The Hierarchical Distribution of the Young Stellar Clusters in Six Local Star Forming Galaxies

TL;DR

This study analyzes the hierarchical clustering of young stellar clusters in six nearby star-forming galaxies, revealing how their spatial distribution evolves over time and supports a unified model of star formation.

Contribution

It provides a detailed analysis of the spatial hierarchy and evolution of stellar clusters using Hubble data, highlighting differences between clusters and associations.

Findings

Clusters become more homogeneously distributed after 40-60 Myr.

Associations are more strongly correlated and disperse quickly after formation.

Clustering patterns resemble turbulent interstellar medium structures.

Abstract

We present a study of the hierarchical clustering of the young stellar clusters in six local (3--15 Mpc) star-forming galaxies using Hubble Space Telescope broad band WFC3/UVIS UV and optical images from the Treasury Program LEGUS (Legacy ExtraGalactic UV Survey). We have identified 3685 likely clusters and associations, each visually classified by their morphology, and we use the angular two-point correlation function to study the clustering of these stellar systems. We find that the spatial distribution of the young clusters and associations are clustered with respect to each other, forming large, unbound hierarchical star-forming complexes that are in general very young. The strength of the clustering decreases with increasing age of the star clusters and stellar associations, becoming more homogeneously distributed after ~40--60 Myr and on scales larger than a few hundred parsecs. In all galaxies, the associations exhibit a global behavior that is distinct and more strongly correlated from compact clusters. Thus, populations of clusters are more evolved than associations in terms of their spatial distribution, traveling significantly from their birth site within a few tens of Myr whereas associations show evidence of disruption occurring very quickly after their formation. The clustering of the stellar systems resembles that of a turbulent interstellar medium that drives the star formation process, correlating the components in unbound star-forming complexes in a hierarchical manner, dispersing shortly after formation, suggestive of a single, continuous mode of star formation across all galaxies.

Tables

Table 1. Table 1 Properties of the LEGUS Galaxies Sample

Name	Morph.	T	Inclin.	Dist.	SFR(UV)	M∗	${\Sigma }_{\mathrm{SFR}}$	R25	Scale	CIcut
			(deg.)	(Mpc)	(M⊙ yr-1)	(M⊙)	(M⊙ yr-1 kpc-2)	(arcm.)	(pc arcs.-1)	(mag)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
NGC 7793	SAd	7.4(0.6)	47.4	3.44	0.52	3.2$\times {10}^9$	0.00907	4.67	16.678	1.3(e)/1.4(w)
NGC 3738	Im	9.8(0.7)	40.5	4.90	0.07	2.4$\times {10}^8$	0.01187	1.26	23.756	1.4
NGC 6503	SAcd	5.8(0.5)	70.2	5.27	0.32	1.9$\times {10}^9$	0.00620	3.54	25.550	1.25
NGC 3344	SABbc	4.0(0.3)	23.7	7.0	0.86	5.0$\times {10}^9$	0.00558	3.54	33.937	1.35
NGC 628	SAc	5.2(0.5)	25.2	9.9	3.67	1.1$\times {10}^{10}$	0.00444	5.23	47.956	1.4(c)/1.3(e)
NGC 1566	SABbc	4.0(0.2)	37.3	13.2	5.67	2.7$\times {10}^{10}$	0.01285	4.16	64.995	1.35

Table 2. Table 2 Color and Compactness of Cluster Classes

Class	mUV – mU	mU – mB	mV – mR	CI
	(mag)	(mag)	(mag)	(mag)
(1)	(2)	(3)	(4)	(5)
NGC 7793
Class 1	$-$0.29	$-$0.64	0.53	1.57(0.18)
Class 2	$-$0.35	$-$1.12	0.57	1.57(0.19)
Class 3	$-$0.46	$-$1.29	0.28	1.62(0.21)
NGC 3738
Class 1	$-$0.14	$-$0.22	0.57	1.72(0.21)
Class 2	$-$0.52	$-$0.62	0.47	1.67(0.18)
Class 3	$-$0.57	$-$0.86	0.56	1.76(0.11)
NGC 6503
Class 1	$-$0.36	$-$0.48	0.67	1.50(0.17)
Class 2	$-$0.53	$-$0.67	0.51	1.53(0.17)
Class 3	$-$0.56	$-$0.99	0.57	1.56(0.23)
NGC 3344
Class 1	$-$0.21	$-$0.58	0.68	1.50(0.12)
Class 2	$-$0.38	$-$1.28	0.40	1.51(0.13)
Class 3	$-$0.50	$-$1.46	0.13	1.60(0.16)
NGC 628
Class 1	$-$0.039	$-$0.38	0.71	1.57(0.14)
Class 2	$-$0.20	$-$0.85	0.59	1.57(0.14)
Class 3	$-$0.30	$-$1.18	0.52	1.62(0.18)
NGC 1566
Class 1	0.065	$-$0.38	0.64	1.48(0.11)
Class 2	$-$0.21	$-$1.02	0.53	1.50(0.14)
Class 3	$-$0.29	$-$1.28	0.42	1.57(0.17)

