Convergence and multiplicities for the Lempert function

Given a domain $\Omega \subset \mathbb C$, the Lempert function is a functional on the space Hol (\D,\Omega) of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. We generalize its definition to the case where poles have multiplicities given by local indicators (in the sense of Rashkovskii's work) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the indicators. In particular, this is an improvement over the previous generalization used by the same authors to find an example of a set of poles in the bidisk so that the (usual) Green and Lempert functions differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for Matemati

Refined physical properties and g',r',i',z',J,H,K transmission spectrum of WASP-23b from the ground

Multi-band observations of planetary transits using the telescope defocus technique may yield high-quality light curves suitable for refining the physical properties of exoplanets even with small or medium size telescopes. Such observations can be used to construct a broad-band transmission spectrum of transiting planets and search for the presence of strong absorbers. We have thoroughly characterised the orbital ephemeris and physical properties of the transiting planet and host star in the WASP-23b system, constructed a broad-band transmission spectrum of WASP-23b and performed a comparative analysis with theoretical models of hot Jupiters. We observed a complete transit of WASP-23b in seven bands simultaneously, using the GROND instrument on the MPG/ESO 2.2m telescope at La Silla Observatory and telescope defocussing. The optical data were taken in the Sloan g',r',i' and z' bands. The resulting light curves are of high quality, with a root-mean-square scatter of the residual as low as 330ppm in the z'-band, with a cadence of 90s. Near-infrared data were obtained in the JHK bands. We performed MCMC analysis of our photometry plus existing radial velocity data to refine measurements of the ephemeris and physical properties of the WASP-23. We constructed a broad-band transmission spectrum of WASP-23b and compared it with a theoretical transmission spectrum of a Hot Jupiter. We measured the central transit time with a precision about 8s. From this and earlier observations we obtain an orbital period of P=2.9444300+/-0.0000011d. Our analysis also yielded a larger radius and mass for the planet (Rp=1.067+0.045-0.038 RJup and, Mp=0.917+0.040-0.039MJup). The transmission spectrum is marginally flat, given the limited precision of the measurements for the planet radius and poor spectral resolution of the data.Comment: 8 pages, 5 figures, accepted for publication in Astronomy & Astrophysic

Physical properties, starspot activity, orbital obliquity, and transmission spectrum of the Qatar-2 planetary system from multi-colour photometry

We present seventeen high-precision light curves of five transits of the planet Qatar-2b, obtained from four defocussed 2m-class telescopes. Three of the transits were observed simultaneously in the SDSS griz passbands using the seven-beam GROND imager on the MPG/ESO 2.2-m telescope. A fourth was observed simultaneously in Gunn grz using the CAHA 2.2-m telescope with BUSCA, and in r using the Cassini 1.52-m telescope. Every light curve shows small anomalies due to the passage of the planetary shadow over a cool spot on the surface of the host star. We fit the light curves with the prism+gemc model to obtain the photometric parameters of the system and the position, size and contrast of each spot. We use these photometric parameters and published spectroscopic measurements to obtain the physical properties of the system to high precision, finding a larger radius and lower density for both star and planet than previously thought. By tracking the change in position of one starspot between two transit observations we measure the orbital obliquity of Qatar-2 b to be 4.3 \pm 4.5 degree, strongly indicating an alignment of the stellar spin with the orbit of the planet. We calculate the rotation period and velocity of the cool host star to be 11.4 \pm 0.5 d and 3.28 \pm 0.13 km/s at a colatitude of 74 degree. We assemble the planet's transmission spectrum over the 386-976 nm wavelength range and search for variations of the measured radius of Qatar-2 b as a function of wavelength. Our analysis highlights a possible H2/He Rayleigh scattering in the blue.Comment: 20 pages, 14 figures, to appear in Monthly Notices of the Royal Astronomical Societ

Simultaneous follow-up of planetary transits: revised physical properties for the planetary systems HAT-P-16 and WASP-21

Context. By now more than 300 planets transiting their host star have been found, and much effort is being put into measuring the properties of each system. Light curves of planetary transits often contain deviations from a simple transit shape, and it is generally difficult to differentiate between anomalies of astrophysical nature (e.g. starspots) and correlated noise due to instrumental or atmospheric effects. Our solution is to observe transit events simultaneously with two telescopes located at different observatories. Aims. Using this observational strategy, we look for anomalies in the light curves of two transiting planetary systems and accurately estimate their physical parameters. Methods. We present the first photometric follow-up of the transiting planet HAT-P-16 b, and new photometric observations of WASP-21 b, obtained simultaneously with two medium-class telescopes located in different countries, using the telescope defocussing technique. We modeled these and other published data in order to estimate the physical parameters of the two planetary systems. Results. The simultaneous observations did not highlight particular features in the light curves, which is consistent with the low activity levels of the two stars. For HAT-P-16, we calculated a new ephemeris and found that the planet is 1.3 \sigma colder and smaller (Rb = 1.190 \pm 0.037 RJup) than the initial estimates, suggesting the presence of a massive core. Our physical parameters for this system point towards a younger age than previously thought. The results obtained for WASP-21 reveal lower values for the mass and the density of the planet (by 1.0 \sigma and 1.4 \sigma respectively) with respect to those found in the discovery paper, in agreement with a subsequent study. We found no evidence of any transit timing variations in either system.Comment: 8 pages, 6 figures, accepted for publication in A&

