BARRIO MIRAFLORES
2.2.2. La Construcción Informal
We constructed the KLF of NGC 3603 applying all corrections previously mentioned, such as the field star decontamination based on the color-cut, and the incompleteness correction. Fig. 10.3 shows the KLF derived from 7514JHKSdetected stars inr≤11000. The NACO field ofr ≤1300
and the ISAAC field of 1300
< r≤11000
are used. A variable incompleteness correction depending on the radial distance is applied.
Here we note that, because of the highly crowded inner region and relatively sparse outer region, the variation of the incompleteness is so large across the field that de- termining a single representative completeness limit for the LF is not adequate. We therefore compute the 50 % completeness limits (at which 50% of the stars are detected in the images, and another 50% are added in the incompleteness correction) from two regions, an inner region atr ≤1300
from the NACO field, and an adjacent outer annulus at 1300
< r≤3000
from the ISAAC field. The resulting 50 % completeness limits in the both regions have coincidentally almost the same value of mJ ∼19.4 mag.
From that J-band limit we obtain aKS-band 50 % completeness limit of 17.4 mag, using the typical J −KS color of ∼ 2 mag for low-mass PMS stars in NGC 3603. The 50 % completeness limit is indicated by a vertical dashed line in the figure. Note that the completeness limit is an average limit for each region. Because of the strong spatial variation of the crowding, there are also strong variations of the 50 % limit. For example, the J-band completeness limit in the innermost r ≤ 200
is ∼ 15 mag and it increases sharply to ∼20.5 mag at 1000
< r≤1200 . At larger radii 3000< r
≤11000, the detection is not limited by crowding, but simply by the noise in the images. This detection limit is derived from a Monte Carlo simulation adding artificial sources (see Sect. 7.2). TheJ-band limiting magnitude is ∼20.5 mag, corresponding to aKS-band limit of 18.5 mag (indicated by a vertical dotted line in the figure). The power-law slope is computed for the magnitude range from 12 mag up to the 50 % completeness limit of mKS = 17.4 mag.
The LF shows a monotonous increase towards faint magnitude with a power-law index of α = 0.27±0.01. The nature of the flattening at the faint end of the LF at mKS ∼ 17.5−18 mag is not clear. As mentioned in Sect. 7.1 on the incompleteness
correction, we applied a maximum correction factor of 10, corresponding to a 10 % completeness limit. Any corrections beyond this factor is considered to be unreliable, and we can thus not conclude if the observed sign of flattening is a real feature or a result of the observational limitation.
For the sake of comparison of our LF with those in previous publications, we construct several LFs matching as good as possible the field of view.
For this comparison, we construct a KLF for the innermostr ≤3300
10.2. LF of NGC 3603
Figure 10.2: Comparison of KS-band LFs based on three different methods for the field star subtraction. Top panel: KLFs of the field population based on three different estimates. The black solid line indicates the KLF of the field population derived by the color-cut, the gray dashed line indicates the KLF derived from the outermost region (8000
< r ≤12000
) of the ISAAC field, and the gray solid line indicates the KLF extracted from N¨urnberger & Petr-Gotzens (2002). Bottom panel: Observed LF inKS- band (red histogram in Fig. 10.1) subtracted by the three field star KLFs from the top panel. The type and color of the lines indicate a subtraction of the according field LF in the top panel.
CHAPTER 10. LUMINOSITY FUNCTIONS OF NGC 3603
a field star correction derived from a population in an outer annulus of 7500 < r
≤10200, just like NPG02. Note that this outer annulus still contains cluster stars, and hence the derived field star population is most likely substantially overestimated. This effect is obvious from a direct comparison with the KLF derived from the 8000 < r
≤ 12000 region presented in Fig. 10.2. Fig. 10.4 shows the resulting LF. The power-law slope is derived from a fit in the range of 13 ≤ mKS ≤ 16. The power-law index is α = 0.29
for the incompleteness corrected LF (dash-dotted line in Fig. 10.4), and α = 0.26 for the uncorrected number counts (shown as a solid line; extrapolation shown as a dashed line). The according slope in the KLF from NPG02 is α = 0.23, fully consistent with our value (∆α = 0.03). In their study the authors also performed a comparison with a KLF presented in Brandl et al. (1999) (B+99). They found the two KLFs fairly similar except for the absolute number counts (see Fig. 11 therein). A similar discrepancy is found in the number counts of our KLF and the KLF from NPG02, which is attributed to the use of a more stringent detection threshold in NPG02 (see Sect. 10.2.3). We find a slightly higher number counts (× ∼1.5) than B+99 despite the fact that our ISAAC data is the same data set as B+99. This discrepancy is clearly due to the fact that we could resolve more sources in the crowded inner field (r ≤1300
) with our additional NACO data, which could not be detected in the seeing limited ISAAC data.
