EDP Sciences logo
Subscriber Authentication Point
Search
Menu
Home All issues Volume 687 (July 2024) A&A, 687 (2024) A310 Full HTML
Open Access
Issue
A&A
Volume 687, July 2024
Article Number A310
Number of page(s) 10
Section Galactic structure, stellar clusters and populations
DOI https://doi.org/10.1051/0004-6361/202450088
Published online 30 July 2024

© The Authors 2024

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is published in open access under the Subscribe to Open model. Subscribe to A&A to support open access publication.

1. Introduction

The Large Magellanic Cloud (LMC) hosts globular clusters (GCs) of various ages, ranging from a few million to billions of years (Bica et al. 2008; Nayak et al. 2016). Its star formation history differs significantly from that of the Milky Way (MW), which predominantly hosts very old GCs (t >  10 Gyr). As suggested, for example, by Fig. 15 of Mackey & Gilmore (2003) and Fig. 1 of Ferraro et al. (2019), during the initial stages of star formation in the LMC (around 13 Gyr ago), massive clusters (M >  105 M⊙) formed at various distances from the galaxy centre. This phase was followed by a period of quiescence, known as the ‘age gap’, which lasted about 10 billion years. Then, approximately 3 Gyr ago, a period of strong tidal interaction between the MW and the LMC and/or between the LMC and the Small Magellanic Cloud (SMC) likely began, triggering significant collisions among gas clouds that boosted a second burst of star formation, during which the less massive clusters now observed in the LMC’s central regions were generated (Da Costa 1991; Rich et al. 2001; Bekki et al. 2004; Mazzi et al. 2021).

Unlike the MW, the LMC provides an opportunity to explore the properties of GCs spanning a large range of ages and masses (Elson et al. 1989; Elson 1991; Olszewski et al. 1996; Olsen et al. 1998; Brocato et al. 1996; Mackey & Gilmore 2003; Baumgardt et al. 2013; Ferraro et al. 1995, 2004; Mucciarelli et al. 2006). These studies show that a peculiar trend emerged between the core radius (rc) and the chronological (stellar) age of the clusters about 30 years ago, the so-called size–age conundrum. Specifically, while young clusters all have small core radii (rc <  2.5 pc), the older ones exhibit a broader range of sizes, reaching up to rc = 10 pc (Elson et al. 1989; Elson 1991; Mackey & Gilmore 2003). Different solutions to the size–age conundrum have been proposed in the literature, with the most acknowledged one being that presented in Mackey et al. (2008). These authors suggest an evolutionary connection between the younger and older clusters, with the former representing how the latter appeared at the epoch of their formation. Hence, in this framework all clusters were born compact, and subsequent interactions among single stars and binary stellar-mass black holes drove core expansion up to the large values of rc currently observed for the oldest systems.

However, Ferraro et al. (2019) show that there is a significant difference between the young and old LMC clusters, and challenged such an evolutionary connection. Specifically, they pointed out that all the young clusters are significantly less massive than the old ones (see the middle panel in Fig. 1 of Ferraro et al. 2019). Ferraro et al. (2019) proposed instead a new hypothesis to explain the size–age conundrum: the differences in the core radius values among the oldest systems are attributed to variations in their dynamical ages. In fact, GCs are collisional systems, in which the interactions among stars can significantly alter the internal energy budget. Because of these interactions, the heavier stars tend to progressively migrate towards the central regions through the action of dynamical friction, causing a contraction of the core and an increase in the central density: this continues until the collapse is halted by the energy provided by interactions with primordial or dynamically formed binary stars (Heggie & Hut 2003). The evolutionary path of a cluster depends on both its internal structure and the tidal field of its host galaxy (see e.g., Meylan & Heggie 1997). For instance, clusters with a higher central density experience a more rapid dynamical evolution than others, due to a higher probability of stellar interactions. Similarly, in clusters located at small galactocentric distances, the stripping action of low-mass stars by the galactic tidal field accelerates the process. This implies that clusters of the same chronological age can be at different stages of their dynamical evolution due to differences in their initial structural properties and the external environment where they evolved. In particular, in the scenario proposed to explain the observed variety of core radii for the old GCs, loose systems represent dynamically young systems, while compact ones are in more advanced stages of their dynamical evolution.

Ferraro et al. (2019) demonstrated this hypothesis by measuring the dynamical ages of five old and coeval clusters in the LMC through the ‘dynamical clock’ method. This approach relies on the properties of a distinct stellar population routinely observed within GCs and known as blue straggler stars (BSSs). The formation processes of these peculiar objects are not yet fully understood, but two main formation scenarios have been proposed so far (see also Bailyn 1995): (i) mass transfer in binary systems (McCrea 1964) and (ii) stellar mergers due to direct collisions between two or more stars (Hills & Day 1976). These are both mass-increasing processes, making BSSs more massive (M ∼ 1 − 1.4 M⊙; Fiorentino et al. 2014; Raso et al. 2019) than the average normal star in old clusters (M ∼ 0.3 − 0.4 M⊙). Therefore, under the action of dynamical friction, they sink towards the central region faster than less massive stars. For this reason, they act as excellent gravitational probes, and their degree of central segregation compared to that of a normal cluster population can be used as a clock-hand of a ‘dynamical chronometer’ to measure the dynamical stage of a system (see Ferraro et al. 2012, 2018, 2019; Ferraro et al. 2020, 2023; Lanzoni et al. 2016). To quantify the level of BSS central segregation, Alessandrini et al. (2016, see also Lanzoni et al. 2016) introduced the A rh + $ A^+_{\mathrm{rh}} $ parameter. It is defined as the area enclosed between the cumulative radial distribution of BSSs and that of a reference population (lighter stars, such as main sequence or red giant branch stars) within one half-mass radius (rh) of the cluster centre. The value of A rh + $ A^+_{\mathrm{rh}} $ provides a measure of the degree of mass segregation of BSSs and generally increases during dynamical cluster evolution (see also Alessandrini et al. 2016 for a discussion of the effects of dark remnants on the evolution of BSS segregation and the A rh + $ A^+_{\mathrm{rh}} $ parameter). This is evidenced by the strong correlation between A rh + $ A^+_{\mathrm{rh}} $ and the number of central relaxation times undergone by the system over its lifetime (Nrelax) in a sample of about 50 Galactic GCs (Ferraro et al. 2018, 2023; Beccari et al. 2023). By applying the dynamical clock to five old clusters in the LMC (namely NGC 1466, NGC 1841, NGC 2210, NGC 2257, and Hodge 11), Ferraro et al. (2019) found that they follow the same correlation between Nrelax and A rh + $ A^+_{\mathrm{rh}} $ drawn by the MW systems, thus demonstrating the validity of the method beyond our Galaxy. Furthermore, this study proved the expected anti-correlation between the core radius and the dynamical age of the five systems, confirming that the wide range of core radii observed for the old LMC clusters is due to their different dynamical stages.

