Spatial Structures in the Globular Cluster Distribution of Fornax Cluster Galaxies

Raffaele D’Abrusco; David Zegeye; Giuseppina Fabbiano; Michele Cantiello; Maurizio Paolillo; Andreas Zezas

doi:10.3847/1538-4357/ac4be2

1. Introduction

The study of Globular Cluster (GC) systems of massive elliptical galaxies has been spurred by growing evidence that these systems can be used as fossil records of the formation history of their host galaxies (Harris & Racine 1979; Brodie & Strader 2006) and can constrain the virial mass of the halo of the hosts (Blakeslee 1997; Spitler & Forbes 2009; Burkert & Forbes 2020). This opportunity has led, in turn, to the quick growth of our knowledge of the global properties of GC systems. The large-scale spatial distribution of GCs has been investigated in depth: GCs extend radially to larger radii than the diffuse stellar light of the galaxies (Harris 1986) and the most luminous galaxies have more centrally concentrated GC distributions than fainter hosts (Ashman & Zepf 1998). The radial profiles of metal-rich (red) and metal-poor (blue) GCs differ: red GCs follow more closely the light profile of the stellar bulge, with the exception of central flattened cores in the GC distribution, and blue GCs show a flatter, more extended distribution (Rhode & Zepf 2001; Dirsch et al. 2003; Bassino et al. 2006; Mineo et al. 2014).

Several studies of the full two-dimensional (2D) spatial distributions of GC systems have indicated that their ellipticity and position angles are consistent, on average, with those of the stellar spheroids of the host galaxy (e.g., NGC 4471 in Rhode & Zepf 2001; NGC 1399 in Dirsch et al. 2003 and Bassino et al. 2006; NGC 3379, NGC 4406, and NGC 4594 in Rhode & Zepf 2004; NGC 4636 in Dirsch et al. 2005; multiple galaxies in Hargis & Rhode 2012; NGC 3585 and NGC 5812 in Lane et al. 2013; NGC 4621 in Bonfini et al. 2012 and D'Abrusco et al. 2013). More recent works that took advantage of Hubble Space Telescope (HST) imaging data collected for several galaxies in the Advanced Camera for Surveys (ACS) Virgo Cluster Survey (ACSVCS) (Côté et al. 2004) have uncovered azimuthal anisotropy in the GC distributions (Wang et al. 2013), with GCs preferentially aligned with the major axis in host galaxies that have significant elongation and intermediate to high luminosity. By combining HST and large-field, ground-based observations, the geometry of the GC color subclasses in Early Type Galaxies (ETGs) have also been found to differ: red GCs correlate with the ellipticity and size of the host's stellar halo, while the blue GC populations show smaller ellipticities and extend to larger radii (Park & Lee 2013; Kartha et al. 2014). These results suggest two different formation mechanisms for red and blue GCs and the potential presence of two distinct halo components, with red GCs forming at the same time as the stars of the galaxy and blue GCs possibly forming in low-mass dwarf galaxies subsequently accreted to their current host (Forbes et al. 1997; Côté et al. 1998; Cantiello et al. 2018).

The average radial distributions and metallicity properties of the red and blue GCs are reproduced by N-body smoothed particle hydrodynamical simulations (Bekki et al. 2002) under the assumption that the elliptical galaxy was the result of early major dissipative merging. Tidal stripping of GCs and accretion of satellites in elliptical galaxies in high-density regions have been suggested as the main mechanisms to reconcile the simulations with the data (Bekki et al. 2003). The gap between observations of the spatial distribution of GCs and galaxy evolution models has been further narrowed by recent cosmological simulations combined with semianalytic models for the formation and evolution of stellar systems (E-MOSAICs; see Pfeffer et al. 2018) that have achieved sufficient mass and spatial resolutions to resolve individual GCs and match their evolving spatial distribution with the growth of the host galaxy. In particular, Kruijssen et al. (2019) showed that the spatial distributions of in situ and accreted GCs in Milky Way–like galaxies differ from each other and deviate significantly from smooth radial and azimuthal distributions (see Figure 1 therein).

Although a comprehensive model connecting GCs and galaxy formation is still missing, major merging (either dissipative or dissipationless), tidal interactions, and minor mergers/accretion of satellite galaxies have been demonstrated to have important roles in shaping the observed GC systems. While the formation of young, metal-rich GCs during mergers is emerging as an important ingredient in the makeup of observed GCs of elliptical galaxies (Bekki et al. 2003; Brodie & Strader 2006; Wang et al. 2013), early works from Côté et al. (1998) and Pipino et al. (2007) found that the global properties of the GC systems of massive elliptical galaxies (radial distribution, specific frequency, and metallicity) can be only explained if one assumes that a large fraction of GCs originated from satellite galaxies and have been stripped by the accreting galaxy. More recently, cosmological simulations have shown that in the Milky Way, the fraction of GCs accumulated through the accretion of satellite galaxies can be as large as 50% of the total observed GCs (Kruijssen et al. 2020). The importance of satellite accretion in the buildup of massive GC populations has been emphasized by the observation of localized, 2D inhomogeneities and streams in the GC systems of elliptical galaxies. Significant features in the projected spatial distribution of GCs have been observed in NGC 4261 (Bonfini et al. 2012; D'Abrusco et al. 2013), NGC 4649 (D'Abrusco et al. 2014b), NGC 4278 (D'Abrusco et al. 2014a), and NGC 4365 (Blom et al. 2012). D'Abrusco et al. (2015) observed multiple spatial structures in the distributions of the GC systems of the 10 brightest Virgo cluster galaxies.

In this paper, we analyze the 2D spatial distribution of the GCs in 10 galaxies that are among the brightest in the Fornax cluster using a method based on the K-Nearest-Neighbor (KNN) technique and Monte Carlo simulations that have been previously applied to several other galaxies (D'Abrusco et al. 2013, 2014a, 2014b, 2015). After the Virgo cluster, the Fornax cluster is the second closest rich cluster of galaxies: at its distance of ≈20.0 Mpc (Blakeslee et al. 2009), GCs are marginally resolved and can be detected down to relatively low flux levels with reasonable integration times in HST imaging. Moreover, our method (D'Abrusco et al. 2013) for the characterization of the spatial distribution of GCs is more accurate for large samples of GCs like those hosted by the bright galaxies in the Fornax cluster (Liu et al. 2019). Similarly to Virgo, the Fornax cluster provides a wide range of local densities and allows us to probe different stages of the evolution of massive galaxies in different environments. The Fornax cluster has two dynamically distinct components (Drinkwater et al. 2001): the main cluster centered on NGC 1399 and a subcluster, located SW of NGC 1399 and centered on NGC 1316, which is likely infalling toward the cluster core. Additional studies suggest that the core of the main cluster is dynamically evolved, and there are several lines of evidence supporting the ongoing infall of single galaxies in its outskirts (Liu et al. 2019) and interactions between galaxies in the core (Iodice et al. 2016). Moreover, the displacement of the X-ray emission from the hot intracluster gas relative to the closest Fornax galaxies suggests that the cluster is not relaxed and may be undergoing a merger (Paolillo et al. 2002).

The paper is organized as follows: In Section 2 we describe the main properties of the Fornax cluster galaxies investigated and the archival data used to characterize the spatial distributions of their GC systems, while Section 3 focuses on the spatial coverage of the observations. Section 4 synthetically describes the method used to discover the GC spatial structures and determine their properties, and the structures discovered in each of the galaxies studied in this work are described in Appendix A. The properties of the GC structures are discussed in Section 6 and its subsections. Finally, our conclusions are summarized in Section 7.

We use CGS units unless otherwise stated. Optical magnitudes used in this manuscript are in the Vega system and are not corrected for the Galactic extinction. Standard cosmological parameter values have been used for all calculations (Bennett et al. 2014), and we used galaxy distances from Blakeslee et al. (2009).

2. Data

In this paper, we use the catalog of GCs extracted from images obtained with the HST Advanced Camera for Survey (ACS) for the ACS Fornax Cluster Survey (ACSFCS) project (Jordán et al. 2007), complemented by wide-field ACS observations by Puzia et al. (2014) for the region surrounding NGC 1399 (more details RE in Appendix A.1). ACSFCS obtained ACS pointings for 43 early-type Fornax cluster galaxies in the F475W (SDSS g) and F850LP (SDSS z) bandpasses, with exposures of 680 and 1130 s, respectively. Jordán et al. (2015) extracted a catalog of 9136 GC candidates using both photometry and half-light radii measured in both filters. The total number of bona fide GCs, i.e., with a probability p_GC ≥ 0.5,⁹ in the ACSFCS catalog is 6275. We investigate the spatial distribution of GCs in 10 galaxies among the brightest ones that are associated with the largest numbers of ACSFCS GCs. Nine galaxies in this sample are among the 10 brightest Fornax cluster galaxies in B_T magnitude (ESO 359-G07 ranks 8th), with the exception of NGC 1336, which ranks 16th (Jordán et al. 2007). Table 1 lists the galaxies in the sample and their main properties. In order to investigate the distribution of GCs for red and blue GC subclasses separately, we model the g − z color distribution of each galaxy with two Gaussians. The g − z color thresholds used to separate the two GC color classes are determined using the Gaussian Mixture Modeling code (GMM) (Muratov & Gnedin 2010) as the value corresponding to equal probabilities of belonging to the red- or blue-component Gaussians (Table 1). Even in the cases of GC color distributions whose bimodality is not statistically significant, we assumed as a color threshold the g − z value for which the probability of being a red or a blue GC is equal in order to compare the properties of the spatial distributions of GCs in different color intervals.

Table 1. Properties of the Galaxies Investigated in This Paper Sorted by Decreasing Total Size of Their GCs Systems

Name (a)	N_GC (b)	N_blue (c)	N_red (d)	Morphology (e)	% D₂₅ Area Covered (f)	B_T (g)	r_e ('') (h)	D₂₅ (r_e) (i)	PA (j)	(g − z)_thresh (k)
NGC 1399	1077 (1126)	426	651	E0	45%	10.6	367.28	1.13	0	1.22
NGC 1316	647 (1006)	325	322	S0 (pec)	37%	9.4	288.40	2.5	50	1.10**
NGC 1380	424 (558)	117	307	S0/a	78%	11.3	86.10	3.35	7	1.12*
NGC 1404	380 (429)	169	211	E2	100%	10.9	86.10	2.31	0	1.17
NGC 1427	362 (412)	256	106	E4	99%	11.8	65.31	3.33	76	1.19*
NGC 1344	280 (397)	182	98	E5	65%	11.3	86.14	3.31	165	1.02*
NGC 1387	306 (381)	96	210	SB0	100%	12.3	50.70	3.32	0	1.13
NGC 1374	320 (367)	154	166	E0	100%	11.9	52.48	2.80	0	1.09*
NGC 1351	274 (357)	132	142	E5	100%	12.3	65.31	2.58	140	1.08*
NGC 1336	276 (355)	91	185	E4	100	13.3	50.70	2.53	22	1.11*

Note. (a) NGC identifier of the galaxy. (b) Number of p_GC ≥ 0.5 ACSFCS GCs used in the experiments described in this paper (in parentheses, the total number of ACSFCS candidate GCs). (c) Number of blue GCs. (d) Number of red GCs. (e): Morphology of the galaxy from Jordán et al. (2007) and Ferguson (1989). (f): Fraction of the D₂₅ area of each galaxy covered by the ACSFCS observation. (g) B-band magnitude from Jordán et al. (2007) and Ferguson (1989). (h) Effective radius of the galaxy in arcseconds from Lauberts & Valentijn (1989). (More recently, Iodice et al. 2019 measured the effective radii of galaxies within the Fornax virial radius using Fornax Deep Survey (FDS, Iodice et al. 2016) observations. Their r_e in the g band are all in agreement within 10% with the Lauberts & Valentijn (1989) values for all galaxies in our sample except NGC 1404, for which effective radius reported by Iodice et al. (2019) is ∼201''.) (i) Major diameter of the elliptical isophote of the galaxy corresponding to a surface brightness of 25 mag arcsec⁻² from Corwin et al. (1994), expressed in units of r_e. (j) Position angle of the galaxy from Corwin et al. (1994). (k) Color (g − z) threshold used to define red and blue GC subclasses. One or two asterisks identify color distributions characterized by bimodality with low or no statistical significance.

