PHAT STELLAR CLUSTER SURVEY. II. ANDROMEDA PROJECT CLUSTER CATALOG

A star cluster can be defined in the most general sense as a grouping of stars that are spatially and temporally correlated. Beyond this broad definition, the notion of a star cluster can vary significantly, depending mostly on whether the system is still embedded in its natal gas or exposed (Lada & Lada 2003). Older (>10–30 Myr) gas-free systems are relatively straightforward to classify using a criterion based on the gravitational boundedness of individual members to a larger group. In contrast, young groupings of stars that are still embedded within the ISM make classification a difficult, uncertain task. These embedded clusters are still forming through hierarchical merging of sub-clumps (Allison et al. 2010), and the application of various stellar density thresholds to identify distinct features of a continuous (scale-free) distribution leads to interpretative challenges (Bressert et al. 2010; Gieles et al. 2012). Embedded environments are dynamically evolving and membership within a particular gravitational grouping is neither well-defined nor unique.

For the PHAT cluster catalog, we work mostly in the exposed, gas-free regime because our identification is based on optical imaging. Once the gas has been expelled from a star cluster and its stars have evolved through multiple dynamical times, it becomes possible to infer whether a grouping of stars is either gravitationally bound or expanding and dissolving (Gieles & Portegies Zwart 2011). Therefore, uncertainties pertaining to boundedness are minimal for our sample because a majority of PHAT clusters are already many dynamical times old, as inferred from the age and mass distributions of the Year 1 catalog (Fouesneau et al. 2014).

At young ages (<10 Myr), the use of boundedness as a selection criterion for clusters becomes difficult. Due to the similar appearance (i.e., radial spatial profile) of bound clusters and unbound stellar associations at young ages, determining boundedness becomes an uncertain and contentious enterprise (e.g., see Chandar et al. 2010a; Bastian et al. 2012; Whitmore et al. 2014). In the work that follows, we include all objects identified as part of our search. As a result, our catalog may include a heterogeneous mix of bound and unbound objects at ages <10–30Myr. We choose this approach in an effort to maximize the return for science cases that do not depend on the differentiation between bound clusters and unbound associations, while allowing open discussion of differing cluster definitions where they affect the resulting scientific interpretation. Overall, we seek a catalog of objects that are spatially and temporally correlated and can be reasonably approximated as simple stellar populations. While this goal is easily achieved for a majority of the sample, we will make a point to identify regions of parameter space that contain debatable objects, allowing the reader to make informed decisions with regards to boundedness. A full exploration of the question of boundedness requires detailed age and spatial structure information (Gieles & Portegies Zwart 2011), which is beyond the scope of this work.

The inclusive philosophy that we adopt in this work represents a shift from the approach we took in Paper I, where we discarded objects that were classified as likely associations. This paper's inclusive methodology leads to a modest ∼15% increase in clusters when compared to the Year 1 catalog within their shared imaging footprint. We discuss these catalog differences in detail in Section 6.2, but find good overall agreement between the two samples.

The Andromeda Project (AP)¹³ is a Web site built and hosted by the Zooniverse¹⁴ citizen science platform. The AP interface is based on previous tools and code used for the Seafloor Explorer project, another Zooniverse project that aims to survey scallops, seastars, and other aquatic life using underwater imaging.

Upon entering the AP website, visitors are presented with the primary option to start classifying data, as well as links to find out more about the project. Individuals who start classifying for the first time are directed to a tutorial image, where the basic functionality of the classification screen is explained. The classification screen is shown in Figure 1. By default, the site displays a color image constructed from F475W and F814W imaging. By clicking on the "B/W" button, participants can change the image to an inverted F475W gray scale image in which it is often easier to distinguish individual stars and faint image features. The site's marking tool is set for cluster identification by default; modes for identifying background galaxies and three types of image artifacts are also available. Markers for clusters, galaxies, or ghost artifacts are circular, positioned by clicking the center of an image feature and dragging outward to select the desired radius. Only the cluster and galaxy markings are utilized in this paper.

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After clicking on the "Finished" button, volunteers are shown the location of the field they were classifying within M31 and given the option to discuss the images in the AP Talk¹⁵ forum. This feature enables new volunteers to get help identifying clusters and allows participants to highlight interesting or confusing objects and discuss them with other volunteers and the science team. After choosing whether or not to enter the Talk forum, volunteers are presented a new search image; the AP image database ensures that no user sees the same image twice.

Volunteers are urged to log-in or create a Zooniverse account, but participants are allowed to classify an unlimited number of images as an unregistered user. Unregistered users do, however, receive periodic messages suggesting that they log-in or create an account. Registration allows analysis of volunteers' classification behavior using consistent (anonymous) identifiers. Input from unregistered users can still be aggregated from within a single classification session; however, the (anonymous) identifiers tend not to carry over from session to session and could be shared by multiple unregistered users, limiting the depth of analysis we can perform.

Each search image shown on the AP site was extracted from high-resolution (0.05 arcsec pixel⁻¹) HST/Advanced Camera for Surveys (ACS) images of M31. A vast majority of these images came from the PHAT dataset; we show the survey's imaging footprint in Figure 2. The prominent rectangular regions in Figure 2 that divide the survey into 23 parts are referred to as "bricks"; their numbering increases from SW to NE along the major axis, starting with the brick enclosing the galaxy nucleus, B01 (see Figure 1 in Dalcanton et al. 2012). In addition to the optical (F475W, F814W; equivalent to g, I) ACS images, PHAT also obtained near-UV (F275W, F336W; the latter is equivalent to U) and near-IR (F110W, F160W; similar to J, H) imaging using the HST/Wide Field Camera 3 (WFC3) instrument. Additional information about PHAT imaging data and survey design is available in Dalcanton et al. (2012) and Paper I.

