STAR CLUSTERS IN THE TIDAL TAILS OF INTERACTING GALAXIES: CLUSTER POPULATIONS ACROSS A VARIETY OF TAIL ENVIRONMENTS

Twelve interacting galaxies with seventeen tidal tails were selected for observation with the HST WFPC2 in the Cycle 16 program 11134 (PI: K. Knierman). This sample reflects an expansion of the K03 sample of six tidal tails (from four individual galaxies) as well as the parameter space of interaction characteristics—interaction age, progenitor galaxy mass ratios, H i and optical properties—they define. The "H i Rogues Gallery" was used for selection guidance (Hibbard et al. 2001). The tidal tails selected in this study are displayed in Figure 1, as Sloan Digital Sky Survey (SDSS) r-band images with HST WFPC2 footprints overlaid. In systems where there are two obvious, separated tails or debris regions, they are indicated by an additional letter after their names, corresponding to their orientations (E for "East," W for "West," etc.). All other tails are indicated by their primary catalog designations.

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Wide Field Planetary Camera 2 (WFPC2) images were taken from 2007 September to 2008 August in both F606W and F814W ("V₆₀₆" and "I₈₁₄" hereafter¹⁴); a log of these observations is given in Table 1. Exposure times, t_exp, range from 900 to 2100 s in V₆₀₆ and I₈₁₄, representing the total integration time of at least two separate exposures in each filter. This was meant to facilitate the identification and removal of cosmic rays. Images at two different dither positions were obtained for AM 1054-325/ESO 376- G 028, NGC 1614N/S, NGC 2444, NGC 2535, and NGC 6872E/W, with an offset of 2.5 and 5.5 pixels in the WF and Planetary Camera (PC) chips, respectively. Integration times were selected to equal image depths of K03, allowing for direct comparison of analyses and results. In all cases, a gain of 7 e⁻¹ ADU⁻¹ was used.

Pairs of images were reduced, averaged with the IRAF¹⁵ task GCOMBINE, and cleaned for hot pixels with COSMICRAYS. Moreover, the low bias problem of WF4 has only been corrected for NGC 1487E/W. According to Maybhate et al. (2008), this problem is manifested in image streaking whose photometric corrections are most pronounced in faint objects. Given this work's preferential avoidance of this chip for tail placement, this issue would ordinarily only affect the tails of NGC 4747, NGC 2782, NGC 2535, and NGC 6872. However, our images for these systems employed deep exposures and are clean of image streaking (WF4 mean biases are on par with those of the WF2 and WF3 chips; ≳300 DN). Thus, this will not have an appreciable effect on the data analysis. In addition, the PC chip was not analyzed because source detection was compromised by a greater readnoise contribution from the larger number of pixels across each source.

Neutral hydrogen data for NGC 2782, NGC 2992/3, NGC 2444, and NGC 2535 were taken from the VLA archives¹⁶. The data were reduced in AIPS (Greisen 1990), using standard procedures. The neutral hydrogen data for NGC 6872 and NGC 1487 were obtained from the ATCA archives¹⁷ and calibrated using the standard procedures of the ATNF version of Miriad (Sault et al. 1995). An upcoming publication that focuses on the H i distribution of these tails on kpc scales (B. Mullan et al. 2012, in preparation) will document the reduction procedures in greater detail. H i data for NGC 520 and NGC 1614 were obtained from Hibbard & van Gorkom (1996) and Hibbard & Yun (1996), respectively.

Following K03, contiguous regions bounded by SAO DS9 contours of one count above the average background in V₆₀₆-band images were defined as "in tail." We applied this criterion to histogram-equalized images smoothed with a Gaussian kernel with a 5–7 pixel (05–07) FWHM. The tail surface brightness limit ranges between 24.7 and 25.8 mag arcsec⁻² in V. All other regions were designated "out of tail." Where galaxy interiors are imaged (e.g., AM 1054-325 E/W, MCG -03-13-063, NGC 2782E, and NGC 6872W), the inner extent of the tail was defined by DS9 contours set to where radial light profiles (measured by IRAF PVEC) showed a change in scale length as the disk connects to the tail. This method isolates "antitruncated" tails that may be the result of gravitational interactions (Erwin et al. 2005).

For AM 1054-325, radial light profiles from the inner galactic region were azimuthally averaged into an ellipse (center at 10:46:58.877, −33:08:23.60; position angle 6495, major axis 5989, minor axis 5661). This system's tail may extend into this interior, but this superposition of tidal debris and host galaxy is unfit for our purposes. NGC 2444 is one final exception—it has no optical tail evident in WFPC2 images. Consequently, its in-tail definition relies on its H i debris. To be clear, all other tail definitions rely on said optically delineated tails in order to allow direct comparison to K03.

Tail regions were converted from SAO DS9 contours to IMAGEJ (Rasband 1997) polygons for optical photometry. Regions were masked to exclude obvious foreground stars and resolved background galaxies. Mean count measurements and errors from IMAGEJ were converted to WFPC2 and Johnson–Cousins magnitudes using the zero points and filter transformations of Dolphin (2008) and Holtzman et al. (1995). Corrections for Galactic extinction were made using A_V values from Schlegel et al. (1998), transformed to the appropriate bandpasses according to the Girardi et al. (2008) prescription. For this extinction treatment, we used an effective cluster temperature T_eff = 15,000 K, representing an aggregation of late-B–early-A stars, of ages 10–300 Myr for the input spectrum.

Table 2 presents a phenomenological summary of the tails. Tails are ordered by increasing luminosity distance (these values are provided in Sections 3 and 4); we separate our sample from that of K03 in order to isolate any systematic errors that may accrue from the different bandpasses used in the observations. Many of these data from that paper are reproduced here for convenience.

Table 2. Properties of Tidal Tail Sample

Global Properties									WFPC2 FOV Properties
Tail	Interaction	Mass	Galaxy SFRa	SDSS Tail	H i Tail	M$_{\rm {{{{\rm H}\,\mathsc{ i}}}}}^{{\rm tot}}$b	TDG		Tail Vc	Tail	〈M$_{\rm {{{{\rm H}\,\mathsc{ i}}}}}$/Atail〉b
	Aged (Myr)	Ratiod	(M☉ yr−1)	Lengthc (kpc)	Lengthb,c (kpc)	(109 M☉)	Candidatese		(mag arcsec−2)	V − Ic	(106 M☉ kpc−2)
NGC 1487E	500	0.25	0.12 ± 0.01	9	19	0.614 ± 0.12	no		24.02	0.84	25.5 ± 5.1
NGC 1487W	500	0.25	0.12 ± 0.01	12	17	0.541 ± 0.11	no		24.57	1.10	33.2 ± 6.6
NGC 4747	320f	0.05	0.27 ± 0.02	22	...	...	no		24.64	0.94	...
NGC 520	300	0.05	6.5 ± 0.5	112	227	1.12 ± 0.22	yes		24.21	1.04	3.81 ± 0.76
NGC 2992	100	1	3.3 ± 0.2	23	33	1.43 ± 0.28	yes		23.47	1.14	6.44 ± 1.3
NGC 2993	100	1	5.0 ± 0.3	37	55	0.727 ± 0.15	no		24.78	0.73	5.77 ± 1.2
NGC 2782E	200	0.25	3.7 ± 0.3	37	17	2.41 ± 0.48	no		23.81	1.02	7.08 ± 1.4
NGC 2782W	200	0.25	3.7 ± 0.3	76	58	3.14 ± 0.63	no		25.49	1.05	5.17 ± 1.0
MCG -03-13-063	100f	0.25	0.43 ± 0.03	41	...	...	no		23.91	1.01	...
ESO 376- G 028	85f	1	...	10	...	...	no		22.76	1.33	...
AM 1054-325	85f	1	0.64 ± 0.04	16	...	...	yes		22.65	0.84	...
NGC 2444	100	0.50	...	175	233	5.20 ± 1.0	no		...	...	1.40 ± 0.28
NGC 2535	100	0.30	2.9 ± 0.2	25	79	4.45 ± 0.89	no		24.37	1.02	6.84 ± 1.4
NGC 6872E	150	0.20	2.9 ± 0.2	38	21	3.52 ± 0.50	no		24.06	0.75	2.94 ± 0.59
NGC 6872W	150	0.20	2.9 ± 0.2	21	21	3.52 ± 0.50	no		23.57	1.16	1.68 ± 0.34
NGC 1614N	750	1	35. ± 3.	21	21	0.768 ± 0.16	no		22.27	0.88	2.56 ± 0.52
NGC 1614S	750	1	35. ± 3.	21	21	0.964 ± 0.19	no		23.00	0.68	2.89 ± 0.59
The K03 Sample
NGC 4038	420f	1	5.2 ± 0.4	78	85	0.200 ± 0.040	yes		24.54	1.05	1.09 ± 0.22
NGC 3256E	400f	1	33. ± 2.	51	77	1.40 ± 0.28	no		24.04	0.76	1.51 ± 0.30
NGC 3256W	400f	1	33. ± 2.	46	57	2.20 ± 0.44	no		23.75	0.70	2.96 ± 0.59
NGC 7252E	730f	1	5.4 ± 0.4	40	66	1.50 ± 0.30	yes		25.42	0.89	0.593 ± 0.12
NGC 7252W	730f	1	5.4 ± 0.4	94	156	2.20 ± 0.44	yes		24.46	1.09	0.573 ± 0.11
NGC 3921S	460f	1	1.9 ± 0.1	43	53	4.30 ± 0.86	yes		24.72	0.94	0.872 ± 0.17

Notes. ^aGalaxy SFRs based on IRAS IR fluxes (Helou & Walker 1988). See K03 and Kennicutt et al. (1998) for the details of the calculation. IRAS measurements are unavailable for ESO 376-G 028 and NGC 2444. ^bH i measurements were performed as per Section 2.2. Dashes indicate where H i data are unavailable. H i data and maps for K03 tails were obtained from Maybhate et al. (2007) and references therein. ^cTail photometry and length measurements were performed with IMAGEJ and corrected to standard V and I filters following Holtzman et al. (1995); see Section 2.3. No optical tail detection or photometry is possible for NGC 2444, so no values are given. Errors are ≈0.1 for V and 0.14 for V − I. ^dWhen available, ages and mass ratios are adopted from the literature. We adopt errors in ages of ±50 Myr and 25% for mass ratio. See Appendix A for references. The mass ratio is defined as the mass of the perturbing galaxy divided by that of the main galaxy. ^eBased on visual inspection of SDSS and WFPC2 images. ^fThese tails lacked age estimates in the literature, so these values were obtained by dividing the projected length of the tail by the estimated escape velocity. Similarly calculated ages of K03 tails are reproduced from that publication.

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The first eight parameters listed pertain to "global properties" of the interacting systems. Interaction ages (measured from periapse) and mass ratios are supplied by the literature; see Appendix A for specific references for each system. In cases where reliable ages were not found, they were estimated by dividing the projected length of the tail by an estimate of the escape or rotation velocity. This was demonstrated to provide acceptable accuracy (±50 Myr) in K03. Mass ratios are defined as the mass of the perturbing galaxy divided by the mass of the primary system. Table 2 also lists host galaxy star formation rates (SFRs) based on IRAS IR fluxes (Helou & Walker 1988). K03 and Kennicutt et al. (1998) have details of the calculation.

Tail lengths were measured with freehand lines in IMAGEJ, tracing the tail curvature evident in SDSS r-band images and our H i maps. Note that in many cases, the H i debris evidently extends beyond the optical tails (NGC 2782 is an interesting counterexample). Furthermore, we calculated the total H i mass of entire tidal tails, M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$. In every channel of the H i data cubes, we measured the total H i flux (Jy km s⁻¹) and summed the flux in each channel to get the total H i flux F$_{\rm H\,{\mathsc i}}^{\rm {tot}}$. The total H i mass M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$ is then (e.g., Verschuur & Kellermann 1988)

$$\begin{equation} \hbox{$M$$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$}[\hbox{${M}_{\odot }$}] = 2.36 \times 10^5 (D[\mathrm{Mpc}])^2 {F}_{\rm H\,{\mathsc i}}^{\rm {tot}}[\mathrm{Jy\, km\, s}^{-1}], \end{equation} \tag{ 1 }$$

where D is the distance to the tail in Mpc. We additionally indicate in Table 2 which of these tails have visually identified TDG candidates.

