AN EXTENDED STAR CLUSTER AT THE OUTER EDGE OF THE SPIRAL GALAXY M 33^*

The color–magnitude diagram (CMD) of a region of 20'' radius, centered on the star cluster M 33-EC1, is dominated by red giant branch (RGB) stars; see Figure 2. Reduction and photometry procedures enable us to recognize and remove obvious bright non-stellar objects (star/galaxy separation was performed by eye referring to PSF fitting parameters—sharpness and χかい²); however, faint unresolved background galaxies can still be present in this diagram.

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In order to resolve the well-known age–metallicity degeneracy of the RGB position in the CMD, inherent to old populations, it is helpful to introduce faint RGB and horizontal branch stars into the isochrone fitting procedure; see, e.g., Martin et al. (2006). The global shape of our CMD resembles the CMD plotted in Figure 7 from Martin et al. (2006), implying the presence of a very old population with a prominent horizontal branch. However, the limiting magnitude of our observations is too shallow for a reliable morphology study of the lower part of the CMD. Therefore, to estimate the intrinsic RGB width over the entire magnitude range, and to derive radial and magnitude dependence of data completeness, we performed an artificial star test (AST) on R- and I-band images. The AST results quantify in detail the photometry errors, confusion limits and data completeness, making the isochrone fitting procedure more robust and better constrained.

Six reference points on the observed RGB (I, R − I = 20.90, 0.72; 21.90, 0.65; 22.90, 0.57; 23.40, 0.53; 23.90, 0.49; 24.40, 0.46) were selected to represent the entire magnitude range of the cluster's stellar population. DAOPHOT's addstar procedure was employed to add artificial stars to the images. To avoid self-crowding we generated individual AST images at every reference point. Each AST image contains 400 artificial stars of the same magnitude distributed on a regular grid (step 3'') over the region of 60'' × 60'' centered on the cluster. However, only 140 artificial stars fall within the actual cluster radius of 20''. In order to increase the number of artificial stars and derive radial data completeness distributions more reliably, we generated 21 individual images for each passband and every reference point by shifting the grid around the initial position to 8 and 12 symmetrically distributed locations around the initial position at radial distances of ∼06 and ∼12, respectively. Therefore, within a radius of 20'' we used 2940 artificial stars in total at each reference point on the RGB. The photometry procedure of the AST images was exactly the same as the one employed for the real-star photometry.

To understand the morphology of star distribution in the lower part of the CMD, we constructed an artificial-star CMD. The radial distribution of the artificial stars at every reference AST point on the RGB was chosen to represent the observed radial density distribution of the cluster stars. However, to increase the robustness of the artificial star CMD, we used a number of artificial stars five times greater than the number of real stars. The observed cluster stars overplotted on the artificial star CMD are shown in Figure 2 (panel (b)).

The "Christmas tree-like" artificial star CMD (Figure 2, panel (b)) implies that the CMD of the star cluster M 33-EC1 is composed solely of RGB stars, experiencing very low contamination by foreground stars and background galaxies. Note, however, the enhanced (with respect to the artificial stars) density of the faint blue (R − I < 0.25) objects, which could be attributed to the horizontal branch stars of the cluster or faint blue galaxies. Therefore, the straightforward isochrone fit to the observed stars can be applied down to I = 23^m, using only the RGB part of the isochrones.

We constructed a radial data completeness plot (Figure 3) by counting the recovered artificial stars in 2'' wide annulus zones centered on the cluster. Stars down to I = 23^m are well recovered even at the very center of the cluster. At this magnitude level we are able to find and measure more than 70% of the stars at the cluster's center and more than 95% at larger radii (Figure 3).

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The ∼100% data completeness of the brightest RGB stars is of high importance for the cluster's distance determination by fitting the tip of the RGB (TRGB). This method is based on the assumption (valid for [Fe/H] ⩽−0.7 and ages of ≳2 Gyr) that the absolute I-band magnitude of TRGB (M_I = 4.05 ± 0.10) is independent of metallicity and age (Lee et al. 1993; Bellazzini et al. 2001). The AST data completeness results imply that the TRGB method can be applied throughout the radial extent of the star cluster.

