The Mass Function of omega Centauri down to 0.15 M_s
aa r X i v : . [ a s t r o - ph ] A ug Mon. Not. R. Astron. Soc. , 1–8 (2006) Printed 27 October 2018 (MN L A TEX style file v2.2)
The Mass Function of ω Centauri down to 0.15 M ⊙ ⋆ A. Sollima † , F.R. Ferraro and M. Bellazzini Dipartimento di Astronomia, Universit`a di Bologna, via Ranzani 1, Bologna, 40127-I, Italy INAF Osservatorio Astronomico di Bologna, via Ranzani 1, Bologna, 40127-I, Italy
Accepted 2006, ???; Received 2006, ???; in original form 2006, ???
ABSTRACT
By means of deep FORS1@VLT and ACS@HST observations of a wide area in thestellar system ω Cen we measured the luminosity function of main sequence starsdown to R=22.6 and I F W =24.5 . The luminosity functions obtained have beenconverted into mass functions and compared with analytical Initial Mass Functions(IMFs) available in the literature. The mass function obtained, reaching M ∼ . M ⊙ ,can be well reproduced by a broken power-law with indices α = − . M > . M ⊙ and α = − . M < . M ⊙ . Since the stellar populations of ω Cen have beenproved to be actually unaffected by dynamical evolution processes, the mass functionmeasured in this stellar system should represent the best approximation of the IMFof a star cluster. The comparison with the MF measured in other Galactic globularclusters suggests that possible primordial differences in the slope of the low-mass endof their MF could exist.
Key words: methods: observational – techniques: photometric – stars: mass function– globular cluster: ω Cen
The determination of the stellar Initial Mass Function (IMF)still represents one of the most crucial questions in astro-physics. In fact, it is a critical ingredient in the understand-ing of a large number of basic astronomical phenomena suchas the formation of the first stars, galaxy formation andevolution, and the determination of the possible dark mat-ter content of galaxy halos. After the pioneering study bySalpeter (1955), a number of works have been carried outwith the aim of studying the shape of the IMF in the solarneighborhood (Miller & Scalo 1979; Larson 1998; Chabrier2001; Kroupa 2002).Star clusters provides a useful tool to investigate thelow-mass end of the IMF. They offer the possibility of ob-serving large samples of unevolved low-mass stars that arecoeval and at the same distance with the same chemicalcomposition. However, the derivation of the IMF in star clus-ters is complicated by the tidal interaction with the Galaxythat drives star clusters preferentially to lose low-mass starsacross the tidal boundary as a result of the ever-continuing ⋆ Based on observations collected at the European Southern Ob-servatory within the observing program 74.D-0369(B).Also basedon observations with the NASA/ESA Hubble Space Telescope,obtained at the Space Telescope Science Institute, which is oper-ated by the Association of Universities for Research in Astronomy,Inc., under NASA contract NAS5-26555. † E-mail: [email protected] (AS) redistribution of energy on the two-body relaxation time-scale. De Marchi et al. (2005) found that the luminosityfunction (LF) of Galactic globular clusters (GC) is well re-produced by adopting a Mass Function (MF) in which thenumber of stars per unit mass decreases below a criticalmass. Table 1 lists the most used analytical descriptions ofthe IMF available in literature. A number of other power-law indices have been measured in stellar associations andyoung star clusters in the local Universe (see Kroupa 2002for a recent review).The stellar system ω Centauri (NGC 5139) is themost massive and luminous GC of the Milky Way (M ∼ . M ⊙ , Van de Ven et al. 2006) and plays a key role inthe understanding of the properties of the mass spectrum forlow-mass stars. Ferraro et al. (2006) showed that the mostmassive objects in the cluster (blue straggler stars and inter-acting binaries) are not centrally segregated, at odds withany other GC. This evidence suggests that ω Cen is still farfrom being completely relaxed even in the core region. Forthis reason its present-day MF should reflect the IMF muchmore closely than in any other Galactic GC.In this paper we measured the LF of ω Cen by meansof wide-field ground-based photometry using FORS1 andACS@HST observations of a peripheral region of the clus-ter. The obtained LFs have been compared with the LFs ofother Galactic GCs and converted into mass function (MF).In § § § c (cid:13) Sollima et al.