The last three columns of Table 2 list WFPC2 field of view (FOV) scale properties of the tidal tails. We include the WFPC2-imaged optical tail V-band surface brightness and V − I color; for the K03 sample, tail photometry was conducted identically to our sample and corrected from theF555W/F814W bands to Johnson–Cousins magnitudes (Holtzman et al. 1995; Dolphin 2008). Lastly, Table 2 lists the average observed H i surface density 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 within the optical tail areas (A_tail) of the WFPC2 FOVs. 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 is expressed as

$$\begin{eqnarray} && {\langle M_{{ {{{\rm H}\,{\mathsc i}}}}}/A_{{\rm tail}}\rangle }[{{M}_{\odot }}\,\mathrm{kpc}^{-2}] = 2.36 \times 10^5 (D[\mathrm{Mpc}])^2 \nonumber \\ && \quad \times {F}_{\rm H\,{\mathsc i}}^{\rm {tail}}[\mathrm{Jy\, km\, s}^{-1}]/{A}_{\rm {tail}}[\mathrm{kpc}^{2}]. \end{eqnarray} \tag{ 2 }$$

Here, $F_{\rm H\,{\mathsc i}}^{\rm {tail}}$ is the H i flux for the optical tail region within the WFPC2 FOV and A_tail is the area of the optical tail region measured from the H i images. This is similar to the area measured from the HST images, modulo differences in pixel sizes. The uncertainty in this quantity represents the uncertainties in measuring the flux of H i and assumes a 20% error in measuring the distance.

Thus, we have a "global" gas-richness parameter M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$ and a WFPC2-scale H i density metric 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 directly comparable to the optical counterparts and the populations of star clusters they may contain. Given the paucity of numerical modeling for many of these interactions, inclinations remain highly uncertain and therefore no attempts at adjusting projection-dependent quantities (e.g., 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉, tail lengths, and optical properties) have been made.

Sources were detected using the DAOFIND algorithm in the IRAF package DAOPHOT. The criteria for detection were chosen to match K03 and provide a source list for photometry and analysis. These include the following:

• 1.  
  At least 2 counts per object in V₆₀₆ and I₈₁₄, along with a count threshold 2σ above the local background. A sky annulus with 5–8 pixel radii was used for both measuring noise around each object and determining its sky background.
• 2.  
  A signal-to-noise ratio (S/N) > 3.
• 3.  
  An error in V₆₀₆-band magnitude <0.25.
• 4.  
  Detections in at least one dither position, accounting for the pixel offsets.

For every in- and out-of-tail region, obvious background galaxies or foreground stars were removed manually.

Aperture photometry was performed on the source lists and cleaned images using the PHOT task in the package APPHOT. In light of potential source crowding, we used apertures with radii of 2, 5, and 8 for object, inner background, and outer background annuli, respectively. Most importantly, these apertures were selected for consistency with K03.

Such a small object aperture is not problematic. Even the closest systems in our sample would not likely have individual clusters marginally resolved by WFPC2; NGC 1487E/W and NGC 4747 images have a pixel scale of ≈5–10 pc, compared to probable r_eff values ∼4 pc (Larsen 2004, and references therein) to ∼10 pc (Trancho et al. 2007). Thus, before diffraction, an object aperture with a 2 pixel radius will encompass >1–2 effective radii of a cluster, or 50%–100% of its light, and is therefore acceptable.

Corrections for Galactic extinction were made with the procedure documented in Section 2.2. Nonoptimal charge transfer efficiency (CTE) was corrected following Dolphin (2000), with the formulation of Dolphin (2008). Uncertainties for all values as well as photometric errors were propagated into the final values of all magnitudes and colors. Zero points were obtained from Dolphin (2008).

Moreover, the concentration index Δ_V—the difference in V₆₀₆ magnitude between apertures of 0.5 pixel and 3 pixel radii—was calculated, with annuli of 6–9 pixel radii for background subtraction. Similar work can be found in Whitmore et al. (1993), Miller et al. (1997), and K03. The latter paper employs cutoff values for this structural parameter of 2.4–3, depending on distance, to eliminate extended objects from their source lists and concentrate on point sources. Because clusters would be largely unresolved and there would be no physical link between Δ_V and the size of single clusters, no restrictions on Δ_V have been made here. Furthermore, we do not wish to exclude marginally resolved cluster complexes or young clusters embedded in nebular emission (Hα is present in the V₆₀₆ bandpass); these would appear more diffuse in Δ_V than individual compact clusters. We retain Δ_V data in Appendix A for reference.

Aperture corrections of 0.33 in V₆₀₆ and 0.36 in I₈₁₄, based on the brightest 5–10 point sources in each chip on all images, were applied (this includes the 0.1 mag correction between 05 and infinite apertures as per Holtzman et al. 1995). We calculate uncertainties of 0.008 and 0.01 for these values, respectively. Errors in using stellar aperture corrections versus cluster candidate aperture corrections for the most cluster-deficient tails—a few hundredths of a magnitude—are negligible for this investigation.

Objects detected and measured with the above methodology were defined as SCCs if they met the following color–magnitude criteria.

• 1.  
  V − I < 2.0. When translated into WFPC2 bandpasses, this color limit V₆₀₆ − I₈₁₄ ≈ 1.43. This criterion allows for populations of old, metal-poor globular clusters (V − I ∼ 1) akin to those observed in the Galaxy (Reed et al. 1988) as well as metal-rich clusters with V − I < 1.5 (Peterson 1993; Ajhar et al. 1994; Whitmore et al. 1995; Kundu & Whitmore 2001). This also includes globular clusters with V − I ∼ 1.2–1.3 (Lee et al. 2002) and solar metallicity. This color limit also allows clusters with redder colors from the stochastic populating of the stellar initial mass function (IMF) at these low cluster masses (Maíz Apellániz 2009), additional extinction (even if overall A_V ≲ 0.5 mag), and uncertainties in metallicities. This V − I limit is also needed to account for problems in modeling binarity in stellar populations, mass segregation, and other dynamical effects than can influence a cluster's integrated magnitudes and colors (see Portegies Zwart et al. 2010 for a review). Furthermore, Anders et al. (2009) suggests that real clusters, subject to a variety of age- and environment-dependent disruption mechanisms, will fade and redden more rapidly with time than these traditional photometric models indicate, necessitating a more lenient color cutoff.
• 2.  
  M_V < −8.5 (≈−8.6 in the WFPC2 system). To compare the SCC quantity across all tidal debris regions, a constant magnitude limit relatively unaffected by completeness is required. Most studies typically use such a bright magnitude cutoff (M_V −8 to −9: K03; Knierman 2007; Schweizer et al. 1996; Whitmore et al. 1999). This limit protects against a level of contamination from single main sequence and post main sequence stars prohibitive to statistical in-tail SCC identification (Efremov & Ivanov 1987); Appendix B has more on this subject.

We find median errors in V₆₀₆ and I₈₁₄ of 0.08 and 0.15, respectively, for all sources. This includes contributions from photometric errors, CTE, and aperture correction uncertainties. Finally, despite identical absolute magnitude limits, K03 used a different V − I < 0.7 threshold to select SCCs. This color distinction was arbitrary, based on a comparison of the in-tail SCC colors with photometry reported for clusters within their host galaxies. The follow-up work of Maybhate et al. (2007) employ an equally valid V − I < 2.0 criterion that also avoids selecting individual, luminous stars. In order to compare the results of those two benchmark works and combine with our own analyses, we chose the latter color and opt to recalculate many quantities published in K03 from their original source lists and their tails. We present them alongside our own in Section 3.

Completeness curves are provided in Figure 2 for optically defined in-tail and out-of-tail regions, in both V₆₀₆ and I₈₁₄. The completeness fraction for each tail was determined using 10,000 artificial stars, sampled 100 at a time with the ADDSTAR procedure in the package DAOPHOT. K03 and Whitmore et al. (1999) find similar completeness fractions for their samples derived from WFPC2 data; ∼50% is reached at V ≈ 25.7 (V₆₀₆ ≈ 25.5). This corresponds roughly to a visual estimate for completeness from the color–magnitude diagrams (CMDs) of this project's sample (Section 3 and Figure 3). Completeness limits for out-of-tail regions are typically lower by 0.1–0.5 mag, i.e., by typical A_V values for tidal tails. Beyond the tidal debris, detections are 50% complete at V ≈ 25.7–26.0 or V₆₀₆ ≈ 25.6–25.9.

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Translated to absolute magnitudes, these tail regions are 50% complete to M_V = −4.6 for the closest debris (NGC 1487E/W) to −8.6 for the most distant tails (NGC 1614N/S). The optically bright merger AM 1054-325 has the brightest absolute 50% completeness limit of M_V = −8.7. In Section 3.2, we discuss the ramifications of using a magnitude limit encumbered by the incompleteness of these tails.

When smoothed with a 12 pixel (≈12) Gaussian kernel, three of the V₆₀₆ − I₈₁₄ color maps in Figure 3 show evidence for "beads on a string" star formation, particularly for the bluest (and possibly youngest) objects we detect in the tails. NGC 1487E, MCG -03-13-063, and AM 1054-325 all exhibit this morphology when their spatial resolution is sufficiently downgraded, and our compact objects blend to clumps of ∼10⁵–10⁶ M_☉. These beads are all separated by ∼3 kpc, adjusting for possible tail inclinations.

We also compared these separations with those measured for a set of Galaxy Evolution Explorer (GALEX) imaged tidal tails presented in Smith et al. (2010). These approaches are heuristically compatible, as both employ images with >1'' resolution and the identification of young blue clumps of star formation within them. In the GALEX sample, we remeasure clump separations of ∼1–7 kpc, with reasonable agreement between the GALEX-imaged beads of NGC 2535 (3–4 kpc; Smith et al. 2010) and its optical counterpart (our study).

This type of star formation is typically attributed to gravitational instabilities within the host environment (Elmegreen & Elmegreen 1983; Bournaud et al. 2004), scaling with the local Jeans mass. Within spiral arms of galaxies, these clumps are separated by the Jeans wavelength (the minimum radius necessary for collapse), which for that environment is ∼1–4 kpc (Elmegreen & Elmegreen 1983). This is also similar to the clump separations observed in interacting galaxies at intermediate redshifts (Elmegreen et al. 2007). The masses estimated here are at the low end of the observable mass range for the clumps of that study, which range from 10⁶ to a few 10⁸ M_☉.

Star-forming clumps with separations ∼3 kpc, while consistent with gravitational collapse scales of spiral galaxies and interacting pairs at intermediate redshifts, are not pronounced in all tails' color maps. It is possible that a combination of metallicity, age/star formation history, orientation, and smoothing effects contributes to this observed morphology in some tails but not in others. There may be more physical motivations as well. This formation morphology is pronounced in small subsets of this sample and the tidal debris of interactions surveyed by Smith et al. (2010), implying that not all tails share the physical conditions necessary for promoting these structures. Certain ISM velocity dispersions and/or mass densities within the host environment are required to produce these beads, but determining these local quantities in the cluster-forming regions is beyond the scope of this work.

In this set of interacting pairs, several have visually striking abundances of in-tail sources relative to regions beyond the tail. To quantitatively compare these systems, the relative areas of in-tail and out-of-tail regions on the three chips must be considered, along with foreground and background object contamination by non-cluster objects. Distance-related selection effects must also be acknowledged.

Table 3 presents the tails, their host galaxy luminosity distances in Mpc (from the NASA Extragalactic Database), their completeness limits (Section 2.5), and their pixel sizes (in pc). We also include the number of SCCs detected within (N^SCC_in) and outside (N^SCC_out) of the debris, and the area of the in-tail and out-of-tail regions in kpc², A_in, and A_out. The in-tail excesses Σ_SCC are then quantified as the difference between N^SCC_in/A_in and N^SCC_out/A_out, with uncertainties from Poisson statistics of N^SCC_in and N^SCC_out. Errors of 2.5σ are recorded. If there are local clusters outside the optically defined tail, this method for background subtraction is systematically too large and gives a lower limit to actual cluster surface density. Thus, SCC excesses at the 2.5σ level are statistically significant.

