LEGUS and H_α-LEGUS Observations of Star Clusters in NGC 4449: Improved Ages and the Fraction of Light in Clusters as a Function of Age

The initial selection of star cluster candidates in NGC 4449 followed the basic steps described in Adamo et al. (2017) for LEGUS galaxies. Briefly, point-like sources were identified using SExtractor, and sources brighter than M_V = −6 (after including an average aperture correction) that have a concentration index (difference in magnitudes within 1 and 3 pixel radii) greater than 1.3 were selected as cluster candidates. For reference, isolated stars have a concentration index value around 1.2 (e.g., see Adamo et al. 2017). One of the authors (B.C.W.) then visually classified each candidate cluster using the following categories, as defined in LEGUS: 1 = symmetric extended source, 2 = asymmetric extended source, 3 = clustered grouping of close point sources (i.e., compact association), 4 = likely artifact (e.g., individual star, close pair of stars, background galaxies). We define a source to be category 3 in NGC 4449 if it has at least four stars within a five-pixel radius. Out of the original 1361 candidates, 473 were classified as category 1, 2, or 3, while the remaining 888 (i.e., 65%) objects were considered artifacts.

In addition to classifying each source visually, a grid search of the images by one of us (BCW) identified cluster candidates that were added from the original LEGUS list. In general, these objects were clearly visible but were either slightly below the M_V = −6 limit or were missing from the original SExtractor detection because they were slightly more diffuse than other clusters. Each of these sources has a peak pixel count of at least 0.1 ct s⁻¹. This flux level was selected since it can be seen against the background level of the galaxy almost into the central region. Some of these added objects were in the original source catalog but were removed because they were fainter than the M_V = −6 cutoff. The added sources tend to be more diffuse, and therefore have larger-than-average aperture corrections. An additional 121 cluster candidates were identified and added to the sample, resulting in a total of 594 category 1 + 2 + 3 cluster candidates in the final catalog. This will be called the H_α-LEGUS catalog, and is somewhat different from the LEGUS catalog used in, e.g., Cook et al. (2019), as described below. Figure 3 shows three examples of objects that were added (the white circles) in Region 23, along with several original category 1 and 2 objects for comparison. The sample, including the added clusters, was also vetted by Dave Cook as part of the Cook et al. (2019) study. He retained 94% of the added cluster candidates.

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The High Level Science Product (HLSP) available from the LEGUS website contains the cluster categories defined in the Cook et al. (2019) study rather than from the current H_α-LEGUS study. Unlike LEGUS, the Hα-LEGUS catalog includes narrowband photometry, does not correct for foreground extinction (the age-dating software fits for the foreground + local extinction), and applies aperture corrections that do not depend on the filter, i.e., no color-dependence is introduced. We note that the foreground reddening is very low, i.e., E(B – V) = 0.019 according to Schlegel et al. (1998).

The addition of these clusters increases the level of completeness in our sample. The luminosity function of the original sample (i.e., before including the added clusters) for category 1 + 2 candidates begins to artificially flatten near M_V = −6.8, due to issues with completeness. A fit to the bright portion of the luminosity function, with an extrapolation to fainter magnitudes, indicates that the 50% completeness level occurs near M_V = −6.4 and that the sample is only complete at about the 20% level at the M_V = −6 cutoff. With the addition of the 121 clusters, the flattening now occurs at M_V ≈ −6.4 and the M_V = −6.0 cutoff is closer to a 50% completeness level. The H_α-LEGUS sample presented here has a more gradual cutoff, and includes some very faint clusters with M_V ≈ −4 in the outer parts of the galaxy. The addition of these clusters allows us to more completely examine the ages of clusters in the outer regions with faint backgrounds. More stringent criteria (i.e., M_V = −6.4; ≈ 80% completeness) are imposed for various subsamples when constructing the mass and age distributions, as will be discussed in Section 7.

Little effort was made to add category 3 compact associations (i.e., only four of the added 121 cluster candidates), since this becomes quite a difficult and subjective exercise in crowded regions. In general, the category 3 populations should be considered less certain for this reason than category 1 and 2 sources. While their inclusion provides a way to study the properties of the lower-density stellar groupings, their completeness and absolute numbers are not as well-defined.

The final number of objects in categories 1, 2, and 3 are 120 (20%), 261 (44%), and 213 (36%), respectively. This is very similar to the relative percentages found for other LEGUS galaxies, as reported in Grasha et al. (2017) and H. Kim et al. (2020, in preparation), with a slightly larger fraction of category 2 clusters.

The visual classification was performed by B.C.W. using the normal method of LEGUS classification described in Adamo et al. (2017) (i.e., using a DS9-based tool, the IMEXAMINE task, and the contrast control as the primary tools), but with just one rather than three classifiers. Color images produced using the ACS F438W, F555W, F814W, and H_α image from the HLA (Whitmore et al. 2016) were also examined during the grid search for each cluster. This allowed us to include a visual determination of the morphology of associated H_α emission present around each cluster. This procedure was inspired by the results from the Whitmore et al. (2011) study of M83, which found a strong correlation between H_α morphology and cluster age. We use the following classification system for H_α morphology: objects with H_α-class = 1 have line emission on top of and largely coincident with the candidate cluster, H_α-class = 2 show a ring-like structure around the candidate cluster, H_α-class = 3 have some diffuse H_α in the general area that may or may not be associated with the object, and H_α-class = 4 sources show no H_α emission around them at all. As will be seen in Section 4, the H_α morphology provides very useful constraints during the age-dating procedure.

Photometry was performed using apertures with radii of five pixels and sky values in annuli with radii between seven and eight pixels. While different size apertures and assumptions about aperture corrections would affect our results at some level, our experience (e.g., Chandar et al. 2010; Whitmore et al. 2014) has been that this represents a relatively minor uncertainty. We do not apply any correction for foreground extinction to the magnitudes, unlike the LEGUS catalog where small corrections (i.e., 0.03 in F814W to 0.11 in F275W from the NASA/IPAC Extragalactic Database) were made; instead, we fit for the total extinction (foreground plus internal) for each cluster, as described in Section 4.1. These small adjustments would introduce very minor differences in the results—much smaller than the larger effects discussed in Sections 4.2 and 4.3 (e.g., use of H_α measurements, different spectral energy distribution (SED) models, assumptions about reddening). We apply aperture corrections to the measured magnitudes in two ways: (1) an average aperture correction determined from bright, fairly isolated clusters; and (2) a CI-dependent aperture correction: Apcorr = −4.452 + 6.4638 × CI − 2.3469 × CI² − 0.04518 × CI³, which can be applied over the CI range 1.3 − 2.23. In both cases, the determinations are made from the V band measurement and applied to all filters, to avoid introducing uncertainties in the colors of the clusters. Cook et al. (2019) demonstrate that the method used to determine aperture corrections has very little impact on the resulting age and mass distributions (see also Chandar et al. 2010).

Figure 4 shows a region (including, but extending outside of, region 11 in Figure 1) that illustrates the object selection and classification system. The top panel shows an F555W image while the bottom panel shows an F438W, F555W, F814W color image from the HLA (Whitmore et al. 2016). Red circles are category 1 (symmetric), green circles are category 2 (asymmetric), and blue circles are category 3 (compact associations). The eight slightly smaller orange circles are the clusters in this region from a study by Annibali et al. (2011), which will be discussed in Section 5.1. The final log age values are shown in yellow. The diffuse green light in the bottom panel is indicative of emission line flux (i.e., H_β at 4861 Å and [O iii] at 5007 and 4959 Å) that leaks into the F555W filter. Note that most of the clusters with this green emission have very young ages (i.e., log age ≈ 6.5–6.7 Myr).

