THE LOW-MASS INITIAL MASS FUNCTION IN THE 30 DORADUS STARBURST CLUSTER

We have obtained HST/NICMOS Camera 2 images through the F160W band of the central 56'' × 57'' region around R136 in the 30 Dor cluster (HST program ID 7370). The observations were centered on the cluster (R.A., decl.) = (05:38:43.3, −69:06:08) and on two adjacent control fields centered on (05:38:42.4,−68:52:00), and (05:38:56.9,−68:52:00). The observing dates were 1997 October 14 and 16. The field of view of the 256 × 256 pixel NICMOS Camera 2 is 19'' × 19'' with a pixel scale of 0075, resulting in Nyquist sampling of diffraction-limited F160W band data. Each position in a 3 × 3 mosaic centered on R136 was observed 4 times with small dithers of ∼16 pixels. The data were obtained in non-destructive MULTIACCUM mode such that the photometry of the bright stars can be retrieved due to the first short integration in each exposure. The integration time for each dither position was 896 s, resulting in a total integration time of 3584 s for each position in the mosaic. The two control fields were observed in a similar manner.

The location of the mosaic is shown in Figure 1 and the NICMOS mosaic is shown in Figure 2. The faintest stars visible with the stretch used here have an F160W magnitude of ∼21.5 mag, corresponding to a mass of 0.8 M_☉, based on the pre-main sequence models of Siess et al. (2000), adopting an age of 3 Myr (Hunter et al. 1995), half solar metallicity, and an extinction of A_V = 1.85 mag (see Section 3.2). For comparison, the similar detection limit in an uncrowded environment without nebulosity would be ∼23.5 mag according to the NICMOS exposure time calculator.

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Each individual image was processed through the calnica and calnicb pipelines as well as the biaseq and pedsky procedures within the IRAF environment. The tasks are described in detail in the NICMOS Data Handbook. We used synthetic dark frames and flat fields created for the appropriate instrument temperature at each exposure. The biaseq task corrects differences in bias levels for each chip between different sub-exposures. The pedsky task corrects differences in the bias level for each quadrant of the chip when the array is reset before the exposure. The data for each position in the mosaic were combined using the drizzle task. The reduced pixel size (00375) was chosen as half the detector pixel size. Bad pixels, bad columns, and the coronagraphic hole were flagged as bad pixels before the images were combined.

Source detection was done using daofind and photometry was performed via point-spread function (PSF) photometry utilizing allstar within the IRAF environment. It was difficult to obtain a good PSF model from the data due to the high degree of crowding and the spatial variability of the PSF. Instead, the TINYTIM software (Hook & Krist 1997) was used to create a synthetic PSF. TINYTIM allows to create a PSF that varies as a function of the location on the array. The source detection and photometry was performed on each individual position in the mosaic due to the linearly varying PSF. A hot template star (O5V) was used for the spectral energy distribution in order to achieve the best fit for the brightest stars to limit their residuals. The TINYTIM PSF was created for five different positions on the NICMOS Camera 2 array and the PSFs were placed in an empty frame with the same number of pixels as the NICMOS Camera 2 array. four frames were created with offsets between each PSF identical to the offsets used for the science data in order to replicate the data as closely as possible. The four PSF frames were then combined using drizzle together in the same manner as the science data and a linearly varying PSF was created from the drizzled frame.

Source detection is complicated due to the diffraction features present in NICMOS data. Adoption of a low threshold for source detection led to numerous diffraction spots from bright stars being erroneously identified as fainter stars. Instead the source detection was done in the following way in order to limit false detections. We first detected the brightest stars (brighter than 1000σ) in each frame and used allstar to remove these with the synthetic PSF. A search for fainter stars (brighter than 500σ) was then performed in the frame with the bright stars removed. Since the removal of the brightest stars also removed the diffraction pattern associated with them, we did not detect the diffraction spots as stars. The two star lists (the brightest stars and the fainter stars) were joined into one and these stars were removed from the original frame, again using allstar. Fainter stars are then found from the frame with the already detected stars removed. This process was iterated until stars at 10σ peak pixel intensity over the background were detected and removed. The frame with the stars removed was then ring-median filtered to remove stellar residuals but to retain the large-scale nebulosity in each frame. The median-filtered image was then removed from the original frame and the star detection process was repeated in this frame but now continued to a detection threshold of 5σ. A 5σ instead of, e.g., a 3σ threshold was selected to limit the risks of false detections due to noise spikes. We finally made sure by visual inspection that every detection indeed was a point source and that it was not a spurious detection due to the diffraction spikes and spots from bright stars.