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3. Spatial Coverage

The discovery of structures in the distribution of GCs within galaxies depends critically on the spatial coverage of the GC system. D'Abrusco et al. (2015) estimated that the available ACS HST observations of the 10 Virgo cluster galaxies employed in their study covered less than 50% of the total area of the galaxies within the D₂₅ elliptical isophote at 1.5 effective radii for most targets. Figure 1 shows the percentage of Fornax cluster galaxy areas analyzed in this paper as a function of the projected galactocentric distance (left) and the effective radius (right) of each target galaxy, respectively. While the fraction of galaxy area covered is negligible for all targets at $r\geqslant 3^{\prime}$ , the fraction of total area covered at r/r_e = 2 and r/r_e = 2.5 is ∼75% and ∼55%, respectively, and coverage for five galaxies is ≥90% at 2.5 r_e, thanks to the combined effect of the larger distance of the Fornax cluster relative to the Virgo cluster (≈20.0 Mpc versus ≈16.5 Mpc according to Blakeslee et al. 2009) and the relatively smaller effective radii of 7 of the 10 galaxies (Table 1).

**Figure 1.** Left: coverage of the ACSFCS galaxies studied in this paper as a function of the projected galactocentric distance. Right: coverage of the ACSFCS galaxies as a function of the galactocentric distance in units of effective radius of each galaxy. In both plots, gray lines in the background represent the coverage of Virgo cluster galaxies investigated in D'Abrusco et al. (2015). Additional ACS observations of NGC 1399 from Puzia et al. (2014) (see Appendix A.1) increase the coverage to ≈1 r_e but are not reported in the plot because the GC selection method is not consistent with the ACSFCS sample.
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4. Method

The spatial distribution of GCs around the 10 galaxies studied in this paper has been characterized using the method described in D'Abrusco et al. (2013, 2015). This method employs residual maps obtained by comparing the density map derived from the observed spatial distribution of GCs with the density maps of simulated random spatial distributions of GCs that follow the spatial distribution of the observed stellar surface brightness of the host galaxy. The procedure for determining the residual maps of the GC distributions can be summarized as follows:

1.
Density maps of the observed spatial distribution of GCs are obtained with the KNN method (Dressler 1980) on a fixed rectangular grid covering the area of the galaxy where GCs are observed. The density at the center of each cell is defined as
$\begin{eqnarray}&&{D}_{K}=\displaystyle \frac{K}{{A}_{D}({d}_{K})},\end{eqnarray} \tag{ 1 }$
where K indicates the Kth closest GC (or neighbor) and ${A}_{D}({d}_{K})=\pi \cdot {d}_{k}^{2}$ is the area of the circle with a radius equal to the distance of the Kth neighbor.
2.
Multiple simulated realizations of the observed GC system are generated using a Monte Carlo approach. The radial and azimuthal positions of the simulated GCs are drawn from the elliptical radial distribution of the observed GCs with flattening and orientation set to the observed values of the diffuse stellar light of the host galaxy. The total and radial bin-by-bin numbers of simulated GCs match the observed values.
3.
Density maps of the observed GC distribution are generated for each distinct realization of the simulated GC spatial distribution on the same spatial grid and for each different value of the K parameter;
4.
The residual map is obtained by subtracting, on a cell-by-cell basis, from the observed density map the average density of all simulated maps, so that the residual value R_i of the ith cell of the grid is defined as
$\begin{eqnarray}&&{R}_{i}=\displaystyle \frac{({O}_{i}-\langle S{\rangle }_{i})}{\langle S{\rangle }_{i}},\end{eqnarray} \tag{ 2 }$
where O_i and 〈S〉_i are the observed density and the average of the density from all of the simulations in cell i. Details on the determination of the cell size for the results discussed in this paper can be found in Section 5.

The simulated GCs are drawn from the radial distribution of observed GCs in elliptical bins obtained with a fixed bin size of 15''. The properties of the residual maps change negligibly with bin sizes in the [10'', 20''] interval. Bins larger than 20'' introduce step-like artifacts in the 2D distribution of simulated GCs, while below 10'' the number of empty bins increases very rapidly for galactocentric distance larger than 1 farcm 5.

K is a free parameter of the KNN method: it measures the expected scale of the investigated spatial structures and the density contrast of these structures over the average local density. Different K values highlight spatial features at different scales: small K values allow the exploration of small features, while larger values of K bring out more extended structures. The loss of spatial resolution for large K values is balanced by the smaller relative fractional error, which is proportional to the inverse of the square root of K:

$\begin{eqnarray}&&\displaystyle \frac{{\sigma }_{D(K)}}{D(K)}=\displaystyle \frac{1}{\sqrt{K}}.\end{eqnarray} \tag{ 3 }$

Moreover, larger values of K are more suitable to detect structures located within the D₂₅ of the galaxies, where the overall density of GCs is larger, because only high-contrast structures can be reliably detected over this high-density background. Smaller K values, on the other hand, are more apt at detecting structures in regions where the total number of GCs is smaller, as in the outskirts of the host galaxies.

The distributions of simulated density values for each cell of the final residual maps are well approximated by Gaussians, thus simplifying the estimation of the statistical significance of each cell. The spatial structures in the residual maps are determined by selecting sets of N ≥ 30 adjacent cells with nonnegative residual values. The total significance of each observed spatial structure (which differs from the significance of the single cells included in the structure) is determined by estimating the frequency of structures with comparable features (number of cells, average residual value, and shape; see Section 6.2) across residual maps obtained from a single, distinct simulated distribution of GCs. The search for simulated structures with properties similar to those of the observed ones is performed over the whole area of each host galaxy where GCs are observed (i.e., is not limited to the specific range of galactocentric distances where the structures are detected), therefore yielding a lower limit to the statistical significance of the structures. The search for structures in each simulated residual distribution is performed similarly to the observed GC residual distribution: according to Equation (2); the value of the residual in the ith cell of the S^j simulated distribution of GCs is defined as

$\begin{eqnarray}&&{R}_{i}({S}^{j})=\displaystyle \frac{({S}_{i}^{j}-\langle S{\rangle }_{i})}{\langle S{\rangle }_{i}}.\end{eqnarray} \tag{ 4 }$

The same algorithm used for the detection of structures in the observed residual map is then applied to each of the single simulated residual maps. The statistical significance of each observed residual structure is then expressed as the fraction of simulated density maps where mock residual structures with comparable features have been detected.

While the efficiency of the detection of GCs as a function of the radial position relative to the center of the host galaxy varies because of the specific shape of the density profile of the host and the surface brightness profile that changes the background over which GCs are detected, the method described above is self-consistent because it is based on the GC observed radial density profile used to seed the simulations. For this reason, GC structures detected at different galactocentric distances with the same significance are associated with the same relative density contrast with respect to the underlying GC population. Given the differences between the density profiles and GC detection efficiencies in different hosts, the comparison of significance of structures observed in different host galaxies is not meaningful, especially in the core of the galaxies where the shape of the stellar light brightness profile can affect significantly the density of observed GCs.

5. The Spatial Distribution of Globular Clusters in Fornax Cluster Galaxies

In this paper, we investigate the spatial distributions of GCs observed in 10 galaxies that are among the brightest in the Fornax cluster. The descriptions of the GC structures observed in each galaxy and their relation with the known properties of the GC system of the host can be found in Appendix A. To maximize the statistical significance of our results, the entire GC system (blue + red) was used to detect the GC spatial structures. The statistical significance of each structure was then evaluated also for the red and blue GC distributions (see Table 2), assuming the shape and size of the structures as determined in the residual maps for the entire GC samples. The properties of the structures for all GCs are discussed in the context of the features of the color-based residual maps in Appendix A. The residual maps were estimated on a regular grid of cells with approximately equal angular extents along the R.A. and decl. axes. The cell sizes range from ∼3'' to ∼5'' along both axes for different host galaxies, corresponding to physical linear sizes from 0.3 to 0.5 kpc that lead to a factor ∼2 maximum difference between physical areas of structures containing the same number of cells. This choice guarantees that residual maps of different GC distributions account for a similar number of cells in the regions where GCs are observed so that meaningful comparison is possible across the residual maps of the different galaxies investigated here and between Fornax and Virgo galaxies (see Section 3 of D'Abrusco et al. 2015). The adoption of a weakly galaxy-dependent cell size ensures that the residual maps for each galaxy are insensitive to the varying fraction of the host-galaxy area imaged relative to its total extension (see column f in Table 1). Following D'Abrusco et al. (2015), we compared the residual maps obtained by picking 10 different, linearly spaced cell sizes (along both axes) within a ±30% interval centered on the adopted cell size to rule out significant systematic effects on the spatial features observed.