The cluster sample surveyed so far, however, leaves the oldest LMC systems with very compact core radii still totally unexplored. To fill this gap, here we apply the dynamical clock method to NGC 1835. This cluster is very old (approximately 12.5 Gyr old; Giusti et al. 2024; Olsen et al. 1998) and very compact (rc <  0.8 pc), with a high mass (approximately 6 × 105 M⊙; Mackey & Gilmore 2003) and a low metallicity ([Fe/H] ∼ −1.7 dex; Mucciarelli et al. 2021). The present analysis is based on a set of high-resolution Hubble Space Telescope (HST) images acquired with the Wide Field Camera 3 (WFC3) in the cluster direction. These exposures had already been used to characterise the properties of a small stellar system named KMK 88-10 located only 2′ from the cluster, providing evidence that it has possibly been captured by NGC 1835 and is on the verge of tidal disruption (Giusti et al. 2023). Moreover, in Giusti et al. (2024) we presented the discovery of a very extended blue tail in the horizontal branch (HB) of NGC 1835, and we provided the most precise estimate so far of the cluster age (12.5 ± 1 Gyr), confirming that it is very old. In this paper we determine the star density profile of the cluster to characterise its structural parameters and to investigate its possible core-collapse nature, as proposed in Mackey & Gilmore (2003). We also measure its dynamical age by using the level of BSS segregation, and discuss the results in the context of the size–age conundrum.

2. Data analysis

The present study is based on high-resolution images collected with the UVIS channel of the HST/WFC3 in the F300X, F606W, and F814W filters, complemented with simultaneous parallel observations in the F606W and F814W filters acquired with the Wide Field Camera of the Advanced Camera for Surveys (ACS/WFC) under programme GO 16361 (PI: Ferraro). The dataset and data reduction procedures are described in Giusti et al. (2024). Here we briefly summarise the main points.

The WFC3 has a total field of view of 160″ × 160″, and the cluster centre has been located at the UVIS1 aperture. These data therefore sample the cluster population, both in the optical (F606W and F814W) and in the near-ultraviolet (near-UV) band (F300X). The parallel ACS observations sample an LMC field located at ∼5′ from the WFC3 pointing, and are therefore used for decontamination purposes. The data reduction procedure was executed with the DAOPHOT II software, following the methodologies delineated in earlier publications (see e.g., Cadelano et al. 2022a; Onorato et al. 2023; Chen et al. 2023). The only peculiarity is that for the WFC3 dataset we followed the so-called UV-guided search, which is specifically designed to maximise the detection of hot stars (like extremely blue HB stars, BSSs, and white dwarfs) in stellar populations where giant stars are dominant (see Paresce et al. 1992; Ferraro et al. 1997, 1998, 1999; Ferraro et al. 2001, 2003a; Lanzoni et al. 2007; Dalessandro et al. 2013; Raso et al. 2017; Chen et al. 2021, 2022). This approach has led to the discovery of the extended HB blue tail in NGC 1835 (Giusti et al. 2024), which remained undetected in all the previous optical studies of the cluster, and plays a crucial role in the present paper, where the collection of a complete sample of BSSs is required. The approach consists in generating a master list of stars identified in at least half of the near-UV (F300X) images, and then force fitting the point spread function model to the position of these stars in all the other filters. The magnitude values estimated for each star from different images have been combined using DAOMATCH and DAOMASTER, and finally calibrated onto the VEGAMAG photometric system by applying the aperture corrections and zero points quoted in the dedicated HST web pages. The instrumental positions have been corrected for geometric distortions (see Bellini et al. 2011 and Meurer et al. 2003 for the WFC3 and the ACS, respectively) and then transformed into absolute coordinates through cross-correlation with the Gaia Data Release 3 catalogue (Gaia Collaboration 2023).

The left-hand and central panels of Fig. 1 show the near-UV and optical colour-magnitude diagrams (CMDs) of NGC 1835, respectively: only stars within the innermost 13″ (corresponding to the cluster half mass radius; see Sect. 4.1) are plotted to more clearly highlight the cluster population. As high-temperature stars (Teff ∼ 7000 K), BSSs are better distinguishable in the near-UV plane, where they span a range of about 2.5 mag (20.5 <  mF300X <  23) above the main sequence turn-off (MS-TO) region. On the other hand, the cold red giant branch (RGB) sequence is better delineated in the optical CMD (at 17.5 <  mF814W <  21.5). For these reasons, the BSS sample and the RGB reference population used in the following analysis (see Sect. 5) will be selected in the near-UV and optical CMDs, respectively. In the right-hand panel we show the CMD of the LMC field region sampled by the ACS parallel observations, in the same filter combination of the cluster optical CMD.

thumbnail Fig. 1.

CMDs of the cluster region and the field region in different filter combinations. Left panel: near-UV CMD of NGC 1835 for the stars sampled within r <  13″ from the centre. Central panel: optical CMD of NGC 1835 for the same stars as in the left panel. Right panel: optical CMD of the LMC field region sampled by the ACS parallel observations.

3. Gravitational centre

As already discussed in many works (e.g., Ferraro et al. 1999, 2003b; Lanzoni et al. 2007; Ibata et al. 2009; Miocchi et al. 2013), the precise location of the centre of gravity plays a very important role in the accurate determination of the star density and surface brightness profiles. Mackey & Gilmore (2003) determined the centre position of NGC 1835 from the location of the cluster’s surface brightness peak, finding: α = 05h : 05m : 06s.7, δ = −69° :24′:15″. However, this method is prone to significant biases due to the possible presence of even a few bright stars not located at the cluster’s centre, because the surface brightness peak would be systematically shifted towards them. Thanks to our high-resolution dataset, we have been able, instead, to determine the position of the gravitational centre (Cgrav) from resolved star counts using the method outlined in Montegriffo et al. (1995 see also Lanzoni et al. 2007, 2019).

This consists of an iterative procedure that starts from a test value of the centre (e.g., a literature value) and determines the average of the coordinates of a sample of stars within a fixed distance, r. This procedure produces a new estimate of the centre, from which the next iteration starts. The convergence is fixed when the difference between the position of two successive centres is less than 0.01″. The search radius r must be chosen carefully. It should be larger than the core radius rc (4.76″ for NGC 1835; Mackey & Gilmore 2003), to work in a region where the stellar density is not uniform. On the other hand, excessively large radii lead to decreased sensitivity to the central concentration. The procedure also allows for a magnitude selection of the sample stars. A faint magnitude limit is necessary to obtain sufficient statistics, but a too high value introduces spurious incompleteness effects. In consideration of these compromises, we iterated the process considering different radius values (r ≤ 10″, 15″, 20″) and different magnitude limits (mF814W <  21.5, 22, 22.5), ensuring in each combination a minimum of 70% completeness (see Sect. 6) and thousands of stars included within the search radius. We repeated the iterative procedure for the nine possible combinations. The final value of Cgrav was then obtained from the average of these nine values: α = 05h : 05m : 6s.71, δ = −69° :24′:14″.78. Their dispersion provided us with an uncertainty σ = 0.25″. Our new estimate of Cgrav is consistent within 1σ with that quoted by Mackey & Gilmore (2003).

