THE ANTENNAE GALAXIES (NGC 4038/4039) REVISITED: ADVANCED CAMERA FOR SURVEYS AND NICMOS OBSERVATIONS OF A PROTOTYPICAL MERGER^*

Observations of the main bodies of NGC 4038/39 were made with the Hubble Space Telescope (HST), using the ACS, as part of Program GO-10188. Multi-band photometry was obtained in the following optical broadband filters: F435W (≈B), F550M (≈V), and F814W (≈I). Observations in V were made using the medium-width filter F550M rather than the more widely used broadband filter F555W to minimize possible contamination from [O iii] and other nebular emission lines. Additional observations were made using the narrowband filter F658N to study Hα emission at the redshift of the Antennae. All optical observations were made with the Wide Field Camera (WFC) of the ACS, with a scale of 0049 pixel⁻¹ yielding a FOV of ∼202'' × 202''. Four separate exposures were taken for each of the filters F435W, F658N, and F814W, yielding total exposure times of 2192 s, 2300 s, and 1680 s, respectively. Six separate exposures were taken through the F550M filter, with a total exposure time of 2544 s. The longer integration and larger number of dither pointings maximized the spatial resolution of the F550M observations. Slightly shorter ACS/WFC exposures were also taken at two positions in the Southern tail, using the filters F435W, F550M, F658N, and F814W, and will be presented in a future paper.

Archival F336W photometry of the Antennae (Program GO-5962) was used to supplement our optical ACS/WFC observations. Two sub-pixel dither positions separated by 0025 were observed through the F336W filter, yielding a total exposure time of 4500 s.

The flatfielded ACS/WFC images were co-added using the task MULTIDRIZZLE (Koekemoer et al. 2002) in PyRAF/STSDAS. A PIXFRAC value of 0.9 and a final scale of 0045 pixel⁻¹ were used for each of the filters. A second, higher resolution F550M image was constructed to take advantage of the additional pointings. This "super-resolution" image was constructed using a PIXFRAC value of 0.7 and has a scale of 003 pixel⁻¹. From here on we will use the term "super-res" to denote the 003 pixel F550M image. The archival WFPC2/F336W images were co-added in a manner similar to that used by Whitmore et al. (1999), but using MULTIDRIZZLE rather than the older DRIZZLE task. Each chip was treated separately, creating four final output images (PC, WF2, WF3, and WF4). A PIXFRAC value of 0.8 was used for all four chips, resulting in final scales of 0035 pixel⁻¹ for the PC chip and 0075 pixel⁻¹ for each of the WF chips.

Figure 1 shows a color image of the Antennae produced by Lars Christensen (ESA). The F435W image is shown in blue, F550M is shown in green, and a combination of the F814W and F658N (Hα) images is shown in red. One intriguing aspect of this color image is that it makes it possible to tell the difference between regions that are red because they have strong Hα emission (these have a pinkish tint) and regions that are red because they suffer strong reddening due to dust (these have an orange tint).

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Catalogs of cluster candidates were constructed from the F550M "super-res" image using the task DAOFIND in IRAF. The higher resolution of the "super-res" image is better suited to separate close objects that might otherwise remain blended in the lower resolution images. Removal of artifacts (e.g., hot pixel residuals, remaining cosmic rays) and background galaxies was aided by the calculation of a "Concentration Index" C for each object, which is taken to be the difference between magnitudes measured within a 1 and a 3 pixel radius (see Whitmore et al. 1999). We note that more concentrated objects, such as stars, have lower values of C (i.e., ≈1.45), while extended objects, such as clusters, have larger values of C (i.e., >1.52). Hence, this parameter might more properly be called a "diffuseness" index. However, for historical uniformity we prefer to retain the term "Concentration" index. We also used the FWHM measured by the IRAF task RADPROF, and a parameter which we refer to as the "Flux Ratio," which is defined to be the ratio of the flux in a 3 pixel radius aperture to the flux measured in the background annulus. This parameter was found to be useful for removing false detections in areas of dust. The final object catalog was assembled using parameter values of C>0.0, 1.5 pixels <FWHM < 5.5 pixels, and a flux ratio > 1, and contained 60,790 candidate objects. For reference, a typical FWHM for stars in the Antennae is 1.7 pixels and for clusters is 2.0 pixels.

It has been suggested that the C technique, which uses the difference between magnitudes measured within two different apertures, may be sensitive to the precise center of an object at the sub-pixel level (Anders et al. 2006). If true, this would mean that objects of the same intrinsic size, but falling at the center of a pixel versus near the edge of a pixel, might have values of C that differ by as much as a magnitude or more according to Figure 29 in Anders et al. We tested for this effect by comparing our measured values of C for a number of isolated point sources believed to be foreground stars (i.e., Training Set 1 below). Figure 2(a) shows little, if any, trend. That is, if we break the sample in half, objects with more central pixel values have a mean $\bar{\mbox{$C$}} = 1.437\, \pm \, 0.014$, while objects centered more on the pixel edges have a value of $\bar{\mbox{$C$}} = 1.459 \pm 0.013$. Hence, the difference in $\bar{\mbox{$C$}}$ is only 0.022 ±  0.019. We can increase the sample by including all objects with C < 1.52 and V < 23 mag. While this sample may include some unresolved clusters in addition to stars (as discussed in Section 4), we again see no discernible trend, with more centrally positioned objects having a mean $\bar{\mbox{$C$}} = 1.459 \pm 0.005$, while objects with centers closer to the edge of a pixel have $\bar{\mbox{$C$}}=1.460 \pm 0.005$. Hence, the difference is 0.001 ± 0.006. These comparisons show that centering has a negligible effect on our measurements of C. We also note that while using as large a radius as advocated by Anders et al. (i.e., ∼5 pixels) might be optimal when objects are well separated, in crowded fields similar to the Antennae smaller apertures are clearly to be preferred.

