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Planet-disc interactions build up local pressure maxima that may halt the radial drift of protoplanetary dust, and pile it up in rings and crescents. ALMA observations of the HD135344B disc revealed two rings in the thermal continuum stemming from ~mm-sized dust. At higher frequencies the inner ring is brighter relative to the outer ring, which is also shaped as a crescent rather than a full ring. In near-IR scattered light images, the disc is modulated by a 2-armed grand-design spiral originating inside the ALMA inner ring. Such structures may be induced by a massive companion evacuating the central cavity, and by a giant planet in the gap separating both rings, that channels the accretion of small dust and gas through its filamentary wakes while stopping the larger dust from crossing the gap. Here we present ALMA observations in the J=(2-1)CO isotopologue lines and in the adjacent continuum, with up to 12km baselines. Angular resolutions of 0.03" reveal the tentative detection of a filament connecting both rings, and which coincides with a local discontinuity in the pitch angle of the IR spiral, proposed previously as the location of the protoplanet driving this spiral. Line diagnostics suggest that turbulence, or superposed velocity components, is particularly strong in the spirals. The 12CO(2-1) 3-D rotation curve points at stellocentric accretion at radii within the inner dust ring, with a radial velocity of up to ~6%+-0.5% Keplerian, which corresponds to an excessively large accretion rate of ~2E-6M_sun/yr if all of the CO layer follows the 12CO(2-1) kinematics. This suggests that only the surface layers of the disc are undergoing accretion, and that the line broadening is due to superposed laminar flows., accepted to MNRAS

We test the hypothesis that an embedded giant planet in the IM Lupi protostellar disc can produce velocity kinks seen in CO line observations as well as the spiral arms seen in scattered light and continuum emission. We inject planets into 3D hydrodynamics simulations of IM Lupi, generating synthetic observations using Monte Carlo radiative transfer. We find that an embedded planet of 2-3 times the mass of Jupiter can reproduce non-Keplerian velocity perturbations, or `kinks', in the 12CO J=2-1 channel maps. Such a planet can also explain the spiral arms seen in 1.25mm dust continuum emission and 1.6 micron scattered light images. We show that the wake of the planet can be traced in the observed peak velocity map, which appears to closely follow the morphology expected from our simulations and from analytic models of planet-disc interaction., 10 pages, 6 figures, accepted to ApJL. Radiative transfer models and a movie showing change with azimuth available from https://doi.org/10.26180/20145620.v3

We present ALMA observations of the $^{12}$CO, $^{13}$CO, C$^{18}$O J=2-1 transitions and the 1.3\,mm continuum emission for the circumbinary disc around HD 142527, at an angular resolution of $\approx$\,0\farcs3. We observe multiple spiral structures in intensity, velocity and velocity dispersion for the $^{12}$CO and $^{13}$CO gas tracers. A newly detected $^{12}$CO spiral originates from the dust horseshoe, and is rotating at super-Keplerian velocity or vertically ascending, whilst the inter-spiral gas is rotating at sub-Keplerian velocities. This new spiral possibly connects to a previously identified spiral, thus spanning > 360$^\circ$. A spatial offset of ~30 au is observed between the $^{12}$CO and $^{13}$CO spirals, to which we hypothesize that the gas layers are propagating at different speeds (``surfing'') due to a non-zero vertical temperature gradient. Leveraging the varying optical depths between the CO isotopologues, we reconstruct temperature and column density maps of the outer disc. Gas surface density peaks at r\,$\approx$\,180\,au, coincident with the peak of continuum emission. Here the dust grains have a Stokes number of $\approx$\,1, confirming radial and azimuthal trapping in the horseshoe. We measure a cavity radius at half-maximum surface density of $\approx$\,100\,au, and a cavity eccentricity between 0.3 and 0.45.

We present 1.3 mm continuum ALMA long-baseline observations at 3-5 au resolution of 10 of the brightest discs from the Ophiuchus DIsc Survey Employing ALMA (ODISEA) project. We identify a total of 26 narrow rings and gaps distributed in 8 sources and 3 discs with small dust cavities (r $$20 au). We find that the 1.3 mm radial profiles of these objects are in good agreement with those produced by numerical simulations of dust evolution and planet-disc interactions, which predict the accumulation of mm-sized grains at the edges of planet-induced cavities. Our long-baseline observations resulted in the largest sample of discs observed at $\sim$3-5 au resolution in any given star-forming region (15 objects when combined with Ophiuchus objects in the DSHARP Large Program) and allow for a demographic study of the brightest $\sim5\%$ of the discs in Ophiuchus (i.e. the most likely formation sites of giant planets in the cloud). We use this unique sample to propose an evolutionary sequence and discuss a scenario in which the substructures observed in massive protoplanetary discs are mainly the result of planet formation and dust evolution. If this scenario is correct, the detailed study of disc substructures might provide a window to investigate a population of planets that remains mostly undetectable by other techniques., Comment: 21 pages, 10 figures. Appendix with 3 additional figures. Version 2, identical to previous one, but now accepted for publication (in MNRAS)

How does the cavity size in circumbinary discs depend on disc and binary properties? We investigate by simulating disc cavities carved by binary companions using smoothed particle hydrodynamics (SPH). We find that a cavity is quickly opened on the dynamical time, while the cavity size is set on the viscous time. In agreement with previous findings, we find long term cavity sizes of 2-5 times the binary semi-major axis, increasing with eccentricity and decreasing with disc aspect ratio. When considering binaries inclined with respect to the disc we find three regimes: i) discs that evolve towards a coplanar orbit have a large cavity, slightly smaller than that of an initially coplanar disc; ii) discs that evolve towards a polar orbit by breaking have a small cavity, equal in size to that of an initially polar disc; iii) discs that evolve towards a polar orbit via warping have an intermediate-sized cavity. We find typical gas depletions inside the cavity of $\gtrsim 2$ orders of magnitude in surface density., Comment: 12 pages, 13 figures, accepted to MNRAS

