3 Evaluation of the accuracy of the method

About 100 galaxies were measured twice using the procedure described in the previous section. The internal accuracy is high, the deviation never exceeding three arcsec in one coordinate. The accuracy is not limited by the polynomial plate solution which gives an uncertainty of a few arcseconds but by the visual estimation of the galaxy center.

In order to quantify this uncertainty, we extracted a list of 1522 galaxies, with accurate coordinates in LEDA and apparent diameter in the range [1.6' - 1.8']. This relatively large mean diameter will give an upper value of the standard deviation because the center is more difficult to determine for large galaxies. Besides, it guarantees a better identification because there is generally only one galaxy of that size in a $5' \times 5'$ field. Even if there are two objects, our selected object should be close to the center of the frame owing to the fact that it already has accurate coordinates.

   

Table 1: Beginning of the control table. For each galaxy the new J2000.0 coordinates are given first. The second coordinates are those extracted from LEDA and known to be accurate. The full table is available in electronic form

PGC	Name		RA - DEC (2000)	RA - DEC (2000)
			This paper	LEDA
PGC 0000038	UGC	12893	000028.2+171309	000028.0+171310
PGC 0000186	UGC	3	000246.4+185310	000246.4+185311
PGC 0000205	UGC	5	000305.7-015450	000305.7-015447
PGC 0000263	NGC	7816	000348.9+072847	000349.0+072845
PGC 0000286	UGC	20	000414.5+801721	000413.7+801705
PGC 0000305	UGC	27	000429.2+055046	000429.5+055035
PGC 0000364	IC	1529	000513.3-113009	000513.2-113012
PGC 0000382	ESO	193-19	000528.8-501612	000529.0-501612
PGC 0000485	NGC	7832	000628.5-034258	000628.4-034257
PGC 0000499	UGC	48	000637.0+475242	000636.9+475243
PGC 0000564	NGC	1	000715.9+274230	000715.9+274232
PGC 0000645	NGC	12	000844.8+043645	000844.8+043647
PGC 0000654	UGC	79	000904.4+253708	000904.3+253708
PGC 0000679	NGC	20	000932.7+331831	000932.8+331835
PGC 0000690	NGC	22	000948.3+274956	000947.5+274948
PGC 0000800	ESO	293-45	001124.6-412353	001124.1-412349
PGC 0000875	NGC	43	001300.9+305455	001300.9+305457
PGC 0000926	ESO	50-6	001358.9-700122	001359.4-700119
PGC 0000929	NGC	48	001402.2+481405	001402.1+481407
PGC 0000982	NGC	53	001443.1-601941	001441.8-601943
...

In Table 1 we present this control sample of 1522 galaxies. All the coordinates are given for the equinox 2000 in hours minutes, seconds and tenths for the Right ascension and degrees, arcmin and arcsec for the Declination. This notation (HHMMSS.T $\pm$ DDMMSS) will be adopted throughout this paper. For each galaxy the following data are given:
Column 1: PGC number according to LEDA.
Column 2: Alternate name according to LEDA (Paturel et al. 1989).
Column 3: 2000-RA and DEC. from the present paper.
Column 4: Previous 2000-RA and DEC. from LEDA.

The full sample is available in electronic form at the CDS.

Figures 1 and 2 present the histograms of the differences between our measurements and those available in LEDA. The following results are obtained:

$$\Delta \alpha \cos \delta = 0.3'' \pm 0.2 \ \ \ \sigma =7.2'' \ \ \ \ (n=1522)$$ (1)

$$\Delta \delta = -0.2'' \pm 0.1 \ \ \ \sigma =5.2'' \ \ \ \ (n=1522).$$ (2)

Figure 1: Histogram of deviations between RA from LEDA and the present measurements

Figure 2: Histogram of deviations between DEC from LEDA and the present measurements

There is no significant systematic deviation. The final accuracy on the position is defined from the square root of the quadratic sum of RA- and DEC-standard deviations, i.e., about 8.9 arcsec. Figure 3 illustrates the distribution of relative deviations. This shows that coordinates in LEDA, classified to be more accurate than 10 arcsec are probably better than this limit. Assuming that they have the same precision as our own measurements gives a standard deviation of 6 arcsec ( $8.9/ \sqrt{2}$) for both LEDA and the present measurements, i.e., less than 5 arcsec in each direction (RA and DEC). In any case our method gives coordinates which can be classified as accurate according to LEDA's criterion.

Figure 3: Distribution of deviations in both RA and DEC by comparing accurate coordinates from LEDA and from the present measurements. Note that the horizontal strips are due to the discretization of values with a 1 arcsec step. This does not appear on x-axis because of the $\cos \delta$ function