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Astronomical Data Analysis Software and Systems VI ASP Conference Series, Vol. 125, 1997 Gareth Hunt and H. E. Payne, eds.

Towards Optimal Analysis of HST Crowded Stellar Fields
Peter Linde and Ralph Snel Lund Observatory, Box 43, S-221 00 Lund, Sweden, E-mail: peter@astro.lu.se Abstract. A Nordic group is using the Hubble Space Telescop e in a study of stellar p opulations in the Bar of the Large Magellanic Cloud. Through Stromgren uvby photometry, we determine ages, metallicities, Ё and the luminosity function. We have designed and applied an exp osure dithering pattern in order to decrease the effects of undersampling. This also enables a detailed study of detector prop erties, which is essential for accurate photometry. Careful studies of low level background features are presented. Algorithms develop ed to analyse the PSF shap e reveal variation of this shap e with p osition in the PC field. A comparison verifies improved photometric quality for dithered versus undithered images. The faint end of the luminosity function is studied through application of statistical techniques to very faint background fluctuations.

1.

Introduction

A Nordic group (Ardeb erg et al. 1997) is using the Hubble Space Telescop e in a study of stellar p opulations in the Bar of the Large Magellanic Cloud (LMC). A total of 35 hours of exp osure have b een obtained using the WFPC2 camera om with StrЁ gren uvby filters. Through accurate photometry, we determine ages, metallicities, and the luminosity function. Accurate photometry is essential, and we are investigating various effects affecting the measurements. New algorithms have b een develop ed. Here we present some initial results.

2.

Bias Jumps Affecting Image Background

We have noted weak background variations in some of our exp osures, typically the shorter ones. Figure 1 shows a set of calibration exp osures (with two stars) using the StrЁ gren uvby filters. In order to see the variations through the om noise, the images have b een smoothed. The two calibration stars are seen as squares. Typical amplitudes of the background variations are 0.5 ADUs. Ap erture photometry results for the v filter, as a function of ap erture radius, are shown in Figure 2. The individual frame numb ers are given as data p oints, as well as a standard deviation for each set of p oints. The spread is larger than exp ected from photon statistics. A simple attempt to correct for the background variations was made, using an average over all image columns and then reex431

© Copyright 1997 Astronomical Society of the Pacific. All rights reserved.


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Linde and Snel

y1

y2

y3

y4

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b4

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Figure 1. Faint background variations revealed after smoothing. Four images are shown for each filter. The two bright ob jects are stars.

panding into a background image. In Figure 3, the corresp onding results are given. Only a marginal improvement can b e noted.

3.

Effects of Dithering on Photometry

Sixteen images were obtained of our target LMC field using the F547M (y) filter. For each set of four exp osures, consecutive exp osures have a quarter pixel offset with resp ect to the axes of the detector pixel grid. After reconstruction, this effectively improves the sampling of the image. We have analysed these data using p oint spread function (PSF) fitting techniques (Daophot/Allstar, Stetson 1987), b oth as a set of 16 individual exp osures and as four sets of dithered images. Figure 5 shows the mean error as a function of magnitude; the dotted line shows non-dithered results and the solid line shows dithered results. A significant improvement in accuracy is noted. The improvement will b e more pronounced in our crowded Wide Field Camera (WFC) images, and may b e increased further through use of a more sophisticated method of combining the individual dithered images.


Towards Optimal Analysis of HST Crowded Stellar Fields

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4 2 3 1 2 1 4 2 1 4 3 3

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2 4 3 1 2 1 4 2 1 4 3 3

2 4 3 1

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4 1 3 2 4 1 4 1 2 3 2 3 1 4 3 2

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Figure. 2. Aperture photometry mag- Figure. 3. Same as Fig. 2, but with a nitude as function of aperture radius. correction for background variations.

Figure. 5. Dithering e ect on photometric accuracy. Full drawn line shows Figure. 4. Variations of PSF shape as errors derived from 4 dithered images, function of position on the PC detector. dashed line from 16 individual images.

Figure. 6. Luminosity functions. Full Figure. 7. Goodness of t for hisdrawn line: extrapolated LF. Dashed tograms of simulated images, compared to the histogram of the observed imline: observed, uncorrected LF. age. Full drawn line: extrapolated LF. Dashed line: observed LF.


434 4.

Linde and Snel PSF Shap e Variations in the PC Field

Our analysis allows us to check for p oint spread function shap e variations in the HST Planetary Camera (PC) field. Algorithms were develop ed to extract PSFs from dithered and oversampled images. Each PSF was defined from approximately 20 stars. Figure 4 shows a sequence of panels with PSFs derived from different parts of the field. In the figure, the grid represents pixel p osition on the PC detector, with each PSF enlarged a factor of 20. From Figure 4, a noticeable shap e change with p osition is verified. For comparison, see Biretta et al. (1996). We are now analysing the effect on our photometry, and are developing algorithms to prop erly include this in the data analysis. 5. The Faint End of the Stellar Luminosity Function

In crowded field images, we are deriving information ab out the faint end of the luminosity function (LF) from the texture of the image background. This algorithm aims at studying ob jects fainter than can b e reached using conventional completeness estimation techniques. Intensity deviations due to many undetectable faint stars are always p ositive, which will affect the statistical prop erties of the pixel intensity distribution. From this, the numb er and the intensity distribution of faint stars can b e estimated. Characteristics such as the shap e of the PSF, detector noise prop erties, etc., influence the texture of the background and have to b e modeled carefully. We compare a simulated image to an observed one. If the images are statistically similar enough, it is assumed that the LFs are similar. As a measure of similarity, the 2 measure b etween the two histograms of the simulated and observed images is used. A lower value of 2 indicates a b etter fit to the histogram. By iteratively adjusting and extrap olating the observed LF, simulated images with increased statistical similarity are created. Figure 6 shows an example of an observed LF derived from a single WFC image, together with a preliminary model LF. The simple model used has two free parameters: the steepness of the LF and the level of the background. Figure 7 shows the statistical differences b etween histograms derived from the real image, with a background level of 355 ADU, and two simulated images. One was created using the LF derived from standard measurements of the detectable stars. The other was created using the model LF. The decreased chi-square values for the histogram of the latter shows that the model LF is closer than the observed to the true LF. References Ardeb erg, A., Gustafsson, B., Linde, P., & Nissen, P.-E. 1997, A&A, in prep. Biretta, J. A., et al. 1996, WFPC2 Instrument Handb ook, vers. 4.0 (Baltimore: STScI) Stetson, P. B. 1987, PASP, 99, 191