Measuring the Characteristic Sizes of Convection Structures in AGB Stars with Fourier Decomposition Analyses : the Stellar Intensity Analyzer (SIA) Pipeline.
Abstract: Context. Theoretical studies predict that the length scale of convection in stellar atmospheres isproportional to the pressure scale height, which implies that giant and supergiant stars should have convection granules of sizes comparable to their radii. Numerical simulations and the observation of anisotropies on stellar discs agree well with this prediction. Aims. To measure the characteristic sizes of convection structures of models simulated with the CO5BOLD code, to look at how they vary between models and to study their limitations due to numerical resolution. Methods. Fourier analyses are performed to frames from the models to achieve spatial spectral power distributions which are averaged over time. The position of the main peak and the averagevalue of the wavevector are taken as indicators of these sizes. The general shape of the intensity map of the disc in the frame is fitted and subtracted so that it does not contaminate the Fourier analysis. Results. A general relationship of the convection granule size being more or less ten times larger than the pressure length scale is found. The expected wavevector value of the time-averaged spectral power distributions is higher than the position of the main peak. Loose increasing trends with the characteristic sizes by the pressure scale height increasing against stellar mass, radius, luminosity,temperature and gravity are found, while a decreasing trends are found with the radius and modelresolution. Bad resolution subtracts signals on the slope at the side of the main peak towards larger wavevector values and in extreme cases it creates spurious signal towards the end of the spectrum due to artifacts appearing on the frames. Conclusions. The wavevector position of the absolute maximum in the time-averaged spectral power distribution is the best measure of the most prominent sizes in the stellar surfaces. The proportionality constant between granule size and pressure length scale is of the same order ofmagnitude as the one in the literature, however, models present sizes larger than the ones expected, likely because the of prominent features do not correspond to convection granules but to larger features hovering above them. Further studies on models with higher resolution will help in drawing more conclusive results. Appendix. The SIA pipeline takes a set of time-dependent pictures of stellar disks and uses a Fourier Analysis to measure the characteristic sizes of their features and other useful quantities, such as standard deviations or the spatial power distributions of features. The main core of the pipeline consists in identifying the stellar disc in the frames and subtracting their signal from the spatial power distributions through a general fit of the disc intensity. To analyze a time sequence, the SIA pipeline requires at least two commands from the user. The first commandorders the SIA pipeline to read the .sav IDL data structure file where the frame sequence is stored and to produce another .sav file with information on the spectral power distributions, the second command orders the reading of such file to produce two more .sav files, one containing time-averaged size measurements and their deviations while the other breaking down time-dependant information and other arrays used for the calculations. The SIA pipeline has been entirely written in Interactive Data Language (IDL). Most of the procedures used here are original from the SIA pipeline, but a small handfull like ima3_distancetransform.pro, power2d1d.pro, extremum.pro and smooth2d.pro from Bernd Freytag and peaks.pro and compile opt.pro amongst others are actually external.
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