Ages Of Globular Clusters Research Articles

Galaxy archaeology for wet mergers: Globular cluster age distributions in the Milky Way and nearby galaxies

Context. Identifying past wet merger activity in galaxies has been a longstanding issue in extragalactic formation history studies. Gaia’s 6D kinematic measurements in our Milky Way (MW) have vastly extended the possibilities for Galactic archaeology, leading to the discovery of a multitude of early mergers in the MW’s past. As recent work has established a link between younger globular clusters (GCs; less than about 10–11 Gyr old) and wet galaxy merger events, the MW provides an ideal laboratory for testing which GC properties can be used to trace extragalactic galaxy formation histories. Aims. To test the hypothesis that GCs trace wet mergers, we relate the measured GC age distributions of the MW and three nearby galaxies, M 31, NGC 1407, and NGC 3115, to their merger histories and interpret the connection with wet mergers through an empirical model for GC formation. Methods. The GC ages of observed galaxies are taken from a variety of studies to analyze their age distributions side-by-side with the model. For the MW, we additionally cross-match the GCs with their associated progenitor host galaxies to disentangle the connection to the GC age distribution. For the modeled GCs, we take galaxies with similar GC age distributions as observed to compare their accretion histories with those inferred through observations. Results. We find that the MW GC age distribution is bimodal, mainly caused by younger GCs (10–11 Gyr old associated with Gaia-Sausage/Enceladus (GSE) and in part by unassociated high-energy GCs. The GSE GC age distribution also appears to be bimodal. We propose that the older GSE GCs (12–13 Gyr old) were accreted together with GSE, while the younger ones formed as a result of the merger. For the nearby galaxies, we find that clear peaks in the GC age distributions coincide with active early gas-rich merger phases. Even small signatures in the GC age distributions agree well with the expected wet formation histories of the galaxies inferred through other observed tracers. From the models, we predict that the involved cold gas mass can be estimated from the number of GCs found in the formation burst. Conclusions. Multimodal GC age distributions can trace massive wet mergers as a result of GCs being formed through them. From the laboratory of our own MW and nearby galaxies we conclude that the ages of younger GC populations of galaxies can be used to infer the wet merger history of a galaxy.

Measuring M31 globular cluster ages and metallicities using both photometry and spectroscopy

ABSTRACT The ages and metallicities of globular clusters play an important role not just in testing models for their formation and evolution but also in understanding the assembly history of their host galaxies. Here, we use a combination of imaging and spectroscopy to measure the ages and metallicities of globular clusters in M31, the closest massive galaxy to our own. We use the strength of the near-infrared calcium triplet spectral feature to provide a relatively age-insensitive prior on the metallicity when fitting stellar population models to the observed photometry. While the age–extinction degeneracy is an issue for globular clusters projected on to the disc of M31, we find generally old ages for globular clusters in the halo of M31 and in its satellite galaxy NGC 205 in line with previous studies. We measure ages for a number of outer halo globular clusters for the first time, finding that globular clusters associated with halo substructure extend to younger ages and higher metallicities than those associated with the smooth halo. This is in line with the expectation that the smooth halo was accreted earlier than the substructured halo.

Radiative capture of proton through the 14N(p,γ)15O reaction at low energy

The CNO cycle is the main source of energy in stars more massive than our Sun. This process defines the energy production, the duration of which can be used to determine the lifetime of massive stars. The cycle is an important tool for determining the age of globular clusters. Radiative proton capture via , at energies of astrophysical interest, is an important process in the CNO cycle. In this project, we apply a potential model to describe both non-resonant and resonant reactions in the channels where radiative capture occurs through electric transitions. We employed the R-matrix method to describe the ongoing reactions via resonant transitions, when it was not possible to correctly reproduce the experimental data using the potential model. The partial components of the astrophysical S-factor are calculated for all possible electric and magnetic dipole transitions in 15O. The linear extrapolated S-factor at zero energy (S(0)) agrees well with earlier reported values for all transition types considered in this work. Based on the value of the total astrophysical S-factor, depending on the collision energy, we calculate the nuclear reaction rates for . The computed rates agree well with the results reported in the NACRE II Collaboration and most recent existing measurements.

