3 Astrometry

The absolute astrometry presented here is based on comparison with the Guide Star Catalogue II (GSC-II) and has an average error of approximately $0\hbox{$.\!\!^{\prime\prime}$ }2$ per axis.

 

 

Table 1: GRB RA and Dec and the best fit pixel localisation (incl. 1-$\sigma$ errors) of the OA in the drizzled CL images. For each OA, the host candidate and three reference objects are given including their pixel positions and host offset from OA location

Target	RA	Dec	X		Y		$\alpha_{\rm off}$		$\delta_{\rm off}$
980329	07:02:38.02	+38:50:44.3	999.36	$\pm 1.34$	1032.33	$\pm 1.22$	0.0		0.0
host	07:02:38.07	+38:50:44.3	995.55	$\pm 0.05$	1027.35	$\pm 0.04$	0.097	$\pm 0.034$	-0.127	$\pm 0.031$
ref. 1	07:02:38.15	+38:51:03.7	941.32		1800.06
ref. 2	07:02:37.43	+38:50:34.2	1274.41		635.89
ref. 3	07:02:38.97	+38:50:33.2	564.13		598.21
980519	23:22:21.54	+77:15:43.2	1039.19	$\pm 0.68$	990.77	$\pm 0.71$	0.0		0.0
host	23:22:21.34	+77:15:43.7	1045.27	$\pm 0.07$	975.98	$\pm 0.01$	-0.154	$\pm 0.017$	-0.376	$\pm 0.018$
ref. 1	23:22:17.78	+77:15:51.3	416.04		1128.28
ref. 2	23:22:20.25	+77:15:23.8	1410.45		1673.18
ref. 3	23:22:27.36	+77:15:43.7	1514.40		462.34
990308	12:23:11.49	+06:44:04.7	813.46	$\pm 2.79$	922.50	$\pm 2.03$	0.0		0.0
OA/host1	12:23:11.49	+06:44:04.7	811.70	$\pm 0.05$	921.80	$\pm 0.07$	0.045	$\pm 0.071$	-0.018	$\pm 0.052$
host2	12:23:11.49	+06:44:04.7	815.55	$\pm 0.05$	910.90	$\pm 0.22$	-0.053	$\pm 0.071$	-0.295	$\pm 0.052$
ref. 1	12:23:10.06	+06:43:50.0	1651.27		341.10
ref. 2	12:23:12.30	+06:44:24.3	340.29		1698.05
ref. 3	12:23:10.95	+06:44:20.8	1131.42		1558.46

The procedure used for relative astrometry from ground-based images of the afterglow to the STIS data depends on the available ground-based data, but for all three objects least squares affine transformations were used. An affine transformation is the simplest possible transformation which allows for deviations from square pixels in reference and target images. It is known that some of our ground-based reference data were obtained with CCDs which have slightly non-square pixels. As we were not able to establish any clear correlation between position and astrometric residuals, it is justified to keep all transformations strictly linear, as is also preferred with a limited number of tie objects. The accuracy by which the position of a (point) source in a well sampled image can be determined is dependent on the signal-to-noise ratio (S/N) with which the source is detected, and the full width at half maximum (FWHM) of the point spread function (PSF). For low S/N the astrometric standard error per axis can be approximated with $\sigma_{\rm pos} = \sigma_{\rm PSF} / (S/N)$, where $\sigma_{\rm PSF}$ is the standard deviation of the Gaussian approximating the PSF, which formally equals FWHM/2.35. For high S/N, accuracy is limited by errors in the detector pixel geometry, usually at the level of 1/20 of a pixel or less. The level of accuracy is hence determined by how well the pixel borders are defined, which relies solely on the detector fabrication technology used. For a source detected with a S/N of 20 in $1\hbox{$^{\prime\prime}$ }$ seeing, the expected 1-$\sigma$ accuracy is $0\hbox{$.\!\!^{\prime\prime}$ }02$ per axis. If the S/N is significantly above 20 or the FWHM is sampled by less than about 3 pixels, this approximation of the astrometric error is not valid. Whenever several individual images of the afterglow is available, a transformation to the STIS reference frame is established for each image. As the error in the transformed afterglow position in the STIS image is always completely dominated by the astrometric error in the ground-based image, the errors of individually transformed afterglow positions are in practice independent. The standard deviation of the transformed positions is therefore an estimate of the actual astrometric error. To illustrate the estimation of the astrometric error, the individual transformed coordinates and the associated error budget is given in the case of GRB 990308 (Sect. 6).