The theory of transmission spectra revisited: a semi-analytical method for interpreting WFC3 data and an unresolved challenge

The computation of transmission spectra is a central ingredient in the study of exoplanetary atmospheres. First, we revisit the theory of transmission spectra, unifying ideas from several workers in the literature. Transmission spectra lack an absolute normalization due to the a priori unknown value of a reference transit radius, which is tied to an unknown reference pressure. We show that there is a degeneracy between the uncertainty in the transit radius, the assumed value of the reference pressure (typically set to 10 bar) and the inferred value of the water abundance when interpreting a WFC3 transmission spectrum. Second, we show that the transmission spectra of isothermal atmospheres are nearly isobaric. We validate the isothermal, isobaric analytical formula for the transmission spectrum against full numerical calculations and show that the typical errors are ~0.1% (~10 ppm) within the WFC3 range of wavelengths for temperatures of 1500 K (or higher). Third, we generalize the previous expression for the transit radius to include a small temperature gradient. Finally, we analyze the measured WFC3 transmission spectrum of WASP-12b and demonstrate that we obtain consistent results with the retrieval approach of Kreidberg et al. (2015) if the reference transit radius and reference pressure are fixed to assumed values. The unknown functional relationship between the reference transit radius and reference pressure implies that it is the product of the water abundance and reference pressure that is being retrieved from the data, and not just the water abundance alone. This degeneracy leads to a limitation on how accurately we may extract molecular abundances from transmission spectra using WFC3 data alone. Finally, we compare our study to that of Griffith (2014) and discuss why the degeneracy was missed in previous retrieval studies. [abridged]Comment: Accepted by MNRAS. 11 pages, 7 figures, 2 table

The Galactic Faraday depth sky revisited

The Galactic Faraday depth sky is a tracer for both the Galactic magnetic field and the thermal electron distribution. It has been previously reconstructed from polarimetric measurements of extra-galactic point sources. Here, we improve on these works by using an updated inference algorithm as well as by taking into account the free-free emission measure map from the Planck survey. In the future, the data situation will improve drastically with the next generation Faraday rotation measurements from SKA and its pathfinders. Anticipating this, the aim of this paper is to update the map reconstruction method with the latest development in imaging based on information field theory. We demonstrate the validity of the new algorithm by applying it to the Oppermann et al. (2012) data compilation and compare our results to the previous map.\\ Despite using exactly the previous data set, a number of novel findings are made: A non-parametric reconstruction of an overall amplitude field resembles the free-free emission measure map of the Galaxy. Folding this free-free map into the analysis allows for more detailed predictions. The joint inference enables us to identify regions with deviations from the assumed correlations between the free-free and Faraday data, thereby pointing us to Galactic structures with distinguishably different physics. We e.g. find evidence for an alignment of the magnetic field within the line of sights along both directions of the Orion arm.Comment: 16 pages, 15 figure

Absolute linear instability in laminar and turbulent gas/liquid two-layer channel flow

We study two-phase stratified flow where the bottom layer is a thin laminar liquid and the upper layer is a fully-developed gas flow. The gas flow can be laminar or turbulent. To determine the boundary between convective and absolute instability, we use Orr--Sommerfeld stability theory, and a combination of linear modal analysis and ray analysis. For turbulent gas flow, and for the density ratio r=1000, we find large regions of parameter space that produce absolute instability. These parameter regimes involve viscosity ratios of direct relevance to oil/gas flows. If, instead, the gas layer is laminar, absolute instability persists for the density ratio r=1000, although the convective/absolute stability boundary occurs at a viscosity ratio that is an order of magnitude smaller than in the turbulent case. Two further unstable temporal modes exist in both the laminar and the turbulent cases, one of which can exclude absolute instability. We compare our results with an experimentally-determined flow-regime map, and discuss the potential application of the present method to non-linear analyses.Comment: 33 pages, 20 figure

The Stellar Halo in the Large Magellanic Cloud: Mass, Luminosity, and Microlensing Predictions