Young multiple systems accrete most of their final mass in the first few Myr of their lifetime, during the protostellar and protoplanetary phases. Previous studies showed that in binary systems the majority of the accreted mass falls onto the lighter star, thus evolving to mass equalisation. However, young stellar systems often comprise more than two stars, which are expected to be in hierarchical configurations. Despite its astrophysical relevance, differential accretion in hierarchical systems remains to be understood. In this work, we investigate whether the accretion trends expected in binaries are valid for higher order multiples. We performed a set of 3D Smoothed Particle Hydrodynamics simulations of binaries and of hierarchical triples (HTs) embedded in an accretion disc, with the code Phantom. We identify for the first time accretion trends in HTs and their deviations compared to binaries. These deviations, due to the interaction of the small binary with the infalling material from the circum-triple disc, can be described with a semi-analytical prescription. Generally, the smaller binary of a HT accretes more mass than a single star of the same mass as the smaller binary. We found that in a HT, if the small binary is heavier than the third body, the standard differential accretion scenario (whereby the secondary accretes more of the mass) is hampered. Reciprocally, if the small binary is lighter than the third body, the standard differential accretion scenario is enhanced. The peculiar differential accretion mechanism we find in HTs is expected to affect their mass ratio distribution., Comment: Accepted for publication in MNRAS, 15 pages, 13 figures, 1 tables, 2 appendices

Tidal encounters in star clusters perturb discs around young protostars. In Cuello et al. (2019a, Paper I) we detailed the dynamical signatures of a stellar flyby in both gas and dust. Flybys produce warped discs, spirals with evolving pitch angles, increasing accretion rates, and disc truncation. Here we present the corresponding observational signatures of these features in optical/near-infrared scattered light and (sub-) millimeter continuum and CO line emission. Using representative prograde and retrograde encounters for direct comparison, we post-process hydrodynamical simulations with radiative transfer methods to generate a catalogue of multi-wavelength observations. This provides a reference to identify flybys in recent near-infrared and sub-millimetre observations (e.g., RW Aur, AS 205, HV Tau & DO Tau, FU Ori, V2775 Ori, and Z CMa)., 11 pages, 5 figures, accepted for publication in MNRAS

Nearly all young stars are initially surrounded by `protoplanetary' discs of gas and dust, and in the case of single stars at least 30\% of these discs go on to form planets. The process of protoplanetary disc formation can result in initial misalignments, where the disc orbital plane is different to the stellar equator in single star systems, or to the binary orbital plane in systems with two stars. A quirk of the dynamics means that initially misaligned `circumbinary' discs -- those that surround two stars -- are predicted to evolve to one of two possible stable configurations, one where the disc and binary orbital planes are coplanar, and one where they are perpendicular (a `polar' configuration). Prior work has found coplanar circumbinary discs, but no polar examples were known until now. Here we report the first discovery of a protoplanetary circumbinary disc in the polar configuration, supporting the predictions that such discs should exist. The disc shows some characteristics that are similar to discs around single stars, and that are attributed to dust growth. Thus, the first stages of planet formation appear able to proceed in polar circumbinary discs., Comment: Submitted version - do not read. Published in Nature Astronomy, free PDF at https://rdcu.be/bgNSO

Of the 21 known gaseous debris discs around white dwarfs, a large fraction of them display observational features that are well described by an eccentric distribution of gas. In the absence of embedded objects or additional forces, these discs should not remain eccentric for long timescales, and should instead circularise due to viscous spreading. The metal pollution and infrared excess we observe from these stars is consistent with the presence of tidally disrupted sub-stellar bodies. We demonstrate, using smoothed particle hydrodynamics, that a sublimating or partially disrupting planet on an eccentric orbit around a white dwarf will form and maintain a gas disc with an eccentricity within 0.1 of, and lower than, that of the orbiting body. We also demonstrate that the eccentric gas disc observed around the white dwarf SDSS J1228+1040 can be explained by the same hypothesis., 5 pages, 5 figures, accepted to MNRAS Letters

Misalignments within protoplanetary discs are now commonly observed, and features such as shadows in scattered light images indicate departure from a co-planar geometry. VLT/SPHERE observations of the disc around HD 143006 show a large-scale asymmetry, and two narrow dark lanes which are indicative of shadowing. ALMA observations also reveal the presence of rings and gaps in the disc, along with a bright arc at large radii. We present new hydrodynamic simulations of HD 143006, and show that a configuration with both a strongly inclined binary and an outer planetary companion is the most plausible to explain the observed morphological features. We compute synthetic observations from our simulations, and successfully reproduce both the narrow shadows and the brightness asymmetry seen in IR scattered light. Additionally, we reproduce the large dust observed in the mm continuum, due to a 10 Jupiter mass planet detected in the CO kinematics. Our simulations also show the formation of a circumplanetary disc, which is misaligned with respect to the outer disc. The narrow shadows cast by the inner disc and the planet-induced "kink" in the disc kinematics are both expected to move on a time-scale of $\sim$ 5-10 years, presenting a potentially observable test of our model. If confirmed, HD 143006 would be the first known example of a circumbinary planet on a strongly misaligned orbit., Accepted for publication in MNRAS, 10 pages, 8 figures. Movies of the simulation available at the following links: https://www.youtube.com/watch?v=F8GAw-Fzpyg&list=PLgaPAkHEP_RqxHJUvj9DIcsjEpWqbTPwQ&index=3 and https://www.youtube.com/watch?v=HCZQdS3t4l8&list=PLgaPAkHEP_RqxHJUvj9DIcsjEpWqbTPwQ&index=1

Understanding how giant planets form requires observational input from directly imaged protoplanets. We used VLT/NACO and VLT/SPHERE to search for companions in the transition disc of 2MASS J19005804-3645048 (hereafter CrA-9), an accreting M0.75 dwarf with an estimated age of 1-2 Myr. We found a faint point source at $\sim$0.7'' separation from CrA-9 ($\sim$108 au projected separation). Our 3-epoch astrometry rejects a fixed background star with a $5\sigma$ significance. The near-IR absolute magnitudes of the object point towards a planetary-mass companion. However, our analysis of the 1.0-3.8$\mu$m spectrum extracted for the companion suggests it is a young M5.5 dwarf, based on both the 1.13-$\mu$m Na index and comparison with templates of the Montreal Spectral Library. The observed spectrum is best reproduced with high effective temperature ($3057^{+119}_{-36}$K) BT-DUSTY and BT-SETTL models, but the corresponding photometric radius required to match the measured flux is only $0.60^{+0.01}_{-0.04}$ Jovian radius. We discuss possible explanations to reconcile our measurements, including an M-dwarf companion obscured by an edge-on circum-secondary disc or the shock-heated part of the photosphere of an accreting protoplanet. Follow-up observations covering a larger wavelength range and/or at finer spectral resolution are required to discriminate these two scenarios., Comment: 24 pages, 14 figures, 4 tables, to be published in MNRAS