4. Star count density profile

We constructed the projected density profile of NGC 1835 from resolved star counts following the procedure described in Miocchi et al. (2013), Lanzoni et al. (2019), Raso et al. (2020). We used only evolved stars (mF300X <  22.5), in order to work with objects of approximately the same mass and to ensure a completeness of ∼80% in the central region. We also excluded the brightest sources (mF300X <  18) to avoid possible biases due to saturation. We divided the WFC3 field of view into 18 radial rings centred on the cluster centre (see Sect. 3) and we divided each ring into four sub-sectors. For each sub-sector, we counted the number of stars in it and we divided the result by the sector’s area. We adopted as the density value in each ring the average of the values in the four corresponding sub-sectors, while the error was calculated as their standard deviation. The resulting projected density profile, Σ*(r), is shown in the left panel of Fig. 2 (empty circles). The profile shows a central plateau out to ∼3″, followed by a gradually decrease in stellar density as the distance from the centre increases. A centrally flat profile suggests that the cluster is not core-collapsed yet, since a steep power-law cusp in the innermost portion of the density distribution is expected for systems that already experienced this process (see e.g., Meylan & Heggie 1997). In the outer regions (r >  40″), where the LMC field contribution becomes predominant over that of the cluster, a constant density value is observed. From averaging the values of the last 4 bins we derived the LMC mean field density (logΣ* ∼ −0.9; see the horizontal dashed line in Fig. 2). We subtracted this quantity from the density value measured in each bin and we then obtained the background decontaminated profile, which is shown as filled circles in the left panel of the figure.

thumbnail Fig. 2.

Density and brightness profiles of NGC 1835. Left panel: projected density profile of NGC 1835 obtained from star counts in concentric annuli around the cluster centre (empty circles). The horizontal dashed line marks the LMC field density that has been subtracted from the observed points to determine the background subtracted profile (filled circles). The solid red line represents the best-fit King model to the cluster density profile, and the red stripe outlines the range of ±1σ solutions. The vertical lines mark the locations of the core radius (dashed line), half-mass radius (dot-dashed line), and tidal radius (dotted line), with their respective 1σ uncertainties indicated with grey stripes. The values of the main structural parameters determined from the fitting process are also marked (see details in the main text). Right panel: same as in the left panel, but for the surface brightness profile of NGC 1835 in the F606W filter.

4.1. Fit of the density profile

To determine the structural parameters of NGC 1835, we determined the best-fit model to the cluster’s background decontaminated density profile by comparing it with the family of spherical, isotropic, single-mass King models (King 1966). The single-mass assumption works with our observed density profile since it was constructed by selecting a sample of stars of approximately the same mass. We followed the procedure outlined in Raso et al. (2020, see also Pallanca et al. 2023; Deras et al. 2023, 2024). It consists in a Monte Carlo Markov chain (MCMC) fitting technique assuming flat priors for the fitting parameters (namely the central density, the concentration parameter c, and the core radius rc) and a χ2 likelihood. The resulting best-fit model is represented by the red line in the left panel of Fig. 2.

From this procedure we find that NGC 1835 is a cluster characterised by a relatively high concentration parameter ( c = 1 . 47 − 0.14 + 0.15 $ c=1.47^{+0.15}_{-0.14} $, corresponding to a dimensionless central potential W0 = 6.8 ± 0.5), a very compact core radius r c = 3 . 5 − 0.5 + 0.7 $ r_{\mathrm{c}} = 3.5^{+0.7}_{-0.5} $ arcsecs, a half-mass radius r h = 13 − 1 + 3 $ r_{\mathrm{h}} = 13^{+3}_{-1} $ arcsec, and a tidal radius r t = 109 − 18 + 36 $ r_{\mathrm{t}} = 109^{+36}_{-18} $ arcsec. Knowing the LMC distance (49.6 kpc, Pietrzyński et al. 2019) the results can be expressed as rc = 0.84 pc, rh = 3.13 pc, and rt = 26.23 pc (see Table 1). Mackey & Gilmore (2003) had previously determined some of the structural parameters of the cluster by fitting the observed surface brightness profile with an EFF model (Elson et al. 1987). In particular, they find rc = 4.76″, the small difference with respect to our result being likely attributable to the different adopted approaches. The residuals of the fit (see the bottom panel of Fig. 2) show no significant discrepancy from the trend expected from a King model profile in the central regions, further confirming that NGC 1835 is not a core collapse cluster. This is in disagreement with the work of Mackey & Gilmore (2003), where NGC 1835 was classified as a possible core collapse system since a low significance cusp was detected.

Table 1.

Main properties of NGC 1835.

4.2. Surface brightness profile

To obtain further confirmation of the cluster’s structural parameters, we also analysed the surface brightness profile. The procedure is analogous to the one adopted for the density profile (see Sect. 4). Also in this case, we divided the WFC3 field of view into several concentric rings (21 rings from Cgrav up to ∼120″) and each ring into four sub-sectors. We adopted as integrated surface brightness of each ring the average of the four values of the corresponding sub-sectors and we assumed the standard deviation as its uncertainty. The resulting surface brightness profile obtained in the mF606W filter is shown in the right panel of Fig. 2 (open circles). The average surface brightness of the last 3 points provided us with the mean surface brightness of the LMC background (μF606W ∼ 21.5 mag arcsec−2). We subtracted this value from all the observed points, obtaining the background decontaminated profile (solid circles). The fit to the profile was carried out following the same procedure described above, comparing it with the family of King models. The results have provided a King concentration index c = 1.57 ± 0.02, a central surface brightness μF606W, 0 = 15.6 mag arcsec−2, a core radius r c = 3 . 45 − 0.04 + 0.06 arcsec $ r_{\mathrm{c}}=3.45^{+0.06}_{-0.04} \,\mathrm{arcsec} $ (0.83 pc), an half-mass radius r h = 15 − 0.3 + 0.2 arcsec $ r_{\mathrm{h}}= 15^{+0.2}_{-0.3}\,\mathrm{arcsec} $ (3.61 pc), and a tidal radius rt = 137 ± 3 arcsec (32.72 pc). All these quantities are in good agreement within the errors with the results obtained from the fit of the star count density profile. Even in this case, no evidence of central cusp is found.

5. Measuring the dynamical age

This work is mainly devoted to determine the dynamical age of NGC 1835 through the dynamical clock, which measures the level of central sedimentation of BSSs with respect to a lighter reference population, using the A rh + $ A^+_{\mathrm{rh}} $ parameter (Alessandrini et al. 2016). Hence, after estimating the central relaxation time through the standard approximated approach described in Djorgovski (1993), in this section we discuss the necessary preliminary steps and the final determination of A rh + $ A^+_{\mathrm{rh}} $.

