Cooling in the shade of warped transition disks

The mass of the gaseous reservoir in young circumstellar disks is a crucial initial condition for the formation of planetary systems, but estimates vary by orders of magnitude. In some disks with resolvable cavities, sharp inner disk warps cast two-sided shadows on the outer rings; can the cooling of the gas as it crosses the shadows bring constraints on its mass? The finite cooling timescale should result in dust temperature decrements shifted ahead of the optical/IR shadows in the direction of rotation. However, some systems show temperature drops, while others do not. The depth of the drops and the amplitude of the shift depend on the outer disk surface density Sigma through the extent of cooling during the shadow crossing time, and also on the efficiency of radiative diffusion. These phenomena may bear observational counterparts, which we describe with a simple one-dimensional model. An application to the HD142527 disk suggests an asymmetry in its shadows, and predicts a >~10deg shift for a massive gaseous disk, with peak Sigma > 8.3 g/cm2. Another application to the DoAr44 disk limits the peak surface density to Sigma < 13g/cm2Comment: accepted to MNRAS Letter

Uniqueness of the de Sitter spacetime among static vacua with positive cosmological constant

We prove that, among all (n + 1)-dimensional spin static vacua with positive cosmological constant, the de Sitter spacetime is characterized by the fact that its spatial Killing hori-zons have minimal modes for the Dirac operator. As a consequence, the de Sitter spacetime is the only vacuum of this type for which the induced metric tensor on some of its Killing horizons is at least equal to that of a round (n -- 1)-sphere. This extends unique-ness theorems shown by Boucher-Gibbons-Horowitz and Chruciel to more general horizon metrics and to the non-single horizon case.Comment: in Annals of Global Analysis and Geometry, Springer Verlag (Germany), 201

Adversarial Semi-Supervised Audio Source Separation applied to Singing Voice Extraction

The state of the art in music source separation employs neural networks trained in a supervised fashion on multi-track databases to estimate the sources from a given mixture. With only few datasets available, often extensive data augmentation is used to combat overfitting. Mixing random tracks, however, can even reduce separation performance as instruments in real music are strongly correlated. The key concept in our approach is that source estimates of an optimal separator should be indistinguishable from real source signals. Based on this idea, we drive the separator towards outputs deemed as realistic by discriminator networks that are trained to tell apart real from separator samples. This way, we can also use unpaired source and mixture recordings without the drawbacks of creating unrealistic music mixtures. Our framework is widely applicable as it does not assume a specific network architecture or number of sources. To our knowledge, this is the first adoption of adversarial training for music source separation. In a prototype experiment for singing voice separation, separation performance increases with our approach compared to purely supervised training.Comment: 5 pages, 2 figures, 1 table. Final version of manuscript accepted for 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Implementation available at https://github.com/f90/AdversarialAudioSeparatio

On a Liu--Yau type inequality for surfaces

Let $\Omega$ be a compact and mean-convex domain with smooth boundary $\Sigma:=\partial\Omega$, in an initial data set $(M^3,g,K)$, which has no apparent horizon in its interior. If $\Sigma$ is spacelike in a spacetime (\E^4,g\_\E) with spacelike mean curvature vector $\mathcal{H}$ such that $\Sigma$ admits an isometric and isospin immersion into $\mathbb{R}^3$ with mean curvature $H\_0$, then: \begin{eqnarray*} \int\_{\Sigma}|\mathcal{H}|d\Sigma\leq\int\_{\Sigma}\frac{H\_0^2}{|\mathcal{H}|}d\Sigma. \end{eqnarray*} If equality occurs, we prove that there exists a local isometric immersion of $\Omega$ in $\mathbb{R}^{3,1}$ (the Minkowski spacetime) with second fundamental form given by $K$. In Theorem liu-yau-minkowski, we also examine, under weaker conditions, the case where the spacetime is the $(n+2)$-dimensional Minkowski space $\mathbb{R}^{n+1,1}$ and establish a stronger rigidity result

Spiral waves triggered by shadows in transition disks

Circumstellar asymmetries such as central warps have recently been shown to cast shadows on outer disks. We investigate the hydrodynamical consequences of such variable illumination on the outer regions of a transition disk, and the development of spiral arms. Using 2D simulations, we follow the evolution of a gaseous disk passively heated by the central star, under the periodic forcing of shadows with an opening angle of $\sim$28$^\circ$. With a lower pressure under the shadows, each crossing results in a variable azimuthal acceleration, which in time develops into spiral density waves. Their pitch angles evolve from $\Pi \sim 15^\circ-22^\circ$ at the onset, to $\sim$11$^\circ$-14$^\circ$, over $\sim$65~AU to 150~AU. Self-gravity enhances the density contrast of the spiral waves, as also reported previously for spirals launched by planets. Our control simulations with unshadowed irradiation do not develop structures, except for a different form of spiral waves seen at later times only in the gravitationally unstable control case. Scattered light predictions in the $H$-band show that such illumination spirals should be observable. We suggest that spiral arms in the case-study transition disk HD~142527 could be explained as a result of shadowing from the tilted inner disk.Comment: 6 pages, 4 figures, 1 table. Accepted for publication in ApJ