Spectropolarimetric signatures of Earth-like extrasolar planets

We present results of numerical simulations of the flux (irradiance), F, and the degree of polarization (i.e. the ratio of polarized to total flux), P, of light that is reflected by Earth-like extrasolar planets orbiting solar-type stars, as functions of the wavelength (from 0.3 to 1.0 micron, with 0.001 micron spectral resolution) and as functions of the planetary phase angle. We use different surface coverages for our model planets, including vegetation and a Fresnel reflecting ocean, and clear and cloudy atmospheres. Our adding-doubling radiative transfer algorithm, which fully includes multiple scattering and polarization, handles horizontally homogeneous planets only; we simulate fluxes and polarization of horizontally inhomogeneous planets by weighting results for homogeneous planets. Like the flux, F, the degree of polarization, P, of the reflected starlight is shown to depend strongly on the phase angle, on the composition and structure of the planetary atmosphere, on the reflective properties of the underlying surface, and on the wavelength, in particular in wavelength regions with gaseous absorption bands. The sensitivity of P to a planet's physical properties appears to be different than that of F. Combining flux with polarization observations thus makes for a strong tool for characterizing extrasolar planets. The calculated total and polarized fluxes will be made available through the CDS.Comment: 31 pages text, 17 figures, 1 table Submitted to A&

Modeled flux and polarisation signals of horizontally inhomogeneous exoplanets, applied to Earth--like planets

We present modeled flux and linear polarisation signals of starlight that is reflected by spatially unresolved, horizontally inhomogeneous planets and discuss the effects of including horizontal inhomogeneities on the flux and polarisation signals of Earth-like exoplanets. Our code is based on an efficient adding--doubling algorithm, which fully includes multiple scattering by gases and aerosol/cloud particles. We divide a model planet into pixels that are small enough for the local properties of the atmosphere and surface (if present) to be horizontally homogeneous. Given a planetary phase angle, we sum up the reflected total and linearly polarised fluxes across the illuminated and visible part of the planetary disk, taking care to properly rotate the polarized flux vectors towards the same reference plane. We compared flux and polarisation signals of simple horizontally inhomogeneous model planets against results of the weighted sum approximation, in which signals of horizontally homogeneous planets are combined. Apart from cases in which the planet has only a minor inhomogeneity, the signals differ significantly. In particular, the shape of the polarisation phase function appears to be sensitive to the horizontal inhomogeneities. The same holds true for Earth-like model planets with patchy clouds above an ocean and a sandy continent. Our simulations clearly show that horizontal inhomogeneities leave different traces in flux and polarisation signals. Combining flux with polarisation measurements would help retrieving the atmospheric and surface patterns on a planet

The influence of forward-scattered light in transmission measurements of (exo)planetary atmospheres

[Abridged] The transmission of light through a planetary atmosphere can be studied as a function of altitude and wavelength using stellar or solar occultations, giving often unique constraints on the atmospheric composition. For exoplanets, a transit yields a limb-integrated, wavelength-dependent transmission spectrum of an atmosphere. When scattering haze and/or cloud particles are present in the planetary atmosphere, the amount of transmitted flux not only depends on the total optical thickness of the slant light path that is probed, but also on the amount of forward-scattering by the scattering particles. Here, we present results of calculations with a three-dimensional Monte Carlo code that simulates the transmitted flux during occultations or transits. For isotropically scattering particles, like gas molecules, the transmitted flux appears to be well-described by the total atmospheric optical thickness. Strongly forward-scattering particles, however, such as commonly found in atmospheres of Solar System planets, can increase the transmitted flux significantly. For exoplanets, such added flux can decrease the apparent radius of the planet by several scale heights, which is comparable to predicted and measured features in exoplanet transit spectra. We performed detailed calculations for Titan's atmosphere between 2.0 and 2.8 micron and show that haze and gas abundances will be underestimated by about 8% if forward-scattering is ignored in the retrievals. At shorter wavelengths, errors in the gas and haze abundances and in the spectral slope of the haze particles can be several tens of percent, also for other Solar System planetary atmospheres. We also find that the contribution of forward-scattering can be fairly well described by modelling the atmosphere as a plane-parallel slab.Comment: Icarus, accepted for publicatio