5.1. The central relaxation time

Under the assumption of a spherically symmetric and isotropic stellar system well reproduced by a King model, we computed the central relaxation time (trc) of the cluster following Eq. (10) in Djorgovski (1993 see also Spitzer 1987):

t rc = 1.491 × 10 7 × k ln ( 0.4 N ∗ ) m ∗ ρ M , 0 1 / 2 r c 3 , $$ \begin{aligned} t_{\rm rc}=1.491\times 10^7 \times \frac{k}{\ln (0.4N_{*})m_{*}}\rho _{M,0}^{1/2}r_{\rm c}^3, \end{aligned} $$(1)

where the constant k ∼ 0.5592, N* = Mcl/m* is the number of stars in the cluster of mass Mcl, m* = 0.3 M⊙ is the average stellar mass, ρM, 0 is the central mass density in units of M⊙ pc−3, rc is the core radius in parsecs, and trc is expressed in years. We adopted the cluster total mass provided in Mackey & Gilmore (2003) (logM/M⊙ = 5.83 that was estimated by using a mass-to-light ratio M/LV = 3.56) rescaled to M/LV = 2, which is the typical value for 10–13 Gyr old clusters (Maraston 1998). In addition, to keep the work consistent with the assumptions of Ferraro et al. (2019), we measured ρM, 0 from the Eqs. (4), (5), (6) of Djorgovski (1993), adopting the concentration parameter c and the core radius rc determined from the star density profile fit (see Table 1), and the central surface brightness μ555(0)=16.37 quoted in Mackey & Gilmore (2003). The result for NGC 1835 is log(trc/yr)=8.16.

We used this value to obtain a first indication about the dynamical status of the cluster through the parameter Nrelax. This is defined as the ratio between the system’s chronological age and its current central relaxation time, thus quantifying the number of trc experienced by the system during its lifetime. A high value of Nrelax identifies dynamically evolved clusters, whereas a low value corresponds to dynamically young systems. For NGC 1835, using the chronological age by Giusti et al. (2024) (12.5 Gyr) we find Nrelax = 86.9. This is one of the largest value obtained so far in the LMC (see Ferraro et al. 2023), meaning that NGC 1835 is highly dynamically evolved.

5.2. Selection of BSSs and reference population

The first step for estimating the A rh + $ A^+_{\mathrm{rh}} $ parameter of NGC 1835 is to select its population of BSSs and reference stars. In a cluster’s CMD, BSSs are found in the region bluer and brighter than the cluster MS-TO. We followed the selection procedure already described in several works (see Ferraro et al. 1992, 2001, 2003a; Ferraro et al. 2023).

Due to effective temperatures larger than those of MS and RGB stars, BSSs are best selected in CMDs built with blue and possibly UV filters. We therefore drew the BSS selection box in the (mF300X, mF300X − mF814W) UV plane (see the multi-sided polygon shown in the left panel of Fig. 3). We constructed the left side of the polygon by adopting as an approximate reference the cluster zero-age main sequence (ZAMS), represented in the figure by a PARSEC (Marigo et al. 2017) isochrone with a very young age (40 Myr, red dotted line). The top and right-hand sides are designed to exclude the bulk of HB and RGB stars. In general, the location of the bottom side of the box is somehow arbitrary, as there is no clear division between the MS-TO and BSSs. Usually, it is assumed that the BSS population begins 4–5σ magnitudes above the MS-TO, where σ is the photometric error at this magnitude level. However, both to minimise the risk of contamination from MS-TO stars and blends, and to increase the efficiency of the A rh + $ A^+_{\mathrm{rh}} $ parameter, Ferraro et al. (2018) selected only the brightest portion of the BSS sequence, where the most massive BSSs are expected to be located. Thus, they considered only BSSs that are approximately 0.2 M⊙ more massive than MS-TO stars. To construct the stellar evolutionary tracks in the F300X, we downloaded PARSEC isochrones1 (Marigo et al. 2017) in this filter in a very wide age range (500 Myr–21 Gyr) in steps of 10 Myr and with properties compatible with those of NGC 1835: metallicity [Fe/H] = −1.7 and α-element abundance [α/Fe]= + 0.4 (Mucciarelli et al. 2021), and standard helium abundance (Y = 0.248). The track corresponding to the 0.8 M⊙ stars (rightmost solid line in Fig. 3), as expected, reproduces the MS-TO region well. Hence, we adopted as threshold for the bright BSS sample the position of the 1 M⊙ evolutionary track (leftmost solid line in Fig. 3). The final BSS sample is shown by the blue circles in the figure, and it contains 86 objects.

thumbnail Fig. 3.

BSS and RGB samples selection. Left panel: near-UV CMD of NGC 1835, with the selected BSS sample shown with blue circles. The rightmost solid line is the evolutionary track corresponding to a mass of 0.8 M⊙. The leftmost solid line is the evolutionary track of a 1 M⊙ mass. The dotted line is the PARSEC isochrone corresponding to a very young age (40 Myr), representing the cluster ZAMS. Right panel: optical CMD of NGC 1835, with the selected RGB sample shown with red circles.

Since the MS-TO region is contaminated from LMC field stars, we chose the RGB stars as reference population. We selected them in the optical CMD (where they appear more evident and brighter than hot populations) and in a magnitude range similar to that covered by the BSS sample in this plane (see the black box in the right panel of Fig. 3). This avoids both faint magnitudes, to prevent incompleteness problems, and bright magnitudes, to prevent saturation effects. We obtained a very rich final sample of 596 objects. Given the large statistics of this sample, small differences in the selection lead to negligible differences in the value of A rh + $ A^+_{\mathrm{rh}} $ (see below).

5.3. The A rh + $ A^+_{\mathrm{rh}} $ parameter

As mentioned in Sect. 1, the A rh + $ A^+_{\mathrm{rh}} $ parameter is defined as the area enclosed between the normalised cumulative radial distribution of BSSs and that of a reference population of lighter stars, counted within one half-mass radius from the cluster centre. To obtain a meaningful value of A rh + $ A^+_{\mathrm{rh}} $, it is therefore crucial to assess the level of photometric completeness and of field contamination of both population.

To estimate the completeness information, we carried out artificial star experiments using the prescriptions discussed in Dalessandro et al. (2015), Cadelano et al. (2020). We determined the mean ridge lines of the BSS sequence (down to mF300X ∼ 23) and of the RGB+MS population (between mF814W ∼ 17.8 and mF814W ∼ 26) in the (mF606W, mF300X − mF606W) and (mF606W, mF606W − mF814W) CMDs, respectively. We then generated a list of artificial stars with an input mF606W magnitude within the considered range, and assigned to each star the corresponding (mF300X − mF606W) or (mF606W − mF814W) colour according to the respective mean ridge line. These artificial stars have then been added to the acquired images using the DAOPHOT/ADDSTAR software. They have been positioned in a grid of cells with side corresponding to ten times the typical full width at half maximum of the point spread function and, in order to avoid artificial crowding effects, only one star at a time was simulated in each cell. Using the point spread function model already derived, we repeated the data reduction process in the multiple modified images, and we obtained a catalogue of ∼454 000 and ∼208 100 stars for the BSS and the MS+RGB populations, respectively. We simulated the stars only for the WFC3 UVIS1 detector. This choice is dictated by the fact that the A rh + $ A^+_{\mathrm{rh}} $ parameter is determined from the stars located within one half-mass radius, which is just 13″ for NGC 1835 (see Sect. 4). The completeness C is defined as the ratio between the number of stars recovered in output at the end of the artificial star test (No), and the number of input stars actually simulated (Ni). The completeness curves for the three radial bins (r/rh ≤ 1/3, 1/3 <  r/rh ≤ 2/3, 2/3 <  r/rh ≤ 1) that will be used in the calculation of A rh + $ A^+_{\mathrm{rh}} $ (see Sect. 5) are shown in Fig. 4. The left panel shows the completeness curves as a function of the mF300X magnitude in the three radial bins for the simulated BSSs, while the right panel shows C versus mF814W for the simulated MS+RGB population. These results guarantee that the selected BSS and RGB populations, which extend down to mF300X ∼ 22 and mF814W ∼ 20.2, respectively, are poorly affected by incompleteness, both showing C >  80%. Nevertheless, we corrected the two samples by using the derived completeness curves: to build the cumulative radial distributions, each star has been counted as 1/C (instead of 1), with the value of C being derived from the incompleteness curves based on the star magnitude and cluster-centric distance. Thus, the completeness-corrected total numbers of BSSs and RGB stars amount to 93.9 and 623.6 stars, respectively, with a correction of the observed sample of only a few percent (9% and 5%, respectively).

thumbnail Fig. 4.