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In addition to the PHAT data, we also processed and prepared ACS data from the HST archive (PID: 10273; PI: Crotts) that covered portions of M31 not imaged by PHAT. The imaging footprint for these data are also shown in Figure 2. This program obtained two-filter optical imaging using filters (F555W, F814W) similar to those used by PHAT, allowing easy incorporation into the AP search. Due to significant differences in data richness for objects identified in the archival dataset compared to the PHAT imaging, we choose not to include these objects in any further analysis, but we present object catalogs in Appendix E.

We created AP search images using 725 × 500 pixel (36.25 × 25 arcsec; ∼6.9 × 4.8 pc in projected size) extractions from single-field ACS images. This subimage size efficiently divides the image area, includes 100 pixels of overlap between neighboring subimages to reduce incompleteness and biases caused by image edges, and allows participants to search images at full resolution. The parent ACS images have missing data due to the camera's chip gap that we filled using overlapping data from neighboring ACS images. Gaps, edges, and other artifacts are still present in some images, but our efforts mitigated most issues concerning missing data. We created a total of 13,017 subimages (4.7 gigapixels) from imaging that spans the entire PHAT survey region, as well as 1728 addition subimages from archival imaging.

In addition to the normal imaging, we also produced additional search images that included synthetic clusters. The primary reason for inserting these synthetic test objects is to measure the cluster catalog completeness as a function of age, mass, size, and environment. In addition, the synthetics provided feedback to our volunteers: when a participant identified a synthetic cluster, they were notified that the object was synthetic and congratulated on their find. Participants on the site's Talk forum confirm that these notifications acted as positive reinforcement that they were performing the task they set out to accomplish.

We used the Year 1 cluster catalog results and its small number of accompanying synthetic cluster tests to create a realistic variety of clusters for insertion into AP search images. To begin, we choose age, mass, metallicity, attenuation, and effective radius values for the synthetic clusters drawn from distributions in each parameter:

• 1.  
  Ages were drawn from a flat distribution of discrete log(Age/yr) values between 6.6 and 10.1, spaced at an increment of 0.05 dex to match the grid of stellar isochrones from the Padova stellar evolution models (Marigo et al. 2008; Girardi et al. 2010).
• 2.  
  Masses were drawn randomly from a continuous flat distribution of log(Mass/${{M}_{\odot }}$) between 2.0 and 5.0, yielding usable sample sizes across the full range of masses.
• 3.  
  Solar metallicity (Z = 0.019) was assumed for ages less than 5 Gyr. For ages greater than 5 Gyr, the metallicity was selected from a grid of Z to simulate the presence of metal-poor globular clusters: 0.0001 (0.005 ${{Z}_{\odot }}$), 0.001 (0.05 ${{Z}_{\odot }}$), 0.004 (0.2 ${{Z}_{\odot }}$), 0.008 (0.4 ${{Z}_{\odot }}$), 0.019 (${{Z}_{\odot }}$).
• 4.  
  Extinctions were drawn from an exponential A_V distribution ranging from 0.17 mag (foreground Galactic extinction; Schlafly & Finkbeiner 2011) to 3.0 mag following the expression

  $$\begin{eqnarray}&&P\left( {{A}_{V}} \right)\propto {{e}^{-{{A}_{V}}/1.34}}.\end{eqnarray} \tag{ 1 }$$

  This distribution was chosen to match the extinction distribution derived by Fouesneau et al. (2014) from their integrated light fitting of the Year 1 cluster catalog.
• 5.  
  Spatial profiles are defined using a King (1962) profile with a fixed concentration (${{R}_{{\rm tidal}}}/{{R}_{{\rm core}}}=30$) and an effective radius ( ${{R}_{{\rm eff}}}$; equivalent to half-light radius) drawn from a distribution of measured half-light radii presented in Paper I, but with a linear bias toward larger radii. We include this bias to boost the number of extended objects and ensure our ability to characterize the completeness of diffuse clusters. The resulting ${{R}_{{\rm eff}}}$ distribution peaks at 1.5 pc (0.39 arcsec) and extends from 0.5 to 9.0 pc (0.13–2.4 arcsec).

After drawing cluster parameter combinations, we populated individual cluster star lists using the Padova models, assuming a Kroupa (2001) IMF. We computed total luminosities for each cluster and selected a subset for insertion into search images that straddle the detection limit, as computed for the Year 1 catalog. In Paper I, we found that the sample was 100% complete for clusters brighter than ${{m}_{{\rm F}475{\rm W}}}=18.5$ and 0% complete for clusters fainter than ${{m}_{{\rm F}475{\rm W}}}=23.5$. Furthermore, when we take cluster age into account we can narrow the range of acceptable ${{m}_{{\rm F}475{\rm W}}}$ values even more: for 6.6 < log(Age/yr) < 8.0 we adopted $18.5\;\lt \;{{m}_{{\rm F}475{\rm W}}}\;\lt \;22.0$; for 8.0 < log(Age/yr) < 9.0 we adopted $19.5\;\lt \;{{m}_{{\rm F}475{\rm W}}}\;\lt \;22.5$;1 and for 9.0 < log(Age/yr) < 10.0 we adopted $20.0\;\lt \;{{m}_{{\rm F}475{\rm W}}}\;\lt \;23.0.$ These ranges allow us to efficiently map the functional form of completeness as a function of F475W magnitude at all ages.

Once we were satisfied with the sample, we inserted synthetic clusters into F475W and F814W images using the DOLPHOT photometry package, an updated version of HSTphot (Dolphin 2000) that is used by the PHAT collaboration for point-spread function photometry. These synthetic clusters were added into search images, one cluster per subimage, positioned pseudo-randomly within the image but always >120 pixels from the image edge. We spatially distributed the synthetic clusters across the PHAT survey footprint, covering a wide range of galactic environments to ensure our ability to evaluate completeness throughout M31. We selected fields that sample the survey's image variety, as defined by per-image red giant branch (RBG) star counts.¹⁶ We inserted synthetic clusters into fields with ${{10}^{2}}\;\lt \;N({\rm RGB})\;\lt \;{{10}^{3}}$, and inserted proportionally fewer synthetics into fields with $N({\rm RGB})\;\lt \;400$ to achieve a uniform number of synthetic clusters per N(RGB) bin within this range. This selection results in the placement of synthetic clusters into regions where a majority of cluster identifications are made.

