material onto young protostars is episodic. We present a computational method to include the effects of episodic accretion in radiation hydrodynamic simulations of star formation. We find that during accretion e
vents protostars are switched on, heating and stabilising the discs around them. However, these events typically last only a few hundred years, whereas the intervals in between them may last for a few thousand years. During these intervals the protostars are effectively switched off, allowing gravitational instabilities to develop in their discs and induce fragmentation. Thus, episodic accretion promotes disc frag- mentation, enabling the formation of low-mass stars, brown dwarfs and planetary-mass objects. The frequency and the duration of episodic accretion events may be responsible for the low-mass end of the IMF, i.e. for more than 60% of all stars.
A star acquires much of its mass by accreting material from a disc. Accretion is probably not continuous but episodic. We have developed a method to include the effects of episodic accretion in simulations of star formation. Episodic accretion result
s in bursts of radiative feedback, during which a protostar is very luminous, and its surrounding disc is heated and stabilised. These bursts typically last only a few hundred years. In contrast, the lulls between bursts may last a few thousand years; during these lulls the luminosity of the protostar is very low, and its disc cools and fragments. Thus, episodic accretion enables the formation of low-mass stars, brown dwarfs and planetary-mass objects by disc fragmentation. If episodic accretion is a common phenomenon among young protostars, then the frequency and duration of accretion bursts may be critical in determining the low-mass end of the stellar initial mass function.
A large fraction of brown dwarfs and low-mass H-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 (>100 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 Msun and size 100 AU fragments. The disc mass, radius, and the ratio of disc-to-star mass (Mdisc/Mstar~0.36) are smaller than in previous studies. We find that fragmenting discs decrease in mass and size within a few 10^4 yr of their formation, since a fraction of their mass, especially outside 100 AU is consumed by the new stars and brown dwarfs that form. Fragmenting discs end up with masses ~0.001-0.1 Msun, and sizes ~20-100 AU. On the other hand, discs that are marginally stable live much longer. 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 (>0.2 Msun), extended (>100 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 cannot exclude the mechanism of disc fragmentation.
We suggest that a high proportion of brown dwarfs are formed by gravitational fragmentation of massive extended discs around Sun-like stars. Such discs should arise frequently, but should be observed infrequently, precisely because they fragment rapi
dly. By performing an ensemble of radiation-hydrodynamic simulations, we show that such discs fragment within a few thousand years, and produce mainlybrown dwarf (BDs) stars, but also planetary mass (PM) stars and very low-mass hydrogen-burning (HB) stars. Most of the the PM stars and BDs are ejected by mutual interactions. We analyse the statistical properties of these stars, and compare them with observations. After a few hundred thousand years the Sun-like primary is typically left with a close low-mass HB companion, and two much wider companions: a low-mass HB star and a BD star, or a BD-BD binary. There is a BD desert extending out to at least ~100 AU; this is because BDs tend to be formed further out than low-mass HB stars, and then they tend to be scattered even further out, or even into the field. BDs form with discs of a few Mj and radii of a few tens of AU, and they are more likely to retain these discs if they remain bound to the primary star. Binaries form by pairing of the newly-formed stars in the disc, giving a low-mass binary fraction of ~0.16. These binaries include close and wide BD/BD binaries and BD/PM binaries. BDs that remain as companions to Sun-like stars are more likely to be in BD/BD binaries than are BDs ejected into the field. Disc fragmentation is a robust mechanism; even if only a small fraction of Sun-like stars host the required massive extended discs,this mechanism can produce all the PM stars observed, most of the BD stars, and a significant proportion of the very low-mass HB stars.
We suggest that a high proportion of brown dwarfs are formed by gravitational fragmentation of massive, extended discs around Sun-like stars. We argue that such discs should arise frequently, but should be observed infrequently, precisely because the
y fragment rapidly. By performing an ensemble of radiation-hydrodynamic simulations, we show that such discs typically fragment within a few thousand years to produce mainly brown dwarfs (including planetary-mass brown dwarfs) and low-mass hydrogen-burning stars. Subsequently most of the brown dwarfs are ejected by mutual interactions. We analyse the properties of these objects that form by disc fragmentation, and compare them with observations.