We present the implementation of a dust growth and fragmentation module in the public Smoothed Particle Hydrodynamics (SPH) code PHANTOM. This module is made available for public use with this paper. The coagulation model considers locally monodisperse dust size distributions around single values that are carried by the SPH particles. Along with the presentation of the model, implementation and tests, we showcase growth and fragmentation in a few typical circumstellar disc simulations and revisit previous results. The module is also interfaced with the radiative transfer code MCFOST, which facilitates the comparison between simulations and ALMA observations by generating synthetic maps. Circumstellar disc simulations with growth and fragmentation reproduce the `self-induced dust trap' mechanism first proposed by Gonzalez et al., which supports its existence. Synthetic images of discs featuring this mechanism suggest it would be detectable by ALMA as a bright axisymmetric ring at several tens of au from the star. With this paper, our aim is to provide a public tool to be able to study and explore dust growth in a variety of applications related to planet formation., 22 pages, 27 figures, accepted for publication in MNRAS

IRAS~04158+2805 has long been thought to be a very low mass T-Tauri star (VLMS) surrounded by a nearly edge-on, extremely large disc. Recent observations revealed that this source hosts a binary surrounded by an extended circumbinary disc with a central dust cavity. In this paper, we combine ALMA multi-wavelength observations of continuum and $^{12}$CO line emission, with H$\alpha$ imaging and Keck astrometric measures of the binary to develop a coherent dynamical model of this system. The system features an azimuthal asymmetry detected at the western edge of the cavity in Band~7 observations and a wiggling outflow. Dust emission in ALMA Band 4 from the proximity of the individual stars suggests the presence of marginally resolved circumstellar discs. We estimate the binary orbital parameters from the measured arc of the orbit from Keck and ALMA astrometry. We further constrain these estimates using considerations from binary-disc interaction theory. We finally perform three SPH gas + dust simulations based on the theoretical constraints; we post-process the hydrodynamic output using radiative transfer Monte Carlo methods and directly compare the models with observations. Our results suggest that a highly eccentric $e\sim 0.5\textrm{--}0.7$ equal mass binary, with a semi-major axis of $\sim 55$ au, and small/moderate orbital plane vs. circumbinary disc inclination $\theta\lesssim 30^\circ$ provides a good match with observations. A dust mass of $\sim 1.5\times 10^{-4} {\rm M_\odot}$ best reproduces the flux in Band 7 continuum observations. Synthetic CO line emission maps qualitatively capture both the emission from the central region and the non-Keplerian nature of the gas motion in the binary proximity., Comment: 19 pages, 14 figures, 1 table, accepted for publication in MNRAS

Black hole - neutron star (BH-NS) mergers are a major target for ground-based gravitational wave (GW) observatories. A merger can also produce an electromagnetic counterpart (a kilonova) if it ejects neutron-rich matter that assembles into heavy elements through r-process nucleosynthesis. We study the kilonova signatures of the unbound dynamical ejecta of a BH-NS merger. We take as our initial state the results from a numerical relativity simulation, and then use a general relativistic hydrodynamics code to study the evolution of the ejecta with parameterized r-process heating models. The unbound dynamical ejecta is initially a flattened, directed tidal tail largely confined to a plane. Heating from the r-process inflates the ejecta into a more spherical shape and smooths its small-scale structure, though the ejecta retains its bulk directed motion. We calculate the electromagnetic signatures using a 3D radiative transfer code and a parameterized opacity model for lanthanide-rich matter. The light curve varies with viewing angle due to two effects: asphericity results in brighter emission for orientations with larger projected areas, while Doppler boosting results in brighter emission for viewing angles more aligned with the direction of bulk motion. For typical r-process heating rates, the peak bolometric luminosity varies by a factor of $\sim 3$ with orientation while the peak in the optical bands varies by $\sim 3$ magnitudes. The spectrum is blue-shifted at viewing angles along the bulk motion, which increases the $V$-band peak magnitude to $\sim -14$ despite the lanthanide-rich composition., Comment: 26 pages, 15 figures; revised paper after reviewer's comments

The nebular circumstellar environments of cool evolved stars are known to harbour a rich morphological complexity of gaseous structures on different length scales. A large part of these density structures are thought to be brought about by the interaction of the stellar wind with a close companion. The S-type asymptotic giant branch star Pi1 Gruis, which has a known companion at ~440 au and is thought to harbour a second, closer-by (, 19 pages, 20 figures

Protoplanetary disks with large inner dust cavities are thought to host massive planetary or substellar companions. These disks show asymmetries and rings in the millimeter continuum, caused by dust trapping in pressure bumps, and potentially vortices or horseshoes. The origin of the asymmetries and their diversity remains unclear. We present a comprehensive study of 16 disks for which the gas surface density profile has been constrained by CO isotopologue data. We compare the azimuthal extents of the dust continuum profiles with the local gas surface density in each disk, and find that the asymmetries correspond to higher Stokes numbers or low gas surface density. We discuss which asymmetric structures can be explained by a horseshoe, a vortex or spiral density waves. Second, we reassess the gas gap radii from the $^{13}$CO maps, which are about a factor 2 smaller than the dust ring radii, suggesting that companions in these disks are in the brown dwarf mass regime ($\sim 15-50 M_{\rm Jup}$) or in the Super-Jovian mass regime ($\sim 3-15 M_{\rm Jup}$) on eccentric orbits. This is consistent with the estimates from contrast curves on companion mass limits. These curves rule out (sub)stellar companions ($q>$0.05) for the majority of the sample at the gap location, but it remains possible at even smaller radii. Third, we find that spiral arms in scattered light images are primarily detected around high luminosity stars with disks with wide gaps, which can be understood by the dependence of the spiral arm pitch angle on disk temperature and companion mass., 36 pages, 16 figures. Accepted by the Astronomical Journal. Version 2 has fixed Figure 11 for which the subplots got mixed up

We present a method for simulating the dynamics of a mixture of gas and multiple species of large Stokes number dust grains, typical of evolved protoplanetary discs and debris discs. The method improves upon earlier methods, in which only a single grain size could be represented, by capturing the differential backreaction of multiple dust species on the gas. This effect is greater for large dust-to-gas ratios that may be expected in the later stages of the protoplanetary disc life. We benchmark the method against analytic solutions for linear waves, drag and shocks in dust-gas mixtures, and radial drift in a protoplanetary disc showing that the method is robust and accurate., 13 pages, 8 figures, accepted for publication in MNRAS, update to corrected version