We obtained AP data during two rounds of collection; the first ran from 2012 December 5 to 21 and included 72% of the PHAT images. The remaining PHAT images and archival images were searched between 2013 October 22 to 30. Defining a classification as a volunteer's submitted response to a single image (containing zero to many individual markings), AP volunteers performed a total of 1.82 million image classifications. This corresponds to an average rate of about 70,000 classifications per day; our peak classification rate was over 80,000 classifications per hour.

A total of 29,262 unique users participated in the AP; 9663 of these participants logged in using a Zooniverse account. While the median number of classified images among all users was only three images (27 when only considering registered participants), 90.5% of our image classifications were performed by volunteers who examined at least 50 images. The distribution of work completed by the AP volunteer community is shown in Figure 3. The combined effort of AP volunteers totals approximately 24 months of constant human attention.

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Each image was classified a minimum of 80 times, but the distribution of classifications per image extends up to 108 with a median of 88. The classification counts vary slightly between the two rounds of data collection: the median for the 2012 campaign is 86, while the median for the 2013 campaign is 101. In all, participants made >2 million individual cluster and galaxy identifications.

To demonstrate the robustness of our ${{f}_{{\rm cluster}}}$ metric, quantify its associated uncertainties, and establish its consistency across two separate rounds of data collection, we carried out a repeatability experiment during the 2013 campaign. We selected 741 images (397 normal, 344 synthetic) searched during the 2012 campaign (Round 1; R1) that included highly-ranked cluster candidates and repeated data collection for these images during the 2013 campaign (Round 2; R2). We match the catalogs that emerge from each run and compare ${{f}_{{\rm cluster}}}$ scores for 1241 objects whose R1 and R2 scores average to >0.35 (891 from normal data, 350 from synthetic data) to test the repeatability of ${{f}_{{\rm cluster}}}$ scores for likely clusters. We present the distribution of ${{f}_{{\rm cluster}}}$ differences between the two rounds in Figure 7. We model the Δ ${{f}_{{\rm cluster}}}$ $({\rm R}1-{\rm R}2)$ scatter using an expression for the combined variance of two drawing experiments governed by the binomial distribution

$$\begin{eqnarray}&&\sigma \left( p \right)=\sqrt{\frac{2p(1-p)}{N}},\end{eqnarray} \tag{ 3 }$$

where N = 88, representing the median number of image views, and p is the averaged R1 and R2 ${{f}_{{\rm cluster}}}$ score for each object, representing our best estimate of an object's "true" ${{f}_{{\rm cluster}}}$ value. We plot 1, 2, and 3σ contours as predicted by our noise model, which accurately captures the scatter shown in the data.

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These results demonstrate that image classifications collected during the 2012 and 2013 campaigns are functionally equivalent, allowing us to easily combine data from the two rounds. This experiment also shows that our procedure of combining >80 image classifications from the pool of AP participants provides consistent ${{f}_{{\rm cluster}}}$ results with minimal systematic biases.

Up to this point, we have assumed that the abilities of all classifiers are equal on average. In this section we investigate whether weighting individual volunteers based on the quality of their classifications can improve the cluster sample. User weighting has been applied in several other citizen science projects (Lintott et al. 2008; Schwamb et al. 2012) and seems naturally applicable to our AP data. In line with these previous implementations, we calculate weightings based on the level of agreement between a participant's classifications and the consensus opinion of all the volunteers. Individuals who agree with the consensus opinion are up-weighted, while those who disagree with the consensus opinion are down-weighted. Expanding beyond previous implementations, we vary the strength and form of weighting, evaluating the success of each iteration by comparing completeness versus contamination curves (derived through comparison to the Year 1 sample) to the unweighted case presented earlier in Section 3.

We could have chosen another way to assign weights, such as assessing a volunteer's performance with respect to expert-derived Year 1 results, or basing weights on a participant's recovery rate of synthetic clusters. One downside suffered by both of these alternative methods: resulting weights are based on only a fraction of the available classification data. Decreasing the volume of classifications considered by the weighting system leads to an increasing number of participants with little or no assessment information, and noisier ability estimates for every volunteer. Additionally, weighting systems tend to produce catalogs that resemble the data used for training and calibration. We were concerned that defining weights based on data that did not sample the variety and parameter ranges included in the full cluster sample might result in unwanted biases. Particularly in the case of the synthetic cluster data, which was specifically designed to characterize cluster recovery near the detection limit, these biases could be significant. To exploit the unique benefits provided by our crowd-sourced methodology, we utilize the unfiltered opinion of AP volunteers.

Figure 8 shows two quantities that we use to characterize the performance of our volunteers: the fraction of consensus clusters a volunteer identified, ${{f}_{{\rm consensus}}}$ and the mean ${{f}_{{\rm cluster}}}$ of all cluster identifications made by a volunteer, ${{\bar{f}}_{{\rm cluster}}}$. We define consensus clusters as objects that show a high degree of agreement among AP participants, where ${{f}_{{\rm cluster}}}$ $\gt 0.6$ and ${{f}_{{\rm galaxy}}}$ $\lt 0.2$; these limits provide a sample with a sufficient number of clusters to enable weighting of individual participants while ensuring that weights are not based on questionable candidates (see Figure 4).