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The IRAF tasks XY2RD and RD2XY were used to convert object coordinates in the "super-res" F550M image to the F435W, F550M, F658N, and F814W ACS/WFC image coordinate system, as well as to the F336W WFPC2 coordinate system. Any remaining small shifts in object positions were determined for each filter from the task GEOMAP. Aperture photometry for the ACS/WFC data was performed using the IRAF task PHOT, with a 2 pixel radius and inner and outer background annuli of 4 and 7 pixels, respectively, corresponding to angular sizes of 009, 018, and 0315 in radius. The VEGAMAG zeropoint values for ACS/WFC of 25.779, 24.867, and 25.501 mag were used for the F435W, F550M, and F814W images (Sirianni et al. 2005). Aperture photometry for the F336W WFPC2 data on the PC chip was conducted using an aperture with a 2 pixel radius and inner and outer background annuli of 4 and 7 pixels, respectively, corresponding to angular sizes of 007, 014, and 0245, respectively. An aperture radius of 1.5 pixels, and inner and outer background annuli of 3 and 6 pixel radii, corresponding to 0112, 0225, and 045, respectively, were used for the WF2, WF3, and WF4 chips.

Aperture corrections, defined as the amount of light in magnitudes required to extrapolate from an aperture magnitude to a total magnitude, were derived by making photometric measurements of isolated, high signal-to-noise (S/N) clusters in each filter (for the F550M filter this was done on both the normal and "super-res" ACS/WFC images) and for each individual CCD in the WFPC2 data. Aperture corrections for clusters were found to be significantly larger than those for isolated stars, for all instruments and filters. A median value was used for the aperture corrections for each filter. The aperture corrections used for the 2 pixel photometry of the normal ACS/WFC images correspond to 0.905, 0.890, and 0.915 mag for the F435W, F550M, and F814W images, respectively. The aperture corrections for the 3 pixel photometry of the "super-res" F550M image was 0.886 mag. These aperture corrections are for the 2 or 3 pixel apertures to a 05 radius aperture. Aperture corrections from 05 to infinity were taken from Sirianni et al. (2005).

Taking the different sizes of clusters into account properly would require different aperture corrections for each cluster. We experimented with making such corrections by deriving a formula relating aperture corrections and C indices for isolated, high S/N clusters. While this works well for many clusters, in crowded regions where values of C can be very uncertain the use of the formula adds considerable noise. Hence, corrections for variable cluster sizes have not been made in this paper, but will be revisited in a future paper (R. Chandar et al. 2010, in preparation). We note that while this use of constant corrections typically makes individual absolute magnitudes of clusters uncertain by a few tenths of a magnitude (and more than a full magnitude in a few exceptional cases), the effects on colors are negligible since the latter are determined from fixed apertures.

Aperture corrections for the F336W images and the 2 pixel PC and 1.5 pixel WF2, WF3, and WF4 apertures correspond to 1.041, 0.989, 0.937, and 1.055 mag, respectively. These corrections take the photometry in 2 or 1.5 pixel radius apertures to 05. The standard 0.1 mag correction from 05 to infinity was then added to the above corrections (Holtzman et al. 1995). We also applied charge transfer efficiency (CTE) corrections to the WFPC2/F336W photometry based on the prescription given by Dolphin (2000).⁹ We computed the X and Y coordinates for each object on the original images for each dither position. For objects appearing in both dither positions we adopted weighted averages of the CTE correction.

In addition to the data described above, long-slit Hα observations using the Space Telescope Imaging Spectrograph (STIS) were planned as part of this proposal, similar to those reported by Whitmore et al. (2005). Unfortunately, STIS stopped working before these observations could be obtained.

Completeness corrections were determined by adding artificial clusters in regions of different background levels to the F550M "super-res" image, using the IRAF task MKOBJECT. These artificial clusters had the same median values of C and FWHM as real cluster candidates over a magnitude range of 18–28. The artificial clusters were then run through the same detection algorithms as used for real cluster candidates. Recovery of the artificial clusters was based on two criteria: (1) whether the recovered luminosity was within ± 0.1 mag of the input magnitude, and (2) whether the recovered artificial cluster was detected within ± 0.5 pixel of its input coordinates. The numbers of recovered artificial clusters were then sorted as a function of the background level (we used seven different background levels), binned in 0.25 mag bins, and compared with the initial numbers of artificial clusters. Completeness curves were constructed by smoothing the binned data using a boxcar smoothing algorithm and interpolating a curve through these points. Figure 3 shows the completeness curves for the different background levels. The dashed horizontal line marks the 50% completeness level. The completeness limits in V at 50% for the seven background levels are 26.5, 26.4, 26.0, 25.3, 24.7, 24.2, and 23.3 mag, respectively.

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In the rest of this paper, we will sometimes use the loose terminology "U" for the F336W filter for brevity, and similarly "B" for F435W, "V" for F550M, and "I" for F814W.

Infrared observations were made using the Near Infrared Camera and Multi-Object Spectrometer (NICMOS) camera on HST as part of Program GO-10188. Observations were made using the NIC2 camera with the F160W, F187N, and F237M filters, and the NIC3 camera with the F110W, F160W, F164W, F187N, and F222M filters. Only the NIC3 results are briefly discussed here. See B. Rothberg et al. (2010, in preparation) for a more detailed presentation of the NICMOS data.

Two sets of NIC3 observations of the "overlap region" were carried out, one including the northern nucleus (NGC 4038) and the other the southern nucleus (NGC 4039). The NIC3 data were not reduced using the standard pipeline products. Instead, raw files were obtained from the archives and were first processed with the routine CALNICA, which flattens the data and performs instrumental calibration of the data, including dark current subtraction, non-linearity correction, conversion to count rates, and cosmic-ray identification. The output data were then processed with the task PEDSUB, which subtracts quadrant-dependent residual biases. Next, hot pixels were identified manually and masked. Finally, foreground stars were identified and masked. The F222M observations included an additional set of observations of a blank field for the purpose of background subtraction, since thermal contributions from the telescope are important in this bandpass.