Table 3. Table 3 Power-Law Parameters for Individual Galaxies

Class	Number	$A_1$	${\alpha }_1$	$\beta$	$A_2$	${\alpha }_2$
				(”)
NGC 7793
Class 1,2,3	350	14.0(6)	$-1.16\left(5\right)$	$\cdots$
NGC 3738
Class 1,2,3	281	3.27(3)	$-0.394\left(12\right)$	$\cdots$
NGC 6503
Class 1,2,3	298	3.97(19)	$-0.46\left(6\right)$	$\cdots$
NGC 3344
Class 1,2,3	391	4.7(3)	$-1.68\left(13\right)$	1.3	3.37(13)	$-$0.42(3)
NGC 628
Class 1,2,3	1264	4.81(5)	$-0.75\left(4\right)$	3.3	2.39(5)	$-0.16\left(2\right)$
NGC 1566
Class 1,2,3	1101	6.06(6)	$-0.492\left(13\right)$	$\cdots$

Table 4. Table 4 Power-Law Parameters for Weighted Average

Class	$A_1$	${\alpha }_1$	$\beta$	$A_2$	${\alpha }_2$
			(pc)
All Ages
Class 1	62(2)	$-0.86\left(2\right)$	59	3.2(3)	$-$0.14(3)
Class 2	63(3)	$-0.73\left(7\right)$	112	4.8(3)	$-$0.18(3)
Class 3	463(40)	$-1.13\left(7\right)$	112	6.6(4)	$-$0.23(07)
Class 1,2	25(4)	$-0.58\left(4\right)$	93	3.6(2)	$-$0.15(2)
Class 1,2,3	69(5)	$-0.77\left(7\right)$	112	4.0(3)	$-$0.17(4)
Age $\le 40$ Myr
Class 1	52(10)	$-0.66\left(14\right)$	128	6.4(3)	$-$0.23(3)
Class 2	119(15)	$-0.83\left(3\right)$	112	8.1(5)	$-$0.26(2)
Class 3	565(18)	$-1.15\left(13\right)$	112	7.3(4)	$-$0.232(16)
Class 1,2	39(2)	$-0.60\left(3\right)$	186	3.51(13)	$-$0.139(19)
Class 1,2,3	115(6)	$-0.85\left(3\right)$	112	5.6(3)	$-$0.21(2)
Age $>40$ Myr
Class 1	2.45(14)	$-0.13\left(2\right)$	$\cdots$
Class 2	3.98(10)	$-0.160\left(18\right)$	$\cdots$
Class 3	3.3(3)	$-0.161\left(14\right)$	$\cdots$
Class 1,2	2.90(13)	$-0.130\left(18\right)$	$\cdots$
Class 1,2,3	2.61(15)	$-0.164\left(6\right)$	$\cdots$

Equations

$$\begin{array}{c}{x}^{\prime }=x\cos \theta +y\sin \theta \\ y^{\prime }=-x\sin \theta +y\cos \theta ,\end{array}$$

$${\omega }_{\mathrm{LS}}(\theta )=\frac{DD(\theta )-2DR(\theta )+RR(\theta )}{RR(\theta )},$$

$$\begin{array}{c}DD(\theta )=\frac{P_{DD}(\theta )}{N(N-1)/2}\\ DR(\theta )=\frac{P_{DR}(\theta )}{N{N}_R}\\ RR(\theta )=\frac{P_{RR}(\theta )}{N_R(N_R-1)/2},\end{array}$$

$$1+\omega (\theta )=A_{\omega }{\theta }^{\alpha },$$

$$\log[1+\omega(\theta)]=\left\{\begin{array}[]{lr}A_{1}+\alpha_{1}\log(\theta)&:\log(\theta)<\beta\\ A_{2}+(\alpha_{1}-\alpha_{2})\beta+\alpha_{2}\log(\theta)&:\log(\theta)>\beta,\end{array}\right.$$

Full text

††slugcomment: Accepted for Publication in the Astrophysical Journal

1. Introduction

Star clusters are gravitationally bound stellar structures, with radii between 0.5 to several parsecs and masses between $10^{3}$ and $10^{7}$ $M_{\odot}$ (Portegies Zwart et al., 2010). Because most, if not all, stars form in some type of stellar aggregate (Lada & Lada, 2003), stellar clusters are a direct product of the star formation process within galaxies. Compounded by the fact that young stellar clusters are intrinsically brighter than single stars, star clusters become important tracers of the recent star formation history in galaxies beyond which individual stars cannot be detected.

