Black hole mergers: do gas discs lead to spin alignment?

In this Letter we revisit arguments suggesting that the Bardeen-Petterson effect can coalign the spins of a central supermassive black hole binary accreting from a circumbinary (or circumnuclear) gas disc. We improve on previous estimates by adding the dependence on system parameters, and noting that the nonlinear nature of warp propagation in a thin viscous disc affects alignment. This reduces the disc's ability to communicate the warp, and can severely reduce the effectiveness of disc-assisted spin alignment. We test our predictions with a Monte Carlo realization of random misalignments and accretion rates and we find that the outcome depends strongly on the spin magnitude. We estimate a generous upper limit to the probability of alignment by making assumptions which favour it throughout. Even with these assumptions, about 40% of black holes with $a \gtrsim 0.5$ do not have time to align with the disc. If the residual misalignment is not small and it is maintained down to the final coalescence phase this can give a powerful recoil velocity to the merged hole. Highly spinning black holes are thus more likely of being subject to strong recoils, the occurrence of which is currently debated.Comment: 6 pages, 2 figures, accepted in MNRA

Wave-like warp propagation in circumbinary discs II. Application to KH 15D

KH 15D is a protostellar binary system that shows a peculiar light curve. In order to model it, a narrow circumbinary precessing disc has been invoked, but a proper dynamical model has never been developed. In this paper, we analytically address the issue of whether such a disc can rigidly precess around KH 15D, and we relate the precessional period to the main parameters of the system. Then, we simulate the disc's dynamics by using a 1D model developed in a companion paper, such that the warp propagates into the disc as a bending wave, which is expected to be the case for protostellar discs. The validity of such an approach has been confirmed by comparing its results with full 3D SPH simulations on extended discs. In the present case, we use this 1D code to model the propagation of the warp in a narrow disc. If the inner truncation radius of the disc is set by the binary tidal torques at {\sim} 1 AU, we find that the disc should extend out to 6-10 AU (depending on the models), and is therefore wider than previously suggested. Our simulations show that such a disc does reach an almost steady state, and then precesses as a rigid body. The disc displays a very small warp, with a tilt inclination that increases with radius in order to keep the disc in equilibrium against the binary torque. However, for such wider discs, the presence of viscosity leads to a secular decay of the tilt on a timescale of {\approx} 3000 ({\alpha}/0.05)^(-1) years, where {\alpha} is the disc viscosity parameter. The presence of a third body (such as a planet), orbiting at roughly 10 AU might simultaneously explain the outer truncation of the disc and the maintenance of the tilt for a prolonged time.Comment: 8 pages, 3 figures, accepted for publication in MNRA

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 potential for Earth-mass planet formation around brown dwarfs

Recent observations point to the presence of structured dust grains in the discs surrounding young brown dwarfs, thus implying that the first stages of planet formation take place also in the sub-stellar regime. Here, we investigate the potential for planet formation around brown dwarfs and very low mass stars according to the sequential core accretion model of planet formation. We find that, for a brown dwarfs of mass 0.05M_{\odot}, our models predict a maximum planetary mass of ~5M_{\oplus}, orbiting with semi-major axis ~1AU. However, we note that the predictions for the mass - semi-major axis distribution are strongly dependent upon the models chosen for the disc surface density profiles and the assumed distribution of disc masses. In particular, if brown dwarf disc masses are of the order of a few Jupiter masses, Earth-mass planets might be relatively frequent, while if typical disc masses are only a fraction of Jupiter mass, we predict that planet formation would be extremely rare in the sub-stellar regime. As the observational constraints on disc profiles, mass dependencies and their distributions are poor in the brown dwarf regime, we advise caution in validating theoretical models only on stars similar to the Sun and emphasise the need for observational data on planetary systems around a wide range of stellar masses. We also find that, unlike the situation around solar-like stars, Type-II migration is totally absent from the planet formation process around brown dwarfs, suggesting that any future observations of planets around brown dwarfs would provide a direct measure of the role of other types of migration.Comment: 11 pages, accepted for publication in MNRA

Supermassive black hole formation during the assembly of pre-galactic discs

In this paper we discuss the evolution of gravitationally unstable pre-galactic discs that result from the collapse of haloes at high redshift $z \approx 10$ or so, which have not yet been enriched by metals. In cases where molecular hydrogen formation is suppressed the discs are maintained at a temperature of a few thousand degrees Kelvin. However, when molecular hydrogen is present cooling can proceed down to a few hundred degrees Kelvin. Analogous to the case of the larger scale proto-galactic discs, we assume that the evolution of these discs is mainly driven by angular momentum redistribution induced by the development of gravitational instabilities in the disc. We also properly take into account the possibility of disc fragmentation. We thus show that this simple model naturally predicts the formation of supermassive black holes in the nuclei of such discs and provides a robust determination of their mass distribution as a function of halo properties. We estimate that roughly 5% of discs resulting from the collapse of haloes with $M\approx 10^7 M_{\odot}$ should host a massive black hole with a mass $M_{\rm BH}\approx 10^5 M_{\odot}$. We confirm our arguments with time-dependent calculations of the evolution of the surface density and of the accretion rate in these primordial discs. This mechanism offers an efficient way to form seed black holes at high redshift. The predicted masses for our black hole seeds enable the comfortable assembly of $10^9 M_{\odot}$ black holes powering the luminous quasars detected by the Sloan Digital Sky Survey at $z = 6$ for a concordance cosmology. (abridged)Comment: 12 pages, 8 figures, submitted to MNRA