The NICMOS observations were combined using the MULTIDRIZZLE task in STSDAS with the default values. The linear scale of NIC3 images is 020 pixel⁻¹. However, the NIC3 observations were dithered, and the increased sampling made it possible to produce higher resolution data. The data in all three filters were rescaled to a final linear scale of 015 pixel⁻¹ using a PIXFRAC value of 0.8. The data were rotated to a position angle of 0°, and all bad pixels were ignored in the final combination. No interpolation was used to correct for saturated or bad pixels. Testing of interpolation showed that leaving this turned on in MULTIDRIZZLE produces spurious results in cluster detection and photometry.

Photometry was conducted on the final data once they were divided by an ADCGAIN value of 6.5. The photometric zeropoints used for the photometry correspond to 22.610, 21.818, and 20.134 mag in the F110W, F160W, and F222M filters, respectively, and are on the VEGAMAG system. The aperture sizes used for the candidate-cluster photometry were 1.5 pixels in each filter, which corresponds to an angular size of 0225 and a spatial size of 24.1 pc. Aperture corrections were measured to compensate for missing flux. Unfortunately, due to the limited FOV no high S/N isolated clusters could be identified for measuring aperture corrections. Hence, archival data for Program 9997 (PI: Dickinson, Photometric Recalibration of NICMOS) were retrieved and processed in the exact same manner as the target observations for the purpose of obtaining aperture corrections. The FWHM of cluster candidates on the NIC3 images of the Antennae was found to be very similar to point sources from Program 9997, justifying the use of point-source aperture corrections for the slightly resolved (at least by ACS standards) clusters in the Antennae. Two sets of aperture corrections were applied. The first corrected the 0225 aperture to a 11 aperture used for the photometry zeropoint determination.¹⁰ These aperture corrections correspond to 0.548, 0.628, and 0.723 mag for the F110W, F160W, and F222M filters, respectively. Additional aperture corrections of 0.059, 0.090, and 0.121 mag for the F110W, F160W, and F222M filters, respectively, were used to extrapolate to infinity.

The MF for a population of star clusters provides important information on the formation and dynamical evolution of the clusters, and in principle is more straightforward to interpret than the LF, where the dimming of older clusters can affect the slope. A comparison between the mass and LFs can yield insights into the age distribution of the clusters as well as the processes responsible for the formation and dissolution of clusters. However, it is important to keep in mind that mass is a derived property, introducing additional biases and uncertainties. Hence, we must be careful to only use it in age and mass ranges that are reliable.

The top three panels of Figure 15 show the MFs for cluster candidates (i.e., M_V < −9) in the Antennae in three intervals of age, log τ < 7.0, 7.0⩽ log τ < 8.0, and 8.0⩽ log τ ⩽ 8.6. The corresponding lower mass limits range from 10⁴ to 10⁵ M_☉, respectively, as shown by the dashed red lines in Figure 9.

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The bottom panels show the MFs in the same intervals of age, but with only resolved objects selected (i.e., C>1.52). Each panel shows the MF resulting from two different bin selections: our preferred version with variable bin sizes, where there are an equal number of clusters in each bin (filled circles), and a version with approximately fixed bin sizes (open circles).

We find that over the plotted mass–age range, the MF declines monotonically, with no evidence for a flattening or a peak. Similarly, we do not see any obvious steepening of the MF at the high mass end as suggested by Gieles et al. (2006), which would be expected if there was a physical cutoff to the masses with which clusters can form. Hence, the MFs for clusters in the Antennae can be described by a single power law of the form dN/dM ∝ M^β (or dN/dlogM ∝ M^β+1 plotted logarithmically). The solid lines are best fits to the variable-binning data (filled circles), while dashed lines are fits to the fixed-bin data (open circles). The values of β given in Figure 15 are for the variable-bin data, and the mean value for the six panels is $\bar{\beta } = -2.10 \pm 0.13$. A more realistic value for the uncertainty in β is 0.2, based on the discussion of uncertainties in α (Section 6) and the fact that the mass is a derived property, thus introducing additional artifacts and uncertainties (e.g., uncertainty in the metallicity).

The results presented here confirm and extend those based on previous WFPC2 data (Zhang & Fall 1999; FCW09). We find that the MF continues as a power law with β ≈ −2 to lower masses (i.e., ∼10⁴ M_☉ for ages <10⁷ yrs) and to older ages (∼3 × 10⁸ yr for >10⁵ M_☉) than reported previously. This has a number of physical implications, which are discussed in detail in FCW09. In particular, the shape of the MF does not change for the first ∼3 × 10⁸ yr over the observed mass–age range, at least within the uncertainties, which constrains various models for cluster disruption.

Figure 16 shows the MFs (top row) and LFs (bottom row) for four of the ∼0.5 kpc size areas that will be discussed in Section 8. In general, the indices α and β are essentially the same within the errors, as already found for the entire distribution of objects in the Antennae (i.e., α = −2.13 ±  0.07 and β = −2.10 ±  0.20). Fall (2006) shows that this similarity between the cluster LFs and MFs is only expected if the MF is a power law, and if the cluster age and mass distributions are approximately independent of one another.

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The shape of the age distribution for star clusters provides clues to the formation and survival of the clusters. We previously found, based on WFPC2 data, that the age distribution of star clusters in the Antennae declines more or less continuously and in approximately power-law fashion, dN/dτ ∝ τ^γ, with γ ≈ −1.0 for the first few 10⁸ yr. We also found that the shape of dN/dτ was similar in two different intervals of mass (FCW05; WCF07; FCW09), suggesting that the age distribution does not depend strongly on the mass of the clusters. Here we confirm and extend these two important conclusions, using the higher quality ACS data and the results from our detailed investigation of the 50 most massive clusters in the Antennae. A more detailed treatment will be presented by R. Chandar et al. (2010, in preparation).

