Stefano Facchini

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 bendingwave 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 stea dy state shape of an inviscid disc subject to the binary torques. The steady state tilt is a mono tonically increasing function of radius, but misalignment is found at the disc inner edge. 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. The simulations have been performed with the PHANTOM SPH code using 2 million particles. We find a good agreement both in the tilt an d 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 be haviour when α > H/R, where α 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 o wn 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 li kely, and in multiple systems. Moreover, the evolution of the angular momentum of the disc will affect the history of the angular momentum of forming planets.

External photoevaporation of protoplanetary discs in sparse stellar groups: the impact of dust growth

We estimate the mass loss rates of photoevaporative winds launched from the outer edge of protoplanetary discs impinged by an ambient radiation field. We focus on mild/moderate environments (the number of stars in the group/cluster is N ~ 50), and explore disc sizes ranging between 20 and 250 AU. We evaluate the steady-state structures of the photoevaporative winds by coupling temperature estimates obtained with a PDR code with 1D radial hydrodynamical equations. We also consider the impact of dust dragging and grain growth on the final mass loss rates. We find that these winds are much more significant than have been appreciated hitherto when grain growth is included in the modelling: in particular, mass loss rates > 1e-8 M_sun/yr are predicted even for modest background field strengths ( ~ 30 G_0) in the case of discs that extend to R > 150 AU. Grain growth significantly affects the final mass loss rates by reducing the average cross section at FUV wavelengths, and thus allowing a much more vigorous flow. The radial profiles of observable quantities (in particular surface density, temperature and velocity patterns) indicate that these winds have characteristic features that are now potentially observable with ALMA. In particular, such discs should have extended gaseous emission that is dust depleted in the outer regions, characterised by a non-Keplerian rotation curve, and with a radially increasing temperature gradient.

A tidal encounter caught in the act: modelling a star–disc fly-by in the young RW Aurigae system

RW Aurigae (RW Aur) is a binary star system with a long molecular arm trailing the primary star. Cabrit et al. (2006) noted the resemblance between this extended structure and the tidal arm stripped from the primary star in the simulations of stardisc encounters by Clarke & Pringle (1993). In this paper we use new hydrodynamical models and synthetic observations to t many of the parameters of RW Aur. Using hydrodynamic models we nd that the morphological appearance of RW Aur can be indeed explained by a tidal encounter with the secondary star. We reproduce all the major morphological and kinematic features of the system. Using radiative transfer calculations, we nd that synthetic CO and dust continuum observations of our hydrodynamic models agree well with observations. We reproduce all the main features of the line proles, from emission uxes to the optical depth of the dierent components of the system. The agreement between observations and simulations thus lends strong support to the hypothesis of a tidal encounter scenario. Finally, we propose a possible solution for the origin of the dimming of the primary star observed in 2010/2011 by Rodriguez et al. (2013).

Robustness of N2H+ as tracer of the CO snowline

Context. Snowlines in protoplanetary disks play an important role in planet formation and composition. Since the CO snowline is difficult to observe directly with CO emission, its location has been inferred in several disks from spatially resolved ALMA observations of DCO + and N 2 H + . Aims. N 2 H + is considered to be a good tracer of the CO snowline based on astrochemical considerations predicting an anti-correlation between N 2 H + and gas-phase CO. In this work, the robustness of N 2 H + as a tracer of the CO snowline is investigated. Methods. A simple chemical network was used in combination with the radiative transfer code LIME to model the N 2 H + distribution and corresponding emission in the disk around TW Hya. The assumed CO and N 2 abundances, corresponding binding energies, cosmic ray ionization rate, and degree of large-grain settling were varied to determine the effects on the N 2 H + emission and its relation to the CO snowline. Results. For the adopted physical structure of the TW Hya disk and molecular binding energies for pure ices, the balance between freeze-out and thermal desorption predicts a CO snowline at 19 AU, corresponding to a CO midplane freeze-out temperature of 20 K. The N 2 H + column density, however, peaks 5–30 AU outside the snowline for all conditions tested. In addition to the expected N 2 H + layer just below the CO snow surface, models with an N 2 /CO ratio ≳0.2 predict an N 2 H + layer higher up in the disk due to a slightly lower photodissociation rate for N 2 as compared to CO. The influence of this N 2 H + surface layer on the position of the emission peak depends on the total CO and N 2 abundances and the disk physical structure, but the emission peak generally does not trace the column density peak. A model with a total (gas plus ice) CO abundance of 3 × 10 -6 with respect to H 2 fits the position of the emission peak previously observed for the TW Hya disk. Conclusions. The relationship between N 2 H + and the CO snowline is more complicated than generally assumed: for the investigated parameters, the N 2 H + column density peaks at least 5 AU outside the CO snowline. Moreover, the N 2 H + emission can peak much further out, as far as ~50 AU beyond the snowline. Hence, chemical modeling, as performed here, is necessary to derive a CO snowline location from N 2 H + observations.

Grand Challenges in Protoplanetary Disc Modelling

The Protoplanetary Discussions conference—held in Edinburgh, UK, from 2016 March 7th–11th—included several open sessions led by participants. This paper reports on the discussions collectively concerned with the multi-physics modelling of protoplanetary discs, including the self-consistent calculation of gas and dust dynamics, radiative transfer, and chemistry. After a short introduction to each of these disciplines in isolation, we identify a series of burning questions and grand challenges associated with their continuing development and integration. We then discuss potential pathways towards solving these challenges, grouped by strategical, technical, and collaborative developments. This paper is not intended to be a review, but rather to motivate and direct future research and collaboration across typically distinct fields based on community-driven input, to encourage further progress in our understanding of circumstellar and protoplanetary discs.

