Cluster Main Sequence Research Articles

Photometric variable stars in the young open cluster NGC 6823

ABSTRACT We present stellar variability towards the young open cluster NGC 6823. Time series V- and I-band CCD photometry led to identification and characterization of 88 variable stars, of which only 14 have been previously recognized. We ascertain the membership of each variable with optical UBVI and infrared photometry, and with Gaia EDR3 parallax and proper motion data. Seventy two variable stars are found to be cluster members, of which 25 are main sequence stars and 48 are pre-main-sequence stars. The probable cluster members collectively suggest an isochrone age of the cluster to be about 2 Myrs based on the GAIA photometry. With the colour and magnitude, as well as the shape of the light curve, we have classified the main sequence variables into β Cep, δ Scuti, slowly pulsating B type, and new class variables. Among the pre-main-sequence variables, eight are classical T Tauri variables, and four are Herbig Ae/Be objects, whereas the remaining belong to the weak-lined T Tauri population. The variable nature of 32 stars is validated with TESS light curves. Our work provides refined classification of variability of pre-main-sequence and main-sequence cluster members of the active star-forming complex, Sharpless 86. Despite no strong evidence of the disc-locking mechanism in the present sample of TTSs, one TTS with larger Δ(I − K) is found to be a slow rotator.

The family pictures of our neighbours: investigating the mass function and dynamical parameters of nearby open clusters

ABSTRACT We determine the mass functions (MFs) and the dynamical parameters of 15 nearby open clusters (OCs), using the unprecedented data set of the Gaia Early Data Release 3. We select the members of each cluster by combining the photometric (colour and magnitude) and astrometric (parallax and proper motions) parameters of stars, minimizing the contamination from Galactic field interlopers. By comparing the observed distribution of stars along the cluster main sequence with the best-fitting synthetic population, we find the present-day MF and the binary fraction of the OCs, along with their dynamical parameters like mass, half-mass radius, and half-mass relaxation time. We found that the global present-day MF of OCs are consistent with a single power-law function, F(m) ∝ mα, with slopes −3 < α < −0.6 including both subsolar, 0.2 < m/M⊙ < 1, and supersolar mass regimes. A significant correlation between the MF slope and the ratio of age to half-mass relaxation time is evidenced, similarly to the same conclusion already observed among Galactic globular clusters. However, OCs evolve along different tracks in comparison with the globular clusters, possibly indicating primordial differences in their initial mass function (IMF). The comparison with Monte Carlo simulations suggests that all the analysed OCs could be born with an IMF with slope αIMF < −2.3. We also show that the less evolved OCs have an MF consistent with that of the solar neighbourhood, indicating a possible connection between the dissolution of OCs and the formation of the Galactic disc.

Expanding the Time Domain of Multiple Populations: Evidence of Nitrogen Variations in the ∼1.5 Gyr Old Star Cluster NGC 1783

Abstract We present the result of a detailed analysis of Hubble Space Telescope UV and optical deep images of the massive and young (∼1.5 Gyr) stellar cluster NGC 1783 in the Large Magellanic Cloud. This system does not show evidence of multiple populations (MPs) along the red giant branch (RGB) stars. However, we find that the cluster main sequence (MS) shows evidence of a significant broadening (50% larger than what is expected from photometric errors) along with hints of possible bimodality in the MP sensitive (m F343N − m F438W, m F438W) color–magnitude diagram (CMD). Such an effect is observed in all color combinations including the m F343N filter, while it is not found in the optical CMDs. This observational evidence suggests we might have found light-element chemical abundance variations along the MS of NGC 1783, which represents the first detection of MPs in a system younger than 2 Gyr. A comparison with isochrones including MP-like abundances shows that the observed broadening is compatible with a N abundance enhancement of Δ([N/Fe]) ∼ 0.3. Our analysis also confirms previous results about the lack of MPs along the cluster RGB. However, we find that the apparent disagreement between the results found on the MS and the RGB is compatible with the mixing effects linked to the first dredge up. This study provides new key information about the MP phenomenon and suggests that star clusters form in a similar way at any cosmic age.