The cluster age distribution is the result of a combination of formation and disruption processes. A value of γ = −1 for the shape of the age distribution implies that there should be equal numbers of clusters in equal bins of log τ above a given mass, which means that there are approximately 10 times fewer clusters each subsequent decade in log τ. If we assume that the star formation rate (SFR) is roughly constant, this implies a 90% cluster disruption rate each decade in log τ. While the assumption of a constant SFR is clearly an oversimplification, especially for merging galaxies where bursts of star formation are expected, the rapid drop in dN/dτ by 2 orders of magnitude from 5 to 500 Myr, when compared to the predicted increase in the SFR from a model simulation of the Antennae (a factor of a few; see Mihos et al. 1993), suggests that the dominant influence for understanding the demographics of clusters are disruption processes rather than fluctuations in the formation rate. Other arguments supporting this conclusion are presented in FCW05 and WFC07. Specifically, the dN/dτ diagram declines in a similar fashion throughout the Antennae (see Figures 8 and 9 in WCF07), even though there are no hydrodynamical processes that could synchronize the formation rate of the clusters this precisely over such large separations. In addition, the dN/dτ diagram looks similar in many star forming galaxy (see WCF07; Mora et al. 2009; Chandar et al. 2010a, 2010b).

In WCF07, our best-fit model for the Antennae clusters suggested an infant mortality rate of ∼80% per log τ decade, corresponding to a value of γ ≈ −0.7, which is only slightly flatter than the canonical value of −1 discussed above.

Recently, Bastian et al. (2009) have attempted to take into account variations in the SFR in the Antennae when interpreting the cluster age distribution, by adopting the SFR found in the simulation by Mihos et al. (1993). This is an interesting approach. Yet, it is limited by the large uncertainties imposed by our lack of understanding of the star formation process (e.g., shock-induced versus density-induced star formation; see Barnes 2004), the fraction of gas in the progenitors, etc. Perhaps most worrisome in using the Mihos et al. (1993) model for the Antennae to predict the varying SFR is the fact that according to this model most of the star formation should occur in the nuclear regions, while in reality most of it is currently distributed throughout the disks of the two galaxies. A new N-body/SPH simulation by Karl et al. (2010) predicts more distributed star formation, similar to the observations, and has a nearly constant SFR in the age range 6.7 < log τ < 8.7, in contrast to the Mihos et al. (1993) model where the SFR increases a factor of a few. This demonstrates the large uncertainties involved with making these simulations, and hence in using the Bastian et al. approach for estimating the cluster dissolution rate.

Probably the best approach for determining the disruption rate of clusters will be to combine the data from a much larger sample of galaxies, especially non-interacting spiral galaxies, where the assumption of a roughly constant SFR is better justified statistically. The recent study by Mora et al. (2009) provides a promising start in this direction. Using HST imaging, they found power-law age distributions for star clusters in five nearby spiral galaxies. Although they used a somewhat different technique, counting clusters brighter than a given V-band luminosity rather than above a given mass, they found that the age distributions are all consistent with ≈80% of the clusters being disrupted every decade in age for τ ≲ 10⁹ yr, nearly identical to our results for the Antennae (see their Figure 15).

Table 7 lists the 50 most massive star clusters found in the present study of the Antennae. We can use its data to derive a mass-limited (log M>5.8) age distribution up to log τ = 8.6 (i.e., limited by artifacts that manifest themselves at higher ages; see discussion in Section 5). Making the first-order assumption of a roughly constant SFR during this period, a value of γ = −1 would imply that there should be approximately equal numbers of clusters in the three intervals log τ = 6–7, 7–8, and 8–9, while a value of γ = −0.7 (i.e., the preferred value from WCF07) would imply a factor of 2 increase for successive intervals. Counting the clusters in Table 7, we find that the above three age intervals contain 10, 19, and 45 clusters (extrapolating from a logarithmic range 8–8.6 for the last bin), respectively, in good agreement with the prediction from an 80% disruption model with roughly constant SFR.

Because Table 7 contains only 50 clusters, thus leading to low number statistics, we also checked the number of clusters in a second range of masses, 5.3 ⩽ log(M/M_☉) ⩽ 5.7. Here we find that the three age intervals log τ = 6–7, 7–8, and 8–9 contain 28, 41, and 126 clusters, respectively. Hence, the lower mass clusters have a similar age distribution as the higher mass clusters, increasing in number by approximately a factor of 2 in successive unit intervals of log τ, as predicted from an 80% disruption model with roughly constant SFR.

To conclude, our new results confirm that the number of massive star clusters in the Antennae increases only slightly in bins of log τ and, therefore, must decline fairly steeply as a function of linear τ, with an index of γ ≈ −0.7. We have interpreted this steep decline as being primarily due to the disruption, rather than the formation, of clusters (see also FCW05; WCF07; FCW09). In addition, the similarity of the relative numbers of clusters in different age intervals, but at different masses, also supports the idea that any disruption that affects these clusters does so in a manner nearly independent of the cluster mass, at least for the first few 10⁸ yr.

We begin by examining general trends in the properties of the selected areas and then discuss possible physical interpretations for these trends. Some of the most prominent correlations for clusters in the selected areas are shown in Figure 18. The top left panel shows the M_V(brightest) versus log N diagram, where M_V(brightest) is the absolute magnitude of the brightest cluster in each area and log N is the number of clusters brighter than M_V = −9 in that area. This is the strongest correlation (8σ level of significance) of those shown in the figure. A version of this diagram for cluster populations in entire galaxies was first shown by Whitmore (2003) and has been subsequently studied by several other authors (Larsen 2002; WCF07; Bastian 2008; Larsen 2009). The diagram was one of the primary drivers in developing the "universal" cluster demographics model described in WCF07, since the observed correlation can be explained by a statistical "size-of-sample" effect, assuming all young cluster systems in galaxies have power-law LFs with a value of α ≈ −2. A comparison of the data from our area-by-area analysis with the best-fit line for cluster populations in entire galaxies (mergers, starbursts, dwarfs, spirals) from WC07 (dotted line) shows that the relationship is essentially identical. This again provides evidence for a universal relationship, at least down to the ∼0.5 kpc scales we have studied here.