A magnitude of the brightest RGB star (it is located within the cluster's core, however, in an uncrowded area, and thus measured accurately) is of I = 20.81 ± 0.01. Taking into account the MW foreground extinction (A_I = 0.11), this converts to a distance modulus of (m − M)₀ = 24.75 ± ^0.10_0.20 and places the star cluster M 33-EC1 at a distance of 890 ± ⁴⁰₈₀ kpc. The distance modulus error is dominated by the systematic error of the TRGB calibration (±0.10) and by an additional increase of the distance modulus, arising due to a probability, that the brightest observed star is below the very tip of the theoretical RGB, because of a small total number of RGB stars in the cluster.

It is worthwhile to stress that we determine the RGB tip of the M 33 galaxy's outer disk at I = 20.68 ± 0.02, which converts, by applying the MW foreground extinction, A_I = 0.08, and assuming the validity of the TRGB method for the case of the M 33 outer disk's metallicity, to ∼850 kpc. The derived distance of M 33 is in agreement with recent M 33 galaxy distance determinations, based on the TRGB method, by Galleti et al. (2004) and Tiede et al. (2004)—855 kpc and 867 kpc, respectively. However, the detached eclipsing binary method gives a significantly longer distance of 964 kpc (Bonanos et al. 2006), while a cepheid based distance is shorter—802 kpc (Lee et al. 2002). Therefore, in the remainder of this paper we will use the distance modulus of 24.75, which places M 33-EC1 at a projected distance of 12.5 kpc from the M 33 center.

To estimate the cluster's age and metallicity we compared the shape and slope of the observed RGB with the isochrones of Girardi et al. (2002) and VandenBerg et al. (2006). In the case of Girardi et al. (2002) isochrones, we achieved the best fit for the interpolated isochrone of the age of 13 Gyr and metallicity of [M/H] =−1.2 (Figure 2, panel (a); isochrone of the age of 14 Gyr and metallicity of [M/H] =−1.3 is overplotted). However, the isochrone of lower metallicity, [M/H] =−1.4, and age of ∼18 Gyr, as well as the isochrone of higher metallicity, [M/H] =−1.0, and age of ∼2.5 Gyr, can also be fitted reasonably well. Therefore, additional information is needed in order to break the age (2.5–18 Gyr) and metallicity ([M/H] =−1.4– − 1.0) degeneracy.

We obtained more constrained fits by employing VandenBerg et al. (2006) isochrones (2–18 Gyr), which are available on the finer metallicity grid for three alpha element abundance ratios ([αあるふぁ/Fe] = 0.0, 0.3, 0.6). We achieved good, although degenerate, fits for ages of >7 Gyr and metallicity of [M/H] <−1.4 independent on alpha element abundance, see Figure 4. The isochrones spanning a narrow age and metallicity range are overplotted on CMDs for illustrative purposes. Assuming a reasonably old cluster age of 13 Gyr, we derived a metallicity of [M/H] =−1.6. Note that for the same age (13 Gyr) metallicity derived from the Girardi et al. (2002) isochrones is higher by 0.4 dex. The derived metallicity [M/H] ≲−1.4 is in good agreement with the recent spectroscopic metallicity determination of the M 33 halo stars in a nearby field to the M 33-EC1 location (McConnachie et al. 2006).

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The M 33-EC1 age of >7 Gyr, estimated from the isochrone fitting, implies that it should possess a globular cluster-like surface number density profile, which is traditionally fitted by the King model (King 1962):

$$$ \rho (r)=\rho _0\cdot [(1+(r/r_{\rm c})^2)^{-1/2}-(1+(r_{\rm t}/r_{\rm c})^2)^{-1/2}\,]^2, $$$

where ρろー₀ (central surface number density), r_c (core radius), and r_t (tidal radius) are profile fitting parameters. However, due to a small number of bright stars and an incompleteness of the stellar photometry catalogue at fainter magnitudes (see Figure 3), we decided to fit the King model to the surface brightness rather than to the surface number density profile. This assumption is reasonable for the surface brightness profiles, constructed from aperture photometry, which even at large radial distances sample the cluster's stellar population satisfactorily well.