Table 2. Properties of the Intermediate and Large GC Spatial Structures

Galaxy (a)	Structure (b)	Class (c)	Significance (d)	Size (e)	${N}_{\mathrm{GCs}}^{(\mathrm{obs})}$ (f)	${N}_{\mathrm{GCs}}^{(\mathrm{exc})}$ (g)	Physical Size (h)	$\overline{g-z}$ (i)	${\overline{g-z}}_{\mathrm{bluest}}$ (j)	Class (k)	M_dyn (l)
NGC 1399	A1	All, red, blue**	3.4 × 10⁻⁵	219 (3504)	110	37.4	25	1.25	0.93	RS	9.94
	A2	All, blue*	<10⁻⁵	272 (4352)	151	47.9	43.5	1.25	0.93	RS	10.04
	A3	All, red, blue*	4.1 × 10⁻⁵	85 (1360)	21	8.1	13.6	1.25	1.09	AD	9.30
	a1	All, blue	1.3 × 10⁻⁴	55 (880)	14	3.5	8.8	1.23	0.82	⋯	⋯
	a2	All, red	1.5 × 10⁻⁵	50 (800)	17	7	8	1.28	1.05	⋯	⋯
	a3	All, red	6.3 × 10⁻⁴	58 (928)	16	6	9.3	1.16	0.8	⋯	⋯
	a4	All, red	7.2 × 10⁻⁴	42 (672)	15	2.7	6.7	1.23	0.83	⋯	⋯
NGC 1316	B1	All, blue**	<10⁻⁵	434 (6944)	118	42.4	69.4	1.08	0.82	Hy	*
	B2	All, red**, blue	1.7 × 10⁻⁵	133 (2128)	22	7.2	21.3	1.09	0.84	AD	9.25
	B3	All, red, blue**	1.9 × 10⁻⁵	304 (4864)	49	21	48.6	1.14	0.94	RS	9.70
	b1	All, blue	7.3 × 10⁻⁵	55 (880)	11	5.6	8.8	1.09	0.94	⋯	⋯
	b2	All, red, blue	5.4 × 10⁻⁴	37 (592)	17	8.6	5.9	1.19	0.97	⋯	⋯
	b3	All, blue	7.2 × 10⁻⁴	54 (864)	15	3.8	8.6	1.17	0.68	⋯	⋯
	b4	All, red	8.6 × 10⁻⁴	30 (480)	7	2.7	4.8	0.98	0.72	⋯	⋯
NGC 1380	C1	All, blue	4.6 × 10⁻⁵	162 (2592)	5	2.4	25.9	0.98	0.78	AD	8.79
	C2	All, red, blue	<10⁻⁵	211 (3376)	20	8.1	33.8	1.14	0.98	RS	9.30
	C3	All, red**, blue	9.8 × 10⁻⁵	202 (3232)	41	12.6	32.3	1.23	0.92	Hy	*
	C4	All, red, blue	2.3 × 10⁻⁵	177 (2832)	21	6.8	38.3	1.19	0.9	AD	9.22
	c1	All, red, blue**	2.7 × 10⁻⁵	49 (784)	27	11.4	7.8	1.20	0.99	⋯	⋯
	c2	All, blue	8.6 × 10⁻⁴	34 (544)	16	6.4	5.4	1.19	0.98	⋯	⋯
NGC 1404	D1	All, blue	<10⁻⁵	208 (3328)	16	7.2	33.3	1.05	0.86	AD	9.25
	D2	All, red*	4.1 × 10⁻⁵	97 (1552)	9	3.9	15.5	1.20	0.9	AD	8.99
	D3	All, red*	6.1 × 10⁻⁵	71 (1136)	9	2.7	11.4	1.24	1.1	AD	8.84
	D4	All, red, blue	3.5 × 10⁻⁵	206 (3296)	18	6.8	33	1.18	0.89	AD	9.23
	D5	All, red, blue	4.6 × 10⁻⁵	63 (1008)	28	12.6	10.1	1.24	0.97	AD	9.48
	D6	All, red, blue	<10⁻⁵	173 (2768)	22	11.4	27.7	1.12	0.95	TS	9.44
	d1	All, red	2.5 × 10⁻⁴	33 (528)	5	1.7	5.4	1.19	0.95	⋯	⋯
	d2	All	9.3 × 10⁻⁴	52 (832)	11	3.8	8.3	1.35	1.11	⋯	⋯
NGC 1427	E1	All, blue	1.4 × 10⁻⁵	171 (2736)	6	2	27.4	1.12	0.97	AD	8.70
	E2	All, blue	3.7 × 10⁻⁵	112 (1792)	29	11.8	17.9	1.08	0.97	AD	9.46
	E3	All, red, blue*	2.1 × 10⁻⁵	133 (2128)	15	6.6	21.3	1.05	0.85	AD	9.21
	E4	All, red, blue***	<10⁻⁵	575 (9200)	73	29.1	92	1.09	0.88	Hy	*
	E5	All, blue	<10⁻⁵	165 (2640)	19	8.9	26.4	1.06	0.92	AD	9.34
	e1	All, blue	7.0 × 10⁻⁴	30 (480)	20	9.6	4.8	1.14	0.94	⋯	⋯
NGC 1344	F1	All, red, blue	<10⁻⁵	458 (7328)	42	19.3	73.3	0.94	0.75	RS	9.66
	F2	All, red, blue*	3.1 × 10⁻⁵	218 (3488)	38	11	34.9	1.00	0.76	RS	9.42
	F3	All, blue	4.8 × 10⁻⁴	201 (3216)	12	4	32.2	0.94	0.78	RS	9.00
	F4	All, (red), blue	3.1 × 10⁻⁵	336 (5376)	11	4.4	53.8	1.03	0.85	AD	9.04
	f1	(All), red	4.6 × 10⁻³	37 (592)	12	5.8	5.9	1.01	0.87	⋯	⋯
NGC 1387	G1	All, red, (blue)	3.4 × 10⁻⁵	458 (7328)	20	3.7	73.3	1.22	0.88	TS	9.27
	G2	(All), (red), (blue)	4.8 × 10⁻⁴	150 (2400)	2	−0.9	24	1.47	⋯	AD	↓
	G3	All, red, blue	6.4 × 10⁻⁴	61 (976)	18	6.9	9.8	1.31	0.98	AD	9.22
	G4	All, (blue*)	5.9 × 10⁻⁵	192 (3072)	15	3.8	30.7	1.25	0.75	Hy	*
	G5	All, red, blue	4.2 × 10⁻⁵	91 (1456)	22	7.2	14.6	1.24	0.93	AD	9.2
NGC 1374	H1	All, blue	8.4 × 10⁻⁵	95 (1520)	6	1.6	15.2	1.12	0.89	TS	8.61
	H2	All, red, blue	<10⁻⁵	536 (8576)	42	19.9	85.8	1.12	0.93	RS	9.67
	H3	All, red, blue*	5.8 × 10⁻⁵	87 (1392)	32	14.5	13.9	1.18	0.96	AD	9.54
	H4	All*, red	2.3 × 10⁻⁵	196 (3136)	21	8.8	31.4	1.15	0.92	TS	9.33
	h1	All*, red, (blue)	7.8 × 10⁻⁴	37 (592)	15	5.6	5.9	1.14	0.92	⋯	⋯
NGC 1351	I1	All, (red), blue**	1.8 × 10⁻⁵	368 (5888)	20	5.9	58.9	1.03	0.84	TS	9.16
	I2	All, red*, blue	4.5 × 10⁻⁵	266 (4256)	48	18.6	42.6	1.15	0.91	RS	9.65
	I3	(All)	5.3 × 10⁻⁵	113 (1808)	3	0.9	18.1	0.99	⋯	AD	8.39
	i1	(All), (red), (blue)	4.7 × 10⁻³	37 (592)	0	−0.7	5.9	⋯	⋯	⋯	⋯
	i2	All, red	7.5 × 10⁻⁵	46 (736)	9	2.9	7.4	1.10	0.83	⋯	⋯
	i3	(All), (blue)	3.7 × 10⁻³	47 (752)	1	0	7.5	1.17	⋯	⋯	⋯
NGC 1336	J1	All, (red), blue	<10⁻⁵	309 (4944)	25	8.9	49.4	1.02	0.86	AD	9.34
	J2	All, (blue)	5.4 × 10⁻⁵	167 (2672)	3	−0.9	26.7	0.92	⋯	AD	↓
	J3	All, red, blue***	7.5 × 10⁻⁵	256 (4096)	70	27.3	41	1.11	0.9	Hy	*
	J4	All, (blue)	4.7 × 10⁻³	109 (1744)	5	1.4	17.4	1.09	1.01	TS	8.55
	j1	All, red	6.5 × 10⁻³	33 (528)	1	0.3	5.3	0.91	⋯	⋯	⋯

Note. (a) Name of the host galaxy. (b) Label of the GC structures. (c) Significance of each structure in the residual maps generated for all, red. and blue GCs: boldface is used for GC color classes where the structure has high statistical significance, plain text is used for classes where the structure is still reliably detected with lower significance and plain text within parenthesis indicate low significance. GC color classes where the structure is not detected are not reported. Asterisks indicate structures whose shape or size across suggest the presence of multiple substructures. (d) Statistical significance of the structure (see Section 4 for details). (e) Size of the structures measured in pixels and in square arcseconds (in parentheses). (f) Total number of GCs within the structures. (g) Number of excess GCs within the structures (see Section 6.4 for details). (h) Approximate physical area of the structure (kpc²). (i) Average g − z color of all GCs in the structure. (j) Average g − z color of the ${N}_{\mathrm{GCs}}^{(\mathrm{exc})}$ bluest GCs in the structure. (k) Classification of the structure (Section 6.2): AD for Amorphous Dweller, TS for Tangential Streamer, RT for Radial Streamer, and Hy for Hybrid. (l) Logarithm of the dynamical mass of the progenitor of the large structures calculated according to Equation (5) for the full sample (see details in Section 6.4). Asterisks and arrows indicate hybrid/composite structures (Section 6.2) and structures with a negative ${N}_{\mathrm{GCs}}^{(\mathrm{exc})}$ , respectively, for which M_dyn is not calculated.

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The residual maps were generated for 10⁵ distinct simulated distributions for each galaxy and GC color class (all, red and blue) with K = {2, 5, 10, 15, 20}. Because the ACSFCS data employed in this paper cover both the central, dense regions of the galaxies as well as very-low-density outskirts, the results presented in this paper are those obtained with an intermediate value K = 10. Moreover, K = 10 produces structures whose typical scale, measured as the average of the structures' largest transversal size, matches the average spatial scale of the GC spatial structures detected in the spatial distribution of the ACSVCS by D'Abrusco et al. (2015). With this K value, our approach can detect spatial structures of scales ranging between ≈1 and ≈30 kpc across different density and background regimes. Large values of K tend to produce residual maps where distinct spatial structures mesh and their spatial properties are averaged out, while for lower values, the residuals are dominated by small-scale density peaks that make it very difficult to determine the shape, extension, and orientation of the structures.

Each detected spatial structure can be characterized by (1) the statistical significance (see Section 4 for details), (2) the size measured as the number of connected cells contained in a structure, (3) the total number of observed GCs ${N}_{\mathrm{GCs}}^{(\mathrm{obs})}$ within the structure, (4) the excess number of GCs ${N}_{\mathrm{GCs}}^{(\mathrm{exc})}$ , and (5) the physical area. Based on their size, the spatial structures have been classified as intermediate (30 ≤ N_pxl ≤ 60) and large (N_pxl ≥ 60). In the remainder of the paper, large and intermediate structures detected in each galaxy will be labeled with a capital or small letter, respectively, uniquely associated with the host followed by a unique numerical index (e.g., A2 for the second among the large structures in NGC 1399 and c1 for the first among the intermediate structures in NGC 1380). The excess number of GCs ${N}_{\mathrm{GCs}}^{(\mathrm{exc})}$ is calculated by subtracting from the observed number of GCs ${N}_{\mathrm{GCs}}^{(\mathrm{obs})}$ in each spatial structure the number of expected GCs ${N}_{\mathrm{GCs}}^{(\exp )}$ in the same structure, where ${N}_{\mathrm{GCs}}^{(\exp )}$ is the average number of GCs located in the same set of cells included in the observed structure across the simulated GC distributions used to estimate the residual maps (Section 4). Because the detection of spatial structures is performed on the residual maps based on the observed and simulated spatial densities of the GC distribution, ${N}_{\mathrm{GCs}}^{(\mathrm{exc})}$ can be negative in some lower-significance structures because of the uneven distribution of GCs within the spatial boundaries of the structures. The smooth boundaries of the spatial structures shown in the plots in the following subsections and Appendix A have been determined by applying a smoothing algorithm to the rectangular boundaries derived from the set of cells included in each structure. The values of the main properties for all intermediate and large structures detected are listed in Table 2.

6. Discussion

The GC spatial structures discovered in the investigated Fornax galaxies as discussed in Section 5 are described in the context of the characteristics of the GC systems of the hosts in Appendix A. In what follows, we will investigate the possible dependencies of the intrinsic properties (size, shape, and significance) of these GC structures on the geometry of the host galaxies, the color distribution of the overall GC populations, and the galaxy and GC density of their environments.