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The second best correlation is the log E(B − V) versus log τ relation shown in Figure 18(b) (7σ-level of significance). This is similar to the result from Figure 10(c) in Whitmore & Zhang (2002), but we now use the median value of log E(B − V) for clusters within a defined area instead of plotting values of log E(B − V) for individual clusters. Similar results have also been found by Bastian et al. (2005) for M51 and Mengel et al. (2005) for the Antennae. Using areas instead of individual clusters, we find a typical E(B − V) value of ∼0.3 mag (i.e., A_V ≈ 1 mag) for areas dominated by the youngest clusters with logarithmic ages (in years) log τ ≈ 6.5, declining to values of E(B − V) ≈ 0.1 mag (A_V ≈ 0.3 mag) for areas with logarithmic ages log τ ≈ 8.0.

Figures 18(c) and 18(d) show values of α (the slope of the LF) and β (the slope of the MF) as a function of the median age of the clusters in each region. We first note that for ages greater than log τ = 7, the slope values are relatively constant, and the mean values of α and β are roughly equal within the uncertainties (i.e., $\bar{\alpha } = -2.12 \pm 0.04$ (rms = 0.17) and $\bar{\beta } = -2.09 \pm 0.06$ (rms = 0.24)). This is similar to what we found for the total distributions of clusters in the Antennae, as discussed in Section 7.1, and provides further evidence that the mass and age distributions are independent of each other, as discussed in Fall (2006).

Figures 18(c) and 18(d) also show tentative evidence for flatter slopes for α and β when log τ < 7. However, it is possible that this is due to observational biases, for example difficulties in making completeness corrections for the youngest clusters, which tend to lie in areas of higher background brightness. In principle, our completeness corrections should take care of this effect, but the combination of high background and severe crowding makes this task more difficult. Another potential problem is extinction, since fainter clusters might suffer more extinction than highly luminous clusters due to their lack of massive stars needed to clear out the surrounding dust. We can test for this hypothetical effect fairly easily by comparing the colors of the bright and faint clusters. This comparison shows that a very small effect does exist (i.e., −0.02 mag in U − B when comparing clusters in the knots brighter than M_V = −10 with those in the range M_V = −10 to −9), but this effect is too small to cause more than a very minor difference in the LFs.

One of our primary goals for the outer areas, where the background is very low, is to push the LF to M_V ≈ −6. This is particularly interesting because most of the clusters in these regions have intermediate ages, having probably been formed during the first encounter between the two galaxies (e.g., see Figure 17 of Whitmore et al. 1999). We should therefore be able to search for a possible turnover in the LF that is expected to eventually appear if the power-law form of the LF for young clusters evolves dynamically—assuming evaporation processes typical of the Milky Way—to the peaked form found for old globular clusters. Based on Fall & Zhang (2001) we might expect this turnover to occur around M_V ≈ −4, assuming that most of the outer clusters are 100–300 yr old and that two-body relaxation is the dominant process.

Figure 19 shows the data and values of α for the best fits for the three outer areas with the most clusters (Outer 2, 5, and 7). We find no clear evidence for a turnover in the LFs of the cluster population in the tails, consistent with an extrapolation from the Fall & Zhang (2001) model.

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On the largest scales, a number of long "linear" (or gently curved) features can be discerned in the Antennae. The most obvious examples are the two long tidal tails (∼130 kpc in projection tip to tip) that give this system its nickname. Most of the clusters in the inner parts of these tails (the only parts covered by the central pointings; results from outer pointings along the tails will be reported in a future paper) have ages of roughly 200 Myr and were probably formed during the first-pass encounter between the two galaxies. However, an intriguing feature is the existence of ongoing star formation at a low level, as evidenced by the existence of about a dozen faint Hα knots strung along the inner edge of the southern tail near its base, where it connects to the disk of NGC 4038 (i.e., Outer 5; see Figures 17 and 20a).

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A possible continuation of this feature is the increasingly strong Hα "streak" seen passing through knots N and P and extending to the "Western Loop" that includes knots G, R, S, T, M, and L (Figures 20(b) and 17). A faint but, again, increasingly strong dust lane is associated with this Hα emission. In the outer regions it is first aligned with the Hα knots themselves, but further into the galaxy it becomes offset to the inside of the Hα emission. A similar trend in alignment between Hα emission and dust is observed in M51. In fact, this whole aligned feature of Hα emission plus dust lane in the Antennae is reminiscent of, though perhaps less regular than, the spiral arms and outer tidal features in M51.

Similar large-scale features are the "spiral-looking tail" in Region 1 (Figure 20(e), ∼3.4 kpc) and the long (Figure 20(c), ∼8.2 kpc) dust lane running from the bottom of Outer 6 through Outer 3 and Outer 2, to near the end of Outer 1. A less prominent example is the nearly linear string of giant H ii regions following a line from Knot F to E to Region 3 (Figure 20(d)). This nearly straight string was used to good advantage by Whitmore et al. (2005), who aligned the long-slit of the STIS spectrograph with it. This string also forms the eastern edge of the overlap region. Hence, its apparent regularity in both morphological linearity and a smooth velocity field suggests that even the overlap region might be less chaotic than commonly believed.

Several other linear features are seen on slightly smaller scales. Examples are the two linear dust lanes that run from near the nucleus of NGC 4038 out to regions 13 and 14 (Figure 20(f)), respectively, with regions of prominent star formation along one edge of each dust lane (e.g., Knot L). The side-by-side arrangement of star formation and dust lanes is reminiscent of normal spiral arms (although the linear rather than spiral arrangement is not typical).

Note that while clusters form currently at the highest rate in the chaotic overlap region, other clusters are also forming throughout most of the two galaxies. In particular, the velocity pattern of the ionized gas in most of the northern half of NGC 4038 is quite regular (Amram et al. 1992), yet a large fraction of the clusters are forming in this region at the present time. Hence, high collision velocities are not required for making clusters, a result also found by Zhang et al. (2001) and Whitmore et al. (2005), and supported by theory (Renaud et al. 2008).