The main interest here is in the low-mass (faint) stellar content in R136 and one concern is the detection of residuals from the bright stars as false stellar objects. Some false sources were detected by daofind but are rejected during the PSF fitting routine. A few remained from the brightest stars. They typically produced at most a few false detections in the diffraction spikes that were ∼6–7 mag fainter than the bright source. We removed these detections together with other false detection through the visual inspection of all sources. We have further utilized the artificial star experiments described below to examine how many detections are false due to the residuals from bright stars. We had only false positives associated with the brightest artificial stars (F160W < 12 mag). For artificial stars fainter than F160W ∼14 mag, no false detections were present. The false detections for the bright stars were located at the diffraction spikes and would have been identified in the manual inspection of the source list.

We found a total of 10,108 uniquely detected sources with a formal error smaller than 0.1 mag and brighter than F160W = 22.5 mag in the nine frames. Below this magnitude limit the incompleteness is substantial, as discussed below. Table 1 presents the list of detected stars.

The effects of crowding were examined by placing artificial stars in the individual frames using the PSF created from the synthetic TINYTIM PSF. The artificial stars followed a luminosity function (LF) with a similar slope to that of the observed stars (see Section 3) but with a surface density 10% that of the detected number of stars to avoid affecting the crowding characteristics of the real stars. We performed 100 artificial star experiments for each frame, for a total of 10 times more artificial stars than real stars. Figure 3 shows the resulting recovery fractions as a function of the input magnitudes for several annuli around the cluster center. The difference of the size of the error bars as a function of distance from the cluster center is due to a lower number of artificial stars placed in the central parts of the cluster. This is a consequence of adding 10% artificial stars relative to observed stars in each artificial star experiment and the relative number of stars in each annulus. The IMF is not determined in regions with this low completeness. We are mainly interested in the low-mass stellar content of the cluster, which is below the 50% completeness in the central parts. The uncertainty in the completeness corrections for the inner parts of the cluster will therefore not affect the conclusions drawn for the stellar populations further out.

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The completeness is a strong function of the radial distance from the center. For the outer regions of the cluster, 50% or more of the stars brighter than F160W = 21.5 mag are detected, whereas only the very brightest stars are detected in the innermost region. In an annulus at 0.6–1 pc radius from the center, we detect 50% or more of the stars brighter than F160W = 18.0 mag. Adopting the PMS models of Siess et al. (2000) and the main sequence models of Marigo et al. (2008), F160W = 21.5 mag corresponds to a 0.8 M_☉, half solar metallicity, 3 Myr old object, whereas F160W = 18 mag corresponds to a 7.5 M_☉ star, assuming an extinction of A_V = 1.85 mag in both cases.

We have investigated the accuracy of the derived photometry by using the stars detected in the overlap regions of several fields. Figure 4 shows the difference in derived magnitude for stars detected in the overlap regions of the mosaic. Dots denote stars outside a 2 pc radius and plus signs denote stars between 1.25 and 2 pc radius, respectively.

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The F160W band photometry has been compared with the ground-based H-band photometry obtained using adaptive optics observations by Brandl et al. (1996). Figure 4 shows the magnitude difference between the adaptive optics photometry and this study based on 829 stars common to both data sets. Stars were considered detected in both data sets if the spatial position coincided within 2.5 drizzled pixels, corresponding to 0094. Some scatter is present between the two data sets, especially for the fainter stars. However, the median difference between the magnitudes derived for the two data sets is less than 6% for objects F160W <18 mag. We have in the following treated the F160W observations as a standard Cousins H band.

Conversely, there appears to be a tendency for the fainter stars to be brighter in the F160W data than in the H-band data of Brandl et al. (1996). The tendency for the fainter stars to be skewed toward fainter H-band magnitudes is an effect also seen in other comparisons between HST/NICMOS and AO data (e.g., Stolte et al. 2002) who suggest it is due to the extended halos present in AO observations around bright stars.

The star counts in the central 0.6 pc radius region are heavily affected by low number statistics, crowding even for the brightest stars, and relatively uncertain incompleteness corrections. We therefore focus on the sources outside 0.6 pc in this paper. Figure 5 shows the F160W band LFs for the 0.6–7 pc radius region of the 30 Dor cluster divided into several radial bins to show the difference in photometric depth due to crowding. Overplotted are the completeness-corrected LFs, where each bin has been divided by the corresponding recovery fraction from the artificial star experiments.