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Examination of Figure 8 reveals that there is a wide variation of classification behavior among AP volunteers. Individuals that lie in the upper left part of the plot are conservative classifiers; everything they clicked was an obvious cluster, leaving many consensus clusters unmarked. On the other hand, participants in the lower right are liberal classifiers; they identified a large fraction of consensus cluster sample, but also identified many other low-ranked objects that are not likely clusters. Volunteers with scores that lie in the upper right portion of Figure 8 are desirable classifiers, obtaining high completeness but with little sacrifice to the overall quality of their identifications. We note that because of the intrinsic ${{f}_{{\rm cluster}}}$ distribution of the good clusters, volunteers who identify a large fraction of the good clusters cannot have an average ${{f}_{{\rm cluster}}}$ of 1.0; we compute the upper limit to average ${{f}_{{\rm cluster}}}$ based on the ${{f}_{{\rm cluster}}}$ distribution of good clusters and plot this envelope as a dashed line in Figure 8.

To make the best use of classifications from both conservative and liberal cluster identifiers, we apply separate weightings to volunteer's detections and non-detections. Specifically, we weight a participant's detections based on the average ${{f}_{{\rm cluster}}}$ of clusters they identified, while non-detections are weighted based on ${{f}_{{\rm consensus}}}$, the fraction of consensus clusters the volunteer identified. As an example: in the case where a liberal classifier in the lower right corner of Figure 8 did not click on a cluster, their non-detections are up-weighted because they are known to identify most good clusters. The detections from the same classifier, however, are down-weighted because this individual identifies many low-quality cluster candidates in addition to the high-quality ones.

We adopt a threshold number of subimage classifications above which we can assume we have adequately characterized a participant's classification behavior. Volunteers with fewer than 50 subimage classifications are distributed with greater randomness across the ${{\bar{f}}_{{\rm cluster}}}$ versus ${{f}_{{\rm consensus}}}$ plane, suggesting large uncertainties in the values of their performance metrics; we adopt 50 classifications as the threshold. Individuals who fall below this classification threshold are assigned mean detection and non-detection weights. Even when this limit is imposed, ∼90% of all image classifications are weighted using individually determined user weights. We note that anonymous accounts from unregistered users are treated in the same way as those from registered users for weighting purposes. Most of these users are assigned mean detection and non-detection weights due to the fact that they submit a small number of classifications (median number of classifications is 2); ∼5% of unregistered users surpass the minimum subimage threshold for individual weight assignment.

Next we determine how to translate performance metric scores into relative user weights. We adopt a general form for the transformation based on the generalized logistic function. Favorable aspects of this functional form include its tunable scaling and that it allows for the saturation of weights at high and low input metric scores. Our "constrained" logistic function is defined as:

$$\begin{eqnarray}&&W\left( x \right)=B\times \left( A+\frac{1}{1+{{e}^{-{{m}_{{\rm logistic}}}(x-{{b}_{{\rm logistic}}})}}} \right),\end{eqnarray} \tag{ 4 }$$

where x represents the input performance metric (either ${{\bar{f}}_{{\rm cluster}}}$ or ${{f}_{{\rm consensus}}}$) while ${{m}_{{\rm logistic}}}$ and ${{b}_{{\rm logistic}}}$ are the slope (growth rate) and the offset (position of maximum growth) of the logistic curve, respectively. The variables A and B are normalizations set such that W varies from 0 to 1 over the interval $x=[0,1]$, providing the constrained aspect of this function. Once a set of logistic function parameters have been chosen for the detection and non-detection weighting functions, we apply user weightings to individual cluster votes on an image-by-image basis and recalculate weighted ${{f}_{{\rm cluster}}}$ values, ${{f}_{{\rm cluster},\;{\rm W}}}$.

We vary the input logistic function parameters to search for a set of values that produce the best possible weighted catalog. We construct a grid of weighting systems by varying the values of the four free parameters: the slope and offset values for both the detection and non-detection weights. For each set of parameters, we calculate a completeness versus contamination curve and its corresponding minimum distance to the corner of optimal completeness and contamination, ${{d}_{{\rm optimal}}}$. We gradually extended the weighting grid to include an increasing range of logistic parameter values until we identified a minimum ${{d}_{{\rm optimal}}}$ value that was unsurpassed. We defined the set of parameters that yielded this minimum ${{d}_{{\rm optimal}}}$ value as our optimal AP weighting system.

The range of completeness versus contamination curves is represented by the gray region in the top panel of Figure 6. We also plot the individual curve derived for the optimal weighting system and list its logistic function parameters in Table 1. The optimal weighting system provides a contamination fraction of 9.8% at a completeness of 88.1%. When compared to the uniform weighting results, applying user weighting decreases the number of contaminants by 36% (from ${{f}_{{\rm contamination}}}$ of 0.152 to 0.098 at completeness of 88.1%), or alternately increases completeness from 84.6 to 88.1% (at ${{f}_{{\rm contamination}}}$ of 0.098). While user weighting does not dramatically change the total number of cataloged clusters or the Year 1 completeness percentage, we are able to reduce the number of possible contaminants by a significant amount.

We compare original versus weighted ${{f}_{{\rm cluster}}}$ values to illustrate the impact of user weighting on individual clusters. Figure 9 shows that user weighting tends to increase the separation between high and low ${{f}_{{\rm cluster}}}$ objects, providing better differentiation at moderate ${{f}_{{\rm cluster}}}$ values that lie near the catalog cutoff. To visualize how the choice of ${{f}_{{\rm cluster},\;{\rm W}}}$ cutoff affects the output cluster catalog, we represent four different threshold values as horizontal lines in the figure, each labeled according to its corresponding Year 1 completeness fraction. We also plot a vertical line in Figure 9 representing the approximate ${{f}_{{\rm cluster}}}$ cutoff that best approximates the optimal ${{f}_{{\rm cluster},\;{\rm W}}}$ threshold.

