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Fragmentation of colliding planetesimals with water content  [PDF]
Thomas I. Maindl,Rudolf Dvorak,Christoph Sch?fer,Roland Speith
Physics , 2014, DOI: 10.1017/S1743921314008059
Abstract: We investigate the outcome of collisions of Ceres-sized planetesimals composed of a rocky core and a shell of water ice. These collisions are not only relevant for explaining the formation of planetary embryos in early planetary systems, but also provide insight into the formation of asteroid families and possible water transport via colliding small bodies. Earlier studies show characteristic collision velocities exceeding the bodies' mutual escape velocity which - along with the distribution of the impact angles - cover the collision outcome regimes 'partial accretion', 'erosion', and 'hit-and-run' leading to different expected fragmentation scenarios. Existing collision simulations use bodies composed of strengthless material; we study the distribution of fragments and their water contents considering the full elasto-plastic continuum mechanics equations also including brittle failure and fragmentation.
The fragmentation of protostellar discs: the Hill criterion for spiral arms  [PDF]
Patrick D. Rogers,James Wadsley
Physics , 2011, DOI: 10.1111/j.1365-2966.2012.21014.x
Abstract: We present a new framework to explain the link between cooling and fragmentation in gravitationally unstable protostellar discs. This framework consists of a simple model for the formation of spiral arms, as well as a criterion, based on the Hill radius, to determine if a spiral arm will fragment. This detailed model of fragmentation is based on the results of numerical simulations of marginally stable protostellar discs, including those found in the literature, as well as our new suite of 3-D radiation hydrodynamics simulations of an irradiated, optically-thick protostellar disc surrounding an A star. Our set of simulations probes the transition to fragmentation through a scaling of the physical opacity. This model allows us to directly calculate the critical cooling time of Gammie (2001), with results that are consistent with those found from numerical experiment. We demonstrate how this model can be used to predict fragmentation in irradiated protostellar discs. These numerical simulations, as well as the model that they motivate, provide strong support for the hypothesis that gravitational instability is responsible for creating systems with giant planets on wide orbits.
Quantification of stochastic fragmentation of self-gravitating discs  [PDF]
Matthew D. Young,Cathie J. Clarke
Physics , 2015, DOI: 10.1093/mnras/stv2378
Abstract: Using 2D smoothed particle hydrodynamics, we investigate the distribution of wait times between strong shocks in a turbulent, self-gravitating accretion disc. We show the resulting distributions do not depend strongly on the cooling time or resolution of the disc and that they are consistent with the predictions of earlier work (Young & Clarke 2015; Cossins et al. 2009, 2010). We use the distribution of wait times between shocks to estimate the likelihood of stochastic fragmentation by gradual contraction of shear-resistant clumps on the cooling time scale. We conclude that the stochastic fragmentation mechanism (Paardekooper 2012) cannot change the radius at which fragmentation is possible by more than ~20%, restricting direct gravitational collapse as a mechanism for giant planet formation to the outer regions of protoplanetary discs.
On the fragmentation criteria of self-gravitating protoplanetary discs  [PDF]
Farzana Meru,Matthew R. Bate
Physics , 2010, DOI: 10.1111/j.1365-2966.2010.17465.x
Abstract: We investigate the fragmentation criterion in massive self-gravitating discs. We present new analysis of the fragmentation conditions which we test by carrying out global three-dimensional numerical simulations. Whilst previous work has placed emphasis on the cooling timescale in units of the orbital timescale, \beta , we find that at a given radius the surface mass density (i.e. disc mass and profile) and star mass also play a crucial role in determining whether a disc fragments or not as well as where in the disc fragments form. We find that for shallow surface mass density profiles (p<2, where \Sigma \propto R^{-p}), fragments form in the outer regions of the disc. However for steep surface mass density profiles (p \gtrsim 2), fragments form in the inner regions of a disc. In addition, we also find that the critical value of the cooling timescale in units of the orbital timescale found in previous simulations is only applicable to certain disc surface mass density profiles and for particular disc radii and is not a general rule for all discs. We find an empirical fragmentation criteria between the cooling timescale in units of the orbital timescale, \beta , the surface mass density, the star mass and the radius.