Galactic GCs. In § ω Cen is presentedand compared with the analytical IMFs available in the lit-erature. We discuss our results in § The analysis presented here is based on two photometricdatasets: (i)
A mosaic of eight deep images obtained withFORS1@VLT in the B and R passbands and (ii) a set ofhigh-resolution images obtained with ACS@HST throughthe F606W and F814W filters in an external region of thecluster.FORS1 observations sample the Main Sequence (MS)population of ω Cen down to R ∼
24 containing more than70,000 stars between 6’ and 27’ ( ∼ r c ) from the clus-ter center. The photometry has been performed with thePSF-fitting code DoPhot (Schechter et al. 1993). A detaileddescription of the data reduction and calibration procedurecan be found in Sollima et al. (2007). The outermost fieldof the FORS1 observations partially overlaps the deep ACSphotometry allowing one to link these two datasets (see Fig.1). ACS observations cover a small region of 3 . ′ × . ′ in an external field at ∼ ′ from the cluster center. Theyconsists in a set of four 1300 s and 1340 s long exposuresthrough the F606W and F814W filters, respectively. Thephotometric analysis have been performed using the SEx-tractor photometric package (Bertin & Arnouts 1996). Giventhe small stellar density in this field ( ∼ . stars/arcsec ),crowding does not affect the aperture photometry, allowingto properly estimate the magnitude of stars. For each starwe measured the flux contained within a radius of 0.125”( ∼ FWHM). The source detection and photometric analy-sis have been performed independently on each image. Onlystars detected in three out of four frames have been includedin the final catalog. The most isolated and brightest stars inthe field have been used to link the 0.125”- to 0.5”-aperturephotometry, after normalizing for exposure time. Instrumen-tal magnitudes have been transformed into the VEGA-MAGsystem by using the photometric zero-points by Sirianni etal. (2005). The obtained catalog contains 5,440 stars reach-ing the limiting magnitudes V F W ∼
27 and I F W ∼
25. Fig. 2 shows the color-magnitude diagrams (CMDs) ob-tained for the two samples. The main features of the pre-sented CMDs are schematically listed below: • The CMDs sample the unevolved population of ω Cenfrom the turn-off down to the lower MS; • A narrow blue MS (bMS), running parallel to the dom-inant MS population, can be distinguished at 19 . < R < < I F W <
21 . This feature has been already de-scribed and discussed in Bedin et al. (2004) and Sollima etal. (2007); • ACS observations reach a fainter limiting magnitude,sampling also the region close to the hydrogen burning limit.In the following section we describe the adopted proce-dure to derive the LFs and the global MF of ω Cen fromthese data-sets.
Figure 1.
Map of the region sampled by the FORS1 observations.North is up, East on the right. The eight fields observed withFORS1 are shown. The grey box indicates the position of theACS field. The cluster center and half-mass radius are indicatedby the black cross and the dashed line, respectively.
To compute the LF of ω Cen we followed the procedure de-scribed below. As a first step, we computed the MS ridge lineby averaging the colors of stars in the CMD over 0.2 magboxes and applying a 2 σ clipping algorithm. Then, the LFhas been computed by counting the number of objects in 0.5mag wide bins separated by 0.1 mag along the R and I F W axes. Only stars within ± . ω Cen is well known to harbour stellar populationswith different metallicity (Norris, Freeman & Mighell 1996and references therein) and, possibly, helium content (Norris2004). The CMDs shown in Fig. 2 do not allow one to dis-tinguish the different MS components of the cluster (exceptfor the bMS population), making impossible to disentanglethe contribution of each population to the LF. However, themetal-poor population of ω Cen comprises more than 70% ofthe entire cluster content (Pancino et al. 2000), thus dom-inating the shape of the LF. To check the validity of thisassumption, we measured the LF of MS stars by exclud-ing bMS stars in the magnitude range where this sequenceis clearly distinguishable from the dominant cluster popu-lation. For this purpose, we considered bMS stars all theobjects lying at a distance between 0.5 and 2.5 times thecolor standard deviation around the cluster ridge line onthe blue side of the dominant cluster MS in the magnituderange 19 . < R < . . < I F W < . c (cid:13) , 1–8 he Mass Function of ω Cen Table 1.