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The user weighting applied here enhanced final AP catalog results by achieving small but quantifiable improvements through a combination of decreased contamination and increased completeness. We note that we were fortunate to obtain a large number of classifications per image (>80), allowing us to account for variations in participant performance by averaging over a large number of classifications. Many citizen science projects cannot afford to collect a similar number of per-image classifications because they need to distribute effort over a larger volume of data, or because the project is working on time-sensitive tasks that cannot wait for additional input to be collected. In these cases, we expect that user weighting would play an essential role in obtaining high-quality results.

We utilize the ${{f}_{{\rm cluster},\;{\rm W}}}$ values as defined by the optimal user weighting system throughout the rest of the paper.

We apply the catalog construction techniques and user weighting methodology presented in Section 3 to define an AP cluster catalog, adopting final selection criteria of:

$$\begin{eqnarray}&&{{f}_{{\rm cluster},\;{\rm W}}}\gt 0.6416\ {\rm AND}\ {{f}_{{\rm galaxy}}}\;\lt \;0.3.\end{eqnarray} \tag{ 5 }$$

These criteria yield a sample of 2714 clusters. We add two additional sets of clusters to these initial selections. First, we add 35 clusters to the sample that are located in the bulge-dominated region within ∼3 kpc of M31's center, as defined by an ellipse with a center of (10.684575, +41.268972), semimajor axis of 815 arcsec, semi-minor axis of 410 arcsec, position angle of 45°, and bounded by the PHAT footprint. These objects are primarily globular clusters that were identified and confirmed by previous surveys. These objects suffer from systematically low ${{f}_{{\rm cluster},\;{\rm W}}}$ scores due to their atypical appearance (compact and smooth with few individually resolved stars), high-surface brightness backgrounds, and suboptimal search image scalings. We decided that the most straightforward solution to correct for these missed objects was to include all previously confirmed clusters (high-quality Year 1 or RBC flag of 1) that lie within the defined region and evaluate all candidate or possible objects. We confirmed by eye that each of the previously confirmed objects has an appearance consistent with that of a cluster, and confirmed two additional candidate objects. Second, we include four additional expert cluster identifications from the B03 tooth images that were not included in the AP search due to delayed data availability.

The final AP cluster catalog includes 2753 objects. Figure 12 shows the positions of the clusters within the PHAT survey footprint. Andromeda's ∼10 kpc star-forming ring is a prominent feature visible in the cluster's spatial distribution. We assign identifiers in descending order of their maximum per-image, uniformly weighted ${{f}_{{\rm clst}+{\rm gal}}}$ score. Positions, aperture sizes, and other relevant catalog metadata are presented in Table 2.

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Table 2.  AP Cluster Catalog

AP ID	R.A. (J2000)	Decl. (J2000)	${{R}_{{\rm ap}}}$ ('')	${{R}_{{\rm eff}}}$ ('')	${{m}_{{\rm ApCor}}}$ a	F275W$_{{\rm ap}}$	σ	F336W$_{{\rm ap}}$	σ	F475W$_{{\rm ap}}$	σ
${{f}_{{\rm clst}+{\rm gal}}}$	${{f}_{{\rm galaxy}}}$	${{f}_{{\rm cluster},\;{\rm W}}}$	PC ID	Alt ID	Flags	F814W$_{{\rm ap}}$	σ	F110W$_{{\rm ap}}$	σ	F160W$_{{\rm ap}}$	σ
1	11.435516	41.698562	2.19	0.60	−0.01	20.12	0.04	19.16	0.01	18.77	0.01
1.0000	0.0000	1.0000	⋯	B374-G306	⋯	17.69	0.08	17.19	0.15	16.59	0.20
2	11.366514	41.701013	1.86	0.61	−0.04	20.91	0.10	20.25	0.02	20.01	0.10
0.9717	0.0083	0.9894	⋯	M085	⋯	19.05	0.21	>18.06	⋯	>17.06	⋯
3	11.471290	42.049246	1.95	0.88	−0.14	21.27	0.14	20.81	0.03	20.67	0.08
1.0000	0.0000	1.0000	⋯	⋯	⋯	20.07	0.31	>18.97	⋯	>18.07	⋯
4	11.474664	42.038351	2.87	0.98	−0.05	20.10	0.04	19.10	0.02	18.75	0.03
1.0000	0.0227	0.9909	⋯	B483-D085	⋯	17.78	0.08	17.29	0.16	16.66	0.21
5	10.991636	41.359328	1.46	0.40	−0.01	20.88	0.04	20.29	0.03	20.09	0.06
1.0000	0.0000	1.0000	⋯	M005	⋯	19.36	0.10	18.73	0.21	17.72	0.25

Notes. Three-sigma upper limits are denoted by a ">" symbol. PC ID and Alt ID refer to cluster identifiers from the Year 1 catalog and other literature sources, respectively. Flags: E = Extended Object (see Section 6.2); B = Bulge or B03 object manually added (see Section 5.1).

^aAperture Corrections are provided such that ${{m}_{{\rm Total}}}={{m}_{{\rm ap}}}+{{m}_{{\rm ApCor}}}$.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

All AP candidates with ${{f}_{{\rm clst}+{\rm gal}}}$ ≥ 0.1 that are not included in the cluster catalog (or galaxy catalog; see Appendix B) are listed in an ancillary table in Appendix C. We include information on these additional candidates to allow other workers the opportunity to make different choices concerning catalog selection.

We cross-match our AP cluster catalog with a selection of previously published catalogs: the Year 1 catalog, the RBC, Caldwell et al. (2009), and the HKC. We include alternate identifiers for previously classified objects in Table 2 and summarize the high degree of consistency between the AP catalog and previous results below.