On the other hand, large M 33-EC1 extent and relatively low luminosity (mass), as well as long (∼12.5 kpc) projected distance from the host galaxy's center, can lead to the assumption that the cluster is dynamically young and possesses a surface brightness profile, which could be reproduced by the empirical EFF (Elson et al. 1987) profile derived for young (<300 Myr) Large Magellanic Cloud clusters. We employed the EFF model in differential form representing surface brightness profile

$$$ \mu (r)=\mu _0\cdot (1+(r/r_{\rm e})^2)^{-n}, $$$

and in integral form representing integrated luminosity profile

$$$ \Sigma (r)=\Sigma _0\cdot r_{\rm e}^2\big/(n-1)\cdot [1-(1+(r/r_{\rm e})^2)^{1-n}], $$$

where μみゅー₀ is the central surface brightness, Σしぐま₀ is the central luminosity, r_e is the scale-length, and n is the power-law index.

The determination of an accurate center of the well resolved cluster is a sensitive procedure in constructing the surface brightness profile. In the central part of M 33-EC1 luminous stars are distributed slightly asymmetrically (see Figure 1); therefore, the location of the center was derived by fitting the luminosity weighted and spatially smoothed surface brightness profile in an area of 20'' × 20''. M 33-EC1 exhibits perfectly round isophotes at large radii, suggesting that the mass distribution is spherical in general—hence we used circular apertures for the construction of surface brightness and integrated luminosity profiles, by integrating in 04 wide annuli up to a radius of 20''.

The sky background was determined in a circular annulus centered on the cluster and spanning the radial range from 20'' to 30'' (see Figure 1). The correct sky-background subtraction is critical for determining the shape of a surface brightness profile in the cluster's outer region (for a detailed discussion, see Hill & Zaritsky 2006); therefore, systematic sky-background subtraction errors were evaluated by constructing the profiles with oversubtracted and undersubtracted sky background. The sky-background variation by rms of the sky-background value led to insignificant structural parameter changes.

The resultant M 33-EC1 radial surface brightness profiles are smooth up to ∼16'' radius, where a bright RGB star is located. Therefore, we performed the King and EFF model profile fitting up to a radius of 14''. The best model fits to the V-band sky background-subtracted integrated luminosity (top panel) and surface brightness (bottom panel) radial profiles are presented in Figure 5.

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Directly fitted and derived (r_h and full-width at half maximum, FWHM) M 33-EC1 structural parameters, as well as corresponding standard deviations, are listed in Table 1. The derived parameters were computed based on transformation Equations (6), (7), (9) and (10) presented by Larsen (2006) for the EFF profile

$$$ {\rm FWHM}=2\cdot \,r_{\rm e}\cdot \,\sqrt{2^{1/n} - 1}, $$$

$$$ {r_{\rm h}}=r_{\rm e}\cdot \,\sqrt{0.5^{1/(1-n)} - 1}, $$$

and the King profile

$$$ {\rm FWHM}=2\cdot \,r_{\rm c}\cdot \,\sqrt{((1-\sqrt{0.5})/\sqrt{1+(r_{\rm t}/r_{\rm c})^2}+\sqrt{0.5})^{-2}-1}, $$$

$$$ {r_{\rm h}}=0.547\cdot \,r_{\rm c}\cdot \,(r_{\rm t}/r_{\rm c})^{0.486}. $$$

For further discussion we choose the conservative lower limit of the cluster's half-light radius of r_H = 47, which, at the estimated distance of 890 kpc, converts to ∼20.3 pc, revealing the extended M 33-EC1 nature. It is also important to note that the differences between V-, R-, I-band profile fit parameters are smaller than their standard deviations. Therefore, in Table 1 we give averaged parameters for the three passbands. It is worth noting that a change of the fitting radius from 12'' to 19'' does not influence the derived cluster parameters significantly. Integrated magnitudes and colors derived at the cluster's center and radii of (1–4) · r_H are listed in Table 2. We find no significant color gradient over the entire radial cluster's extent. The V − I color of M 33-EC1, taking into account that only foreground extinction is present at this galactocentric distance, is in the color range of the intermediate- and old-age (≳5 Gyr) M 33 clusters (Sarajedini & Mancone 2007).