While the specific details of how star formation is triggered may still be obscure, it is clear that compression and shocks play an important role (e.g., along spirals arms). One method for studying triggered star formation is to age-date stars or star clusters and then look for patterns that might indicate the presence of sequential star or cluster formation. A classic example of this is 30 Doradus, where Walborn et al. (1999) found evidence for several generations of star formation. Does our age-dating of clusters in the Antennae provide similar evidence of sequential cluster formation?

Figure 21 shows the pattern of ages obtained for clusters in Knot S, along with an Hα image of Knot S. There is some evidence for triggering as shown by the preponderance of 5–10 Myr clusters (green circles; including the central dominant cluster) positioned in what appears to be a hole in the Hα. The younger clusters (blue circles) are primarily to the left, as the star formation apparently works its way into the dust reservoir (see the ACS/HRC image in Figure 28). There is also a smaller region of triggered formation in the upper right, as evidenced by both the age dating and the presence of Hα in that area. We also note a scattering of older clusters throughout much of the region with ages 10–100 Myr (red circles), which may have triggered earlier episodes of star formation in this region.

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Knot B (Figure 22) presents a similar, but even more dramatic example of triggered cluster formation. In this case, we find a single cluster with an apparent age of ∼50 Myr (and a mass of ∼10 ⁶M_☉) located off to the right side, but also a population of younger clusters with a total mass of ∼8 × 10⁶ M_☉, about eight times greater than the mass of the cluster that appears to have triggered their formation. Note that the Hα shell is centered on the older cluster and that the young clusters are located where the shell intersects a major dust lane at the edge of the overlap region (see Figure 1). Dividing the radius of the Hα bubble by the age of the central cluster yields an expansion velocity of ∼6 km s⁻¹. This is smaller than values of 20–30 km s⁻¹ derived for the bubbles in knots S and J by Whitmore et al. (1999), and than the direct measurements of Hα velocities by Amram et al. (1992). One possibility is that the age of this cluster is closer to 10–20 Myr, which lies in the range that is hard to measure (see Figure 9 and discussion in Whitmore et al. 1999). This slightly smaller age would give expansion velocities in the range 15–30 km s⁻¹ and would also be more compatible with the age gradient shown in Figure 22. Presumably, the dust lane in the overlap region provides a much greater reservoir of raw material needed to form massive clusters than is the case for Knot S. An analogy might be that a match dropped on a field of dry grass might only result in a few minor brushfires, but a match dropped next to a tinder box can result in a much more impressive, explosive fire (e.g., Knot B).

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In general, early star formation tends to occur on the edges of gas reservoirs and then work its way into the dust lanes, creating a linear rather than circular gradient of sequential star formation. This is sometimes known as the "blister model" (Israel 1978). Several other knots and regions in the Antennae (e.g., knots A, E, F, K, L, and T; and regions 3, 4, and 13) have this linear morphology of sequential cluster formation with the gradient in the direction toward a major dust lane, as shown in Figure 23 (e.g., knots E and F and region 13). We note, however, that similar morphologies might also result from large-scale processes such as a density wave or collision between two large gas clouds. In fact, it is likely that both large- and small-scale triggering are happening simultaneously.

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Another interesting case is a dark, relatively circular dust cloud with a small amount of star formation on only one side of the cloud that is found near Outer 3 (see Figures 20(c) and 20(g)) in the southern outskirts of NGC 4039. The lack of an obvious trigger in this case suggests the possibility that the cloud is falling back into the galaxy and the star formation results from the ram pressure being exerted by the interstellar medium. Perhaps velocity measurements with ALMA will be able to test this hypothesis. This appears to be a relatively unique case in the Antennae, but we note that other examples may be harder to discern due to the geometry of their encounter. One possible second case might be near the center of Knot N, with a dust cloud falling back into the galactic disk along our line of sight (see Figure 20(b)).

Training Set 1 includes reddish and yellow–red objects (V − I>0.5) in relatively low-background areas around the edges of the visually luminous galaxy disks. Most of these objects were identified as candidate foreground stars of our Galaxy in Table 4 of Whitmore et al. (1999). We contrast this set of 26 candidate stars with the 11 candidate old globular clusters from Table 3 of Whitmore et al. (1999). Information about the candidate foreground stars is given in Table 1. Information on the 11 candidate old globular clusters used as part of Training Set 1 is included in Table 2 (top group).

Figure 6(a) shows a plot of the absolute magnitude M_V versus the concentration index C (i.e., the difference in magnitude using 1 and 3 pixel radius apertures) for the candidate foreground stars and old globular clusters of Training Set 1. We find that in general there is good separation between the two samples, with all of the candidate foreground stars lying in the range 1.37 < C < 1.52 ($\bar{C} = 1.448$ mag, sample rms = 0.049 mag) and all but two of the candidate old globular clusters lying in the range 1.62 < C < 1.78 ($\bar{C} = 1.676$ mag, rms = 0.052 mag). Note that the discrepant concentration indices for two of the candidate old globular clusters were already known (1 and 9 in Table 2, corresponding to 8 and 1, respectively, in Table 3 of Whitmore et al. 1999), but the objects were retained since they had colors appropriate for old globular clusters.

The measured U − B and V − I colors for our training-set objects are compared with a CB07 evolutionary track for a model star cluster in Figure 6(b). Note that only about half of the candidate stars (open circles) are detected in the U filter and can, therefore, be placed on this diagram. Most of the candidate globular clusters (filled circles) fall very close to the CB07 model predictions. There is only one discrepant object (1) which falls well below the track, where most of the candidate stars rather than globular clusters are found. Hence, object 1 is likely to be a star, based on both its color and its small value of C. The other globular cluster candidate (9) that has a value of C overlapping with those measured for individual stars has colors that are indistinguishable from those of other old globular clusters. Turning our attention to the candidate stars, we find that all but two lie in the bottom-right part of the two-color diagram, well separated from the globular clusters. While most of the candidate stars and globular clusters are separated in the two-color diagram, it is clear that some stars can have colors similar to old globular clusters (typically early F-type stars). Hence, we can use a combination of size and color information to more reliably differentiate between stars and clusters. The dotted line in Figure 6(b) shows the region of the U − B versus V − I diagram which we call "foreground-star space."