6.1. The Properties of the GC Spatial Structures

We studied the spatial distribution of the structures detected in the GC residual maps of the 10 Fornax cluster galaxies described in detail in Section 5 with respect to the geometry of their host galaxies. Figure 2 shows the positions of the significance-weighted centers of all GC structures in the radial versus azimuthal coordinates plane relative to the center of each galaxy. The radial distance is the galactocentric distance measured as the projected angular separation (left panel) or in units of effective radii r_e (right panel); the azimuthal position is defined as the angular separation from the local S direction of the major axis. Different symbols and colors indicate different host galaxies, and large structures (≥60 cells) are circled. The areas for each galaxy covered by the ACSFCS observations are displayed in the background. Figure 2 shows that GC structures are inhomogeneously distributed in this plane: Few structures are detected at radial distances smaller than 0 farcm 5, likely because of the combined effects of the size threshold applied to individual intermediate structures (≥30 cells) and the very inefficient detection of GCs in the core of the galaxies due to the very high background. The underpopulated areas in the right panel of Figure 2 are mostly occupied instead by large, spatially extended structures at r(r_e) ≈ 1.

**Figure 2.** Distribution of the overdensity structures shown in Table 2 in the galactocentric radius vs. azimuthal angle plane (measured clockwise from the S direction of the major axis of the galaxy). Circled symbols identify large GC structures. In the left and right panels, the galactocentric radius is expressed as a projected angular distance and measured in units of the effective radii r_e of each galaxy respectively. The shaded background areas in both panels represent the regions of the plane that can be accessed with the sample of GCs used in this paper for each galaxy. These regions follow the same color-coding used for the points. In both plots, each different symbol is located in the significance-weighted central positions of the intermediate and large GC spatial structures discussed in Section 5.
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Figure 3 shows separately the galactocentric distances and azimuthal positions of all GC structures investigated in this paper as a function of the size of the structures measured in a number of cells. As mentioned in Section 5, the linear size of the cells in the residual maps ranges from ∼3'' to ∼5'' along both axes depending on the actual distance of the host galaxy. These angular sizes correspond to physical sizes from 0.3 to 0.5 kpc along the axes and to physical transversal sizes from ∼0.4 to ∼0.5 kpc. The intermediate structures (upper panel) appear to be homogeneously distributed along the radial range spanned by the observations, while large structures peak between 1' and 2' from the centers of their host galaxies, with the nine largest structures (≥300 cells) all located between 1' and 2 farcm 1, although this could be an effect of the available observed area because structures identified as large in this work cannot be located too close to the edges of the field where they would be truncated. At distances larger than 2 farcm 5, the spatial coverage of the ACSFCS observations rapidly declines (see the left panel of Figure 1), likely leading to a significant incompleteness in both radial and angular coverage. The angular distribution of intermediate GC spatial structures is roughly homogeneous (lower panel of Figure 3), while the large structures peak around the minor axis direction of their host galaxies, with ∼65% of them located within θ = [90°, 270°] ± 45° (lower panel). Unlike D'Abrusco et al. (2015), who found that a majority of the total area of the GC structures was located along the major axes of the host galaxies in the Virgo cluster, we observe that ∼70% of the total area of the large structures in the Fornax cluster galaxies are located within ±20° from the minor axis of their hosts and ∼60% of the area of all structures is observed in the same azimuthal range.

Figure 4 shows the whole areal extension of large residual structures in the same galactocentric versus azimuthal distance plane of Figure 2. The vertical marginal histogram in the plot shows that large GC structures occupy a larger fraction of the total available area sampled by ACSFCS observations along the minor axes of the hosts (close to or larger than 25%), while the fraction occupied along the major axis is ∼10%.

Figure 5 displays the average g − z colors of all GCs located within the boundaries of all intermediate and large GC structures, superimposed on the general color distribution of the GC population of host galaxies (upper panel) and on the radial color profiles of the GC systems obtained after removing the GCs within the boundaries of the GC structures (lower panel). The colors of the GC structures in NGC 1399, NGC 1316, NGC 1344, NGC 1427, and NGC 1374 do not vary significantly and are very close to the average colors of the overall GC populations of their hosts, suggesting comparable metallicities and similar formation mechanisms. The colors of the GC structures in NGC 1380, NGC 1404, NGC 1387, NGC 1351, and NGC 1336 span a larger interval of colors, hinting at different possible formation mechanisms at play. In particular, the structures with the largest color offset relative to the mean value of the general GC color distribution of the host are G2 in NGC 1387 (redder than the host GC systems at the same radial distances), D1 and d2 in NGC 1404 (bluer and redder respectively than the host GC populations at the same radial distances), and J2 and j1 in NGC 1336 (both redder than the GCs at observed at the same galactocentric distances). In the case of G2, the spatial structure is located in the SW corner of the region of the host galaxy observed by the ACSFCS along a direction opposite to the direction connecting NGC 1387 to NGC 1399 and not associated with an observed overdensity of galaxies. Similarly, D1 is located in the SE corner of the NGC 1404 field and opposite to the direction connecting its host to NGC 1399, in a region with a high density of intracluster GCs (ICGCs) (see Figure 10).

**Figure 5.** Upper panel: g − z color distributions of ACSFCS GCs for the 10 galaxies investigated in this paper; the vertical black lines show the average colors of the large and intermediate GCs' residual structures based on all GCs within the boundaries of the structures, while the vertical blue lines display the average color of the bluest ${N}_{\mathrm{GCs}}^{(\mathrm{exc})}$ GCs within the boundaries of each structure. Lower panel: radial g − z color profiles of the host-galaxy GC systems (GCs located within the boundaries of the large and intermediate structures have been removed) with the mean colors of all the GCs (white circles) and the bluest ${N}_{\mathrm{GCs}}^{(\mathrm{exc})}$ GCs (blue triangle) included in each structure. The colored areas represent the uncertainty of the radial profiles, while the black horizontal segments display the full radial extension of GC structures. The blue and red arrows pointing down and up, respectively, indicate whether each structure has a large statistical significance in the blue and red GC color subclasses (see column C in Table 2). In both panels, the shaded areas highlight the color interval occupied by the GC systems of Virgo cluster dEs from Peng et al. (2006) for comparison.
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In the remainder of this paper, we assume that the GCs associated with residual structures are the relics of the GC systems of satellite galaxies accreted by the host during its assembly (see details in Section 6.4). Under this hypothesis, the GCs observed within the boundaries of the structures belong either to the GC system of the structure's progenitor or to the host galaxy. Given that the colors of the GC systems of dwarfs in clusters of galaxies are typically bluer than the GCs of massive ETGs (the host) in the same environment (Peng et al. 2006), the average of the colors of all GCs located within the boundaries of each structure is an upper limit on the real average color of GCs of the progenitor of the structure. For this reason, in order to provide a lower limit to the colors of residual structure GCs, we also calculated the average colors of the ${N}_{\mathrm{GCs}}^{(\mathrm{exc})}$ bluest GCs in each structure (reported in column (j) of Table 2). These values are shown in Figure 5 in the context of the general color distribution of all GCs in each host and their color radial profiles as blue lines (upper panel) and blue triangles (lower panel). The "blue" limits on the colors of the GC structures (shaded regions of both panels in Figure 5) mostly lie in the interval of colors of the GC systems of galaxies with M_B ≥ −18 from Figure 3 of Peng et al. (2006).

6.2. Morphological Classification of the GC Spatial Structures

Based on the morphology and the orientation of the spatial structures detected in the distribution of all GCs observed in the galaxies investigated in this paper (as discussed in Section 4, we did not perform the detection of structures in the residual maps obtained from red and blue GCs), we define four classes as shown in the left panel of Figure 6: "Amorphous Dwellers" (ADs), "Radial Streamers" (RSs), "Tangential Streamers" (TSs), and "Hybrids." The structures are first split according to their shape: the full set of cells belonging to each structure is fitted with an elliptical model whose major and minor axes are free to vary, and the structures with minor axis to major axis ratio d/D ≥ 0.6 (where d and D are the minor and major axes of the best-fit elliptical model) are identified as ADs. While most detected GC structures have shapes that are not well modeled by an ellipse, this step permits us to separate flattened from generally unflattened shapes. The elongated structures are further split according to their orientation: if the direction of their fitted major axis is contained within a ±20° cone centered on the direction of the tangent to the D₂₅ elliptical isophote of the host galaxy in the intersection of the structures with (or the closest point to) D₂₅, they are classified as TSs. Given an arbitrary reference direction, this condition translates to ∣∣Θ_{major_axis} − Θ_{D25_tangent}∣∣ ≤ 20, where Θ_{major_axis} is the angular distance of the major axis of the fitted ellipse of the GC residual structure from the reference direction, and Θ_{D25_tangent} is the angular distance of the tangent to D₂₅ in the intersection between the ellipse major diameter (or its closest point) and D₂₅. All other elongated structures are labeled as RSs. The fourth class, "Hybrids," includes spatial structures whose large size and/or complex morphology do not permit a straightforward classification in one of the classes defined above and suggest that they are composite. The right panel of Figure 6 shows an example of morphological classification for the four large residual structures observed in NGC 1374, where at least one structure for each class (excluded Hybrids) has been observed.

**Figure 6.** Left panel: decision tree used to determine the classification of the large residual structures investigated in this paper. Right panel: K = 10 residual map for the distribution of all GCs observed in NGC 1374. The best-fit ellipses of the large residual structures and their major axes are shown with solid blue lines. The shaded gray regions represent the ±20° cones centered on the direction of the tangent to the elliptical D₂₅ elliptical isophote in the intersection between the major axis of the fitted ellipses for the GC residual structures and the D₂₅ of the host galaxy. The cones are used to classify elongated structures in TSs or RSs according to their orientation. In the insets, the label, the axial ratio of the best-fit ellipse, and the morphological classification of each structure are reported.
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Figure 7 shows the large spatial structures in the galactocentric versus azimuthal distances plane split by their classes. These plots highlight the following results:

1.
ADs (upper-left panel) are almost equally distributed along the major and minor axes of their host galaxies: ∼55% of the total area of ADs is located within ±30° of the Θ = {90°, 270°} directions along the azimuthal axis. They are observed along the whole interval of radial distances investigated.
2.
RSs (upper-right panel) span a large range along the galactocentric distance axis and are more likely not located along the major axes of their host galaxies, with only ∼12% of their total areas within ±30° from the θ = {0°, 180°} directions.
3.
TSs (lower-left panel) are, by definition, only located at radial distances ≥1 r_e. Their azimuthal distribution shows that they display a slight preference for the direction of the major axis (∼31% of their total areas within ±30° from the θ = {0°, 180°} direction), and are not observed along the minor axes of the host galaxies.
4.
The Hybrids structures (lower right panel) usually occupy large intervals along the azimuthal axis, with the exception of G4 and C3, and they can almost straddle the directions of both axes (B1 and E4). Only G4 is entirely located at a galactocentric distance larger than 1 r_e, while E4 covers the largest radial interval, between 0.25 and 1.8 r_e.

The class of a structure depends on both its intrinsic properties, i.e., the position of the structure relative to the host galaxy and its shape, and on the orientation of both the host galaxy and the structures relative to the line of sight. Under different projections, the same three-dimensional spatial structure could be classified as AD, TS, or RS. Assuming that each observed GC structure is the relic of the GC system of a single satellite accreted by the main galaxy, different classes identify different initial orbits along which the satellite was moving relative to the host, the line of sight, and its orbital phase.