We present observations of the young multiple system UX Tauri to look for circumstellar disks and for signs of dynamical interactions. We obtained SPHERE/IRDIS deep differential polarization images in the J and H bands. We also used ALMA archival CO data. Large extended spirals are well detected in scattered light coming out of the disk of UX Tau A. The southern spiral forms a bridge between UX Tau A and C. These spirals, including the bridge connecting the two stars, all have a CO (3-2) counterpart seen by ALMA. The disk of UX Tau C is detected in scattered light. It is much smaller than the disk of UX Tau A and has a major axis along a different position angle, suggesting a misalignment. We performed PHANTOM SPH hydrodynamical models to interpret the data. The scattered light spirals, CO emission spirals and velocity patterns of the rotating disks, and the compactness of the disk of UX Tau C all point to a scenario in which UX Tau A has been perturbed very recently (about 1000 years) by the close passage of UX Tau C., Comment: Accepted for publication in Astronomy & Astrophysics Letters. (8pages, 8 figures). 2 movies will be available on-line

Recent mm-wavelength surveys performed with the Atacama Large Millimeter Array (ALMA) have revealed protoplanetary discs characterized by rings and gaps. A possible explanation for the origin of such rings is the tidal interaction with an unseen planetary companion. The protoplanetary disc around DS Tau shows a wide gap in the ALMA observation at 1.3 mm. We construct a hydrodynamical model for the dust continuum observed by ALMA assuming the observed gap is carved by a planet between one and five Jupiter masses. We fit the shape of the radial intensity profile along the disc major axis varying the planet mass, the dust disc mass, and the evolution time of the system. The best fitting model is obtained for a planet with $M_{\rm p}=3.5\,M_{\rm Jup}$ and a disc with $M_{\rm dust}= 9.6\cdot10^{-5}\,M_{\odot}$. Starting from this result, we also compute the expected signature of the planet in the gas kinematics, as traced by CO emission. We find that such a signature (in the form of a "kink" in the channel maps) could be observed by ALMA with a velocity resolution between $0.2-0.5\,\rm{kms}^{-1}$ and a beam size between 30 and 50 mas., 16 pages, 15 figures, accepted for publication on MNRAS

Spiral arms in protoplanetary discs are thought to be linked to the presence of companions. We test the hypothesis that the double spiral arm morphology observed in the transition disc MWC 758 can be generated by an $\approx 10$ M$_{\rm Jup}$ companion on an eccentric orbit internal to the spiral arms. Previous studies on MWC 758 have assumed an external companion. We compare simulated observations from three dimensional hydrodynamics simulations of disc-companion interaction to scattered light, infrared and CO molecular line observations, taking into account observational biases. The inner companion hypothesis is found to explain the double spiral arms, as well as several additional features seen in MWC 758 -- the arc in the northwest, substructures inside the spiral arms, the cavity in CO isotopologues, and the twist in the kinematics. Testable predictions include detection of fainter spiral structure, detection of a point source south-southeast of the primary, and proper motion of the spiral arms., Comment: 13 pages, 6 figures, resubmitted to MNRAS

We study the mutual evolution of the orbital properties of high mass ratio, circular, co-planar binaries and their surrounding discs, using 3D Smoothed Particle Hydrodynamics simulations. We investigate the evolution of binary and disc eccentricity, cavity structure and the formation of orbiting azimuthal over-dense features in the disc. Even with circular initial conditions, all discs with mass ratios $q>0.05$ develop eccentricity. We find that disc eccentricity grows abruptly after a relatively long time-scale ($\sim 400\textrm{--}700$ binary orbits), and is associated with a very small increase in the binary eccentricity. When disc eccentricity grows, the cavity semi-major axis reaches values $a_{\rm cav}\approx 3.5\, a_{\rm bin}$. We also find that the disc eccentricity correlates linearly with the cavity size. Viscosity and orbit crossing, appear to be responsible for halting the disc eccentricity growth -- eccentricity at the cavity edge in the range $e_{\rm cav}\sim 0.05\textrm{--} 0.35$. Our analysis shows that the current theoretical framework cannot fully explain the origin of these evolutionary features when the binary is almost circular ($e_{\rm bin}\lesssim 0.01$); we speculate about alternative explanations. As previously observed, we find that the disc develops an azimuthal over-dense feature in Keplerian motion at the edge of the cavity. A low contrast over-density still co-moves with the flow after 2000 binary orbits; such an over-density can in principle cause significant dust trapping, with important consequences for protoplanetary disc observations., 20 pages, 17 figures, 1 table, accepted for publication in MNRAS

We report the discovery of a low-mass stellar companion around the young Herbig Be star MWC 297. We performed multi-epoch high-contrast imaging in the near infrared (NIR) with the Very Large Telescope (VLT)/Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) instrument. The companion is found at projected separation of 244.7$\pm$13.2 au and a position angle of 176.4$\pm$0.1 deg. The large separation supports formation via gravitational instability. From the spectrum, we estimate a mass of 0.1-0.5 M$_{\odot}$, the range conveying uncertainties in the extinction of the companion and in evolutionary models at young ages. The orbit coincides with a gap in the dust disk inferred from the Spectral Energy Distribution (SED). The young age ($\lesssim$ 1 Myr) and mass ratio with the central star ($\sim 0.01$) makes the companion comparable to PDS 70~b, suggesting a relation between formation scenarios and disk dynamics., Comment: 4 figures

The disc surrounding PDS 70, with two directly imaged embedded giant planets, is an ideal laboratory to study planet-disc interaction. We present three-dimensional smoothed particle hydrodynamics simulations of the system. In our simulations, planets, which are free to migrate and accrete mass, end up in a locked resonant configuration that is dynamically stable. We show that features observed at infrared (scattered light) and millimetre (thermal continuum) wavelengths are naturally explained by the accretion stream onto the outer planet, without requiring a circumplanetary disc around planet c. We post-processed our near-infrared synthetic images in order to account for observational biases known to affect high-contrast images. Our successful reproduction of the observations indicates that planet-disc dynamical interactions alone are sufficient to explain the observations of PDS 70., 15 pages, 11 figures

