Algebraic analysis of the phase‐calibration problem in the self‐calibration procedures

This paper presents an analysis of the phase‐calibration problem encountered in astronomy when mapping incoherent sources with aperture‐synthesis devices. More precisely, this analysis concerns the phase‐calibration operation involved in the self‐calibration procedures of phase‐closure imaging. The paper revisits and completes a previous analysis presented by Lannes in the Journal of the Optical Society of America A in 2005. It also benefits from some recent developments made for solving similar problems encountered in global navigation satellite systems. In radio‐astronomy, the related optimization problems have been stated and solved hitherto at the phasor level. We present here an analysis conducted at the phase level, from which we derive a method for diagnosing and solving the difficulties of the phasor approach. In the most general case, the techniques tobe implemented appeal to the algebraic graph theory and the algebraic number theory. The minima of the objective functionals to be minimized are identified by raising phase‐closure integer ambiguities. We also show that in some configurations, to benefit from all the available information, closure phases of order greater than three are to be introduced. In summary, this study leads to a better understanding of the difficulties related to the very principle of phase‐closure imaging. To circumvent these difficulties, we propose a strategy both simple and robust (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimising optimal image subtraction

Difference imaging is a technique for obtaining precise relative photometry of variable sources in crowded stellar fields and, as such, constitutes a crucial part of the data reduction pipeline in surveys for microlensing events or transiting extrasolar planets. The Optimal Image Subtraction (OIS) algorithm of Alard & Lupton (1998) permits the accurate differencing of images by determining convolution kernels which, when applied to reference images with particularly good seeing and signal‐to‐noise (S/N), provide excellent matches to the point‐spread functions (PSF) in other images of the time series to be analysed. The convolution kernels are built as linear combinations of a set of basis functions, conventionally bivariate Gaussians modulated by polynomials. The kernel parameters, mainly the widths and maximal degrees of the basis function model, must be supplied by the user. Ideally, the parameters should be matched to the PSF, pixel‐sampling, and S/N of the data set or individual images to be analysed. We have studied the dependence of the reduction outcome as a function of the kernel parameters using our new implementation of OIS within the IDL‐based TRIPP package. From the analysis of noise‐free PSF simulations of both single objects and crowded fields, as well as the test images in the ISIS OIS software package, we derive qualitative and quantitative relations between the kernel parameters and the success of the subtraction as a function of the PSF widths and sampling in reference and data images and compare the results to those of other implementations found in the literature. On the basis of these simulations, we provide recommended parameters for data sets with different S/N and sampling. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

High‐fidelity spectroscopy at the highest resolutions

High‐fidelity spectroscopy presents challenges for both observations and in designing instruments. High‐resolution and high‐accuracy spectra are required for verifying hydrodynamic stellar atmospheres and for resolving intergalactic absorption‐line structures in quasars. Even with great photon fluxes from large telescopes with matching spectrometers, precise measurements of line profiles and wavelength positions encounter various physical, observational, and instrumental limits. The analysis may be limited by astrophysical and telluric blends, lack of suitable lines, imprecise laboratory wavelengths, or instrumental imperfections. To some extent, such limits can be pushed by forming averages over many similar spectral lines, thus averaging away small random blends and wavelength errors. In situations where theoretical predictions of lineshapes and shifts can be accurately made (e.g., hydrodynamic models of solar‐type stars), the consistency between noisy observations and theoretical predictions may be verified; however this is not feasible for, e.g., the complex of intergalactic metal lines in spectra of distant quasars, where the primary data must come from observations. To more fully resolve lineshapes and interpret wavelength shifts in stars and quasars alike, spectral resolutions on order R = 300 000 or more are required; a level that is becoming (but is not yet) available. A grand challenge remains to design efficient spectrometers with resolutions approaching R = 1 000 000 for the forthcoming generation of extremely large telescopes (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A procedure for modelling asymptotic g‐mode pulsators: The case of γ Doradus stars