Signatures of broken protoplanetary discs in scattered light and in sub-millimetre observations

Spatially resolved observations of protoplanetary discs are revealing that their inner regions can be warped or broken from the outer disc. A few mechanisms are known to lead to such 3D structures; among them, the interaction with a stellar companion. We perform a 3D SPH simulation of a circumbinary disc misaligned by $60^\circ$ with respect to the binary orbital plane. The inner disc breaks from the outer regions, precessing as a rigid body, and leading to a complex evolution. As the inner disc precesses, the misalignment angle between the inner and outer discs varies by more than $100^\circ$. Different snapshots of the evolution are post-processed with a radiative transfer code, in order to produce observational diagnostics of the process. Even though the simulation was produced for the specific case of a circumbinary disc, most of the observational predictions hold for any disc hosting a precessing inner rim. Synthetic scattered light observations show strong azimuthal asymmetries, where the pattern depends strongly on the misalignment angle between inner and outer disc. The asymmetric illumination of the outer disc leads to azimuthal variations of the temperature structure, in particular in the upper layers, where the cooling time is short. These variations are reflected in asymmetric surface brightness maps of optically thick lines, as CO $J$=3-2. The kinematical information obtained from the gas lines is unique in determining the disc structure. The combination of scattered light images and (sub-)mm lines can distinguish between radial inflow and misaligned inner disc scenarios.Comment: 17 pages, 17 figures. Accepted for publication in MNRA

Probing the presence of planets in transition discs' cavities via warps: the case of TW Hya

We are entering the era in which observations of protoplanetary discs properties can indirectly probe the presence of massive planets or low mass stellar companions interacting with the disc. In particular, the detection of warped discs can provide important clues to the properties of the star-disc system. In this paper we show how observations of warped discs can be used to infer the dynamical properties of the systems. We concentrate on circumbinary discs, where the mass of the secondary can be planetary. First, we provide some simple relations that link the amplitude of the warp in the linear regime to the parameters of the system. Secondly, we apply our method to the case of TW Hya, a transition disc for which a warp has been proposed based on spectroscopic observations. Assuming values for the disc and stellar parameters from observations, we conclude that, in order for a warp induced by a planetary companion to be detectable, the planet mass should be large ($M_{\rm p} \approx 10 - 14M_{\rm J}$) and the disc should be viscous ($\alpha \approx 0.15 - 0.25$). We also apply our model to LkCa 15 and T Cha, where a substellar companion has been detected within the central cavity of the transition discs.Comment: 12 pages, 4 figures, 2 tables. Accepted for publication in MNRA

Wave-like warp propagation in circumbinary discs I. Analytic theory and numerical simulations

In this paper we analyse the propagation of warps in protostellar circumbinary discs. We use these systems as a test environment in which to study warp propagation in the bending-wave regime, with the addition of an external torque due to the binary gravitational potential. In particular, we want to test the linear regime, for which an analytic theory has been developed. In order to do so, we first compute analytically the steady state shape of an inviscid disc subject to the binary torques. The steady state tilt is a monotonically increasing function of radius. In the absence of viscosity, the disc does not present any twist. Then, we compare the time-dependent evolution of the warped disc calculated via the known linearised equations both with the analytic solutions and with full 3D numerical simulations, which have been performed with the PHANTOM SPH code using 2 million particles. We find a good agreement both in the tilt and in the phase evolution for small inclinations, even at very low viscosities. Moreover, we have verified that the linearised equations are able to reproduce the diffusive behaviour when {\alpha} > H/R, where {\alpha} is the disc viscosity parameter. Finally, we have used the 3D simulations to explore the non-linear regime. We observe a strongly non-linear behaviour, which leads to the breaking of the disc. Then, the inner disc starts precessing with its own precessional frequency. This behaviour has already been observed with numerical simulations in accretion discs around spinning black holes. The evolution of circumstellar accretion discs strongly depends on the warp evolution. Therefore the issue explored in this paper could be of fundamental importance in order to understand the evolution of accretion discs in crowded environments, when the gravitational interaction with other stars is highly likely, and in multiple systems.Comment: 15 pages, 17 figures, accepted for publication in MNRA