Slope Of Mass Function Research Articles

Teutsch 76: A deep near-infrared study

We have performed a detailed analysis on the Teutsch 76 (T76) open cluster using the deep near-infrared (NIR) observations taken with the TANSPEC instrument mounted on the 3.6m Devasthal optical telescope along with the recently available high quality proper motion data from the Gaia data release 3 and deep photometric data from Pan-STARRS1 survey. We have found that the T76 cluster is having a central density concentration with circular morphology, probably due to the star-formation processes. The radius of the T76 cluster is found to be 45 $$^{\prime \prime }$$ (1.24 pc) and 28 stars within this radius were marked as highly probable cluster members. We have found that the cluster is located at a distance of $$5.7\pm 1.0$$ kpc and is having an age of $$50\pm 10$$ Myr. The mass function slope ( $$\Gamma $$ ) in the cluster region in the mass range of $$\sim $$ $$0.75<M/M_\odot <5.8$$ is estimated as $$-1.3\pm 0.2$$ , which is similar to the value of −1.35 given by Salpeter (1955). The cluster is not showing any signatures of mass-segregation and is currently undergoing dynamical relaxation.

Rapid determination of LISA sensitivity to extreme mass ratio inspirals with machine learning

ABSTRACT Gravitational wave observations of the inspiral of stellar-mass compact objects into massive black holes (MBHs), extreme mass ratio inspirals (EMRIs), enable precision measurements of parameters such as the MBH mass and spin. The Laser Interferometer Space Antenna is expected to detect sufficient EMRIs to probe the underlying source population, testing theories of the formation and evolution of MBHs and their environments. Population studies are subject to selection effects that vary across the EMRI parameter space, which bias inference results if unaccounted for. This bias can be corrected, but evaluating the detectability of many EMRI signals is computationally expensive. We mitigate this cost by (i) constructing a rapid and accurate neural network interpolator capable of predicting the signal-to-noise ratio of an EMRI from its parameters, and (ii) further accelerating detectability estimation with a neural network that learns the selection function, leveraging our first neural network for data generation. The resulting framework rapidly estimates the selection function, enabling a full treatment of EMRI detectability in population inference analyses. We apply our method to an astrophysically motivated EMRI population model, demonstrating the potential selection biases and subsequently correcting for them. Accounting for selection effects, we predict that with 116 EMRI detections LISA will measure the MBH mass function slope to a precision of 8.8 per cent, the CO mass function slope to a precision of 4.6 per cent, the width of the MBH spin magnitude distribution to a precision of 10 per cent, and the event rate to a precision of 12 per cent with EMRIs at redshifts below z = 6.

Globular cluster formation histories, masses, and radii inferred from gravitational waves

ABSTRACT Globular clusters (GCs) are found in all types of galaxies and harbour some of the most extreme stellar systems, including black holes that may dynamically assemble into merging binary black holes (BBHs). Uncertain GC properties, including when they formed, their initial masses and sizes, affect their production rate of BBH mergers. Using the gravitational-wave transient catalogue (GWTC-3), we measure that dynamically assembled BBHs – those that are consistent with isotropic spin directions – make up ${61^{+29}_{-44}\%}$ of the total merger rate, with a local merger rate of ${10.9^{+16.8}_{-9.3}}$ Gpc−3 yr−1 rising to ${58.9^{+149.4}_{-46.0}}$ Gpc−3 yr−1 at z = 1. We assume that this inferred rate describes the contribution from GCs and compare it against the Cluster Monte Carlo (cmc) simulation catalogue to directly fit for the GC initial mass function, virial radius distribution, and formation history. We find that GC initial masses are consistent with a Schechter function with slope ${\beta _m = -1.9^{+0.8}_{-0.8}}$ . Assuming a mass function slope of βm = −2 and a mass range between 104–$10^8\, \mathrm{ M}_\odot$ , we infer a GC formation rate at z = 2 of ${5.0^{+9.4}_{-4.0}}$ Gpc−3 yr−1, or ${2.1^{+3.9}_{-1.7}}\times 10^6\, \mathrm{ M}_\odot$ Gpc−3 yr−1 in terms of mass density. We find that the GC formation rate probably rises more steeply than the global star formation rate between z = 0 and z = 3 (82 per cent credibility) and implies a local number density that is ${f_\mathrm{ev} = 22.6^{+29.9}_{-16.2}}$ times higher than the observed density of survived GCs. This is consistent with expectations for cluster evaporation, but may suggest that other environments contribute to the rate of BBH mergers with significantly tilted spins.