Mode identification is one of the first and main problems we encounter in trying to develop the complete potential of asteroseismology. In the particular case of g‐mode pulsators, this is still an unsolved problem, from both the observational and theoretical points of view. Nevertheless, in recent years, some observational and theoretical efforts have been made to find a solution. In this work we use the latest theoretical and computational tools to understand asymptotic g‐mode pulsators: 1) the Frequency Ratio Method, and 2) Time Dependent Convection. With these tools, a self‐consistent procedure for mode identification and modelling of these g‐mode pulsators can be constructed. This procedure is illustrated using observational information available for the γ Doradus star 9Aurigae. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Few projections astrotomography: radio astronomical approach to 3D reconstruction

We develop a radio astronomical approach to 3D‐reconstruction in few projections tomography. It is based on the 2‐CLEAN DSA method which consists of two clean algorithms by using a synthesized beam. In complex cases two extreme solutions are used for the analysis of the image structure. These solutions determine the limits of permissible energy redistribution on the image among the components of small and large scales. Two variants of 3D‐reconstruction proceeding from a set of two‐dimensional projections (3D_2D) and from a set of one‐dimensional ones (3D_1D) are considered. It is shown that the quality of 3D_2D‐reconstruction should be similar to the quality of 2D_1D‐reconstruction if the same number of equally spaced scans is used. But a doubled number of projections is required for 3D_1D‐reconstruction. We have simulated 3D‐reconstruction of an optically thin emitting object. The present technique is a component of astrotomography and it has good prospects for a wide range of remote sensing. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparing modal noise and FRD of circular and non‐circular cross‐section fibres

Modal noise is a common source of noise introduced to the measurements by optical fibres and is particularly important for fibre‐fed spectroscopic instruments, especially for high‐resolution measurements. This noise source can limit the signal‐to‐noise ratio and jeopardize photon‐noise limited data. The subject of the present work is to compare measurements of modal noise and focal‐ratio degradation (FRD) for several commonly used fibres. We study the influence of a simple mechanical scrambling method (excenter) on both FRD and modal noise. Measurements are performed with circular and octagonal fibres from Polymicro Technology (FBP‐Series) with diameters of 100, 200, and 300μm and for square and rectangular fibres from CeramOptec, among others. FRD measurements for the same sample of fibres are performed as a function of wavelength. Furthermore, we replaced the circular fibre of the STELLA‐échelle‐spectrograph (SES) in Tenerife with an octagonal and found a SNR increase by a factor of 1.6 at 678 nm. It is shown in the laboratory that an excenter with a large amplitude and low frequency will not influence the FRD but will reduce modal noise rather effectively by up to 180%. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Initial Mass Function as given by the fragmentation

The dichotomy between a universal mass function (IMF) and a variable IMF which depends on local physical parameters characterises observational and theoretical stellar astronomy. In this contribution the available distributions of probability are briefly reviewed. The physical nature of two of them, gamma variate and lognormal, is then explained once the framework of the fragmentation is introduced. Interpolating techniques are then applied to the sample of the first 10 pc and to the open cluster NGC 6649: in both cases lognormal distribution produces the best fit. The three power law function has also been investigated and visual comparison with an artificially generated sample of 100000 stars suggests that the variations in the spectral index are simply due to the small number of stars available in the observational sample. In order to derive the sample of masses, a new formula that allows us to express the mass as a function of the absolute magnitude and (B‐V) for MAIN V, GIANTS III and SUPERGIANTS I is derived. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The road to Earth twins – Karl Schwarzschild Award Lecture 2010

A rich population of low‐mass planets orbiting solar‐type stars on tight orbits has been detected by Doppler spectroscopy. These planets have masses in the domain of super‐Earths and Neptune‐type objects, and periods less than 100 days. In numerous cases these planets are part of very compact multiplanetary systems. Up to seven planets have been discovered orbiting one single star. These low‐mass planets have been detected by the HARPS spectrograph around 30 % of solar‐type stars. This very high occurrence rate has been recently confirmed by the results of the Kepler planetary transit space mission. The large number of planets of this kind allows us to attempt a first characterization of their statistical properties, which in turn represent constraints to understand the formation process of these systems. The achieved progress in the sensitivity and stability of spectrographs have already led to the discovery of planets with masses as small as 1.5 M_⊕ (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Big Bear Solar Observatory Ca II K‐line index for solar cycle 23