Dark Energy Camera photometry reveals extra-tidal stars around the Milky Way globular cluster NGC 6864 (M75)

ABSTRACT Globular clusters are prone to lose stars while moving around the Milky Way. These stars escape the clusters and are distributed throughout extended envelopes or tidal tails. However, such extra-tidal structures are not observed in all globular clusters, and yet there are no structural or dynamical parameters that can predict their presence or absence. NGC 6864 is an outer halo globular cluster with reported no observed tidal tails. We used Dark Energy Camera photometry reaching ∼4 mag underneath its main-sequence turnoff to confidently detect an extra-tidal envelope, and stellar debris spread across the cluster outskirts. These features emerged once robust field star filtering techniques were applied to the fainter end of the observed cluster main sequence. NGC 6864 is associated to the Gaia-Enceladus dwarf galaxy, among others 28 globular clusters. Up-to-date, nearly 64${{\ \rm per\,cent}}$ of them have been targeted looking for tidal tails and most of them have been confirmed to exhibit tidal tails. Thus, the present outcomes allow us to speculate on the possibility that Gaia-Enceladus globular clusters share a common pattern of mass loss by tidal disruption.

The surroundings of the Milky Way globular cluster NGC 6809

ABSTRACT We study the outer regions of the Milky Way globular cluster NGC 6809 based on Dark Energy Camera observations, which reach nearly 6 mag below the cluster main-sequence (MS) turn-off. In order to unveil its fainter outermost structure, we built stellar density maps using cluster MS stars, once the contamination of field stars was removed from the cluster colour–magnitude diagram. We found that only the resulting stellar density map for the lightest stars exhibits some excesses of stars at opposite sides from the cluster centre that diminish soon thereafter at ∼ 0.32°.Studied globular clusters with apogalactic distances smaller than that of NGC 6809 (5.5 kpc) do not have observed tidal tails. The lack of detection of tidal tails in the studied inner globular cluster sample could be due to the reduced diffusion time of tidal tails by the kinematically chaotic nature of the orbits of these globular clusters, thus shortening the time interval during which the tidal tails can be detected. Further investigations with an enlarged cluster sample are needed to confirm whether chaotic and non-chaotic orbits are responsible for the existence of globular clusters with tidal tails and those with extra-tidal features that are different from tidal tails or without any signatures of extended stellar density profiles.

Accurate distances to Galactic globular clusters through a combination of Gaia EDR3, HST, and literature data

ABSTRACT We have derived accurate distances to Galactic globular clusters by combining data from the Gaia Early Data Release 3 (EDR3) with distances based on Hubble Space Telescope (HST) data and literature-based distances. We determine distances either directly from the Gaia EDR3 parallaxes, or kinematically by combining line-of-sight velocity dispersion profiles with Gaia EDR3 and HST-based proper motion velocity dispersion profiles. We furthermore calculate cluster distances from fitting nearby subdwarfs, whose absolute luminosities we determine from their Gaia EDR3 parallaxes, to globular cluster main sequences. We finally use HST-based stellar number counts to determine distances. We find good agreement in the average distances derived from the different methods down to a level of about 2 per cent. Combining all available data, we are able to derive distances to 162 Galactic globular clusters, with the distances to about 20 nearby globular clusters determined with an accuracy of 1 per cent or better. We finally discuss the implications of our distances for the value of the local Hubble constant.

A near-infrared and UBVRI photometric analysis of the open cluster IC 361

We present here the detailed optical and infra-red photometric analysis of the open star cluster IC 361. On studying the radial density profile, radial extent of the cluster is found to be 8.0 +/- 0.5 arcmin. The basic physical parameters of the cluster such as E(B-V) = 0.56 +/- 0.10 mag, E(V-K) = 1.72+/-0.12 mag, log(Age)=9.10+/-0.05, and (m-M)0 = 12.54 +/-.05 mag are obtained using the color-color and color-magnitude diagrams. IC 361 is found to be located at a distance of 3.22 +/- 0.07 kpc. Using the archival proper motion catalogues, we estimate mean proper motions of IC 361 as 4.97+/-0.17 mas yr-1 and -5.80+/-0.18 mas yr-1 in the direction of RA and DEC, respectively. We derive the luminosity and mass functions for the cluster main sequence stars. The mass function slope is found to be -1.06+/-0.09 which is too low compare than Salpeter value.