We present results from radiation non-ideal magnetohydrodynamics (MHD) calculations that follow the collapse of rotating, magnetised, molecular cloud cores to stellar densities. These are the first such calculations to include all three non-ideal effects: ambipolar diffusion, Ohmic resistivity and the Hall effect. We employ an ionisation model in which cosmic ray ionisation dominates at low temperatures and thermal ionisation takes over at high temperatures. We explore the effects of varying the cosmic ray ionisation rate from $\zeta_\text{cr}= 10^{-10}$ to $10^{-16}$ s$^{-1}$. Models with ionisation rates $\gtrsim 10^{-12}$ s$^{-1}$ produce results that are indistinguishable from ideal MHD. Decreasing the cosmic ray ionisation rate extends the lifetime of the first hydrostatic core up to a factor of two, but the lifetimes are still substantially shorter than those obtained without magnetic fields. Outflows from the first hydrostatic core phase are launched in all models, but the outflows become broader and slower as the ionisation rate is reduced. The outflow morphology following stellar core formation is complex and strongly dependent on the cosmic ray ionisation rate. Calculations with high ionisation rates quickly produce a fast (~14km s$^{-1}$) bipolar outflow that is distinct from the first core outflow, but with the lowest ionisation rate a slower (~3-4 km s$^{-1}$) conical outflow develops gradually and seamlessly merges into the first core outflow., Comment: 22 pages, 24 figures. Accepted for publication in MNRAS

We present results from the first radiation non-ideal magnetohydrodynamics (MHD) simulations of low-mass star cluster formation that resolve the fragmentation process down to the opacity limit. We model 50~M$_\odot$ turbulent clouds initially threaded by a uniform magnetic field with strengths of 3, 5 10 and 20 times the critical mass-to-magnetic flux ratio, and at each strength, we model both an ideal and non-ideal (including Ohmic resistivity, ambipolar diffusion and the Hall effect) MHD cloud. Turbulence and magnetic fields shape the large-scale structure of the cloud, and similar structures form regardless of whether ideal or non-ideal MHD is employed. At high densities ($10^6 \lesssim n_{\rm H} \lesssim 10^{11}$~cm$^{-3}$), all models have a similar magnetic field strength versus density relation, suggesting that the field strength in dense cores is independent of the large-scale environment. Albeit with limited statistics, we find no evidence for the dependence of the initial mass function on the initial magnetic field strength, however, the star formation rate decreases for models with increasing initial field strengths; the exception is the strongest field case where collapse occurs primarily along field lines. Protostellar discs with radii $\gtrsim 20$~au form in all models, suggesting that disc formation is dependent on the gas turbulence rather than on magnetic field strength. We find no evidence for the magnetic braking catastrophe, and find that magnetic fields do not hinder the formation of protostellar discs., 24 pages, 19 figures. Accepted for publication in MNRAS. Videos available at https://www.youtube.com/watch?v=CLhmaOhj5RU&list=PLwI7am9c6sBjW69kfhfRDMR3Gz6nzOPOi

Recent observations of protoplanetary discs reveal disc substructures potentially caused by embedded planets. We investigate how the gas surface density in discs changes the observed morphology in scattered light and dust continuum emission. Assuming that disc substructures are due to embedded protoplanets, we combine hydrodynamical modelling with radiative transfer simulations of dusty protoplanetary discs hosting planets. The response of different dust species to the gravitational perturbation induced by a planet depends on the drag stopping time - a function of the generally unknown local gas density. Small dust grains, being stuck to the gas, show spirals. Larger grains decouple, showing progressively more axisymmetric (ring-like) substructure as decoupling increases with grain size or with the inverse of the gas disc mass. We show that simultaneous modelling of scattered light and dust continuum emission is able to constrain the Stokes number, ${\rm St}$. Hence, if the dust properties are known, this constrains the local gas surface density, $\Sigma_{\rm gas}$, at the location of the structure, and hence the total gas mass. In particular, we found that observing ring-like structures in mm-emitting grains requires ${\rm St} \gtrsim 0.4$ and therefore $\Sigma_{\rm gas} \lesssim 0.4\,\textrm{g/cm}^{2}$. We apply this idea to observed protoplanetary discs showing substructures both in scattered light and in the dust continuum., Comment: Accepted for publication on MNRAS, 12 pages, 6 figures

We still do not understand how planets form, or why extra-solar planetary systems are so different from our own solar system. But the last few years have dramatically changed our view of the discs of gas and dust around young stars. Observations with the Atacama Large Millimeter/submillimeter Array (ALMA) and extreme adaptive-optics systems have revealed that most --- if not all --- discs contain substructure, including rings and gaps, spirals, azimuthal dust concentrations, and shadows cast by misaligned inner discs. These features have been interpreted as signatures of newborn protoplanets, but the exact origin is unknown. Here we report the kinematic detection of a few Jupiter-mass planet located in a gas and dust gap at 130 au in the disc surrounding the young star HD 97048. An embedded planet can explain both the disturbed Keplerian flow of the gas, detected in CO lines, and the gap detected in the dust disc at the same radius. While gaps appear to be a common feature in protoplanetary discs, we present a direct correspondence between a planet and a dust gap, indicating that at least some gaps are the result of planet-disc interactions., preprint Nature Astronomy, 4 figures, 1 table, 8 suplementary figures

We present a method for general relativistic smoothed particle hydrodynamics (GRSPH), based on an entropy-conservative form of the general relativistic hydrodynamic equations for a perfect fluid. We aim to replace approximate treatments of general relativity in current SPH simulations of tidal disruption events and accretion discs. We develop an improved shock capturing formulation that distinguishes between shock viscosity and conductivity in relativity. We also describe a new Hamiltonian time integration algorithm for relativistic orbital dynamics and GRSPH. Our method correctly captures both Einstein and spin-induced precession around black holes. We benchmark our scheme in 1D and 3D against mildly and ultra relativistic shock tubes, exact solutions for epicyclic and vertical oscillation frequencies, and Bondi accretion. We assume fixed background metrics (Minkowski, Schwarzschild and Kerr in Cartesian Boyer-Lindquist coordinates) but the method lays the foundation for future direct coupling with numerical relativity., 23 pages, 22 figures, accepted to MNRAS

We test the hypothesis that the disc cavity in the `transition disc' Oph IRS 48 is carved by an unseen binary companion. We use 3D dust-gas smoothed-particle hydrodynamics simulations to demonstrate that marginally coupled dust grains concentrate in the gas over-density that forms in in the cavity around a low binary mass ratio binary. This produces high contrast ratio dust asymmetries at the cavity edge similar to those observed in the disc around IRS 48 and other transition discs. This structure was previously assumed to be a vortex. However, we show that the observed velocity map of IRS 48 displays a peculiar asymmetry that is not predicted by the vortex hypothesis. We show the unusual kinematics are naturally explained by the non-Keplerian flow of gas in an eccentric circumbinary cavity. We further show that perturbations observed in the isovelocity curves of IRS 48 may be explained as the product of the dynamical interaction between the companion and the disc. The presence of a $\sim$0.4 M$_{\odot}$ companion at a $\sim$10 au separation can qualitatively explain these observations. High spatial resolution line and continuum imaging should be able to confirm this hypothesis., Comment: 9 pages, 7 figures, accepted for publication in MNRAS

