Extrasolar Planets in the Classroom

The field of extrasolar planets is still, in comparison with other astrophysical topics, in its infancy. There have been about 300 or so extrasolar planets detected and their detection has been accomplished by various different techniques. Here we present a simple laboratory experiment to show how planets are detected using the transit technique. Following the simple analysis procedure describe we are able to determine the planetary radius to be 1.27 +/- 0.20 R_{J} which, within errors agrees with the establish value of 1.32 +/- 0.25 R_{J}.Comment: 7 pages, 2 figures, published in Physics Educatio

Small angle neutron scattering contrast variation reveals heterogeneities of interactions in protein gels

The structure of model gluten protein gels prepared in ethanol/water is investigated by small angle X-ray (SAXS) and neutrons (SANS) scattering. We show that gluten gels display radically different SAXS and SANS profiles when the solvent is (at least partially) deuterated. The detailed analysis of the SANS signal as a function of the solvent deuteration demonstrates heterogeneities of sample deuteration at different length scales. The progressive exchange between the protons (H) of the proteins and the deuteriums (D) of the solvent is inhomogeneous and 60 nm large zones that are enriched in H are evidenced. In addition, at low protein concentration, in the sol state, solvent deuteration induces a liquid/liquid phase separation. Complementary biochemical and structure analyses show that the denser protein phase is more protonated and specifically enriched in glutenin, the polymeric fraction of gluten proteins. These findings suggest that the presence of H-rich zones in gluten gels would arise from the preferential interaction of glutenin polymers through a tight network of non-exchangeable intermolecular hydrogen bonds.Comment: Soft Matter, Royal Society of Chemistry, 201

Detection of atmospheric haze on an extrasolar planet: the 0.55-1.05 μm transmission spectrum of HD 189733b with the Hubble Space Telescope

The nearby transiting planet HD 189733b was observed during three transits with the Advanced Camera for Surveys of the Hubble Space Telescope in spectroscopic mode. The resulting time-series of 675 spectra covers the 550-1050 nm range, with a resolution element of ∼8 nm, at extremely high accuracy (signal-to-noise ratio up to 10 000 in 50-nm intervals in each individual spectrum). Using these data, we disentangle the effects of limb darkening, measurement systematics and spots on the surface of the host star, to calculate the wavelength dependence of the effective transit radius to an accuracy of ∼50 km. This constitutes the ‘transmission spectrum' of the planetary atmosphere. It indicates at each wavelength at what height the planetary atmosphere becomes opaque to the grazing stellar light during the transit. In this wavelength range, strong features due to sodium, potassium and water are predicted by atmosphere models for a planet like HD 189733b, but they can be hidden by broad absorption from clouds or hazes higher up in the atmosphere. We observed an almost featureless transmission spectrum between 550 and 1050 nm, with no indication of the expected sodium or potassium atomic absorption features. Comparison of our results with the transit radius observed in the near and mid-infrared (2-8 μm), and the slope of the spectrum, suggest the presence of a haze of submicrometre particles in the upper atmosphere of the plane

Detection of atmospheric haze on an extrasolar planet: The 0.55 - 1.05 micron transmission spectrum of HD189733b with the Hubble Space Telescope

The nearby transiting planet HD 189733b was observed during three transits with the ACS camera of the Hubble Space Telescope in spectroscopic mode. The resulting time series of 675 spectra covers the 550-1050 nm range, with a resolution element of ~8 nm, at extremely high accuracy (signal-to-noise ratio up to 10,000 in 50 nm intervals in each individual spectrum). Using these data, we disentangle the effects of limb darkening, measurement systematics, and spots on the surface of the host star, to calculate the wavelength dependence of the effective transit radius to an accuracy of ~50 km. This constitutes the ``transmission spectrum'' of the planetary atmosphere. It indicates at each wavelength at what height the planetary atmosphere becomes opaque to the grazing stellar light during the transit. In this wavelength range, strong features due to sodium, potassium and water are predicted by atmosphere models for a planet like HD 189733b, but they can be hidden by broad absorption from clouds or hazes higher up in the atmosphere. We observed an almost featureless transmission spectrum between 550 and 1050 nm, with no indication of the expected sodium or potassium atomic absorption features. Comparison of our results with the transit radius observed in the near and mid-infrared (2-8 microns), and the slope of the spectrum, suggest the presence of a haze of sub-micron particles in the upper atmosphere of the planet.Comment: 11 pages, MNRAS, accepted, minor correction

Magnetic cycles of the planet-hosting star Tau Bootis: II. a second magnetic polarity reversal