Within the hierarchical model, star formation occurs within structures that have smoothly varying densities and sizes that range from pc to kpc scales, with denser regions nested within larger, less dense areas (e.g., Elmegreen et al., 2006; Bastian et al., 2007). Bound star clusters form at these peak densities within the hierarchy. Most structures within the hierarchy are themselves gravitationally unbound and the stellar components are expected to inherit their clustered substructure from the molecular clouds from which they are born (Scalo, 1985). Recent analyses of 12 local galaxies (Elmegreen et al., 2014) found that the clustering of star formation remains scale-free, up to the largest scales observable, for both starburst galaxies and more quiescent star-forming galaxies. This result is consistent within the framework where the self-similar structure of the interstellar medium (ISM), regulated by turbulence, is believed to be the primary driver for the hierarchical nature of star formation (Elmegreen & Efremov, 1996; Elmegreen et al., 2014). Thus, extensive star-forming regions of several hundred parsecs or larger are expected to represent common structures, related in both space and time in a hierarchical manner that determines the structure and morphology of all galaxies.

The evolution and erasure of the unbound hierarchical structures has been the focus of investigation in recent years, where observations of local galaxies support an age-dependent clustering of the stellar components (e.g., Pellerin et al., 2007; Bastian et al., 2009; Scheepmaker et al., 2009; Gieles et al., 2011; Pellerin et al., 2012; Baumgardt et al., 2013; Gouliermis et al., 2014, 2015; Grasha et al., 2015), and the clustering becomes progressively weaker for older populations. Hierarchical clustering is expected to dissipate with age (Elmegreen et al., 2006; Elmegreen, 2010) as the densest regions with the shortest mixing timescales lose their substructures first, whereas the larger, unbound regions will lose their substructure over longer periods of time owing to tidal forces and random velocities (Bate et al., 1998), dispersing over time to form the field population. Characterizing the clustered nature of star formation provides insight into how star formation is organized across a galaxy, by correlating local environmental conditions at sub-galactic scales – such as feedback and turbulence – to the global properties – such as dynamics and morphology – of entire galaxies and constrain the migration timescale for which stars and clusters abandon their natal structure. This will in-turn provide a vital connection between the inherently different processes of clustered star formation seen within local galaxies and the large kpc-scale star-forming structures that appear to be common at high-redshift (Immeli et al., 2004; Elmegreen et al., 2009; Förster Schreiber et al., 2011; Guo et al., 2012).

In this paper, we study the young stellar cluster populations of six galaxies as part of the Legacy ExtraGalactic UV Survey111https://legus.stsci.edu/ (LEGUS; Calzetti et al., 2015), a Cycle 21 Hubble Space Telescope (HST) program with images of 50 nearby ($\sim$3.5–15 Mpc) galaxies in five UV and optical bands (NUV,U,B,V,I) with the UV/Visible (UVIS) channel on the Wide Field Camera 3 (WFC3) and re-using archival ACS images when appropriate. The aim of LEGUS is to investigate the relation between star formation and its galactic environment in nearby galaxies, over scales ranging from individual star systems to kpc-sized structures. These data will help to establish a more accurate picture of galaxy formation and the physical underpinning of the gas-star formation relation. The relatively nearby location of these galaxies provides us with the high-angular resolution needed to acquire large numbers of star clusters to perform statistically accurate tests for changes in clustering strength across a representative range of galactic environments. Investigations of a few galaxies from the LEGUS project have already observationally demonstrated the relatively young ($\sim$40–60 Myr) dispersal timescales of star-forming structures (Gouliermis et al., 2015; Grasha et al., 2015).

This work builds on our previous paper (Grasha et al., 2015) on a study of the nearby star-forming galaxy NGC 628 using the two-point correlation function as a tool to quantify the clustering properties of the young stellar clusters, finding that the youngest clusters are spatially clustered within unbound, star-forming complexes that disperse with time. In this work, we expand our sample to investigate the clustering distribution of the stellar clusters within a larger sample of galaxies and a wider range of galactic environments. We will use the correlation function to identify common age structures, the extent that the distribution of clusters is hierarchical, on which timescale it disperses, and the dependencies of global properties (galaxy type) has on the clustering results, if any. This will in turn inform on the nature of local, resolved star formation.

The galaxy selection is described in Section 2 and the cluster identification process is described in Section 3. The methodology of two-point correlation function is introduced in Section 4. In Section 5, we describe the results and analysis and how we use the correlation function to draw conclusions about the properties of our star clusters. We discuss our results concerning hierarchy of the stellar clusters in Section 6. Finally, we summarize the findings of this study in Section 7.

2. Sample Selection

In this paper, we select six local ($<$13 Mpc) galaxies, ranging from dwarf to grand design spirals, with visually identified stellar cluster catalogs available (see Section 3), from the LEGUS survey. The galaxies and their general properties are listed in Table 2 and shown in Figure 1 along with the clusters. All galaxies were observed in five broad band filters: NUV, U, B, V, and I; the list of filters used can be found in Calzetti et al. (2015). Both NGC 628 and NGC 7793 have two pointings, combined into a single mosaic for analysis; the remaining galaxies have one pointing.