Signatures of tidal disruption in the Milky Way globular cluster NGC 6981 (M72)

We study the outer regions of the Milky Way globular cluster NGC 6981 based on publicly available BV photometry and new Dark Energy Camera (DECam) observations, both of which reach nearly 4 mag below the cluster main sequence (MS) turnoff. While the BV data sets reveal the present of extra-tidal features around the cluster, the much larger field of view of the DECam observations allowed us to identify some other tidal features, which extend from the cluster toward the opposite direction to the Milky Way center. Such structural features of clusters arise from stellar density maps built using MS stars, following a cleaning of the cluster color-magnitude diagram to remove the contamination of field stars. We also performed N-body simulations in order to help us to understand the spatial distribution of the extra-tidal debris. The outcomes reveal the presence of long trailing and leading tails that are mostly parallel to the direction of the cluster velocity vector. We find that the cluster loses most of its mass by tidal disruption during its perigalactic passages, each of which lasted nearly 20 Myr. Hence, a decrease in the density of escaping stars near the cluster is expected from our N-body simulations, which, in turn, means that stronger extra-tidal features could be found by exploring much larger areas around NGC 6891.

Fast-rotating giant stars behind the Coma Berenices star cluster

ABSTRACT In the frame of a study of the empirical isochrones of young stellar clusters, we have carried out BVIc Johnson–Cousins photometry of a sample of K and M stars of the Coma Berenices star cluster. All these stars have known rotational periods. Our main goal is to get a valuable reference on the colour–magnitude diagram, Mv versus B − V, for stars with ages within 400–800 Myr. For this purpose, we obtained BVIc photometry with an average upper limit for the precision of about 0.025 mag and used parallaxes from the Gaia Data Release 2. We found that one-third of our sample is located well above the cluster main sequence and these stars are confirmed as background giants by their radial velocities in the Gaia Data Release 2. This misclassification shows that giants with short-surface rotational periods can mimic main-sequence stars if they are located at the appropriate distance. We recommend caution when using rotational periods in order to determine cluster membership. Besides, the gyrochronology technique should be used only when the luminosity class of the stars is well known. Finally, our cleared sample supports an age of ∼600 Myr for Coma Berenices, rather than an age of ∼800 Myr.

Binary star sequence in the outskirts of the disrupting Galactic open cluster UBC 274

We report the identification of a numerous binary star population in the recently discovered ∼3 Gyr old open cluster UBC 274. It becomes visible when the cluster color-magnitude diagram is corrected by differential reddening and spans mass ratio (q) values from 0.5 up to 1.0. Its stellar density radial profile and cumulative distribution as a function of the distance from the cluster center reveal that it extends out to the observed boundaries of the tidal tails of the cluster (about six times the cluster radius) following a spatial distribution indistinguishable from that of cluster main-sequence (MS) stars. Furthermore, binary stars withqvalues lower or higher than 0.75 do not show any spatial distribution difference either. FromGaiaDR2 astrometric and kinematics data we computed Galactic coordinates and space velocities with respect to the cluster center and mean cluster space velocity, respectively. We found that cluster members located throughout the tidal tails move relatively fast, regardless of whether they are a single or binary star. The projection of their motions onto the Galactic plane resembles that of a rotating solid body, while the motions along the radial direction from the Galactic center and perpendicular to the Galactic plane suggest that the cluster is being disrupted. The similarity of the spatial distributions and kinematic patterns of cluster MS and binary stars reveals that UBC 274 is facing an intense process of disruption that has apparently swept out any signature of internal dynamic evolution, such as mass segregation driven by two-body relaxation.

New insight into the stellar mass function of Galactic globular clusters

ABSTRACT We present the results of the analysis of deep photometric data of 32 Galactic globular clusters. We analysed 69 parallel field images observed with the Wide Field Channel of the Advanced Camera for Surveys of the Hubble Space Telescope which complemented the already available photometry from the globular cluster treasury project covering the central regions of these clusters. This unprecedented data set has been used to calculate the relative fraction of stars at different masses (i.e. the present-day mass function) in these clusters by comparing the observed distribution of stars along the cluster main sequence and across the analysed field of view with the prediction of multimass dynamical models. For a subsample of 31 clusters, we were able to obtain also the half-mass radii, mass-to-light ratios, and the mass fraction of dark remnants using available radial velocity information. We found that the majority of globular clusters have single power-law mass functions F(m) ∝ mα with slopes α > −1 in the mass range 0.2 < m/M⊙ < 0.8. By exploring the correlations between the structural/dynamical and orbital parameters, we confirm the tight anticorrelation between the mass function slopes and the half-mass relaxation times already reported in previous works, and possible second-order dependence on the cluster metallicity. This might indicate the relative importance of both initial conditions and evolutionary effects on the present-day shape of the mass function.