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In Figure 5, we present the U − B versus V − I color–color diagram for the full cluster catalog (top left), as well as for each of the three cluster categories individually: category 1 or symmetric clusters (top right), category 2 or asymmetric clusters (bottom left), and category 3 or compact associations (bottom right). The 121 clusters that were added to the sample (as described in Section 2.1) are shown as open circles. In general, we find that their distribution roughly matches the distribution of the original cluster candidates. A reddening vector with amplitude of A_v = 1 (Fitzpatrick 1999) mag is included in each panel. The solid curve in each panel shows the predicted progression from the 1/4 solar metallicity Bruzual & Charlot (2003) model (as appropriate for young clusters in NGC 4449; see Annibali et al. 2011) in color–color space for a cluster as it ages from 1 Myr in the upper left to 10 Gyr in the lower right.

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The locations of key ages from the Bruzual–Charlot models, which are used to produce the Hα-LEGUS cluster properties, are shown in the upper right panel of Figure 6 (triangles). We note that the triangles for 1 and 2 Myr have been slightly displaced from each other for clarity; in the Bruzual–Charlot models, they actually have identical colors. This is why there are no clusters with age estimates of 1 Myr in the H_α-LEGUS catalog. We also show the predictions from the Zackrisson et al. (2011) Yggdrasil models for the same metallicity (dashed lines) in the upper left panel of Figure 5 and in Figure 6. The Yggdrasil models are used to estimate the LEGUS ages.¹⁷

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The most notable difference between the Yggdrasil predictions and the Bruzual–Charlot ones used here is that emission from ionized gas is included in the former (but not the latter), leading to bluer predicted V − I colors at the youngest ages. The Yggdrasil models appear to better match the few clusters with very strong line emission, but the colors of the majority of the very young, blue clusters in NGC 4449 appear to better follow the predicted colors of the Bruzual & Charlot models (i.e., they have values V − I ≈ −0.2).

Category 1 objects are found in two distinct knots in the color–color diagram, old globular clusters farthest to the bottom right with V − I in the range 1.0–1.2, and a second group just above them and to the left. This second group has V − I values in the range ≈0.4–0.6, indicative of ages in the few hundred Myr range. We will discuss this second population in more detail in Section 7.3. There is also a sprinkling of very young clusters with U − B ≈ −1.5, indicative of very young (≈few Myr) ages.

Category 2 clusters also fall in two knots in color–color space. The first is similar to the few hundred Myr old knot found in the category 1 objects, but extends to slightly younger ages. The second enhancement is similar to the young distribution in the category 1 diagram, but with roughly a factor of three more objects.

Category 3 objects ("compact associations") consist of essentially all young objects, but with a longer extension to the red due primarily to the random presence of red supergiants (i.e., stochasticity), which is more important in these typically lower-mass objects—e.g., see Fouesneau et al. (2012). This stochasticity will be discussed in more detail in Section 3.3.

Six snapshot images show typical objects in different parts of Figure 5 ranging from reddish old globular clusters and whitish intermediate-age clusters in category 1 to emission-dominated (greenish) compact associations in the upper left of category 3. Note that this very young object is better fit with the Yggdrasil models, as expected since these broadband colors include nebular line+continuum emission, while the Bruzual–Charlot models used here do not. However, this does not appear to affect the age estimates very much, because the seven bluest points in V − I have a median log age value = 6.0 (i.e., 1 Myr) using LEGUS ages and 6.5 (i.e., 3 Myr) using H_α-LEGUS ages. This is because the inclusion of the narrowband F658N filter in the H_α-LEGUS fitting procedure compensates for the lack of nebular emission in the predicted broadband colors from the Bruzual–Charlot models, as will be discussed in Section 4.

In this section, we use the color–color diagram to set constraints on the maximum amount of reddening allowed by the SSP age-dating algorithm that will be discussed in more detail in Section 4. Constraints on the expected range of extinction values toward optically visible clusters can help to improve the age-dating results for a given galaxy. Most SED fitting routines allow any value of Av, hence a cluster with the colors of an old globular cluster can be appropriately fitted with an age of 10 Gyr and Av ≈0 mag, or erroneously fitted with an age ≈10 Myr and Av ≈1.0 mag, because of the degeneracy between age and reddening in broadband filters. Spectroscopic observations can often be used to remove this degeneracy, as will be shown in Section 5.1.

In Figure 6, we estimate the highest likely values of reddening in NGC 4449 using the clusters embedded in Hα (those with Hα-class = 1), by estimating the amount of reddening toward the clusters that fall redward of the models. We then use this value to set constraints on the maximum reddening allowed by the SSP fitting routine. Note that a number of strong Hα-emitting clusters fall blueward (to the left) of the Bruzual–Charlot model; we find that these clusters are assigned young (≈few Myr) ages no matter what assumption we make for E(B − V). Therefore, we do not consider them when setting constraints on the maximum allowed reddening. As might be expected, most (69%) of these strong Hα regions are found in the blue boxes in Figure 1, with nine in or near Region 11, and four in Region 15. Twenty-two percent are found in the yellow boxes, with three each in regions 13 and 24. Dwarf and lower-mass irregular galaxies often have lower extinction (and hence lower reddening) than more massive galaxies: for example, Zaritsky et al. (2002) find little or no extinction in the Magellanic Clouds, except around the youngest stars. Hence, we might expect NGC 4449 to have relatively low values of reddening as well.

Previously, Whitmore et al. (2011) found evidence for moderate extinction toward very young, embedded clusters in the more massive spiral galaxy M83, based on the locations of strong, Hα-emitting clusters in the color–color diagram. These values are included as open circles in Figure 6 for comparison with NGC 4449.

This figure reveals a key difference between the colors of very young clusters in NGC 4449 and M83: in M83, very young, embedded clusters follow the reddening vector nearly all of the way down to the end of the model tracks, but in NGC 4449, the distribution of colors appears to be fairly horizontal rather than following the reddening vector diagonally down and to the right. As discussed further in Section 4, this leftward ∼scatter in V − I probably results from the contamination of gaseous emission lines around young stars in the F555W filter, which are included in the Yggdrasil models but not in the Bruzual–Charlot models. Only two NGC 4449 data points in Figure 6 are slightly low, and these are consistent with ages of 7 Myr or less. These ages are compatible with expectations for regions with Hα emission, hence there is no need for reddening to explain their location in the color–color diagram, unlike the case for M83. We conclude that the clusters in our NGC 4449 catalog appear to have very low total reddening (foreground plus internal), with $E(B-V)\,\lesssim 0.2-0.3$ mag. We adopt an upper limit ≈3× larger (i.e., E(B – V) = 0.75) when age dating our clusters, as described in Section 4.1.

Figure 7 shows the reddening values from the LEGUS age-dating solution (upper panel), the reddening values using the H_α-LEGUS algorithm and a limit of E(B − V) <0.75 (middle panel), and a hybrid using the 0.75 mag limit for the youngest clusters and a value of 0.0 mag for clusters with age estimates greater than 10 Myr (note that this is done in two iterations: the first where reddening is allowed to vary to determine the age, and the second where E(B − V) is set to 0.0 mag for the older clusters). This latter strategy is what is actually used in the final H_α-LEGUS catalog, as will be discussed in more detail in Section 4.1. We note that most of the clusters with E(B − V) values greater than 0.4 in the final Hα-LEGUS fits are those discussed earlier, with strong Hα emission pushing their colors blueward of the model.