Transition discs are prime targets to look for protoplanets and study planet-disc interactions. We present VLT/SINFONI observations of PDS~70, a transition disc with a recently claimed embedded protoplanet. We take advantage of the angular and spectral diversity present in our data for an optimal PSF modeling and subtraction using principal component analysis (PCA). We report the redetection of PDS 70 b, both the front and far side of the outer disc edge, and the detection of several extended features in the annular gap. We compare spectral differential imaging applied before (PCA-SADI), and after (PCA-ASDI) angular differential imaging. Our tests suggest that PCA-SADI better recovers extended features, while PCA-ASDI is more sensitive to point sources. We adapted the negative fake companion (NEGFC) technique to infer the astrometry of the companion, and derived $r = 193.5 \pm 4.9 \mathrm{mas}$ and PA = 158.7deg $\pm$ 3.0deg. We used both NEGFC and ANDROMEDA to infer the $K$-band spectro-photometry of the protoplanet, and found results consistent with recent VLT/SPHERE observations, except for their 2018/02 epoch measurement in the $K2$ filter. Finally, we derived an upper limit of $\dot{M_b} < 1.26 \times 10^{-7} \big[ \frac{5 M_{\rm Jup}}{M_b} \big] \big[ \frac{R_b}{R_{\rm Jup}}\big] M_{\rm Jup} $ yr$^{-1}$ for the accretion rate of the companion based on an adaptation of PCA-SADI/PCA-ASDI around the Br$\gamma$ line., Comment: 20 pages, 12 figures. This is a pre-copyedited, author-produced PDF of an article accepted for publication in MNRAS on 2019 April 29

We estimate the accretion rates produced when a circumprimary gas disc is pushed into the primary supermassive black hole (SMBH) by the tidal force of the decaying secondary during a SMBH merger. Using the 3D Smoothed Particle Hydrodynamics (SPH) code {\sc phantom}, we extend previous investigations of co-planar discs to the case where the disc and binary orbital planes are misaligned. We consider a geometrically thin disc with inclination angles varying from 1 to 180 degrees and a binary with mass ratio $q$=$10^{-3}$. We find that discs with small inclination angles (< 10 degrees) produce an increase in luminosity exceeding the Eddington rate. By contrast, discs with inclinations between 20 and 30 degrees show a less pronounced rise in the accretion rate, whilst discs inclined by 180 degrees show no peak in the mass accretion rate. While previous analytic work predicted that the effective tidal torque drops with increasing inclination angle, we show that the misaligned snowplough effect remains important even for angles larger than the disc aspect ratio. The rise in the accretion rate produced by discs inclined at small angles to the binary orbit can produce an electromagnetic counterpart to the gravitational wave signal emitted from final stages of the binary orbital decay., Accepted 2018 December 11. Received 2018 December 4; in original form 2018 September 18

We present 1D-MESA2HYDRO-3D, an open source, Python-based software tool that provides an accessible means of generating physically motivated initial conditions (ICs) for hydrodynamical simulations from 1-D stellar structure models. We test 1D-MESA2HYDRO-3D on five stellar models generated with the MESA stellar evolution code and verify its capacity as an IC generator with the Phantom smoothed-particle hydrodynamics code \citep{MESAIV, Phantom}. Consistency between the input density profiles, the 1D-MESA2HYDRO-3D-rendered particle distributions, and the state of the distributions after evolution over $10$ dynamical timescales is found for model stars ranging in structure and density from a radially extended supergiant to a white dwarf., Comment: Accepted to ApJ; 14 pages, 13 figures

We test the hypothesis that the initial mass function (IMF) is determined by the density probability distribution function (PDF) produced by supersonic turbulence. We compare 14 simulations of star cluster formation in 50 solar mass molecular cloud cores where the initial turbulence contains either purely solenoidal or purely compressive modes, in each case resolving fragmentation to the opacity limit to determine the resultant IMF. We find statistically indistinguishable IMFs between the two sets of calculations, despite a factor of two difference in the star formation rate and in the standard deviation of $\log(\rho)$. This suggests that the density PDF, while determining the star formation rate, is not the primary driver of the IMF., Comment: 6 pages, 7 figures, accepted to MNRAS

We study the evolution of galactic magnetic fields using 3D smoothed particle magnetohydrodynamics (SPMHD) simulations of galaxies with an imposed spiral potential. We consider the appearance of reversals of the field, and amplification of the field. We find magnetic field reversals occur when the velocity jump across the spiral shock is above $\approx$20km s$^{-1}$, occurring where the velocity change is highest, typically at the inner Lindblad resonance (ILR) in our models. Reversals also occur at corotation, where the direction of the velocity field reverses in the co-rotating frame of a spiral arm. They occur earlier with a stronger amplitude spiral potential, and later or not at all with weaker or no spiral arms. The presence of a reversal at a radii of around 4--6 kpc in our fiducial model is consistent with a reversal identified in the Milky Way, though we caution that alternative Galaxy models could give a similar reversal. We find that relatively high resolution, a few million particles in SPMHD, is required to produce consistent behaviour of the magnetic field. Amplification of the magnetic field occurs in the models, and while some may be genuinely attributable to differential rotation or spiral arms, some may be a numerical artefact. We check our results using Athena, finding reversals but less amplification of the field, suggesting that some of the amplification of the field with SPMHD is numerical., 15 pages, 13 figures, accepted for publication in MNRAS

We identify two distinct physical mechanisms for dust gap opening by embedded planets in protoplanetary discs based on the symmetry of the drag-induced motion around the planet: I) A mechanism where low mass planets, that do not disturb the gas, open gaps in dust by tidal torques assisted by drag in the inner disc, but resisted by drag in the outer disc; and II) The usual, drag assisted, mechanism where higher mass planets create pressure maxima in the gas disc which the drag torque then acts to evacuate further in the dust. The first mechanism produces gaps in dust but not gas, while the second produces partial or total gas gaps which are deeper in the dust phase. Dust gaps do not necessarily indicate gas gaps., 5 pages, 5 figures. Accepted for publication in MNRAS Letters