By design, the AP catalog bears a strong resemblance to the Year 1 catalog. When we consider the portion of the AP catalog that lies within the Year 1 imaging footprint (including B01, differing slightly from the Section 3 analysis), we count 688 clusters, which is a 14.5% increase over the 601 object Year 1 catalog. The agreement between the two samples is good: the AP catalog includes 88.5% (532/601) of the good Year 1 clusters, and 91% of the AP cluster catalog were previously classified as high-quality or possible Year 1 objects. The AP catalog includes 39 Year 1 catalog rejections and 22 objects not classified in the Year 1 search. While the majority of object-by-object classification differences are caused by clusters with ${{f}_{{\rm cluster},\;{\rm W}}}$ scores that lie near the catalog cutoff, we discuss a number of meaningful systematic differences between the two catalogs in Section 6.2.

Comparison of the AP catalog to the RBC and the Caldwell et al. (2009) catalog provides an opportunity to cross-reference with commonly cited sources, linking our present work to a wealth of ancillary information about these clusters, including a great deal of follow-up spectroscopy. These ground-based catalogs do not reach the faint objects accessible to the PHAT imaging, therefore the following comparison mostly consists of verifying or discarding previously unconfirmed candidates that lie at the middle or bright end of the AP sample.

Cross-matching the AP catalog with the RBC, we find that 260 previously confirmed, candidate, or controversial clusters (RBC flag = 1, 2, or 3) match to AP clusters, while 42 AP classifications conflict with those from the RBC (40 AP clusters are not RBC clusters, 2 RBC clusters are not AP clusters), and 18 additional RBC candidate or controversial classifications were rejected. PHAT's high spatial resolution imaging is often used as a definitive tool for classifying objects, so we defer to AP classifications for these conflicting cases. We also find good agreement between the AP and the Caldwell et al. (2009) catalogs. Only 18 conflicts arise from the Caldwell catalog (8 AP clusters are not Caldwell clusters, 10 Caldwell clusters are not AP clusters), while 232 cluster classifications are common to both the Caldwell and the AP catalogs.

Finally, we compare the AP catalog with the HKC catalog compilation. These clusters represent the low-mass additions to previous ground-based catalogs provided by early targeted HST observations, and therefore include many objects that lie at or near completeness limits. As such, a direct comparison shows 156 previously identified clusters confirmed by our AP classifications, while 57 are not confirmed. This 73% yield is nearly identical to the 72% yield we found for the Year 1 catalog during a similar comparison exercise. A vast majority of HKC objects that were not confirmed by the AP catalog are borderline, marginal candidates where there is a subjective difference in opinion between the HKC authors and the consensus judgement of AP volunteers; rejected objects are distributed uniformly in ${{f}_{{\rm cluster},\;{\rm W}}}$, such that half of these rejected objects have ${{f}_{{\rm cluster},\;{\rm W}}}$ > 0.3.

Overall, the comparison between the AP catalog and previous non-PHAT M31 cluster catalogs shows good agreement with few conflicting classifications. A total of 733 unique, previously cataloged objects (both cluster and non-cluster classifications) match to AP candidates; 468 were previous (confirmed) cluster classifications, of which 404 were confirmed by the AP catalog. Within the PHAT survey footprint, we have increased the sample of confirmed clusters by a factor of ∼6 (from 468 to 2753). The HST-based AP catalog provides improvement in terms of catalog completeness and quality, and builds upon the firm foundation laid by these previous works. Commentary on individual classification differences can be found Appendix D.

We perform integrated aperture photometry for each of the AP catalog entries. Our photometry procedures are described in Paper I; we summarize the main ideas here, but refer the reader to that paper for additional details. We use the mean center and median radius of an object's merged classifications to define the position and radius (${{R}_{{\rm ap}}}$) of the photometric aperture. The sky background is calculated within an annulus ten times the size of the photometric aperture, extending from 1.2 ${{R}_{{\rm ap}}}$ to ∼3.4 ${{R}_{{\rm ap}}}$. Photometric uncertainties are dominated by uncertainties in the sky background determination; this source of uncertainty is often ignored in extragalactic cluster photometry. Identical apertures (constant angular size) are employed across all six PHAT images. Aperture magnitudes for significant detections (S/N ≥ 3 with respect to the variation in the sky background) are listed for each photometric passband in Table 2; 3σ upper limits are provided for non-detections, and blank entries denote incomplete image coverage.

We obtain photometric ${{R}_{{\rm eff}}}$ estimates by interpolating radial flux profiles. These values are then used to derive aperture corrections, which help account for cluster light that falls outside of the photometric aperture. We compare synthetic cluster input luminosities to measured magnitudes and find that this effect causes losses on the order of 0.1–0.3 mag. Corrections assume a King (1962) profile with a concentration ($c={{R}_{{\rm tidal}}}/{{R}_{{\rm core}}}$) of 7, scaled to match the cluster's photometrically determined F475W ${{R}_{{\rm eff}}}$, then extrapolated to radii beyond ${{R}_{{\rm ap}}}$ to obtain a magnitude correction, ${{m}_{{\rm ApCor}}}$. Aperture corrections can be applied to raw aperture magnitudes to obtain total magnitude¹⁷ estimates. These estimates accurately recover the photometry of synthetic clusters with no bias at brighter magnitudes (<19) and <0.2 mag bias for fainter clusters (see Section 4.2 in Paper I).

We summarize the photometric measurements in Table 3 where we tabulate the number of detections in each band, as well as the number of objects with detections spanning various combinations of photometric bands.

We found that accounting for the presence of image artifacts was critical to obtain accurate cluster photometry in the F275W, F336W, and F110W filter bandpasses. Images in these three wavelengths proved problematic due to their small number of repeat observations and minimal spatial overlap between neighboring images, hindering typical artifact rejection techniques that require three or more exposures. Interpolating over pipeline-rejected pixels in the F110W images was relatively straightforward; however, detecting and rejecting UV cosmic ray image artifacts was more difficult. We conservatively identify F275W and F336W artifacts by flagging bright, single-passband objects by comparing flux ratios of F275W, F336W, and F475W images. This method allows us to reject hundreds of artifacts that tend to bias measurements to brighter magnitudes; however, we caution that some uncorrected artifacts may continue to affect our UV photometry.