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A consistency check is possible via comparison of our E(B − V) values to those for H ii regions in NGC 4449 based on Balmer decrement observations (Annibali et al. 2017). They find values ranging from 0.10 to 0.24 for six H ii regions. This is consistent with our estimate of $E(B-V)\lesssim 0.2-0.3$ mag from Figure 6 for the objects with strong H_α, and also with the mean value of E(B − V) = 0.16 for the 104 clusters with H_α-LEGUS ages less than 10 Myr in Figure 7. Annibali et al. (2017) also make estimates of E(B − V) for older planetary nebulae in NGC 4449. While these estimates have larger uncertainties, four of the five values are consistent with E(B − V) = 0.0.

Note that the LEGUS solution (top panel) has a large number of clusters with E(B − V) ≈ 1. Essentially all of these objects are actually old globular clusters with overestimated values of E(B − V), based on comparisons with either spectroscopic (Annibali et al. 2018) or integrated photometry (Annibali et al. 2011) observations. This topic will be revisited in Section 5.1.

While our results suggest that it is appropriate to restrict the range of reddening and extinction that is considered in our fitting algorithm for NGC 4449, we note that more massive and metal-rich galaxies such as M83 or the Antennae require a higher reddening limit (e.g., Whitmore et al. 2010, Whitmore et al. 2011).

If reddening is a relatively minor effect in NGC 4449, then why are there so many points well to the right of the models in Figure 5? In Figure 8, we isolate 79 objects with these colors. In Figure 9, we show part of Region 8, where 10 of these objects reside (i.e., the yellow circles). In all 10 yellow circles, we find that the reddish V − I colors are caused by the presence of red stars in the aperture. A visual examination of all 79 objects shows that 76 of them have bright red stars in the aperture! We note that Johnson et al. (2012) found a similar distribution of objects in M31 (see their Figure 12).

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This effect is often called stochasticity; the random presence of at least one red supergiant in a low-mass cluster or association. For low-mass clusters, the chance of containing a single red supergiant is often less than 50%, hence there are no red stars in the aperture for some associations. Five of these all blue-star compact associations are shown by blue circles in Figure 9, (note that the five-pixel apertures used to measure the photometry are roughly half the size of the circles shown in Figure 9). The locations in the color–color diagram for these regions with only blue stars are shown by the squares in the top panel of Figure 8. As expected, all five are well to the left of the objects where the red stars are found. This stochasticity introduces a large random component in the age dating of low-mass clusters, as discussed in several papers (e.g., Maiz Apellaniz 2009; Fouesneau & Lancon 2010; Fouesneau et al. 2012; Krumholz et al. 2015).

More specifically, stochastic effects can result in underestimated ages from most SED fitting procedures, since the algorithm assigns a large reddening vector to bring it into better correspondence with the models. This is shown in the middle panel of Figure 8, where LEGUS assigns log age = 7 for nearly all of the objects in this part of the diagram. The Hα-LEGUS age estimates are older, with mean values around 7.5 (i.e., 30 Myr). This is more realistic because there is essentially no Hα in the region, indicative of ages greater than 10 Myr. The bottom panel of Figure 8 shows that age differences estimated by H_α-LEGUS are interpreted as large reddening values in the LEGUS estimates. A more detailed discussion of stochasticity, and a potential method of reducing its effects by the "stacking" of objects, is included in Hannon et al. (2019).

The lack of any clear evidence for strong extinction in NGC 4449 (i.e., Figure 6) and the fact that stochasticity can result in the underestimate of cluster ages (i.e., Figure 8) lead us to adopt "zero reddening" for cluster ages greater than the 10 Myr solution for the H_α-LEGUS catalog, as shown in the bottom panel of Figure 7. We note that this is also compatible with several recent findings showing that the dust is generally cleared around young clusters in only a few Myr (e.g., Whitmore et al. 2011; Hollyhead et al. 2015; Grasha et al. 2018; Matthews et al. 2018). In addition, the adoption of the zero-reddening solution for older clusters is similar to the procedure used by Annibali et al. (2011), who assumed no internal extinction for all clusters in NGC 4449.

In principle, it might be possible to limit the effects of stochasticity by only including relatively high-mass clusters. However, as shown in Figure 10, this does not work particularly well, since the fractions of sources with colors in the "stochastic zone" (i.e., U − B < −0.6 and V − I > 0.7) for the fairly massive clusters (i.e., greater than 10,000 solar mass) are fairly similar to those for the lower-mass clusters (less than 3000 solar mass). We also note that only 2 of the 122 added clusters are in the stochastic zone, primarily because very few category 3 (compact associations) were added. One way to limit the effects of stochasticity is to only include category 1 and 2 sources (see Figure 5), as we and several other LEGUS studies have done in various parts of the analysis.

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We find the best-fit combination of age and extinction for each cluster by comparing the magnitudes measured in five broadband filters (UV, U, B, V, and I) and one narrowband filter (Hα), with predictions from the Bruzual & Charlot (2003) stellar evolution models. The narrowband filter contains nebular line plus stellar continuum emission. The Bruzual & Charlot models used here do not include nebular emission, but do predict the number of Lyman continuum photons. We use this to predict the Hα line luminosity as a function of age, using Equation (9) from Leitherer & Heckman (1995), and combine it with the predicted stellar continuum to get a total (line+continuum) predicted magnitude for this filter.

The measured and predicted magnitudes are compared by performing a least χ² fit in which each filter is weighted by ${W}_{\lambda }={\left[{\sigma }_{\lambda }^{2}+{(0.05)}^{2}\right]}^{-1}$, where σ_λ is the photometric uncertainty, and assuming a fixed metallicity of Z = 0.004 (∼1/4 solar), a Chabrier (2003) initial stellar mass function, and a Galactic extinction law (Fitzpatrick 1999). The mass of each cluster is determined by multiplying the predicted M/L_V at the best-fit age, with the extinction-corrected V-band luminosity of the cluster, using an assumed distance modulus of Δ(m − M) = 27.91. Our final cluster catalog is called 'Hα-LEGUS' in what follows.

The method for including the narrowband H_α measurements is updated here, over the one described in Chandar et al. (2010), based on the additional information provided by the H_α morphological classification discussed in Section 2.1, which allows us to characterize the presence or absence of associated line emission beyond the five-pixel radius used directly for the H_α measurement. For Hα-morph class 1 and 2, the actual magnitude measured for the narrowband filter is used (including both line and continuum emission). For H_α-morph classes 3 and 4, which have little or no associated H_α line emission, respectively, the F658N filter is effectively treated as a measure of the R-band continuum.

We make two additional updates to our age-dating method based on the discussion of reddening in Sections 3.2 and 3.3, as well as the graphics in Figure 6. The first is to set an upper limit of E(B − V) ≤0.75 mag, reflecting the low extinction in this galaxy even for the youngest clusters. The second is to adopt a zero reddening (E(B − V) = 0) age-solution for clusters with estimated ages older than 10 Myr (based on an initial iteration where the reddening is allowed to vary).

With these revisions included, the age estimates for older clusters from our H_α-LEGUS catalog are in much better agreement with the spectroscopic determinations (see Section 5.1 and Table 1). In addition, we find a larger, more reasonable number of clusters with ages $\gtrsim {10}^{9}\,\mathrm{yr}$ (77 instead of just 5).