We present evidence for localised deviations from Keplerian rotation, i.e., velocity "kinks", in 8 of 18 circumstellar disks observed by the DSHARP program: DoAr 25, Elias 2-27, GW Lup, HD 143006, HD 163296, IM Lup, Sz 129 and WaOph 6. Most of the kinks are detected over a small range in both radial extent and velocity, suggesting a planetary origin, but for some of them foreground contamination prevents us from measuring their spatial and velocity extent. Because of the DSHARP limited spectral resolution and signal-to-noise in the 12CO J=2-1 line, as well as cloud contamination, the kinks are usually detected in only one spectral channel, and will require confirmation. The strongest circumstantial evidence for protoplanets in the absence of higher spectral resolution data and additional tracers is that, upon deprojection, we find that all of the candidate planets lie within a gap and/or at the end of a spiral detected in dust continuum emission. This suggests that a significant fraction of the dust gaps and spirals observed by ALMA in disks are caused by embedded protoplanets., Accepted for publication in ApJ letters, 10 pages, 3 figures

Are the kG-strength magnetic fields observed in young stars a fossil field left over from their formation or are they generated by a dynamo? We use radiation non-ideal magnetohydrodynamics simulations of the gravitational collapse of a rotating, magnetized molecular cloud core over 17 orders of magnitude in density, past the first hydrostatic core to the formation of the second, stellar core, to examine the fossil field hypothesis. Whereas in previous work we found that magnetic fields in excess of 10 kG can be implanted in stars at birth, this assumed ideal magnetohydrodynamics (MHD), i.e. that the gas is coupled to the magnetic field. Here we present non-ideal MHD calculations which include Ohmic resistivity, ambipolar diffusion and the Hall effect. For realistic cosmic ray ionization rates, we find that magnetic field strengths of $\lesssim$ kG are implanted in the stellar core at birth, ruling out a strong fossil field. While these results remain sensitive to resolution, they cautiously provide evidence against a fossil field origin for stellar magnetic fields, suggesting instead that magnetic fields in stars originate in a dynamo process., Comment: 8 pages, 8 figures. Accepted for publication in MNRAS

We test the hypothesis that the sub-millimetre thermal emission and scattered light gaps seen in recent observations of TW Hya are caused by planet-disc interactions. We perform global three-dimensional dusty smoothed particle hydrodynamics simulations, comparing synthetic observations of our models with dust thermal emission, CO emission and scattered light observations. We find that the dust gaps observed at 24 au and 41 au can be explained by two super-Earths ($\sim 4 \mathrm{M}_{\oplus}$). A planet of approximately Saturn-mass can explain the CO emission and the depth and width of the gap seen in scattered light at 94 au. Our model produces a prominent spiral arm while there are only hints of this in the data. To avoid runaway growth and migration of the planets we require a disc mass of $\lesssim 10^{-2}\,\mathrm{M}_{\odot}$ in agreement with CO observations but 10$-$100 times lower than the estimate from HD line emission., 6 pages, 5 figures, accepted for publication in MNRAS

We have simulated a common envelope interaction of a 0.88-M$_{\odot}$, 90-R$_{\odot}$, red giant branch star and a 0.6-M$_{\odot}$, compact companion with the smoothed particle hydrodynamics code, Phantom, from the beginning of the Roche lobe overflow phase to the beginning of the self-regulated inspiral, using three different resolutions. The duration of the Roche lobe overflow phase is resolution dependent and would lengthen with increased resolution beyond the $\sim$20 years observed, while the inspiral phase and the post-common envelope separation are largely independent of resolution. Mass transfer rates through the Lagrangian points drive the orbital evolution during the Roche lobe overflow phase, as predicted analytically. The absolute mass transfer rate is resolution dependent, but always within an order of magnitude of the analytical value. Similarly, the gravitational drag in the simulations is close to the analytical approximation. This gives us confidence that simulations approximate reality. The $L_2$ and $L_3$ outflow observed during Roche lobe overflow remains bound, forming a circumbinary disk that is largely disrupted by the common envelope ejection. However, a longer phase of Roche lobe overflow and weaker common envelope ejection typical of a more stable binary may result in a surviving circumbinary disk. Finally, we examine the density distribution resulting from the interaction for simulations that include or omit the phase of Roche lobe overflow. We conclude that the degree of stability of the Roche lobe phase may modulate the shape of the subsequent planetary nebula, explaining the wide range of post-common envelope planetary nebula shapes observed., Submitted to MNRAS, comments and feedback are welcomed

Discs of gas and dust surrounding young stars are the birthplace of planets. However, direct detection of protoplanets forming within discs has proved elusive to date. We present the detection of a large, localized deviation from Keplerian velocity in the protoplanetary disc surrounding the young star HD163296. The observed velocity pattern is consistent with the dynamical effect of a two Jupiter-mass planet orbiting at a radius $\approx$ 260au from the star., Accepted for publication to ApJL, 8 pages, 5 figures

We present a new algorithm, MULTIGRAIN, for modelling the dynamics of an entire population of small dust grains immersed in gas, typical of conditions that are found in molecular clouds and protoplanetary discs. The MULTIGRAIN method is more accurate than single-phase simulations because the gas experiences a backreaction from each dust phase and communicates this change to the other phases, thereby indirectly coupling the dust phases together. The MULTIGRAIN method is fast, explicit and low storage, requiring only an array of dust fractions and their derivatives defined for each resolution element., 13 pages, 8 figures. Accepted for publication in MNRAS

We present 3D hydrodynamical models of the HD142527 protoplanetary disc, a bright and well studied disc that shows spirals and shadows in scattered light around a 100 au gas cavity, a large horseshoe dust structure in mm continuum emission, together with mysterious fast radial flows and streamers seen in gas kinematics. By considering several possible orbits consistent with the observed arc, we show that all of the main observational features can be explained by one mechanism - the interaction between the disc and the observed binary companion. We find that the spirals, shadows and horseshoe are only produced in the correct position angles by a companion on an inclined and eccentric orbit approaching periastron - the 'red' family from Lacour et al. (2016). Dust-gas simulations show radial and azimuthal concentration of dust around the cavity, consistent with the observed horseshoe. The success of this model in the HD142527 disc suggests other mm-bright transition discs showing cavities, spirals and dust asymmetries may also be explained by the interaction with central companions., 16 pages, 12 figures, accepted to MNRAS. Movies at http://users.monash.edu.au/~dprice/pubs/HD142527/

We present Phantom, a fast, parallel, modular and low-memory smoothed particle hydrodynamics and magnetohydrodynamics code developed over the last decade for astrophysical applications in three dimensions. The code has been developed with a focus on stellar, galactic, planetary and high energy astrophysics and has already been used widely for studies of accretion discs and turbulence, from the birth of planets to how black holes accrete. Here we describe and test the core algorithms as well as modules for magnetohydrodynamics, self-gravity, sink particles, H_2 chemistry, dust-gas mixtures, physical viscosity, external forces including numerous galactic potentials as well as implementations of Lense-Thirring precession, Poynting-Robertson drag and stochastic turbulent driving. Phantom is hereby made publicly available., Comment: 88 pages, 60 figures, accepted to PASA. Code available from https://phantomsph.bitbucket.io/