Completeness curves of the BSS and MS+RGB populations as a function of the mF300X and the mF814W magnitudes, respectively (left and right panels). The different line colours refer to three different radial distances from the cluster centre (see the labels).

To correct for LMC field contamination, we took advantage of the parallel ACS observations. Indeed, the CMD plotted in the rightmost panel of Fig. 1 shows that both the BSS and the RGB regions suffer from a non-negligible contamination from field stars, as expected in the case of a GC located near the central bar of the LMC. The decontamination via proper motions is not possible. In fact, just another HST dataset centred on NGC 1835 is available in the archive, but it has been acquired with the Wide Field and Planetary Camera 2 (WFPC2) in 1995 (Olsen et al. 1998), while higher quality observations and a longer time baseline would be necessary, given the distance of the LMC and the similar motion of the GC and the host galaxy. For this reason, we decided to perform a statistical decontamination exploiting the parallel ACS pointing (e.g., Dalessandro et al. 2019). First of all, since for this dataset only the F606W and F814W filters are available, we transported the BSS selection box (previously defined in the near-UV CMD; see Fig. 3) in the optical (mF814W, mF606W − mF814W) plane. This is shown in panel a of Fig. 5, where the blue circles are the BSSs selected in the near UV, and the box has been drawn to enclose them. Panel b shows the same box superposed to the ACS sample. The selection box of RGB stars was already defined in the optical plane, and it is shown superposed to the cluster WFC3 and the field ACS CMDs in panels c and d of Fig. 5, respectively. We counted the number of field stars falling in the two boxes and we divided the values by the area sampled by the ACS/WFC observations, obtaining the number density of field stars populating the CMD regions covered by the two boxes: ρfield, BSS = 0.0562 ± 0.0012 arcsec−2, ρfield, RGB = 0.0092 ± 0.0005 arcsec−2. Thus, we expect that within one half-mass radius (rh = 13″), a total of 30 LMC stars contaminate the BSS sample, and 5 contaminate the RGB sample. However, the different radial distribution of field stars with respect to that of cluster stars must be taken into account for a proper field decontamination procedure. In fact, while the distribution of the LMC field is essentially uniform over the cluster size scale, the radial distributions of cluster BSSs and RGB stars follow the King profile (see Fig. 2), with a sensibly increasing star density towards the centre of the system. Thus, we divided the field of view included within rh in the same three concentric radial annuli adopted above: r/rh ≤ 1/3, 1/3 <  r/rh ≤ 2/3, and 2/3 <  r/rh ≤ 1. Then, by multiplying the estimated star density by the area of each radial bin (Abin), we determined the number of contaminating field stars expected in the bin: Nfield, pop(r)=ρfield, pop × Abin (with pop=BSS, RGB). The resulting values are listed in Table 2.

thumbnail Fig. 5.

Decontamination process for the BSS and RGB samples. Panel (a): optical CMD for the stars sampled by the WFC3 observations within one half-mass radius from the cluster centre (grey dots). The blue circles mark the position of the BSSs selected using the near-UV box drawn in Fig. 3, and the blue contour enclosing these objects is the adopted BSS selection box in the optical CMD. Panel (b): optical CMD of the stars sampled by the ACS parallel observations (grey dots). The blue contour is the optical selection box defined in panel (a), and the blue circles marks all the stars included within it. Panel (c): optical CMD for the WFC3 stars sampled within one half-mass radius from the cluster centre (grey dots). The RGB selection is marked in black. Panel (d): optical CMD of the ACS stars sampled (grey dots), with the same selection box marked in panel (c). The black circles highlight the stars included within it.

Table 2.

BSS and RGB samples information.

To build the cumulative radial distributions, we randomly subtracted these numbers of stars from the completeness-corrected samples of BSSs and RGB stars, and we obtained the value of A rh + $ A^+_{\mathrm{rh}} $ as the area of the region bounded by the two cumulative functions. We repeated the measurement of A rh + $ A^+_{\mathrm{rh}} $ 100 times, each time randomly removing from the samples a number of stars equal to Nfield, pop(r) in each bin. We then adopted as final estimate of the parameter the average of the 100 values of A rh + $ A^+_{\mathrm{rh}} $ computed in this way, finding ⟨ A rh + $ A^+_{\mathrm{rh}} $⟩=0.30. Once the photometric incompleteness and field contamination are taken into account, the main uncertainty affecting the result is due to the limited statistics of the BSS sample. We therefore evaluated it by using a jackknife bootstrapping technique (see Lupton 1993). Given a sample of N BSSs, it consists in repeating the calculation of A rh + $ A^+_{\mathrm{rh}} $ for N times, each time removing one different star. The final uncertainty is therefore calculated as σ A rh + = σ distr × ( N − 1 ) $ \sigma_{A^+_{\mathrm{rh}}} = \sigma_{\mathrm{distr}} \times \sqrt{(N-1)} $, where σdistr is the standard deviation of the N estimates of the A rh + $ A^+_{\mathrm{rh}} $. We found σA+ = ±0.04. One of the random realisations of the cumulative radial distributions of BSSs (blue curve) and RGB stars (in red) is shown in Fig. 6, where the grey-shaded area represents the A rh + $ A^+_{\mathrm{rh}} $ parameter.

thumbnail Fig. 6.

Normalised cumulative radial distributions of BSSs (solid blue line) and RGB stars (dashed red line) in one of the random realisations used to estimate the A rh + $ A^+_{\mathrm{rh}} $ parameter in NGC 1835. The area enclosed between the two curves corresponds to the value of A rh + $ A^+_{\mathrm{rh}} $ (see the label).

6. Discussion and conclusions

The result obtained for NGC 1835 can now be compared with the outcomes of previous works. Similar studies have been conducted for a total of 52 Galactic GCs (48 systems in Ferraro et al. 2018, NGC 6256 in Cadelano et al. 2022b, and three other clusters in Ferraro et al. 2023), plus a total of seven clusters in the Magellanic Clouds (five old systems in the LMC and two young ones in the SMC; see Ferraro et al. 2019 and Dresbach et al. 2022, respectively). The left panel of Fig. 7 shows the trend between Nrelax (the number of central relaxation times suffered by each system) and the value of A rh + $ A^+_{\mathrm{rh}} $ for all the clusters consistently investigated in previous studies and for NGC 1835 (shown in red). The new determination fits well into, and therefore further reinforces, the close correlation observed between the two parameters.

thumbnail Fig. 7.