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The completeness–corrected LFs are relatively smooth and have been fitted with power laws down to the 50% completeness limit. The derived slopes with their 1σ uncertainties and the 50% completeness limits are presented in Table 2. Although the slope in the inner annulus is found to be more shallow, the derived slopes are consistent with each other within 2σ with an average slope of 0.31 and the shallow slope is not significant.

The completeness-corrected combined histogram for the stars detected in the two off-cluster control fields is shown in the lower right panel in Figure 5. From the histogram, it can be seen that the field star contamination found from the star counts is ≈10%–15% for the faintest stars in the 5–7 pc annulus and less closer to the center as well as for brighter stars. Although the contamination of field stars is found to be relatively small it is not negligible and they are therefore statistically subtracted from the cluster population in the following analysis (Section 4).

Next, the F160W band photometry is combined with the optical data presented by Hunter et al. (1995). A star was considered detected in both surveys if the spatial position agreed within 2.5 drizzled NICMOS Camera 2 pixels (0094). In the cases where two optical stars were located within the search radius of the star detected in the NICMOS Camera 2 observations, the brightest star was chosen as the match.

We find in total 2680 in common with the Hunter et al. (1995) survey that detected 3623 stars the inner 35'' of the cluster. 1848 of those sources have a combined formal photometric error in the F555W–F160W color of less than 0.1 mag. Within the area covered by Hunter et al. (1995) we detect a total of 5095 sources. Most of the stars detected by the NICMOS survey but not the WFPC2 observations are fainter than F160W = 20 mag. Assuming an object age of 3 Myr and an average extinction of A_V = 1.85 mag (see below), the similar object would have a magnitude in the F814W band of ∼22 mag. For objects with more extinction, they will be even harder to detect in the F814W band. Hunter et al. (1995) essentially do not detect any stars within a 1 pc radius at this magnitude or fainter. Only 1 in 4 stars in the magnitude interval F814W = 21–22 mag was detected outside 1 pc. It is thus not surprising that a significant population of faint stars are detected in the NICMOS survey relative to the WFPC2 survey. Nevertheless, the lower spatial resolution of the NICMOS observations results in a low recovery fraction at these magnitudes in the central few pc of the cluster.

The majority of the sources not detected in the NICMOS survey but at optical wavelengths are located within a radius of 1 pc. The lack of detection is due to the lower spatial resolution in this study relative to the optical HST data. The resolution is almost a factor of 2 better in the F814W band than in the F160W band. Sources not detected in the NICMOS data outside 1 pc are mainly due to crowding as well. Indeed, visual inspection of the location of the stars detected in the optical but not near-infrared shows that they are often located either very close to the core or on the first Airy ring of a bright source.

The F555W–F160W versus F160W color–magnitude diagram is shown in Figure 6. Overplotted are a 3 Myr isochrone for the high-mass stars adopted from the Marigo et al. (2008) models and 2, 3, and 4 Myr isochrones adopted from Siess et al. (2000) for stars below 7 M_☉. The stars above 7 M_☉ and up to the maximum mass we fit the IMF in Section 4.1 (20 M_☉) are all expected to be on the main sequence. Both isochrones were calculated adopting a metallicity of half the solar value, typical for the LMC (Smith 1999). The two isochrones have a small offset in both the V (0.06 mag) and H (0.07 mag) bands. We have forced the Marigo et al. (2008) isochrone to match the Siess et al. (2000) isochrone at 7 M_☉.

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It is evident that there is a significant scatter in the color–magnitude diagram. The scatter is likely due to a combination of binary systems (both physical and chance alignments), differential extinction, photometric errors, and a possible age spread. The median extinction is found for the main sequence part of the isochrone. For objects in the range 7–20 M_☉, we find a median extinction of A_V = 1.85 mag which is slightly higher than the reddening found by Selman et al. (1999) in the inner part of the 30 Dor region.

At masses below 7 M_☉, the spread in the color–magnitude diagram is larger but almost exclusively extends to the red part of the diagram. This indicates the lower mass objects on average have an excess amount of extinction relative to the higher mass objects. Selman et al. (1999) observed stars more massive than 10 M_☉ and would not detect the additional reddening for the lower mass sources. The possible sources for the additional reddening is described in Section 3.3.

We have estimated an average age for the cluster by utilizing the fact the isochrone is almost horizontal in the color range F555W–F160W = 1.5–2.5 mag and around F160W ∼ 19 mag. The median F160W magnitude is 19.0 mag in this region of the color–magnitude diagram. Adopting an average extinction of A_V = 1.85 mag, this corresponds to the F160W magnitudes of the 3 Myr isochrone in the same color range. We have thus adopted 3 Myr as the mean age of the low mass cluster population and a 3 Myr isochrone is adopted to create a mass–luminosity relation in order to turn the luminosities into masses for objects below 7 M_☉ and the 3 Myr Marigo et al. (2008) isochrone above. We will in Section 4 discuss the effects on the derived IMF when an age spread of 2 Myr is adopted.

