Data Reduction And Error Analysis For The Physical Sciences

1. Introduction 2. Radial velocities 3. Astrometry 4. Timing 5. Microlensing 6. Transits 7. Imaging 8. Host stars 9. Brown dwarfs and free-floating planets 10. Formation and evolution 11. Interiors and atmospheres 12. The Solar System Appendixes References Index.

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The Exoplanet Handbook

Magnetic activity similar to that of the Sun is observed on a variety of cool stars with external convection envelopes. Stellar rotation coupled with convective motions generate strong magnetic fields in the stellar interior and produce a multitude of magnetic phenomena including starspots in the photosphere, chromospheric plages, coronal loops, UV, X-ray, and radio emission and flares. Here I review the phenomenon of starspots on dierent types of cool stars, observational tools and diagnostic techniques for studying starspots as well as starspot properties including their temperatures, areas, magnetic field strengths, lifetimes, active latitudes and longitudes, etc. Evolution of starspots on various time scales allows us to investigate stellar dierential rotation, activity cycles, and global magnetic fields. Together these constitute the basis for our understanding of stellar and solar dynamos and provide valuable constraints for theoretical models.

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Starspots: A Key to the Stellar Dynamo

Eclipsing binaries can improve multiple system statistics via the light-time effect and radial velocity shifts. Here an algorithm operates on data of mixed type to exploit these opportunities. Main reasons for enhanced reliability are that (1) combined light and velocity curves give better timewise coverage than either type alone, (2) properly weighted solutions impersonally balance light and velocity information, and (3) the entire theory is within the computer model, so observations are used directly without corrections. A brief history of mixed whole-curve solutions is given and the relative importance of light-time and radial velocity input for third-body parameters is discussed and quantified. Period sifting by power spectral analysis is essentially indispensable in preliminary work. Applications are to the Algol-type system DM Persei and the detached system VV Orionis. An assumption of coplanarity for DM Per's inner and outer orbits is tested and quantified by dynamical experiments. Derived third-body parameters for DM Per are mainly reasonable and self-consistent. For comparison with whole-curve results, we also investigated DM Per's ephemeris in terms of eclipse timings and found whole-curve solutions to give smaller standard errors in reference epoch (T0), binary orbit period (P), and dP/dt, over a similar baseline in time. An astonishing outcome is lack of evidence that can pass reasonable validity tests for VV Ori's well-accepted third star with P ≈ 120 days. Estimates of third light do indicate a third star, but the correct period cannot now be established, so the star cannot be identified as the one heretofore recognized from radial velocity evidence. The much cited 120 day period appears to be an artifact of the window function for VV Ori's historical velocity observations.

http://iopscience.iop.org/article/10.1086/517870/pdf

Third-body parameters from whole light and velocity curves

Most directly imaged giant exoplanets are fainter than brown dwarfs with similar spectra. To explain their relative underluminosity, unusually cloudy atmospheres have been proposed. However, with multiple parameters varying between any two objects, it remained difficult to observationally test this idea. We present a new method, sensitive time-resolved Hubble Space Telescope near-infrared spectroscopy, to study two rotating L/T transition brown dwarfs (2M2139 and SIMP0136). The observations provide spatially and spectrally resolved mapping of the cloud decks of the brown dwarfs. The data allow the study of cloud structure variations while other parameters are unchanged. We find that both brown dwarfs display variations of identical nature: J- and H-band brightness variations with minimal color and spectral changes. Our light curve models show that even the simplest surface brightness distributions require at least three elliptical spots. We show that for each source the spectral changes can be reproduced with a linear combination of only two different spectra, i.e., the entire surface is covered by two distinct types of regions. Modeling the color changes and spectral variations together reveal patchy cloud covers consisting of a spatially heterogeneous mix of low-brightness, low-temperature thick clouds and brighter, thin, and warm clouds. We show that the same thick cloud patches seen in our varying brown dwarf targets, if extended to the entire photosphere, predict near-infrared colors/magnitudes matching the range occupied by the directly imaged exoplanets that are cooler and less luminous than brown dwarfs with similar spectral types. This supports the models in which thick clouds are responsible for the near-infrared properties of these underluminous exoplanets.

http://iopscience.iop.org/article/10.1088/0004-637X/768/2/121/pdf

Hst spectral mapping of l/t transition brown dwarfs reveals cloud thickness variations

A method of determination of parameter sets characterizing models of starspots is described. The method makes use of a systematic integral notation in the description of the darkening due to spots and optimization procedures to evaluate appropriate parameters. The method is applied to light curves of YY Gem and CC Eri. In the latter case a comparison is made with the results of Bopp and Evans's (1973) study. The physical meaning of the derived parameter set and possibly correlated effects are considered for YY Gem.

The interpretation of cyclical photometric variations in certain dwarf Me-type stars

A direct method of analysis of the light curves of eclipsing binary systems is proposed, which, as an alternative to numerical integration methods, adopts the associated alpha functions of Kopal as the means of description of eclipses. Alpha functions can be internally generated, corresponding to given trial parameters and orbital phase, in a computer program which then goes on to optimize the trial parameter set. The method has been applied to a number of light curves including those of YZ Cas, WW Aur, YY Gem and SZ Cam. Second order coefficient of limb darkening have been determined for the YZ Cas stars. Finally, a comparative discussion is given of various methods of light curve analysis.

Analysis of eclipsing binary light curves on automatic computers

The extensive, homogeneous and automatically obtained OAO-2UV data on VV Ori at six different wavelengths, as presented by Eaton (1975), are subjected to detailed numerical analysis, and the extent of derivable information on this star from such photometry is critically assessed.

The system VV Ori and the consistency of photometric analysis of eclipsing binary light curves

The iterative optimization procedures described in a previous paper by the author have been extended to cover unrectified light curves of eccentric eclipsing binary systems. Two stars have been studied in detail: namely, α Coronae Borealis and V477 Cygni. In both cases improved element sets have been obtained. Moreover, in the case of V477 Cygni the obtained values of the longitude of periastron for three different light curves are found to provide a useful basis for discussion of the apsidal motion of this system.

Optimization analysis of the light curves of eccentric eclipsing binary systems

The basic physical picture of the Algol system is reviewed, and, using collected red and infrared observations, photometric curve fits are investigated by applying numerical quadratures to determine theoretical light curves appropriate to Roche model stars. The ‘contact’ nature of Algol B appears to be confirmed, and effective temperatures of the three components areTA=11 400°,TB=5300°,TC=7600°. In terms of a Lambert's law approach to the ‘reflection effect’, the effective heat-albedo is required to be reduced from unity to one half; and it is also found that the averaged ‘gravity-darkening coefficient’ is close to a value appropriate for a diffusion type of heat-transfer mechanism operating in sub-photospheric layers.

E. Budding

Papers

The interpretation of cyclical photometric variations in certain dwarf Me-type stars

Analysis of eclipsing binary light curves on automatic computers

The system VV Ori and the consistency of photometric analysis of eclipsing binary light curves

Optimization analysis of the light curves of eccentric eclipsing binary systems

Analysis of Red and Infrared Wide-Band Photometry of Algol