3 The results

   
3.1 Colour-magnitude diagram

The CM diagrams of regions C, E and F (see Fig. 1b) are shown in Fig. 3, where stars from region C are shown as open circles, stars from region E as filled diamonds and stars from the region F as dots.

Figure 3: Colour-Magnitude diagram for 337 stars in NGC 6789. The circles correspond to stars measured in the central region (C), the filled diamonds indicate stars in the periphery (E) and dots stars outside the galaxy (F)

The [(V-I), I] CM diagram of the NGC 6789 shows characteristics typical of the CM diagrams of other dwarf galaxies, with evidence for both old and young populations. The main feature of the stars in the periphery of NGC 6789 CM diagram is the concentration that extends between and , which corresponds to RGB and asymptotic giant branch (AGB) old and intermediate-age stars. There is also a considerable population of blue stars ( ) in the CM diagram of the central region. It is remarkable that these blue stars are entirely absent in the outer part of the galaxy. The presence of these stars in the central region, as well as the candidate H II regions in H$\alpha$ image, shows that NGC 6789 is a BCD galaxy rather than a dE. Most of the bright stars ( 20 $\hbox{$.\!\!^{\rm m}$ }$5) are likely foreground stars. According to our spectral long slit observations the brightest foreground star near the center of the galaxy is an F star.

The diagram shown in Fig. 3 has not been corrected for interstellar extinction. The galactic coordinates of NGC 6789 are $l_{{\rm II}}~=~94\hbox{$.\!\!^\circ$ }97, b_{{\rm II}}~=~21\hbox{$.\!\!^\circ$ }52$, and it lies in a region of moderate gradient with $E(B-V)~=~0\hbox{$.\!\!^{\rm m}$ }076$in the extinction maps of Burstein & Heiles ([1984]). Using the extinction law of Cardelli et al. ([1989]) with R_V = 3.3, the extinction is: $A_B~=~0\hbox{$.\!\!^{\rm m}$ }32$, $A_V~=~0\hbox{$.\!\!^{\rm m}$ }24$, $A_R~=~0\hbox{$.\!\!^{\rm m}$ }21$ and $A_I~=~0\hbox{$.\!\!^{\rm m}$ }15$.

   
3.2 Metallicity

The average stellar metallicity can be obtained from the index $(V-I)_{\rm -3.5}$, which is the colour index of the RGB half a magnitude below the tip of the RGB (TRGB) (see Da Costa & Armandroff [1990]; Lee et al. [1993]). We believe that the TRGB is at $I_{\rm TRGB}=22\hbox{$.\!\!^{\rm m}$ }7$ (see next section). The median colour between $I=23\hbox{$.\!\!^{\rm m}$ }4$ and $I=24\hbox{$.\!\!^{\rm m}$ }0$, that we take as $(V-I)_{\rm -3.5}$, is $1\hbox{$.\!\!^{\rm m}$ }7\pm0\hbox{$.\!\!^{\rm m}$ }2$.

The corresponding dereddened value is $(V-I)_{\rm -3.5,0}=1\hbox{$.\!\!^{\rm m}$ }6~\pm~0.2$. Using the calibration by Lee et al. ([1993]), we obtain a metallicity [Fe/H] $\simeq-1$ dex, and an internal abundance spread with total range of -0.8 dex is suggested by the intrinsic colour width of the RGB.

   
3.3 Distance

The absolute I magnitude of the TRGB gives a good estimate of distance (Lee et al. [1993]). It is slightly dependent on the metallicity. To obtain the magnitude of the TRGB we have used the luminosity function (LF) of the stars in the colour interval $1\hbox{$.\!\!^{\rm m}$ }0<(V-I)\leq 3\hbox{$.\!\!^{\rm m}$ }0$ for the external ring part of the galaxy (region E). 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 $I_{\rm TRGB}=22\hbox{$.\!\!^{\rm m}$ }7$. The resulting dereddened value is $I_{\rm TRGB,0}=22\hbox{$.\!\!^{\rm m}$ }55$.

The colour of the TRGB is necessary to calculate the bolometric correction to be used in the $I_{\rm TRGB}$-distance calibration. It is taken as the median colour index of the stars with $22\hbox{$.\!\!^{\rm m}$ }7 \le I \leq 22\hbox{$.\!\!^{\rm m}$ }9$. We find $(V-I)_{\rm TRGB}=1\hbox{$.\!\!^{\rm m}$ }84$ which when corrected for external extinction yields $(V-I)_{\rm TRGB,0}=1\hbox{$.\!\!^{\rm m}$ }75$. Using the calibration by Lee et al. (1993b), we obtain $M_{I,{\rm TRGB}}=-4\hbox{$.\!\!^{\rm m}$ }10$.