Multimass modelling of Milky Way globular clusters – I. Implications on their stellar initial mass function above 1 M⊙

ABSTRACT The distribution of stars and stellar remnants (white dwarfs, neutron stars, and black holes) within globular clusters holds clues about their formation and long-term evolution, with important implications for their initial mass function (IMF) and the formation of black hole mergers. In this work, we present best-fitting multimass models for 37 Milky Way globular clusters, which were inferred from various data sets, including proper motions from Gaia EDR3 and HST, line-of-sight velocities from ground-based spectroscopy and deep stellar mass functions from HST. We use metallicity-dependent stellar evolution recipes to obtain present-day mass functions of stars and remnants from the IMF. By dynamically probing the present-day mass function of all objects in a cluster, including the mass distribution of remnants, these models allow us to explore in detail the stellar (initial) mass functions of a large sample of Milky Way GCs. We show that, while the low-mass mass function slopes are strongly dependent on the dynamical age of the clusters, the high-mass slope (α3; m &amp;gt; 1 M⊙) is not, indicating that the mass function in this regime has generally been less affected by dynamical mass loss. Examination of this high-mass mass function slope suggests an IMF in this mass regime consistent with a Salpeter IMF is required to reproduce the observations. This high-mass IMF is incompatible with a top-heavy IMF, as has been proposed recently. Finally, based on multimass model fits to our sample of Milky Way GCs, no significant correlation is found between the high-mass IMF slope and cluster metallicity.

Evidence for a bottom-light initial mass function in massive star clusters

ABSTRACT We have determined stellar mass functions of 120 Milky Way globular clusters and massive Large Magellanic Cloud/Small Magellanic Cloud star clusters based on a comparison of archival Hubble Space Telescope photometry with a large grid of direct N-body simulations. We find a strong correlation of the global mass function slopes of star clusters with both their internal relaxation times and their lifetimes. Once dynamical effects are being accounted for, the mass functions of most star clusters are compatible with an initial mass function described by a broken power-law distribution N(m) ∼ mα with break masses at 0.4 and 1.0 M⊙ and mass function slopes of αLow = −0.3 for stars with masses m &amp;lt; 0.4 M⊙, αHigh = −2.30 for stars with m &amp;gt; 1.0 M⊙, and αMed = −1.65 for intermediate-mass stars. Alternatively, a lognormal mass function with a characteristic mass log MC = −0.36 and width σC = 0.28 for low-mass stars and a power-law mass function for stars with m &amp;gt; 1 M⊙ also fit our data. We do not find a significant environmental dependence of the initial mass function on cluster mass, density, global velocity dispersion, or metallicity. Our results lead to a larger fraction of high-mass stars in globular clusters compared to canonical Kroupa/Chabrier mass functions, increasing the efficiency of self-enrichment in clusters and helping to alleviate the mass budget problem of multiple stellar populations in globular clusters. By comparing our results with direct N-body simulations, we finally find that only simulations in which most black holes are ejected by natal birth kicks correctly reproduce the observed correlations.