The right-hand panel in Figure 6 shows the I–F160W versus F160W color–magnitude diagram. It is evident that the clustering around the isochrone is tighter than for the V–F160W versus F160W color–magnitude diagram. This is expected if a large part of the scatter is due to differential extinction. We can calculate the scatter around the main sequence in both color–magnitude diagrams and compare with the difference predicted from extinction.

If the spread in the color–magnitude diagrams is due to extinction we expect the ratio of spread in the V–F160W versus F160W diagram to be the ratio of the extinction in each color, i.e., (1 − 0.192)/(0.62 − 0.192) = 1.88 times larger than in the I–F160W versus F160W color–magnitude diagram. Since the isochrone is almost vertical in both diagrams, we have calculated the standard deviation around the reddened isochrone in both color–magnitude diagrams. We have used the stars with good photometry, better than 5% in each filter, and in the magnitude range 13 mag < F160W < 17 mag. The standard deviation found for the V–F160W and I–F160W color–magnitude diagrams are 0.60 mag, and 0.36 mag and the ratio is 1.7. If the measurement errors are taken into account this ratio increases. The typical errors for the culled sample are 0.04, 0.02, and 0.03 mag for the V, I, and F160W bands, respectively. After taking the measurement errors into account, the ratio is found to be 1.9, assuming the measurement errors in two filters are independent. Due to blending, this is not necessarily the case. Thus, 1.9 is an upper limit and we thus find the ratio to be between 1.7 and 1.9, in agreement with the scatter being due to differential extinction.

Since the amount of differential extinction does not affect the F160W band photometry significantly, the single band photometry presented here is competitive with the 2-band optical photometry. There is a unique translation from the F160W band magnitude to the object mass for the majority of the mass range. For the optical photometry, the color information is used to determine the extinction and the mass function is thus effectively determined by the de-reddened V-band magnitude.

The main advantage of the optical relative to the near-infrared HST photometry is the improved resolution due to the smaller diffraction limit. The stellar content can therefore be resolved to lower masses closer to the cluster core than is possible with the near-infrared observations. However, phenomena associated with the star formation process can introduce additional reddening that can complicate the derivation of the low-mass IMF from optical data. The low-mass objects may still be associated with a circumstellar disk. There is evidence from, e.g., the Orion Nebula Cluster that circumstellar disks can survive the UV radiation from massive stars (Robberto et al. 2004). Even if the disks are being evaporated by the ration field from the early-type stars, the evaporated material will be a further source of reddening. Patchy extinction associated with the 30 Dor complex and located in the foreground of R 136 will be an additional source of differential reddening. There are signs in the optical images presented in Figure 1 of Sirianni et al. (2000) of patches of extinction, e.g., to the east–north–east of the cluster center. If variable extinction is present or if a significant fraction of the stars are associated with disks or outflows, an extinction limited sample has to be created in order to avoid biases against detection of the low-mass stars.

The near-infrared photometry is effected by differential extinction as well but the effect is less than 20% of that measured in the V band. Thus, whereas the IMF derived from optical observations where an extinction limited sample is not defined might be severely affected for the low-mass objects, the effect on near-infrared observations is modest. Therefore, in the outer parts of the cluster where crowding is a smaller issue than closer to the center, the near-infrared observations are more suitable to detect and characterize the low-mass stellar population in the cluster.

On the other hand, single-band photometry has the disadvantage that there is no information on the age of individual objects. We investigate in the following section how this might affect the derived IMF. We note that if differential extinction is present, the situation is no better for the optical photometry. Even though the cluster was observed through two filters in the optical, there is still a degeneracy between age and extinction. Sirianni et al. (2000) converted the V–i photometry into an effective temperature and used that effective temperature to obtain a bolometric correction. Without de-reddening the sources, the age of a cluster member can be in error and hence the mass estimates will be uncertain.

A mass–luminosity relation is needed to convert the derived F160W band magnitude for each star to a mass. We use the Siess et al. (2000) isochrones for stars below 7 M_☉ and the Marigo et al. (2008) 3 Myr isochrone for the more massive stars as discussed in Section 3.2. The age of the cluster is first assumed to be 3 Myr and is later varied to examine the effects on the derived IMF for different cluster ages. Stars below ∼3 M_☉ are on the pre-main sequence isochrone, whereas the more massive stars up to our upper mass limit of 20 M_☉ (see below) are on the main sequence. The adopted mass–luminosity relation is shown in Figure 7.