Table 3. In-tail Cluster Candidate Excesses, M_V < −8.5

Tail	Distance	M$_{V, 50\%}$	Pixel Size	NSCCin	NSCCout	Ain	Aout	NSCCin/Ain	NSCCout/Aout	ΣaSCC
	(Mpc)		(pc)			(kpc2)	(kpc2)	(kpc−2)	(kpc−2)	(kpc−2)
NGC 1487E	10.8	−4.6	5.22	0	1	16.49	40.93	0	0.024	−0.024 ± 0.061
NGC 1487W	10.8	−4.5	5.22	2	0	16.39	41.03	0.122	0	0.122 ± 0.216
NGC 4747	20.2	−6	9.75	7	5	43.66	68.01	0.160	0.074	0.087 ± 0.172
NGC 520	27.2	−6.4	13.13	0	4	26.40	375.97	0	0.011	−0.011 ± 0.013
NGC 2992	36.6	−7.2	17.67	37	15	214.38	198.58	0.173	0.076	0.097 ± 0.086
NGC 2993	36.6	−7.3	17.67	15	7	142.10	270.86	0.106	0.026	0.080 ± 0.072
NGC 2782E	38.1	−7.5	18.40	87	4	336.79	165.83	0.258	0.024	0.234 ± 0.076
NGC 2782W	38.1	−7.3	18.40	10	7	235.91	266.71	0.042	0.026	0.016 ± 0.042
MCG -03-13-063	46.2	−7.8	22.31	88	26	230.18	632.29	0.382	0.041	0.341 ± 0.104
ESO 376- G 028	52.9	−8.1	25.54	4	60	80.97	1036.73	0.049	0.058	−0.008 ± 0.065
AM 1054-325	52.9	−8.7	25.54	180	60	136.28	981.42	1.321	0.061	1.260 ± 0.247
NGC 2444	58.2	−8.2	28.10	27	15	716.94	543.56	0.038	0.028	0.010 ± 0.025
NGC 2535	59.8	−8.4	28.88	44	49	295.03	995.44	0.149	0.049	0.100 ± 0.059
NGC 6872E	62.6	−8.3	30.23	163	63	588.99	999.53	0.277	0.063	0.214 ± 0.058
NGC 6872W	62.6	−8.5	30.23	195	36	788.90	799.62	0.247	0.045	0.202 ± 0.048
NGC 1614N	65.6	−8.6	31.68	33	28	362.63	1386.52	0.091	0.020	0.071 ± 0.041
NGC 1614S	65.6	−8.6	31.68	43	28	288.50	1460.65	0.149	0.019	0.130 ± 0.058
The K03 Sample
NGC 4038	13.8	−5.1	6.66	3	3	76.92	76.92	0.039	0.039	0.000 ± 0.080
NGC 3256E	42.8	−7.8	20.67	49	55	290.32	333.33	0.169	0.165	0.004 ± 0.082
NGC 3256W	42.8	−7.8	20.67	62	58	205.88	428.57	0.301	0.135	0.166 ± 0.105
NGC 7252E	62.2	−8.1	30.03	23	32	700	1181.82	0.033	0.027	0.006 ± 0.021
NGC 7252W	62.2	−8.1	30.03	31	29	684.21	1250	0.045	0.023	0.022 ± 0.023
NGC 3921S	84.5	−8.8	40.80	14	30	692.31	2333.33	0.020	0.013	0.007 ± 0.015

Note. ^aErrors of 2.5σ are quoted.

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Completeness may also have an effect on AM 1054-435 and NGC 1614N/S. Since the 50% completeness limit of these systems is approximately the M_V selection criterion (M$_{V,50\%}$ = −8.6 to −8.7), these tails will have a systematic underrepresentation of in-tail and out-of-tail SCCs. We estimate, using a power-law LF with a logarithmic slope α = 2–2.5 for the in-tail sources (see Section 3.3), and extrapolating from the corresponding V₆₀₆ distribution for the out-of-tail sources, that the Σ_SCC values quoted for these two tails may be underestimated by ≈25%. No corrections to these excesses have been made.

Figure 4 outlines these results, including the interacting pairs of K03 to the right of the vertical dotted line, and their identically calculated excesses. Note that Σ_SCC values for K03 tails are different than those originally published, because of our V − I < 2.0 criterion and the different luminosity distances we use here (for consistency, H₀ = 73 km s⁻¹ Mpc⁻¹; we use the distance derived by Saviane et al. 2004 for NGC 4038). The horizontal line marks where Σ_SCC = 0; any points within 2.5σ of this level imply the host tail is most likely devoid of star clusters within the limit of our broadband observations (for clarity, only 1σ errors are shown). Overplotted boxes indicate tails with statistically insignificant SCC excesses, including tails whose SCCs reside primarily in TDG candidates (NGC 2992 and NGC 7252E/W; see Section 3.2.2). Black circles show the results of the Σ_SCC analysis performed with the M_V < −8.5 and V − I < 2.0 criteria. Blue triangles and red asterisks in Figure 4 show the results of similar calculations, but with fainter M_V limits by 1 and 2 mag (M_V < −7.5 to −6.5), respectively. As the M_V threshold increases, NGC 1487 through NGC 520 enjoy increase in Σ_SCC. More distant systems experience similar changes in SCC excess as the magnitude limit is increased, but only until their completeness limits are reached.

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To further explore the differences in source populations between in- and out-of-tail regions, we performed Kolmogorov–Smirnov (K-S) tests on the distributions of V₆₀₆ and V₆₀₆ − I₈₁₄ for all in-tail versus out-of-tail sources (N_in and N_out); these are presented in Table 4, along with each tail's Σ_SCC for comparison. The results of K03 are also shown. PKS$_{\mbox{\scriptsize {\hbox{$V_{606}$}}}}$ and PKS$_{\mbox{\scriptsize {\hbox{$V_{606}-I_{814}$}}}}$ values list the probabilities that the in-tail and out-of-tail objects are drawn from the same distribution of V₆₀₆ and V₆₀₆ − I₈₁₄, respectively. This provides a measure of the independence of in-tail sources from the out-of-tail sources. Note that in-tail and out-of-tail populations are likely to be independent in terms of color and magnitude distributions if their K-S probabilities are <0.02, i.e., that the populations are distinct at the ≈2.5σ level. In three cases (AM 1054-325 and NGC 1614N/S), tails with statistically distinguishable populations in color and magnitude also have statistically significant SCC populations. This largely confirms that these tails have clusters. Tails with Σ_SCC = 0 all have PKS$_{\mbox{\scriptsize {\hbox{$V_{606}$}}}}$ and PKS$_{\mbox{\scriptsize {\hbox{$V_{606}-I_{814}$}}}}$ values >0.02, reaffirming that they are devoid of star clusters at the M_V < −8.5 level.

Table 4. K-S Probabilities

Tail	Nin	Nout	PKS$_{\mbox{\scriptsize {\hbox{$V_{606}$}}}}$	PKS$_{\mbox{\scriptsize {\hbox{$V_{606}-I_{814}$}}}}$	ΣSCCa (kpc−2)
NGC 1487E	122	45	0.341	0.0263	−0.024 ± 0.061
NGC 1487W	121	67	0.593	0.396	0.122 ± 0.216
NGC 4747	117	45	0.878	0.646	0.087 ± 0.172
NGC 520	21	66	1.37 × 10−3	0.757	−0.011 ± 0.013
NGC 2992	104	45	0.0187	0.660	0.097 ± 0.086
NGC 2993	37	43	0.0172	0.652	0.080 ± 0.072
NGC 2782E	187	8	0.875	0.963	0.234 ± 0.076
NGC 2782W	49	31	0.0588	0.249	0.016 ± 0.042
MCG -03-13-063	141	48	0.324	0.0617	0.341 ± 0.104
ESO 376- G 028	4	82	0.793	0.0735	−0.008 ± 0.065
AM 1054-325	184	82	2.36 × 10−10	9.22 × 10−25	1.260 ± 0.247
NGC 2444	34	16	0.545	0.241	0.010 ± 0.025
NGC 2535	45	59	0.0904	1.16 × 10−4	0.100 ± 0.059
NGC 6872E	180	93	7.26 × 10−5	0.209	0.214 ± 0.058
NGC 6872W	219	38	5.17 × 10−3	0.119	0.202 ± 0.048
NGC 1614N	33	28	1.94 × 10−3	3.33 × 10−4	0.071 ± 0.041
NGC 1614S	43	28	2.61 × 10−4	1.27 × 10−6	0.130 ± 0.058
The K03 Sample
NGC 4038	44	26	0.270	0.890	0 ± 0.080
NGC 3256E	70	60	0.200	1.00 × 10−3	0.004 ± 0.082
NGC 3256W	106	84	0.0300	2.20 × 10−6	0.166 ± 0.105
NGC 7252E	25	40	0.950	0.910	0.006 ± 0.021
NGC 7252W	33	34	0.0500	0.900	0.022 ± 0.023
NGC 3921S	14	30	0.980	0.0500	0.007 ± 0.015

Note. ^aErrors of 2.5σ are quoted.

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Other tails with significant SCC excess but unfavorable K-S statistics still likely contain clusters, however. MCG -03-13-063, NGC 2535, and NGC 3256W have distinct source population differences in V₆₀₆ − I₈₁₄ and not in V₆₀₆as well as SCC excesses. The similarities in the magnitude distributions may be due to a slight contamination of foreground sources for tails at low galactic latitudes (|b| < 30° in these cases). NGC 2993 and NGC 6872E/W conversely show significant source distribution differences in magnitude but not in color. For NGC 2993, its H i tail extends beyond its optical debris, so contamination of the out-of-tail sources by faint, similarly aged clusters within the H i tail but beyond the optical debris may account for its high PKS$_{\mbox{\scriptsize {\hbox{$V_{606}-I_{814}$}}}}$. Sources within NGC 6872E/W debris may have variable extinction and metallicities (Konstantopoulos 2010), and/or may be contaminated by red (V₆₀₆ − I₈₁₄ ≲ 1) foreground sources (b ≈ −325). Lastly, NGC 2782E has a nonzero SCC excess, but shows insignificant source differences between its in-tail and out-of-tail regions in both V₆₀₆ and V₆₀₆ − I₈₁₄. It is probable that the out-of-tail regions of NGC 2782E are undersampled—with only eight sources detected, it is difficult to determine their independence in color and magnitude from the ample in-tail objects.

In summary, by combining K03 with this study, cluster candidate excesses at M_V < −8.5 exist at the 2.5σ level in 10 out of 23 tails (NGC 2993, NGC 2782E, MCG -03-13-063, AM 1054-325, NGC 2535, NGC 6872E/W, NGC 1614N/S, and NGC 3256W). Our detection of these SCCs in the tidal debris regions are all complete to at least ≈50% to that magnitude. Many of the tails with excesses also have V₆₀₆ − I₈₁₄ and V₆₀₆ distributions that differ between tail and out of tail sources, indicating the in tail sources are real and associated with the tail. The tails with statistically nonzero cluster candidate excesses and source distributions indistinguishable from out-of-tail objects in color or magnitude can be explained by foreground contamination or poor statistics from undersampled out-of-tail areas. These tails are still likely to have clusters.

3.2.1. Σ_SCC and Global Tail Characteristics

3.2.2. Σ_SCC and TDG Candidates

The variations in SCC quantities we see in the tail sample and for different magnitude limits must depend of the logistics of star cluster formation in tidal tails as well as the details of their evolution. Each generation of star clusters is imprinted with the physical mechanisms that dictate how they form. What we observe forms the basis for constructing the clusters' LFs, which encode their underlying, heavily age-dependent MFs. These MFs are shaped over time from cluster initial mass functions (CIMFs) by conditions in the tidal tail environment and their own internal physics.

One method to tackle the LF is to plot the brightest cluster M_V versus number of clusters observed brighter than M_V = −9 in each tail. Linear relationships between these two variables arise if the luminosities of the clusters are drawn from a power-law distribution LF with a slope ≈−2.0 (Whitmore et al. 2007; Weidner et al. 2004; Billett et al. 2002). This size-of-sample effect connects a heightened local SFR (introducing large numbers of clusters) with an increasing probability of producing high-mass, luminous clusters (brightest M_V) In effect, the actual LF may not be a uniform power law, but appears as one for particular luminosity ranges. For the luminosities spanned by our SCC populations, Gieles (2010) suggests that a more accurate LF slope is ≈−2.5, while Larsen (2009) offers ≈−2.2 for populations of more strongly disrupting clusters. These values are strictly for spiral galaxies.

We present our results in Figure 5 for two test cases—one where we count all in-tail SCCs in defining the number of clusters (Figure 5(a)) and a second where we statistically subtract out-of-tail SCCs to estimate the cluster number (Figure 5(b)). The latter method subtracts the number of out-of-tail SCCs per unit area (N^SCC_out/A_out) from the number density within the tail (N^SCC_in/A_in) and multiplies that by the area of the tail A_in. The "true" number of clusters should fall between these bracketing situations. In both cases, NGC 3256E/W and NGC 7252E/W have been removed, as these tails have unreliable, anomalously luminous brightest SCCs (M_V ≲ −14) that are not likely clusters. These tails exhibit a degree of contamination in their CMDs (K03) that prevents a safe determination of this quantity.