INSPIRE: INvestigating Stellar Population In RElics – IV. The initial mass function slope in relics

ABSTRACTIn the last decade, growing evidence has emerged supporting a non-universal stellar initial mass function (IMF) in massive galaxies, with a larger number of dwarf stars with respect to the Milky Way (bottom-heavy IMF). However, a consensus about the mechanisms that cause IMF variations is yet to be reached. Recently, it has been suggested that stars formed early-on in cosmic time, via a star formation burst, could be characterized by a bottom-heavy IMF. A promising way to confirm this is to use relics, ultra-compact massive galaxies, almost entirely composed by these ‘pristine’ stars. The INvestigating Stellar Population In RElics (INSPIRE) Project aims at assembling a large sample of confirmed relics, that can serve as laboratory to investigate on the conditions of star formation in the first 1–3 Gyr of the Universe. In this third INSPIRE paper, we build a high signal-to-noise spectrum from five relics, and one from five galaxies with similar sizes, masses, and kinematical properties, but characterized by a more extended star formation history (non-relics). Our detailed stellar population analysis suggests a systematically bottom-heavier IMF slope for relics than for non-relics, adding new observational evidence for the non-universality of the IMF at various redshifts and further supporting the above proposed physical scenario.

An Investigation of Open Clusters Berkeley 68 and Stock 20 Using CCD UBV and Gaia DR3 Data

We performed detailed photometric and astrometric analyses of the open star clusters Berkeley 68 and Stock 20. This was based on ground-based CCD UBV photometric data complemented by space-based Gaia Data Release 3 (DR3) photometry and astrometry. A total of 198 and 51 stars were identified as likely cluster members for Berkeley 68 and Stock 20, respectively. Two-color diagrams were used to derive the reddening and photometric metallicity for each cluster. The reddening for Berkeley 68 and Stock 20 is E(B − V) = 0.520 ± 0.032 mag and 0.400 ± 0.048 mag, respectively. Photometric metallicity [Fe/H] is −0.13 ± 0.08 dex for Berkeley 68 and −0.01 ± 0.06 dex for Stock 20. Keeping as constant reddening and metallicity, we determined the distance moduli and ages of the clusters through fitting isochrones to the UBV and Gaia-based color–magnitude diagrams. Photometric distances are d = 3003 ± 165 pc for Berkeley 68 and 2911 ± 216 pc for Stock 20. The cluster ages are 2.4 ± 0.2 Gyr and 50 ± 10 Myr for Berkeley 68 and Stock 20, respectively. Present-day mass function slopes were found to be Γ = 1.38 ± 0.71 and Γ = 1.53 ± 0.39 for Berkeley 68 and Stock 20, respectively. These values are compatible with the value of Salpeter. The relaxation times were estimated as 32.55 and 23.17 Myr for Berkeley 68 and Stock 20, respectively. These times are less than the estimated cluster ages, indicating that both clusters are dynamically relaxed. Orbit integration was carried out only for Berkeley 68 since radial velocity data were not available for Stock 20. Analysis indicated that Berkeley 68 was born outside the solar circle and belongs to the thin-disk component of the Milky Way.

Dynamical state of the globular clusters Rup 106 and IC 4499

The dynamical evolution of globular clusters is theoretically described by a series of well-known events typical of N-body systems. Still, the identification of observational signatures able to empirically describe the stage of dynamical evolution of a stellar system with a density typical of a globular cluster represents a challenge. In this paper, we study the dynamical age of the globular clusters Rup 106 and IC 4499. To this aim, we study the radial distribution of the blue straggler stars (BSSs) via the A+ parameter and of the slope of the main sequence mass function. Both tracers show that Rup 106 and IC 4499 are dynamically young clusters where dynamical friction has just started to segregate massive stars towards their respective centres. Furthermore, we observe that the BSSs are more centrally concentrated in both clusters than the reference population. Similarly, we find that in both cases the slope of the mass function significantly decreases as a function of the cluster-centric distance. This result provides additional support for the use of the radial distribution of the BSSs as a powerful and observationally convenient indicator of the cluster dynamical age.