6.3. Position and Properties of the GC Spatial Structures in the Cluster of Galaxies

Figure 8 shows the location of the 10 galaxies discussed in this paper within the Fornax cluster compared with the density maps derived using two different methods from the positions of galaxies that are likely cluster members included in the Fornax Cluster Catalog (FCC) (Ferguson 1989), which is complete at a ∼90% level at the B_T = 19 magnitude for Es and dEs within the core of the Fornax cluster. The upper plot in Figure 8 shows the full residual maps of the ACSFCS GC distribution overlaid on the FCC galaxy density calculated with the KNN method with K = 21 to highlight relatively small-scale spatial structures in the projected galaxy density. The lower panel displays only the large GC structures overplotted on the density map of FCC galaxies obtained with the Kernel Density Estimation¹⁰ (KDE) method: the two solid green lines represent the isodensity contours corresponding to the 40% and 80% of the density value at the peak that we used to separate low-, intermediate-, and high-galaxy-density regions in the cluster. Using these thresholds, NGC 1374, NGC 1387, NGC 1399, and NGC 1404 are located in the high-density regions; NGC 1427 and NGC 1380 lie in the intermediate-density region; and the remaining galaxies (NGC 1316, NGC 1351, and NGC 1336) are in the low-density area. NGC 1344 is located outside of the footprint of the FCC catalog and is not considered in this analysis.

Figure 9 shows the size of all GC spatial structures as a function of galaxy density at the location of the host galaxy (normalized to the peak density) derived from the FCC catalog using the KDE method (Figure 8). The data are inconclusive regarding the existence of a correlation between the size of structures and local galaxy density (Pearson's sample correlation parameter r = −0.1 with a p-value 0.442); unlike in the case of the Virgo cluster (D'Abrusco et al. 2016), large structures are found with similar frequency in both high- and low-density regions of the cluster of galaxies, although intermediate structures are more frequently detected in galaxies in the lower-density area of the cluster (8 of 17 total structures outside of the 50% isodensity contour versus 10 of 35 inside the 50% isodensity contour). The marginal histograms in Figure 9 show the percentage of the areas occupied by GC structures relative to the total imaged areas of the galaxies when the cluster is divided again into high- and low-galaxy-density regions (upper histogram) and high-, intermediate-, and low-galaxy-density regions (lower histogram) using the isodensity contours associated with 50% and 40%, and 80% of the peak galaxy density, respectively (red and green lines in Figure 8). The data available do not permit conclusions to be drawn even when correlations between the local galaxy density and the average or maximum size of all GC structures detected in the same structures are investigated.

Assuming that the spatial features of the overdensities in the distribution of GCs trace the accretion history of the hosts and depend on the mass ratios and the time passed since the accretion events, we should expect large GC structures to be observed more frequently than intermediate structures in lower-density regions of the cluster, where the accretions of large satellites and minor mergers have occurred more recently and/or more often than in high-density areas. The absence of conclusive evidence regarding the lack of a correlation between the galaxy density and the properties of the GC structures in the Fornax cluster does not allow us to draw final conclusions about this aspect. Should the lack of a correlation be confirmed and deemed statistically significant with additional data, it may either indicate that the scenario above is not always applicable or that it strongly depends on the global history of the cluster where the observed galaxies reside. The Fornax cluster is traditionally thought to be more relaxed than the Virgo cluster, a notoriously dynamically young and unrelaxed cluster, from the analysis of the velocity distribution of member galaxies (Drinkwater et al. 2001), although there are emerging pieces of evidence that point toward a more lively recent history, including a potential ongoing merger (based on the asymmetry of the intracluster diffuse X-ray emission; Paolillo et al. 2002), recent infall of NGC 1399 (from the spatial variation of the intracuster matter temperature in the cluster core; Murakami et al. 2011), and the recent accretion of a galaxy group (from the properties of the diffuse stellar light and GCs in the N–NW area within the Fornax virial radius; Iodice et al. 2019).

Moreover, the properties of the observed GC structures likely depend also on additional parameters (i.e., the geometry of the accretion events, the gas content of the satellites, and the ratio of early-to-late type galaxies that can all determine the degree of asymmetry in the distribution of GCs formed in tidal tails and streamers) that, in the case of the Fornax cluster, might have had a significant effect in shaping the GC populations.

Recent investigations of the ICGCs in Fornax (D'Abrusco et al. 2016; Cantiello et al. 2020), based on observations from the Fornax Deep Survey (FDS) survey (Iodice et al. 2016), have confirmed the existence of an abundant population of ICGCs in the core of this cluster. Cantiello et al. (2020) report the observation of an elongated overdensity extending ∼10 Mpc, centered around NGC 1399 and stretching in the W–E direction with a (∼10°) tilt. Figure 10 shows the density map of the Cantiello et al. (2020) catalog of candidate FDS GCs, estimated with the KNN method with K = 10 (this value is chosen to highlight spatial structures of a scale similar to that of the GC residual structures detected in the spatial distribution of GCs in the 10 galaxies investigated in this paper), around NGC 1399, where the insets display the density contours from the full residual maps obtained from all GCs detected in NGC 1399, NGC 1404, and NGC 1387 with K = 10 (lower panel) and the large structures only (upper panel) detected in the K = 10 residual maps of ACSFCS GCs for all galaxies located in the core of the cluster of galaxies. The qualitative agreement between the positions of the overdensities within the ACSFCS footprints and the FDS GC distribution is particularly evident along the higher-density "bridges" connecting the central galaxies to NGC 1404 and NGC 1387 and the complex structures in the outskirts of NGC 1399. These similarities suggest a continuity in the spatial properties of the different populations of GCs in the core of the Fornax cluster and hints at the possibility that the large-scale ICGC spatial features discovered by Cantiello et al. (2020) extend within the core of the cluster and are coherent with the smaller-scale spatial structures observed in the ACSFCS GC distribution within a few effective radii. More detailed modeling of the GC systems of the host galaxies and the Fornax ICGC population would be needed to explore this possibility, but there is growing evidence of the existence of a connection between the anisotropies of the GC spatial distributions at very small galactocentric distances and on scales typical of the core of clusters for other galaxies, for example, in the cases of NGC 4365 (Blom et al. 2014; D'Abrusco et al. 2015) and NGC 4406 (D'Abrusco et al. 2015; Lambert et al. 2020).

**Figure 10.** Upper panel: Density map of the spatial distribution of GC candidates from the Fornax Deep Survey (FDS) collaboration (Cantiello et al. 2020) (gray points) in the core of the Fornax cluster, with the large K = 10 residual GC structures of the galaxies investigated in this paper and derived from the spatial distributions of the ACSFCS GCs overplotted. Ten isodensity contours of the FDS GC density distribution, logarithmically spaced between 2% and 99% of the peak density, are shown (gray lines). The three green lines represent the 5% and 20% of the peak GC density and separate low-, intermediate-, and high-density regions of the cluster. Lower panel: zoom of the FDS GC density distribution showing the high-density region centered between NGC 199 and NGC 1387, with density contours of the full K - 10 residual maps derived from the distribution of ACSFCS GCs in NGC 1399, NGC 1404, and NGC 1380. Ten logarithmically scaled isodensity contours of the GC distribution inside this region are shown (gray lines).
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The frequency of large spatial structures of different morphological classes (described in Section 6.2) as a function of the type of density environment where their hosts reside is displayed in Figure 11. In this plot, the absolute number and fraction of GC structures of different classes in low-, intermediate-, and high-density regions based on the spatial distributions of both FCC galaxies (left) and FDS ICGCs (right) are shown. The number and fraction of ADs increase from the low- to the high-galaxy-density regions (lower-left plot in Figure 11), while RSs and TSs are more frequent in the high- and low-galaxy-density regions; Hybrids are only observed in galaxies located outside of the high-galaxy-density area instead. Similar trends can be observed when galaxies are split into low- and high-density areas (separated by the isodensity contour corresponding to 50% of the peak density), as shown by the upper-left plot.

Also in the case of density regions based on the FDS GC distribution (right plot in Figure 11), we notice that the fraction of ADs increases from low- to high-density regions and Hybrids structures are only detected outside of the highest-density area. The fraction and number of TSs, instead, is largest in galaxies in the low GC density area and lowest in the high-density galaxies.

Assuming that all GC structures are formed through the interaction of the host galaxy with satellite galaxies, the observed differences in the frequency of different types of GC structures as a function of the galaxy density in the cluster of galaxies indicate different properties of the seed population of satellites. In the higher-galaxy-density regions, the larger fraction of ADs may be caused by earlier mergers and accretion events that resulted in more tightly bound and regularly shaped GC overdensities (as described by Pfeffer et al. 2020 using E-MOSAICS simulations of Milky Way–sized galaxies) that also tend to be located at smaller galactocentric distances than structures of the same type observed in hosts in medium- and low-density regions. Another effect potentially shaping the morphology of GC structures observed in the high-density region is the destruction and/or spatial degradation of coherent structures due to gravitational interaction with neighbors and the deeper cluster potential. The observed class and position of the GC structures can also be the footprint of anisotropies in the distribution of galaxies relative to the geometry of the cluster, namely, the alignment of the orbits of the satellite with the cluster major axis reported for nearby clusters (Knebe et al. 2004) and the nonrandom orientation of satellite galaxies relative to their hosts (Agustsson & Brainerd 2006; Wang et al. 2021).

6.4. Progenitors of the GC Structures

The ΛCDM model of hierarchical galaxy formation (White & Rees 1978; Di Matteo et al. 2005) predicts that galaxies continuously evolve through the merging and accretion of satellites. Observational evidence of this process in the local universe is abundant and convincing. The observations of the Sagittarius Stream (Ibata et al. 1994), Milky Way companions undergoing tidal disruption (Belokurov et al. 2006), and streams and dwarf galaxies in the halo of M31 (McConnachie et al. 2006) support this model. More recently, data from the Gaia mission allowed the discovery of ancient merger events that contributed to the buildup of the stellar mass currently observed in the Milky Way (Belokurov et al. 2018; Helmi et al. 2018). At larger distances, ongoing accretion of satellite galaxies has been inferred from the kinematical signature left on the GC systems of the hosts (Strader et al. 2011; Blom et al. 2012; Romanowsky et al. 2012).

Following D'Abrusco et al. (2015), we assume that all structures detected in the spatial distribution of the GCs in the 10 Fornax ETGs studied in this paper are the relics of the GC systems of accreted satellite galaxies, detected over the smooth and relaxed GC distribution of the host. The only exception is represented by GC structures classified as Hybrids: Given their large sizes and peculiar morphologies, Hybrids are more likely to be either composite structures or resulting from different physical mechanisms, like major dissipationless mergers or wet dissipation mergers that might have triggered the formation of young, metal-rich GCs along the major axis of the newly formed galaxy (as observed in Virgo by Wang et al. 2013). In particular, in disk–disk major mergers, the increased pressure in metal-rich molecular clouds triggers the collapse and subsequent formation of GCs concentrated along the major axis of the remnant (Bekki et al. 2002; Brodie & Strader 2006).

Moreover, other effects that may contribute to their features are the existence of a sizable disk component in the spatial distribution of metal-rich GCs (as observed in Virgo cluster galaxies by Wang et al. 2013) and the chance superposition of multiple distinct structures. For this reason, Hybrids GC structures have been excluded from the analysis performed in this section.

Harris et al. (2013) determined observational correlations between the dynamical mass of the host galaxy and the total number of GCs for a full sample of galaxies of different morphological types and a subsample of dwarf ellipticals (dEs) (Table 2 and Figure 9 therein):

$\begin{eqnarray}&&\begin{array}{l}\mathrm{Full}\ \mathrm{sample}\to {N}_{\mathrm{GCs}}={M}_{\mathrm{dyn}}^{1.04\pm 0.03}\\ \mathrm{dEs}\to {N}_{\mathrm{GCs}}={M}_{\mathrm{dyn}}^{0.37\pm 0.09}.\end{array}\end{eqnarray} \tag{ 5 }$

The relation for the full sample is based on galaxies with M_dyn ≥ 10¹⁰ M_⊙ and average $\mathrm{log}(M/{M}_{\odot })=11.2$ , while the dEs correlation is observed for a sample of dwarf ellipticals with average $\mathrm{log}(M/{M}_{\odot })=9.2$ and covers a much larger interval at low masses. By inverting these relations, we calculated the dynamical masses of the progenitor galaxies of the GC structures from the number of GCs in the structure for both the general and dEs samples (Figure 12). Dynamical masses $\mathrm{log}(M/{M}_{\odot })\lt 7.7$ resulting from Equation (5) for dEs were not considered in the following analysis because they lie outside the range of masses occupied by the galaxies used by Harris et al. (2013) to determine the correlations.

