From erik Wed Aug 5 11:24:04 1998 Subject: CUO_43.txt Simulations BBP: 2 To: gaia-sag@astro.estec.esa.nl (GAIA SAG), Frederic.Arenou@obspm.fr (Arenou), BERNACCA@ASTRAS.pd.astro.it (P.L. Bernacca) Date: Wed, 5 Aug 1998 11:24:04 +0200 (MET DST) X-Mailer: ELM [version 2.4 PL23] MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit Content-Length: 10182 Status: RO Simulation of final GAIA photometry ----------------------------------- E. Hoeg, C. Fabricius 5 Aug. 1998 SAG_CUO_43 ABSTRACT: Towards the end of GAIA data reduction the positions of all measurable stars will be known as function of time. In order to achieve this goal in an optimal way a photometric sky mapper (PSM) is proposed to map about 3 sq.arcsec around each astrometric star. On this basis the most accurate photometric data reduction can be made. The resulting accuracy of the broad-band photometry is estimated from simulations of double star observations. Double stars with an A component of I=20.0 mag were considered. 100 observations in random scan directions in the Sloan i' band were superposed and analyzed with a cross- correlation method giving slit photometry, but no positions. The standard errors and systematic errors were, as expected, generally smaller than with the method 1 used in CUO_42 where also the position was determined. Introduction ------------ Monte-Carlo simulations of observations with the broad-band photometer have been carried out. Observations of patches in random scan directions in the Sloan i' band were superposed and analyzed with a cross- correlation (CC) method using the known PSF and obtaining slit photometry for double stars. This method is the second of the following two methods for which we investigate the photometric precision. The first method was studied in CUO_42. (1) The positions of both components of double stars are estimated by maximum cross-correlation from the set of patches, and the magnitude is then estimated by a cross correlation of the PSF and the observation data at the given position. (2) The positions of both components are known from other sources, i.e. from the estimation in white light and all broad bands. The magnitude is then estimated as in (1). In both methods a star position is assumed predicted from astrometric parameters and attitude, not containing the uncertainty as if it were predicted from an astrometric sky mapper estimation for every BBP observation. Only the proper motion and parallax (and possibly an orbit) must be known with high accuracy in Method 1. We assumed a binning of 1*8 pixels/sample and 16 samples/patch. This allows solution of double stars with separations of, e.g., 100- 300 mas if the patch is centred on one of the components. Thus a larger separation than the 200 mas allowed with method 1 could be used with the same size of patch because no iteration of the position is required. The standard errors were estimated from the internal agreement of 150 stars each one with 100 observations. With 150 degrees of freedom the relative error of the standard errors should be 0.058 (=sqrt(1/300)). The background was assumed to be V=21.0 mag/arcsec^2, and was determined from N_b=12 undisturbed samples. Double stars ------------ Photometry simulations and solutions for various separations of double stars are shown in Table 1. The values from Table 3 in CUO_42 are included for comparison. The brighter component (A) was always of I=20.0 mag. A fainter component (B) at a distance from 300 to 50 mas and with I_B=21.0, 22.0, 23.0 mag was considered. For separations from 300 to 100 mas the standard errors hardly change with the separation: 0.027 mag for A and 0.07, 0.15, 0.42 mag for B, respectively. The systematic errors are generally small. For the smaller separations of 70 and 50 mas the standard errors are smaller than with method 1, and the systematic errors much smaller. For I_B=23.0, though, the photometry is inaccurate with a standard error about 0.6 mag. Photometric sky mapper ---------------------- The stars around an astrometric star may disturb the astrometry and photometry of that star. Knowing the positions and magnitudes of the disturbing stars it is possible either to correct an observation (patch) for the disturbance or to reject the observation in case of large disturbances. This is being done in the Tycho2 reduction (see Annex to CUO_42, Section 2.3, parasite subtraction). It is proposed to use the last astrometric CCD before the BBP not only for astrometry but also as a photometric sky mapper (PSM), without colour filter. A provisional description of the application is this. A patch with about 30 samples of 2*14 pixels/sample is collected and transmitted. This