Pal 13: its moderately extended low-density halo and its accretion history

We present results based on Dark Energy Camera Legacy Survey (DECaLS) DR8 astrometric and photometric data sets of the Milky Way globular cluster Pal 13. Because of its relatively small size and mass, there is not yet a general consensus on the existence of extra-tidal structures surrounding it. While some previous results suggest the absence of such features, others show that the cluster is under the effects of tidal stripping. We have built a cluster stellar density map from DECaLS g, r magnitudes – previously corrected for interstellar reddening – of stars placed along the cluster main sequence in the color-magnitude diagram. The resulting density map shows nearly smooth contours around Pal 13 out to approximately 1.6 t the most recent estimate of its Jacobi radius, which was derived whilst taking into account the variation along its orbital motion. This outcome favors the presence of stars escaping the cluster, a phenomenon frequently seen in globular clusters that have crossed the Milky Way disk a comparably large number of times. Particularly, the orbital high eccentricity and large inclination angle of this accreted globular cluster could have been responsible for the relatively large amount of lost cluster mass.

Bayesian Characterization of Main-sequence Binaries in the Old Open Cluster NGC 188

Abstract The binary fractions of open and globular clusters yield powerful constraints on their dynamical state and evolutionary history. We apply publicly available Bayesian analysis tools to a UBV RIJHK S photometric catalog of the open cluster NGC 188 to detect and characterize photometric binaries along the cluster main sequence. This technique has the advantage of self-consistently handling photometric errors, missing data in various bandpasses, and star-by-star prior constraints on cluster membership. Simulations are used to verify uncertainties and quantify selection biases in our analysis, illustrating that among binaries with mass ratios >0.5, we recover the binary fraction to better than 7% in the mean, with no significant dependence on binary fraction and a mild dependence on assumed mass-ratio distribution. Using our photometric catalog, we recover the majority (65% ± 11%) of spectroscopically identified main-sequence binaries, including eight of the nine with spectroscopically measured mass ratios. Accounting for incompleteness and systematics, we derive a mass-ratio distribution that rises toward lower mass ratios (within our q > 0.5 analysis domain). We observe a raw binary fraction for solar-type main-sequence stars with mass ratios q > 0.5 of 42% ± 4%, independent of the assumed mass-ratio distribution to within its uncertainties, consistent with literature values for old open clusters but significantly higher than the field solar-type binary fraction. We confirm that the binaries identified by our method are more concentrated than single stars, in agreement with previous studies, and we demonstrate that the binary nature of those candidates that remain unidentified spectroscopically is strongly supported by photometry from Gaia DR2.

Blue Lurkers: Hidden Blue Stragglers on the M67 Main Sequence Identified from Their Kepler/K2 Rotation Periods

Abstract At an age of 4 Gyr, typical solar-type stars in M67 have rotation rates of 20–30 days. Using K2 Campaign 5 and 16 light curves and the spectral archive of the WIYN Open Cluster Study, we identify 11 3D kinematic members of M67 with anomalously fast rotation periods of 2–8 days, implying ages of less than 1 Gyr. We hypothesize that these anomalously fast rotators have been spun up by mass transfer, mergers, or stellar collisions during dynamical encounters within the 1 Gyr and thus represent lower-luminosity counterparts to the blue straggler stars. These 11 candidate post-interaction stellar systems have much in common with the blue stragglers, including a high binary fraction (73%); a number of long-period, low-eccentricity binary systems; and in at least one case a UV excess consistent with the presence of a hot white dwarf companion. The identification of these 11 systems provides the first picture of the low-luminosity end of the blue straggler distribution, providing new constraints for detailed binary evolution models and cluster population studies. This result also clearly demonstrates the need to properly account for the impact of binaries on stellar evolution, as significant numbers of post-interaction binaries likely exist on cluster main sequences and in the field. These stars are not always easy to identify but make up ∼10% or more of the spectroscopic binary population among the solar-type stars in M67.