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The slope we obtain for the resulting trend is −2.33 ± 0.36 for the first case and −1.81 ± 0.44 for the second. These are in rough agreement within errors with the value −2.3 ± 0.2 derived from clusters in a variety of starbursts and quiescent spirals by Whitmore et al. (2007). Our uncertainties are higher given the nature of this study, but ultimately this indicates that the underlying LFs of clusters in our tidal tail sample are similar to those elsewhere in the local universe. The apparent similarity in LFs between our tidal tail clusters and elsewhere in the local universe is insightful. For LF slopes ≈−2 to −2.5, this implies that the underlying mechanisms at work in tidal tails are extremely similar in effect, if not in form, to those shaping the cluster populations observed in starburst and quiescent galaxies. Of course, our picture is incomplete, as star cluster LFs in tidal debris may be complicated by complex formation and dissolution histories from multiple sequences of extensive and compressive tides (Renaud et al. 2009), and/or their passage through the ISM (e.g., Gieles et al. 2006). There will also be stochastic effects at detectable masses and contributions from clusters born at different ages, as well as systematic effects and unseen variables in this study, all of which may contribute to the trends or scatter witnessed in Figure 5.

Though the dependence of Σ_SCC on the properties in Table 2 is generally not straightforward, the most SCC-rich tails are all younger than 250 Myr. Since the Σ_SCC differences cannot be statistically attributed to age alone, there may be other factors at work. To elucidate this, we plot a tail V versus V − I CMD in Figure 6 (panel (a)), along with Σ_SCC versus tail V (panel (b)). Each graph presents the combined tail sample of this work and K03, color-coded by the progenitor system's interaction age. Boxed data points again indicate tails with no evidence of SCCs at the M_V= −8.5 level. An extinction vector of 1 mag in V is shown in (a), and a histogram of the surface brightnesses of cluster-rich and cluster-empty tails is displayed in (b). We also note that NGC 2444 had no optical tail and was eliminated from this figure.

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Figure 6(a) shows that clusters are found in tails of a variety of surface brightness, V − I colors, and ages. As was seen in Section 3.2.1, the tail sample is simply too phenomenologically diverse for distinguishable tail populations in terms of age. For example, NGC 2992 and NGC 2782W are young tails devoid of M_V < −8.5 clusters, while the ≈750 Myr old debris of NGC 1614N/S have two of the highest SCC excess of the sample (Σ_SCC ∼ 0.1 kpc⁻²).

In terms of color, multiwavelength observations of other tidal tails (Smith et al. 2010) that better circumvent the metallicity–extinction degeneracy show that blue colors typically imply young star formation and/or subsolar metallicity, rather than extinction effects. Thus, one might expect blue tail colors to correlate with clustered star formation here. However, K-S tests reveal that tails with Σ_SCC statistically consistent with zero have a 33.1% probability of sharing the same V − I distribution as those with Σ_SCC > 0. There may be a number of explanations for this behavior. For instance, small variations of even 0.5 mag of internal extinction may erase any trends of Σ_SCC with tail V − I, which may be already unclear with our finite, 23-tail sample size. It is also possible that the blue colors expected of star formation are localized phenomena in most moderately star-forming tails, much as it is inferred in Bergvall et al. (2003) for galaxy interiors.

Comparing Σ_SCC excesses to tail surface brightness, we find a K-S probability of 0.0102 that cluster-bearing and cluster-devoid tails belong to the same tail V distribution. Evidently, tails with cluster excesses tend to be brighter. This is presented in Figure 6(b) to demonstrate that it is not simply a trivial relationship of having more luminous clusters contributing to an overall more luminous tail. The accompanying histogram reflects the statistically significant difference between cluster-rich and cluster-poor tails in terms of surface brightness, but it is also a reminder of the small sample size and the difficulties in interpretation, especially given variations in internal extinctions and projection effects.

This could still be a promising result. Drawing upon the work of Blitz & Rosolowsky (2006) and Elmegreen (1993), Meurer et al. (2009) reason that the R-band surface brightness roughly traces the midplane pressure of galaxies. This pressure regulates the pressure within molecular clouds, which is important for producing clustered star formation and other bound structures (Elmegreen & Efremov 1997). Although many of the underlying assumptions of this deduction—hydrostatic equilibrium of thin gas layers embedded in thin stellar disks, and the relative contributions of both of these components and their dynamics—are invalid for tidal tails, the general preference for cluster-forming tails to be brighter on average in V (which of course is not the same as R) may present a parallel paradigm. On more local scales tail surface brightness may offer a more accurate diagnostic of ambient pressure and the star clusters that form, but it is likely that the contribution of the gas potential and dynamics also needs to be more thoroughly addressed.

Interestingly, the most cluster-rich tails (Σ_SCC ≳ 0.2 kpc⁻²) are all young (≲250 Myr), and brighter than the median (V ≲ 24 mag arcsec⁻²). Though we determined the age distributions for cluster-rich and cluster-devoid tails were indistinguishable, interaction age may be an additional "bonus" for tails like AM 1054-325, MCG -03-13-063, NGC 2782E, and NGC 6872E, whose images capture strong bursts of star formation relatively near periapse for their interactions. This is typically seen in models of star-forming tidal debris (Chien 2010; Di Matteo et al. 2008; Mihos & Hernquist 1994). Thus, should higher surface brightness loosely trace higher ambient pressures and thus star formation capacity, SCC detection is contingent on strong overall star formation, which is typically seen at younger dynamical ages for a variety of interacting systems.

Although in Section 3.2, there was no clear relationship between tail gas richness and cluster candidate excess, the H i content of tidal tails warrant further investigation. In Figure 7, we explore the complex relationship between the optical/H i properties of the tidal tails and their Σ_SCC measurements. Boxed points are the same as in the previous figures, and we plot points whose "color-coded" data are either missing or unreliable in black. This includes the abnormally high H i densities of the NGC 1487E/W tails, which exhibit a superposition of disk and tail gas (〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 > 10⁷ M_☉ kpc⁻²), and the brightest cluster candidate magnitudes of NGC 3256E/W and NGC 7252E/W (Section 3.3).

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Figure 7(a) first offers a tail CMD whose points correspond to their 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 values. As in Figure 6(a), tails with and without clusters span a range ages and 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 with no obvious relationship to integrated V or V − I. Examining the interplay of 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉, M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$, and Σ_SCC reveals a different picture, however. Figure 7(b) shows the variation of Σ_SCC with M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$, with data points colored according to a scale of 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉. Despite an overall increase of Σ_SCC with tail H i richness, there is too much scatter for M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$ to be a useful diagnostic of cluster candidate excess. But between the boxed and unboxed data sets, tails lacking SCCs (boxed) appear generally less H i-dense on WFPC2 FOV scales than SCC-containing tails (unboxed). Without the aberrant NGC 1487E/W tails, K-S tests compute that tails without SCCs have a probability of 0.0216 of being drawn from the same 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 distribution as those with SCCs.

Thus, while 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 is not a direct measure of the sub-kpc scales that are important in star formation (e.g., Maybhate et al. 2007; Bigiel et al. 2008; Schaye 2004), and the differences in 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 populations are borderline distinct, it may be a useful zeroth-order diagnostic. Cluster-deficient tails overall appear to have a different distribution of H i surface densities than tails with SCC excesses. Many of the boxed points in Figure 7(a) are bluer—have lower 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉—than the normal points, although there is scatter (e.g., the H i-dense and highly inclined NGC 2992 whose SCCs are largely confined to its TDG).

It is therefore interesting to consider whether there is some cutoff value or transition range of 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 that would account for the different distributions. According to Schaye (2004), it is possible to estimate a critical gas surface density for star formation, whose H i component we would observe here. Varying the input parameters of the Schaye (2004) models (see their Equation 25) and estimating the contribution of molecular gas yields plausible critical H i surface densities $\Sigma _{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}\rm {, crit}}}}$ ≈ (2.7–3.4) × 10⁶ M_☉ kpc⁻². Here, we have assumed mean metallicities ≲Z_☉ and H i-ionizing UV radiation fields of 10⁴–10⁶ photons cm⁻² s⁻¹, which are reasonable estimates for tidal tails given their range of luminosities, ages, and sizes. We estimate that H₂ contributes no more than 10% to the total gas density from Figure 13 of Bigiel et al. (2008). We will hereafter refer to (2.7–3.4) × 10⁶ M_☉ kpc⁻² (2.7–3.4 M_☉ pc⁻²) as the fiducial critical gas density for star formation in tidal tails. Again, it is crucial to stress that a threshold density technically applies to sub-kpc scales, not the mean 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 values quoted here. However, tails such as NGC 2444, NGC 7252E/W, and NGC 3921S, with 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 ≲ 1.7 × 10⁶ M_☉ kpc⁻², on average may be unable to generate significant SCC excesses on WFPC2 FOV scales. This does not prohibit more localized concentrations of cluster-forming activity, but may just imply an overall suppression of cluster formation.

To further visualize the role of WFPC2 FOV-scale H i density, Figure 7(c) relates 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 to interaction age. 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 declines with respect to the interaction age (again, the anomalous NGC 1487E/W debris should be overlooked). Across the sample, there appears to be an exponential decline in 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 with time; we plot example curves of 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 ∝ e$^{-t/t_{\rm {dep}}}$ for two depletion timescales t_dep. We include t_dep = 100 Myr (blue dashed lines) and 1 Gyr (violet dotted lines). There are necessarily strong inter-tail differences in depletion timescales from star formation, orientations, and time-dependent gas dispersal. There is also a distance-related 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 bias—clumps of H i emission at different places along a tail can influence 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 measurements depending on the extent of coverage and placement of the WFPC2 FOV, and therefore distance. But in general, an average depletion timescale of ∼500 Myr for these tidal tails may be reasonable. This is on par with typical tidal tail lifetimes (Binney & Tremaine 2008).

In addition, red dashed lines in Figure 7(c) highlight our estimate of $\Sigma _{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}\rm {, crit}}}}$. Evidently, the notion of a critical H i surface density does not successfully translate to a critical 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 for cluster formation. There are several tails (e.g., NGC 6872E/W) around or below this H i limit with an ample supply of clusters. Conversely, several tails above the $\Sigma _{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}\rm {, crit}}}}$ limits are statistically lacking in clusters. Each point in Figure 7(c) glosses over the particular dynamics of each interaction that obtain varying quantities of the gas, the true three-dimensional densities and pressures of the tail ISM, and the multiple generations of stars and clusters that form a complex recycling and feedback network with said ISM. Thus, there are clearly more complicated and local physics at work in determining cluster formation thresholds.

The points plotted in Figure 7(c) are colored according to the corresponding scale of the brightest cluster candidate M_V. Between the tails with and without significant cluster excesses, we find a K-S probability of 0.0224 for their brightest M_V values being drawn from the same distribution. Like the K-S results for 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉, the differences in the brightest M_V distributions are marginal, but probably real. From the size-of-sample effect (e.g., Larsen 2004; Section 3.3), tails with cluster candidates likely have strong local star and cluster formation rates, and therefore have more luminous brightest cluster magnitudes. This does not seem to conspicuously relate to 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 or interaction age, again obfuscating any additional attempts to connect overall tail star and cluster formation with dynamical age and large-scale H i content.

Lastly, Figure 7(d) compares 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 to Σ_SCC, using the colors of the plotted points to again represent the brightest cluster candidate magnitudes for each tail. Since most of these tails are presumably produced from the H i-dominated gas of their progenitor galaxies' outer regions, 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 may approximately represent the total mean gas density. If tidal tails behave like spiral galaxies, the area-normalized tail SFR Σ_SFR may possibly then scale with 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 by a Schmidt–Kennicutt law; Σ_SFR∝ 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉^N for some index N (Kennicutt 1998). If we assume from the size-of-sample effect that the total number of clusters produced a tail scales roughly with the tail SFR, then Σ_SCC ∝ 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉^N. N = 1 implies a constant cluster formation efficiency; curves of constant cluster formation efficiency are indicated on the plot. Steeper curves for a certain average H i surface density indicate higher cluster formation efficiency. We avoid reporting efficiencies directly as they require a conversion of Σ_SCC to the total cluster mass density with a currently unreliable estimate of cluster population masses. In reality, the translation from Σ_SCC to Σ_SFR would include a treatment of how the luminosity evolution of clusters from earlier episodes and their appropriate timescales affects the measured SCC count, but this is an acceptable approximation given our other uncertainties.