**Figure 12.** Distribution of dynamical masses of progenitors of the large GC spatial structures observed in the Fornax cluster galaxies. For each spatial structure, the expected and maximal masses of the progenitor satellite galaxies are determined by applying the relation between dynamical mass and the total number of GCs of a galaxy determined by Harris et al. (2013) (see Section 6.4) to the excess number of GCs ${N}_{\mathrm{GCs}}^{(\mathrm{exc})}$ (base of the arrows) and the total observed number of GCs in the structure ${N}_{\mathrm{GCs}}^{(\mathrm{obs})}$ (tip of the arrows). The masses of the progenitors have been calculated using both the Harris et al. (2013) correlations for the general sample of galaxies and for dEs only. Hybrids structures are excluded, while structures with negative ${N}_{\mathrm{GCs}}^{(\mathrm{exc})}$ are displayed as arrows pointing downwards, with the base showing the maximal mass of the progenitor derived from their N_obs,GC. The dynamical masses of the host galaxies (Harris et al. 2013) are shown as horizontal lines in the grayed-out region. The box plot based on the distribution of satellite progenitors of GC spatial structures in Virgo cluster galaxies (D'Abrusco et al. 2015) is also shown for reference.
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For each structure, we also determined the "maximal" mass of the progenitor using the same procedure and assuming that all the observed GCs within a structure belong to the GCS of the potential progenitor (i.e., ${N}_{\mathrm{GC}}^{(\mathrm{exc})}\equiv {N}_{\mathrm{GC}}^{(\mathrm{obs})}$ ). Before calculating the dynamical mass of the progenitors, both the excess and total numbers of GCs in each structure have been corrected for completeness using the Fornax cluster GCLF (Villegas et al. 2010).

Figure 12 shows the distribution of the masses of the progenitors derived from the excess and total GC numbers in the large spatial structures of the Fornax cluster galaxies compared to the distribution of M_dyn of the progenitors of the spatial GC structures detected in a sample of bright Virgo cluster galaxies by D'Abrusco et al. (2015). The masses of the progenitors are shown both for the general and dEs relations (Equations (5)). Maximal masses are indicated in Figure 12 by the tips of the arrows pointing upwards. The range of dynamical masses of GC structures in the Fornax galaxies for the general prescription is compatible with the distribution of masses for GC overdensities in the Virgo cluster of galaxies, although the total interval covered is slightly wider. In general, the progenitors of GC structures in the most massive galaxies have larger M_dyn than those in less massive galaxies. As expected, the average mass of dEs progenitors is lower and the covered range larger than in the case of the general correlation, and we do not see an increase in the masses of the progenitors with the mass of the host.

The mass ratios for the progenitors of the large GC spatial structures in the Fornax cluster galaxies calculated with the general and the dEs correlations are shown in Figure 13 (left and right columns, respectively). Larger mass ratios are observed for less massive galaxies for both prescriptions (upper panels), similar to the trend observed for progenitors of GC structures in Virgo cluster galaxies (D'Abrusco et al. 2015). This confirms that the mass of different galaxies grows by accreting satellites of different masses or that the observed GC structures in different hosts are relics of different stages of a similar galaxy mass growth process. The lack of a clear pattern observed for mass ratios as a function of both the distance of the host from the center of the cluster and the local 2D galaxy density (middle and lower panels) suggests that the environment does not significantly affect the mass ratios of the satellite accretion inferred from the current spatial distribution of GCs.

**Figure 13.** Distribution of the ratios of the mass of the progenitors of the large GC spatial structures to the total dynamical mass of their host galaxies vs. the host M_dyn (top panels); the distance from the center of the Fornax cluster, assumed to coincide with the position of NGC 1399 (middle panels); and percentage of the peak density derived from the spatial distribution of FCC galaxies (Ferguson 1989) (low panels). The left and right columns show the same plot for masses of progenitors calculated with the general (left) and dEs relation (right) in Equation (5). The gray circles in the background represent the values from GC structures detected in the Virgo cluster galaxies (D'Abrusco et al. 2015).
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6.5. The Physical Nature of GC Structures and Projection Effects

The results presented in this paper are based on the assumption that all statistically significant GC structures may be associated with either the accretion of satellite galaxies or mergers undergone by the host galaxy. Because the full knowledge of the three-dimensional distribution of GCs around the host galaxy is unobtainable, indirect approaches to confirm the nature of the structures are necessary.

One way to confirm the physical nature of the GC residual structures is to search for coherent substructures in the phase space of GCs spatially associated with the 2D residual GC structures sufficiently distinct from the surrounding host-galaxy GC system distribution in the phase space. However, the available data do not allow this investigation: GC structures all reside at smaller galactocentric radii than the 13 cold streams discovered by Napolitano et al. (2021) in a sample of spectroscopically observed GCs in the core of the Fornax cluster. We also compared the positions of GCs with line-of-sight velocity measurements from both catalogs of spectroscopically observed GCs presented by Napolitano et al. (2021) and Chaturvedi et al. (2022) (including all the data available in the literature), and we found at best five GCs within a single GC residual structure and most structures with no corresponding GC (both catalogs only cover the core of the Fornax cluster). The low statistics does not allow to draw conclusions on the nature of the structures.

Even if a larger number of GCs with measured velocities were available, the approach described above would be potentially hindered by the difficulty in obtaining spectra of GCs at small galactocentric distances (due to the very bright galaxy background) and in disentangling GCs belonging to the system of the progenitor from the underlying host-galaxy populations. A subtler issue that can also affect this diagnostic is the bias caused by the fact that bright GCs, for which high-quality spectra are more easily achieved, are redder and, thereby, more likely to belong to the host galaxy than to the less massive progenitor GC, whose GC systems tend to have a bluer average color (Peng et al. 2006). Finally, we can expect to be able to distinguish substructures in the phase space only for GCs whose progenitors' orbits had a large component along the line-of-sight direction.

Some of the structures presented in Section 5 might not be physical and be the result of the chance superposition of GCs due to projection effects. Such bias cannot be excluded a priori, but several considerations that significantly mitigate the risk of misidentifying chance superpositions as GC structures can be made.

1.
It is reasonable to assume that the importance of projection effects decreases with decreasing galactocentric distance as the density of GCs shrinks. Woodley & Harris (2011) investigated the presence of physical groups of GCs and planetary nebulae (PNs) in NGC 5128, a giant elliptical galaxy, and assessed through simulations that the probability of observing a fake 2D subgroup of GCs as the result of projection effects is <1%, while the probability of observing real subgroups overlap is ∼4% over the whole galaxy. All simulated fake subgroups were observed at <2r_e.
2.
Most GC structures discussed in this paper have complex morphologies that cannot be explained with simple projection effects, assuming a smooth 3D spatial distribution of GCs, even when considering distinct components associated with the bulge, halo, and disk of the host galaxies. Some of the structures have large sizes and extend to radii larger than r_e.
3.
Projection effects cannot explain the differences observed in the properties of the same GC structures in different color classes if one assumes that the radial profiles of red and blue GCs only differ in their slope and extent.

7. Conclusions

We studied the 2D spatial distributions of the GC systems of 10 galaxies that are among the most massive Fornax cluster galaxies using the GC catalogs extracted from the ACSFCS data (Jordán et al. 2007). We characterized the GC structures detected by estimating their statistical significance, size, shape, morphological classification, and position relative to the host galaxies for both the total GC samples and the red and blue color subclasses, separately. Our results can be summarized as follows.

1.
We detected 60 GC spatial structures in the 10 galaxies investigated, confirming that large-scale overdensities in the GC systems of massive ETGs are common (D'Abrusco et al. 2015). Among these structures, 17 are classified as intermediate structures and 43 as large structures based on their size.
2.
The spatial distribution of the observed GC structures, in general, is radially and azimuthally homogeneous except for the innermost ( $r\leqslant 0\buildrel{\,\prime}\over{.} 5$ ) regions of the host galaxies. The largest and statistically most significant structures are typically located at galactocentric distances between 1' and 2', while intermediate structures are homogeneously distributed at all radial positions probed. Similarly, 65% of the significance-weighted centers of the large structures and 70% of the total area of large clusters are found within 45° and 20° from the direction of the minor axis, respectively, while the centers of the intermediate structures are uniformly distributed along the azimuthal direction. Large structures also tend to occupy the largest fraction of total observed area along the minor axes directions.
3.
We proposed a classification of GC structures based on their morphology, position, and orientation relative to the geometry of the host galaxy and investigated their distribution relative to the host galaxy. We found that amorphous, roughly circular, and small structures (ADs) are homogeneously distributed along both the radial and azimuthal axes, while elongated structures tend to be less likely located along the major axes of the hosts than along the minor axes when their orientation is radial (RSs), and they are spread evenly along both radial and angular axes when their orientation is tangential (TSs). A small number of very large, morphologically complex, and possibly composite structures (Hybrids) occupy large azimuthal and radial intervals, straddling the directions of both the minor and major axes of the host galaxies.
4.
We have estimated the average color of GCs in residual structures by either considering all GCs located within the geometrical boundaries of each structure or by only averaging over the bluest ${N}_{\mathrm{GCs}}^{(\mathrm{exc})}$ GCs. The first approach produced mean colors that are likely skewed toward red because of the contribution of the typically red GCs belonging to the massive host galaxy, while the second recipe provides a lower estimate of the real color of the GCs belonging to the progenitors of the structure. Based on the distribution of the average colors of all the GCs included in the GC spatial structures, two families of galaxies can be distinguished: NGC 1399, NGC 1316, NGC 1427, NGC 1344, and NGC 1374, where the colors of the GC structures are very similar and tightly distributed around the average color of the general GCS of the host, and NGC 1380, NGC 1404, NGC 1387, NGC 1351, and NGC 1336, whose GC structures colors show a larger variance and are more widely scattered along the GC color distribution of the host. The analysis of the statistical significance of the large GC structures in the red and blue GC subclasses shows that in the first class of galaxies, the majority of large structure are more significant in red GCs than in blue (eight versus six, while the remaining structures have comparable significance in both color classes), while the structures in the second group of galaxies tend to be more significant in the blue GCs than in the red (10 versus 7). On the other hand, the average "bluest" colors are all consistent with the interval of colors observed in dwarfs in rich clusters of galaxies (see Peng et al. 2006 for the GCSs of dwarf galaxies in the Virgo cluster).
5.
Large, statistically significant GC structures are observed in galaxies located in all galaxy density levels within the Fornax clusters, while intermediate structures are more frequent relative to the total number of structures detected in hosts in the low-galaxy-density region of the cluster. This scenario contradicts what was observed in Virgo (D'Abrusco et al. 2015), where larger GC structures are more likely to be detected in relatively low-galaxy-density regions where the accretion of large satellites probably occurred more recently than in the core of the cluster. The data available do not permit statistically robust conclusions to be drawn regarding the existence of a correlation between the size of the structures and the galaxy density in the position of the host.
6.
Similarities in the spatial distributions of ACSFCS GCs and the population of ICGCs are observed in the core of the cluster, where NGC 1399, NGC 1404, and NGC 1387 reside, suggesting a continuity between the spatial properties of the GC populations of these galaxies and the surrounding population of GCs. Split by class, the fraction of ADs is largest for hosts located in the highest galaxy and GC density regions, while elongated structures (TSs and RSs) are more frequent in the low- and high-galaxy-density regions and tend to be found more likely in low-GC-density regions. These differences can hint at the different geometries of the satellite systems that were the progenitors of the structures currently observed in the GC distribution.
7.
The dynamical masses of the progenitors of the GC structures in the Fornax cluster galaxies, inferred using both the Harris et al. (2013) relations based on the complete sample of galaxies and dEs only, range between ≈10⁸ and 4 × 10¹⁰ M_⊙. The M_dyn of the progenitors are larger for more massive host galaxies and cover an interval comparable with the range occupied by the dynamical masses of the progenitors of GC structures in the Virgo cluster galaxies (D'Abrusco et al. 2015). Conversely, larger mass ratios are observed for the least-massive host galaxies, while no clear pattern emerges between the mass ratios and both the projected distance of the host galaxy from the center of the cluster and the local galaxy density.

