Asymptotic shallow water models for internal waves in a two-fluid system with a free surface

In this paper, we derive asymptotic models for the propagation of two and three-dimensional gravity waves at the free surface and the interface between two layers of immiscible fluids of different densities, over an uneven bottom. We assume the thickness of the upper and lower fluids to be of comparable size, and small compared to the characteristic wavelength of the system (shallow water regimes). Following a method introduced by Bona, Lannes and Saut based on the expansion of the involved Dirichlet-to-Neumann operators, we are able to give a rigorous justification of classical models for weakly and strongly nonlinear waves, as well as interesting new ones. In particular, we derive linearly well-posed systems in the so called Boussinesq/Boussinesq regime. Furthermore, we establish the consistency of the full Euler system with these models, and deduce the convergence of the solutions.Comment: 32 pages, 4 figure

Orbits and Masses in the T Tauri System

We investigate the binary star T Tauri South, presenting the orbital parameters of the two components and their individual masses. We combined astrometric positions from the literature with previously unpublished VLT observations. Model fits yield the orbital elements of T Tau Sa and Sb. We use T Tau N as an astrometric reference to derive an estimate for the mass ratio of Sa and Sb. Although most of the orbital parameters are not well constrained, it is unlikely that T Tau Sb is on a highly elliptical orbit or escaping from the system. The total mass of T Tau S is rather well constrained to 3.0 +0.15/-0.24 M_sun. The mass ratio Sb:Sa is about 0.4, corresponding to individual masses of M_Sa = 2.1+/-0.2 M_sun and M_Sb = 0.8+/-0.1 M_sun. This confirms that the infrared companion in the T Tauri system is a pair of young stars obscured by circumstellar material.Comment: 10 pages, 11 figures, accepted by Astronomy and Astrophysic

Multiple protostellar systems. II. A high resolution near-infrared imaging survey in nearby star-forming regions

(abridged) Our project endeavors to obtain a robust view of multiplicity among embedded Class I and Flat Spectrum protostars in a wide array of nearby molecular clouds to disentangle ``universal'' from cloud-dependent processes. We have used near-infrared adaptive optics observations at the VLT through the H, Ks and L' filters to search for tight companions to 45 Class I and Flat Spectrum protostars located in 4 different molecular clouds (Taurus-Auriga, Ophiuchus, Serpens and L1641 in Orion). We complemented these observations with published high-resolution surveys of 13 additional objects in Taurus and Ophiuchus. We found multiplicity rates of 32+/-6% and 47+/-8% over the 45-1400 AU and 14-1400 AU separation ranges, respectively. These rates are in excellent agreement with those previously found among T Tauri stars in Taurus and Ophiuchus, and represent an excess of a factor ~1.7 over the multiplicity rate of solar-type field stars. We found no non-hierarchical triple systems, nor any quadruple or higher-order systems. No significant cloud-to-cloud difference has been found, except for the fact that all companions to low-mass Orion protostars are found within 100 AU of their primaries whereas companions found in other clouds span the whole range probed here. Based on this survey, we conclude that core fragmentation always yields a high initial multiplicity rate, even in giant molecular clouds such as the Orion cloud or in clustered stellar populations as in Serpens, in contrast with predictions of numerical simulations. The lower multiplicity rate observed in clustered Class II and Class III populations can be accounted for by a universal set of properties for young systems and subsequent ejections through close encounters with unrelated cluster members.Comment: 15 pages, 6 figures, accepted for publication in Astronomy & Astrophysic

Discovery of the Fomalhaut C debris disc

Fomalhaut is one of the most interesting and well studied nearby stars, hosting at least one planet, a spectacular debris ring, and two distant low-mass stellar companions (TW PsA and LP 876-10, a.k.a. Fomalhaut B & C). We observed both companions with Herschel, and while no disc was detected around the secondary, TW PsA, we have discovered the second debris disc in the Fomalhaut system, around LP 876-10. This detection is only the second case of two debris discs seen in a multiple system, both of which are relatively wide ($\gtrsim$3000 AU for HD 223352/40 and 158 kAU [0.77 pc] for Fomalhaut/LP 876-10). The disc is cool (24K) and relatively bright, with a fractional luminosity $L_{\rm disc}/L_\star = 1.2 \times 10^{-4}$, and represents the rare observation of a debris disc around an M dwarf. Further work should attempt to find if the presence of two discs in the Fomalhaut system is coincidental, perhaps simply due to the relatively young system age of 440 Myr, or if the stellar components have dynamically interacted and the system is even more complex than it currently appears.Comment: Published in MNRAS Letters. Merry Xma