In comparing sub-kpc H i surface density to SFR density for a set of 18 nearby normal and H i-dominated galaxies and multiple resolution scales within them, Bigiel et al. (2008) demonstrate that neither the total gas density nor the H i surface density is the critical quantity in determining the SFR. Many galaxies can span about an order of magnitude in star formation efficiency for constant values of H i surface density. Employing similar methods to study regions beyond R₂₅ in galaxy disks, however, Bigiel et al. (2010) regain a Kennicutt–Schmidt scaling of the SFR to H i density, reporting a suppression of star formation efficiency relative to the galaxy interiors. Our data do not show such a scaling, but rather tails spread across different cluster formation efficiencies and Σ_SCC values for limited ranges of 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉. The Schmidt–Kennicutt law applies strictly to rotating disks, and not tidal tails, so it is either possible no similar relationship would be observed between Σ_SCC and any variety of gas for these environments at any scale, or a more directed, local study akin to Bigiel et al. (2010) and Maybhate et al. (2007) would be more illuminating.

For now, it is interesting to note that tails with the most luminous brightest cluster magnitudes tend to lie around curves of higher , implying that some of our more cluster-rich tails (NGC 6872E/W and NGC 1614N/S) have generally higher star formation efficiencies (with respect to measured H i reservoirs) than other tails. But ultimately, the scatter in all the plots of Figure 7 implies that cluster formation in tidal tails is determined less by H i richness and mean density on WFPC2 FOV scales, and more by other variables that set star formation efficiencies and gas consumption timescales. While cluster-containing tails tend to have higher observed H i densities (often combined with young dynamical ages and bright, star-forming environments) than those without them, the number of cluster candidates observed in these tails cannot be well predicted by our current H i properties. Complex gas dynamics, star formation histories, and tail orientations do not allow a determination of critical gas properties required to produce SCCs. In an upcoming work, we will concentrate on H i densities on more localized scales and may better uncover the role of neutral hydrogen in cluster formation within tidal tails.

Of the 23 tails examined, 10 have nonzero SCC excesses at M_V < −8.5, the range of which has few obvious dependences on many observable parameters. Provided the implications of Figures 4 and 5, fainter clusters are more numerous, and in the closest tails, detectable. While we cannot infer LFs and MFs from the current data, it is interesting to ascertain if star clusters exist to the faintest possible limit in each tail. In short, do star clusters of some magnitude form in all tidal tails?

Ideally, to detect the maximum number of cluster candidates in each tail, changing the magnitude criterion to the completeness limits of the tails is desired. The generally higher Σ_SCC values for M_V < −6.5 in Figure 4 are illustrative of this concept. On the other hand, extending M_V to fainter limits risks contaminating source lists with bright, high-mass main sequence stars from current bursts of star formation, as well as post main sequence stars above a certain mass around the red supergiant stage (e.g., Efremov & Ivanov 1987). The combination of these two effects is a strongly age-dependent function of the tails' star formation histories and the minimum single stellar mass that the new M_V or completeness limit provides. The blue and red (M_V < −7.5 and −6.5) points in Figure 4 cannot be interpreted without this caveat.

Appendix B explores these topics in further detail for the interested reader. Combining the extended magnitude limits with a treatment of single stellar contamination, we find that the NGC 520 TDG candidate probably has clusters to M_V = −6.5, when there were no clusters brighter than M_V = −8.5. NGC 1487E/W and NGC 4747 are also complete to fainter magnitudes, but their statistics are too poor for interpretation or their potential contamination was not negligible. For more distant tails, it cannot be determined for certain whether they have cluster excesses at fainter magnitudes than M_V = −8.5. Some tails have insightful clues to their dearth of cluster candidates, however. We offer an explanation of some of these tails below.

NGC 1487E/W, NGC 4038, NGC 3256E, NGC 7252E/W, and NGC 3921. It may be no coincidence that these mergers, which have no significant SCC excess at M_V < −8.5, are all >400 Myr old. A current low tail SFR and significant fading for any clusters formed near periapse may combine to generate an apparent paucity of star clusters. It is not necessarily true that there are no clusters that were formed in the these tails, but rather that the few that are there do not create a statistically significant excess above the background level at the magnitude limit of the WFPC2 images. Their cluster formation events may have been too weak, poorly timed, and/or poorly placed along the tails (the K03 tail pointing is a small fraction of the full length of the NGC 4038 debris region; see their Figure 1). Renaud et al. (2009) provide a useful illustration of this age effect with their model of compressive and extensive tides in NGC 4038/9 (their Figure 3). If some fraction of cluster formation occurs where compressive tides arise in tidal tails, the nature of the tidal field may be a useful tracer of the star formation history. Their simulations show that, while the galaxy interiors always enjoy compressive tides along with the observationally obvious signatures of continuous nuclear star formation, these tides in the tails are sporadic at best. They preferentially occur at early ages (≲100 Myr) and will only occur at later times at particular points along the tails.

NGC 2444. This system, whose tail definition was assigned based on its H i debris and had no detectable optical debris in WFPC2 images, may similarly be devoid of significant star formation. This tail has the lowest recorded 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉, 1.34 × 10⁶ M_☉ kpc⁻², of the tails in the sample; this system's H i-dependent tail definition warrants caution in comparing its mean H i density to those of the rest of the sample, however. Even if this medium were gravitationally bound, the average free fall timescale (1/$\sqrt{G\rho }$) would be ≳1 Gyr, longer than the estimated tail age (100 Myr). So overall, star formation may be suppressed. Localized concentrations of H i on sub-WFPC2 FOV scales (kpc², as opposed to the current ≈400 kpc²) may reveal more reasonable collapse timescales, however.

Numerical models of Duc & Bournaud (2008) suggest that high-velocity encounters (V ∼ 1000 km s⁻¹) between galaxies generally produce asymmetric, low-mass, gas-dominated tails without much star formation, as opposed to the optically bright (and star forming), clumpy tails generated by slower mergers. Their model of NGC 4254 reproduces the 250 kpc-long H i stream with a rapid encounter velocity and mass ratio identical to that of NGC 2444/5. Their prototypes of these kinds of collisions produce average H i surface densities ∼2 M_☉ pc⁻² or 2 M_☉ × 10⁶ kpc⁻², comparable to our result for that quantity.

Appleton et al. (1987) posit that the diffuse H i plume of NGC 2444 is a result of a recent (∼100 Myr), low impact parameter collision between NGC 2444 and a low surface brightness, H i-rich companion (not NGC 2445, which still interacts with the system). That unseen companion has since disrupted and its stellar component dispersed enough to fall below our optical tail detection threshold; they cite the velocity structure of the bloated bubble structure to the north of our WFPC2 FOV (online Figure 3.12) as kinematic evidence of this event. This model agrees with the timescales at play in this tail. To produce a ∼100 kpc long H i streamer in 100 Myr (the time required for an expanding H i shell in the tail to reach its current size from its velocity maps), collision speeds ≳1000 km s⁻¹ are needed, rather than the tidal removal of disk gas comparable to orbital speeds at the outer disk radii.

This suggests that merger dynamics play a dominant role in determining the SCC-harboring capacity of tidal tails. High-speed galaxy encounters may produce low-density tidal gas whose conditions, i.e., low metallicities, H₂ deficiencies, and high velocity dispersions, are unfavorable for star formation in detectable quantities.

NGC 2782W. It is interesting that the eastern tail of NGC 2782 has a profusion of in-tail sources (≈0.2 kpc⁻²), while the western H i-rich, optically faint tail does not (≈0 kpc⁻²). Optical colors and 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 measurements are similar for these tails (V − I ≈ 1 and 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 ≈ (5–8) × 10⁶ M_☉ kpc⁻²). The main difference, aside from tail length, is optical brightness. The eastern tail is ≈1.5 mag arcsec⁻² brighter in V than the western tail. The physical reason for the difference between the two tails has been explored. Smith (1994) predicts that the eastern tail is predominantly the consumed, optically bright merger remnant of NGC 2782's companion, while the western tail is the metal-poor debris left behind from the outer regions NGC 2782 itself. Therefore, the eastern tail has an ample molecular hydrogen supply from a merging galaxy interior to fuel its observed SCC density.

The absence of CO emission and inferred lack of H₂ in the western tail makes the apparent absence of young cluster candidates understandable (Braine et al. 2001). A low metallicity of this tail, and differences in the survivability of H₂ and CO at low tail extinctions, may account for a nondetection of CO and an inaccurate translation to molecular hydrogen. But if the absence of cluster candidates in this tail is a question of gas availability, projection effects may be to blame. Theoretical models require large relative inclinations between the two galaxies (Smith 1994), resulting in an extended H i plume with a sizable component along our line of sight. Thus, this system's gas surface density may represent the same physical density as a "flatter" tail with a lower surface density by as much as a factor of ∼3.

Using Gemini optical spectroscopy, S. Torres-Flores et al. (2011, in preparation) confirm cluster status for several objects in NGC 2782W we label as SCCs and assign them masses ∼10⁵ M_☉ and ages consistent with in situ formation. Since there are still only a few clusters in the ∼10⁵ M_☉ range, so this system suffers from a "weak" cluster formation history compared to many of the other tails studied here, perhaps for reasons proposed above. NGC 2782W therefore has clusters, but they are effectively hidden in the statistics of our study.

In summary, certain merger dynamics like encounter velocity, or variations in molecular gas content may account for some of the dispersion in Σ_SCC and the range of cluster magnitudes possible across tidal debris. This could be especially pertinent for tails that have no demonstrable SCC excess even at the faintest M_V limits. Variations in completeness (distance) and limited prior observations and theoretical work make this difficult to assess across the entire tail sample. Finding SCCs may be optimal in the closest, youngest tails that are actively star forming. Disentangling other, potentially more promising effects provided by dark matter halos, merger geometries, etc. require further efforts in high-resolution modeling.

NGC 1487 is the optically bright remnant of a ∼500 Myr old merger between two comparably massed galaxies (Lee & Lee 2005), whose eastern tail features a long "spine" curving into the bottom right corner of WF3, surrounded by an extended plume that reaches into the other chips. There is one non-tail source and zero in-tail sources meeting the cluster selection M_V and V − I criteria. The in-tail color distribution of detected objects is very broad, peaking at V₆₀₆ − I₈₁₄ ∼ 0.5–0.8. The bluest sources of this distribution are concentrated in the blue knots evident in this tail's color map, which trace the spine to the collection of sources at the tail's tip. These may be either very young (≲10 Myr) or metal-poor.

There is considerable scatter in the concentration index plot. At this distance, the largest sources may be marginally resolved (1 pixel = 5.22 pc), so these concentration indices may loosely correspond to a range of physical sizes. For most in-tail sources, the V − I colors indicate ages ∼100 Myr, so many faint sources detected in this study may be clusters ∼10⁴ M_☉. Thus, we see evidence of star formation around the time of perigalacticon, with more recent, superimposed populations across the tail. These regions in particular paint a high-resolution "beads on a string" across the color map. Considering possible projection effects, these young clumps are separated by ∼2–3 kpc.

K-S tests reveal a 34.1% and 2.63% probability that all the in-tail and out-of-tail sources detected originate from the same distribution of V₆₀₆ and V₆₀₆ − I₈₁₄, respectively. The lack of SCCs is strange, given the high average H i densities measured for this tail (〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 = (2.55 ± 0.51) × 10⁷ M_☉ kpc⁻²). Overall, the tail has one of the lowest total H i masses, however; M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$ = (6.14 ± 1.2) × 10⁸ M_☉. Why the debris with the highest H i content should also be devoid of cluster candidates ≳10⁵ M_☉ is not easily explained. In M_☉ pc⁻², 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 = 25.5 ± 5.1, well above the H i saturation threshold of 9 M_☉ pc⁻² of Bigiel et al. (2008). Above this limit, most of the gas available in the tail may be molecular, so inclination effects or the superposition of disk and tail gas may be responsible in artificially increasing the observed average H i density.

If the true H i surface density of NGC 1487E is significantly lower and in the expected H i-dominated regime of typically low-Z, H₂-poor outskirts of galactic disks (Bigiel et al. 2008), the overall SFR of the tail may be relatively low (cf. the host galaxy IRAS SFR of 0.12 M_☉ yr⁻¹). This may imply an underpopulation of the high-mass end of a star-forming generation's CIMF. This would then result in zero objects observed with photometric characteristics of ∼10⁵ M_☉ clusters.

It is easy to check on the logical consistency behind this reasoning. If we reasonably assume that these clusters are drawn from a power-law LF with a slope of −2 to −2.5 (Section 3.3), then it is possible to analytically estimate how many clusters we should observe brighter than a certain magnitude. Using the number of sources we observe between adjacent, complete luminosity bins (of size 1 mag) to normalize the LF, we calculate that there should be ≲1–3 sources brighter than M_V = −7.5, and no objects brighter than M_V = −8.5. With the tail age limits, this verifies that there should not be clusters present with masses ≳10⁴ M_☉ in this tail.