The results presented in this paper provide additional evidence that 2D structures are common in GC systems of massive early-type galaxies. The trends of the GC structure size and orientation relative to the geometry of the host galaxy as a function of the local galaxy density in the Fornax cluster differ from those of Virgo cluster galaxies (D'Abrusco et al. 2015), hinting at a different assembly history for galaxies in the two clusters. Shedding light on the cause of these differences, whether they are exclusively informed by the specific assembly history of each host galaxy or they are influenced by the general evolution of the cluster, will require a joint investigation of the spatial properties of GC populations at larger galactocentric radii and of the spatial distribution of the surrounding ICGCs. While the interval of effective radii that can be probed by ACSFCS observations extends significantly over the coverage available for Virgo cluster galaxies, the lack of deep, high-spatial-resolution data in the outskirts (10 ≤ r_e ≤ 5) for a large sample of ETGs in the nearby universe is still the main limiting factor preventing the observation of recently formed GC overdensities in the halo of their hosts, which is necessary to draw a complete picture of the properties of the GC structures as a function of their location in the host galaxy.

A new generation of cosmological simulations capable of resolving mass and spatial scales typical of GCs (Pfeffer et al. 2020) provides the exciting opportunity of a direct comparison with the observations and to fine-tune our interpretation of the presence of GC structures as a powerful tool to infer the past merging/accretion history of the host galaxies and to move along our understanding of how galaxies grow and evolve.

R.D'A. is supported by NASA contract NAS8-03060 (Chandra X-ray Center). M.C. acknowledges support from MIUR, PRIN 2017 (grant 20179ZF5KS). M.P. acknowledges the financial support from ASI-INAF agreement 2017-14-H.O. A.Z. acknowledges funding from the European Research Council under the European Union's Seventh Framework Program (FP/ 2007-2013)/ERC grant Agreement No. 617001. This project has also received funding from the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie RISE action, grant agreement No. 691164 (ASTROSTAT). The SAO REU program is funded by the National Science Foundation REU and Department of Defense ASSURE programs under NSF grant AST-1659473 and by the Smithsonian Institution. This research has also made use of results from NASA's Astrophysics Data System. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.

Appendix A: GC Structures in 10 Galaxies of the Fornax Cluster

A summary of the properties of the spatial structures detected in the distribution of ACSFCS GCs for each galaxy studied can be found below. Details on the procedure used to detect the GC structures can be found in Section 5, while Section 2 provides details on the definition of red and blue GC color classes.

A.1. NGC 1399

NGC 1399 is the central galaxy of the Fornax cluster and, in the optical light, is classified as a peculiar elliptical galaxy. Given its large size (r_e = 367 farcs 6), the single ACSFCS pointing is entirely located within the D₂₅ diameter of the galaxy. Figure 14 shows the distribution of GCs in NGC 1399 (upper left) and the K = 10 residual maps obtained for all, red, and blue GCs (upper-right, bottom-left, and right panels, respectively). The largest and most significant overdensity in the residual maps for all GCs (A2) is located W of the nucleus and extends toward the NW corner of the observed field along a mostly radial direction. This structure is also visible in the blue residual map, where it shows three apparently disjointed substructures, while in the red GC map no coherent structure is visible, with only a few isolated peaks located in the area occupied by A2. Four significant spatial structures, potentially connected, are observed E of the center of the galaxy. Among these structures, A1 and A3 are the largest: A1 has an elongated shape extending radially from the center of the galaxy toward the NE direction, while the other three structures in this region (A3, a2, and a3) are approximately circular and are located at larger galactocentric distances than A1 and closer to the E edge of the observed field. Two smaller, less significant circular structures are located along the W boundary of the observed field (a1 and a4). In the E half of the observed field, A1 and A3 can be clearly associated with similar overdensity regions in the spatial distribution of both red and blue GCs, while a2 and a3 are clearly detected only in the red residual map. The structures a1 and a4 are most prominent in the red GCs. The presence of very significant red GC spatial structures in the outskirts of the imaged region, especially in the E side of the field, reflects the reported abundance of red GCs at relatively large galactocentric distances, possibly due to a recent history of wet mergers experienced by this galaxy (Goudfrooij et al. 2004).

**Figure 14.** Spatial distribution of GCs of NGC 1399. Upper left: positions of GCs, where blue and red points are associated with blue and red GCs, respectively. Upper right: the residual map generated by the entire sample of GCs, with large (solid lines) and intermediate (dotted lines) spatial structures labeled. Orange and green pixels refer to overdense and underdense regions of GCs, respectively. Darker shades indicate a larger statistical significance, horizontal bars and crosses mark cells whose significance is between 2σ and 3σ and larger than 3σ, respectively. Lower left: the residual map for blue GCs. Lower -right: the residual map for red GCs. The ellipse displays the D₂₅ elliptical isophote, and the red line represents the galaxy major axis.
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Puzia et al. (2014) investigated the trends of the GC structural parameters in the NGC 1399 GCS as a function of the distance from the center of the galaxy using a catalog of GCs extracted from a mosaic of nine HST ACS observations (PI Puzia) in the F606W filter, arranged to cover a large field of view reaching a maximum galactocentric distance of $\sim 8\buildrel{\,\prime}\over{.} 76$ , corresponding to ∼5.2 r_e. Figure 15 shows the residual map (K = 50) derived from the spatial distribution of all Puzia et al. (2014) GC candidates overplotted with the boundaries of the large and intermediate GC structures detected in the ACSFCS GC distribution. The large K value used to derive the residual map of this catalog of GCs qualitatively matches the spatial resolution of the ACSFCS maps over a larger field of view and balances the larger density of GC candidates. The ACSFCS overdensities are clearly visible in the residual map of the Puzia et al. (2014) GCs; outside the ACSFCS field of view, a prominent area of enhanced density is observed E of the NGC 1399 D₂₅ elliptical isophote, while more structures are located near the S and W corners of the observed field.

**Figure 15.** Residual map of the spatial distribution of all GCs from Puzia et al. (2014) (K = 50). The red lines show the large and intermediate GC spatial structures detected in the ACSFCS GC spatial distribution. The black polygon represents the field of- view of the ACSCFCS observation in the core of NGC 1399. The ellipse displays the D₂₅ elliptical isophote, and the red line represents the galaxy major axis.
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A.2. NGC 1316

The investigation of the kinematics of the GC system of the giant elliptical NGC 1316 has revealed that this galaxy is the likely remnant of a merger that occurred ≈3 Gyr ago (Goudfrooij et al. 2001; Sesto et al. 2018). Sesto et al. (2016), in particular, using Gemini ground-based observations, have established the existence of four different color components whose spatial distributions differ for ellipticities and radial profiles, consistent with the presence of an almost spherical low-metallicity halo and a more flattened and chemically enriched bulge. Goudfrooij et al. (2004) observed different turnover magnitudes of the luminosity functions of the inner and outer red GC subpopulations, drawing a picture of the complex stratification of GC color classes and confirming the merger scenario, according to which the metal-rich GC subsystems formed during mergers can dynamically evolve into the normal giant elliptical red GC systems.

As in the case of NGC 1399, the region of NGC 1316 where ACSFCS data are available is entirely contained within the D₂₅ elliptical isophote. The residual map of the general distribution of GCs in NGC 1316 (upper-right panel in Figure 16) features two large, complex regions of significant overdensities (B1 and B3) located S and E of the center of the galaxy. B1 partially overlaps the S section of the major axis of the galaxy and is characterized by a complex morphology and the presence of several density peaks that suggest the existence of multiple underlying physical structures. B1 is clearly visible in the residual maps of blue GCs while in red GCs only two peaks are detected in the B1 area. B3 extends radially and is visible in both red and blue GCs, but in red GCs, it is split into two separate substructures. N and E of the center of the galaxy, four roughly circular structures (B2, b2, b3, and b4) are aligned in a radial direction perpendicular to the major axis of the galaxy. B2 is clearly visible in both GC color classes, while the other less significant structures are only clearly detected in the red GCs. The structure b1, on the other hand, is located along the S major axis and is only detected in the blue residual map.

**Figure 16.** Spatial distribution of GCs in NGC 1316 (see caption of Figure 14 for details).
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A.3. NGC 1380

NGC 1380 is an unbarred, lenticular galaxy whose GCS, investigated both from the ground (Kissler-Patig et al. 1997) and using HST data (Chies-Santos et al. 2007), features two clearly distinct color classes: the blue GCs, which are spherically distributed and mostly located in the outskirts of the galaxy, and the red GCs, which follow more closely the geometry of the photometric components of the disk and bulge.

Three major overdensities are observed in the residual map generated by all ACSFCS GCs in NGC 1380 (Figure 17) along the D₂₅ elliptical isophote: C1 is located on the E side of the galaxy, C2 and C4 are located on the W side. While C1 is only barely visible in the blue residual map, C2 and C4 are clearly detected in both the blue and red GCs, although in the red only one overdensity region engulfing both structures is observed. The blue residual map suggests that the morphology of C2 and C4 is elongated and aligned along radial directions toward the center of the galaxies. C3 is a morphologically complex structure with multiple peak densities and located at a small galactocentric distance NE of the galaxy center; C3 is only visible in the red GCs. Two additional small, low significance structures (c1 and c2) are detected W of the center and could represent the low radius extremities of C2 and C4 that are located at larger galactocentric distances (the continuity between the structures being more evident in the blue residual map). The observation of large overdensity structures at relatively large distances from the center of the galaxy, especially in the spatial distribution of blue GCs, confirms results in the literature (Kissler-Patig et al. 1997; Chies-Santos et al. 2007) that found that blue GCs dominate the NGC 1380 GCS at large galactocentric distances. A relatively large region of enhanced positive residual not detected in the other maps is observed N and NW of the NGC 1380 center in the distribution of red GCs.

A.4. NGC 1404

The GC system of NGC 1404, an E2 elliptical galaxy that is the closest neighbor of NGC 1399 and is located only 9' from its very extended GC system, has been investigated in the past using observations from the ground (Richtler et al. 1992) that have highlighted a relatively compact and spherical geometry. More recently, Bekki et al. (2003) used simulations of the NGC 1404 GCS, including the Fornax cluster tidal field, to find that the low NGC 1404 specific frequency can be explained by tidal stripping of NGC 1404 GCs caused by NGC 1399. They observed that the stripped GCs have likely contributed to the formation of tidal streams in the cluster core ICGC population whose geometric, metallicity, and kinematical properties depend on the orbit of their former host galaxy relative to the cluster center and to past global properties of NGC 1404 GCS.