Discovery of a Double Blue Straggler Sequence in M15: New Insight into the Core-collapse Process

Abstract In this paper we report the discovery of a double blue straggler star (BSS) sequence in the core of the core-collapsed cluster M15 (NGC 7078). We performed a detailed photometric analysis of the extremely dense core of the cluster using a set of images secured with the Advanced Camera for Survey in the High Resolution Channel mode on board the Hubble Space Telescope. The proper combination of the large number of single frames in the near-UV (F220W), and blue (F435W) filters allowed us to perform a superb modeling of the point-spread function and an accurate deblending procedure. The color–magnitude diagram revealed the presence of two distinct parallel sequences of blue stragglers. In particular, the blue BSS sequence is characterized by the intriguing presence of two different branches. The first branch appears extremely narrow, it extends up to 2.5 mag brighter than the cluster main-sequence turnoff (MS-TO) point, and it is nicely reproduced by a 2 Gyr old collisional isochrone. The second branch extends up to 1.5 mag from the MS-TO and it is reproduced by a 5.5 Gyr old collisional isochrone. Our observations suggest that each of these branches is mainly constituted by a population of nearly coeval collisional BSSs of different masses generated during two episodes of high collisional activity. We discuss the possibility that the oldest episode corresponds to the core-collapse (CC) event (occurred about 5.5 Gyr ago), while the most recent one (occurred about 2 Gyr ago) is associated with a core oscillation in the post-CC evolution. The discovery of these features provides further strong evidence in support of the connection between the BSS properties and globular cluster dynamical evolution, and it opens new perspectives on the study of CC and post-CC evolution.

The Magellanic Bridge Cluster NGC 796: Deep Optical AO Imaging Reveals the Stellar Content and Initial Mass Function of a Massive Open Cluster

Abstract NGC 796 is a massive young cluster located 59 kpc from us in the diffuse intergalactic medium of the 1/5–1/10 Z ☉ Magellanic Bridge, allowing us to probe variations in star formation and stellar evolution processes as a function of metallicity in a resolved fashion, and providing a link between resolved studies of nearby solar-metallicity and unresolved distant metal-poor clusters located in high-redshift galaxies. In this paper, we present adaptive optics griHα imaging of NGC 796 (at 0.″5, which is ∼0.14 pc at the cluster distance) along with optical spectroscopy of two bright members to quantify the cluster properties. Our aim is to explore whether star formation and stellar evolution vary as a function of metallicity by comparing the properties of NGC 796 to higher-metallicity clusters. We find an age of 20 − 5 + 12 Myr from isochronal fitting of the cluster main sequence in the color–magnitude diagram. Based on the cluster luminosity function, we derive a top-heavy stellar initial mass function (IMF) with a slope α = 1.99 ± 0.2, hinting at a metallicity and/or environmental dependence of the IMF, which may lead to a top-heavy IMF in the early universe. Study of the Hα emission-line stars reveals that classical Be stars constitute a higher fraction of the total B-type stars when compared with similar clusters at greater metallicity, providing some support to the chemically homogeneous theory of stellar evolution. Overall, NGC 796 has a total estimated mass of 990 ± 200 M ⊙, and a core radius of 1.4 ± 0.3 pc, which classifies it as a massive young open cluster, unique in the diffuse interstellar medium of the Magellanic Bridge.

The K2 M67 Study: A Curiously Young Star in an Eclipsing Binary in an Old Open Cluster*

Abstract We present an analysis of a slightly eccentric (e = 0.05), partially eclipsing, long-period (P = 69.73 days) main-sequence binary system (WOCS 12009, Sanders 1247) in the benchmark old open cluster M67. Using Kepler K2 and ground-based photometry, along with a large set of new and reanalyzed spectra, we derived highly precise masses (1.111 ± 0.015 and 0.748 ± 0.005 M ⊙) and radii (1.071 ± 0.008 ± 0.003 and 0.713 ± 0.019 ± 0.026 R ⊙, with statistical and systematic error estimates) for the stars. The radius of the secondary star is in agreement with theory. The primary, however, is approximately 15% smaller than reasonable isochrones for the cluster predict. Our best explanation is that the primary star was produced from the merger of two stars, as this can also account for the nondetection of photospheric lithium and its higher temperature relative to other cluster main-sequence stars at the same V magnitude. To understand the dynamical characteristics (low measured rotational line broadening of the primary star and low eccentricity of the current binary orbit), we believe that the most probable (but not the only) explanation is the tidal evolution of a close binary within a primordial triple system (possibly after a period of Kozai–Lidov oscillations), leading to merger approximately 1 Gyr ago. This star appears to be a future blue straggler that is being revealed as the cluster ages and the most massive main-sequence stars die out.