The Role of Discs in the Collapse and Fragmentation of Prestellar Cores  [PDF]
O. Lomax,A. P. Whitworth,D. A. Hubber
Physics , 2015,
Abstract: Disc fragmentation provides an important mechanism for producing low mass stars in prestellar cores. Here, we describe Smoothed Particle Hydrodynamics simulations which show how populations of prestellar cores evolve into stars. We find the observed masses and multiplicities of stars can be recovered under certain conditions. First, protostellar feedback from a star must be episodic. The continuous accretion of disc material on to a central protostar results in local temperatures which are too high for disc fragmentation. If, however, the accretion occurs in intense outbursts, separated by a downtime of $\sim10^4\,\mathrm{years}$, gravitational instabilities can develop and the disc can fragment. Second, a significant amount of the cores' internal kinetic energy should be in solenoidal turbulent modes. Cores with less than a third of their kinetic energy in solenoidal modes have insufficient angular momentum to form fragmenting discs. In the absence of discs, cores can fragment but results in a top heavy distribution of masses with very few low mass objects.
The lower limits of disc fragmentation and the prospects for observing fragmenting discs  [PDF]
Dimitris Stamatellos,Anaelle Maury,Anthony Whitworth,Philippe Andre
Physics , 2010, DOI: 10.1111/j.1365-2966.2011.18254.x
Abstract: 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.
Triggered fragmentation in gravitationally unstable discs: forming fragments at small radii  [cached]
Meru Farzana
EPJ Web of Conferences , 2013, DOI: 10.1051/epjconf/20134607003
Abstract: We carry out three dimensional radiation hydrodynamical simulations of gravitationally unstable discs using to explore the movement of mass in a disc following its fragmentation. Compared to a more quiescent state before it fragments, the radial velocity of the gas increases by up to a factor of ≈ 2 – 3 after fragmentation. While the mass movement occurs both inwards and outwards, the inwards motion can cause the inner spirals to be suciently dense that they may become unstable and potentially fragment. Consequently, the dynamical behaviour of fragmented discs may cause subsequent fragmentation at smaller radii after an initial fragment has formed in the outer disc.
The properties of discs around planets and brown dwarfs as evidence for disc fragmentation  [PDF]
Dimitris Stamatellos,Gregory J. Herczeg
Physics , 2015, DOI: 10.1093/mnras/stv526
Abstract: 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 predictions 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.
Triggered fragmentation in self-gravitating discs: forming fragments at small radii  [PDF]
Farzana Meru
Physics , 2015, DOI: 10.1093/mnras/stv2128
Abstract: We carry out three dimensional radiation hydrodynamical simulations of gravitationally unstable discs to explore the movement of mass in a disc following its initial fragmentation. We find that the radial velocity of the gas in some parts of the disc increases by up to a factor of approximately 10 after the disc fragments, compared to before. While the movement of mass occurs in both the inward and outward directions, the inwards movement can cause the inner spirals of a self-gravitating disc to become sufficiently dense such that they can potentially fragment. This suggests that the dynamical behaviour of fragmented discs may cause subsequent fragmentation to occur at smaller radii than initially expected, but only after an initial fragment has formed in the outer disc.
Dependence of fragmentation in self-gravitating accretion discs on small scale structure  [PDF]
Matthew D. Young,Cathie J. Clarke
Physics , 2015,
Abstract: We propose a framework for understanding the fragmentation criterion for self-gravitating discs which, in contrast to studies that emphasise the `gravoturbulent' nature of such discs, instead focuses on the properties of their quasi-regular spiral structures. Within this framework there are two evolutionary paths to fragmentation: i) collapse on the free-fall time, which requires that the ratio of cooling time to dynamical time ($\beta$) $< 3$ and ii) quasistatic collapse on the cooling time at a rate that is sufficiently fast that fragments are compact enough to withstand disruption when they encounter spiral features in the disc. We perform 2D grid simulations which demonstrate numerically converged fragmentation at $\beta < 3$ (in good agreement with Paardekooper et al. (2011) and others) and argue that this is a consequence of the fact that such simulations smooth the gravitational force on the scale $H$, the scale height of the disc. Such simulations thus only allow fragmentation via route i) above since they suppress the quasistatic contraction of fragments on scales $< H$; the inability of fragments to contract to significantly smaller scales then renders them susceptible to disruption at the next spiral arm encounter. On the other hand, 3D simulations indeed show fragmentation at higher $\beta$ via route ii). We derive an analytic prediction of fragmentation by route ii) when $\beta \lesssim 12$, based on the requirement that fragments must contract sufficiently to withstand disruption by spiral arms. We also discuss the necessary numerical requirements on both grid based and SPH codes if they are to model fragmentation via route ii).
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