The western, also H i-dense yet H i-poor (〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 = (33.2 ± 6.6) × 10⁶ M_☉ kpc⁻²; M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$ = (5.41 ± 1.1) × 10⁸ M_☉), tail is a patchy assembly of diffuse light stretching across WF3 and WF4. Similar star-formation hotspots as in the eastern tail are observed, but are not identified as SCCs. There are two cluster candidates found within the tail, and zero beyond it. One SCC has a magnitude and color consistent with a ∼10⁵ M_☉ cluster from the same ∼100–300 Myr generation as most of the sources fainter than the M_V selection limit. The color map shows most of the cluster and field light is produced from this generation of star formation, with scattered bursts of younger and less massive (≲100 Myr; ∼10⁴ M_☉) objects. This is qualitatively similar to the eastern tail.

There is a 59.3% and 39.6% probability of in-tail and out-of-tail sources being drawn from the same V₆₀₆ and V₆₀₆ − I₈₁₄ distribution. It is possible that the true tail boundary extends to the H i contours pictured in the online figure, with several out-of-tail sources belonging to the in-tail source list. However, if this were true, the out-of-tail CMD still indicates that there would still be only two SCCs counted in this tail. The concentration index plot shows no useful distinction between in-tail and out-of-tail detections.

In the galaxy interior, Mengel et al. (2008) investigate several clusters whose discrepancies between photometric and dynamical masses offer insight into their current disruption. Their clusters are ≈8.5 Myr old and between 10⁵ and 10⁶ M_☉. Lee & Lee (2005) performed WFPC2 B- and I-band photometry on 560 clusters similar to this study, and while their age and mass estimates for clusters are also limited to two bandpasses, they suspect a similar, roughly bimodal age distribution in the NGC 1487 clusters, peaked at 15 Myr and 500 Myr.

This system is a ∼320 Myr old minor merger interacting with NGC 4725 (Haynes 1979; Wevers et al. 1984), featuring a long, optically faint tail extending through the third and fourth WFPC2 CCD chips. There is a concentration of sources in the third chip, with estimated ages ≲50 Myr (and corresponding masses ≲10⁵ M_☉). Of the sources shown in the CMDs, seven and five cluster candidates were detected in and outside the tidal regions, respectively, with V₆₀₆ − I₈₁₄ ∼ 0–0.7 and 0.3–0.7. Population differences may be seen in the Δ_V diagrams; in-tail sources show a slight preference for Δ_V ≲ 2.0, compared to the more even dispersion for objects beyond the tail. Given the distribution of colors, SSP models posit ages of ∼30–300 Myr for ∼10⁵ M_☉ cluster candidates in this image.

The V₆₀₆ and V₆₀₆ − I₈₁₄ K-S probabilities for all sources are 0.878 and 0.646, respectively. H i was not detected in this tail, and the interior of the merger has an IRAS-derived SFR of ≈0.27 M_☉ yr⁻¹.

NGC 520 appears to be a minor merger remnant (Stanford & Balcells 1991). WFPC2 images present an optically faint, H i-defined (M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$ = (1.12 ± 0.22) × 10⁹ M_☉) curved tail extending to the north. The HST pointing here is situated on the tidal dwarf candidate in this system (UGC 957), which may either be a genuine TDG or a small satellite galaxy engaged in a three-body interaction with the other galaxies (Stanford & Balcells 1991). This object coincident with bright H i emission (〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 = (3.81 ± 0.76) × 10⁶ M_☉ kpc⁻²), but no CO has been detected at this location (Stanford & Balcells 1991).

Within the host galaxy, infrared emission indicates an SFR of ≈6.5 M_☉ yr⁻¹. Given the TDG candidate's distance from the galactic interior (112 kpc), the tail/galaxy SFRs may not correlate well. GALEX observations (Neff et al. 2005) have revealed that no current star formation has occurred within NGC 520, and the youngest regions are ∼300 Myr old. Moving out to the tail, they find massive 10⁸–10⁹ M_☉ clumps of ages ≳300 Myr. Optical spectroscopy of the NGC 520 nucleus confirm a 300 Myr old episode of star formation, with little current activity Stanford (1991). This matches dynamical simulations of this interaction (Stanford & Balcells 1991) that place the age of this interaction at 300 Myr.

The distribution of colors detected in the TDG is extremely broad in the CMD and color map and lacks an obvious peak. We detect zero and four SCCs in and beyond the tail, respectively. Given the above age constraint, many sources fainter than M_V = −8.5 may be ∼10⁴ M_☉ clusters ≲10 Myr old, or ≲5 × 10⁴ M_☉ clusters with ages ∼150–500 Myr.

From the Δ_V diagram in the online figure, NGC 520 may contain a marginally distinct population of compact objects, whereas the external sources are generally more extended and fainter (M_V ≲ −7). K-S tests estimate a probability of 1.37 × 10⁻³ and 0.757 for all detections originating from the same V₆₀₆ and V₆₀₆ − I₈₁₄ distributions.

NGC 2992 is a peculiar Sa galaxy with an unusual optical condensation at the edge of its tail in WF2. With a combination of Hα, CO, optical, and H i data, Bournaud et al. (2004) asserts that this is a genuine TDG. Sources detected within outline prominent CO emission; with standard conversion factors, Bournaud et al. (2004) estimate that the TDG contains 3.5 × 10⁷ M_☉ of H₂, contributing to a total of ≈2 × 10⁹ M_☉ of stellar and gaseous material.

There appears to be a deficit of sources in the middle of the tail on WF3, which is visibly smoother and undisturbed. The V₆₀₆ − I₈₁₄ color map is remarkably homogeneous, with colors consistent with ages of ∼100 Myr–1 Gyr. Brinks et al. (2004) find that this tail has a high metallicity within the TDG (12 + log(O/H) = 8.6), so redder colors are expected. The embedded SCC population with similar V₆₀₆ − I₈₁₄ would be mostly composed of ∼10⁵ M_☉ clusters. It is also possible from the CMDs that lower mass, ≲10 Myr old clusters contribute to the tail light. Of the sources indicated, 37 and 15 are SCCs in and out of the tail, respectively. Between these two regions, there do not appear to be distinctions in terms of concentration index. We find K-S V₆₀₆ and V₆₀₆ − I₈₁₄ probabilities of 0.0187 and 0.660 for the entire source list. The location of SCCs coincides with the brightest H i contours; this tail has a mean H i density of 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉= (6.44 ± 1.3) × 10⁶ M_☉ kpc⁻². It also has an interior IRAS-derived SFR of ≈3.4 M_☉ yr⁻¹.

This galaxy is in the early phases of merging with its similarly massed companion NGC 2993. They both exhibit moderate H i masses (M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$ = (1.43 ± 0.29) × 10⁹ M_☉ for NGC 2992), optical brightnesses, and short (apparent) tails relative to their disks. 100 Myr have elapsed since perigalacticon (Duc et al. 2000), and the final merger should occur in ∼700 Myr. Given this constraint, SCCs that form in situ must be ≲5 × 10⁵ M_☉, as mentioned above. Prior studies have noted difficulties in isolating central starbursts in this active galactic nucleus powered Seyfert galaxy (e.g., Davies et al. 2007; Fanelli et al. 1997), so the star cluster populations of that system remain unresolved.

The interacting counterpart to NGC 2992, NGC 2993 features an optically faint, moderately H i-rich (M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$ = (7.27 ± 1.5) × 10⁸ M_☉; 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉= (5.77 ± 1.2) × 10⁶ M_☉ kpc⁻²) tail that curves through the second and third chips of the V₆₀₆-band mosaic. The interior of this galaxy supports an infrared-derived SFR of ≈5.0 M_☉ yr⁻¹. The color map exhibits a strong regional variation of V₆₀₆ − I₈₁₄, from the blue spine to the redder outlying plume.

In the CMD for the debris, in-tail objects are roughly distributed across the tail and its color gradient, and mixed with the out-of-tail sources in the concentration index diagram. There are 15 in-tail SCCs and 7 out-of-tail counterparts, the former of which show a degeneracy of possible high masses/old ages or lower masses and young ages akin to NGC 2992. From Hα equivalent widths, Duc et al. (2000) find groups of 5–7 Myr old starbursts in the main body of this system, which are systematically younger than the estimated ∼10 Myr–700 Myr age range of objects detected here. If tail populations of NGC 2992/3 are around the same age, then our detected SCCs may have masses ∼10⁴ M_☉. K-S tests reveal a 1.72% and 65.2% probability that all the in-tail and out-of-tail sources detected originate from the same V₆₀₆ and V₆₀₆ − I₈₁₄ distribution, respectively.

NGC 2782 is an SABa-type, ∼200 Myr old minor merger (Knierman 2007). The eastern tail is short compared to the face-on optical disk and rich in H i (M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$ = (2.41 ± 0.48) × 10⁹ M_☉; 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 = (7.08 ± 1.4) × 10⁶ M_☉ kpc⁻²). The aftermath of the interaction is evident in the disrupted appearance of the main disk in WF4, highlighted by ripples and density inhomogeneities that continue down into the tail in the other two chips. The detected sources seem loosely correlated with the optically clumpy parts of the tidal debris and appear only partially correlated with the bluer regions in the color map. We find 87 potential clusters in the tail and 4 beyond.

For all the in-tail objects, the CMD reveals a broad V₆₀₆ − I₈₁₄ distribution of colors representative of a correspondingly broad range of putative cluster ages. SCCs may have a spread of ages and masses, from ≲ 10 Myr, ∼10⁴ M_☉ clusters to those aged nearly 1 Gyr and 10⁵ M_☉ in mass. Given the age constraint and 100 Myr old cluster estimates for this tail of Knierman (2007), our SCCs are more likely closer to the former than the latter.

Contours of H i emission for the eastern tail abruptly end halfway across the third chip; this is also where the bluest (or conversely metal-poor) regions of the tail are. As seen in the online figure, many of these sources tend to be photometrically extended (Δ_V ≳ 2), similar to the few external sources with generally high concentration indices and more limited spread of colors. Blue colors (V₆₀₆ − I₈₁₄ ≲ 0) and extended profiles may indicate young ages and concordant nebular emission. The majority of fainter in-tail SCCs appear more concentrated, with Δ_V < 2.0. We determine K-S probabilities of 0.875 and 0.963 for V₆₀₆ and V₆₀₆ − I₈₁₄, respectively, for all sources.

The western tail of NGC 2782 is markedly different, barely tracing WF3 to the PC and down into WF2. The optical extent of the tail does not perfectly match the H i tail illustrated on the SDSS image; the latter extends further into WF4 and WF2 than the optical boundary we employ here. This tail is also more H i-rich on average than its eastern companion (M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$ = (3.14 ± 0.63) × 10⁹ M_☉; 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 = (5.17 ± 1.0) × 10⁶ M_☉ kpc⁻²). Its relative paucity of SCCs is in stark contrast to NGC 2782E. With a common progenitor galaxy IRAS SFR of ≈3.7 M_☉ yr⁻¹, it is once more apparent that this infrared diagnostic may not correlate with tail SFR in all cases and cannot be interpreted too deeply.

In terms of concentrations and colors, in-tail and non-tail sources are evenly dispersed about the V₆₀₆ − I₈₁₄ cutoff and do not show immediately recognizable differences in Δ_V. The ages and masses of these SCCs are similar to those of the eastern tail. Assuming the Knierman (2007) inference that the tails are host to population of young clusters of ages <100 Myr, our sources (if they are clusters) are probably between 10⁴ and 10⁵ M_☉. 10 SCCs are found in the tail, and 7 are located outside it. Here, K-S tests anticipate a 5.65% and 2.49% chance that all in-tail and out-of-tail sources came from a single distribution of V₆₀₆ and V₆₀₆ − I₈₁₄.

This SBb-type, optically faint galaxy with unknown H i appears slightly perturbed by its ∼100 Myr old minor merger, with thin filamentary tails drawn from the main disk, enriched with classic "beads on a string" hotspots of star formation. Assuming an approximately face-on orientation, the separation between these clumps is about 3 kpc.

The tidal debris and galaxy interior (WF2-WF3) show an extended distribution in V₆₀₆ − I₈₁₄, down to very blue (V₆₀₆ − I₈₁₄ < −0.25) colors indicative of young ages and nebular emission not tracked by the SSP models. These sources overall are uniformly distributed in the Δ_V diagram. Since any clusters would be unresolved at this distance, some may be crowded cluster complexes rather than individual clusters. CMDs show these objects as potentially very young (several <10 Myr and others ≲100 Myr) and massive. With in situ age constraints, these SCCs would be ∼5 × 10⁴–10⁵ M_☉.