Summary of the most common analytical IMF in the literatureSalpeter (1955)
A m α α = − . Am e − ( log m − log m σ log m log m = − . σ log m = 0 . A m α e − m m α = − . m = 0 . M ⊙ Larson (1998)(b)
A m α (1 − e − mm ) α = − . m = 0 . M ⊙ Chabrier (2001)
A m − δ e − m m β δ = 3 . m = 716 . M ⊙ Kroupa (2002) A ( mm ) α m = 0 . M ⊙ ; α = − . for . M ⊙ < M < . M ⊙ m = 0 . M ⊙ ; α = − . for . M ⊙ < M < . M ⊙ m = 0 . M ⊙ ; α = − . for . M ⊙ < M < M ⊙ Figure 2.
FORS1 (R, B-R; left panel ) and ACS( I F W , V F W − I F W ; right panel ) CMDs of ω Cen. ples the deviations from the constant difference lie within∆ log N < .
03 over the entire magnitude range consideredhere (see Fig. 3). This indicates that although bMS starsconstitute a significant fraction of the cluster population ( ∼ (i) the photometric incompleteness and (ii) the contamination from field stars. In the following sec-tions the adopted techniques to correct for these effects aredescribed. Figure 3.
Difference between the LFs calculated with and with-out bMS stars for the FORS1 (upper panel ) and the ACS (lower panel ) sample. The average constant trend is indicated as adashed line in both panels . A reliable determination of the LF from the CMDs of Fig.2 requires the assessment of the degree of photometric in-completeness as a function of magnitude and color. For eachindividual field, the adopted procedure for artificial star ex-periments has been performed as follows (see Bellazzini etal. 2002): • The magnitude of artificial stars was randomly ex-tracted from a LF modeled to reproduce the observed LFfor bright stars (
R < I F W <
22) and to provide largenumbers of faint stars down to below the detection limitsof our observations ( R ∼ I F W ∼ . The color of Note that the assumption for the fainter stars is only for sta-tistical purposes, i.e., to simulate a large number of stars in thec (cid:13) , 1–8
Sollima et al. each star was obtained by deriving, for each extracted R and I F W magnitude, the corresponding B and V F W mag-nitude, for the two datasets respectively, by interpolating onthe cluster ridge line. Thus, all the artificial stars lie on thecluster ridge line in the CMD; • We divided the frames into grids of cells of known width(30 pixels) and randomly positioned only one artificial starper cell for each run ; • For the FORS1 sample, artificial stars were simulatedwith the DoPhot (Schechter et al. 1993) model for the fit, in-cluding any spatial variation of the shape of the PSF. For theACS sample, artificial stars were simulated as gaussians witha
F W HM = 0 . • The results of each single set of simulations were ap-pended to a file until the desired total number of artificialstars was reached. The final result for each sub-field is alist containing the input and output values of positions andmagnitudes.More than 100,000 artificial stars have been producedproviding a robust estimate of the photometric completenessover the entire magnitude extension of the MS. Fig. 4 showsthe completeness factor ( φ ) as a function of the R magni-tude at three different distances from the cluster center forthe FORS1 sample and as a function of the I F W magni-tude for the ACS sample. Only stars lying in the magnituderanges where φ > . The contamination due to field stars was taken into accountby using the Galaxy model of Robin et al. (2003). A syn-thetic catalog covering an area of 0.5 square degrees in thecluster direction has been retrieved. A sub-sample of starshas been randomly extracted from the entire catalog scaledto the ACS and FORS1 field of view. For the ACS sample,the V and I Johnson-Cousin magnitudes were converted intothe ACS photometric system with the transformations ofSirianni et al. (2005). The number of stars contained in eachmagnitude bin within the color window used to measure theLF (see above) has been subtracted from the completeness-corrected MS star counts. The density of field objects in eachmagnitude bin is rather low (of the order of < range of magnitude where significant losses, due to incomplete-ness, are expected. We constrain each artificial star to have a minimum distance (5pixels) from the edges of the cell. In this way we can control theminimum distance between adjacent artificial stars. At each runthe absolute position of the grid is randomly changed in a waythat, after a large number of experiments, the stars are uniformlydistributed in coordinates.