Table 1.  Comparison of log Age Values

ID/alias	LEGUS	E(B − V)	Hα-LEGUS	Annibali et al. (2011)	Annibali et al. (2018)	R.A.	Decl.	V − I	$(U-B)$
				Photometry	Spectra
	(log Myr)	(mag)	(log Myr)	(log Myr)	(log Myr)			(mag)	(mag)
582/CL3	6.85	0.86	9.40	9.85	9.95	187.06849	44.12486	1.253	0.035
592/CL77	6.78	0.91	9.65	9.86	10.08	187.05641	44.14404	1.135	⋯
32/CL79	6.70	0.92	9.26	9.91	10.04	186.99944	44.07870	1.070	⋯
13/CL76	9.48	0.02	9.40	10.08	10.04	187.01615	44.07090	1.165	⋯
28/CL67	8.70	0.00	8.86	8.49	⋯	187.03891	44.07748	0.712	−0.025
153/CL20	9.60	0.03	9.70	9.16	10.04	187.07843	44.08878	1.219	−0.011
417/CL8	9.30	0.00	9.41	9.71	⋯	187.07828	44.10641	1.015	−0.010

Note. 1. Values with discrepancies greater than 1.4 from the Annibali et al. (2011, 2018) values are shown in italics.

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To this point, we note that integrated colors are significantly worse at providing age estimates of ancient globular clusters than integrated spectroscopy, at least in part because of the age–metallicity degeneracy. We estimate the age we would determine for the bluest known, most metal-poor Galactic globular clusters, which are confirmed to have ages ≈13 Gyr from their main-sequence turnoffs (VandenBerg et al. 2013), by comparing their colors of U − B ≈ 0.0 and V − I ≈ 0.8 to the Z = 0.004 Bruzual & Charlot model. We find that these colors would give a predicted age of ≈9.1 in log age; we use this value as a lower limit for candidate globular clusters in NGC 4449. We note that this is consistent with our results from Table 1, where we find that all of the confirmed old globular clusters from Annibali et al. (2018) have H_α-LEGUS ages greater than 9.2 in log age.

Our final age estimates have random uncertainties of ≈0.3 in log age, or a factor of 2. There are also systematic uncertainties near log age ≈7.0, when the model colors loop back on themselves, leading to "gaps" in the age–mass diagram (e.g., see the upper right panel of Figure 6). See Chandar et al. (2010) for further discussion of error estimates.

In this section, we take a detailed look at the age results from Hα-LEGUS, and compare them with the ages determined as part of the LEGUS survey. It is important to remember that there are a number of differences in the methods used to estimate the ages in the two cluster catalogs.

• 1.  
  The catalogs use different fitting codes: the procedure used for Hα-LEGUS is described above (Section 4.1), and that for LEGUS is described in Adamo et al. (2017).
• 2.  
  The catalogs use different filter combinations, with and without the narrowband Hα measurement.
• 3.  
  The treatment of reddening is different, as discussed in Section 3.
• 4.  
  The catalogs use different methods for making aperture corrections: Hα-LEGUS applies an aperture correction that does not vary from filter to filter, and hence does not affect the colors, whereas LEGUS applies independent aperture corrections to each filter (see Adamo et al. 2017).
• 5.  
  The catalogs use different SSP models: Bruzual & Charlot (Hα-LEGUS) versus Yggdrasil (LEGUS).

In this section, we compare the age results from the catalogs generated by H_α-LEGUS and LEGUS.¹⁸ In Section 4.3, we examine the impact of different assumptions one at a time by using the same fitting code (i.e., the H_α-LEGUS code described in Section 4.1). The same photometry is used to assess the impact that different combinations of filters, reddening, SSP models, and assumed metallicities have on the results.

In Figure 11, we compare our Hα-LEGUS results with those from the LEGUS HLSP catalog available from the LEGUS public website. The filled circles show results when photometry in all filters is available (i.e., UV, UBVIHα for Hα-LEGUS and UV, UBVI for LEGUS), and the open circles show results when no UV or U band photometry is available (i.e., BVIHα for Hα-LEGUS, and BVI for LEGUS).

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It is important to note that the standard procedure for LEGUS is to only include age estimates when four or more broadband filters are available. However, we have relaxed this constraint for our study of NGC 4449, since there are a number of clusters in the outer parts of the galaxy with only BVI (and Hα) observations. While age dating that does not include the UV or U band filters can result in larger uncertainties in general, if zero internal extinction is appropriate (e.g., for nearly all the clusters in the outer portions of NGC 4449 where only BVI observations are available), good age estimates are possible, as will be shown below.

It is illustrative to examine clusters that fall in different parts of this diagram. Four representative cluster snapshots are shown for this purpose.

The top image shows an example of a cluster near the top of the most prominent vertical chimney, with an age of log age ≈ 6.7 from LEGUS, and log age ≈ 9.4 from H_α-LEGUS. This cluster, and essentially all others in the top of this chimney, are identified as old globular clusters based on their appearance, colors, and spectra (the spectra are discussed further in Section 5.1). Hence, the older H_α-LEGUS ages are more accurate. If we follow the chimney down farther, to log age(Hα-LEGUS) > 7.9, we find a larger fraction of category 2 clusters coming in. There are essentially no category 3 objects in the chimney (i.e., 33 of the 34 are category 1 or 2). Hence, this chimney is caused by effects related to the inclusion of H_α and differences in the treatment of reddening, as will be discussed in Section 4.3, not by stochasticity—which is mainly relevant for category 3 objects.

While many of the clusters in this chimney do not have UV or U band photometry, a number do; therefore, it is not only the lack of information in these bluer filters that drives the discrepancy between the Hα-LEGUS and LEGUS ages.

The second snapshot down shows an example of a cluster further down in the most prominent chimney, with an estimate log age ≈ 6.7 from LEGUS, and log age ≈ 8.8 from H_α-LEGUS. The older age appears to be more appropriate for this and most of the other objects in this part of the chimney, since the cluster is diffuse and whitish instead of blue, and there is no evidence of H_α emission.

The third snapshot down shows one of the many (≈100) clusters that are assigned young best-fit ages from both methods. These are generally very blue, often with evidence of H_α emission in the vicinity as in this particular snapshot (i.e., the diffuse, green emission). The main difference in the results for the few clusters that show strong line emission (those that follow the Yggdrasil model extension along the top left in the color–color diagrams shown in Figures 5 and 6) is that H_α-LEGUS returns best-fit ages of log age ∼ 6.4, while LEGUS returns best-fit ages of log age = 6.0.

The bottom snapshot shows an example where both LEGUS and H_α-LEGUS find intermediate ages, with log Age ≈ 8.0 from LEGUS, and log age ≈ 9.0 from H_α-LEGUS. It is unclear which age, the H_α-LEGUS or the LEGUS, is more appropriate based on the appearances of these clusters.

We now look at the overall comparison in Figure 11 in more detail. The first obvious difference is the much larger number of clusters in Hα-LEGUS with ages >10⁹ yr, as noted above. The numbers of clusters represented by each of the four snapshots are 17 (top snapshot: LEGUS <= 7.0 and Hα-LEGUS >= 9.0 in log age), 39 (second snapshot down: LEGUS <= 7.0 and Hα-LEGUS between 8.0–9.0 in log age), 98 (third snapshot down: LEGUS <= 7.0 and Hα-LEGUS <= 7 in log age), and 20 (bottom snapshot: LEGUS between 7.5 and 8.0 and Hα-LEGUS >= 8.3 in log Age).