We present an analysis of 2634 Ca II K‐line full‐disk filtergrams obtained with the 15‐cm aperture photometric full‐disk telescope at Big Bear Solar Observatory during the period from 1996 January 1 to 2005 October 24. Using limb darkening corrected and contrast enhanced filtergrams, solar activity indices were derived, which are sensitive to the 11‐year solar activity cycle and 27‐day rotational period of plages around active regions and the bright chromospheric network. The present work extends an earlier study (solar cycle 22), which was based on video data. The current digital data are of much improved quality with higher spatial resolution and a narrower passband ameliorating photometric accuracy. The time series of chromospheric activity indices cover most of solar cycle 23. One of the most conspicuous features of the Ca II K indices is the secondary maximum in late 2001/early 2002 after an initial decline of chromospheric activity during the first half of 2001. We conclude that a secular trend exists in the Ca II K indices, which has its origin in the bright chromospheric network and brightenings related to decaying active regions. Superposed on this secular trend are the signatures of recurring, long‐lived active regions, which are clusters of persistent and continuously emerging magnetic flux. Such features are less visible, when the activity belts on both side of the equator are devoid of the brightenings related to decaying active regions as was the case in October/November 2003 at a time when a superactivity complex including several naked‐eye sunspots emerged (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Techniques for reducing fiber‐fed and integral‐field spectroscopy data: An implementation on R3D

This paper describes the general characteristics of raw data from fiber‐fed spectrographs in general and fiber‐fed IFUs in particular. The different steps of the data reduction are presented, and the techniques used to address the unusual characteristics of these data are described in detail. These techniques have been implemented in a specialized software package, R3D, developed to reduce fiber‐based integral field spectroscopy (IFS) data. The package comprises a set of command‐line routines adapted for each of these steps, suitable for creating pipelines. The routines have been tested against simulations, and against real data from various integral field spectrographs (PMAS, PPAK, GMOS, VIMOS and INTEGRAL). Particular attention is paid to the treatment of cross‐talk. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Search for circum‐planetary material and orbital period variations of short‐period Kepler exoplanet candidates

A unique short‐period (P = 0.65356(1) d) Mercury‐size Kepler exoplanet candidate KIC012557548b has been discovered recently by Rappaport et al. (2012). This object is a transiting disintegrating exoplanet with a circum‐planetary material–comet‐like tail. Close‐in exoplanets, like KIC012557548b, are subjected to the greatest planet‐star interactions. This interaction may have various forms. In certain cases it may cause formation of the comet‐like tail. Strong interaction with the host star, and/or presence of an additional planet may lead to variations in the orbital period of the planet. Our main aim is to search for comet‐like tails similar to KIC012557548b and for long‐term orbital period variations. We are curious about frequency of comet‐like tail formation among short‐period Kepler exoplanet candidates. We concentrate on a sample of 20 close‐in candidates with a period similar to KIC012557548b from the Kepler mission. We first improved the preliminary orbital periods and obtained the transit light curves. Subsequently we searched for the signatures of a circum‐planetary material in these light curves. For this purpose the final transit light curve of each planet was fitted with a theoretical light curve, and the residuals were examined for abnormalities. We then searched for possible long‐term changes of the orbital periods using the method of phase dispersion minimization. In 8 cases out of 20 we found some interesting peculiarities, but none of the exoplanet candidates showed signs of a comet‐like tail. It seems that the frequency of comet‐like tail formation among short‐period Kepler exoplanet candidates is very low. We searched for comet‐like tails based on the period criterion. Based on our results we can conclude that the short‐period criterion is not enough to cause comet‐like tail formation. This result is in agreement with the theory of the thermal wind and planet evaporation (Perez‐Becker & Chiang 2013). We also found 3 cases of candidates which showed some changes of the orbital period. Based on our results we can see that orbital period changes are not caused by comet‐like tail disintegration processes, but rather by possible massive outer companions. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cosmic‐ray rejection for single spectroscopic CCD images by means of template matching

This article describes a novel algorithm for cosmic‐ray rejection in single spectroscopic CCD images. This algorithm is based on a variation of template matching. It focuses on identifying those pixels belong to spectra, while other conventional algorithms tried to locate the cosmic‐ray hits directly. The main principle is applying template matching to find suspicious blocks, which is followed by surface patching to locate the legitimate pixels accurately. Therefore, the rest pixels are the ones corrupted by cosmic‐ray hits. Meanwhile, almost all the parameters are automatically extracted from the images. Examples of its performance are given for both simulated and observed images. It shows an advantage of significantly low false alarm rate with relatively high detection rate (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study of the effect of metallicity on the amplitudes of Cepheids