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We have limited knowledge of the extinction for the majority of our objects. Instead, we have adopted an average extinction of A_V = 1.85 mag, as determined from the V–H versus H color–magnitude diagram in Figure 6. Since the amount of extinction ranges between A_V = 0.7–3 mag (Brandl et al. 1996) the extinction for an individual object might be wrong by up to A_V ∼ 1 mag, a maximum error <0.2 mag in the F160W band. This corresponds to an error of ∼10% when the luminosity is transformed into a mass.

Figure 8 shows the derived mass functions outside 0.6 pc for a 3 Myr isochrone after field stars have been subtracted statistically in each annulus. The mass functions are in general smooth and well fit by power laws. However, there appears to be some structure in the derived IMFs at intermediate masses, 2–4 M_☉, which is the region where the pre-main sequence track joins the main sequence. The mass–luminosity relation is plagued by a non-monotonous feature at this mass range (see Figure 7), which marks the radiative-convective gap (Mayne et al. 2007) and the transition region from pre-main sequence to main sequence (see also Stolte et al. 2004). A similar structure in the derived IMF is seen in the results from, e.g., NGC 3603 but at a slightly higher mass since the cluster is younger (e.g., Stolte et al. 2006). The turn-on mass is higher for a younger cluster. Thus, we would expect the kink in the mass–luminosity relation to move to higher masses for a younger cluster. Since this is what is seen comparing NGC 3603 and R 136, it indicates indeed a feature of the isochrones and not a feature intrinsic to the cluster. The number of stars in each mass bin is provided in Table 3.

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Power laws have been fitted to each of the histograms in order to derive the slopes of the mass function in each annulus. The fit was done over the mass range from 20 M_☉ down to the 50% completeness limit for each annulus. The mass for stars above ∼20 M_☉ is very poorly constrained from near-infrared observations due to uncertainties in the bolometric corrections (e.g., Massey 2003). The derived slopes Γ, where dN/dlog M ∝ M^Γ, are indicated in Figure 8 and are also presented in Table 4. The derived slopes for annuli outside 1 pc are consistent with each other within 2σ error bars. For the 3–5 pc and 5–7 pc annuli where the data are complete to below 2 M_☉, the slopes are found to be −1.2 ± 0.1 and −0.9 ± 0.2, respectively, slightly shallower than the slope of Γ = −1.28 ±  0.05 derived by Sirianni et al. (2000) above 2 M_☉, except that in our case the IMF continues as a power law down to 0.8 M_☉.

Has the fact that we used the whole mass range for our power-law fit washed out a possible flattening at the low mass end? To test this possibility, we have additionally fitted a separate power law to the low-mass part of the IMF. Only the part of the mass function that is not influenced by the kink in the mass–luminosity relation is used. This region is limited to masses below 1.7 M_☉ for the 3 Myr isochrone. It is therefore only for the 5–7 pc annulus that a reasonable mass range is covered to fit the IMF. We find the slope to be Γ = −0.9 ± 0.2, which is more shallow but consistent at the 2σ level with a Salpeter IMF and is consistent with the slope derived for the full mass range.

We have derived the IMF in the same boxes as done by Sirianni et al. (2000). The completeness correction was calculated independently for each box before the IMFs were combined to the average IMF for direct comparison with the IMF presented by Sirianni et al. (2000). The 50% completeness limit for the NICMOS data varies from 2.8 to 1.4 M_☉ for the four boxes. Following Sirianni et al., we have derived an average completeness limit for the three regions of 2.2 M_☉. As evident, the agreement is good for the common mass range. We appear to underestimate the stars at ∼6 M_☉ compared to Sirianni et al. (2000). However those appear to be recovered at 8 M_☉.

The color–magnitude diagrams show a large spread in the main sequence to pre-main sequence transition at F160W = 18–19 mag. Although shown in Section 3.2 that this scatter can be explained by differential extinction, it cannot be ruled out that there is an age spread present as well as suggested in previous studies (Hunter et al. 1995; Massey & Hunter 1998). It is therefore reasonable to take a star formation history different than a single burst at 3 Myr into account. We show in Figure 9 the IMF in the outer two annuli assuming a cluster age of 2 and 4 Myr, respectively. We also show an "average" IMF found as the average of the IMF's derived for the age range 2–4 Myr in 0.5 Myr increments. The lower mass limit in the average IMF was determined from the 4 Myr isochrone which provides the most restrictive mass limit. We find that both in the case of a 2 and 4 Myr isochrone the IMF is well fit by power laws. The derived slopes are steeper assuming an older isochrone relative to the younger ones. There is no indication for a flattening below 2 M_☉ in either case. The average IMF is also found to be represented by a power law with a slope consistent with a Salpeter slope. The slopes of the derived power laws are given in Table 4. For the average IMF, the number of stars averaged over the different ages in each mass bin is derived. Error bars for the average IMF have been determined as the standard deviation around the mean number of objects in each mass bin.