Determination of dynamical ages of open clusters through the A+ parameter – II

ABSTRACT Blue straggler stars (BSS), one of the most massive members of star clusters, have been used for over a decade to investigate mass segregation and estimate the dynamical ages of globular clusters (GCs) and open clusters (OCs). This work is an extension of our previous study, in which we investigated a correlation between theoretically estimated dynamical ages and the observed $A^+_{\mathrm{rh}}$ values, which represent the sedimentation level of BSS with respect to the reference population. Here, we use the ML-MOC algorithm on Gaia EDR3 data to extend this analysis to 23 OCs. Using cluster properties and identified members, we estimate their dynamical and physical parameters. In order to estimate the $A^+_{\mathrm{rh}}$ values, we use the main sequence and main sequence turnoff stars as the reference population. OCs are observed to exhibit a wide range of degrees of dynamical evolution, ranging from dynamically young to late stages of intermediate dynamical age. Hence, we classify OCs into three distinct dynamical stages based on their relationship to $A^+_{\mathrm{rh}}$ and Nrelax. NGC 2682 and King 2 are discovered to be the most evolved OCs, like Family III GCs, while Berkeley 18 is the least evolved OC. Melotte 66 and Berkeley 31 are peculiar OCs because none of their dynamical and physical parameters correlate with their BSS segregation levels.

Constraining Co-Varying Coupling Constants from Globular Cluster Age

Equations governing the evolution of a star involve multiple coupling constants. Thus, the time it spends as a main-sequence star can be expected to depend on whether or not such constants vary over the time scale of stellar evolution. When the star belongs to a globular cluster, the star’s age cannot exceed that of the globular cluster, and the latter cannot exceed the age of the Universe. This fact can be used to constrain or verify the variation of the coupling constants, i.e., the speed of light c, the gravitational constant G, the Planck constant h, and the Boltzmann constant k. We have estimated the age of the main-sequence star analytically from the time it takes to synthesize all its hydrogen into helium under fixed and varying coupling constants scenarios. When we permitted the interrelated variation of the four constants (G~c3~h3~k3/2) and differentiated between the cosmological energy and local energy conservation laws, we could show that the variation of the constants established in our earlier studies, i.e., G˙/G=3c˙/c=3h˙/h=1.5k˙/k=3.90±0.04×10−10 yr−1 at the current cosmic time is consistent with the present work. Nevertheless, the challenge remains to come up with an experiment, astrometric or terrestrial, that can unequivocally prove or falsify the predicted variation.

Testing feedback from star clusters in simulations of the Milky Way formation

ABSTRACT We present a suite of galaxy formation simulations that directly model star cluster formation and disruption. Starting from a model previously developed by our group, here we introduce several improvements to the prescriptions for cluster formation and feedback, then test these updates using a large suite of cosmological simulations of Milky Way mass galaxies. We perform a differential analysis with the goal of understanding how each of the updates affects star cluster populations. Two key parameters are the momentum boost of supernova feedback fboost and star formation efficiency per free-fall time ϵff. We find that fboost has a strong influence on the galactic star formation rate, with higher values leading to less star formation. The efficiency ϵff does not have a significant impact on the global star formation rate, but dramatically changes cluster properties, with increasing ϵff leading to a higher maximum cluster mass, shorter age spread of stars within clusters, and higher integrated star formation efficiencies. We also explore the redshift evolution of the observable cluster mass function, finding that most massive clusters have formed at high redshift z > 4. Extrapolation of cluster disruption to z = 0 produces good agreement with both the Galactic globular cluster mass function and age–metallicity relation. Our results emphasize the importance of using small-scale properties of galaxies to calibrate subgrid models of star cluster formation and feedback.

Orbit of Galactic Globular Cluster of NGC 7089, NGC 7099, NGC 1851, Pal 1, and Pal 2 Around the Milky Way Galaxy Constructed from the Gaia EDR3

We report that we estimated the mean proper motion, the full space velocity of five Globular clusters, Pal 1, Pal2, NGC 1815, NGC 7089, and NGC 7099, using Gaia Early Data Release 3 (Gaia EDR3). We focus on these five clusters to measure proper motion, internal dispersion, and dynamical properties. Also, we have integrated the orbits using the potential of MWPotential2014 for five backyards Gyr. We have derived energy, angular momentum, and orbital properties for each cluster. In addition, we find that there are four metal-poor GCs with metallicity less than -1.1 dex and only one metal-rich GCs with metallicity greater than -1.0 dex. We estimate the distance modulus of these five globular clusters and examine isochrone fitting to the color-magnitude diagram from the PAdova and TRieste Stellar Evolution Code (PARSEC). Among five globular clusters, we have found that the NGC 7099 is the oldest globular cluster age of ∼ 13 Gyr with metallicity ([Fe/H]) of 2.19, whereas the youngest globular cluster we find in our sample is Pal 1 with metallicity ([Fe/H]) of -0.65 and age of ∼ 8 Gyr.

