A New Method for Comparing Numerical Simulations with ...

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80 Rybák et al.1.41.1SPATIAL SCALE X [arc sec]20-21.31.21.11.00.90.80.70.60.50.4SPATIAL SCALE X [arc sec]20-21.00.90.80.70.60.5-0.2 -0.1 -0.0 0.1 0.2WAVELENGTH [A]0.3-0.2 -0.1 -0.0 0.1 0.2WAVELENGTH [A]0.4Figure 2. Example spectra of a spatial cut from a simulation snapshot(intensities are normalized to the spatially averaged value of the continuumintensity). The left panel shows the original synthetic spectrum of the Feii6456 Å spectral line. The right panel gives for comparison the same spectrumdegraded with all degradation effects taken into account.value of the PSF full-width equal to 1.25 ′′ . This value corresponds to a Friedparameter r 0 of 11 cm what is in agreement with the typical values of r 0 derivedfor the best observing sites like Canary Islands (Brandt & Wöhl 1982) andSacramento Peak (Brandt, Mauter, & Smartt 1987).5. ResultsFigure 2 shows an example of an original and a degraded SIM spectrum. Besidesa decrease in the intensity range from [0.3,1.4] to [0.4,1.1], a remarkabledegradation of the spectral profiles is found. For example, the range of theline-of-sight velocities derived from the Doppler shifts changes from ± 5 km/s toonly ± 1 km/s. Almost all (99.6%) of our observed Doppler shifts are within thelatter velocity interval.The effects of the degradation procedure on distributions of two spectral linecharacteristics – the continuum intensity and the full-width at half minimum ofthe line (FWHM) – are shown in Figure 3, where histograms of these quantitiesare displayed. They have been calculated for the position µ = 0.65 takingeach snapshot individually. The histograms of the continuum intensity of theoriginal SIM data show a wide range of values with an almost flat central partin the interval 0.8 to 1.2. The degradation procedure significantly narrows thesedistributions to the interval [0.9,1.1] but the significant part of the data arewithin the interval [0.94,1.06]. Generally, individual distributions keep theirsignificant statistical differences even after degradation.The distribution of the line width of the original SIM data is very asymmetric.Therefore, the most frequent value of this quantity is shifted by 10 % from themean value. The degradation removes the far wings of the distributions below 0.8
Method for Comparing Simulations with Observations 81CONTINUUM INTENSITY DISTRIBUTIONFWHM DISTRIBUTION1.0001.0000.1000.100Synthetic spectra0.010Synthetic spectra0.0100.0011.0000.0011.000Synthetic spectra + PSF + slit + IPSynthetic spectra + PSF + slit + IP0.1000.1000.0100.0100.0010.6 0.8 1.0 1.2 1.4NORMALIZED CONTINUUM INTENSITY I c0.0010.5 1.0 1.5 2.0 2.5 3.0NORMALIZED FWHMFigure 3. Distributions of the continuum intensity (left column) and the linewidth (right column) for all individual snapshots from the original simulationdata (top row) and for the same data degraded for all effects including thePSF, the slit width, detector pixel sampling, and the estimated instrumentalprofile of the VTT echelle spectrograph (bottom row).and above 1.4. The distributions are still asymmetric and significant variationsbetween individual distributions are present.A comparison of the average distributions of the normalized FWHM comingfrom OBSs and from degraded SIMs for µ=0.65 is given in Figure 4. Both distributionsshow similar asymmetry but the distribution from the SIMs is broader.The difference is more pronounced for the tail of large values (∼20 %). Forchecking purposes, we have calculated a similar distribution for the continuumintensity (Figure 4). It advises that the PSF might be still a bit underestimatedas the distribution of the SIMs is still broader than that of the OBSs. Thesepreliminary results demonstrate the possible usage of this method for statisticalcomparison of high-resolution spectroscopic observations with synthetic dataobtained from numerical simulations.Acknowledgments. The VTT is operated by the Kiepenheuer-Institut fürSonnenphysik, Freiburg, at the Observatorio del Teide. This research is part of
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