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As was the case for the 3 Myr isochrone, the slopes of the IMF for different assumed ages have also been calculated and are provided in Table 4. The slopes are found to be shallower than a Salpeter slope, but at the ∼2σ level consistent with a Salpeter slope. The slopes are also consistent with those derived for all masses up to 20 M_☉, as was the case assuming the 3 Myr isochrone.

The lack of a flattening in the IMF below 2 M_☉ is in contrast to the results presented by Sirianni et al. (2000), who derived the IMF closer to the cluster center. There can be several possible reasons for the difference in the derived IMF slope in the two surveys. First, due to the different spatial resolution in the two studies, the NICMOS IMF is derived further away from the center of the cluster than the WFPC2 IMF by Sirianni et al. (2000). The IMF was derived in the areas shown in Figure 2 as regions B,C, and D. Thus, all of their surveyed area is outside a radius of 1 pc and the majority of their surveyed area is between 2 and 5 pc where crowding precludes NICMOS from detecting stars less massive than 2.2 M_☉ for a 3 Myr isochrone. One possibility for the difference in the derived slopes for the NICMOS and WFPC2 data can therefore be a variation of the IMF as a function of radius. Another possible reason can be differential extinction as suggested by Selman et al. (1999). Both possibilities are discussed in Sections 4.2 and 4.3.

As was suggested by Selman et al. (1999), the presence of differential extinction can potentially alter the low-mass end of the IMF if an extinction-limited sample is not used. In order to estimate the possible effect on the IMF if differential extinction is not taken into account, we have constructed a simple model of the cluster which includes differential extinction and the depth of the data set from Sirianni et al. (2000). A Salpeter slope IMF and a cluster age of 3 Myr were assumed. Each object within the artificial cluster was assigned a V-band magnitude based on its mass from the 3 Myr isochrone computed for a half solar metallicity by Siess et al. (2000). The objects were then reddened by a foreground extinction chosen randomly from a normal distribution with a standard deviation of 0.7 and shifted to peak at A_V = 1.85 mag. If the extinction was found to be less than A_V = 0.7 mag, a new extinction was calculated. Stars were then considered detected if their reddened magnitude is within the 50% completeness limit presented by Sirianni et al. (2000). The model is obviously an oversimplification of the real situation. Nevertheless, it is expected to illustrate how the derived IMF might differ from the underlying IMF.

Figure 10 shows the input Salpeter IMF (solid line), the derived IMF (dashed line) together with the measurements by Sirianni et al. (2000). The model mimics a flattening in the observed IMF similar to that deduced by Sirianni et al. (2000). The ratio of the number of stars below and above 2 M_☉ respectively has been calculated both for the model cluster and the data from Sirianni et al. (2000). For the model cluster it is found to be 0.87, which is in reasonable agreement with the ratio of 0.76 derived from the observations.

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Another explanation for the difference between the results obtained here and the results by Sirianni et al. (2000) can be mass segregation. We have searched for evidence for mass segregation in the two outer annuli in our survey. We used the LFs instead of the mass functions to avoid additional uncertainties due to the mass–luminosity relation. The results obtained for the mass functions are very similar to those from the LFs.

The cumulative luminosity distributions are shown in Figure 11 for the outer two radial bins. These are the only bins where the 50% completeness limit is below 2 M_☉. The two cumulative distributions are very similar. We have performed a Kolmogorov–Smirnov test to quantify the similarity of the cumulative luminosity distributions. The maximum difference between the two distributions is 0.039 and the probability for the two distributions to be drawn from the same parent distribution is 10%. Thus, there is no strong evidence (less than 2σ) for mass segregation in the outer parts of the cluster.

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The fact that there is little evidence for mass segregation outside 3 pc does not exclude the possibility that the cluster is mass segregated out to a radius of several pc. Both Malumuth & Heap (1994) and Brandl et al. (1996) found evidence for mass segregation of the massive stars in the center of the cluster. Brandl et al. (1996) showed the half-mass relaxation time to be 7.8 × 10⁷ yr, much longer than the cluster age. They also point out that the massive stars will experience mass segregation on a much shorter timescale than the lower mass stars; the timescale depends inversely on the stellar mass. It is thus not surprising, from a dynamical point of view, that there is no evidence for mass segregation outside the half-mass radius of 1.7 pc (Hunter et al. 1995).