Based on the results above, we include in Table 2 a new set of candidate old globular clusters (middle and bottom groups). The criteria used for their selection are: age estimates in the range 8.8 < log τ < 10 (note that an examination of objects with estimated log τ>10 shows many of them to be either red foreground stars or distant background galaxies, hence our use of log τ < 10), concentration indices in the range 1.57 < C < 1.80, and locations away from regions with extensive dust (since a heavily reddened young cluster could masquerade as an old globular cluster).

The second training set consists primarily of intermediate-age clusters (∼200 Myr) in what was defined as the northwestern extension in Figure 6 of Whitmore et al. 1999. This area is also designated as "Outer 9" in Figure 17. In a ∼200 Myr old population, the brightest stars should have absolute magnitudes M_V ≈ −3, well below our detection threshold. Hence, the vast majority of objects in this sample should be clusters, with perhaps a foreground star or two also included.

This area contains a loop of material that is believed to have been extracted from NGC 4038 at roughly the same time as the long tidal tails (Whitmore et al. 1999). The loop features three of the best examples of intermediate-age clusters (58549, 58909, and 59721 in Figure 24). These clusters turn out to have nearly identical properties, as shown in Table 3 (first three entries) and in Figure 25. The wide FOV of the ACS allows us to include many other clusters with similar properties. One likely bright foreground star (STAR-60076 in Figure 24) has been removed from the sample based on its small value of C = 1.389, although we note that it has colors similar to those of intermediate-age clusters. We recommend that a spectrum of this object be obtained to make a firm determination of its true nature.

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Figure 7 shows the values C and log τ for the objects of Training Set 2, after the objects have been sorted into three subsamples according to their absolute magnitudes M_V. Note that all objects brighter than M_V = −8 have values of C consistent with them being extended clusters, based on our results for Training Set 1 (i.e., C>1.52). At fainter magnitudes we find that the increased observational scatter results in some estimates of C < 1.52 and log τ < 8.0. Since we do not expect any intermediate-age stars in this region to have magnitudes brighter than our detection threshold, we interpret such values of C and log τ as being due to observational scatter, suggesting that the reliability of our C and age estimates is limited below M_V ≈ −7. A supporting piece of evidence is that there is no Hα emission in this area, which would be expected if there actually were stars present with M_V ≈ −7 and log τ < 8. One other interesting result is the apparent correlation between M_V and C seen in Figure 7(a), in the sense that brighter clusters tend to be larger, as might be expected.

Figure 25 shows the U − B versus V − I diagrams for the objects of Training Set 2, again sorted by absolute magnitude. Note that the scatter for the three brightest clusters (crosses in top panel) is surprisingly small. We again find that a threshold of M_V ≈ −7 marks the point at which a relatively large fraction (∼20%) of the objects would be misclassified (i.e., are in regions of color–color space expected to be occupied only by stars). However, the midpoint of the color distributions remains about the same over the entire magnitude range. This shows that the objects are all very similar and, therefore, likely intermediate-age clusters. For example, we are not suddenly seeing a large percentage of blue or yellow/red stars. Note, however, that there is a small offset between the observations and the model tracks in Figure 25, with the midpoint of the data lying roughly 0.15 mag blueward of the tracks in V − I.

The third training set consists of 23 objects around Knot S that were examined independently by four of us (BCW, RC, BR, and FS) with a variety of techniques that we have used to differentiate between stars and clusters in the past (e.g., visual examination using the IMEXAMINE tools in IRAF, varying contrasts on the DS9 display, circular shape, lack of nebulosity, etc.). This crowded area represents the opposite extreme from the areas containing Training Sets 1 and 2, with both the high density of objects and the high background level making size measurements more difficult. In general, the four independent assessments agreed at about the 85% level. Our final list of objects is based on the majority agreement from the independent assessments and consists of 12 candidate stars and 11 candidate clusters. Figure 26 shows the area around Knot S with the 23 objects marked while Table 4 includes information about the objects.

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Next, Figure 27 shows the M_V versus C and U − B versus V − I diagrams for the objects of Training Set 3. Nine of the 12 candidate stars have concentration indices in the range 1.37 < C < 1.52, appropriate for stars (see Figure 6). The one object (20) below this range is the faintest one in the sample (M_V = −7.3) and also lies within a few pixels of a very bright object. Hence the photometry for this object is suspect. This finding is consistent with our results from Figure 7, where we found that estimates of C and log τ for objects with M_V ≈ −7 were suspect even when the objects were isolated.

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Another object (18) has a much larger value of C than the other candidate stars and is almost certainly a cluster, based on its C value and the fact that it lies right on the CB07 evolutionary track in Figure 27, at an age of ∼4 Myr. This was one of the three objects in crowded subgroups added to the original sample of 20 training-set objects in order to determine whether stars and clusters can be differentiated visually in this environment. While the correct assignments appear to have been made for the objects in the other two crowded subgroups (10 and 21, see Table 4), in the case of 18 the visual assignment of object type appears to have been incorrect.

All of the objects in Training Set 3 that were visually classified as clusters have values of C>1.52, with a mean $\bar{C} = 1.719$ (σ₁ = 0.082) only slightly larger than that for the old globular clusters of Training Set 1. Hence, in general our visual classification agrees with the C criterion at the 80%–90% level.

Figure 27(b) shows that only two of the 11 candidate stars (4 and 22, after having removed 18) lie below the CB07 model tracks in or near the region where young yellowish stars lie, as indicated by the small dots marking Padova models for stars brighter than M_V = −6. The remaining objects (e.g., 2, 5, 18, and 23) have colors expected for young clusters. Hence, size alone is not always sufficient to differentiate between stars and clusters. Many clusters are so compact that they remain indistinguishable from stars even at the improved resolution provided by ACS images. It is also possible that in some clusters the light from a single supergiant star dominates the light profile sufficiently so as to result in a smaller concentration index.

