4 General morphology of the IC1613

4.1 Color-magnitude diagrams

Figures 5 and 6 show the (U-B,V) and (B-V,V) CM diagrams obtained for IC1613. To construct the (U-B,V) color-magnitude diagram we selected only the stars with photometric errors not larger than 0.15 in all filters while in the second (B-V,V) diagram are plotted all stars measured in our field.

  

Figure 5: $(U-B,\ V)$ color - magnitude diagram obtained for IC1613. Only stars with photometric errors larger than 0.15 in all filters are plotted

  

Figure 6: $(B-V,\ V)$ color - magnitude diagram for IC1613

As pointed out by Freedman (1988a), "A first glance at both color - magnitude representations reveals immediately the presence of a bright, young, blue population, an intermediate-color population, and a red population composed of both bright, young supergiants and a fainter red giant population".

All previous photometric works on IC1613 - Baade (1963), Sandage (1971) and Freedman (1988a) pointed out the presence of young, intermediate and old age population using only the general morphology of the color-magnitude diagrams in different filters. In this work we present a detailed investigation of the young stellar content based on the comparison with theoretical isochrones and H-R diagrams.

4.2 Differential reddening

Our first step in the morphology analysis of IC1613 was to determine the differential (internal and foreground) reddening across the galaxy. Sandage (1971) obtained E(B-V) < 0.03 from 7 photoelectrically measured stars. Freedman (1988a) determined E(B-V)=0.04. The latest E(B-V) value for IC1613 derived from spectral measurements is 0.07 (Kingsburgh & Barlow 1995). Our field of investigation is centred on the H II regions of the galaxy and we do not exclude the presence of a higher internal reddening in this area. We used Johnson's Q-parameter technique to measure the reddening (Q=(U-B)-0.72(B-V) is a reddening-free quantity), calculating the Q values for all stars belonging to the main sequence (luminosity class V). These stars stand at V-magnitudes between 20.0 and 23 and at U-B colors between -1.2 and -0.5 (see Fig. 5). The E(B-V) for each star was calculated by means of the equations given in Massey et al. (1995a). We will assume that the "mean" value for E(B-V) in this area of IC1613 is the average of the above determined individual E(B-V) values. Our final value for E(B-V) is 0.06 with $\sigma=0.02$. We thus confirm the very low reddening of IC1613 estimated by Sandage (1971) and Freedman (1988a).

Figure 7 shows the $(B-V,\ U-B)$ "unshifted" color-color diagram of IC1613. This diagram contains only stars with photometric error less than 0.15. The fiducial locus of the stars of luminosity class V and that of luminosity class Iab (dashed line) were superimposed (Schmidt-Kaler 1982). The O-B9 stars closely follow the sequences of luminosity class V and Iab at U-B <0.2 and B-V < 0.2. There are some stars around (U-B) = 0 which follow the fiducial line of the V luminosity class and are probably foreground Galactic stars. The two stars located close to (B-V) = 2, (U-B) = 2 are the variable bright red supergiants V32 and V38 (Sandage 1971).

  

Figure 7: $(U-B,\ B-V)$ color-color diagram obtained for IC1613. Only stars with photometric errors less than 0.15 in all filters are plotted. The fiducial locus of stars of luminosity class V and of luminosity class Iab (dashed line) are superimposed

4.3 Comparisons with theoretical isochrones

Figure 8 shows the ((B-V)₀, M_V) color magnitude diagram with superimposed isochrones from Padua's library (see Bertelli et al. 1994). We chose for our comparison metallicity z = 0.004 which corresponds to the metallicity value measured for IC1613 by Kingsburgh & Barlow (1995). The adopted distance modulus is 24.20 (Freedman 1988a; Saha et al. 1992), while for the extinction we used E(B-V)=0.06 as has been determined by our analysis. The isochrones fit clearly shows the presence of stars in a wide variety of ages. The age of the blue stars is between 5 and 20 Myrs. Most of the yellow to red stars fainter than M_V = -4.0 are roundly matched by the post main-sequence part of the 60 Myrs to 250 Myrs isochrones. The last isochrone in Fig. 8 represents the Vanden Berg (1997) isochrones data set for Population II stars with z = 0.004 and an age of 10 Gyr. The presence of such old stars is not unusual and has been found in other Local dwarf galaxies. Gallart et al. (1996a-c) found in NGC6822 strong evidence for the presence of a considerable amount of old stars. The "most striking" features presented in their CMD are the so called "red-tangle" and "red-tail" - the crowded clumps in the lower red part of their (V-I,V) diagram. The same features are less visible in our CMD for two reasons: such red stars are more evident in red bands (I and R) and in this part of the CMD the completeness of our sample is relatively low (see Table 2).

  

Figure 8: ((V-B)0, MV) color-magnitude diagram for IC1613. The adopted distance modulus and extinction are (M-m) = 24.20 and E(B-V)=0.06. The isochrones from Padua's library with z = 0.004 are superimposed. Labels stand for the corresponding ages in Gyr. The last isochrone represents the 10 Gyr Population II stars (Vanden Berg 1997)

4.4 H-R diagram

To plot the stars on the theoretical H-R diagram we need to determine their effective temperatures ($T_{\rm eff}$) and bolometric corrections (BC). We followed closely the procedure of Massey et al. (1989, 1995a). We have no spectra for stars in this area of IC1613 and we used the transformation equations given in Table 7 of Massey et al. (1995a) to derive ${\rm Log}(T_{\rm eff})$ and BC. We have assumed the slope factor of the reddening law to be E(U-B)/E(B-V)=0.72 as it is for our Galaxy, NGC6822 and M33. Our attempt to determine the effective temperatures of stars, (B-V)₀ colors and bolometric correction with the improved numerical relation given in Flower (1996) yielded unrealistic Log$(T_{\rm eff})$ and $M_{\rm bol}$ for very blue stars (with (B-V)₀ < -0.2), so we preferred to use the calibration equations of Massey et al. (1995a) in the whole B-V interval. Figure 9 shows (Log$(T_{\rm eff}), M_{\rm bol}$)for stars with photometric errors less than 0.15 mag. The evolutionary mass tracks from Charbonnel et al. (1993) for z = 0.004 were superimposed on the same plot.