Recently obtained kinematic data has shown that the Large Magellanic Cloud (LMC) possesses an old stellar halo. In order to further characterize the properties of this halo, parametric King models are fit to the surface density of RR Lyrae stars. Using data from both the MACHO and OGLE II microlensing surveys, the model fits yield the center of their distribution at RA = 05:21.1+-0.8, Dec = -69:45+-6 (J2000) and a core radius of 1.42+-0.12 kpc. As a check the halo model is compared with RR Lyrae star counts in fields near the LMC's periphery previously surveyed with photographic plates. These data, however, require a cautious interpretation. Several topics regarding the LMC stellar halo are discussed. First, the properties of the halo imply a global mass-to-light ratio of M/L_V = 5.3+-2.1 and a total mass of 1.6+-0.6 10^10 M_sun for the LMC in good agreement with estimates based on the rotation curve. Second, although the LMC's disk and halo are kinematically distinct, the shape of the surface density profile of the halo is remarkably similar to that of the young disk. For example, the best-fit exponential scale length for the RR Lyrae stars is 1.47+-0.08 kpc, which compares to 1.46 kpc for the LMC's blue light. In the Galaxy, the halo and disk do not resemble each other like this. Finally, a local maximum in the LMC's microlensing optical depth due to halo-on-disk stellar self-lensing is predicted. For the parameters of the stellar halo obtained, this maximum is located near MACHO events LMC-4 and LMC-23, and is large enough to possibly account for these two events, but not for all of the observed microlensing.Comment: 11 pages, 1 figure, accepted to ApJ Letter

Reliable Hubs for Partially-Dynamic All-Pairs Shortest Paths in Directed Graphs

We give new partially-dynamic algorithms for the all-pairs shortest paths problem in weighted directed graphs. Most importantly, we give a new deterministic incremental algorithm for the problem that handles updates in O~(mn^(4/3) log{W}/epsilon) total time (where the edge weights are from [1,W]) and explicitly maintains a (1+epsilon)-approximate distance matrix. For a fixed epsilon>0, this is the first deterministic partially dynamic algorithm for all-pairs shortest paths in directed graphs, whose update time is o(n^2) regardless of the number of edges. Furthermore, we also show how to improve the state-of-the-art partially dynamic randomized algorithms for all-pairs shortest paths [Baswana et al. STOC\u2702, Bernstein STOC\u2713] from Monte Carlo randomized to Las Vegas randomized without increasing the running time bounds (with respect to the O~(*) notation). Our results are obtained by giving new algorithms for the problem of dynamically maintaining hubs, that is a set of O~(n/d) vertices which hit a shortest path between each pair of vertices, provided it has hop-length Omega(d). We give new subquadratic deterministic and Las Vegas algorithms for maintenance of hubs under either edge insertions or deletions

GASP : Geometric Association with Surface Patches

A fundamental challenge to sensory processing tasks in perception and robotics is the problem of obtaining data associations across views. We present a robust solution for ascertaining potentially dense surface patch (superpixel) associations, requiring just range information. Our approach involves decomposition of a view into regularized surface patches. We represent them as sequences expressing geometry invariantly over their superpixel neighborhoods, as uniquely consistent partial orderings. We match these representations through an optimal sequence comparison metric based on the Damerau-Levenshtein distance - enabling robust association with quadratic complexity (in contrast to hitherto employed joint matching formulations which are NP-complete). The approach is able to perform under wide baselines, heavy rotations, partial overlaps, significant occlusions and sensor noise. The technique does not require any priors -- motion or otherwise, and does not make restrictive assumptions on scene structure and sensor movement. It does not require appearance -- is hence more widely applicable than appearance reliant methods, and invulnerable to related ambiguities such as textureless or aliased content. We present promising qualitative and quantitative results under diverse settings, along with comparatives with popular approaches based on range as well as RGB-D data.Comment: International Conference on 3D Vision, 201