Globular cluster formation with multiple stellar populations: a single-binary composite scenario

ABSTRACT We discuss a GC formation scenario in which the first generation (1G) of single asymptotic giant branch (AGB) stars and intermediate-mass close binaries (IMCBs) eject gas, from which the second generation (2G) of stars can be formed. The two key parameters in the scenario are the fractions of binary stars (fb) and the slopes (α) of the stellar initial mass functions (IMFs) for 1G stars. Principle results derived by analytic and one-zone models of GC formation are as follows. The mass fraction of 2G stars (f2g) can be higher than ≈0.4 for α &amp;lt; 1.8 and is not so dependent on fb. The ratio of the initial mass of a GC to the present-day mass (Mgc) ranges from 2 to 7 depending on α for 0.5 ≤ fb ≤ 0.9. The differences in [Na/Fe] between 1G and 2G stars can be as large as 0.7 for a wide range of model parameters. The Li abundances of 2G stars can be as high as those of 1G even if the pristine gas from IMCBs is assumed to be Li-free. Formation histories of 2G stars show at least two peaks owing to two peaks in the total ejection rate of gas from IMCB populations. The observed correlation between f2g and Mgc can be due to α depending on Mgc. The hypothetical long duration of 2G formation (≈108 yr) is possible, because massive star formation can be suppressed through frequent dynamical interaction between 1G stars and gas clouds.

A Gaia EDR3 search for tidal tails in disintegrating open clusters

ABSTRACT We carry out a search for tidal tails in a sample of open clusters with known relatively elongated morphology. We identify the member stars of these clusters from the precise astrometric and deep photometric data from Gaia Early Data Release 3 using the robust membership determination algorithm, ML-MOC. We identify 46 open clusters having a stellar corona beyond the tidal radius, 20 of which exhibit extended tails aligned with the cluster orbit direction in Galactocentric coordinates. Notably, we find NGC 6940 (at a distance of ∼1 kpc) is the furthest open cluster, exhibiting tidal tails that are ∼50 pc from its centre, while also identifying ∼40 pc long tidal tails for the nearby Pleiades. Using the minimum spanning tree length for the most massive stars relative to all cluster members, we obtain the mass segregation ratio ($\rm \lambda _{MSR}$) profiles as a function of the number of massive stars in each cluster. From these profiles, we can classify the open clusters into four classes based on the degree of mass segregation experienced by the clusters. We find that clusters in the most mass segregated classes are the oldest on average and have the flattest mass function slope. Of the 46 open clusters studied in this work, 41 exhibit some degree of mass segregation. Furthermore, we estimate the initial masses (M$\rm _{i}$) of these open clusters, finding that some of them, having M$\rm _{i}\gtrsim 10^{4} M_{\odot }$, could be the dissolving remnants of young massive clusters.

A Comprehensive Study of Five Intermediate-age Pismis (2, 3, 7, 12, 15) Clusters Using Photometric and Astrometric Data from Gaia EDR3

Open clusters are groups of stars that form simultaneously; hence, these are excellent probes to test theories of star formation, stellar evolution, and dynamics in the Milky Way disk. We carry out a detailed photometric and kinematic study of five poorly studied intermediate-age open clusters, Pismis 2 (Pi 2), Pismis 3 (Pi 3), Pismis 7 (Pi 7), Pismis 12 (Pi 12), and Pismis 15 (Pi 15), using the Gaia EDR3 database. By estimating the membership probabilities of stars, we recognized 635, 1488, 535, 368, and 494 most probable members for these clusters by using proper-motion and parallax data taken from Gaia EDR3. The radial density profiles of cluster members provide cluster radii of 4.′5–6.′5 for these clusters. Their ages range from 0.9 to 2.5 Gyr, and distances range, using parallax, from 2.15 to 5.10 kpc. The overall mass function slopes for main-sequence stars are found as 0.27 ± 0.16 (for 1.0–1.6 M ⊙ stars), 0.86 ± 0.27 (for 1.0–2.1 M ⊙ stars), 1.08 ± 0.32 (for 1.0–2.2 M ⊙ stars), 0.89 ± 0.38 (for 1.0–2.2 M ⊙ stars), and 1.07 ± 0.28 (for 1.0–2.1 M ⊙ stars) for clusters Pi 2, Pi 3, Pi 7, Pi 12, and Pi 15. Our obtained values of slopes are flatter in comparison with Salpeter’s value (x = 1.35) within uncertainty. The present study demonstrates that all these Pismis clusters are dynamically relaxed. We found that these objects follow a circular path around the Galactic center. We compute these clusters’ apex coordinates (A, D) and other kinematic parameters.