We have used the distance modulus as in the isochrone comparison. The individual stellar reddening was calculated using the Q-method for blue main sequence stars and blue supergaints. The mean E(B-V)=0.06 was adopted for all other stars. Equations of Massey et al. (1995a) require knowledge of star's luminosity class. While this is an unknown without spectroscopic classifications we used the calibration of the minimum M_V as a function of Q given in Parker & Garmany (1993) (see their Eq. (3)) to separate supergaints from dwarfs.

As can be seen in Fig. 9 most of the blue stars are located quite close to the ZAMS, including the stars of 60 - 85 $M_\odot$. The stars with masses lower than (5 $M_\odot$) systematically deviate to lower effective temperatures than those on the ZAMS. We have a large incompleteness in the U filter for stars with $M_{\rm bol} < -3.0$, so we consider that this is a systematic deviation resulting from a combination of incompleteness and uncertain Q-parameter. Some stars in the H-R diagram fall far to the left of the ZAMS. A careful check of these stars shows that they have relatively large photometric errors and/or very low Q values. Generally specking the errors in theoretical H-R diagrams are combination of photometric errors (especially in the U magnitudes, which can lead to incorrectly high temperatures and bolometric corrections), transformation equations, reddening determination and adopted distance modulus.

The red part of the H-R diagram contains five very red and luminous supergiants with masses between 12 and $40~ M_\odot$, a large amount of low-mass yellow stars and red giants from the tip of the RGB.

4.5 Variable stars

With no spectra available we calculated the effective temperatures and $M_{\rm bol}$ for all available variable stars in our field in order to check if the red supergiants were correctly located on the H-R diagram. They are marked in Fig. 9 with open squares and listed in Table 4. Freedman (1988b) determines the light curves and periods for most of the Cepheids suspected by Sandage (1971). The Cepheids V10, V18 and V39 have periods of 4.07, 16.44 and 28.72 days respectively and as can be seen in our H-R diagram they lie within the instability strip of the Cepheids. V22 is among the Cepheids with the longest periods having a period of 146 days and therefore the relatively high $M_{\rm bol}$ for this star is not unusual. V32, V38, V40, V43 and V56 are red irregular variables suspected by Sandage (1971) and confirmed by Freedman (1988a). We can see that these stars are located correctly on our H-R diagram. V8 and V21 are especially interesting from our point of view. V8 is an irregular variable (Carlson & Sandage 1990) which varied from B=21.3 to B = 21.9 over a 33 year interval. In our diagram this star is a blue one and has relatively high $M_{\rm bol}$ and $T_{\rm eff}$ (See Table 4). Sandage (1971) notes that V21 is an intermediate color irregular variable with a small amplitude. From 1929 to 1937 the star varied from B=19.60 to B=20.34 mag. The largest variations occurred between 1929 and 1932. The star remained relatively constant after that to within 0.2 mag at B=20 mag. In 1984 (photometry of Freedman 1988a) the star was very blue with B-V=-0.24 and V=20.44. In our photometry based on 9.10.1997 observations the situation is the same - the star is very blue. The star is hot with $T_{\rm eff}$ approx. 30000 K, it is one of the most luminous stars with $M_{\rm bol}=-7.67$ and its mass is approximately 20 $M_\odot$.

  

Table 4: Variable stars

  

Figure 9: H-R diagram for all stars in IC1613. The evolutionary mass tracks from Charbonnel et al. (1993) for z=0.004 are superimposed on the same plot. Eleven variable stars are marked by open squares

4.6 The IMF

From the isochrone fit shown in Fig. 8 we have selected the blue stars in the main sequence with equal age (5 - 10 Myr) in order to construct the IMF. Following again Massey et al. (1989, 1995a,b) we determine the slope $\Gamma$ of IMF as:

$$\Gamma = d \log \xi(\log m)/d\log(m)$$

where $\xi(\log m)$ is the number of stars formed per logarithmic mass interval per unit area. The Salpeter (1955) slope is $\Gamma= -1.35$. To determine our IMF we simply counted the stars that fall between each pair of mass tracks in Fig. 9 and normalized the count to the width of the bin and the area of the observed field. We left out the stars with masses less than 7 $M_\odot$ when the incompleteness in our sample became significant. Our final slope is $\Gamma = -2.0$ with $\sigma = 0.1$ (the uncertainty in the slope is the uncertainty in the least-squares fit to the IMF). The IMF is shown in Fig. 10. If we exclude the highest mass bin ($M_\odot \gt 60$) where the statistical errors are largest and to avoid possible age differences the slope of IMF became $\Gamma = -1.98$ with $\sigma = 0.1$. No correction for unresolved multiple stars has been made.

The comparison with the IMFs of other galaxies given in Haiman et al. (1994) (see their Table 2) shows that our result is consistent within the error range with the results for LMC, SMC and some of the M31 associations. Salpeter IMFs have been measured for intermediate mass stars in the Milky Way open clusters and associations (Phelps et al. 1993; Massey et al. 1995a,b). The IC1613 formation therefore appears to be typical of star formation processes in other nearby galaxies.

  

Figure 10: The initial mass function for IC1613. The error bars indicated statistical fluctuations