The field of planet formation has been transformed recently by the completion of high-resolution imaging techniques in the infrared (SPHERE) and mm-wavelength bands (ALMA) that allow us to obtain images at unprecedented high angular resolution of protostellar discs, that are the site of planet formation. At the same time, large planet-hunting campaigns have been carried out in the last decades, showing us the complexity and the diversity of exo-planetary systems. The architecture of planetary systems is shaped by a variety of mechanisms: from the hydrodynamical interactions between the various components of a protostellar disc (gas, dust, proto-planets), to the N-body interactions between newly formed planets. In this contribution, I will describe the efforts carried out at the University of Milan to understand the hydrodynamics of protostellar discs and how such dynamical mechanisms determine the structures observed with high-resolution imaging. This is done mostly by performing high-resolution numerical simulations of the coupled evolution of gas and dust around a newly born star.

We describe a new implementation of the one-fluid method in the SPH code Phantom to simulate the dynamics of dust grains in gas protoplanetary discs. We revise and extend previously developed algorithms by computing the evolution of a new fluid quantity that produces a more accurate and numerically controlled evolution of the dust dynamics. Moreover, by limiting the stopping time of uncoupled grains that violate the assumptions of the terminal velocity approximation, we avoid fatal numerical errors in mass conservation. We test and validate our new algorithm by running 3D SPH simulations of a large range of disc models with tightly- and marginally-coupled grains., Comment: 6 pages, 3 figures

We present 3D smoothed particle hydrodynamics simulations of protoplanetary discs undergoing a flyby by a stellar perturber on a parabolic orbit lying in a plane inclined relative to the disc mid-plane. We model the disc as a mixture of gas and dust, with grains ranging from 1 {\mu}m to 10 cm in size. Exploring different orbital inclinations, periastron distances and mass ratios, we investigate the disc dynamical response during and after the flyby. We find that flybys induce evolving spiral structure in both gas and dust which can persist for thousands of years after periastron. Gas and dust structures induced by the flyby differ because of drag-induced effects on the dust grains. Variations in the accretion rate by up to an order of magnitude occur over a time-scale of order 10 years or less, inducing FU Orionis-like outbursts. The remnant discs are truncated and warped. The dust disc is left more compact than the gas disc, both because of disc truncation and accelerated radial drift of grains induced by the flyby., Comment: 27 pages, 24 figures, accepted for publication in MNRAS

A tidal disruption event, which occurs when a star is destroyed by the gravitational field of a supermassive black hole, produces a stream of debris, the evolution of which ultimately determines the observational properties of the event. Here we show that a post-periapsis caustic -- a location where the locus of gas parcels comprising the stream would collapse into a two-dimensional surface if they evolved solely in the gravitational field of the hole -- occurs when the pericenter distance of the star is on the order of the tidal radius of the hole. It is demonstrated that this "pancake" induces significant density perturbations in the debris stream, and, for stiffer equations of state (adiabatic index $\gamma \gtrsim 5/3$), these fluctuations are sufficient to gravitationally destabilize the stream, resulting in its fragmentation into bound clumps. The results of our findings are discussed in the context of the observational properties of tidal disruption events., Comment: 18 pages, 14 figures. Accepted for publication in MNRAS

We have developed a modified form of the equations of smoothed particle magnetohydrodynamics which are stable in the presence of very steep density gradients. Using this formalism, we have performed simulations of the collapse of magnetised molecular cloud cores to form protostars and drive outflows. Our stable formalism allows for smaller sink particles (< 5 AU) than used previously and the investigation of the effect of varying the angle, {\theta}, between the initial field axis and the rotation axis. The nature of the outflows depends strongly on this angle: jet-like outflows are not produced at all when {\theta} > 30{\deg}, and a collimated outflow is not sustained when {\theta} > 10{\deg}. No substantial outflows of any kind are produced when {\theta} > 60{\deg}. This may place constraints on the geometry of the magnetic field in molecular clouds where bipolar outflows are seen., Comment: Accepted for publication in MNRAS, 13 pages, 14 figures. Animations can be found at http://www.astro.ex.ac.uk/people/blewis/research/outflows_misaligned_fields.html

Accretion discs are common in binary systems, and they are often found to be misaligned with respect to the binary orbit. The gravitational torque from a companion induces nodal precession in misaligned disc orbits. We calculate whether this precession is strong enough to overcome the internal disc torques communicating angular momentum. For typical parameters precession wins: the disc breaks into distinct planes that precess effectively independently. We run hydrodynamical simulations to check these results, and confirm that disc breaking is widespread and generally enhances accretion on to the central object. This applies in many cases of astrophysical accretion, e.g. supermassive black hole binaries and X--ray binaries., 8 pages, 6 figures, accepted for publication in MNRAS

We investigate the effect of black hole spin on warped or misaligned accretion discs - in particular i) whether or not the inner disc edge aligns with the black hole spin and ii) whether the disc can maintain a smooth transition between an aligned inner disc and a misaligned outer disc, known as the Bardeen-Petterson effect. We employ high resolution 3D smoothed particle hydrodynamics simulations of $\alpha$-discs subject to Lense-Thirring precession, focussing on the bending wave regime where the disc viscosity is smaller than the aspect ratio $\alpha \lesssim H/R$. We first address the controversy in the literature regarding possible steady-state oscillations of the tilt close to the black hole. We successfully recover such oscillations in 3D at both small and moderate inclinations ($\lesssim 15^{\circ}$), provided both Lense-Thirring and Einstein precession are present, sufficient resolution is employed, and provided the disc is not so thick so as to simply accrete misaligned. Second, we find that discs inclined by more than a few degrees in general steepen and break rather than maintain a smooth transition, again in contrast to previous findings, but only once the disc scale height is adequately resolved. Finally, we find that when the disc plane is misaligned to the black hole spin by a large angle, the disc 'tears' into discrete rings which precess effectively independently and cause rapid accretion, consistent with previous findings in the diffusive regime ($\alpha \gtrsim H/R$). Thus misalignment between the disc and the spin axis of the black hole provides a robust mechanism for growing black holes quickly, regardless of whether the disc is thick or thin., Comment: 15 pages, 18 figures, movies available at http://users.monash.edu.au/~rnealon/ or YouTube