3.3. Distance.

The absolute I magnitude of the tip of the RGB (TRGB) has proven to be a remarkably good estimate of distance (Lee et al. 1993). The absolute magnitude of the TRGB is slightly dependent on the metallicity, which we have estimated above in §3.2. To obtain the magnitude of the TRGB we have used the luminosity function (LF) of the stars in the colour interval 1.0<(V-I)<3.0 drawn from the external ring part of the galaxy (region E) (the colour interval 1.0<(V-I)<2.0 gives the same value). We have computed the LF by counting the stars lying inside an interval of ±0.2 magnitudes around the central value of I. The central value has been varied in steps of 0.02 magnitudes to obtain the LF while reducing the dependence of the results upon the particular choice of bin center. Finally, an edge detecting Sobel filter [-1,0,+1] (Sakai et al. 1996) has been applied to the LF. This produces a sharp peak at the TRGB corresponding to I_TRGB=22.70. The resulting dereddened value is I_TRGB,0=22.55.

The colour index of the TRGB is necessary to calculate the bolometric correction to be used in the I_TRGB-distance calibration. It has been estimated from the median colour index of the stars with 22.73.2, for two colour intervals 1.2<(V-I)<2.4 and 1.2<(V-I)<1.9. We find (V-I)_TRGB=1.84 and (V-I)_TRGB=1.56 which when corrected for external extinction yields (V-I)_TRGB,0=1.75 and (V-I)_TRGB,0=1.47. Using the calibration by Lee et al. (1993b), we obtain a very close value of M_I,TRGB=-4.10±0.01.

So we have obtained a distance modulus (m-M)₀=26.65, corresponding to 2.1 Mpc. The intrinsic error of the method is about ±0.1 (see Lee et al. 1993). Our estimate of the stellar photometry errors is ±0.2 due to severe crowding and high surface brightness in this galaxy. This is the adopted error since it is larger than the method and extinction ones.

For examination the nearness of NGC 6789 to the Local Group we construct the V_Sun versus cos diagram (fig. 4) for nearby galaxies closer than 2.5 Mpc, follow the work of van den Bergh (1994) on the basis the data tabulated by Lee (1995), Karachentsev & Makarov (1996) and our compilation available data¹. presents an angle subtended between the center of the galaxy and the solar apex. We adopt the solar motion with respect to the Local Group members of 316 km/s toward the solar apex (l_Sun=93°, b_Sun=-4°) given by Karachentsev & Makarov (1996). The crosses represent the satellite galaxies of the Milky Way Galaxy, the solid diamonds represent the satellite galaxies of M31, the solid triangles are members of the Sculptor group, and the open triangles are members of the IC342/Maffei complex. The open circles galaxies which are not members of these subgroups. Envelopes of the Local Group are represented by the dashed lines at ±60 km/s from the center line with .

Considering both the distance and velocity of the NGC 6789 with respect to the center of the Local Group, we conclude that the NGC 6789 is probably not far from the envelope of the Local Group. Note that NGC 6789 is a very isolated galaxy situated inside the Local Void described by Tully (1988).