In this paper, we present new spectropolarimetric observations of the planet-hosting star Tau Bootis, using ESPaDOnS and Narval spectropolarimeters at Canada-France-Hawaii Telescope (CFHT) and Telescope Bernard Lyot (TBL), respectively. We detected the magnetic field of the star at three epochs in 2008. It is a weak magnetic field of only a few Gauss, oscillating between a predominant toroidal component in January and a dominant poloidal component in June and July. A magnetic polarity reversal was observed relative to the magnetic topology in June 2007. This is the second such reversal observed in two years on this star, suggesting that Tau Boo has a magnetic cycle of about 2 years. This is the first detection of a magnetic cycle for a star other than the Sun. The role of the close-in massive planet in the short activity cycle of the star is questioned. Tau Boo has strong differential rotation, a common trend for stars with shallow convective envelope. At latitude 40 deg., the surface layer of the star rotates in 3.31 d, equal to the orbital period. Synchronization suggests that the tidal effects induced by the planet may be strong enough to force at least the thin convective envelope into corotation. Tau Boo shows variability in the Ca H & K and Halpha throughout the night and on a night to night time scale. We do not detect enhancement in the activity of the star that may be related to the conjunction of the planet. Further data is needed to conclude about the activity enhancement due to the planet.Comment: 9 pages, 5 figures, 3 tables Accepted to MNRA

Application of Edwards' statistical mechanics to high dimensional jammed sphere packings

The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics [Song \emph{et al.}, Nature (London) {\bf 453}, 629 (2008)] is generalized to arbitrary dimension $d$ using a liquid-state description. The asymptotic high-dimensional behavior of the self-consistent relation is obtained by saddle-point evaluation and checked numerically. The resulting random close packing density scaling $\phi\sim d\,2^{-d}$ is consistent with that of other approaches, such as replica theory and density functional theory. The validity of various structural approximations is assessed by comparing with three- to six-dimensional isostatic packings obtained from simulations. These numerical results support a growing accuracy of the theoretical approach with dimension. The approach could thus serve as a starting point to obtain a geometrical understanding of the higher-order correlations present in jammed packings.Comment: 13 pages, 7 figure

Mass-radius relationships for exoplanets

For planets other than Earth, interpretation of the composition and structure depends largely on comparing the mass and radius with the composition expected given their distance from the parent star. The composition implies a mass-radius relation which relies heavily on equations of state calculated from electronic structure theory and measured experimentally on Earth. We lay out a method for deriving and testing equations of state, and deduce mass-radius and mass-pressure relations for key materials whose equation of state is reasonably well established, and for differentiated Fe/rock. We find that variations in the equation of state, such as may arise when extrapolating from low pressure data, can have significant effects on predicted mass- radius relations, and on planetary pressure profiles. The relations are compared with the observed masses and radii of planets and exoplanets. Kepler-10b is apparently 'Earth- like,' likely with a proportionately larger core than Earth's, nominally 2/3 of the mass of the planet. CoRoT-7b is consistent with a rocky mantle over an Fe-based core which is likely to be proportionately smaller than Earth's. GJ 1214b lies between the mass-radius curves for H2O and CH4, suggesting an 'icy' composition with a relatively large core or a relatively large proportion of H2O. CoRoT-2b is less dense than the hydrogen relation, which could be explained by an anomalously high degree of heating or by higher than assumed atmospheric opacity. HAT-P-2b is slightly denser than the mass-radius relation for hydrogen, suggesting the presence of a significant amount of matter of higher atomic number. CoRoT-3b lies close to the hydrogen relation. The pressure at the center of Kepler-10b is 1.5+1.2-1.0 TPa. The central pressure in CoRoT-7b is probably close to 0.8TPa, though may be up to 2TPa.Comment: Added more recent exoplanets. Tidied text and references. Added extra "rock" compositions. Responded to referee comment

A catalogue of bright (K <9) M dwarfs

Using the Position and Proper Motion Extended-L (PPMXL) catalogue, we have used optical and near-infrared colour cuts together with a reduced proper motion cut to find bright M dwarfs for future exoplanet transit studies. PPMXL's low proper motion uncertainties allow us to probe down to smaller proper motions than previous similar studies. We have combined unique objects found with this method to that of previous work to produce 8479 K <9 M dwarfs. Low-resolution spectroscopy was obtained of a sample of the objects found using this selection method to gain statistics on their spectral type and physical properties. Results show a spectral-type range of K7-M4V. This catalogue is the most complete collection of K <9 M dwarfs currently available and is made available here.Peer reviewe

Dimensional dependence of the Stokes--Einstein relation and its violation

We generalize to higher spatial dimensions the Stokes--Einstein relation (SER) and the leading correction to diffusivity in periodic systems, and validate them using numerical simulations. Using these results, we investigate the evolution of the SER violation with dimension in simple hard sphere glass formers. The analysis suggests that the SER violation disappears around dimension d=8, above which SER is not violated. The critical exponent associated to the violation appears to evolve linearly in 8-d below d=8, as predicted by Biroli and Bouchaud [J. Phys.: Cond. Mat. 19, 205101 (2007)], but the linear coefficient is not consistent with their prediction. The SER violation evolution with d establishes a new benchmark for theory, and a complete description remains an open problem.Comment: 20 pages, 10 figure