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Aldo Dell'Oro INAF- Observatory of Turin

Aldo Dell'Oro INAF- Observatory of Turin. Detailed analysis of the signal from asteroids by GAIA and their size estimation. Besançon November 6-7, 2003. Size determination of main belt asteroids: simulating the GAIA signal. Best fit approach:

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Aldo Dell'Oro INAF- Observatory of Turin

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  1. Aldo Dell'Oro INAF- Observatory of Turin Detailed analysis of the signal from asteroids by GAIA and their size estimation Besançon November 6-7, 2003

  2. Size determination of main belt asteroids: simulating the GAIA signal. Best fit approach: If we can simulate the detailed features of the signal produced by GAIA for a given asteroid model and given observing circumstances, after processing all the single detections of the same object, we can determine the best asteroid model reproducing the full set of single observations. Tool (simulator) requirements: In order to obtain this goal we have to reproduce not only the optical properties of the object, like magnitude and photometric surface distribution, but also the exact “instrumental processing” of the collected photons, their aquisition, storage and transmission.

  3. In the last meeting in Paris a simplified analytical model of the signal was developed, in order to perform a preliminary assessment of the expected accuracy in the size estimation of asteroids. The mean conclusions were: • the limit angular size (uncertainty 100 %) that can be estimated is ~ 6 mas at magnitude G ~ 12, and ~ 40 mas at magnitude G ~ 20 • the size of the main belt asteroids with diameter larger than 20 km can be estimated with an accuracy equal or better than 10 %, at least once during the operative life of GAIA • below 20 km, no size estimation can be done That model did not take into account: • the role of finite size of the CCD pixels • the exact (and variable) position of the image in the CCD grid • the finite number of pixels used in signal acquisition (windowing)

  4. How does the instrument work? (1) Incoming angular distribution of photons from the object The number and distribution of photons are determined by: • shape • scattering law • observing conditions • Poisson statistics

  5. How does the instrument work? (2) Diffraction-spread image on focal plane produced by the instrument optics (convolution with PSF)

  6. How does the instrument work? (3) CCD grid superposition: distribution of photons inside CCD pixels The binned distribution of photons depends on: • pixel size • relative position image- -grid • TDI motion

  7. How does the instrument work? (4) Photocenter determination and window definition around the image (astrometric sky mapper)

  8. How does the instrument work? (5) Window selection and read-out of the signal in the window (astrometric field)

  9. How does the instrument work? (6) Binning and final signal (recorded)

  10. Proposed window sizes E. Høg et al. (2003) GAIA-CUO-117 G=12-16 G=16-20 window size (pixels) 6 1 pixel: 10x30 mm 12 6 vertical binning (across-scan integration) along-scan direction read-out signal (photoelectron distribution)

  11. What do we mean by “signal (measure)”? The signal is a vector of 6 or 12 numbers, corresponding to the numbers of collected photoelectrons in each of 6 or 12 column of (6) pixels in the window. The signal is nothing else than the along-scan photoelectrons distribution. From the signal we can derive: Photocenter The photocenter is the mean (in pixels) of the photoelectron distribution. Width The width of the signal is the standard deviation (in pixels) of the photoelectron distribution.

  12. Photocenter and width

  13. Stochastic nature of the signal The number of detected photoelectrons per bin is subject to random fluctuations due to: “Internal” image sources of fluctuation: • photons statistics: difference in number, and in time and spatial distribution of photons arrivals; • differences in relative position between object and CCD grid (i. e., the center of the optical image can be in the center of a pixel or on its edge). “External” sources of fluctuation: • photon statistics of background; • cosmic rays; • electronic-instrumental noise; The signal cannot be predicted in a purely deterministic way

  14. Photons statistics and magnitude

  15. Stochastic signal fluctuations Four repeated observations of the same asteroid model (same object) in identical observing circumstances G = 20 50 mas

  16. Dispersion of the measured width Due to the stochastic nature of signal formation, a single measurement of a given object gives a width belonging in principle to a more or less wide range of possible values. The dispersion of the width values depends on different parameters: apparent magnitude, number of sampling pixels, etc... Width measurements of the signals from two different objects with slightly different sizes, can give identical values. Can we distinguish among different bodies, in such a way as to appreciate small size differences?

  17. Dispersion of the measured width

  18. Single width measurement of the signal of a 200 mas asteroid

  19. Repeated width measurement of the signal of a 200 mas asteroid width dispersion

  20. Repeated width measurement of all asteroids

  21. single width measure Dispersion of compatible sizes Range of sizes compatible with a single measured signal width

  22. width dispersion Dispersion of compatible sizes Predicting the error in estimating the size of a 200 mas object

  23. Precision in estimating the size of an object The theoretical dispersion of compatible sizes can be used to predict the GAIA precision in estimating apparent asteroid sizes. The relative precision is the dispersionofcompatible sizes divided by the real size of the object. The relative precision vs. size provides the real limits in size estimation.

  24. Spheres: phase = 0o velocity = 0 mas/sec

  25. Spheres: phase = 0o velocity = 0 mas/sec

  26. Spheres: phase = 0o velocity = 0 mas/sec

  27. Spheres: phase = 0o velocity = 0 mas/sec

  28. Number of pixels and accuracy What is the best number of pixels in the window for asteroid size measurements? Increasing the number of pixels in the window, the number of sampling bins increases but so does also the noise due to pixels collecting the tails of the photon distribution. As a consequence, by increasing the pixel number we improve the accuracy in measuring large sizes, but we worsen the accuracy in measuring smaller sizes.

  29. Summary The conclusions of the preliminary semi-analytical analysis are substantially confirmed: • Main belt asteroids with diameter larger than 20÷30 km can be measured with an accuracy equal or better than 10 %, at least once during the operative life of GAIA; • below 20 km, no reliable size estimate can be obtained; The minimum angular size that can be measured with an accuracy of 10 % is ~ 20 mas at magnitude G ~ 12, and ~ 120 mas at magnitude G ~ 20 The 6-pixel window represents a reasonable trade-off between accuracy and number of asteroids that can be measured

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