Hence, there are 76 (i.e., 17 + 39 + 20 from above) clusters (i.e., 13% of the 592) in these three "chimneys." The larger number (i.e., 98) of clusters represented by the third snapshot down demonstrates that the overall agreement is actually fairly good; the outliers are spread out more and hence look more dramatic in the figure.

Another way to quantify the differences between ages derived in LEGUS and H_α-LEGUS is to normalize by the mean offset between the two systems and then look for discrepancies greater than a factor of three, i.e., 0.5 in log age, for clusters with H_α-LEGUS ages that are less than log Age = 9, i.e., where SED ages are less reliable (see R. Chandar et al. 2020, in preparation). Twenty-seven percent of the clusters fall in this outlier category using this method of comparison. Hence, to reiterate, while there are some important differences, the overall agreement between the ages from H_α-LEGUS and LEGUS is actually fairly good.

In Section 7, we find that the mass and age distributions based on the Hα-LEGUS and LEGUS catalogs give similar results, despite the differences discussed in this section. This demonstrates that the mass and age distributions are fairly resilient to the detailed differences in age dating.

In this section, we assess the impact that different combinations of filters, different assumptions for reddening, different SSP models, and different assumed metallicities have on the results; we consider each parameter in turn.

4.3.1. Impact of Using Different Filter Combinations

So far, we have focused on the effects that different assumptions about reddening can have on age dating clusters in NGC 4449. However, an equally important effect (actually more important in dusty galaxies, where one cannot assume minimal reddening) is the use of Hα in the SED fitting of young cluster populations, to help break the age/extinction degeneracy. We focus on that question in this section.

We note that it is just as important to know if there is no line emission as it is to measure the line emission when it is present. For example, this is one way to distinguish between young and old clusters in the prominent chimney in Figure 11. We also examine the relative importance of including the UV and U filters in this section.

Here, we examine only the impact on the results from different combinations of filters by rerunning the age dating using the same input photometry, fitting code, and SSP model (Z = 0.004 from Bruzual & Charlot), and allowing E_B − V as a free parameter in the fit, so that only the combination of filters is different.

In Figure 12, we compare the results between the following four filter combinations:

• 1.  
  UV, UBVI, Hα (all six filters).
• 2.  
  UV, UBVI (five filters, drop Hα).
• 3.  
  UBVI, Hα (five filters, drop UV).
• 4.  
  UV, BVI, Hα (five filters, drop U).

Given four sets of results, six comparisons can be made. The main result, which appears in three of the six panels, is that dropping the H_α filter has the strongest impact on the age results. The other panels show that dropping a broadband filter, such as the UV or U band, but keeping Hα does not significantly impact the age results compared with all six filters.

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We also note the similarity between Figure 11 and the three panels in Figure 12 that include the "drop H_α" filter combination. This demonstrates that one of the primary causes of the difference in H_α-LEGUS and LEGUS age estimates is the inclusion of the H_α filter. The other primary difference is the treatment of reddening. After inspecting clusters visually, we confirm that the presence or absence of line emission is important for accurate age dating.

Based on these figures and the differences between the Hα-LEGUS and LEGUS age results discussed in detail in Section 4.2, it appears that adding a measure of the line emission is much more powerful for age dating star clusters in star-forming galaxies than adding another broadband filter at short wavelengths. Both the UV and the U band appear to work equally well for age dating clusters.

4.3.2. Impact of Different Reddening Criteria

After the combination of filters, the next strongest effect in our age-dating procedure comes from our new assumption that reddening only affects cluster colors for the first ∼10 Myr in the case of NGC 4449. As described in Section 4.1, our final cluster ages come from the best-fit combination of age and reddening in the regime log Age < 10 Myr, and from the best-fit zero reddening solution for older ages. We discussed the justification for this in Section 3.2, and in 5.1 we will show that this assumption leads to significantly better estimates for the oldest clusters, based on comparisons with spectroscopically determined ages.

In Figure 13, we compare our final Hα-LEGUS ages with those found when we allow values of E(B − V) < 0.75 at all ages in the left panel, and E(B − V) = 0 at all ages in the right panel. When the reddening is allowed to be a free parameter at all ages, we see that some clusters are assigned younger ages because they are best fit with a combination that includes some reddening (those below the 1-to-1 line). We find that ∼14% of the clusters are significantly affected (at a level of 0.5 in log age or more) by this effect. The estimated ages of clusters with ages below 10 Myr are identical in this case, as expected. In the right panel, we see that the assumption of E(B − V) = 0 has a very small impact on the estimated ages of clusters younger than 10 Myr.

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Overall, we find that both the addition of Hα photometry and applying a maximum E(B − V) during age dating are important, and act primarily to prevent older clusters from being misclassified as younger ones. The age estimates of a similar number of clusters are affected in each case. There are, however, some differences. Including Hα in the age-dating procedure prevents older clusters with little reddening from erroneously being assigned a very young age (<10 Myr) plus high reddening. By itself, however, including Hα does not prevent older globular-like clusters from being assigned ages of ≈100 Myr. A more accurate estimate of the ages of these older clusters depends on restricting the maximum allowed value of E(B − V), regardless of whether or not Hα is included in the fit.

4.3.3. Impact of Assumed SSP Model

We now explore how using different SSP models affects the results, using the same photometry, code (Chandar et al. 2010), metallicity (Z = 0.004 ), and set of filters (UV, UBVI). We retrieved the Yggdrasil models in 2019 from their website. These assume a covering fraction of 0.5, and are somewhat different from those used as part of the LEGUS project, which used a different interpolation scheme.

The results are shown in Figure 14, where we compare ages from the Bruzual & Charlot models (x-axis) and those from the Yggdrasil models (y-axis). There are more striations when using the Yggdrasil models, because of the lower age sampling. We also notice that, unlike the LEGUS results (but similar to ours when using the Bruzual & Charlot models), almost no clusters are assigned ages as young as log age = 6.0 when the Yggdrasil models are used in our fitting code. This suggests that the absolute age values assigned to the youngest clusters may vary between models and fitting methods.

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Overall, we find that the results are fairly similar (with over 80% of the sources having estimated ages within a factor of three), but with some notable differences. There are two areas of the diagram where the ages deviate significantly: one where the Yggdrasil models give ages older by more than 0.5 in log τ or a factor of three (47 clusters), and one where the Bruzual & Charlot models give ages older by a similar amount (12 clusters).

In the cases where the Yggdrasil models give older ages, a visual inspection indicates that most clusters have blue colors, suggesting that they are quite young—consistent with ages of several Myr from the Bruzual–Charlot models, but inconsistent with the older log few × 10 Myr ages from the Yggdrasil models. This is likely related to the fact that the predicted colors from the Yggdrasil models at ages <10 Myr dip below the measured colors of very young clusters in NGC 4449.

4.3.4. Impact of the Assumed Metallicity

While we assume 1/4 solar metallicity for cluster age dating in NGC 4449, it has been suggested that half-solar may be a better match to the abundance of the current gas (Annibali et al. 2017). In Figure 15, we compare the results when the Hα-LEGUS age-dating procedure (with all six filters) is run with half-solar metallicity instead.