patch thus has an area of 2220*1554 mas^2 so that about 3.0 sq.arcsec will be well covered. It can be shown that stars of I=23.0 would be detected with a SNR=5 by only 25 transits, and on average any star in fact obtain 130 transits. The transmission of these 30 samples/star replaces the transmission of 80 samples/star of two-dimensional patch from the ASM2, as proposed in CUO_36. Use of the PSM would result in a mapping in white light of all stars brighter than about I=23.0 (G=23.5, V=23.7 for G2V) in the area. The possibly nebulous surrounding of the main object would be mapped which is especially important for centres of galaxies and quasars. A high star density as e.g. of the bulge globular cluster NGC 6528 in Baade's window can be coped with by the PSM. It contains according to Xavier et al. (SWG_002 p.6) about 3.6 million stars/sq.deg with G<20.0 (~I<19.5) and 26 million stars/sq.deg with G<24.0 (~I<23.5). The latter number is 2 stars/sq.arcsec which will be quite well resolved and detected in the PSM. The necessary condition for a good resolution is that most of the samples receive a significant amount of light from only one star. This is still the case for the measurement of the globular cluster by any of the Astro instruments (cf. the Annex). ANNEX: .ps of a figure: GAIA sky mappers and photometers ------------------------------------------------------------------ Table 1. Double stars. Precision of BBP photometry and astrometry from Sloan i'. Astrometry and photometry give mean values for 150 stars. Standard errors (sg_ ) are for one star with 100 superposed observations. If the table shows sg_x=sg_y > 0.0 the values from method 1 in CUO_42 are given for the sake of easy comparison, i.e. a maximum cross-correlation method was used to find the double star components. Otherwise method 2 was used, i.e. cross correlation at the given positions for the two components. Photometry Astrometry---------- Note Comp i'_true i'_obs sg_m x y sg_x sg_y mag mag mag mas mas mas mas sep 300 mas, PA=90: A 20.0 19.997 0.029 0.0 0.0 0.0 0.0 B 21.0 21.002 0.055 300.0 0.0 0.0 0.0 A 20.0 19.994 0.026 0.0 0.0 0.0 0.0 B 22.0 22.011 0.135 300.0 0.0 0.0 0.0 A 20.0 19.997 0.027 0.0 0.0 0.0 0.0 B 23.0 23.022 0.326 300.0 0.0 0.0 0.0 sep 180 mas, PA=90: A 20.0 19.997 0.027 0.2 0.2 1.9 2.1 B 21.0 21.006 0.065 181.5 -0.2 3.8 3.7 A 20.0 19.998 0.024 -0.1 -0.3 2.3 2.1 B 22.0 21.995 0.146 181.8 -0.5 9.9 12.0 A 20.0 20.006 0.033 -0.0 0.1 2.1 2.1 B 23.0 22.879 0.339 150.7 2.5 69.6 83.3 Outlier in x A 20.0 19.997 0.026 0.0 0.0 0.0 0.0 B 21.0 20.994 0.056 180.0 0.0 0.0 0.0 A 20.0 19.993 0.027 0.0 0.0 0.0 0.0 B 22.0 22.018 0.142 180.0 0.0 0.0 0.0 A 20.0 19.998 0.026 0.0 0.0 0.0 0.0 B 23.0 23.023 0.390 180.0 0.0 0.0 0.0 sep 100 mas, PA=90: A 20.0 19.998 0.037 0.5 0.2 2.6 2.2 B 21.0 20.994 0.086 100.5 -0.2 5.7 4.4 A 20.0 19.997 0.031 0.2 -0.2 2.3 1.8 B 22.0 21.986 0.187 101.1 0.4 12.2 11.4 A 20.0 20.003 0.033 0.1 -0.1 2.2 2.0 B 23.0 22.835 0.389 100.7 -0.7 42.7 41.5 A 20.0 19.997 0.027 0.0 0.0 0.0 0.0 B 21.0 20.999 0.065 100.0 0.0 0.0 0.0 A 20.0 19.996 0.026 0.0 0.0 0.0 0.0 B 22.0 22.007 0.155 100.0 0.0 0.0 0.0 A 20.0 19.992 0.027 0.0 0.0 0.0 0.0 B 23.0 23.074 0.431 100.0 0.0 0.0 0.0 sep 70 mas, PA=90: A 20.0 19.924 0.047 4.0 -0.2 3.6 2.5 B 21.0 21.197 0.177 79.3 -0.1 6.2 6.0 A 20.0 19.979 0.044 1.8 0.1 3.2 2.5 B 22.0 22.185 0.356 78.4 0.3 18.9 18.0 A 20.0 20.003 0.045 0.7 -0.2 2.8 2.3 B 23.0 22.818 0.449 76.7 4.4 55.0 67.5 A 20.0 19.998 0.033 0.0 0.0 0.0 0.0 B 21.0 21.002 0.081 70.0 0.0 0.0 0.0 A 20.0 19.996 0.035 0.0 0.0 0.0 0.0 B 22.0 21.993 0.198 70.0 0.0 0.0 0.0 A 20.0 19.998 0.031 0.0 0.0 0.0 0.0 B 23.0 23.137 0.574 70.0 0.0 0.0 0.0 sep 70 mas, PA=45: A 20.0 19.920 0.047 3.1 2.9 3.6 3.1 B 21.0 21.239 0.230 57.3 58.1 14.7 20.6 A 20.0 19.972 0.045 1.5 1.5 2.9 2.8 B 22.0 22.171 0.329 60.2 54.6 33.0 31.0 A 20.0 20.007 0.044 0.5 1.0 2.5 2.4 B 23.0 22.887 0.546 55.4 38.8 75.4 68.8 A 20.0 19.996 0.029 0.0 0.0 0.0 0.0 B 21.0 20.998 0.075 49.5 49.5 0.0 0.0 A 20.0 19.999 0.032 0.0 0.0 0.0 0.0 B 22.0 21.994 0.188 49.5 49.5 0.0 0.0 A 20.0 20.002 0.030 0.0 0.0 0.0 0.0 B 23.0 23.022 0.470 49.5 49.5 0.0 0.0 149 stars sep 50 mas, PA=90: A 20.0 19.808 0.052 7.4 -0.2 3.4 2.1 B 21.0 21.798 0.373 72.7 1.0 16.5 22.7 A 20.0 19.929 0.042 3.2 0.2 3.3 2.5 B 22.0 22.579 0.518 66.7 -6.8 52.6 46.9 A 20.0 19.995 0.041 1.4 0.2 2.4 2.6 B 23.0 22.956 0.507 53.9 -2.2 64.3 63.8 A 20.0 19.985 0.035 0.0 0.0 0.0 0.0 B 21.0 21.019 0.087 50.0 0.0 0.0 0.0 A 20.0 19.992 0.041 0.0 0.0 0.0 0.0 B 22.0 22.049 0.261 50.0 0.0 0.0 0.0 A 20.0 19.993 0.036 0.0 0.0 0.0 0.0 B 23.0 23.205 0.738 50.0 0.0 0.0 0.0 143 stars ---------------------------------------------------------------======