Final results for NGC 1835 in comparison with other clusters. Left panel: relation between Nrelax and A rh + $ A^+_{\mathrm{rh}} $ for the star clusters homogeneously investigated so far through the dynamical clock approach: the 52 Galactic GCs discussed in Ferraro et al. (2023) are shown as grey circles, the five LMC clusters discussed in Ferraro et al. (2019) are plotted as yellow squares, the two young star clusters in the SMC discussed in Dresbach et al. (2022) are marked as yellow diamonds, and the determination of NGC 1835 obtained in this work is plotted as a filled red square. Right panel: relation between rc and A rh + $ A^+_{\mathrm{rh}} $ for the same star clusters plotted in the left panel (same symbols).

It is interesting to point out that the MW, LMC, and SMC clusters all fall along the same relationship, indicating that the dynamical clock parameter can also provide a measure of a cluster’s dynamical ages outside the MW. As previously discussed, the existence of such a strong correlation between A rh + $ A^+_{\mathrm{rh}} $ and Nrelax clearly shows that they both trace the dynamical ageing of star clusters. However, Ferraro et al. (2023) point out that A rh + $ A^+_{\mathrm{rh}} $ provides a better measure of the dynamical history and dynamical age of a cluster than Nrelax. As discussed in Ferraro et al. (2023), trc is a parameter determined by the present-day dynamical properties of star clusters, which can be the result of quite different combinations of initial conditions and evolutionary paths. Hence, trc is not necessarily representative of a specific and unique dynamical history of each stellar system. Conversely, the current level of the BSS central concentration is the direct outcome of the many internal and external phenomena that, over the entire cluster lifetime, have shaped the mass segregation process. Thus, the main advantages of the A rh + $ A^+_{\mathrm{rh}} $ parameter with respect to trc can be summarised as follows: (i) the A rh + $ A^+_{\mathrm{rh}} $ parameter is entirely and directly measured from observations; (ii) it is specifically designed to have maximum sensitivity in quantifying the mass segregation of the heaviest and brightest (hence, easily identifiable) stellar population (the BSSs); and (iii) at odds with trc, its definition does not require oversimplified assumptions (e.g., spherical symmetry, no rotation, or King model structure) or approximations (for instance, the definition of rc, which is very uncertain, in particular in dynamically evolved stellar systems where the presence of a central cusp makes the definition more complicated and possibly meaningless).

In addition, the value of A rh + $ A^+_{\mathrm{rh}} $ seems to be a very promising discriminator between non-core-collapsed and core-collapsed clusters. In fact, Ferraro et al. (2023) show that seven Galactic GCs with measured A rh + $ A^+_{\mathrm{rh}} $ and classified as post-core-collapsed clusters based on evidence of a central cusp in their density profile all exhibit A rh + $ A^+_{\mathrm{rh}} $ >  0.29. In this respect, NGC 1835 (for which we estimate A rh + $ A^+_{\mathrm{rh}} $ = 0.30 ± 0.04) is likely on the verge of core collapse.

The right panel of Fig. 7 shows the relationship between A rh + $ A^+_{\mathrm{rh}} $ and the core radius for the same systems. As already discussed in Ferraro et al. (2019), it shows that clusters with a larger core radius correspond to dynamically younger systems characterised by low degrees of spatial segregation of their most massive visible stars (corresponding to lower A rh + $ A^+_{\mathrm{rh}} $ values), while those with a smaller core radius are in more advanced dynamical stages with a stronger degree of mass segregation. NGC 1835 falls nicely along this anti-correlation, showing the highest value of A rh + $ A^+_{\mathrm{rh}} $ in the LMC (hence, the most advanced dynamical age), consistent with its very small core radius. So, while Mackey et al. (2008) proposed resolving the size–age conundrum by taking into account the action of binary black holes that progressively drive the core expansion of the systems, the range of cluster core radii may simply be a consequence of differences in the clusters’ dynamical ages. Furthermore, as discussed by Ferraro et al. (2019), young and old clusters exhibit very different masses (older clusters are more massive than younger ones) and distances from the LMC centre, thus ruling out the existence of a simple and direct evolutionary sequence linking the two groups of clusters.

Finally, we point out that the young clusters in the LMC are low-mass systems with small core radii and located in the most central regions of the galaxy (see the middle and bottom panels of Fig. 1 in Ferraro et al. 2019). The lack of young clusters with large core radii may be due to the early disruption of these clusters; as proposed by Ferraro et al. (2019), it is plausible that, in this low-mass regime, only the most compact clusters managed to endure the tidal forces exerted by the host galaxy and survived to the present day, while the low mass and low-concentration systems have been disrupted.

In conclusion, this study of the structure of NGC 1835 and the degree of segregation of its BSS builds on previous investigations by (i) adding information about a dynamically old cluster characterised by a significant BSS spatial segregation and (ii) bridging the gap between the dynamical characterisation of clusters in the MW and the Magellanic Clouds.

Acknowledgments

This work is part of the project Cosmic-Lab at the Physics and Astronomy Department “A. Righi” of the Bologna University (http://www.cosmic-lab.eu/Cosmic-Lab/Home.html).