Looking for the rainbow on exoplanets covered by liquid and icy water clouds

Looking for the primary rainbow in starlight that is reflected by exoplanets appears to be a promising method to search for liquid water clouds in exoplanetary atmospheres. Ice water clouds, that consist of water crystals instead of water droplets, could potentially mask the rainbow feature in the planetary signal by covering liquid water clouds. Here, we investigate the strength of the rainbow feature for exoplanets that have liquid and icy water clouds in their atmosphere, and calculate the rainbow feature for a realistic cloud coverage of Earth. We calculate flux and polarization signals of starlight that is reflected by horizontally and vertically inhomogeneous Earth--like exoplanets, covered by patchy clouds consisting of liquid water droplets or water ice crystals. The planetary surfaces are black. On a planet with a significant coverage of liquid water clouds only, the total flux signal shows a weak rainbow feature. Any coverage of the liquid water clouds by ice clouds, however, dampens the rainbow feature in the total flux, and thus the discovery of liquid water in the atmosphere. On the other hand, detecting the primary rainbow in the polarization signal of exoplanets appears to be a powerful tool for detecting liquid water in exoplanetary atmospheres, even when these clouds are partially covered by ice clouds. In particular, liquid water clouds covering as little as 10%-20% of the planetary surface, with more than half of these covered by ice clouds, still create a polarized rainbow feature in the planetary signal. Indeed, calculations of flux and polarization signals of an exoplanet with a realistic Earth--like cloud coverage, show a strong polarized rainbow feature.Comment: accepted for publication in Astronomy & Astrophysic

Scattering matrices and expansion coefficients of Martian analogue palagonite particles

We present measurements of ratios of elements of the scattering matrix of Martian analogue palagonite particles for scattering angles ranging from 3 to 174 degrees and a wavelength of 632.8 nm. To facilitate the use of these measurements in radiative transfer calculations we have devised a method that enables us to obtain, from these measurements, a normalized synthetic scattering matrix covering the complete scattering angle range from 0 to 180 degrees. Our method is based on employing the coefficients of the expansions of scattering matrix elements into generalized spherical functions. The synthetic scattering matrix elements and/or the expansion coefficients obtained in this way, can be used to include multiple scattering by these irregularly shaped particles in (polarized) radiative transfer calculations, such as calculations of sunlight that is scattered in the dusty Martian atmosphere.Comment: 34 pages 7 figures 1 tabl

Obfuscation for Cryptographic Purposes

An obfuscation of a function F should satisfy two requirements: firstly, using it should be possible to evaluate F; secondly, should not reveal anything about F that cannot be learnt from oracle access to F. Several definitions for obfuscation exist. However, most of them are either too weak for or incompatible with cryptographic applications, or have been shown impossible to achieve, or both. We give a new definition of obfuscation and argue for its reasonability and usefulness. In particular, we show that it is strong enough for cryptographic applications, yet we show that it has the potential for interesting positive results. We illustrat

Large atom number Bose-Einstein condensate of sodium

We describe the setup to create a large Bose-Einstein condensate containing more than 120x10^6 atoms. In the experiment a thermal beam is slowed by a Zeeman slower and captured in a dark-spot magneto-optical trap (MOT). A typical dark-spot MOT in our experiments contains 2.0x10^10 atoms with a temperature of 320 microK and a density of about 1.0x10^11 atoms/cm^3. The sample is spin polarized in a high magnetic field, before the atoms are loaded in the magnetic trap. Spin polarizing in a high magnetic field results in an increase in the transfer efficiency by a factor of 2 compared to experiments without spin polarizing. In the magnetic trap the cloud is cooled to degeneracy in 50 s by evaporative cooling. To suppress the 3-body losses at the end of the evaporation the magnetic trap is decompressed in the axial direction.Comment: 11 pages, 12 figures, submitted to Review Of Scientific Instrument

Effect of solder volume on joint shape with variable chip-to-board contact pad ratio

The objective of this paper is to investigate the effect of the pad size ratio between the chip and board end of a solder joint on the shape of that solder joint in combination with the solder volume available. The shape of the solder joint is correlated to its reliability and thus of importance. For low density chip bond pad applications Flip Chip (FC) manufacturing costs can be kept down by using larger size board pads suitable for solder application. By using “Surface Evolver” software package the solder joint shapes associated with different size/shape solder preforms and chip/board pad ratios are predicted. In this case a so called Flip-Chip Over Hole (FCOH) assembly format has been used. Assembly trials involved the deposition of lead-free 99.3Sn0.7Cu solder on the board side, followed by reflow, an underfill process and back die encapsulation. During the assembly work pad off-sets occurred that have been taken into account for the Surface Evolver solder joint shape prediction and accurately matched the real assembly. Overall, good correlation was found between the simulated solder joint shape and the actual fabricated solder joint shapes. Solder preforms were found to exhibit better control over the solder volume. Reflow simulation of commercially available solder preform volumes suggests that for a fixed stand-off height and chip-board pad ratio, the solder volume value and the surface tension determines the shape of the joint

A gauge invariant and string independent fermion correlator in the Schwinger model

We introduce a gauge invariant and string independent two-point fermion correlator which is analyzed in the context of the Schwinger model (QED_2). We also derive an effective infrared worldline action for this correlator, thus enabling the computation of its infrared behavior. Finally, we briefly discuss possible perspectives for the string independent correlator in the QED_3 effective models for the normal state of HTc superconductors.Comment: 14 pages, LaTe