Globular Cluster Candidates in the Sagittarius Dwarf Galaxy

Abstract Recently, new Sagittarius (Sgr) dwarf-galaxy globular clusters were discovered, which opens the question of the actual size of the Sgr globular cluster population, and therefore on our understanding of the Sgr galaxy formation and accretion history of the Milky Way. Based on Gaia EDR3 and SDSS IV DR16 (APOGEE-2) data sets, we performed an analysis of the color–magnitude diagrams (CMDs) of the eight new Sgr globular clusters found by Minniti et al. from a sound cleaning of the contamination of Milky Way and Sgr field stars, complemented by available kinematic and metal abundance information. The cleaned CMDs and spatial stellar distibutions reveal the presence of stars with a wide range of cluster membership probabilities. Minni 332 turned out to be a younger (<9 Gyr) and more metal-rich ([M/H] ≳ −1.0 dex) globular cluster than M54, the nuclear Sgr globular cluster; as could also be the case of Minni 342, 348, and 349, although their results are less convincing. Minni 341 could be an open cluster candidate (age < 1 Gyr, [M/H] ∼ −0.3 dex), while the analyses of Minni 335, 343, and 344 did not allow us to confirm their physical reality. We also built the Sgr cluster frequency (CF) using available ages of the Sgr globular clusters and compared it with that obtained from the Sgr star formation history. Both CFs are in excellent agreement. However, the addition of eight new globular clusters with ages and metallicities distributed according to the Sgr age–metallicity relationship turns out in a remarkably different CF.

Lifetime measurements of excited states in O15

The CNO cycle is the main energy source in stars more massive than our sun, it defines the energy production and the cycle time that lead to the lifetime of massive stars, and it is an important tool for the determination of the age of globular clusters. One of the largest uncertainties in the CNO chain of reactions comes from the uncertainty in the $^{14}$N$(p,\gamma)^{15}$O reaction rate. This uncertainty arises predominantly from the uncertainty in the lifetime of the sub-threshold state in $^{15}$O at $E_{x}$ = 6792 keV. Previous measurements of this state's lifetime are significantly discrepant. Here, we report on a new lifetime measurement of this state, as well as the excited states in $^{15}$O at $E_{x}$ = 5181 keV and $E_{x}$ = 6172 keV, via the $^{14}$N$(p,\gamma)^{15}$O reaction at proton energies of $E_{p} = 1020$ keV and $E_{p} = 1570$ keV. The lifetimes have been determined with the Doppler-Shift Attenuation Method (DSAM) with three separate, nitrogen-implanted targets with Mo, Ta, and W backing. We obtained lifetimes from the weighted average of the three measurements, allowing us to account for systematic differences between the backing materials. For the 6792 keV state, we obtained a $\tau = 0.6 \pm 0.4$ fs. To provide cross-validation of our method, we measured the known lifetimes of the states at 5181 keV and 6172 keV to be $\tau = 7.5 \pm 3.0$ and $\tau = 0.7 \pm 0.5$ fs, respectively, which are in good agreement with previous measurements.

Predicting images for the dynamics of stellar clusters (π-DOC): a deep learning framework to predict mass, distance, and age of globular clusters

ABSTRACT Dynamical mass estimates of simple systems such as globular clusters (GCs) still suffer from up to a factor of 2 uncertainty. This is primarily due to the oversimplifications of standard dynamical models that often neglect the effects of the long-term evolution of GCs. Here, we introduce a new approach to measure the dynamical properties of GCs, based on the combination of a deep-learning framework and the large amount of data from direct N-body simulations. Our algorithm, π-DOC (Predicting Images for the Dynamics Of stellar Clusters) is composed of two convolutional networks, trained to learn the non-trivial transformation between an observed GC luminosity map and its associated mass distribution, age, and distance. The training set is made of V-band luminosity and mass maps constructed as mock observations from N-body simulations. The tests on π-DOC demonstrate that we can predict the mass distribution with a mean error per pixel of 27 per cent, and the age and distance with an accuracy of 1.5 Gyr and 6 kpc, respectively. In turn, we recover the shape of the mass-to-light profile and its global value with a mean error of 12 per cent, which implies that we efficiently trace mass segregation. A preliminary comparison with observations indicates that our algorithm is able to predict the dynamical properties of GCs within the limits of the training set. These encouraging results demonstrate that our deep-learning framework and its forward modelling approach can offer a rapid and adaptable tool competitive with standard dynamical models.