In Figure 13, we compare the distributions of F475W magnitudes for previously known (and confirmed) clusters in the PHAT footprint and the new AP catalog. The factor of ∼6 increase in the number of clusters shows the staggering improvement made possible by PHAT's high spatial resolution imaging. The ability to differentiate between single bright stars and compact clusters allows us to include fainter, less massive clusters in the AP catalog. Ground-based imaging limited previous efforts to clusters brighter than F475W ∼ 19.5, and while the HKC pushed that limit faint-ward, the amount of HST imaging available to those authors was significantly less than what is now available through PHAT.

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Figures 14 and 15 show the color–color and color–magnitude distributions of AP clusters, providing a glimpse into the age composition of the catalog. While the clusters span a wide range of colors that reflect a diversity in ages, a dominant portion of the catalog lies within the following color and magnitude range: 20 < F475W < 22, 0 < F336W−F475W < 1, and 1 < F475W−F814W < 2. The specified region of color and magnitude parameter space points to a dominant population of ∼10³ ${{M}_{\odot }}$, ∼200–400 Myr old clusters that dominate the catalog by number, consistent with the age distribution found for the Year 1 sample (Fouesneau et al. 2014). This population dominates the cluster catalog because it represents a relatively large linear age range (leading to large number of clusters for a near constant formation history) where catalog completeness is still relatively high (50% complete to ∼1000 ${{M}_{\odot }}$ at 300 Myr). We note that the large color dispersion shown in Figure 14 agrees with predictions of stochastically sampled cluster models (see Figure 4 in Fouesneau et al. 2014). In addition, the vertical sequence spanning 15 < F475W < 19 with a color range of 0.2 < F336W−F475W < 1.3 in Figure 15 represents the old (10–14 Gyr), massive ($\gt {{10}^{5}}$ ${{M}_{\odot }}$) globular clusters. These massive, luminous systems also form a well-defined sequence of bright clusters in Figure 14, running from (F475W−F814W, F336W−F475W) coordinates of approximately (1.4, 0.2) to (2.1, 1.3), corresponding to a metallicity sequence running from −2.5 < [Fe/H] < 0.0 for these systems.

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We fit luminosity functions to the cluster photometry using a simple power law ($N\propto {{L}^{-{{\alpha }_{L}}}}$); we plot the results in Figure 16. Notably, when we remove objects that lie within the previously defined bulge region (see Section 5.1), we find that luminosity functions steepen significantly. As we argued in Paper I, old massive globular clusters dominate the bright end of the luminosity function; removing these objects, which reside primarily in the galaxy's bulge, allows us to examine the luminosity function behavior of younger (≲3 Gyr) cluster populations. The observed population-dependent variations in luminosity function indices affirm that factors such as the underlying cluster formation history, the intrinsic cluster mass function, and the stochastic conversion from mass to luminosity for less massive clusters all play a role in determining the overall distribution of cluster luminosities. Untangling these various effects for the PHAT sample is possible through direct age and mass determinations of the individual clusters; we will perform this analysis as part of future work (L.C. Beerman et al. 2015, in preparation).

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To place the PHAT catalog of M31 star clusters into context, first we compare the luminosity distribution of our sample to those from three nearby star-forming galaxies: M83 (Bastian et al. 2012), M33 (San Roman et al. 2010), and the LMC (Hunter et al. 2003; Popescu et al. 2012). We choose these three galaxies because they are well-known extragalactic cluster targets that have publicly available cluster catalogs; we compare our sample to the much more heterogenous Milky Way catalog in the next subsection. We compare the luminosity distributions of each sample in the left panel of Figure 17, where we convert from PHAT's F475W to V-band apparent magnitudes using the following empirical relation:

$$\begin{eqnarray}&&{{m}_{V}}={{m}_{{\rm F}475{\rm W}}}-0.363({{m}_{{\rm F}475{\rm W}}}-{{m}_{{\rm F}814{\rm W}}})-0.111.\end{eqnarray} \tag{ 6 }$$

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Completeness limits for the three samples scale as a function of distance: M83 has the brightest completeness limit at ${{M}_{V}}\sim -6$, followed by M33's limit at ${{M}_{V}}\sim -5.5$, and the LMC's limit at ${{M}_{V}}\sim -4.5$. The M31 detection limit of ${{M}_{V}}\sim -3.5$ leads to the inclusion of many more clusters, particularly those of moderate mass and intermediate ages: 10³–10⁴ ${{M}_{\odot }}$ between 100 Myr and 1–3 Gyr (Fouesneau et al. 2014). As a result, the PHAT sample contains ∼3 times more clusters than any of the other extragalactic samples compared here.

At bright magnitudes (${{M}_{V}}\;\lt \;-6$) where all four cluster samples are complete, we can compare the number of luminous blue ($B-V\;\lt \;0.5$, or equivalently F475W−F814W < 1.1) clusters in each sample. This provides a first-order comparison of the young cluster populations captured by the catalogs of our set of comparison galaxies. We show in the right panel of Figure 17 that the M83 catalog includes the largest number of blue clusters, followed in order by M33, the LMC, and M31. Differences in the star formation rate (SFR) for the galaxy regions surveyed explain the differences observed in blue cluster populations. The cluster sample from the starburst galaxy M83 corresponds to an SFR of 1.3 ${{M}_{\odot }}$ yr⁻¹(coverage fraction of 2/5 applied to galaxy-wide SFR of 3.3 ${{M}_{\odot }}$ yr⁻¹; Boissier et al. 2005), while M33's SFR is 0.45 ${{M}_{\odot }}$ yr⁻¹(Verley et al. 2009) and the LMC's SFR is 0.25 ${{M}_{\odot }}$ yr⁻¹(Whitney et al. 2008). Within the PHAT footprint, the current SFR is much lower at ∼0.1 ${{M}_{\odot }}$ yr⁻¹(coverage fraction of 1/3 applied to galaxy-wide SFR of 0.25 ${{M}_{\odot }}$ yr⁻¹; Ford et al. 2013). Larger SFRs correlate with larger numbers of blue clusters; the relatively low number of luminous blue clusters in the AP catalog are a consequence of M31's relative quiescent SFR.

