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5 Associations

OB associations are collections of recently formed stars which can be distinguished from the background of field stars by the clustering of bright, young O and B stars. In general they are not gravitationally bound systems and are short-lived features. For these reasons investigations of the OB associations can provide information about the formation and evolution of massive stars.

5.1 Hodge associations

Hodge (1978) identified twenty OB associations concentrated primarily in the core of the galaxy with a mean diameter of 164 pc. Freedman (1988a) presented color-magnitude diagrams for 11 of them and gave some age estimates using period-age relations for Cepheids. In our field of observations we have 9 of the Hodge associations - Nos. 10, 11, 12, 13, 14, 15, 17, 18 and No. 19. Figure 11 shows the ($V-B,\ V$) color-magnitude diagrams of the Hodge associations. The new plot of color-magnitudes diagrams shows well-defined main sequences with widths of typically 0.2, blue and red supergiants in A10, A11 and A14 and some intermediate age stars and red giant stars.

\includegraphics [clip,height=18cm]{ds7636f11.eps}\end{figure} Figure 11: $(B-V,\ V)$ color-magnitude diagrams for Hodge associations Nos. 10, 11, 12, 13, 14, 15, 17, 18 and No. 19

Figure 12 and Fig. 13 show the comparison with the isochrones from Padua's library (see Bertelli et al. 1994) and a (Log$(T_{\rm eff}), M_{\rm bol}$)diagram. They were built in the same manner as in the previous section.

\includegraphics [clip,height=18cm]{ds7636f12.eps}\end{figure} Figure 12: ((V-B)0, MV) color-magnitude diagrams for Hodge associations. Isochrones from Padua's library with z=0.004 are superimposed

On the assumption that all the stars in each association have the same age we can determine the age of the associations following the method of Flannery & Johnson (1982). The distance of the star j of the association to a given isochrone was computed as:

\textstyle d_j^2 = MIN _{i=1,\ldots ,n}\left [\left (\frac{V...
 ...eft (\frac{(B-V)_j-(B-V)_i}{\sigma_{(B-V)_j}}\right )^2\right ]\end{displaymath}

where Vi and (B-V)i are the different points of the isochrone given by different stellar masses. A mean distance of stars to the isochrone can be obtained by:

\psi = \left (\sum_{j,\ldots ,N} d_j\right )/N\end{displaymath}

where N is the number of stars. The minimum value of $\psi$ gives the most probable age of the association. Due to observational errors as well as a certain amount of inaccuracy in the estimation of E(B-V) and [Fe/H] the total external uncertainty of this method is about 2.5 Myr. The "most probable" age of the associations is given in Table  5, Col. 2. We would like to point out however that in most cases the $\psi$ value is rather high and it could indicate the presence of a spread of ages throughout the association. Nevertheless, as can be seen in Table 5 there are significant age differences among the associations which are generally larger than the uncertainty of the method. The youngest associations are A10 and A14 with ages of approx. 5 Myr while the oldest ones are A12, A18 and A19 with ages of approx. 20 Myr.

As can be seen in Fig. 12 there are some yellow and red stars in all associations, which have ages between 100 and 300 Myr. In the theoretical H-R diagram (Fig. 13) they lie between 4 and 7 $M_\odot$. We consider one small part of them to be field stars from our Galaxy (according to Table 3 in V < 21 mag the expected number of field stars is approximately 30) and the rest to be field stars from IC1613. To investigate the behavior of foreground stars we selected the "comparison field area" with the same mean diameter as the Hodge association - 164 pc and far from any known association. The color-magnitude diagram, the isochrone comparison and the H-R diagram were built in the same way as in the associations and are shown in Fig.  14. As can be easily seen except for a few faint blue stars that lie on the main sequence most stars are faint, low-mass and 100 - 300 Myrs old.

In the upper part of the theoretical H-R diagram (masses $\gt 25\ M_\odot$,Fig. 13) most of the associations except A12, A18 and A19 contain young massive stars which have been born almost coeval. Following Massey et al. (1995) we tabulated the most massive stars still present in the associations in Table 5. The masses of the most massive stars are listed in Col. 3 and Col. 4 contains a number of stars with masses higher than $12\ M_\odot$. The analysis of Table 5 shows that the associations containing the most massive stars are the youngest ones while the associations containing only low-mass stars are indeed the oldest.