Inferring the age of the universe with globular clusters

We present an estimate of the absolute age of 68 galactic globular clusters obtained by exploiting the distribution of stars in the full color-magnitude diagram. In particular, we jointly estimate the absolute age, distance, reddening, metallicity ([Fe/H]) and [α/Fe] of each cluster, imposing priors motivated by independent observations; we also estimate possible systematics from stellar modeling. Our derived distances for the globular cluster sample are in agreement with those obtained from GAIA using main-sequence dwarf stars (where available), and the inferred ages are in good agreement with those previously published. The novelty of our approach is that, with the adopted priors, we are able to estimate robustly these parameters from the globular cluster color-magnitude diagram. We find that the average age of the oldest globular clusters is tGC=13.32 0.1 (stat.) 0.5 (sys.), at 68% confidence level, including systematic uncertainties from stellar modeling. These measurements can be used to infer the age of the Universe, largely independently of the cosmological parameters: we find an age of the Universe tU=13.5+0.16−0.14 (stat.) 0.5 (sys.) at 68% confidence level, accounting for the formation time of globular clusters and its uncertainty. This value is compatible with 13.8 0.02 Gyr, the cosmological model-dependent value inferred by the Planck mission assuming the ΛCDM model.

Searching for RR Lyrae Stars by Imbalanced Learning

As standard candles, RR Lyrae stars are taken as distance markers and age indicators, which is helpful to estimate the distance and age of globular clusters as well as galactic and extragalactic (Local Group) locations. At the same time, as tracers, they reveal the structure, chemical and dynamic evolution of the galaxy, as well as the substructure of the halo. However, the number of RR stars is very small compared with other types of stars in nature. With the development and operation of large-scale sky survey projects, they have made a qualitative leap in number. Compared with other types of stars, RR Lyrae stars are still not enough in number. Therefore, separating RR Lyrae stars from stars belongs to an imbalanced learning problem. It may be solved by popular imbalanced learning methods.

Strömgren metallicities for intermediate-age and old star clusters

We report results that show that the straightforward star cluster metallicities obtained from Strömgren vby photometry are age-dependent and need to be corrected for further use. This outcome arises from the comparison of [Fe/H] values derived from Strömgren photometry with those metallicities published in the literature for 26 Large and Small Magellanic Cloud star clusters, whose ages range from ∼1 Gyr up to the oldest-known globular cluster ages in these galaxies. While deriving mean star cluster metallicities, we carried out a thorough selection of red giant branch candidates to comply with the Strömgren metallicity calibration validity regime. We paid attention to the effect of contamination by field stars, particularly those that lie inside the star clusters’ radii, that are distributed along the star cluster red giant branches and that have [Fe/H] values covering a similar range as that for the selected stars. We find that the measured Strömgren metallicities are systematically more metal-poor than the published ones and that a quadratically age-varying function reproduces the relative metallicity values with an overall uncertainty of ∼0.05 dex. We finally performed a similar comparison relying on a fully independent approach, which consisted in using theoretical red giant branches of old globular clusters spanning [Fe/H] values from −2.0 up to 0.0 dex as standards. We then superimposed onto them the red giant branches of star clusters with ages in the range 1.0−12.5 Gyr and estimated their associated metallicities by interpolation. The derived theoretical relative metallicities follow a similar trend as a function of the star clusters’ ages as what has been found from observations of star clusters.

The SLUGGS survey: measuring globular cluster ages using both photometry and spectroscopy

ABSTRACT Globular cluster ages provide both an important test of models of globular cluster formation and a powerful method to constrain the assembly history of galaxies. Unfortunately, measuring the ages of unresolved old stellar populations has proven challenging. Here, we present a novel technique that combines optical photometry with metallicity constraints from near-infrared spectroscopy in order to measure ages. After testing the method on globular clusters in the Milky Way and its satellite galaxies, we apply our technique to three massive early-type galaxies using data from the SAGES Legacy Unifying Globulars and GalaxieS (SLUGGS) survey. The three SLUGGS galaxies and the Milky Way show dramatically different globular cluster age and metallicity distributions, with NGC 1407 and the Milky Way showing mostly old globular clusters, while NGC 3115 and NGC 3377 show a range of globular ages. This diversity implies different galaxy formation histories and that the globular cluster optical colour–metallicity relation is not universal as is commonly assumed in globular cluster studies. We find a correlation between the median age of the metal-rich globular cluster populations and the age of the field star populations, in line with models where globular cluster formation is a natural outcome of high-intensity star formation.