Different dust and gas radial extents in protoplanetary disks : consistent models of grain growth and CO emission

Context. ALMA observations of protoplanetary disks confirm earlier indications that there is a clear difference between the dust and gas radial extents. The origin of this difference is still debated, with both radial drift of the dust and optical depth effects suggested in the literature. Aims. In thermo-chemical models, the dust properties are usually prescribed by simple parametrisations. In this work, the feedback of more realistic dust particle distributions onto the gas chemistry and molecular emissivity is investigated, with a particular focus on CO isotopologues. Methods. The radial dust grain size distribution is determined using dust evolution models that include growth, fragmentation, and radial drift for a given static gas density structure. The vertical settling of dust particles is computed in steady-state. A new version of the code DALI is used to take into account how dust surface area and density influence the disk thermal structure, molecular abundances, and excitation. Synthetic images of both continuum thermal emission and low J CO isotopologues lines are produced. Results. The difference of dust and gas radial sizes is largely due to differences in the optical depth of CO lines and millimeter continuum, without the need to invoke radial drift. The effect of radial drift is primarily visible in the sharp outer edge of the continuum intensity profile. The gas outer radius probed by (CO)-C-12 emission can easily differ by a factor of similar to two between the models for a turbulent alpha ranging between 10(-4) and 10(-2), with the ratio of the CO and mm radius R-CO(out)/R-mm(out) increasing with turbulence. Grain growth and settling concur in thermally decoupling the gas and dust components, due to the low collision rate with large grains. As a result, the gas can be much colder than the dust at intermediate heights, reducing the CO excitation and emission, especially for low turbulence values. Also, due to disk mid-plane shadowing, a second CO thermal desorption (rather than photodesorption) front can occur in the warmer outer mid-plane disk. The models are compared to ALMA observations of HD 163296 as a test case. In order to reproduce the observed CO snowline of the system, a binding energy for CO typical of ice mixtures, with E-b >= 1100 K, needs to be used rather than the lower pure CO value. Conclusions. The difference between observed gas and dust extent is largely due to optical depth effects, but radial drift and grain size evolution also affect the gas and dust emission in subtle ways. In order to properly infer fundamental quantities of the gaseous component of disks, such as disk outer radii and gas surface density profiles, simultaneous modelling of both dust and gas observations including dust evolution is needed.

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 smoothed particle hydrodynamics 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 ∼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 time-scale of ≈3000(α/0.05) −1 yr, where α 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.

An ALMA Survey of protoplanetary disks in the σ Orionis cluster

The σ Orionis cluster is important for studying protoplanetary disk evolution, as its intermediate age (∼3–5 Myr) is comparable to the median disk lifetime. We use ALMA to conduct a high-sensitivity survey of dust and gas in 92 protoplanetary disks around σ Orionis members with M∗ & 0.1 M . Our observations cover the 1.33 mm continuum and several CO J = 2–1 lines: out of 92 sources, we detect 37 in the mm continuum and six in CO, three in CO, and none in CO. Using the continuum emission to estimate dust mass, we find only 11 disks with Mdust & 10 M⊕, indicating that after only a few Myr of evolution most disks lack sufficient dust to form giant planet cores. Stacking the individually undetected continuum sources limits their average dust mass to 5× lower than that of the faintest detected disk, supporting theoretical models that indicate rapid dissipation once disk clearing begins. Comparing the protoplanetary disk population in σ Orionis to those of other star-forming regions supports the steady decline in average dust mass and the steepening of the Mdust–M∗ relation with age; studying these evolutionary trends can inform the relative importance of different disk processes during key eras of planet formation. External photoevaporation from the central O9 star is influencing disk evolution throughout the region: dust masses clearly decline with decreasing separation from the photoionizing source, and the handful of CO detections exist at projected separations > 1.5 pc. Collectively, our findings indicate that giant planet formation is inherently rare and/or well underway by a few Myr of age.

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_p ≈ 10–14M_J) and the disc should be viscous (α ≈ 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.

ALMA Survey of Lupus Protoplanetary Disks. II. Gas Disk Radii

We present Atacama Large Millimeter/Sub-Millimeter Array (ALMA) Band 6 observations of a complete sample of protoplanetary disks in the young (~1–3 Myr) Lupus star-forming region, covering the 1.33 mm continuum and the 12CO, 13CO, and C18O J = 2–1 lines. The spatial resolution is ~0farcs25 with a medium 3σ continuum sensitivity of 0.30 mJy, corresponding to M dust ~ 0.2 M ⊕. We apply Keplerian masking to enhance the signal-to-noise ratios of our 12CO zero-moment maps, enabling measurements of gas disk radii for 22 Lupus disks; we find that gas disks are universally larger than millimeter dust disks by a factor of two on average, likely due to a combination of the optically thick gas emission and the growth and inward drift of the dust. Using the gas disk radii, we calculate the dimensionless viscosity parameter, α visc, finding a broad distribution and no correlations with other disk or stellar parameters, suggesting that viscous processes have not yet established quasi-steady states in Lupus disks. By combining our 1.33 mm continuum fluxes with our previous 890 μm continuum observations, we also calculate the millimeter spectral index, α mm, for 70 Lupus disks; we find an anticorrelation between α mm and millimeter flux for low-mass disks (M dust lesssim 5), followed by a flattening as disks approach α mm ≈ 2, which could indicate faster grain growth in higher-mass disks, but may also reflect their larger optically thick components. In sum, this work demonstrates the continuous stream of new insights into disk evolution and planet formation that can be gleaned from unbiased ALMA disk surveys.