Figure 18 shows the residual maps of the spatial distributions of ACSFCS GCs in NGC 1404. The general spatial distribution (top-right panel) features several large (D1, D2, D4, and D6) spatial structures located in the proximity of the D₂₅ elliptical isophote of the host galaxy. D1 and D6, the two largest and most significant overdensities, are located in the SE and NW corners of the imaged field, respectively, while D2 and D4 are approximately located just outside of D₂₅ along a NE to SW direction crossing the galaxy center. D6 is located along the direction connecting the center of NGC 1404 and NGC 1399 and overlaps the "bridge" observed in the density map of ICGCs in the core of the Fornax cluster by D'Abrusco et al. (2016). D6 is also the only structure to be detected with similar size, shape, and significance in both the red and blue GC residual maps: D2 and D4 are only visible in the red map, while D1 is detected only in blue residuals. Two additional small but statistically significant, roughly circular structures (D3 and D5) are detected at smaller galactocentric distances along the major axis of the galaxy N and SW of the galaxy center, respectively. Both can be associated with similar structures only in the map of red GCs, although in the blue residuals, a moderate circular density peak corresponding to the S end of D5 is visible. The two additional, less significant structures d1 and d2 detected in the general residual map can only be also observed in the red residual map.

A.5. NGC 1427

The Forte et al. (2001) study of the GC system of NGC 1427 showed that this low-luminosity elliptical presents a strongly centrally concentrated red subpopulation and a blue component with a much shallower radial profile. The spatial distribution of ACSFCS GCs in NGC 1427 (Figure 19) is dominated by the very large and statistically significant structure E4 that extends radially and displays a complex morphology with at least two main overdensity regions: the first one, roughly circular, is located W of the center of the galaxy, while the second, much larger region lies across the D₂₅ isophote in the NW quadrant of the galaxy. The E4 morphological complexity and extension suggest that it might be the result of the superposition of two distinct overdensities. E4 is visible in both the red and blue residual maps, although in the blue GCs, the two density peaks are clearly separated by a large gap, unlike in the red residuals, where they are connected. Four additional large spatial structures are observed. The roughly circular E3 and E5 are located respectively close to the N and S intersections of the major axis of the host galaxy with the D₂₅ isophote; both are also clearly detected in the blue residual maps. E1 is located in the SE corner of the imaged field and can be clearly observed also in the blue map, while E2 sits E of the galaxy center; both E1 and E2 are only detected in the blue residual map. An intermediate structure (e1) is close to the center of the galaxy and E2. Because e1 is also only visible in the blue residual map, it may be considered a section of the nearby large E2 structure.

**Figure 19.** Spatial distribution of GCs in NGC 1427 (see caption of Figure 14 for details).
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A.6. NGC 1344

NGC 1344, located in the N, very-low-density outskirt of the Fornax cluster and sometimes classified as an S0 galaxy, is known for low-surface-brightness features resembling thin shells (Malin & Carter 1980), which are considered to be the remnants of relatively recent galactic mergers. Sikkema et al. (2006) studied, among other shell galaxies, the NGC 1344 GCS using large field-of-view, ground-based images and found that the overall NGC 1344 GC population follows closely the photometric geometry of the host, but a significant fraction of the red GC subpopulation is also present at large galactocentric radii where, typically, blue GCs are more likely observed.

The residual map generated by all GCs observed in NGC 1344 (Figure 20) features an excess of GCs in the E side of the galaxy relative to the W side (upper-left panel); this asymmetry is also evident in the residual maps for all GCs, where three large structures (F1, F2, and F4) are detected in the E half of the galaxy, while only one structure (F3) is located in the W section. F1 and F2, both visible in the red and blue GC residual maps, have elongated shapes and are located along radial directions spanning a large range of galactocentric distances. The roughly circular, large structure F4 lies outside of the D₂₅ isophote and is not detected in the red map. F3, which displays at least two separate density peaks, straddles the border of the observed field and extends radially in the NE to SW direction; it is clearly detected in the blue residual map. The intermediate, small structure f1 sits on the N section of the major axis and is only detected in the red residual map although with a much larger statistical significance than in the general GC distribution.

A.7. NGC 1387

The GCS of NGC 1387 is characterized by an almost spherical spatial distribution and the lack of significant azimuthal anisotropy (Bassino et al. 2006); the GC color subclasses display different radial profiles, with red GCs more centrally concentrated and of a shallower but more radially extended blue GC profile. Bassino et al. (2006) suggested that the current properties of the NGC 1387 GCS have been determined by the hierarchical merging evolution history of the host (Beasley et al. 2002) and the tidal interaction with the nearby giant elliptical NGC 1399, which has stripped NGC 1387 of its outermost GCs.

Figure 21 shows the residual maps based on the spatial distribution of the ACSFCS GCs observed in NGC 1387. In the upper-right panel is the map for all GC features' three extended structures straddling or located just outside the D₂₅ isophote of the host galaxy (G1, G2, and G4). G1 and G4 have complex, elongated morphology suggestive of the presence of substructures, partially confirmed by the different shapes of these structures in the residual maps for different-color GC classes, respectively. In the red map, G4 is very weak while G1 is associated with an overdensity region with lower statistical significance and smaller size, which is mostly located along the D₂₅ isophote; both structures are clearly visible in the residual map generated by blue GCs instead. G2 is only detected in the red residual map. Two additional high significance, roughly circular overdensities at small galactocentric distances can be found N (G5) and E (G3) of the center of the galaxy, with similar properties in the residual maps of both red and blue GCs. Structures G1 and G4, clearly visible in the residual map of the blue ACSFCS GCs, are located along the direction connecting NGC 1387 to the center of NGC 1399 and overlap the well-known blue GCs "bridge" in the spatial distribution of Fornax cluster core ICGCs reported by D'Abrusco et al. (2016), Kim et al. (2013), and Bassino et al. (2006) (see Section 6.3).

A.8. NGC 1374

The GC cluster system of NGC 1374 has been investigated, using wide-field imaging data, by Bassino et al. (2006). They observed an evident color bimodality and reported that the radial profiles of the blue and red subclasses at the largest probed galactocentric distances are not consistent with the background source density probably because of contributions from the GC systems of companion galaxies NGC 1375 and NGC 1373.

The spatial distribution of all ACSFCS GCs in NGC 1374 (upper panel in Figure 22) features H1, H2, and H4, three very significant structures located close to the D₂₅ elliptical isophotes of the host galaxy on the S, E, and W sides of the observed field, respectively. These structures have elongated shapes with multiple overdensity peaks suggestive of spatial substructures. H2 points in an almost radial direction, reaching well beyond the D₂₅ ellipse, while H1 and H4 lie almost tangentially to the same isophote. The two additional structures H3 and h1 are located at small galactocentric distances SW and NE of the galaxy center, respectively. The red and blue residual maps (lower panels in Figure 22) display significant differences: in the red GCs, H2, H4, and H3 are clearly detected (although the shapes of H2 and H3 differ from the general residual map and H3 has a much lower statistical significance), while in the blue GCs only H1, H2, and H3 are firmly detected.

A.9. NGC 1351

The GC system of NGC 1351 features several large spatial structures (Figure 23). The very statistically significant overdensities I1 and I2 display similarly elongated morphology: I1 lies along an almost tangential direction to the D₂₅ elliptical isophote of the host galaxy at the S end of the major axis, unlike I2, which originates in the center and radially extends to the W outskirts of the observed field. Both structures are also visible in the blue GC residual map, while I1 is not detected in the red residual map. Four additional density structures (I3 and the smaller i1, i2, and i3) have roughly circular shapes and are located at different galactocentric distances in the E and W sides of the galaxy. i1, i2, and i3 are observed in the blue GC map, while I3 is only weakly detected in the red GC residual map. In the distribution of red GCs, i2 and the E edge of structure I2 are apparently connected, while another significant overdensity peak, not associated with any structure in the residual map generated by all GCs, is located S of the galaxy center. In the blue residual map, a geometrically incoherent region of positive residuals can be seen in the regions occupied by i2, i3, and i1.

A.10. NGC 1336

Recent studies have found that NGC 1336 possesses two kinematically decoupled components that indicate that this galaxy has undergone a major merger (Fahrion et al. 2019). Moreover, the GCS of NGC 1336 has a very high specific frequency (Liu et al. 2019), second only to NGC 1399 in Fornax, that can be explained by the lack of significant GC disruption favored by the isolation from the other members of the Fornax clusters, possibly suggesting that NGC 1336 is infalling in the cluster and has not interacted with other members of the cluster yet.

The spatial distribution of GCs in NGC 1336 (Figure 24) is dominated by two large structures (J1 and J3) that, together, occupy a significant fraction of the area of the host galaxy within the D₂₅ elliptical isophote. J1 is located at the S intersection of the major axis with D₂₅ and extends toward large galactocentric distances. J3 is a geometrically complex, hook-shaped structure containing multiple overdensity peaks that spans a large range of radii and is likely the result of the chance projection of multiple structures. J3 is detected in both the residual maps of red and blue GCs, while J1 is detected only in the blue map where it is connected to J3. The remaining structures (J2, J4, and j1) all have low statistical significance and can only be seen in the blue GCs.

Appendix B: Properties of the GC Spatial Structures as a Function of K

The parameter K of the KNN method determines the number of "neighbors" used to estimate the density maps of both observed and simulated GC distributions and, in turn, the residual maps (see Section 4 for details). For this reason, its choice affects the properties of the spatial structures detected in the GC spatial distributions. As discussed in Section 5, the practical choice of the K value used to study the spatial structures in the GC distribution depends on the scales to be investigated and the desired type of characterization of the structures observed. In general, large values of K produce residual maps with larger spatial structures while lower values produce maps highlighting smaller spatial features that can be difficult to distinguish from noise and whose properties are poorly constrained.

Figure 25 shows the dependence of the residual maps and the properties of the residual structures in the case of NGC 1399: the upper and middle rows display the residual maps for K = {5, 10, 15, 20, 25, 30, 40, 50, 75, 100} obtained from all GCs, with the approximate contours of large and intermediate structures (defined as explained in Section 4) shown as dotted and solid lines, respectively. The panels in the lower row display (from left to right) the size, total, and excess numbers of GCs, the mass of the progenitor, average galactocentric distance, and average azimuthal position of the structures as a function of K. In general, the size and total and excess numbers of GCs of structures grow with larger K either gradually (when the same structure includes nearby cells of the residual maps) or abruptly as two or more structures detected at a given value of K merge at a larger K. Structures can also disappear for growing K's without merging into other existing structures, as it occurs for the small structures located in the NW corner of the NGC 1399 residual maps obtained for K ≤ 25. The evolution of the dynamical mass inferred for the precursors of the GC structures follows the trend observed in the excess number of GCs, as per Equation (5). Both the mass-weighted radial and azimuthal positions of the structures as a function of K quickly stabilize as the major structures start to dominate the residual maps. The dominating structures usually converge toward either amorphous, roughly circular morphology (ADs) as smaller structures with more complex shapes either merge into the major structures or disappear, or form geometrically complex, potentially composite structures (Hybrids).

Figure 26 shows the size, total and excess numbers of CGs, the dynamical mass of the progenitors, radial and azimuthal positions, and morphology for all structures detected in the residual maps of the GC distributions of all galaxies investigated in this paper for values of K = {5, 10, 15, 20, 25, 30, 40, 50, 75, 100}. The same general trends described for the NGC 1399 structures above are observed for the other galaxies.

Spatial Structures in the Globular Cluster Distribution of Fornax Cluster Galaxies

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