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The results show that there is a tendency toward slightly younger absolute ages (by ≈0.1 in log Age) when our default metallicity Z = 0.004 is assumed, compared with the higher metallicity Z = 0.008. Note that the relative age estimates are similar for both metallicities. We find that only 25 out of 594 (∼4%) clusters have ages that differ by more than a factor of 2 or log age = 0.3. We conclude that, if subsolar metallicities are used, the exact value assumed for NGC 4449 has a relatively small impact on the age results.

In a similar way, it might be more realistic to assume an even lower metallicity for the old globular clusters; e.g., Annibali et al. (2018) estimate 1/10 solar. We would expect this to have an effect similar to our experiment comparing 1/2 and 1/4 metallicity (shown in Figure 15), but in the opposite direction.

4.3.5. Summary of Age Comparisons Taken One at a Time

Age estimates from absorption lines measured from integrated, low-resolution spectra in the range 3200–10000 Å have been made by Annibali et al. (2018) for 11 clusters in NGC 4449, seven of which are in common with our sample. In Table 1, we compare the spectroscopic age estimates with those determined from LEGUS, H_α-LEGUS, and Annibali et al. (2011) (using integrated colors) results. In all cases, we find the Annibali et al. (2018) spectroscopic ages to be older than the photometric ages, and especially so for the first three LEGUS values. Two of the three discrepant clusters have no (U − B) values in Table 1, indicating that they have only ACS BVI measurements (i.e., they are in the outskirts of the galaxy as seen in Figure 2). All of the H_α-LEGUS values in Table 1 are also below the Annibali et al. (2018) spectroscopic ages, but none by more than an order of magnitude. We also compare with integrated light age estimates using BVI from Annibali et al. (2011) in Table 1, finding better agreement with the spectroscopic ages, but still slightly lower values for the photometrically determined ages.

For LEGUS, the difference between the ages derived from integrated photometry and spectroscopy appears to be mostly due to the fact that the SSP fitting routine prefers the combination of a young age plus high reddening over an old age with low reddening. For H_α-LEGUS, the lack of detected H_α pushes the algorithm to an older age solution, although they are still lower than the spectroscopic age estimates. We also note that the well-known age–metallicity degeneracy affects the age estimates, because clusters with ages ≳Gyr generally have lower metallicities than the one assumed for younger clusters, resulting in ages lower sometimes by ∼0.6–0.7 dex than found via spectroscopy (the effect is significantly smaller at younger ages).

Comparisons between ages derived from LEGUS (including cases with only three filters, BVI, which is nonstandard for LEGUS and must be done with caution; i.e., only for clusters where there is no evidence of reddening), H_α-LEGUS, and Annibali et al. (2011) (using BVI integrated colors) are shown in Figure 16.

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The comparison between LEGUS and the Annibali et al. (2011) models look very similar to the Figure 11 comparison between H_α-LEGUS and LEGUS, presumably because Annibali et al. (2017) assume that there is no reddening internal to NGC 4449 itself, similar to the assumption we make in the H_α-LEGUS method for log age > 7.0 clusters. This results in older age estimates for many of the clusters in both cases.

Indeed, the right panel comparison between Annibali et al. (2011) and the H_α-LEGUS method is quite good, with a slope near unity, small scatter (rms = 0.42), and a small offset (+0.13 mag). This follows the good agreement we found between H_α-LEGUS and Annibali et al. (2011) in the much smaller sample shown in Table 1.

A comparison of all the clusters in the Annibali et al. (2011) photometric study with the LEGUS sample shows that 16 of the 25 outliers (i.e., in the vertical chimney in the left panel of Figure 16) turn out to be clusters with only BVI measurements. However, the other nine clusters in the chimney do have measurements in all five filters, indicating that this problem is not caused exclusively by the lack of the U filter observations. All filter combinations (i.e., both the open and filled circles) are in agreement in the right panel comparison between Annibali et al. (2011) and H_α-LEGUS.

Recent papers by Sacchi et al. (2018) and Cignoni et al. (2018) provide another potential comparison with our cluster age estimates. These authors use the stellar component of NGC 4449 to determine star formation histories in several large regions in the galaxy. Their results are also used in Section 7 to help separate the effects of cluster formation and disruption. In the current section, we use the PSF-fitting photometry of resolved stars from the stellar catalog provided by Sabbi et al. (2018) to estimate ages for 10 each of the category  2 (asymmetric) and category  3 (compact associations) objects in our catalog using resolved stars. As can be seen from the color–color diagram in Figure 5, most of the category  1 clusters are older, and the individual stars are too faint to be detected. Consequently, this procedure was not attempted for category 1.

Given the extreme crowding conditions and the small size of these samples, we applied an isochrone fitting technique to the CMDs, instead of a full statistical derivation of the cluster SFH. Category 2 and 3 clusters that appeared to have extended halos of resolved stars were selected for this exercise. Stars within a radius of 20 pixels (=15 pc) of the objects were evaluated, using the cluster's appearance to help determine where most of the stars were likely to be associated with the cluster (i.e., the density was higher than the surroundings). There were typically about a dozen stars that appeared to be associated with a cluster. In some cases, especially in the outer annuli, it is likely that some of the stars are in the background rather than in the clusters. However, to the extent that stars in the surrounding region have the same age (i.e., they are both part of a larger association), this will generally give the same result. One of the primary concerns for this approach is the presence of blends, since many of these regions are very crowded. For this reason, it is only possible to provide upper or lower estimates in some cases.

Figure 17 shows an example of how the age dating is done using the CMD for compact association C3-3144-6144 (alias: cluster 401 in Table 2). Note the enhancement of nine blue stars on the left side of the upper panel (i.e., within a radius of 15 pixels). These are only compatible with the 5 or 10 Myr isochrones. The six stars to the right cover a variety of potential ages and are likely to be foreground or background stars. The bottom panel, consisting of the annulus just outside of 15 pixels, allows us to distinguish between the 5 and 10 Myr isochrones (assuming minimal reddening so the points do not move around much on the CMD) with two stars along the 10 Myr isochrone. Hence, this compact association is assigned an age of 10 Myr in Table 2.

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The resulting comparisons with our H_α-LEGUS ages are shown in Figure 18. Keep in mind that some of the CMD estimates are upper or lower limits. While the scatter is relatively large for the comparison in some cases, it does appear that the CMD ages are compatible with our integrated light age estimates in general, and the approximate mean values (the X symbols in Figure 18) are in fairly good agreement. Note that the mean values are calculated without taking into account the fact that many of the points are upper and lower limits. The mean position, (i.e., the "X") would almost certainly be closer to the one-to-one line in the left panel if estimates without upper and lower limits could be made, since there are eight lower limits and only two upper limits.

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A careful examination of the snapshots in Figure 18 provides important insights into the age dating for both methods, and the classification of category 2 (asymmetric clusters) as compared to category 3 (compact associations). The two images on the left of each panel have diffuse weak emission-line flux (the green color), and hence are given slightly younger ages using the H_α-LEGUS method. The two snapshots close to the one-to-one line have no emission and no dominant red stars. The agreement between the two methods is very good in theses cases. The right snapshot in the right panel shows a case where two very bright red supergiants have misled the integrated light measurement into considering them an older cluster. However, these can be well fit as evolved stars with young ages in the isochrone fitting algorithms (i.e., this is cluster 401 shown in Figure 17 and discussed above). This is a good example of the effects of stochasticity for clusters/associations with masses less than a few ×10³ M_solar (e.g., see Fouesneau et al. 2012), as discussed in Section 3.3.