Figure 4.
Completeness factor φ as a function of R magnitudeat three different distances from the cluster center for the FORS1sample (top three panels ) and as a function of I F W magnitudefor the ACS sample (bottom panel ). Fig. 5 shows the R band LF of ω Cen calculated using starslying in annuli of 4’ width at different distances from thecluster center. Note that the φ = 0 . ω Cen with the LF predicted bytheoretical models with and without equipartition. Strongevidence of the lack of equipartition in ω Cen has been pro-vided by Ferraro et al. (2006) on the basis of the comparisonbetween the radial distribution of the blue straggler starswith that of the normal less massive cluster stars. As a con-sequence, the LF measured here can be used to derive a MFwhich can be considered a good approximation of the clusterIMF.The F814W LF calculated for the external ACS field isshown in Fig. 6 and listed in Table 2. The LF reaches a peakat I F W ∼ ω Cen measured by Richer et al. (1991), Elsonet al. (1995), Anderson (1997) and De Marchi (1999) areoverplotted to our data in Fig. 6. The original magnitudesprovided by these authors have been converted into the ACSF814W magnitude with the transformations by Sirianni etal. (2005). All LFs showed in Fig. 6 have been normalizedto have the same number of stars in the magnitude range20 < I F W <
22 . We note that the LF obtained in thepresent analysis extends to fainter magnitudes than those c (cid:13) , 1–8 he Mass Function of ω Cen Figure 5.
R LF of ω Cen calculated between 12’ and 20’ fromthe cluster center. Each LF has been arbitrarily shifted of 0.15 inthe y direction for clearity. The LF measured at 20’ is indicatedfor comparison with dashed lines. by Richer et al. (1991) and Elson et al. (1995), having adeepness comparable with those of De Marchi (1999) andAnderson (1997). Our ACS LF is in good agreement withthat of Elson et al. (1995) and Anderson (1997). The LF byRicher et al. (1991) shows a steeper slope and continues torise below I F W > .
5, at odds with the other LFs. Thisdiscrepancy is likely to be due to uncertainties in the numbercounts and completeness corrections at the faint end of theLF by Richer et al. (1991) whose observations were obtainedfrom ground-based observations where crowding effects canproduce severe incompleteness. The LF by De Marchi (1999)shows a drop for I F W > . ∼ mag brighter than that reached by our observations and is fourtimes less populous than the ACS sample. For these reasons,we consider our LF more reliable at least at its faint end. In Fig. 7 we compare the deep MS-LF of ω Cen (obtainedthrough the F814W filter) with those calculated by Piotto& Zoccali (1999) and Piotto, Cool & King (1997) for fourother Galactic GCs, namely M15, M22, M55 and NGC 6397.To compare the five LFs we assumed the distance andreddening scale described in Sollima et al. (2006), the ex-tinction coefficient A F W = 1 . E ( B − V ) and the pho-tometric conversions by Sirianni et al. (2005). All of the LFshave been normalized to have the same number of stars inthe magnitude range 19 < I F W <
20 .The LF of ω Cen has a slope similar to those of M22and M55, being located between the two extreme cases ofM15 and NGC 6397. In particular, M15 shows a significant
Figure 6.