In total, 88 cluster candidates are found in the tails and 26 are beyond them. The probability that all in-tail and out-of-tail sources originate from one population is 0.324 for V₆₀₆ and 0.0617 for V₆₀₆ − I₈₁₄. In spite of this overwhelming evidence for clustered star formation in this tail, the IRAS-derived SFR is one of the lowest of the tail sample at ≈0.43 M_☉ yr⁻¹. This system is aligned nearly face-on and may register lower IR SFRs than galaxies with higher inclinations.

AM 1054-325 is an optically bright spiral in the early stages (age ≈85 Myr) of merging with a nearby early-type galaxy ESO 376- G 028, as displayed in the online figure. The latter system features four SCCs embedded in a diffuse plume of debris, but the number of equivalent objects per unit area beyond its tidal debris makes it statistically insignificant. The general V₆₀₆ − I₈₁₄ color of this debris is relatively red (V₆₀₆ − I₈₁₄ > 0.8); though H i data do not exist for this galaxy, on morphological and photometric grounds it stands to reason there is simply insufficient gaseous "fuel" to trigger obvious star formation in what is probably a dry merging system. For ESO 376- G 028, we find V₆₀₆ and V₆₀₆ − I₈₁₄ K-S probabilities of 0.445 and 0.291.

AM 1054-325 is the more remarkable of the two, with large clumps of star-forming debris pulled out from the disk in WF3. V₆₀₆ − I₈₁₄ colors in the tidal debris evidenced in the CMDs and color map highlight young and blue episodes of star formation, and some evince possible nebular emission in their blue (V₆₀₆ − I₈₁₄ < 0) colors. The bluest sources are closer to the ∼1–5 Myr estimates of star formation regions within the galaxy by Weilbacher et al. (2000), with some leeway in cluster mass.

The host galaxy IR SFR is ≈0.64 M_☉ yr⁻¹. The tail appears to have a base color consistent with an age ≲100 Myr. "Beads" of newer (≲10 Myr) and/or metal-poor bursts are strewn across the tail. These clumps in the smoothed color map are separated by ∼2–3 kpc, depending on tail orientation. The Δ_V diagram shows the strongest disconnect between in-tail and out-of-tail sources thus far, with the former having typically bluer V₆₀₆ − I₈₁₄ colors than the latter. The wide range of concentration indices may again be symptomatic of cluster complexes that are unresolved at this distance.

180 sources qualify as cluster candidates inside the tail, with 60 outside it. For AM 1054-325 sources, we determine K-S probabilities of 2.36 × 10⁻¹⁰ (V₆₀₆) and 9.22 × 10⁻²⁵ (V₆₀₆ − I₈₁₄). The above age restrictions allow these SCCs masses ∼5 × 10⁴–5 × 10⁵ M_☉. The tail's orientation is unknown, however, and may negatively affect the number of SCCs measured. If the debris extends from the center-right of the galaxy disk and curls northward toward the observer, we may witness a superposition of disk-bound and in-tail clusters that combine to give unusually high SCC counts and exaggerate this tail's cluster bearing capacity. Or if what we identify as a tail is partially a spiral arm pulled by the interaction, we would be observing not tidal debris, but galactic cluster candidates shaped by different arm-related triggering processes like density waves.

NGC 2444 is a peculiar S0-type galaxy featuring a long H i tidal tail visible in Figure 3.12. Appleton et al. (1987) suggest that the H i debris is a result from a collision between NGC 2444 and a low surface brightness, H i-rich companion, and not NGC 2445, which still interacts with the system. That companion has since disrupted and its stellar component dispersed enough to fall below our optical tail detection threshold. This model makes intuitive sense—collision speeds ≳1000 km s⁻¹ are needed to create a ∼100 kpc long H i plume in 100 Myr.

Though an H irich (M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$ = (5.20 ± 1.0) × 10⁹ M_☉) tail through the WFPC2 FOVis visible in the SDSS image of this tail's online figure, any optical counterpart is too faint to be contoured by the 1 count + background technique utilized here. As such, we make an exception for this tail and follow the H i extent (average 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 = (1.40 ± 0.28) × 10⁶ M_☉ kpc⁻²) illustrated in the online figure to determine the tidal tail boundary.

There are 27 sources meeting the SCC selection criteria within this H i tail and 15 outside it. In all, they appear to span an age range of ∼10–500 Myr, depending on masses between 10⁴–10⁵ M_☉. They are also evenly dispersed among the out-of-tail objects in the Δ_V diagram. K-S tests dictate a 54.5% and 24.1% chance that all in-tail and out-of-tail sources came from a single distribution of V₆₀₆ and V₆₀₆ − I₈₁₄.

In contrast, Appleton et al. (1987) and Jeske (1986) find circumnuclear star-forming regions with ages <30–69 Myr. These are approximately timed with the last passage of the interacting galaxies that is thought to have produced the long H i plume and merger morphology characteristic of collisional ring galaxies (Hibbard & Yun 1999). Beirão et al. (2009) investigate the H₂ and PAH properties of star-forming knots within the circumnuclear ring, determining ages of 2–7.5 Myr, contrasted with a nucleus age of about 500 Myr.

An H i-rich (M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$ = (4.45 ± 0.89) × 10⁹ M_☉), optically bright Sc galaxy ∼100 Myr past perigalacticon in its minor merger with NGC 2536 (Hancock et al. 2007), NGC 2535 possesses two main tidal tails; the long northern tail is illustrated in its online figure. It contains a "backbone" of clumps from WF3 to WF2, surrounded by more diffuse emission and anchored to an outer spiral arm in WF4. The optical tail coincides with the H i emission seen in Figure 3.13, (〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 = (6.84 ± 1.4) × 10⁶ M_☉ kpc⁻²). The innermost limit of the tail boundary corresponds to the terminus of the hinge clumps seen at the rightmost side of WF3. These star-forming hotspots accumulate at the low shear tips of spiral arms (Hancock et al. 2009), marking the end of the galaxy proper. It is a convenient check on the validity of our tail/galaxy distinction. These hinge clumps also appear as pronounced blue condensations in V₆₀₆ − I₈₁₄ the color map.

A number of sources are evident, aside from the SCCs selected. The in-tail objects are very blue overall in the CMD (V₆₀₆ − I₈₁₄ < 0.5), as opposed to the out-of-tail sources that have redder (0.2–2) colors. Both are scattered in terms of Δ_V, however. We determine that the cluster candidates (41 in the tail and 49 outside) can be fit with ages of <10 Myr for the brightest objects, to ∼100 Myr for sources located around the evolutionary tracks. Masses would then range from 10⁴ to 10⁵ M_☉. Using optical/UV colors and Hα data, Hancock et al. (2007) constrain the ages of star-forming regions within interior features to ∼9 Myr for the ∼10⁶–10⁹ M_☉ clumps (complexes) they study. They contend that clumps in the tidal regions of this interaction have similar ages, but lower masses (typically by a factor of ∼10).

The K-S probabilities of NGC 2535 sources are 0.0904 (V₆₀₆) and 1.16 × 10⁻⁴ (V₆₀₆ − I₈₁₄). Our galaxy IR SFR calculation estimates a rate of ≈2.9 M_☉ yr⁻¹ in NGC 2535's disk, similar to the 2.0 ± 0.8 M_☉ yr⁻¹ and 4.9 ± 2.0 M_☉ yr⁻¹ SFRs found for the clumps and total system by Hancock et al. (2007).

NGC 6872 is a large, optically bright SABc galaxy well endowed with H i in its combined eastern and western tail pointings (M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$ = (3.52 ± 0.50) × 10⁹ M_☉), though its tremendous size translates this to a low 〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 of ≈(1.5–3) × 10⁶ M_☉ kpc⁻². The galaxy bears long, thin tidal tails from its ∼150 Myr old interaction with a smaller companion, IC 4970 (Horellou & Koribalski 2003; Horellou & Koribalski 2007). The eastern pointing features an intricate stream of tangled hotspots, from irregular clumps to cluster candidates. Sources in all chips have a large spread in V₆₀₆ − I₈₁₄—likely from a combination of age and extinction effects—with several extremely blue objects featuring possible nebular emission. There is a wide variety of concentration indices around V₆₀₆ − I₈₁₄ ∼ 0–1, which is not dissimilar to the out-of-tail sources.

Contours of H i on the SDSS image are roughly aligned with the most populated regions in the optical mosaic and color map. The proliferation of SCCs straddling the WF2-WF3 divide are uniformly blue and young or metal-poor. This may be a hotspot of the most recent episode of star formation or evidence of a metallicity gradient across the tail. The latter scenario is observed in the opposite tail by G. Trancho et al. (2011, in preparation); they find a gradual decline in metallicity from supersolar at the tail base to subsolar at the tip. What we witness in the color map of this tail may be the eastern tail's equivalent gradient, portraying a sequence of cluster formation events beginning at the tail base and proceeding toward the tip, using the metal-poor ISM drawn from the galactic outskirts as fuel. By the time star formation has ignited at terminus of the tail, the base may have endured multiple generations of star formation and concordant metal enrichment.

The western FOV of the tail, dominated by the galaxy body in WF4, has in-tail sources congregating in clumps around the WF2-WF3 divide, a number of objects spread throughout the tidal debris in all chips, and another assemblage east of IC 4970 coincident with a locally dense H i region (Horellou & Koribalski 2007). Both tail and external sources have a broad distribution of colors similar to that of the eastern FOV. In either case, there are significant numbers of extremely blue objects (V₆₀₆ − I₈₁₄ ∼ −0.75–0.0), as well as those with more moderate colors. Tail sources with V₆₀₆ − I₈₁₄ ∼ 0.5–1.5 seem more concentrated at Δ_V = 1.5–2, and the bluest objects tend to have concentration index values ≳2. Out-of-tail sources are more evenly dispersed in V₆₀₆ − I₈₁₄–Δ_V space.

Source ages in both eastern and western FOVs range from ≲10 Myr for a few of the bluest cluster candidates, to 100–300 Myr for dimmer and/or redder hotspots. The former correspond well with the 10⁴–10⁶ M_☉, < 100 Myr old clusters detected and confirmed to be spatially coincident with regions of Hα emission (Bastian et al. 2005; Mihos et al. 1993). It is unclear whether these SCCs form an MF with a logarithmic slope of −1.85 ± 0.11 as the former study suggested with their ground-based, lower resolution work. Many of the sources they pinpoint may be agglomerations of the higher resolution SCCs we define, which may decrease the MF slope to values closer to ≈−2.

We postulate a mass range of a few 10⁴–10⁶ M_☉ for these objects. In the eastern pointing, there are 163 SCCs within the optical tail boundary and 63 outside of it. NGC 6872W sports 195 SCCs in the tail and 36 beyond. We find K-S probabilities of 7.26 × 10⁻⁵ and 0.209 for all sources in V₆₀₆ and V₆₀₆ − I₈₁₄ for the NGC 6872E FOV. For the western pointing, K-S tests predict a 0.517% and 11.9% chance that all in-tail and out-of-tail sources came from a single distribution of V₆₀₆ and V₆₀₆ − I₈₁₄. Our IR SFR of ≈2.9 M_☉ yr⁻¹ for the central galaxy is significantly lower than U-band estimate of the local tail SFR of ≈16.5 M_☉ yr⁻¹ for the combined debris regions (Bastian et al. 2005), but the latter value is likely an overestimate (N. Bastian 2010, private communication). It is likely the "true SFR" for the tail is closer to those quoted by Mihos et al. (1993); ∼3 M_☉ yr⁻¹.

NGC 1614 is ≈750 Myr into its merger with a similarly massed companion (Neff et al. 1990, and references therein), a peculiar SBc galaxy with a nearly linear plume of southern debris and a northern disky tail. Both tails are optically bright and contain comparable amounts of H i (M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}^{{\rm tot}}$ = (7.68 ± 1.6) and (9.64 ± 1.9) × 10⁸ M_☉ for northern and southern tails, respectively). IRAS-derived SFRs are problematic for its tidal tails; it is a heavily dust-obscured ULIRG (Alonso-Herrero et al. 2001) and presents a nuclear cloud-cloud collision triggered SFR (Alonso-Herrero et al. 2001) of ≈35. M_☉ yr⁻¹. Its H i content is unevenly distributed across the optical debris—only the northern and southern tips of the northern tail present H i emission (〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 = (2.56 ± 0.52) × 10⁶ M_☉ kpc⁻²), as does the optically bright "stub" in the inner southern tail (〈M$_{\mbox{\scriptsize {\hbox{{\rm H}\,{\sc i}}}}}$/A_tail〉 = (2.89 ± 0.59) × 10⁶ M_☉ kpc⁻²).