From globular clusters to the disc: the dual life of our Galaxy

The halo and disc globular cluster population can be used as a tracer of the primordial epochs of the Milky Way formation. In this work, literature data of globular clusters ages, chemical abundances, and structural parameters are studied, explicitly focussing on the origin of the known split in the age-metallicity relation (AMR) of globular clusters. When the α-element abundances, which are less strongly affected by the internal light-element spread of globular clusters (Si, Ca), are considered, a very low observational scatter among metal-poor clusters is observed. A plateau at [SiCa/Fe],∼ 0.35 dex, with a dispersion of only 0.05 dex (including abundance errors) is observed up to a metallicity of about −0.75 dex. Only a few metal-poor clusters in this metallicity interval present low [SiCa/Fe] abundances. Moreover, metal-rich globular clusters show a knee in the [α/Fe] vs. [Fe/H] plane around [Fe/H] ∼ −0.75 dex. As a consequence, if a substantial fraction of galactic globular clusters has an external origin, they have to be mainly formed either in galaxies that are massive enough to ensure high levels of α-element abundances even at intermediate metallicity, or in lower mass dwarf galaxies accreted by the Milky Way in their early phases of formation. Finally, clusters in the metal-poor branch of the AMR present an anti-correlation of [SiCa/Fe] with the total cluster magnitude, while this is not the case for metal-rich branch clusters. In addition, this lack of faint high-α clusters in the young metal-poor population is in contrast with what is observed for old and more metal-poor clusters, possibly reflecting a higher heterogeneity of formation environments at lower metallicity. Accretion of high-mass satellites, as a major contribution to the current Milky Way globular cluster system both in the metal-poor and the metal-intermediate regime is compatible with the observations.

Constraints on the Distance Moduli, Helium and Metal Abundances, and Ages of Globular Clusters from their RR Lyrae and Non-variable Horizontal-branch Stars. III. M55 and NGC 6362

Abstract M55 (NGC 6809) and NGC 6362 are among the few globular clusters for which masses and radii have been derived to high precision for member binary stars. They also contain RR Lyrae variables, which, together with their non-variable horizontal-branch (HB) populations, provide tight constraints on the cluster reddenings and distance moduli through fits of stellar models to their pulsational and evolutionary properties. Reliable (m − M) V estimates yield M V and M bol values of comparable accuracy for binary stars, because the V-band bolometric corrections applicable to them have no more than a weak dependence on effective temperature ( ) and [Fe/H]. Chemical abundances derived from the binary mass–M V relations are independent of determinations based on their spectra. The temperatures of the binaries, which are calculated directly from their luminosities and the measured radii, completely rule out the low scale that has been determined for metal-deficient stars in some recent spectroscopic and interferometric studies. If [α/Fe] = 0.4 and [O/Fe] = 0.5 ± 0.1, we find that M55 has , [Fe/H] = −1.85 ± 0.1, and an age of 12.9 ± 0.8 Gyr, whereas NGC 6362 has , [Fe/H] = −0.90 ± 0.1, and an age of 12.4 ± 0.8 Gyr. The HB of NGC 6362 shows clear evidence for multiple stellar populations. Constraints from the RR Lyrae standard candle and from local subdwarfs (with Gaia DR2 parallaxes) are briefly discussed.