On the other hand, this does not rule out the possibility that the cluster might be mass segregated at birth closer to the cluster center. Evidence for mass segregation has been found in, e.g., the Orion Nebula Cluster (ONC; Hillenbrand & Hartmann 1998; Bonnell & Davies 1998). Hillenbrand & Hartmann (1998) showed evidence for mass segregation down to stellar masses of 1–2 M_☉. Due to the youth of the ONC, they concluded the mass segregation had to be at least partly primordial. It is thus possible that R136 is also affected by primordial mass segregation close to the cluster center and that mass segregation is the reason for the difference between the NICMOS and WFPC2 IMFs.

We can obtain a rough estimate of the cluster mass from the near-infrared observations. The main limitation in our mass estimate is the amount of confusion due to crowding in the cluster center: our data mainly sample the IMF down to and below 1.4 M_☉ outside 3 pc. Nevertheless, we can utilize the mass estimates within 2 pc from Hunter et al. (1995) to complement our mass estimate down to 2.1 M_☉. Inside 2 pc and into 0.15 pc, the results are extrapolated from the local completeness limit mass down to 2.1 M_☉ assuming an underlying Salpeter IMF. No stars have been detected less massive than 20 M_☉ within the central 0.15 pc radius due to crowding. The mass in the very center has been estimated from the surface density profile down to 2.8 M_☉ in Hunter et al. (1995) to be 4 × 10⁴ M_☉ pc⁻², resulting in a mass of 3700 M_☉ down to a lower mass limit of 2.1 M_☉. We find the cluster total mass down to 2.1 M_☉ to be 5 × 10⁴ M_☉. The directly determined mass down to 2.8 M_☉ within 4.7 pc is found to be 2.0 × 10⁴ M_☉, almost the same as found by Hunter et al. (1995). If the IMF follows a Salpeter slope down to 0.5 M_☉ as observed in the Galactic field and nearby lower mass clusters (Kroupa 2002), the total mass in the central region would be roughly double the amount given above, and the total cluster mass would be close to ∼10⁵ M_☉.

The velocity dispersion, and hence the dynamical mass, of the whole NGC 2070 region, including R 136 has been determined by Bosch et al. (2009). The dynamical mass was determined to be 4.5 × 10⁵ M_☉, almost 5 times higher than expected for R 136 alone, but consistent with the photometric mass for the same area (Selman et al. 1999). If we take into account that the half mass radius of R 136 is 1.7 pc (Hunter et al. 1995), compared to 14 pc for the whole NGC 2070 region and assuming the velocity dispersion is the same in the inner parts of the cluster, we would expect a dynamical mass of 4.5 × 10⁵ × 1.7/14 M_☉ = 5.5 × 10⁴ M_☉ which is lower than the mass expected if the IMF is consistent with a Galactic IMF down to 0.5 M_☉. Thus, at face value, the velocity dispersion would be low enough that the cluster can stay bound. However, a measurement of the velocity dispersion for the inner regions is necessary to directly compare the photometric mass with the dynamical mass.

We can directly derive the surface brightness profile of the region around R136 in the 30 Dor cluster since the data do not suffer from saturated stars. Although bright stars will saturate through the 1 hr exposure, the non-destructive readout mode ensures that only the first reads are used to derive the magnitude of the brightest stars. The surface brightness profile is shown in Figure 12.

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Between ∼0.2 and 2 pc, the light profile is well fit by a power law, whereas inside 0.2 pc the light profile appears to be flattening. We have therefore fitted the light profile with a power law modified by a core radius, similar to the approach in Elson et al. (1987). Constraining the fit to inside 2 pc, we find a slope of −1.54 ± 0.02, slightly more shallow than −1.72 ± 0.06 derived outside 0.1 pc by Campbell et al. (1992) using F336W Planetary Camera onboard HST observations.

The core radius is found to be 0.025 ± 0.004 pc, which is less than the resolution of the observations and is thus likely and upper limit. Previous HST optical studies determined a small core radius, r_c ⩽ 0.02 pc (Hunter et al. 1995), consistent with our findings here. However, since the derived core radius is smaller than the resolution of the observations, its evidence is weak. One or two bright stars off center by only a small amount could mimic a cluster core.