The color map of NGC 1614N displays a diffuse debris whose V₆₀₆ − I₈₁₄ is generally consistent with its 750 Myr age. Individual SCCs are typically bluer (younger), with V₆₀₆ − I₈₁₄-estimated ages of ∼10–300 Myr. One SCC may be younger than 10 Myr, depending on whether it falls in the ∼5 × 10⁴–10⁵ M_☉ range of its companions. These objects show no particular Δ_V preference in the concentration index diagram, but do approximately coincide with the regions of H i emission. In all, there are 33 and 28 SCCs in and outside the tail, respectively.

The southern tail shows a greater diversity in SCC demographics than the northern debris. Sources populate the in-tail CMD around the 10⁵–10⁶ M_☉ SSP tracks, with corresponding ages ≲300 Myr. The bluest and brightest of these are concentrated in the H i-rich stub forming the base of the tail. Sources outside the H i tail are largely redder, possibly older sources of the aforementioned age range. Like the northern tail, SCCs here do not display any preference for a particular range of Δ_V. We find 38 SCCs in this northern tail.

This system exhibits a ∼300 pc circumnuclear ring of massive Hii regions in the central galaxy (Alonso-Herrero et al. 2001), whose photometric properties imply a series of current (5–8 Myr old), massive (5.6 × 10⁸ M_☉) bursts, over a base population 1 Gyr or older. The bluest sources in the southern tail may be commensurate with this activity; the ages and masses of the remaining SCCs are not well enough constrained to correlate their formation with intragalactic star formation. In the northern tail, V₆₀₆ and V₆₀₆ − I₈₁₄ K-S probabilities for all sources are 1.94 × 10⁻³ and 3.33 × 10⁻⁴, respectively. All southern tail sources show V₆₀₆ and V₆₀₆ − I₈₁₄ K-S probabilities of 2.61 × 10⁻⁴ and 1.27 × 10⁻⁶.

To understand the presence or absence of cluster candidates at fainter luminosities, several key issues must be addressed—the rapid color and magnitude evolution of clusters as they age, the overall level of cluster production in the studied environment, and completeness limits of detected cluster candidates. Thus, cluster detection is heavily contingent on age, size-of-sample effects, and distance. Figure B1 more clearly illustrates the combination of these three influences.

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The top panel of Figure B1 shows the color–magnitude evolution of model clusters from the population synthesis models of Bruzual & Charlot (2003). The blue track follows a theoretical population with a metallicity 0.4 Z_☉, the black shows Z_☉, and the red 2.5 Z_☉. The tracks are repeated for masses of 10⁶, 10⁵, and 10⁴ M_☉; the 10⁵ M_☉ models are outlined in bold for emphasis. The vertical dotted line in the CMDs indicates where M_V = −8.5. For reasonable metallicities, these cutoff values allow the detection of 10⁵ M_☉ clusters with log age (yr) ∼6–8.5. Our objective is to observe clusters born within a tail environment that typically disperses before log age (yr) ∼8.5–9 (Binney & Tremaine 2008), this is a suitable result. Shifting the model on the x-axis by 1 mag corresponds to a factor of 2.5 increase in cluster mass, so our color–magnitude criteria is sensitive to most appropriately aged clusters ≳5 × 10⁵ M_☉. Stochastic effects (Maíz Apellániz 2009) and cluster disruption (Anders et al. 2009) will necessarily introduce some uncertainty.

This also submits an age (or more accurately, star formation history) bias into the analysis—for tails with old (≳300 Myr) tidal debris, if they did not experience sufficiently recent episodes of cluster formation, clusters with masses ≲5 × 10⁴ M_☉ would have faded below our detection threshold. Given the apparent preference for star formation in tidal debris to occur soon after their host galaxies' initial encounter (Chien 2010; Di Matteo et al. 2008, Mihos & Hernquist 1994), cluster detection is favored in young (in our case, ≲250 Myr old) tails. These young tails have a larger mass range of detectable clusters than old tails for populations born at early dynamical ages. This would be less of an issue if all tails produced ample quantities of high-mass clusters. But depending on the debris, more massive clusters may be buried in the statistics of background subtraction or may simply be absent if the cluster formation events of a tail were not powerful enough to populate the ≳5 × 10⁵ M_☉ end of the observed cluster mass function.

The middle panel of Figure B1 considers the observational implications, displaying the M_V606 distributions of sources for three tails. These histograms have been background-subtracted, i.e., the number of background sources was subtracted from the number of in-tail sources for each bin. The background-subtracted numbers of cluster candidates N_SCC are also presented. We plot model LFs suggested by Section 3.3 for these tails—a power law with a slope of −2 (purple lines) and −2.5 (yellow lines). Note that this choice of LF is motivated by statistical diagnostics (Figure 5); we do not infer the LF from the individual distributions, but apply these LFs to them, normalized to the total number of SCCs of each. V₆₀₆ distributions are subject to multiple generations of cluster formation and fading and strong stochastic effects, but the fits are qualitatively acceptable.

AM 1054-325 is the most SCC-rich of the sample; it hosts many strong cluster candidates within the tidal tail boundary. Its cluster formation events were sufficiently powerful to populate the high mass end of the cluster mass function, and therefore the existing LF with sources well to M_V ≲ −12. NGC 2782E is more modestly populated, with dozens of sources detected around the M_V = −8.5 line. Thus, a sizable fraction of these will be selected as SCCs with the current V₆₀₆ and V₆₀₆ − I₈₁₄ criteria. Lastly, despite its complement of sufficiently blue sources (evident in online Figure 3.1), NGC 1487E contains no sources bright enough to be classified as SCCs. If most of the objects in this tail are indeed star clusters, our statistical diagnostics insinuate that the cluster formation events that produced them were insufficiently powerful to generate clusters bright enough for SCC designation. In this case, this tail does in fact contain some clusters, but a cursory glance at sources brighter than conventional magnitude limits would miss them.

Unfortunately, extending magnitude limits to detect fainter, older and/or less massive clusters is only plausible for the closest interacting galaxies. The in-tail completeness curves for the tails examined in the middle panel of Figure B1 are provided in the final panel, translated to absolute magnitudes. The luminosity distances to the host galaxies are provided for reference. The turnovers or breaks in the faint end of the distributions of the middle panel correspond to the distance-defined completeness limits (variations in exposure times in Table 1 provide ancillary effects). Were the tails not completeness-limited, the V₆₀₆ distributions would continue to climb with fainter magnitudes and more SCCs would be uncovered.

Thus, only in the closest tails (NGC 1487E/W through NGC 2782E/W) would low-mass, ∼10⁴ M_☉, clusters be seen in our data. More distant tails (ESO 376- G 028 through NGC 1614N/S) would only allow detection of ∼10⁴ M_☉ clusters younger than ∼100 Myr, or to more massive (∼10⁵ M_☉), luminous clusters at a broader age range (that is, unless the images had longer exposure times). Consequently, debris like NGC 4747 is fortunate in that it is close enough that in-tail cluster candidates may be detected at faint magnitudes (M$_{V,50\%}$ = −6.5). Such a tail with a "weak" cluster formation history may appear devoid of clusters within the limits of our HST photometry if it were placed at larger distances. In summary, tidal tail star cluster detection is heavily dependent on cluster formation histories/strengths, and distances of the tails themselves. Given these fundamental age and interaction constraints, not all tails can be expected to contain cluster populations to M_V ≲ −8.5.

It can be shown that single stellar contaminants pose few problems for some tails at the M_V < −8.5 level. This magnitude limit may also be relaxed to M_V = −6.5 for certain tails, provided they have few bright (M_V < −9) sources and are reasonably local (≲25 Mpc) for our image depths. NGC 1487W and NGC 520 are close enough to consider cluster candidates as faint as M_V = −6.5, and do not have clusters at M_V < −8.5, so we concentrate further discussion on these debris regions. All other proximate tails either have nonzero Σ_SCC values at M_V < −8.5 or have Σ_SCC = 0 within 2.5σ for all magnitude ranges.

It can be safely assumed that the contribution of main sequence stars in the range M_V = −6.5 to −8.5 is negligible; these early O-type, ≳50 M_☉ stars would be extremely rare for tidal tails whose V₆₀₆-band luminosities are typically 3–4 orders of magnitude below that of their host galaxies. The only source of contamination on tail timescales ≲1 Gyr would therefore be red supergiant stars (RSGs) bluer than our adopted V₆₀₆ − I₈₁₄ criterion. To estimate the contribution of these, we first used Padova¹⁹ isochrones to identify the minimum main sequence turnoff mass of stars that would evolve into sufficiently bright and blue RSGs. Translating this into the corresponding isochrone age t_iso, we estimated the appropriate specific evolutionary fluxes B_spec(t_iso) of single stellar population models of Bruzual & Charlot (2003); see Section 2.4. These values are on order of 10⁻¹² L⁻¹_☉ yr⁻¹ for M_V = −7.5 to −6.5 and <4 ×10⁻¹³ L⁻¹_☉ yr⁻¹ for M_V = −8.5.

The number of RSGs N_RSG that evolve to a certain V₆₀₆ − I₈₁₄ in a time t_evol, produced by a population of luminosity L can then be written as N_RSG ≈ B_spec(t_iso) × L × t_evol. Thus, to obtain one RSG, L ≈(B_spec(t_iso) × t_evol)⁻¹. We estimate t_evol as ∼10⁶ yr from the isochrones for a range metallicities 0.4 Z_☉ to 2.5 Z_☉. Combining these, we infer log(L/L_☉) >4.5–6.5 for the cutoff M_V values −6.5 to −8.5.

We then find the absolute V-band magnitude for that L. Translating L to M_V requires applying the age-dependent bolometric correction for the population, which is uncertain with our limited data. By implementing the safest correction given the tail age constraint (i.e., one the would result in the faintest M_V), we find that SSPs with a total M_V ≲ −9 are required to produce one RSG for an M_V < −6.5 selection in tidal tails. For our M_V < −7.5 and −8.5 limits displayed in Figure 4, the populations must be brighter than M_V ≈ −10 and −15, respectively. Thus, if we use a magnitude threshold of −8.5 in culling sources, objects brighter than M_V ≈ −15 may be clusters that are both massive enough to have detectably bright RSGs and have survived disruption. Knowing how many of these bright clusters survived to the present, we may extrapolate how many of these clusters have evaporated into the tidal tail field and how many observable RSGs were left behind to contaminate in-tail source lists.

It is clear that, since we find no sources brighter than M_V = −15 in any tidal debris, and this magnitude limit is a very conservative estimate, our initial color–magnitude criteria for identifying SCCs is secure against in-tail singe stellar contamination. The same cannot be stated for fainter magnitudes, as raising the bar to M_V = −7.5 and −6.5 requires accounting for sources that certainly exist in many tails at M_V ≲ −10 and −9, respectively.

For the faint M_V = −6.5 cutoff, it can be seen in the online CMDs of Figures 3.2–3.4 (NGC 1487W–NGC 520) that there are ⩽6 of these M_V sources in the tails, depending on the debris. If ∼10% of the original M_V < −9 clusters have survived to the present day (following early cluster disruption histories of, e.g., Whitmore et al. 2007; Bastian & Gieles 2008, and references therein), that means each tail is contaminated by a number of RSGs ∼ 10 times the number of these bright SCCs. We do not consider secular evolution (e.g., two-body relaxation) in this simple estimate.

This introduces ⩽60 contaminants for the M_V < −6.5 source lists of NGC 1487W and NGC 4747, and 0 for NGC 520. Repeating the exercise for M_V < −7.5 results in essentially the same number, 20–60 contaminants for the former two tails and 0 for the latter. The number of predicted RSGs in NGC 1487W and NGC 4747 is on par with the number of sources detected, and when compounded with the present counting statistics, precludes successful determination of clusters at M_V < −6.5 to −7.5. Because the TDG of NGC 520 has no sources brighter than M_V = −9, we can be certain of the Σ_SCC excesses seen in Figure 4 for the fainter detection limits. Unfortunately, This WFPC2 pointing reveals clustered star formation in the TDG and not in the NGC 520 tail itself, so nothing can be definitively said of the debris.

It must be noted, however, that this does not mean there are no clusters with M_V ≈ −6.5 to −8.5 in tails close enough for these objects to be detected, but that their presence statistically cannot be confirmed with only V- and I-band data. We choose not to extend M_V further to avoid higher risk of contamination and completeness effects.