Table 5: Parameters of the Hodge associations

Name & Age(Myr) & $M_{\rm up}( M_\odot)$\space & $...
 ...7 & 8 & 70 & 33 \\ A18 & 20 & 20 & 7 \\ A19 & 20 & 15 & 3 \\ \hline\end{tabular}

Table 6: OB associations in IC 1613

 No. & $X $\space & $Y$\space &Size & Members &D...
 ... 715.9 & 68 & 8 & 12 \\  30 & 18.20 & 320.4 & 41 & 8 & 19 \\ \hline\end{tabular}

Table 7: Data for some Hodge clusters and for two new cluster candidates

Cluster & $X$\space & $Y$\space...
 ...$19.38$\space & $-0.08$\space & $-0.97$\space & $4$\space \\ \hline\end{tabular}

Table 8: Data for non-stellar objects

No. & $X$\space & $Y$\space & $FWHM$\space & $...
 ...7.53 & 6.24 & 8.80 & 19.77 & 0.92 & $-$0.09:\hspace{-3pt} \\ \hline\end{tabular}

Hodge (1978) included the brightest red supergiants V32 and V38 in the boundaries of A10 and A14. According to the paper of Massey (1998) they could be real members of those associations. V32 and V38 stand around $40\ M_\odot$(Fig. 13) and have very high $M_{\rm bol}$ -9.84 and -9.70 respectively. On the other hand the age of both A10 and A14 is $5\pm 2$ Myr. As Massey (1998) mentioned. "At 5 Myr we would find only WN stars and few if any RSGs, and at 7 Myr we would find only RSGs". The comparison with the masses and $M_{\rm bol}$ of the red supergaints in M31, M33 and NGC6822 given by Massey (1998) shows that the two supergaints in IC1613 are similar to the red supergaints in NGC6822.

\includegraphics [clip,height=18cm]{ds7636f13.eps}\end{figure} Figure 13: Theoretical H-R diagrams for Hodge associations Nos. 10, 11, 12, 13, 14, 15, 17, 18 and No. 19

\includegraphics [clip,height=9.5cm]{ds7636f14.eps}\end{figure} Figure 14: The color-magnitude diagram, the isochrone comparison and the H-R diagram of the "comparison field area" with mean diameter 164 pc

Three Wolf-Rayet (WR) stars reported by Armandroff & Massey (1985) -- WR4, WR5 and WR8 are in our field of observations. These stars belong to the associations A10, A13 and A14 respectively and have following magnitudes and colors: WR4 -- V=19.16, U-B= -0.39, B-V=-0.41; WR5 -- V=20.78, U-B= -1.00, B-V=-0.27; WR8 -- V=19.56, U-B= -1.80, B-V=0.53. The WR8 is embedded in the supernova remnant S8 (Peimbert et al. 1988), which lead to the very unrealistic magnitude and colors. The presents of the WR stars in A10, A13 and A14 is in good agreement with youngest age of these associations.

It is not possible to calculate the IMF for each association because of small association members and therefore large statistical errors. In order to improve the statistics we summarized Hodge associations in three groups. First group contains the blue stars from A10, A11, A14 and A17 (having ages between 5-8 Myr), second group contains A13 and A15 (having age 10 Myr) and the last one contains the stars from A12, A18 and A19 (with age 20 Myr). The slopes of IMFs for these three groups are $\Gamma = -1.59\pm 0.18$,$\Gamma = -2.22\pm 0.20$ and $\Gamma = -2.65\pm 0.05$ respectively. The uncertainty in the slope is the uncertainty in the least-squares fit to the IMF. According to Fabry Pérot images (Rosado 1998) the stars from the first group of Hodge associations are embedded into shells of gas, while there is not any gas in the last association group (A12, A18 and A19).

The different stellar content, age differences, variations of slopes of IMFs and presence of gas into some of associations, show a signature of a presence of two waves of star formation.

