The response of self-graviting protostellar discs to slow reduction in cooling timescale: the fragmentation boundary revisited

A number of previous studies of the fragmentation of self-gravitating protostellar discs have modeled radiative cooling with a cooling timescale (t_{cool}) parameterised as a simple multiple (beta_{cool}) of the local dynamical timescale. Such studies have delineated the `fragmentation boundary' in terms of a critical value of beta_{cool} (beta_{crit}), where the disc fragments if beta_{cool} < beta_{crit}. Such an approach however begs the question of how in reality a disc could ever be assembled with beta_{cool} < beta_{crit}. Here we adopt the more realistic approach of gradually reducing beta_{cool}, as might correspond to changes in thermal regime due to secular changes in the disc density profile. We find that when beta_{cool} is gradually reduced (on a timescale longer than t_{cool}), the disc is stabilised against fragmentation, compared with models in which beta_{cool} is reduced rapidly. We therefore conclude that a disc's ability to remain in a self-regulated, self-gravitating state (without fragmentation) is partly dependent on its thermal history, as well as its current cooling rate. Nevertheless, a slow reduction in t_{cool} appears only to lower the fragmentation boundary by about a factor two in t_{cool} and thus only permits maximum alpha values (parameterising the efficiency of angular momentum transfer in the disc) that are about a factor two higher than determined hitherto. Our results therefore do not undermine the notion of a fundamental upper limit to the heating rate that can be delivered by gravitational instabilities before the disc is subject to fragmentation. An important implication of this work, therefore, is that self-gravitating discs can enter into the regime of fragmentation via secular evolution and it is not necessary to invoke rapid (impulsive) events to trigger fragmentation.Comment: accepted for publication in MNRA

Constraints on the formation mechanism of the planetary mass companion of 2MASS 1207334-393254

In this paper we discuss the nature and the possible formation scenarios of the companion of the brown dwarf 2MASS 1207334-393254. We initially discuss the basic physical properties of this object and conclude that, although from its absolute mass ($5M_{\rm Jup}$), it is a planetary object, in terms of its mass ratio $q$ and of its separation $a$ with respect to the primary brown dwarf, it is consistent with the statistical properties of binaries with higher primary mass. We then explore the possible formation mechanism for this object. We show that the standard planet formation mechanism of core accretion is far too slow to form this object within 10 Myr, the observed age of the system. On the other hand, the alternative mechanism of gravitational instability (proposed both in the context of planet and of binary formation) may, in principle, work and form a system with the observed properties.Comment: 5 pages, MNRAS in pres

Characterising the Gravitational Instability in Cooling Accretion Discs

We perform numerical analyses of the structure induced by gravitational instabilities in cooling gaseous accretion discs. For low enough cooling rates a quasi-steady configuration is reached, with the instability saturating at a finite amplitude in a marginally stable disc. We find that the saturation amplitude scales with the inverse square root of the cooling parameter beta = t_cool / t_dyn, which indicates that the heating rate induced by the instability is proportional to the energy density of the induced density waves. We find that at saturation the energy dissipated per dynamical time by weak shocks due is of the order of 20 per cent of the wave energy. From Fourier analysis of the disc structure we find that while the azimuthal wavenumber is roughly constant with radius, the mean radial wavenumber increases with radius, with the dominant mode corresponding to the locally most unstable wavelength. We demonstrate that the density waves excited in relatively low mass discs are always close to co-rotation, deviating from it by approximately 10 per cent. This can be understood in terms of the flow Doppler-shifted phase Mach number -- the pattern speed self-adjusts so that the flow into spiral arms is always sonic. This has profound effects on the degree to which transport through self-gravity can be modelled as a viscous process. Our results thus provide (a) a detailed description of how the self-regulation mechanism is established for low cooling rates, (b) a clarification of the conditions required for describing the transport induced by self-gravity through an effective viscosity, (c) an estimate of the maximum amplitude of the density perturbation before fragmentation occurs, and (d) a simple recipe to estimate the density perturbation in different thermal regimes.Comment: 16 pages, 22 figures. Accepted for publication in MNRAS 11 November 200