Physical properties of the WASP-44 planetary system from simultaneous multi-colour photometry

We present ground-based broad-band photometry of two transits in the WASP-44 planetary system obtained simultaneously through four optical (Sloan g', r', i', z') and three near-infrared (NIR; J, H, K) filters. We achieved low scatters of 1-2 mmag per observation in the optical bands with a cadence of 48 s, but the NIR-band light curves present much greater scatter. We also observed another transit of WASP-44 b by using a Gunn-r filter and telescope defocussing, with a scatter of 0.37 mmag per point and an observing cadence around 135 s. We used these data to improve measurements of the time of mid-transit and the physical properties of the system. In particular, we improved the radius measurements of the star and planet by factors of 3 and 4, respectively. We find that the radius of WASP-44 b is 1.002 R_Jup, which is slightly smaller than previously thought and differs from that expected for a core-free planet. In addition, with the help of a synthetic spectrum, we investigated the theoretically-predicted variation of the planetary radius as a function of wavelength, covering the range 370-2440 nm. We can rule out extreme variations at optical wavelengths, but unfortunately our data are not precise enough (especially in the NIR bands) to differentiate between the theoretical spectrum and a radius which does not change with wavelength.Comment: 13 pages, 6 figures, to appear in Monthly Notices of the Royal Astronomical Societ

Exhausting domains of the symmetrized bidisc

We show that the symmetrized bidisc may be exhausted by strongly linearly convex domains. It shows in particular the existence of a strongly linearly convex domain that cannot be exhausted by domains biholomorphic to convex ones.Comment: 6 page

Covariate linkage analysis of GAW14 simulated data incorporating subclinical phenotype, sex, population, parent-of-origin, and interaction

BACKGROUND: We evaluate a method for the incorporation of covariates into linkage analysis using the Genetic Analysis Workshop 14 simulated data. Focusing on a randomly chosen replicate (42) we investigated the effect of the 12 subclinical phenotypes, sex, population, and parent-of-origin on the linkage signal from a model-free linkage analysis of Kofendrerd Personality Disorder. RESULTS: We detected a linkage peak on chromosome 1, at about 175 cM, which varied depending upon individuals' status for subclinical phenotype b. A linkage peak on chromosome 3 (310 cM) was found not to depend upon subclinical phenotype status. Further peaks were found on chromosomes 5 (12 cM), 9 (4 cM), and 10 (95 cM), depending on the status of subclinical phenotypes a, k, and c/d/g, respectively. CONCLUSION: Retrospective comparison of our results with the simulation model showed correct identification of disease loci D1-5 on chromosomes 1, 3, 5, 9 and 10, respectively

Refined physical properties and g',r',i',z',J,H,K transmission spectrum of WASP-23b from the ground

This is the author accepted manuscript. The final version is available from EDP Sciences via the DOI in this recordMulti-band observations of planetary transits using the telescope defocus technique may yield high-quality light curves suitable for refining the physical properties of exoplanets even with small or medium size telescopes. Such observations can be used to construct a broad-band transmission spectrum of transiting planets and search for the presence of strong absorbers. We have thoroughly characterised the orbital ephemeris and physical properties of the transiting planet and host star in the WASP-23b system, constructed a broad-band transmission spectrum of WASP-23b and performed a comparative analysis with theoretical models of hot Jupiters. We observed a complete transit of WASP-23b in seven bands simultaneously, using the GROND instrument on the MPG/ESO 2.2m telescope at La Silla Observatory and telescope defocussing. The optical data were taken in the Sloan g',r',i' and z' bands. The resulting light curves are of high quality, with a root-mean-square scatter of the residual as low as 330ppm in the z'-band, with a cadence of 90s. Near-infrared data were obtained in the JHK bands. We performed MCMC analysis of our photometry plus existing radial velocity data to refine measurements of the ephemeris and physical properties of the WASP-23. We constructed a broad-band transmission spectrum of WASP-23b and compared it with a theoretical transmission spectrum of a Hot Jupiter. We measured the central transit time with a precision about 8s. From this and earlier observations we obtain an orbital period of P=2.9444300+/-0.0000011d. Our analysis also yielded a larger radius and mass for the planet (Rp=1.067+0.045-0.038 RJup and, Mp=0.917+0.040-0.039MJup). The transmission spectrum is marginally flat, given the limited precision of the measurements for the planet radius and poor spectral resolution of the data.N.N. acknowledges support from an STFC consolidated grant. J.S. acknowledges STFC for the award of an Advanced Fellowship

Randomized Benchmarking using Non-Destructive Readout in a 2D Atom Array

Neutral atoms are a promising platform for scalable quantum computing, however prior demonstration of high fidelity gates or low-loss readout methods have employed restricted numbers of qubits. Using randomized benchmarking of microwave-driven single-qubit gates, we demonstrate single qubit gate errors of $8(2)\times10^{-5}$ on 225 atoms using conventional, destructive readout. This exceeds the threshold for fault-tolerance. We further demonstrate suppression of measurement errors via low-loss, non-destructive and state-selective readout on 49 atoms. This enables post-selection for atom loss, which is a primary source of errors in present setups.Comment: 6 pages, 4 figures plus Supplementary Materia