We then derive a distance modulus $(m-M)_0=26\hbox{$.\!\!^{\rm m}$ }65$, corresponding to 2.1 Mpc. The intrinsic error of the method is about $\pm 0\hbox{$.\!\!^{\rm m}$ }1$(see Lee et al. [1993]). Our estimate of the stellar photometry errors is $\pm~0\hbox{$.\!\!^{\rm m}$ }2$ due to severe crowding and high surface brightness in this galaxy. We adopt a total error of $0\hbox{$.\!\!^{\rm m}$ }3$.

To see how near is NGC 6789 to the Local Group we construct a $V_{\rm helio}$ versus $\cos\Theta$ diagram (Fig. 4) for nearby galaxies closer than 2.5 Mpc, following the work of van den Bergh ([1994]) on the basis the data tabulated by Lee ([1995]), Karachentsev & Makarov ([1996]) and our own compilation. $\Theta$ is the angle between the center of the galaxy and the solar apex. We adopt a solar motion with respect to the Local Group members of 316 km s^-1 toward the solar apex ( $l_{\hbox{$\odot$ }}=93\hbox{$^\circ$ }, b_{\hbox{$\odot$ }}=-4\hbox{$^\circ$ }$) given by Karachentsev & Makarov ([1996]). The crosses represent the satellites of the Milky Way Galaxy, the solid diamonds represent the satellites of M 31, the solid triangles are for members of the Sculptor group, and the open triangles are for members of the IC 342/Maffei complex. The open circles are galaxies not members of these subgroups. The envelope of the Local Group is represented by the dashed lines at $\pm 60$ km s^-1 from the central line with $V_{\hbox{$\odot$ }}\!=\!-316\,{\rm cos} \Theta$ km s^-1.

We see that the NGC 6789 is probably not far from the Local Group. Note that NGC 6789 is a very isolated galaxy situated inside the Local Void described by Tully ([1988]).

Figure 4: Heliocentric velocity versus $\cos\Theta$ for nearby galaxies closer than 2.5 Mpc. $\Theta$ is the angle between the center of the galaxy and the solar apex. The crosses represent the satellites of the Milky Way Galaxy, the solid diamonds represent the satellites of M 31, the solid triangles are for members of the Sculptor group, and the open triangles are for members ofthe IC 342/Maffei complex. The open circles are for galaxies not members of these subgroups. The Local Group is defined as within the dashed lines at $\pm 60$ km s-1 from the central line with $V_{\hbox{$\odot$ }}\!=\!-316\,{\rm cos} \Theta$. The star represents the location of the NGC 6789

   
3.4 Integrated light

Figure 5: Results of surface photometry of NGC 6789. a) Equivalent V surface brightness distribution. It can be fitted by an exponential law for the disk, and by a Gaussian law for the central region. The result of the fit is shown by the solid line. b) Surface colour (V-I) profile

Besides the stellar photometry we have performed the V, I and H$\alpha$surface photometry of the galaxy. We determined the surface brightness profiles in two steps. First, we calculated azimuthally averaged equivalent brightness profiles using the surface photometry routines developed at the Potsdam Astrophysical Institute. In this way we reduce the surface photometry to a one-dimensional profile. In addition to the differential radial surface brightness profiles we calculated the growth curve of the galaxy. The total magnitudes were estimated by asymptotic extrapolation of this growth curve.

In order to obtain some information about the two-dimensional structure in a second round of calculations we used an ellipse fitting algorithm, which is based on the formulas given in Bender & Mölenhoff ([1987]) in its realization in the SURPHOT package running within MIDAS.

The resulting equivalent surface brightness distribution is shown in Fig. 5a. In both the V and I bands, the surface brightness distribution falls off as Gaussian from $\sim\!5{\hbox{$^{\prime\prime}$ }}$ to a radius of $\sim\!20{\hbox{$^{\prime\prime}$ }}$, and fairly flat from $\sim\!20{\hbox{$^{\prime\prime}$ }}$. The equivalent V band surface brightness can be well fitted by a Gaussian with a central surface brightness $\mu_0(V)=21.7~{\rm mag/\ifmmode\hbox{\rlap{$\sqcap$ }$\sqcup$ }\else{\unskip\no... ... } \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi\hbox{$^{\prime\prime}$ }}$ and a standard deviation $\sigma_V=15.9\hbox{$^{\prime\prime}$ }$ in the inner regions, and exponential profile with central surface brightness $\mu_0(V)=21.8~{\rm mag/\ifmmode\hbox{\rlap{$\sqcap$ }$\sqcup$ }\else{\unskip\no... ... } \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi\hbox{$^{\prime\prime}$ }}$ and exponential scale length $\alpha=16.2{\hbox{$^{\prime\prime}$ }}$ at larger radii. This gives an angular diameter at the $\mu_V=26~{\rm mag/\ifmmode\hbox{\rlap{$\sqcap$ }$\sqcup$ }\else{\unskip\nobreak... ... } \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi\hbox{$^{\prime\prime}$ }}$isophote of $\theta_{26}=2.1{\hbox{$^\prime$ }}$; this corresponds to an isophote of $\mu_I=25.0~{\rm mag/\ifmmode\hbox{\rlap{$\sqcap$ }$\sqcup$ }\else{\unskip\nobre... ... } \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi\hbox{$^{\prime\prime}$ }}$. Given the distance of the galaxy, the break in the surface brightness profile occurs at $r_{\rm equiv}\approx~600$ pc.