The role of the energy equation in the fragmentation of protostellar discs during stellar encounters

In this paper, we use high-resolution smoothed particle hydrodynamics (SPH) simulations to investigate the response of a marginally stable self-gravitating protostellar disc to a close parabolic encounter with a companion discless star. Our main aim is to test whether close brown dwarfs or massive planets can form out of the fragmentation of such discs. We follow the thermal evolution of the disc by including the effects of heating due to compression and shocks and a simple prescription for cooling and find results that contrast with previous isothermal simulations. In the present case we find that fragmentation is inhibited by the interaction, due to the strong effect of tidal heating, which results in a strong stabilization of the disc. A similar behaviour was also previously observed in other simulations involving discs in binary systems. As in the case of isolated discs, it appears that the condition for fragmentation ultimately depends on the cooling rate.Comment: 9 pages, 10 figures, accepted in MNRA

Industrial clusters and economic performance in Brazil

Industrial clusters, which are commonly targeted to receive financial support allocated to locally based development projects, are seen as an effective industrial policy tool for improving productivity and generating employment. Nevertheless, identifying clusters and assessing their economic performance is a challenge for policymakers. This paper aims to address this challenge by identifying the location of clusters based on neighbor relationships and specialization in Brazil and providing some insights on their effects on employment generation. The paper uses both Location Quotient and Local Indicator of Spatial Association to identify potential clusters in 27 industrial sectors in 5564 Brazilian municipalities. In addition, it uses annual municipal panel data for 2006-2009 to assess whether the presence of potential clusters is correlated with employment generation. The results show that clusters located in municipalities whose neighbors have similar industrial structures perform better than those that present industry specialization only

Long-term stream evolution in tidal disruption events

A large number of tidal disruption event (TDE) candidates have been observed recently, often differing in their observational features. Two classes appear to stand out: X-ray and optical TDEs, the latter featuring lower effective temperatures and luminosities. These differences can be explained if the radiation detected from the two categories of events originates from different locations. In practice, this location is set by the evolution of the debris stream around the black hole and by the energy dissipation associated with it. In this paper, we build an analytical model for the stream evolution, whose dynamics is determined by both magnetic stresses and shocks. Without magnetic stresses, the stream always circularizes. The ratio of the circularization time-scale to the initial stream period is t(ev)/t(min) = 8.3(M-h/10(6) M-circle dot)(-5/3)ss(-3), where M-h is the black hole mass and ss is the penetration factor. If magnetic stresses are strong, they can lead to the stream ballistic accretion. The boundary between circularization and ballistic accretion corresponds to a critical magnetic stresses efficiency v(A)/v(c) approximate to 10(-1), largely independent of M-h and ss. However, the main effect of magnetic stresses is to accelerate the stream evolution by strengthening self-crossing shocks. Ballistic accretion therefore necessarily occurs on the stream dynamical time-scale. The shock luminosity associated with energy dissipation is sub-Eddington but decays as t(-5/3) only for a slow stream evolution. Finally, we find that the stream thickness rapidly increases if the stream is unable to cool completely efficiently. A likely outcome is its fast evolution into a thick torus, or even an envelope completely surrounding the black hole

