8 Comparison with LEDA galaxies

8.1 Equatorial coordinates

The coordinates are compared with coordinates given in LEDA. Only coordinates known as "accurate" in LEDA (i.e. with a standard deviation less than 10 arcsec) are used. The plot of $\Delta \delta$ and $\Delta \alpha$. $\cos \delta$ in Fig. 13 shows that there is no systematic distorsion ($\Delta$ means (DENIS)-(LEDA)). The standard deviation is 6.5 arcsec and 6.7 arcsec for $\alpha.$ $\cos \delta$ and $\delta$, respectively. Assuming an error of the same amplitude in LEDA and DENIS coordinates gives an uncertainty of $6.6/\sqrt{2}$ arcsec for DENIS right ascension and declination, i.e. an uncertainty of 6.6 arcsec for the position of a galaxy.

In fact, the plot of $\Delta \alpha \cos \delta$ vs. $\Delta \delta$exhibited two abnormal zones with a systematic shift of about 30 or 40 arcsec. This problem appeared near the zenith. Thus, only objects with coordinates based on the GSC stars are kept in the present version. In the final catalog, the coordinates will be obtained through a full astrometric solution (mosaicing frames along each strip and with adjacent ones) and this problem will be solved without rejecting galaxies.

  

Figure 13: Comparison of coordinates from LEDA and DENIS.

8.2 Position angle

Position angle is important for studies on the orientation of galaxies, but also for identification. However, for nearly face on galaxies, it becomes very uncertain. The comparison is made only for galaxies with $\log R$(DENIS) > 0.5. The result is given in (Fig. 14). The direct regression gives:

$$\beta ({\rm LEDA}) = 1.009 \pm 0.003 \beta ({\rm DENIS}) +0.07 \pm 0.26$$ (11)

with $\sigma=2.65$, $\rho=0.9987 \pm 0.0001$, n=408 after 21 rejections at $3\sigma$.Among the 21 rejections, only 2 correspond to real discrepancies.

The uncertainty on the measurement of $\beta$ is 2.7 deg. This excellent agreement of position angles validates the reliability of our cross-identification.

  

Figure 14: Comparison of position angles from LEDA and DENIS

8.3 Photometric morphological type code

It is interesting to obtain at least a very crude estimate of the morphological type code. This is particularly important when we plan to start a HI follow-up for which it is compulsory to avoid elliptical galaxies. The log of the standard deviation of pixel intensities is significantly correlated with the morphological type code extracted from LEDA. The relation is almost linear. However, it appears that the solution depends on the size of the galaxy (all very small objects appear identical). The slope and the intercept are found linearly correlated with the log of the number of pixels. In the scale between -5 and 10 defined in the Second Reference Catalog of Bright Galaxies, the photometric morphological type code is calculated as:

$$T({\rm DENIS}) = A \,\log(\sigma(f_{ij})) + B.$$ (12)

Where $\sigma(f_{ij})$ is the standard deviation of flux of all pixels of the matrix representing the galaxy:

$$\sigma(f_{ij}))=\sqrt{\frac{\sum_{i,j} (f_{ij} - \bar{f})^2}{(n-1)}}$$ (13)

with

$$A= \frac{1}{-0.0187 \,\log n -0.0183}$$ (14)

$$B= \frac{1}{ 0.2774 \,\log n +1.7846}$$ (15)

where n is the number of pixels.

The comparison of codes T(DENIS) and T(LEDA) is given in Fig. 15. The correlation is clearly significant (the correlation coefficient is $\rho = 0.69\pm0.01$) but the standard deviation is large ($\sigma(T$(DENIS)) =2.5). This allows us to classify galaxies into "Early", "Intermediate" and "Late" types, with no finer subdivision. In the catalog, photometric morphological type smaller than -5 or greater than 10 will be set to -5 or 10, respectively.

  

Figure 15: Comparison of morphological type codes from LEDA and from the I-band photometry