The upper right snapshot in the Category 2 (left) panel shows a case where the CMD age estimate is probably uncertain due to the presence of faint foreground/background stars, and the true age is much older than the CMD estimate of log age = 8.2. In fact, both Annibali et al. (2011) (integrated light) and Annibali et al. (2018) (spectra) consider this object to be an old globular cluster with log age >10 Gyr, as does our H_α-LEGUS determination. Note that in Table 2, that this object is only assigned a lower limit (i.e., >170 Myr) by the CMD method.

A similar comparison between CMD and integrated light age estimates was performed by Larsen et al. (2011) for relatively nearby, partially resolved clusters in NGC 1313, M83, and three other galaxies that are at similar distances to NGC 4449. As here, there was reasonably good agreement between the two methods of estimating ages, although crowding was identified as a primary difficulty.

While estimating CMD ages for clusters and compact associations is inherently difficult at the distance of a few Mpc, it is reassuring that the mean ages are in reasonably good agreement with the mean ages from our integrated light determinations, as shown in Figure 18. Although the scatter is large, we note that 16 of the 20 points are within 1 dex of the one-to-one line.

Sokal et al. (2015) have used a combination of optical and infrared observations (i.e., Spitzer IRAC 3.6 μm, 4.5 μm, 5.8 μm, and 8.0 μm observations, along with Herschel Space Telescope observations) of the giant H ii region S26 (a strong thermal radio continuum source and the brightest object in our Region 7—a snapshot of this object is shown in the bottom right panel, on the left side, of Figure 5) and estimate an age of 3.1 ± 0.3 Myr for this object. The region has strong Wolf–Rayet features, which are consistent with this age estimate.

The LEGUS age estimate for S26 is 3.0 Myr, whereas the H_α-LEGUS age estimate is 5.0 Myr. There are a total of eight objects in Region 7, all with fairly similar age estimates. The LEGUS age estimates range from 1.0 to 5.0 Myr, with one outlier at 15 Myr. The H_α-LEGUS ages are all between 3.0 and 5.2 Myr. Reines et al. (2008) have estimated ages for 11 H ii regions in NGC 4449, all in the range 2–6 Myr. We conclude that the age estimates for H ii regions from both LEGUS and H_α-LEGUS are in quite good agreement with those from H ii regions in NGC 4449.

We also note that Sokal et al. (2015) estimate a reddening value of E(B − V = 0.13 mag for S26, in good agreement with the values discussed in Section 3.2 for regions with strong H_α. This measurement is also compatible with earlier optical studies of S26 and other H ii regions in NGC 4449 by Reines et al. (2008, 2010).

In Figure 22, we present the mass–age diagrams of the clusters in NGC 4449. The upper panels show our results for categories 1 and 2 (left) and categories 1, 2, and 3 (right), using the H_α-LEGUS age estimates. The bottom panels show the results when using the LEGUS age estimates. The similarity in the diagrams shows that even with fairly important differences in the age-dating procedures, as discussed in Section 4, the resulting changes in the mass and age distributions are likely to be relatively small. This result is confirmed when comparing the slopes in the mass and age functions, as discussed below.

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The points that are circled in the upper left panel are from added clusters, as discussed in Section 2.1. We note that only four of the added clusters are massive enough to be included within the limits used to construct the mass functions and age distributions, which are shown by the dotted lines in Figure 22.

As is generally the case, the mass function of star clusters can be approximately described by a power law, ψ(M) ∝ M^β. In Figure 23, we show the mass functions using H_α-LEGUS ages for category 1, 2, and 3 clusters in the top panels, and for category 1 and 2 in the bottom panels, divided into three different age intervals: <10 Myr (left), 10–100 Myr (middle), and 100–400 Myr (right). The distributions have an equal number of clusters in each bin, as recommended by Maiz Apellaniz & Ubeda (2005), and are not sensitive to the exact number used.

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The best-fit values for β are mostly between ≈ −1.7 and −2.1. The mean value after the high and low values are removed is β ≈ −1.86. If LEGUS ages are used instead of H_α-LEGUS ages, we find values β ≈ −1.9, identical to those found by Cook et al. (2019) for the composite LEGUS dwarf sample, which includes NGC 4449.

The results for β for the different age intervals are mostly similar within the uncertainties, indicating that there is no apparent change in the shape of the mass function over the age–mass ranges studied here. The mass function for cat = 1 + 2 clusters with ages log age = 7–8 appears a bit flatter, but this is the range where the biases in the age dating are strongest, and small number statistics are also playing a role.

We have also checked the mass function of clusters in three different radial bins: R_gc < 1.06 kpc (47''), 1.06–1.82 kpc (47–975), and R_gc > 1.82 kpc (>975). Although the statistics are poor in some cases, the mass function in the different radial bins and in the three age ranges studied above, are also described reasonably well by a single power law with an index β ≈ −2, i.e., there is no clear trend as a function of radius.

A number of studies have reported that the upper end of the cluster mass function drops off compared with a power law (e.g., Gieles et al. 2006; Larsen et al. 2011; Johnson et al. 2017; Messa et al. 2018), and that this upper mass cutoff may correlate with the SFR of the host galaxy (Johnson et al. 2017). However, Mok et al. (2019) applied a maximum likelihood fitting method to the cluster population in NGC 4449 and did not find evidence for a cutoff mass, consistent with the distributions shown here in Figure 23.

The mass–age diagrams in Figure 22 give a preview of the cluster age distributions. If the age distribution was flat (i.e., a power-law slope ≈0), as for the hypothetical case where clusters formed at a constant rate and none were disrupted, there would be a factor of 10 more clusters in a given mass interval for each full dex in log age, because the bin size is a factor of 10 larger for each dex. This would result in a strong horizontal gradient (at a given value of log mass) in Figure 22. However, we find that the horizontal gradient in log age is relatively uniform, which would suggest a decline in the age distribution by roughly a factor of 10 for each decade of log age to compensate for the larger bins. This corresponds to a slope in the age distribution, when fit with a power law, of ≈−1; see Figure 3 of Whitmore et al. (2007) for a graphic illustration. There does appear to be a slight enhancement of clusters around an age of a few 100 Myr, however, which will be discussed in Section 7.3.

Plots of the age distributions of star clusters (i.e., dN/dτ diagrams) are constructed by counting clusters in equal bins of log τ from clusters within a given mass range. These can be described by a power law, χ(τ) ∝ τ^γ. In Figure 24, we present the cluster age functions for category 1, 2, and 3 (right panels), and for category 1 and 2 only (left panels), in three different mass ranges, being careful to stay above the completeness limits, which are shown in Figure 22.

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All of the distributions decline more-or-less continuously, (although there is some evidence for an enhancement around a few hundred Myr, as mentioned above), with γ values between −0.74 and −0.95, i.e., around −1 or slightly flatter, as expected because the horizontal gradient is relatively uniform in Figure 22. This decline is approximately independent of the mass of the clusters, since the fits in different mass ranges are within the uncertainties. Given the range presented here, we find γ = −0.85 ±0.15, very similar to the result found by Rangelov et al. (2011). We have checked, and find a similar value of γ for the NGC 4449 cluster catalog published by Cook et al. (2019).