F814W LF of ω Cen calculated from the ACS externalfield (grey points). LFs by Richer et al. (1991, solid line), Elsonet al. (1995, dotted line), Anderson (1997, short dashed line) andDe Marchi (1999, long dashed line) are overplotted. overabundance of faint stars, incompatible with the mea-surement errors. A similar behaviour is observable also inGCs like M30 and M92 which have a MS-LF similar to thatof M15 (see Piotto & Zoccali 1999).Note that Piotto & Zoccali (1999) measured the LFsclose to the cluster half-mass radius, where mass segregationeffects are expected to be less severe.
The LFs shown in Fig. 5 and 6 have been converted to MFusing the mass-luminosity relation provided by Baraffe etal. (1997). To convert colors and magnitudes in the absolutesystem we adopted the distance modulus ( m − M ) = 13 . E ( B − V ) = 0 .
11 (Lub2001) and the extinction coefficients A R = 2 . E ( B − V )(Savage & Mathis 1979) and A F W = 1 . E ( B − V )(Sirianni et al. 2005). Considering the negligible effects ofdynamical evolution, the averaged LF of the FORS1 samplehas been calculated using all the stars located at distances r > ′ from the cluster center. In Fig. 8 the calculatedMFs are shown. The two MFs have been normalized to havethe same number of stars in the mass range 0 . M ⊙ < M < . M ⊙ . As can be noted, the obtained MFs agree quite wellin the overlap region. The MF shown in Fig. 8 presents awell defined broken power-law shape, with a slope α ∼ − . M > . M ⊙ and a shallower slope ( α ∼ − . c (cid:13) , 1–8 Sollima et al.
Figure 7.
Comparison between the F814W LF of ω Cen (greypoints) and the LFs of M15 (dotted line), NGC 6397 (dot-dashedline), M22 (dashed line) and M55 (solid line). found by Reid & Gizis (1997) from the analysis of a sampleof Galactic disk stars .In principle, two effects can distort the obtained MF: • The presence of a significant spread in the metal andpossibly helium content (Norris et al. 1996; Norris 2004) thatcauses significant changes in the mass-luminosity relation.However, as shown in §
3, the shape of the LF is dominatedby the metal-poor population of ω Cen. For this reason weconsider the MF derived here as representative of the dom-inant cluster population. • Unresolved binary systems are shifted in the CMD to-ward brighter magnitudes and therefore can distort the de-rived MF.To quantify the impact of a significant binary fraction inthe shape of the derived MF, we performed a number ofCMD simulation with different binary frequencies followingthe prescription of Bellazzini et al. (2002). The binary pop-ulation has been simulated by extracting random pairs ofstars from a broken power-low MF with given indices α and α . The F814W and F606W fluxes of the binary com-ponents have been derived using the mass-luminosity rela-tion of Baraffe et al. (1997) and summed in order to obtainthe magnitudes of the unresolved binary system. Field starswere added following the procedure described in § f b = 15% are shown. Asexpected, a significant number of binary systems populatethe synthetic CMD in a region located redward with respect We refer to the power-law fit made by these authors in the massrange 0 . M ⊙ < M < . M ⊙ using the mass-luminosity relationof Baraffe & Chabrier (1996) similar to the one adopted in thiswork (see Table 5 in Reid & Gizis 1997). Figure 8.
Mass Function of ω Cen calculated from the FORS1sample at distances >
12’ from the cluster center (open points)and from the ACS external field (black points). A broken power-law with indices α = − . M > . M ⊙ ) and α = − . M < . M ⊙ ) is overplotted. to the dominant cluster MS ( binary region ). The compari-son of the observed CMD with simulations accounting fora wide range of binary fractions indicates that the binaryfraction in ω Cen must be smaller than f b < binary region in theobserved ACS CMD could be single stars belonging to themetal-rich populations of ω Cen, that are not considered inthe simulated CMD. For this reason, the binary fraction es-timated above represents an upper limit to the true binaryfraction in this stellar system. Then, we derived the LF ofthe simulated CMD adopting the same procedure describedin the previous sections in order to quantify the effect of thepresence of binary systems. We found that a broken power-low MF with indices α = − . M > . M ⊙ ) and α = − . M < . M ⊙ ) reproduces well the observedLF even assuming a binary fraction of f b = 15%. Therefore,we conclude that binary stars have only a negligible effecton the shape of the MF in the considered mass range.Some of the analytical IMF listed in Table 1 and thepresent-day MF derived by De Marchi et al. (2005) for asample of Galactic GCs are overplotted to the MFs obtainedin this paper in Fig. 10 . All MFs have been normalized inthe mass range 0 . M ⊙ < M < . M ⊙ . While for masses M < . M ⊙ all the analytical IMFs reproduce quite wellthe observed MF of ω Cen, at lower masses the MF of ω Cen shows a stronger change of slope than those predictedby the analytical IMFs. In the low-mass range, the MF byDe Marchi et al. (2005) predicts a deficiency of stars withrespect to the MF measured in ω Cen, as expected in relaxedsystems where low-mass stars are lost via evaporation andtidal interaction with the Milky Way. c (cid:13) , 1–8 he Mass Function of ω Cen Figure 9.