Haffner 16 Redux: Revisiting a Young Cluster in the Outer Galaxy* †

Abstract Images and spectra recorded with the Gemini Multi-Object Spectrograph on Gemini South are used to investigate the stellar content of the open cluster Haffner 16. The color–magnitude diagram (CMD) constructed from these data extends over 10 mag in , sampling the cluster main sequence (MS) and 5 mag of the pre-MS (PMS). The fraction of unresolved equal mass binaries among PMS stars is estimated to be 0.6 ± 0.1. The isochrones do not track the PMS on the CMD, in the sense that the PMS has a shallower slope on the CMD than predicted by the models. Still, a dip in star counts, which is associated with the relaxation of PMS stars onto the MS, is identified near . The depth and brightness of this feature—as well as the morphology of the cluster MS on the CMD—are matched by models with a slightly sub-solar metallicity that have an age of ∼20 Myr and a distance modulus of 12.3 ± 0.2. A light profile of Haffner 16 is constructed in the W1 filter ( ), which suggests that the cluster is surrounded by a diffuse stellar halo. Spectra of candidate cluster MS and PMS stars selected according to location on the CMD are presented. The spectra show characteristics that are suggestive of a sub-solar metallicity. Hα emission is common among objects on the PMS locus on the CMD near . It is suggested that the location of the Haffner 16 PMS on the CMD is affected by large-scale cool spot activity, likely induced by rapid stellar rotation.

A Photometric Study of the Outer Halo Globular Cluster NGC 5824

Abstract Multi-wavelength CCD photometry over 21 years has been used to produce deep color–magnitude diagrams (CMDs) together with light curves for the variables in the Galactic globular cluster NGC 5824. Twenty-one new cluster RR Lyrae stars are identified, bringing the total to 47, of which 42 have reliable periods determined for the first time. The CMD is matched using BaSTI isochrones with ages of 13 Gyr, and reddening is found to be using the period–Wesenheit relation in two colors, the distance modulus is corresponding to a distance of 30.9 Kpc. The observations show no signs of populations that are significantly younger than the 13 Gyr stars. The width of the red giant branch does not allow for a spread in greater than , and there is no photometric evidence for widened or parallel sequences. The pseudo-CMD shows a bifurcation of the red giant branch that by analogy with other clusters is interpreted as being due to differing spectral signatures of the first (75%) and second (25%) generations of stars whose age difference is close enough that main-sequence (MS) turnoffs in the CMD are unresolved. The cluster MS is visible against the background out to a radial distance of ∼17 arcmin. We conclude that NGC 5824 appears to be a classical Oosterhoff Type II globular cluster, without overt signs of being a remnant of a now-disrupted dwarf galaxy.

On the determination of the He abundance distribution in globular clusters from the width of the main sequence

One crucial piece of information to study the origin of multiple stellar populations in globular clusters, is the range of initial helium abundances $\Delta{Y}$ amongst the sub-populations hosted by each cluster. These estimates are commonly obtained by measuring the width in colour of the unevolved main sequence in an optical colour-magnitude-diagram. The measured colour spread is then compared with predictions from theoretical stellar isochrones with varying initial He abundances, to determine $\Delta{Y}$. The availability of UV/optical magnitudes thanks to the {\sl HST UV Legacy Survey of Galactic GCs} project, will allow the homogeneous determination of $\Delta{Y}$ for a large Galactic globular cluster sample. From a theoretical point of view, accurate UV CMDs can efficiently disentangle the various sub-populations, and main sequence colour differences in the ACS $F606W-(F606W-F814W)$ diagram allow an estimate of $\Delta{Y}$. We demonstrate that from a theoretical perspective the ($F606W-F814W$) colour is an extremely reliable He-abundance indicator. The derivative d$Y$/d($F606W-F814W$), computed at a fixed luminosity along the unevolved main sequence, is largely insensitive to the physical assumptions made in stellar model computations, being more sensitive to the choice of the bolometric correction scale, and is only slightly dependent on the adopted set of stellar models. From a theoretical point of view the ($F606W-F814W$) colour width of the cluster main sequence is therefore a robust diagnostic of the $\Delta{Y}$ range.