Magnetic field evolution in tidal disruption events

When a star gets tidally disrupted by a supermassive black hole, its magnetic field is expected to pervade its debris. In this paper, we study this process via smoothed particle magnetohydrodynamical simulations of the disruption and early debris evolution including the stellar magnetic field. As the gas stretches into a stream, we show that the magnetic field evolution is strongly dependent on its orientation with respect to the stretching direction. In particular, an alignment of the field lines with the direction of stretching induces an increase of the magnetic energy. For disruptions happening well within the tidal radius, the star compression causes the magnetic field strength to sharply increase by an order of magnitude at the time of pericentre passage. If the disruption is partial, we find evidence for a dynamo process occurring inside the surviving core due to the formation of vortices. This causes an amplification of the magnetic field strength by a factor of \u2dc10. However, this value represents a lower limit since it increases with numerical resolution. For an initial field strength of 1 G, the magnetic field never becomes dynamically important. Instead, the disruption of a star with a strong 1 MG magnetic field produces a debris stream within which magnetic pressure becomes similar to gas pressure a few tens of hours after disruption. If the remnant of one or multiple partial disruptions is eventually fully disrupted, its magnetic field could be large enough to magnetically power the relativistic jet detected from Swift J1644+57. Magnetized streams could also be significantly thickened by magnetic pressure when it overcomes the confining effect of self-gravity

Simulations of Tidal Disruption Events

Numerical simulations have historically played a major role in understanding the hydrodynamics of the tidal disruption process. Given the complexity of the geometry of the system, the challenges posed by the problem have indeed stimulated much work on the numerical side. Smoothed Particles Hydrodynamics methods, for example, have seen their very first applications in the context of tidal disruption and still play a major role to this day. Likewise, initial attempts at simulating the evolution of the disrupted star with the so-called affine method have been historically very useful. In this Chapter, we provide an overview of the numerical techniques used in the field and of their limitations, and summarize the work that has been done to simulate numerically the tidal disruption process

ALMA 870 μ\mum continuum observations of HD 100546. Evidence of a giant planet on a wide orbit

This paper reports on a new analysis of archival ALMA $870\,\mu$m dust continuum observations. Along with the previously observed bright inner ring ($r \sim 20-40\,$au), two addition substructures are evident in the new continuum image: a wide dust gap, $r \sim 40-150\,$au, and a faint outer ring ranging from $r \sim 150\,$au to $r \sim 250\,$au and whose presence was formerly postulated in low-angular-resolution ALMA cycle 0 observations but never before observed. Notably, the dust emission of the outer ring is not homogeneous, and it shows two prominent azimuthal asymmetries that resemble an eccentric ring with eccentricity $e = 0.07$. The characteristic double-ring dust structure of HD 100546 is likely produced by the interaction of the disk with multiple giant protoplanets. This paper includes new smoothed-particle-hydrodynamic simulations with two giant protoplanets, one inside of the inner dust cavity and one in the dust gap. The simulations qualitatively reproduce the observations, and the final masses and orbital distances of the two planets in the simulations are 3.1 $M_{J}$ at 15 au and 8.5 $M_{J}$ at 110 au, respectively. The massive outer protoplanet substantially perturbs the disk surface density distribution and gas dynamics, producing multiple spiral arms both inward and outward of its orbit. This can explain the observed perturbed gas dynamics inward of 100 au as revealed by ALMA observations of CO. Finally, the reduced dust surface density in the $\sim 40-150\,$au dust gap can nicely clarify the origin of the previously detected H$_2$O gas and ice emission.Comment: Accepted for publicatio

Long-lived Dust Rings around HD 169142

Recent Atacama Large Millimeter/submillimeter Array (ALMA) observations of the protoplanetary disk around HD 169142 reveal a peculiar structure made of concentric dusty rings: a main ring at similar to 20 au, a triple system of rings at similar to 55-75 au in millimetric continuum emission, and a perturbed gas surface density from the (CO)-C-12,(CO)-C-13, and (CO)-O-18 (J = 2-1) surface brightness profile. In this Letter, we perform 3D numerical simulations and radiative transfer modeling exploring the possibility that two giant planets interacting with the disk and orbiting in resonant locking can be responsible for the origin of the observed dust inner rings structure. We find that in this configuration the dust structure is actually long lived while the gas mass of the disk is accreted onto the star and the giant planets, emptying the inner region. In addition, we also find that the innermost planet is located at the inner edge of the dust ring, and can accrete mass from the disk, generating a signature in the dust ring shape that can be observed in mm ALMA observations