Observed ACS CMD (left panel ) and simulated CMDwith a binary fraction f b = 0 .
15 (right panel ) in the magnituderange 18 . < I F W < . Figure 10.
Same as Fig. 8. The analytical relation by Salpeter(1955, solid line), De Marchi et al. (2005, dotted line) and Kroupa(2002, dashed line) are overplotted.
In Sect. 3.3 we have shown that the MS-LF measured atdifferent distances from the center does not show significantmodifications, confirming that ω Cen is still dynamicallyyoung. This result is in agreement with that found by An-derson (1997) by comparing the observed MS-LF of ω Cen with the theoretical predictions with and without equipar-tition and by Ferraro et al. (2006) on the basis of the com-parison between the radial distribution of the blue stragglerstars and normal less massive cluster stars. Hence the ob-served MS-LF (and the derived MF) is expected to be es-sentially unaffected by internal dynamical processes (as e.g.mass segregation). Note that the fact that the MF slope de-rived for ω Cen is formally equal to that measured by Reid& Gizis (1997) for disk stars in the solar neighborhood fullysupports this hypothesis.A number of works suggests that ω Cen could be theremnant nucleus of a dwarf galaxy which merged in the pastwith the Milky Way (see Romano et al. 2007 and referencestherein). In this picture, the cluster experienced strong tidallosses during its interaction with the Galaxy. N-body simu-lations by Tsuchiya et al. (2004) suggest that the system lost ∼
90% of its initial mass during the first 2 Gyr. Evidencethat seems to confirm this hypothesis comes from the de-tection of a significant stellar overdensity resembling a pairof tidal tails surrounding ω Cen (Leon et al. 2000). How-ever, this result has been questioned by Law et al. (2003)who found that Leon’s et al. tidal tails were strongly cor-related with inhomogeneities in the reddening distribution.Note however that the lack of equipartition in ω Cen shouldlead the system to lose stars independently on their masses.Therefore, even strong stellar losses should not significantlydistort the MS-LF of the cluster. Hence, the MS-LF shownin Fig. 6 should reflect the global primordial luminosity dis-tribution of MS stars in the cluster.If this consideration is true, the comparison of the MS-LF shown in Figure 7 casts some doubts on the ”universal-ity” of the IMF. In fact, under the assumption that all stellarsystems formed their stars following a ”universal” IMF, wewould expect to observe a general agreement in the MS-LFshape (with respect to that measured in ω Cen) in poorlydynamically evolved clusters or a deficiency of faint (low-mass) stars in highly evolved clusters where dynamical ef-fects have played a significant role. However in no cases wewould expect to see an excess of low-mass stars.Indeed, as shown in Figure 7, the MS-LF of ω Cen seemsto share the same shape as that observed in M22 and M55,but significant differences in the low-luminosity star con-tent are apparent with respect to M15 and NGC6397. Inparticular, while the overabundance of faint stars with re-spect to NGC6397 can be interpreted in terms of systematicevaporation of low-mass stars in the highly evolved clusterNGC6397, the difference with respect to M15 is much morepuzzling. Indeed, if the LF in ω Cen reflects the primordialLF of the cluster, the difference with respect to M15 could beinterpreted only in terms of a ”real” difference in the IMF.It is worth of noticing that other two clusters in the Piotto& Zoccali (1999) sample (M30 and M92) share the samebehaviour of M15, showing a significant overabundance offaint low-mass stars with respect to ω Cen. The slopes ofthe low-mass end of the MF derived in these clusters by Pi-otto & Zoccali (1999) ( α = − . , − . − . ω Cen ( α = − . F e/H ] ∼ −
2) than the mean metallicity of ω Cen([
F e/H ] ∼ − .