Age, Helium Content and Chemical Composition of Globular Clusters in the M31 Neighborhood and in our Galaxy

We present the results of determinations of age, helium abundance (Y), metallicity ([Fe/H]), and estimations of abundances of the elements: C, N, O, Mg, Ca, Ti, Cr, Ni, Sr, and Ba of four globular clusters in the neighborhood of the Andromeda galaxy ([SD2009]GC7,Mayall II, Mackey-GC1 (MGC1), and Bol 298 (MGC6)) and of six Galactic clusters. Medium-resolution long-slit integrated-light spectra from the clusters under study were used to determine the parameters.Observations of extra-galactic objects were carried out with the 6-m SAO RAS telescope using the SCORPIO-1 multimode focal reducer. Galactic globular clusters NGC6341 (M92), NGC6838 (M71), and NGC7078 were observed with the CARELEC spectrograph at the 1.93-m telescope of the Haute-Provence Observatory. The integratedlight spectra of Galactic globular clusters NGC104, NGC6121 (M4), and NGC7078 (M15) were taken from the spectral library by Schiavon.We selected the best isochrone for each cluster by comparison of the shapes and intensities of the observed and theoretical Balmer line profiles.

On the Use of the Main-sequence Knee (Saddle) to Measure Globular Cluster Ages

Abstract In this paper, we review the operational definition of the so-called main-sequence knee (MS-knee), a feature in the color-magnitude diagram (CMD) occurring at the low-mass end of the MS. The magnitude of this feature is predicted to be independent of age at fixed chemical composition. For this reason, its difference in magnitude with respect to the MS turn-off (MS-TO) point has been suggested as a possible diagnostic to estimate absolute globular cluster (GC) ages. We first demonstrate that the operational definition of the MS-knee currently adopted in the literature refers to the inflection point of the MS (which we here more appropriately named MS-saddle), a feature that is well distinct from the knee and which cannot be used as its proxy. The MS-knee is only visible in near-infrared CMDs, while the MS-saddle can be also detected in optical–NIR CMDs. By using different sets of isochrones, we then demonstrate that the absolute magnitude of the MS-knee varies by a few tenths of a dex from one model to another, thus showing that at the moment stellar models may not capture the full systematic error in the method. We also demonstrate that while the absolute magnitude of the MS-saddle is almost coincident in different models, it has a systematic dependence on the adopted color combinations which is not predicted by stellar models. Hence, it cannot be used as a reliable reference for absolute age determination. Moreover, when statistical and systematic uncertainties are properly taken into account, the difference in magnitude between the MS-TO and the MS-saddle does not provide absolute ages with better accuracy than other methods like the MS-fitting.

Constraints on the Distance Moduli, Helium, and Metal Abundances, and Ages of Globular Clusters from Their RR Lyrae and Non-variable Horizontal Branch Stars. II. Multiple Stellar Populations in 47 Tuc, M3, and M13

Abstract We present a new set of horizontal branch (HB) models computed with the MESA stellar evolution code. The models adopt α-enhanced Asplund et al. metal mixtures and include the gravitational settling of He. They are used in our HB population synthesis tool to generate theoretical distributions of HB stars in order to describe the multiple stellar populations in the globular clusters 47 Tuc, M3, and M13. The observed HB in 47 Tuc is reproduced very well by our simulations for and if the initial helium mass fraction varies by , and approximately 21%, 37%, and 42% of the stars have , 0.270, and 0.287, respectively. These simulations yield , implying an age near 13.0 Gyr. In the case of M3 and M13, our synthetic HBs for and match the observed ones quite well if M3 has and , resulting in an age of 12.6 Gyr, whereas M13 has and , implying an age of 12.9 Gyr. Mass loss during giant branch evolution and appear to be the primary second parameters for M3 and M13. New observations for seven of the nine known RR Lyrae in M13 are also reported. Surprisingly, periods predicted for the c-type variables tend to be too high (by up to ∼0.1 days).

Mocca code for star cluster simulations – VI. Bimodal spatial distribution of blue stragglers

The paper presents an analysis of formation mechanism and properties of spatial distributions of blue stragglers in evolving globular clusters, based on numerical simulations done with the MOCCA code. First, there are presented N-body and MOCCA simulations which try to reproduce the simulations presented by Ferraro (2012). Then, the agreement between N-body and the MOCCA code is shown. Finally, we discuss the formation process of the bimodal distribution. We report that so-called bimodal spatial distribution of blue stragglers is a very transient feature. It is formed for one snapshot in time and it can easily vanish in the next one. Moreover, we show that the radius of avoidance proposed by Ferraro (2012) goes out of sync with the apparent minimum of the bimodal distribution after about two half-mass relaxation times. This finding creates a real challenge for the dynamical clock, which uses this radius to determine the dynamical age of globular clusters. Additionally, the paper discusses a few important problems concerning the apparent visibilities of the bimodal distributions which have to be taken into account while studying the spatial distributions of blue stragglers.