Results concerning the dependence of photometric and radial velocity amplitudes on metallicity are presented based on about 200 Galactic classical Cepheids pulsating in the fundamental mode. The Galactic distribution of the [Fe/H] value of Cepheids is also studied. We show that the photometric amplitude ratio A_I/A_V is independent of metallicity. The observed dependence of this ratio on the pulsation period does not correspond to the theoretical predictions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Smear fitting: a new image-deconvolution method for interferometric data

A new technique is presented for producing images from interferometric data. The method, 'smear fitting', makes the constraints necessary for interferometric imaging double as a model, with uncertainties, of the sky brightness distribution. It does this by modelling the sky with a set of functions and then convolving each component with its own elliptical Gaussian to account for the uncertainty in its shape and location that arises from noise. This yields much sharper resolution than clean for significantly detected features, without sacrificing any sensitivity. Using appropriate functional forms for the components provides both a scientifically interesting model and imaging constraints that tend to be better than those used by traditional deconvolution methods. This allows it to avoid the most serious problems that limit the imaging quality of those methods. Comparisons of smear fitting to clean and maximum entropy are given, using both real and simulated observations. It is also shown that the famous Rayleigh criterion (resolution = wavelength/baseline) is inappropriate for interferometers as it does not consider the reliability of the measurements.     

A hydrodynamical study of multiple‐shell planetary nebulae

We present the result of a study on the expansion properties and internal kinematics of round/elliptical planetary nebulae of the Milky Way disk, the halo, and of the globular cluster M 15. The purpose of this study is to considerably enlarge the small sample of nebulae with precisely determined expansion properties (Schönberner et al. 2005b). To this aim, we selected a representative sample of objects with different evolutionary stages and metallicities and conducted highresolution ´echelle spectroscopy. In most cases we succeeded in detecting the weak signals from the outer nebular shell which are attached to the main line emission from the bright nebular rim. Next to the measurement of the motion of the rim gas by decomposition of the main line components into Gaussians, we were able to measure separately, for most objects for the first time, the gas velocity immediately behind the leading shock of the shell, i.e. the post‐shock velocity. We more than doubled the number of objects for which the velocities of both rim and shell are known and confirm that the overall expansion of planetary nebulae is accelerating with time. There are, however, differences between the expansion behaviour of the shell and the rim: The post‐shock velocity is starting at values as low as around 20 km s^–1 for the youngest nebulae, just above the AGB wind velocity of ∼ 10–15 km s^–1, and is reaching values of about 40 km s^–1 for the nebulae around hotter central stars. Contrarily, the rim matter is at first decelerated below the typical AGB‐wind velocity and remains at about 5–10 km s^–1 for a while until finally a typical flow velocity of up to 30 km s^–1 is reached. This observed distinct velocity evolution of both rim and shell is explained by radiation‐hydrodynamics simulations, at least qualitatively: It is due to the ever changing stellar radiation field and wind‐wind interaction together with the varying density profile ahead of the leading shock during the progress of evolution. The wind‐wind interaction works on the rim dynamics while the radiation field and upstream density gradient is responsible for the shell dynamics. Because of these time‐dependent boundary conditions, a planetary nebula will never evolve into a simple self‐similar expansion. Also the metal‐poor objects behave as theory predicts: The post‐shock velocities are higher and the rim flow velocities are equal or even lower compared to disk objects at similar evolutionary stage. The old nebula around low‐luminosity central stars contained in our sample expand still fast and are dominated by reionisation. We detected, for the first time, in some objects an asymmetric expansion behaviour: The relative expansions between rim and shell appear to be different for the receding and approaching parts of the nebular envelope. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

T Tauri star magnetic fields and magnetospheres

Stellar magnetic fields govern key aspects of the evolution of a young star, from controlling accretion to regulating the angular momentum evolution of the system. Spectro‐polarimetric studies of T Tauri stars have revealed a surprising range of magnetic field topologies. Meanwhile multi‐wavelength campaigns have probed T Tauri star systems from stellar photosphere to inner disk, allowing us to study magnetospheric accretion in unprecedented detail. We review recent results and discuss their implications for understanding the evolution of young stars (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