How does the low-mass end of the IMF in 30 Dor compare with that determined for other massive and dense stellar clusters? A top-heavy IMF in massive dense clusters has been suggested on theoretical grounds (e.g., Silk 1995). The most convincing example of a young cluster with a present-day mass function departing significantly from a Salpeter IMF above 1 M_☉ is the Arches cluster (Stolte et al. 2002; Figer et al. 1999). Stolte et al. (2002) found an average slope of Γ = −0.9 ± 0.15 for the central parsec of the Arches cluster, flatter than a Salpeter slope of −1.35. Deeper observations found that the present day mass function in Arches to be well approximated by a power law with a slope of Γ = −0.91 ± 0.08 down to 1.3 M_☉ (Kim et al. 2006). However, recent work taking differential extinction into account suggests the slope of the power law is only slightly more shallow than a Salpeter slope, Γ = −1.1 ± 0.2 (Espinoza et al. 2009). Portegies Zwart et al. (2002) noted that even if the observed IMF is slightly flatter than Salpeter IMF, this can be explained by mass segregation. The mass segregation would be accelerated in the cluster due to the strong gravitational field from the Galactic Center. By adopting realistic parameters for a model cluster and an appropriate distance from the Galactic center, they found that an input Salpeter slope IMF would be transformed to the observed present day mass function via strong dynamical evolution. Stolte et al. (2006) showed that the IMF of the cluster powering the NGC 3603 H ii region was well fitted by a power law but with a slope flatter than Salpeter, Γ = −0.91 ± 0.15. They further showed evidence for mass segregation for the more massive stars, M >4 M_☉. The data indicated a slight flattening of the low-mass content (M < 3 M_☉). NGC 3603 is younger than the Arches cluster and not affected by a strong tidal gravitational field. Thus, it is expected to be less influenced by dynamical mass segregation.

The even more massive starburst clusters appear to be the primary sites (unit cells) of star formation in starburst galaxies, including interacting/colliding galaxies such as The Antennae or The Cartwheel. If starburst clusters are the basic building blocks of certain star-forming galaxies, their stellar content (IMF) will affect much of the observed chemical and photometric evolution of galaxies, both at the present epoch and perhaps even more so in the high-redshift past (Charlot et al. 1993). Several observational claims have been made that the IMF in unresolved starburst clusters is top heavy (Rieke et al. 1993), although observations of the Antennae gave a mixed result (Mengel et al. 2002). However, it has been suggested that the high mass-to-light ratios found in some young starburst clusters are artificially high related to their not being in virial equilibrium due to gas expulsion from the clusters (Goodwin & Bastian 2006). During the first 50 Myr of the cluster, the velocity dispersion and hence the cluster mass might be overestimated if the cluster is assumed to be virialized. Goodwin & Bastian (2006) suggested that the top-heavy IMFs inferred in young unresolved extragalactic star clusters might be spurious due to their non-virialized dynamical state.

With the present data set it is clear that the IMF in the outer parts of R136 continues as a power law down to 1 M_☉, similar to what is found in other star clusters and the slope is similar to what is found in the field. Whether this is true for the cluster as a whole depends on the cause for the flattening observed closer to the cluster center. It would be interesting to know the IMF if the observations could be extended closer to the characteristic mass where the Galactic field star IMF flattens (0.5M_☉; Kroupa 2002), a mass that can be reached in massive young clusters (⩽ 4 Myr) in the LMC with AO systems.

It has long been suggested R136 might be a proto-globular cluster (Meylan 1993; Larson 1993). The question has been whether R136 would remain bound over a Hubble time. One consequence of a top-heavy IMF is that the cluster would dissolve soon after gas expulsion and mass loss due to evolution of the high-mass stars. However, the detection of stars in R136 less massive than 1 M_☉ gives the first direct evidence that low–mass stars are formed in a starburst cluster. The fact that the IMF in the outer parts of R136 appears to be a Salpeter IMF down to at least 1 M_☉ gives support to the notion the cluster might be a proto-globular cluster, albeit a light one. Early gas expulsion and subsequent mass loss through stellar evolution will disrupt star clusters deficient in low–mass stars during the first 5 Gyr of the clusters life (Chernoff & Weinberg 1990; Goodwin 1997) However, a determination of the velocity dispersion in the inner parts of the cluster is necessary to determine its final fate. Thus, the presence of low-mass stars is a necessary, but not sufficient condition for the possibility of the cluster to evolve into a globular cluster. The median mass of Galactic globular clusters is 8.1 × 10⁴ M_☉ (Mandushev et al. 1991), comparable to the mass of R136. Even if R 136 will remain bound it will lose some mass and might end up as a low-mass globular cluster.