In summary we find the slope of our LF consistent with the previous works, but our higher angular resolution NACO data reveals ∼50 % more stars in the central r≤3300
10.2. LF of NGC 3603
Figure 10.3: KS-band luminosity function of NGC 3603. The figure shows the luminosity distribution derived from 7514 JHKS detected stars withinr ≤11000
which are classified as cluster members by the color-cut. The circles and squares show the distribution with and without applying the incompleteness correction. The vertical dashed line represents the 50 % completeness limit in the inner r ≤ 1300 part of the NACO field and the adjacent 13< r≤3000
annulus from the ISAAC field. The vertical dotted line indicates the detection limit in the outer ISAAC field derived in Sect. 7.2. The KS-band completeness limits have been calculated from theJ-band completeness limits assuming a typicalJ−KS color of 2 mag for low-mass PMS stars. The power-law index was measured in a magnitude range from about 12 mag up to the 50 % completeness limit ofmKS = 17.4 mag. The solid line illustrates the best-fit power-law slope.
CHAPTER 10. LUMINOSITY FUNCTIONS OF NGC 3603
Figure 10.4: Comparison of our KLF with previous studies. The plot shows the KLF within r ≤ 3300
. The number counts are corrected for a field population derived from an outer ring at 7700
< r ≤ 10200
. No incompleteness correction is applied to the plot. The solid line indicates a power-law fit for the range of 13 ≤ mKS ≤ 16, the
extrapolation is plotted as a dashed line. The dotted line indicates the best-fit power- law slope for the NPG02 KLF scaled to our number counts at 14 mag. The dash-dotted line shows the power-law slope for our incompleteness corrected number count.
Chapter 11
Initial mass functions of NGC
3603
In this chapter we present the analysis of the IMF of NGC 3603. We first explain the technique we have applied for the IMF determination. We then derive our best estimate of the IMF of NGC 3603 for the full field, and compare that with the IMFs of NGC 3603 reported in previous studies.
Subsequently we present the IMF as a function of distance from the cluster center using the NACO and ISAAC data. We investigate the observed radial trend in the IMF characteristics, and compare it with the results from other studies. In the section we also demonstrate the consistency between the IMFs derived from the NACO and ISAAC data, a prerequisite to safely interpret the observed radial variation of the IMF. The observed radial variation, which is a sign of the presence of a mass segregation, then leads us to investigate the dynamical evolutionary status of the cluster in the following chapters.
11.1
IMF determination
In our determination of the IMF we apply the preparatory treatments: the color-cut method to identify cluster members and the incompleteness correction. Note that, as demonstrated in the LF analysis in the previous chapter, combining the NACO and ISAAC data sets for a single IMF does not impose any systematic bias (see Sect. 10.2.1), and that the IMFs can be directly compared as long as the mass range is carefully chosen.
Fig. 11.1 shows the resulting IMF of the whole field out to r ∼ 11000
(innermost r ≤ 1300
from NACO, the outer field at 1300
< r ≤ 11000
from ISAAC). It is derived from the 7514 stars which are simultaneously detected inJHKS and classified as cluster members based on the color-cut criterion. To compute the stellar masses, we used the combined luminosity-mass relation created from the 3 Myr MS, 0.7 Myr PMS, and 1 Myr low-mass PMS isochrones (see Sect. 8.1.2). All J, H, and KS magnitudes were used to determine the best-fit stellar mass. The number of stars in a logarithmic mass intervals with ∆ logM= 0.2 were calculated. Note that we have used a double size bin at around 4 M to smooth out a discontinuity arose from connecting the MS and PMS isochrones.
As mentioned in Chap. 11, the IMF is generally described by a power-law for masses down to about 1 M, then by a slightly shallower power-law below, thus it can be