7, Suntzeff & Kraft 1996).This evidence might suggest that a ”primordial” dif- c (cid:13) , 1–8 Sollima et al. ference in the IMF of stellar systems as a function of themetallicity (i.e. metal poor clusters tend to produce morelow-mass stars) could exist. The physical reason for thismight be found in the higher efficiency of the fragmenta-tion process in low-metallicity proto-cluster clouds (see Silk1977). A possible dependence of the slope of the faint endof the clusters MFs on metallicity was also discussed andnot excluded by Piotto & Zoccali (1999). Note that a sim-ilar result was also presented by McClure et al. (1986) andDjorgovski, Piotto & Capaccioli (1993) from the analysis ofthe LF of several Galactic GCs.Clearly a deeper investigation is required to finally ad-dress this important question. However, the evidence pre-sented here supports the possibility that the MF measuredin ω Cen could be a reasonable approximation of the clusterIMF and that a variation of the IMF slope with the clustermetallicity could exist.
ACKNOWLEDGEMENTS
This research was supported by the Ministerodell’Istruzione, Universit`a e Ricerca and the AgenziaSpaziale Italiana. We warmly thank Paolo Montegriffo forassistance during catalogs cross-correlation. We also thankElena Pancino, Cristian Vignali and the anonymous refereefor their helpful comments and suggestions.
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LF of ω Cen measured in the ACS field I F W N obs N field φ N19.0 183 4 0.980 183.719.1 190 6 0.980 190.919.2 194 7 0.980 195.019.3 202 7 0.980 202.119.4 202 5 0.980 202.119.5 170 3 0.980 172.519.6 191 3 0.980 191.919.7 189 3 0.980 189.919.8 194 2 0.980 194.019.9 192 2 0.980 193.920.0 187 3 0.980 186.820.1 180 1 0.980 180.720.2 212 5 0.980 212.320.3 234 5 0.980 234.820.4 242 5 0.980 241.920.5 251 5 0.980 252.120.6 268 4 0.980 264.520.7 269 3 0.980 263.520.8 255 4 0.980 250.220.9 268 7 0.980 265.521.0 284 6 0.980 281.821.1 287 7 0.980 287.921.2 298 8 0.980 300.121.3 307 6 0.980 309.321.4 322 6 0.980 324.721.5 319 5 0.979 321.721.6 354 5 0.979 356.521.7 408 5 0.979 408.821.8 458 8 0.979 459.021.9 503 8 0.979 505.222.0 494 7 0.978 499.322.1 530 4 0.977 536.422.2 541 5 0.976 550.122.3 538 9 0.976 545.522.4 536 9 0.974 545.022.5 542 11 0.973 553.922.6 532 11 0.971 544.722.7 492 12 0.969 504.722.8 506 10 0.967 517.322.9 487 8 0.964 500.123.0 483 6 0.961 494.823.1 494 13 0.957 510.323.2 465 11 0.952 485.523.3 439 8 0.946 459.923.4 426 9 0.940 444.323.5 385 13 0.932 405.223.6 361 9 0.923 383.923.7 366 7 0.912 388.223.8 350 6 0.901 379.323.9 324 5 0.889 357.524.0 316 6 0.875 354.024.1 310 5 0.860 351.524.2 289 9 0.841 335.524.3 241 6 0.818 287.524.4 239 8 0.783 298.224.5 194 5 0.724 263.9c (cid:13)000