Next, we compare our PHAT cluster catalog to the sample of known Galactic clusters. Without question, observations of Milky Way star clusters provide rich, detailed data sets for individual clusters and their member stars that cannot be matched in an extragalactic setting. The ability to measure star-by-star proper motions, detect and resolve stars down to the hydrogen burning limit, and efficiently obtain detailed abundance information through spectroscopy of individual members are all major advantages of studying clusters in the Galaxy. However, it is interesting to explore how Galactic cluster samples compare on galaxy-integrated scales. Our Sun's position within the disk of the Milky Way, surrounded by obscuring gas and dust along the Galactic mid-plane, does not provide the optimal vantage point for observing the distribution of clusters throughout our galaxy. In fact, we argue below that extragalactic samples provide a better assessment of overall cluster populations, due to the uniformity of selection and the ability to survey a wide range of galactic environments.

The recent catalog of Milky Way clusters by Kharchenko et al. (2013) contains 2547 clusters,¹⁸ similar to the number of entries in the PHAT cluster catalog. But while the sample sizes are comparable, the uniformity and selection function of the Milky Way clusters differ significantly from the AP clusters in M31. The sample of Milky Way clusters is compiled from a heterogenous set of literature sources, including earlier work of (Dias et al. 2002), leading to an ill-defined selection function and catalog completeness that is difficult to characterize. Assuming a constant surface density of clusters, Kharchenko et al. (2013) suggest that the sample is complete to a radius of ∼1.8 kpc around the Sun thus covering an area of ∼10 kpc². Not only is this area more than an order of magnitude smaller than the physical region covered by PHAT, but the surveyed region of Galaxy is limited to the solar neighborhood. Most of the area within 1.8 kpc of the Sun lies within a Galactic inter-arm region, limiting the amount of on-going star formation and range of environments one can study.

According to estimates compiled in a recent review by Portegies Zwart et al. (2010) (based on the sample of Dias et al. 2002), the young (excluding globular clusters) Milky Way cluster sample includes objects that range in mass from 25 ${{M}_{\odot }}$ to 5 × 10⁴ ${{M}_{\odot }}$. Within a radius of 1.8 kpc, the complete cluster sample includes a mass range that varies over <3 orders of magnitude, up to 4000 M $_{\odot }$, the mass of the Orion Nebula Cluster. The proximity of the Milky Way clusters allows for the inclusion of low mass objects that remain undetected in M31, however the accurate understanding of mass completeness and catalog selection for PHAT, along with the number and variety of clusters included, makes the AP catalog the best available resource for a wide range of cluster science studies: cluster dissolution, mass functions, cluster formation efficiency, and how cluster properties vary with environment.

The cluster definition we use for the AP catalog, as described in Section 1.1, is more liberal than the one used in our previous Year 1 catalog. In Paper I, we excluded three categories of candidate clusters that we do not explicitly reject from the AP catalog:

• 1.  
  Loose Associations—Defined by their lack of centrally concentrated stars, these objects are likely to be gravitationally unbound due to their large spatial extents and low stellar densities, and were therefore rejected from inclusion in the Year 1 catalog. The AP search yielded many high-significance candidates that were not identified during the Year 1 effort.
• 2.  
  Emission Line Regions—Compact, high surface brightness Hii regions show up prominently in F475W imaging ([Oiii] and Hβ emission lines lie within the F475W bandpass) and tends to enhance the visual appearance of associated clusters. While line emission on its own does not provide explicit evidence for or against the presence of a cluster (non-cluster Hii regions and line emitting clusters both exist), we find that cluster candidates associated with emission line flux are accepted more frequently into the AP catalog than by the expert-based Year 1 search. We document this tendency because it reveals a possible systematic affecting catalog completeness that is not captured by our synthetic cluster tests: low mass clusters that produce line emission may be systematically overrepresented in the AP catalog with respect to the completeness function derived in Section 4.
• 3.  
  Small Clusters—While we emphasized a liberal, inclusive approach to cluster identification in Paper I, small candidate clusters were often discarded, with a loosely defined limit requiring three–four spatially correlated stars to trigger inclusion in the catalog. For the AP search, no star count limit was ever discussed.

These three categories of objects represent systematic differences between the Year 1 and AP catalogs. Of these three, the loose associations represent the most conspicuous difference: the number of bright blue objects (F336W−F475W < −0.5 and F475W < 19.75) identified within the Year 1 footprint more than doubled, from 15 to 35 clusters, many of which appear extended and poorly concentrated. In an effort to clearly identify these uncertain and controversial AP clusters, we flag objects that match the following criteria as possible associations: bright (F475W < 19.75), blue (F336W−F475W < −0.5), and spatially extended. A cluster is characterized as spatially extended either through its light profile, according to its half-light radius, or its profile of resolved MS stars, according to the radius that contains 60% of the cluster's MS stars (${{R}_{0.6N({\rm MS})}}$). We adopt the following criteria for spatial extension: ${{R}_{{\rm eff}}}$ > 1.05 arcsec (4 pc), or ${{R}_{0.6N({\rm MS})}}\gt 0.5{{R}_{{\rm ap}}}$ for stars with F475W−F814W < 1 and F475W < 24. The combined color, magnitude, and spatial extension criteria identify 64 association-like objects; flags identifying these objects are included in Table 2. These extended candidates are the most likely examples of regions hosting spatially correlated star formation, but where the stars may not have ever been gravitationally bound to one another. As such, one should carefully evaluate the possibility that these candidates may not be the young progenitors of the older clusters we identify in this catalog.