It is important to understand how an object gets to a position like 23's in the U − B versus V − I diagram of Figure 27, with a blue color in U − B (−0.68 mag), but a yellow color in V − I (+0.62 mag). A single star cannot have such colors, as shown by the Padova stellar models. What is needed is a combination of red or yellow supergiants, which dominate the light in V − I, and blue supergiants, which dominate the light in U − B. This composite nature of cluster light is the reason why clusters with ages from 5 to 8 Myr—when the earliest, most massive red supergiants appear—evolve so rapidly to the right, as is seen in the long horizontal stretch from V-I = −0.1 to +0.8 mag in the U − B versus V − I diagram. The position of some candidate stars in this region of the diagram is indisputable evidence that they are actually clusters, masquerading as stars based on their small C due to the likely dominance of a single red or yellow supergiant (see, e.g., Drout et al. 2009 for a discussion of yellow supergiants).

Figure 8 shows two-color diagrams for all measured objects in and around Knot S, rather than just for the 23 objects of Training Set 3. The major conclusions based on these diagrams are discussed in Section 4. We wish to make an additional point here, related to the discussion above. While most of the resolved objects in the −10 < M_V < −9 diagram hug the CB07 evolutionary track very nicely, five objects lie substantially to its left. We believe most of these are cases where there is a mixture of light from a young cluster with one (or perhaps two) individual very bright star(s), hence resulting in colors that are intermediate between those of the cluster and stellar models. Ubeda et al. (2007) discuss this topic in their study of NGC 4214. This color "stochasticity" does not happen for the most luminous clusters (M_V < −10) because such clusters have enough stars so that a few bright stars cannot greatly affect the total color. This has also been noted by other authors (e.g., Cervino et al. 2002).

In Figure 8, we divided each two-color diagram into four regions: cluster space, foreground-star space, yellow-star space, and blue-star/cluster space. The first three follow from the discussion above. However, the fourth region, blue-star/cluster space, is more problematic, since both individual blue supergiants and the youngest clusters have similar colors according to the models (i.e., the upper left regions of Figures 8 and 27b).

In principle, it should be possible to distinguish stars from clusters in this region of the two-color diagram based on their concentration index. However, as Figure 7 illustrates, the photometric uncertainties make this difficult for objects fainter than M_V ≈ −7. Nevertheless, we note a clear statistical enhancement of objects in blue-star/cluster space for objects in the range −8< M_V <−7 in Figure 8. We suspect that this is indeed caused by the onset of a large number of young blue stars within this absolute-magnitude range (see Section A.4 below for further discussion). A similar enhancement of yellow stars is not seen in yellow-star space, probably because the yellow supergiants are too faint to be observed in the U filter.

Figure 28 shows an ACS/HRC image taken as part of Proposal GO-10187, a study of Supernova 2004gt that went off in Knot S in 2004. The supernova is the very bright, red, and saturated object to the lower left of Knot S marked with a cross. The improved spatial resolution of the ACS/HRC provides an even better opportunity to distinguish between stars and clusters than do our dithered ACS/WFC observations. In Figure 29, which is a graytone version of Figure 28, we show the locations of the most luminous candidate yellow and blue stars around Knot S, based on the C < 1.52 criterion. Table 5 lists these stars and gives their positions and photometric parameters.

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Finally, Figure 30 shows a close-up view of the second-brightest candidate yellow star. As in several other cases, the dominant yellow–red object appears to be embedded in a faint cluster. This is consistent with the object's intermediate position in the two-color diagram between the CB07 cluster tracks and the Padova stellar models. Note also the preponderance of very blue or very yellow-red objects at slightly fainter magnitudes in the ACS/HRC image (Figure 28). Most of these objects are likely to be individual stars that have fallen out of our sample, generally due to the lack of a reliable WFPC2 measurement in the U band (filter F336W).

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We now use what we have learned from Training Sets 1 through 3 to extend our study of objects to the entire galaxies. Figures 31(a)–31(d) plot all objects in the Antennae with M_V < −9 that fall in cluster space, yellow-star space, foreground-star space, and blue-star/cluster space, respectively.

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Figure 31(a) shows that while the vast majority of objects in cluster space are resolved (89% with C > 1.52), there are also objects present in this part of the two-color diagram that are so compact as to be undifferentiable from stars based on their size alone, as discussed in Section A.3 above.

Next, Figure 31(b) shows the dramatic difference in the fraction of unresolved objects in yellow-star space (79%), demonstrating that—while apparent size alone is not a perfect discriminator between stars and clusters—it does provide a good first-order separation, especially for bright objects with M_V < −9. However, one should keep in mind that there probably also are a few heavily reddened clusters in this region of the diagram, although they appear to be rare. Note that there are only four candidate yellow stars brighter than M_V = −9.5; hence, this absolute magnitude appears to be an effective upper limit to the luminosity of yellow supergiants. This upper limit is known as the Humphreys & Davidson (1979) limit.

The fraction of unresolved objects in foreground-star space is an even higher 92%, as seen in Figure 31(c). Note that the objects with apparent "absolute magnitudes" brighter than M_V = −10 are almost certainly all foreground stars in our own Galaxy, whence their "absolute magnitudes"—computed for the adopted distance to the Antennae—are meaningless. The objects fainter than M_V = −10 are likely to be a mix of foreground stars, yellow stars in the Antennae, and a few heavily reddened clusters as, e.g., the two objects with C>1.52.

The fraction of objects in blue-star/cluster space with C>1.52 is essentially the same (87%) as in cluster space (89%), demonstrating that at these bright magnitudes few—if any—of the objects are individual stars. However, when we change our lower limit for M_V from −9 to −8 mag and then on to −7 mag (not shown), we find that the fraction of objects with C < 1.52 increases from 13% to 29% and on to 32%, respectively. While a few percent of these increases may be due to observational uncertainties (e.g., the fraction of objects in cluster space with C < 1.52 also increases from 11% to 20%), it is clear that we are beginning to see a larger fraction of individual blue stars at fainter absolute magnitudes in this part of the diagram.