References

  1. Alessandrini, E., Lanzoni, B., Ferraro, F. R., et al. 2016, ApJ, 833, 252 [NASA ADS] [CrossRef] [Google Scholar]
  2. Bekki, K., Couch, W. J., Beasley, M. A., et al. 2004, ApJ, 610, L93 [NASA ADS] [CrossRef] [Google Scholar]
  3. Bellini, A., Anderson, J., & Bedin, L. R. 2011, PASP, 123, 622 [CrossRef] [Google Scholar]
  4. Bica, E., Bonatto, C., Dutra, C. M., et al. 2008, MNRAS, 389, 678 [NASA ADS] [CrossRef] [Google Scholar]
  5. Baumgardt, H., Parmentier, G., Anders, P., et al. 2013, MNRAS, 430, 676 [NASA ADS] [CrossRef] [Google Scholar]
  6. Bailyn, C. D. 1995, ARA&A, 33, 133 [NASA ADS] [CrossRef] [Google Scholar]
  7. Beccari, G., Cadelano, M., & Dalessandro, E. 2023, A&A, 670, A11 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  8. Brocato, E., Castellani, V., Ferraro, F. R., et al. 1996, MNRAS, 282, 614 [NASA ADS] [CrossRef] [Google Scholar]
  9. Cadelano, M., Dalessandro, E., Webb, J. J., et al. 2020, MNRAS, 499, 2390 [NASA ADS] [CrossRef] [Google Scholar]
  10. Cadelano, M., Dalessandro, E., Salaris, M., et al. 2022a, ApJ, 924, L2 [NASA ADS] [CrossRef] [Google Scholar]
  11. Cadelano, M., Ferraro, F. R., Dalessandro, E., et al. 2022b, ApJ, 941, 69 [CrossRef] [Google Scholar]
  12. Chen, J., Ferraro, F. R., Cadelano, M., et al. 2021, Nat. Astron., 5, 1170 [NASA ADS] [CrossRef] [Google Scholar]
  13. Chen, J., Ferraro, F. R., Cadelano, M., et al. 2022, ApJ, 934, 93 [NASA ADS] [CrossRef] [Google Scholar]
  14. Chen, J., Ferraro, F. R., Salaris, M., et al. 2023, ApJ, 950, 155 [CrossRef] [Google Scholar]
  15. Da Costa, G. S. 1991, The Magellanic Clouds, 148, 183 [CrossRef] [Google Scholar]
  16. Dalessandro, E., Salaris, M., Ferraro, F. R., et al. 2013, MNRAS, 430, 459 [NASA ADS] [CrossRef] [Google Scholar]
  17. Dalessandro, E., Ferraro, F. R., Massari, D., et al. 2015, ApJ, 810, 40 [NASA ADS] [CrossRef] [Google Scholar]
  18. Dalessandro, E., Ferraro, F. R., Bastian, N., et al. 2019, A&A, 621, A45 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  19. Deras, D., Cadelano, M., Ferraro, F. R., et al. 2023, ApJ, 942, 104 [CrossRef] [Google Scholar]
  20. Deras, D., Cadelano, M., Lanzoni, B., et al. 2024, A&A, 681, A38 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  21. Djorgovski, S. 1993, Struct. Dyn. Glob. Clust., 50, 373 [NASA ADS] [Google Scholar]
  22. Dresbach, F., Massari, D., Lanzoni, B., et al. 2022, ApJ, 928, 47 [NASA ADS] [CrossRef] [Google Scholar]
  23. Elson, R. A. W. 1991, ApJS, 76, 185 [NASA ADS] [CrossRef] [Google Scholar]
  24. Elson, R. A. W., Fall, S. M., & Freeman, K. C. 1987, ApJ, 323, 54 [Google Scholar]
  25. Elson, R. A. W., Freeman, K. C., & Lauer, T. R. 1989, ApJ, 347, L69 [NASA ADS] [CrossRef] [Google Scholar]
  26. Ferraro, F. R., Fusi Pecci, F., & Buonanno, R. 1992, MNRAS, 256, 376 [NASA ADS] [CrossRef] [Google Scholar]
  27. Ferraro, F. R., Fusi Pecci, F., Testa, V., et al. 1995, MNRAS, 272, 391 [NASA ADS] [CrossRef] [Google Scholar]
  28. Ferraro, F. R., Paltrinieri, B., Fusi Pecci, F., et al. 1997, A&A, 324, 915 [NASA ADS] [Google Scholar]
  29. Ferraro, F. R., Paltrinieri, B., Fusi Pecci, F., et al. 1998, ApJ, 500, 311 [NASA ADS] [CrossRef] [Google Scholar]
  30. Ferraro, F. R., Paltrinieri, B., Rood, R. T., et al. 1999, ApJ, 522, 983 [CrossRef] [Google Scholar]
  31. Ferraro, F. R., D’Amico, N., Possenti, A., et al. 2001, ApJ, 561, 337 [NASA ADS] [CrossRef] [Google Scholar]
  32. Ferraro, F. R., Sills, A., Rood, R. T., et al. 2003a, ApJ, 588, 464 [NASA ADS] [CrossRef] [Google Scholar]
  33. Ferraro, F. R., Possenti, A., Sabbi, E., et al. 2003b, ApJ, 596, L211 [NASA ADS] [CrossRef] [Google Scholar]
  34. Ferraro, F. R., Origlia, L., Testa, V., et al. 2004, ApJ, 608, 772 [NASA ADS] [CrossRef] [Google Scholar]
  35. Ferraro, F. R., Lanzoni, B., Dalessandro, E., et al. 2012, Nature, 492, 393 [Google Scholar]
  36. Ferraro, F. R., Lanzoni, B., Raso, S., et al. 2018, ApJ, 860, 36 [NASA ADS] [CrossRef] [Google Scholar]
  37. Ferraro, F. R., Lanzoni, B., Dalessandro, E., et al. 2019, Nat. Astron., 3, 1149 [NASA ADS] [CrossRef] [Google Scholar]
  38. Ferraro, F. R., Lanzoni, B., & Dalessandro, E. 2020, Rendiconti Lincei. Scienze Fisiche e Naturali, 31, 19 [NASA ADS] [CrossRef] [Google Scholar]
  39. Ferraro, F. R., Lanzoni, B., Vesperini, E., et al. 2023, ApJ, 950, 145 [NASA ADS] [CrossRef] [Google Scholar]
  40. Fiorentino, G., Lanzoni, B., Dalessandro, E., et al. 2014, ApJ, 783, 34 [NASA ADS] [CrossRef] [Google Scholar]
  41. Gaia Collaboration (Vallenari, A., et al.) 2023, A&A, 674, A1 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  42. Giusti, C., Cadelano, M., Ferraro, F. R., et al. 2023, ApJ, 953, 125 [CrossRef] [Google Scholar]
  43. Giusti, C., Cadelano, M., Ferraro, F. R., et al. 2024, A&A, 686, A6 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  44. Heggie, D., & Hut, P. 2003, The Gravitational Million-Body Problem: A Multidisciplinary Approach to Star Cluster Dynamics (Cambridge: Cambridge University Press), 372 [Google Scholar]
  45. Hills, J. G., & Day, C. A. 1976, Astrophys. Lett., 17, 87 [NASA ADS] [Google Scholar]
  46. Ibata, R., Bellazzini, M., Chapman, S. C., et al. 2009, ApJ, 699, L169 [NASA ADS] [CrossRef] [Google Scholar]
  47. King, I. R. 1966, AJ, 71, 64 [Google Scholar]
  48. Lanzoni, B., Dalessandro, E., Ferraro, F. R., et al. 2007, ApJ, 668, L139 [NASA ADS] [CrossRef] [Google Scholar]
  49. Lanzoni, B., Ferraro, F. R., Alessandrini, E., et al. 2016, ApJ, 833, L29 [NASA ADS] [CrossRef] [Google Scholar]
  50. Lanzoni, B., Ferraro, F. R., Dalessandro, E., et al. 2019, ApJ, 887, 176 [NASA ADS] [CrossRef] [Google Scholar]
  51. Lupton, R. 1993, Statistics in Theory and Practice (Pinceton: Princeton University Press) [Google Scholar]
  52. Mackey, A. D., & Gilmore, G. F. 2003, MNRAS, 338, 85 [Google Scholar]
  53. Mackey, A. D., Wilkinson, M. I., Davies, M. B., et al. 2008, MNRAS, 386, 65 [NASA ADS] [CrossRef] [Google Scholar]
  54. Maraston, C. 1998, MNRAS, 300, 872 [NASA ADS] [CrossRef] [Google Scholar]
  55. Marigo, P., Girardi, L., Bressan, A., et al. 2017, ApJ, 835, 77 [Google Scholar]
  56. Mazzi, A., Girardi, L., Zaggia, S., et al. 2021, MNRAS, 508, 245 [NASA ADS] [CrossRef] [Google Scholar]
  57. McCrea, W. H. 1964, MNRAS, 128, 147 [Google Scholar]
  58. Meylan, G., & Heggie, D. C. 1997, A&A Rev., 8, 1 [NASA ADS] [CrossRef] [Google Scholar]
  59. Meurer, G. R., Lindler, D. J., Blakeslee, J., et al. 2003, Proc. SPIE, 4854, 507 [NASA ADS] [CrossRef] [Google Scholar]
  60. Miocchi, P., Lanzoni, B., Ferraro, F. R., et al. 2013, ApJ, 774, 151 [Google Scholar]
  61. Montegriffo, P., Ferraro, F. R., Fusi Pecci, F., et al. 1995, MNRAS, 276, 739 [NASA ADS] [CrossRef] [Google Scholar]
  62. Mucciarelli, A., Origlia, L., Ferraro, F. R., et al. 2006, ApJ, 646, 939 [NASA ADS] [CrossRef] [Google Scholar]
  63. Mucciarelli, A., Massari, D., Minelli, A., et al. 2021, Nat. Astron., 5, 1247 [NASA ADS] [CrossRef] [Google Scholar]
  64. Nayak, P. K., Subramaniam, A., Choudhury, S., et al. 2016, MNRAS, 463, 1446 [NASA ADS] [CrossRef] [Google Scholar]
  65. Olsen, K. A. G., Hodge, P. W., Mateo, M., et al. 1998, MNRAS, 300, 665 [NASA ADS] [CrossRef] [Google Scholar]
  66. Olszewski, E. W., Suntzeff, N. B., & Mateo, M. 1996, ARA&A, 34, 511 [NASA ADS] [CrossRef] [Google Scholar]
  67. Onorato, S., Cadelano, M., Dalessandro, E., et al. 2023, A&A, 677, A8 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  68. Pallanca, C., Leanza, S., Ferraro, F. R., et al. 2023, ApJ, 950, 138 [NASA ADS] [CrossRef] [Google Scholar]
  69. Paresce, F., de Marchi, G., & Ferraro, F. R. 1992, Nature, 360, 46 [NASA ADS] [CrossRef] [Google Scholar]
  70. Pietrzyński, G., Graczyk, D., Gallenne, A., et al. 2019, Nature, 567, 200 [Google Scholar]
  71. Raso, S., Ferraro, F. R., Dalessandro, E., et al. 2017, ApJ, 839, 64 [NASA ADS] [CrossRef] [Google Scholar]
  72. Raso, S., Pallanca, C., Ferraro, F. R., et al. 2019, ApJ, 879, 56 [NASA ADS] [CrossRef] [Google Scholar]
  73. Raso, S., Libralato, M., Bellini, A., et al. 2020, ApJ, 895, 15 [NASA ADS] [CrossRef] [Google Scholar]
  74. Rich, R. M., Shara, M. M., & Zurek, D. 2001, AJ, 122, 842 [Google Scholar]
  75. Spitzer, L. 1987, Dynamical Evolution of Globular Clusters (Princeton: Princeton University Press) [Google Scholar]