CORA — emission line fitting with Maximum Likelihood

The advent of pipeline‐processed data both from space‐ and ground‐based observatories often disposes of the need of full‐fledged data reduction software with its associated steep learning curve. In many cases, a simple tool doing just one task, and doing it right, is all one wishes. In this spirit we introduce CORA, a line fitting tool based on the maximum likelihood technique, which has been developed for the analysis of emission line spectra with low count numbers and has successfully been used in several publications. CORA uses a rigorous application of Poisson statistics. From the assumption of Poissonian noise we derive the probability for a model of the emission line spectrum to represent the measured spectrum. The likelihood function is used as a criterion for optimizing the parameters of the theoretical spectrum and a fixed point equation is derived allowing an efficient way to obtain line fluxes. As an example we demonstrate the functionality of the program with an X‐ray spectrum of Capella obtained with the Low Energy Transmission Grating Spectrometer (LETGS) on board the Chandra observatory and choose the analysis of the Ne IX triplet around 13.5 Å.     

O'Connell effect in early‐type contact binaries: DU Boo and AG Vir

The paper presents new photoelectric observations of the eclipsing binary systems DU Boo and AG Vir. The systems are somewhat similar – both are A‐type contact binaries with the maximum following the primary minimum being the brighter one. This light curve asymmetry is extremely temporally stable. The phase dependence of the color indices is unexpectedly small for the observed amplitude of the O'Connell effect, amounting to about 0.1 mag in the optical wavelength range which indicates a very large heated area with a temperature contrast of ΔT ≈ 1000–1500 K. The broadening functions (BFs) of the systems do not show any dark solar‐type photospheric spots. On the other hand, there are significant differences of BFs between the quadratures (surprisingly similar in both systems) indicative of stream of matter or bright region causing additional emission seen between the components around the phase 0.25. Absolute parameters of the components slightly depend on the adopted model. Long orbital period of both contact binaries combined with late spectral type indicate that the primary components of either of the systems (but particularly in case of DU Boo) already evolved off the main sequence (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Detection and measurement from narrow-band tunable filter scans

The past 5 years have seen a rapid rise in the use of tunable filters in many diverse fields of astronomy, through Taurus Tunable Filter (TTF) instruments at the Anglo-Australian and William Herschel Telescopes. Over this time we have continually refined aspects of operation and developed a collection of special techniques to handle the data produced by these novel imaging instruments. In this paper, we review calibration procedures and summarize the theoretical basis for Fabry–Perot photometry that is central to effective tunable imaging. Specific mention is made of object detection and classification from deep narrow-band surveys containing several hundred objects per field. We also discuss methods for recognizing and dealing with artefacts (scattered light, atmospheric effects, etc.), which can seriously compromise the photometric integrity of the data if left untreated. Attention is paid to the different families of ghost reflections encountered, and the strategies used to minimize their presence. In our closing remarks, future directions for tunable imaging are outlined and contrasted with the Fabry–Perot technology employed in the current generation of tunable imagers.     

Pointing and tracking analysis of alt‐azimuthal multi‐focus telescopes: the THEMIS case

We discuss the pointing and tracking configuration of THEMIS which may be considered as representative of those alt‐azimuthal telescopes with an optical configuration with multiple focal planes, not all locked to both the alt‐azimuthal coordinates. In the THEMIS case two focal planes are present. The primary focus F1 is locked to the alt‐azimuthal mount, while the secondary focus F2 (which is used by the instruments), is only locked to the azimuth angle. The different contributions to the final accuracy of both absolute pointing and tracking as observed at F2 are defined, and an extimation of the contribution of each component of the whole chain which affects the field position at F2 (software, mechanical and optical) is given. The experimental data are the result of a test campaign carried on at THEMIS in February and March 2002. We can say that (a) for all the used observing configurations, the tracking accuracy is coherent at any point along the trajectory with the correspondent absolute pointing accuracy, which is an indication for the quality of the telescope dynamical performances (b) the main contribution to the residual field shift which is observed at F2 arises from the opto‐mechanical alignment configuration of the optics between F1 and F2, which therefore is the crucial point for such multi‐focus configuration. More informations can be found at the official THEMIS website (http://www.themis.iac.es).