Gas vs dust radial extent in disks: the importance of their thermal interplay

A key parameter governing the secular evolution of protoplanetary disks is their outer radius. In this paper, the feedback of realistic dust grain size distributions onto the gas emission is investigated. Models predict that the difference of dust and gas extents as traced by CO is primarily caused by differences in the optical depth of lines vs continuum. The main effect of radial drift is the sharp decrease in the intensity profile at the outer edge. The gas radial extent can easily range within a factor of 2 for models with different turbulence. A combination of grain growth and vertical settling leads to thermal de-coupling between gas and dust at intermediate scale-heights. A proper treatment of the gas thermal structure within dust gaps will be fundamental to disentangle surface density gaps from gas temperature gaps.Comment: 8 pages, 6 figures. To appear in the Proceedings of IAU Symposium 332: Astrochemistry VII - Through the Cosmos from Galaxies to Planet

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

Decoupled Quantum Walks, models of the Klein-Gordon and wave equations

Decoupling a vectorial PDE consists in solving the system for each component, thereby obtaining scalar PDEs that prescribe the evolution of each component independently. We present a general approach to decoupling of Quantum Walks, again defined as a procedure to obtain an evolution law for each scalar component of the QW, in such a way that it does not depend on the other components. In particular, the method is applied to show the relation between the Dirac (or Weyl) Quantum Walk in three space dimensions with (or without) mass term, and the Klein-Gordon (or wave) equation

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

The complex interplay between gas and dust in protoplanetary disks

The high sensitivity and angular resolution of ALMA and optical and NIR imagers are providing new insights on the typical properties of protoplanetary disks. A plethora of substructures are currently being observed, ranging from rings and gaps to spirals and strong azimuthal asymmetries. Most of these features have been characterized in continuum emission, from optical to cm wavelengths, and many models have been invoked to explain their origin. A key observational diagnostic to discriminate between the different models are spatially resolved molecular line emission, which can directly probe the gas temperature and density structure. In this talk I will show how the combination of continuum and CO observations can put stringent constraints on the physical origin of these substructures, in particular rings, gaps and azimuthal asymmetries. In the hypothesis of embedded planets sculpting the disk, the combined information of gas and dust can be used to infer the mass of the purported planet(s). Both dynamical and thermal coupling between gas and dust has to be considered when interpreting the observations and correctly estimate fundamental disks properties as simple as their outer radius

No-signaling, entanglement-breaking, and localizability in bipartite channels

A bipartite quantum channel represents the interaction between systems, generally allowing for exchange of information. A special class of bipartite channels are the no-signaling ones, which do not allow communication. In Ref. [1] it has been conjectured that all no-signaling channels are mixtures of entanglement-breaking and localizable channels, which require only local operations and entanglement. Here we provide the general realization scheme, giving a counterexample to the conjecture.Comment: 4 pages, revtex