Resolving The Moth at Millimeter Wavelengths

HD 61005, also known as "The Moth," is one of only a handful of debris disks that exhibit swept-back "wings" thought to be caused by interaction with the ambient interstellar medium (ISM). We present 1.3 mm Submillimeter Array (SMA) observations of the debris disk around HD 61005 at a spatial resolution of 1.9 arcsec that resolve the emission from large grains for the first time. The disk exhibits a double-peaked morphology at millimeter wavelengths, consistent with an optically thin ring viewed close to edge-on. To investigate the disk structure and the properties of the dust grains we simultaneously model the spatially resolved 1.3 mm visibilities and the unresolved spectral energy distribution. The temperatures indicated by the SED are consistent with expected temperatures for grains close to the blowout size located at radii commensurate with the millimeter and scattered light data. We also perform a visibility-domain analysis of the spatial distribution of millimeter-wavelength flux, incorporating constraints on the disk geometry from scattered light imaging, and find suggestive evidence of wavelength-dependent structure. The millimeter-wavelength emission apparently originates predominantly from the thin ring component rather than tracing the "wings" observed in scattered light. The implied segregation of large dust grains in the ring is consistent with an ISM-driven origin for the scattered light wings.Comment: 10 pages, 6 figure

Assessment of the fiscal stance appropriate for the euro area in 2019

On 18 June 2018, the European Fiscal Board (EFB) has published its assessment of the general orientation of fiscal policy in the euro area. The report concludes that the favourable economic outlook offers a prime opportunity to rebuild fiscal buffers. Especially euro area Member States with a high government debt-to-GDP ratio need to do more than simply accrue the budgetary benefits of the economic expansion. Lest we repeat the mistakes of the past and rob ourselves of room to manoeuvre when the next crisis hits, this is the time to move towards a somewhat restrictive orientation of fiscal policy in the euro area. It is also the time to upgrade the EU's fiscal framework and prepare a capacity for joint stabilisation for the euro area

The initial period function of late-type binary stars and its variation

The variation of the period distribution function of late-type binaries is studied. It is shown that the Taurus--Auriga pre-main sequence population and the main sequence G dwarf sample do not stem from the same parent period distribution with better than 95 per cent confidence probability. The Lupus, Upper Scorpius A and Taurus--Auriga populations are shown to be compatible with being drawn from the same initial period function (IPF), which is inconsistent with the main sequence data. Two possible IPF forms are used to find parent distributions to various permutations of the available data which include Upper Scorpius B (UScB), Chameleon and Orion Nebula Cluster pre-main sequence samples. All the pre-main sequence samples studied here are consistent with the hypothesis that there exists a universal IPF which is modified through binary-star disruption if it forms in an embedded star cluster leading to a general decline of the observed period function with increasing period. The pre-main sequence data admit a log-normal IPF similar to that arrived at by Duquennoy & Mayor (1991) for main sequence stars, provided the binary fraction among pre-main sequence stars is significantly higher. But, for consistency with proto-stellar data, the possibly universal IPF ought to be flat in log-P or log-semi-major axis and must be similar to the K1 IPF form derived through inverse dynamical population synthesis, which has been shown to lead to the main sequence period function if most stars form in typical embedded clusters.Comment: 13 pages, 8 figures, LaTeX, accepted by A&A, minor change to reference lis

Wave operator bounds for 1-dimensional Schr\"odinger operators with singular potentials and applications

Boundedness of wave operators for Schr\"odinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive estimates and commutator bounds.Comment: 16 pages, 0 figure