Integrating the surface brightness profiles within the V and Ibands out to the $\mu_V=25~{\rm mag/\ifmmode\hbox{\rlap{$\sqcap$ }$\sqcup$ }\else{\unskip\nobreak... ... } \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi\hbox{$^{\prime\prime}$ }}$ isophote, we find $m_I\!=\!13\hbox{$.\!\!^{\rm m}$ }63~\pm~0\hbox{$.\!\!^{\rm m}$ }15$, and $m_V\!=\!14\hbox{$.\!\!^{\rm m}$ }62~\pm~0\hbox{$.\!\!^{\rm m}$ }15$, not corrected for internal or galactic extinction. The quoted errors are an upper limit computed assuming that every point in Fig. 3 is systematically off by 1 $\sigma$. After correction for extinction (see Sect. 3.1) and considering the error in the distance modulus, the total absolute magnitude of NGC 6789 is $M_{I,0}=-13\hbox{$.\!\!^{\rm m}$ }26\pm0\hbox{$.\!\!^{\rm m}$ }35$ and $M_{V,0}=-12\hbox{$.\!\!^{\rm m}$ }36\pm0\hbox{$.\!\!^{\rm m}$ }35$. The integrated colour index (V-I)₀ increases smoothly from $0\hbox{$.\!\!^{\rm m}$ }67$in the center of NGC 6789 up to $0\hbox{$.\!\!^{\rm m}$ }90$ within the largest visible radii (Fig. 5b). This is comparable to the colours of Scd & Im galaxies ( $(V-I)\!=\!0\hbox{$.\!\!^{\rm m}$ }82$) for the Coleman et al. ([1980]) composite spectral energy distributions.

We also estimated a total H$\alpha$ flux of NGC 6789, $F_{{\rm H}{\alpha}} \simeq 1.36~10^{-12}$ erg/(cm² s), after correction for galactic extinction. Since H$\alpha$-light comes from the gas excited by young hot stars, one can estimate a star formation rate on the basis of this line flux. Equation (1) is taken from the Hunter ([1984]):

$$SFR = 1.27 \ 10^9 \cdot F_{{\rm H}_{\alpha}} \cdot D^2 .$$ (1)

Here: SFR in ${\cal M}_{\hbox{$\odot$ }}/{\rm year}$ units, $F_{{\rm H}_{\alpha}}$ is the H$_{\alpha}$ flux corrected for interstellar extinction, in erg/(cm² s) units, D is the distance in the Mpc. Using our distance estimation we receive the full star formation rate in NGC 6789, $SFR \simeq 7.6~10^{-3} {\cal M}_{\hbox{$\odot$ }}/{\rm year}$, that is $\sim 3~10^{-8} {\cal M}_{\hbox{$\odot$ }}/{\rm year\, pc^2}$ on the part of area.

From the H$\alpha$ luminosity it is possible to evaluate a number of young stars, whose light ionizes hydrogen in a galaxy. The number of Layman continuum quants (Ly-c), radiated by galaxy stars in one second is

$${\cal N}_{\rm Ly-c} = 7.43~10^{11} \, L_{{\rm H}{\alpha}}.$$ (2)

The galaxy luminosity in H$\alpha$, $L_{{\rm H}{\alpha}}$, is calculated from the flux and galaxy distance. This equation is taken from the work of Mass-Hess & Kunth ([1991]). Taking into account that one O7 V type star emits $\sim10^{49}$ Ly-c quants per second we obtain an approximate number of such stars in NGC 6789, ${\cal N}_{\rm Ly-c} \simeq 50$. We have successfully resolved about twenty brightest blue stars in the central part of this galaxy. The most part of these stars hides in the compact star formation regions.