5.2 Criterion for the identification of OB associations

The stellar associations were identified by Hodge (1978) by eye estimation. The present criterion is the objective determination of the boundaries of OB associations. It suggests that OB stars should be assigned to one and the same stellar association if they have a statistically significant peak of surface stellar density above the mean level of the surrounding OB stars. The OB associations are groups with the highest stellar density. The neighbour distances between the stars inside the associations are substantially smaller than those of the background ones outside the association. The mean value of the distance to the nearest neighbour in an OB association is a measure for stellar density (see Appendix in Ivanov 1996). The stellar density function in the association is defined as $ f(\delta_j)$, for $j = 1, 2, \ldots ,N$,where N is the number of candidate OB associations in the galaxy. A reliable function for statistical evaluation of the possible maximal density of the N stellar groups is the Fourier transform of the function $ f(\delta_j)$ for the different candidates for OB associations:

F(\nu_k)= \sum _j^N f(\delta_j) {\rm e}^{i2\pi s_j\nu_k},\end{displaymath} (1)
where $ s_j = (j-1) (d_j- d_{\rm lim}) $ is the interval of discretion of the mean neighbour distances for individual candidates for OB associations in the galaxy, $j, k = 1, 2,\ldots ,N$, and $ d_{\rm lim}$ is a limiting search neighbour distance between stars which is a free parameter and corresponds to the highest possible stellar density inside the OB associations. The frequencies were defined as:

\nu_k = \frac{k-1}{d_{\rm max}- d_{\rm lim}},\end{displaymath} (2)
where $ d_{\rm max} $ is the largest neighbour distance between the stars in the galaxy.

The amplitude of the Fourier transform is:

FF(\nu_k) &=& \frac {1} {N} \left \{ \left [ \sum _j^N f(\delta...
 ...j^N f (\delta_j)\sin (2\pi s_j \nu_k) \right ]^2 \right \}^{1/2} .\end{eqnarray}
The OB associations have widely different stellar densities which is related to the mean neighbour distance for a given group dj as one can see from the relation (A6) of Ivanov (1996). In order to eliminate the random clumps of OB stars we introduce another free parameter, the minimum number of stars per OB association $ N_{\rm min}$. The OB associations can be selected within some stellar densities varying the parameters dj and $ N_{\rm min}$. The function $ FF_{\rm max}= \max {FF(\nu_k)}$ corresponds to the sum of stellar density fluctuations of the selected stellar groups above the local OB stellar background which is the highest. The maximum of function $FF_{\rm max}$ was obtained for $ d_j = 20.4~{\rm px} \approx 7 ~{\rm arcsec} $ and $ N_{\rm min} = 4$.

These parameters select the smallest groups in IC1613 with a mean size ($\approx$) 60 pc. These 30 groups have the smallest size in the hierarchy of OB stellar groups but they have the highest stellar density in IC1613.

Following the present criterion we select relatively small groups with high stellar density which is at least 4 times higher than that of the surrounding OB stars. However the mean stellar density of the 30 selected groups is 35 times above the background OB stars.

The re-determined OB associations are shown in Table  6. Column 1 gives the number of the group, Cols. 2 and 3 give the mean coordinates of the group in pixels, Col. 4 gives the average size of the group in pc, Col. 5 gives the number of member stars and column 6 gives the mean stellar density. A map of the new associations is shown in Fig. 15.

Most of the stellar associations outlined by Hodge coincide with our groups but the present criterion divides Hodge's associations into several smaller groups. They look like bright cores within Hodge's associations. The present criterion selects a core structure of OB stars in the classic associations. They are probably the youngest OB stars in the associations. It is known that young associations in the Galaxy like Trapezium contain small compact subgroups similar to those selected by the present criterion in IC1613 while the older associations consist of randomly distributed stars and they could not be divided into subgroups. Using the present criterion we identified 30 small groups of OB stars with a mean size of about 60 pc. Hodge (1986) describes the problem of the different sizes of the stellar associations in the Magellanic clouds and other nearby galaxies as M31 and M33. He concluded that the mean size of the associations depends on the plate scale and the distance to the galaxy. The present criterion is very strong, the result being that only the youngest associations are identified. This may explain the smaller mean size of the stellar groups identified in the present paper than those presented by Hodge (1986).

\includegraphics [clip,height=8.6cm]{ds7636f15.eps}\end{figure} Figure 15: Observational area for IC1613 with superimposed boundaries of new associations. The two new open cluster candidates are marked by dashed line.North is on top, East is to the left

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