Overall, we find that the shape of the age distribution of clusters in NGC 4449 appears to be similar regardless of the exact method used to select the clusters or the specific age intervals used in the analysis. Making similar fits using the LEGUS rather than the H_α-LEGUS ages results in γ values between −0.62 and −1.02, with a mean of −0.82 ± 0.17, very similar to the value of −0.85 using H_α-LEGUS ages. Hence, even though differences in detail can be seen in the four mass–age diagrams in Figure 22 (i.e., using subsamples with different categories or age-dating methods), the slopes of the age distribution derived from the data are relatively resilient. If we limit the sample to only category 1 clusters from the H_α-LEGUS catalog, the slopes are slightly shallower, with values between −0.60 and −0.69 and a mean of −0.66. The shallower slopes are due to the large number of category 1 objects with ages in the range of roughly a few hundred Myr (resulting from an enhancement in formation), as seen in Figure 5 and discussed in Section 7.3.

An observed logarithmic cluster age distribution with an index of −0.85 indicates that clusters are destroyed at a rate of (1−10^−0.85) × 100 = 86% each decade of time, similar to the results for a number of spiral, merging, and dwarf galaxies (Whitmore et al. 2007; Chandar et al. 2010; Bastian et al. 2012, Fall & Chandar 2012, Cook et al. 2019). We note, however, that some works have found significantly flatter age distributions as well (e.g., Silva-Villa & Larsen 2011, Fouesneau et al. 2014; Mora et al. 2009) for other galaxies.

We have examined the age function of clusters in three different radial bins: R_gc < 1.06 kpc (47''), 1.06−1.82 kpc (47−975), and R_gc > 1.82 kpc (>975), using two different mass ranges, categories 1 + 2 + 3, and excluding the youngest data point because there are very few clusters in most of the samples for this bin. The resulting values of γ range from an average of −0.89 ± 0.07 for the central region, to −0.96 ± 0.09 for the intermediate region, to −1.13 ± 0.24 in the outer region. Thus, there are no clear trends for the slopes of the age distributions to vary with radius from the center in NGC 4449, although we note that the statistics are fairly poor when breaking the sample into these smaller subsamples.

The observed cluster age distribution is the product of the formation and disruption histories of the clusters. In order to determine the cluster disruption history, we need independent information about the formation history, i.e., has the formation rate been relatively constant during the relevant period of time, as is generally assumed? The stellar formation history of NGC 4449 has been determined from the LEGUS data, as described in detail in Sacchi et al. (2018), and is a possible proxy for the cluster formation rate under the assumption that star and cluster formation track one another closely. Chandar et al. (2017) find that this is a good assumption for the eight galaxies examined in that paper, for example.

In Figure 25, we show the composite SFH of the galaxy, as well as the history in the three different galaxy radii defined above. While there is a modest enhancement in the SFH in the last 10 Myr, resulting in NGC 4449 being known as a starburst galaxy, beyond 20 Myr there is no systematic trend for the SFR to increase or decrease over the past several hundred Myr. A fit to the total SFH beyond 20 Myr, which is the focus of the current discussion, gives a power-law index of γ_form ≈ 0.49 ± 0.56, i.e., broadly, the formation rate is essentially flat, without any systematic increases or decreases over the last several 100 Myr.

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Hence, with the assumption that the stellar and cluster formation rates track each other, this means that the observed age distribution, with γ = −0.85, primarily reflects the disruption history of the clusters. There are, however, some variations at the factor of ≈2–3 level in the SFRs over shorter time intervals. In particular, we note the enhancement that occurred a few hundred Myr ago, for both the stellar and cluster populations. This will be discussed in more detail in the next section.

Here, we estimate the level of enhancement in the star and cluster formation rate a few hundred Myr ago. As discussed in Section 2, there is evidence that NGC 4449 had an interaction with one or more companions roughly 100–500 Myr ago (Hunter et al. 1998, 1999; Theis & Kohle 2001; Karachentsev et al. 2007; Martínez-Delgado et al. 2012; Rich et al. 2012), probably resulting in the enhanced star and cluster formation rates. The enhancement in the cluster population is seen in the color–color diagram (i.e., the category 1 clusters in Figure 5) as well as the mass–age diagrams (Figure 22), and therefore is not due to systematic biases in the age dating or to binning.

The SFHs determined from independent data sets by McQuinn et al. (2010) and Sacchi et al. (2018) for NGC 4449 both show a similar enhancement in the rate of star formation a few hundred Myr ago, although there may be differences in the exact timing of the enhancement.

Figure 25 shows both the SFH, which is based on the analysis of individual stars from Sacchi et al. (2018) but extracted for the radial bins discussed in Sections 7.1 and 7.2, and the cluster formation history, which is based on the data in Figure 24. To obtain the cluster formation history, we divide the observed cluster age distribution by the best-fit, smooth power law (i.e., γ = −0.85), to remove the effects of disruption. This leaves behind variations in the cluster formation history. We repeat this procedure for age distributions with three different bin widths (0.4, 0.5, and 0.6 in log age), and for two different sets of bin centers, for a total of six realizations. Each one shows an enhancement in the cluster formation history, which range from factors of ≈1.5–4, around ages of ≈ few × 100 Myr. The mean value for these six realizations is a factor of 2.2 ± 0.7.

An enhancement is also seen in the SFH at similar ages, with a mean value of 1.8 ± 0.6 when comparing the three radial bins in the time range from 100 to 300 Myr, normalized by the two adjoining ranges (i.e., 30–100 Myr and 300–1000 Myr). If only the two inner bins are used, which might be more appropriate because there is no apparent recent star or cluster formation in the outer regions of the galaxy, the enhancement for the stars is 2.1 ± 0.4, even closer to the estimate for clusters. Hence, while the statistics are relatively poor, there does appear to be some evidence for similar levels of enhancement for both the clusters and stars in the range 100–300 Myr old. This suggests roughly constant values of T_L and (presumably) Γ as a function of increasing SFR.

There are few galaxies where direct comparisons between the star and cluster formation histories have been made. Two of the most promising galaxies for such studies are the Small and Large Magellanic Clouds. Although not yet definitive, recent studies of the cluster populations suggest that there was an enhancement in the populations ≈few × 100 Myr ago (e.g., Glatt et al. 2010; Bitsakis et al. 2017, 2018), during the time of the last closest approach. The star formation histories of both galaxies also show an enhancement around this same time period (e.g., Harris & Zaritsky 2004, 2009), although the strength of the enhancement for the stars and the clusters is not yet well-determined. Future studies will be needed in order to determine if these enhancements had similar strengths.

We note that the precision of the cluster (and stellar) age dating does not allow us to quantify the duration of the enhanced formation period very well. It might be an enhancement of a factor of 2 over the period from 100 to 300, or a factor of 20 enhancement over a 20 Myr old period around 200 Myr ago. The main conclusion here is that we observe an enhancement in both the star and cluster formation rates in NGC 4449 at a similar factor of ~2–3 level, a few hundred Myr ago. Hence, it appears that the cluster and stellar formation rates are closely related, and that T_L and (presumably) Γ are relatively constant during the burst.

Figure 26 shows a portion of NGC 4449 (region 16 and slightly to the west; see Figure 1) where nearly all of the clusters formed during this burst (i.e., 18 of the 22 clusters in this region have log age in the range from 8 to 9 Myr). Region 23 and just eastward, on the opposite side of the nucleus at a similar distance, shows a similar distribution with 29 of 40 clusters in the log age = 8–9 age range. No other regions show such a clear enhancement over this time period. This suggests that the original plane of the galaxy interaction that caused the starburst a few Myr ago was probably oriented in roughly an east–west direction. A more detailed study of these two regions (i.e., determining the star formation histories) might provide a more statistically significant comparison between cluster and star populations during a burst.

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