All Tables

Table 1.

Main properties of NGC 1835.

In the text
Table 2.

BSS and RGB samples information.

In the text

All Figures

thumbnail Fig. 1.

CMDs of the cluster region and the field region in different filter combinations. Left panel: near-UV CMD of NGC 1835 for the stars sampled within r <  13″ from the centre. Central panel: optical CMD of NGC 1835 for the same stars as in the left panel. Right panel: optical CMD of the LMC field region sampled by the ACS parallel observations.
In the text
thumbnail Fig. 2.

Density and brightness profiles of NGC 1835. Left panel: projected density profile of NGC 1835 obtained from star counts in concentric annuli around the cluster centre (empty circles). The horizontal dashed line marks the LMC field density that has been subtracted from the observed points to determine the background subtracted profile (filled circles). The solid red line represents the best-fit King model to the cluster density profile, and the red stripe outlines the range of ±1σ solutions. The vertical lines mark the locations of the core radius (dashed line), half-mass radius (dot-dashed line), and tidal radius (dotted line), with their respective 1σ uncertainties indicated with grey stripes. The values of the main structural parameters determined from the fitting process are also marked (see details in the main text). Right panel: same as in the left panel, but for the surface brightness profile of NGC 1835 in the F606W filter.
In the text
thumbnail Fig. 3.

BSS and RGB samples selection. Left panel: near-UV CMD of NGC 1835, with the selected BSS sample shown with blue circles. The rightmost solid line is the evolutionary track corresponding to a mass of 0.8 M⊙. The leftmost solid line is the evolutionary track of a 1 M⊙ mass. The dotted line is the PARSEC isochrone corresponding to a very young age (40 Myr), representing the cluster ZAMS. Right panel: optical CMD of NGC 1835, with the selected RGB sample shown with red circles.
In the text
thumbnail Fig. 4.

Completeness curves of the BSS and MS+RGB populations as a function of the mF300X and the mF814W magnitudes, respectively (left and right panels). The different line colours refer to three different radial distances from the cluster centre (see the labels).
In the text
thumbnail Fig. 5.

Decontamination process for the BSS and RGB samples. Panel (a): optical CMD for the stars sampled by the WFC3 observations within one half-mass radius from the cluster centre (grey dots). The blue circles mark the position of the BSSs selected using the near-UV box drawn in Fig. 3, and the blue contour enclosing these objects is the adopted BSS selection box in the optical CMD. Panel (b): optical CMD of the stars sampled by the ACS parallel observations (grey dots). The blue contour is the optical selection box defined in panel (a), and the blue circles marks all the stars included within it. Panel (c): optical CMD for the WFC3 stars sampled within one half-mass radius from the cluster centre (grey dots). The RGB selection is marked in black. Panel (d): optical CMD of the ACS stars sampled (grey dots), with the same selection box marked in panel (c). The black circles highlight the stars included within it.
In the text
thumbnail Fig. 6.

Normalised cumulative radial distributions of BSSs (solid blue line) and RGB stars (dashed red line) in one of the random realisations used to estimate the A rh + $ A^+_{\mathrm{rh}} $ parameter in NGC 1835. The area enclosed between the two curves corresponds to the value of A rh + $ A^+_{\mathrm{rh}} $ (see the label).
In the text
thumbnail Fig. 7.

Final results for NGC 1835 in comparison with other clusters. Left panel: relation between Nrelax and A rh + $ A^+_{\mathrm{rh}} $ for the star clusters homogeneously investigated so far through the dynamical clock approach: the 52 Galactic GCs discussed in Ferraro et al. (2023) are shown as grey circles, the five LMC clusters discussed in Ferraro et al. (2019) are plotted as yellow squares, the two young star clusters in the SMC discussed in Dresbach et al. (2022) are marked as yellow diamonds, and the determination of NGC 1835 obtained in this work is plotted as a filled red square. Right panel: relation between rc and A rh + $ A^+_{\mathrm{rh}} $ for the same star clusters plotted in the left panel (same symbols).
In the text

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.