The galaxy-wide stellar initial mass function in the presence of cluster-to-cluster IMF variations

We calculate the stellar integrated galactic initial mass function (IGIMF) in the presence of cluster-to-cluster variations of the IMF. Variations of the IMF for a population of coeval clusters that populate the initial cluster mass function (ICLMF) are taken into account in the form of Gaussian distribution functions of the IMF parameters. For the tapered power-law function used in this work, these are the slope at the high-mass end, Γ, the slope at the low-mass end, γ, and the characteristic mass Mch. The level of variations is modeled by varying the width of the Gaussian distributions. The reference values are the standard deviations of the parameters observed for the population of young clusters in the present-day Milky Way, which are σΓ = 0.6, σγ = 0.25, and σMch = 0.27 M⊙. We find that increasing the levels of dispersion for γ and Γ tends to moderately flatten the IGIMF at the low and high-mass end, respectively. The characteristic mass of the IGIMF is, however, strongly impacted by variations in Mch. Increasing the value of σMch shifts the peak of the IGIMF to lower masses, rendering the IGIMF more bottom heavy. This can provide a simple explanation for the bottom-heavy stellar mass function that is inferred for early-type galaxies since these are likely the result of a merger of disk galaxies where the physical conditions of the star-forming gas may vary significantly both in time and space in the merging system. The effect of IMF variations on the IGIMF is compared to the effects of other processes and sources of systematic variations such as those due to variations in the shape of ICLMF, the gas-phase metallicity, and the galactic star formation rate (SFR) which can potentially affect the maximum mass of stellar clusters in a galaxy and set the mean value of the characteristic mass in clusters. For the various dependencies we have explored, we found that the effect of IMF variations is a dominant factor that always affects the characteristic mass of the IGIMF. For the regimes at low metallicity where the IGIMF resembles a single power law, an increased level of IMF variations renders the IGIMF steeper and more bottom heavy, especially at low SFRs. On the other hand, variations in the IMF in the high mass regime can be easily dominated by variations in the slope of the ICLMF. We compare our results of the metallicity and SFR-dependent IGIMF to a sample of Milky Way ultra-faint dwarf (UFD) satellite galaxies that have available metallicity measurements. The present-day stellar mass function of these galaxies is a good analog to the IGIMF at the time their overall population of stars formed. We show that the slope of the stellar mass function of the UFD galaxies measured for stars in the mass range [0.4, 0.8] M⊙ can only be reproduced when IMF variations of the same order as those measured in the present-day Milky Way are included. Our results suggest that the inclusion of IMF variations in models of galaxy formation and evolution is of vital importance in order to improve our understanding of star formation and star formation feedback effects on galactic scales.

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 &amp;lt; α &amp;lt; −0.6 including both subsolar, 0.2 &amp;lt; m/M⊙ &amp;lt; 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 &amp;lt; −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.

Stellar collisions in globular clusters: Constraints on the initial mass function of the first generation of stars

Globular clusters display an anticorrelation between the fraction of the first generation of stars (N(G1)/N(tot)) and the slope of the present-day mass function of the clusters (αpd), which is particularly significant for massive clusters. In the framework of the binary-mediated collision scenario for the formation of the second-generation stars in globular clusters, we test the effect of a varying stellar initial mass function (IMF) of the G1 stars on the (N(G1)/N(tot)) − αpd anticorrelation. We use a simple collision model that has only two input parameters, the shape of the IMF of G1 stars and the fraction of G1 stars that coalesce to form second-generation stars. We show that a variable efficiency of the collision process is necessary in order to explain the (N(G1)/N(tot)) − αpd anticorrelation; however, the scatter in the anticorrelation can only be explained by variations in the IMF, and in particular by variations in the slope in the mass interval ≈(0.1–0.5) M⊙. Our results indicate that in order to explain the scatter in the (N(G1)/N(tot)) − αpd relation, it is necessary to invoke variations in the slope in this mass range between ≈ − 0.9 and ≈ − 1.9. Interpreted in terms of a Kroupa-like broken power law, this translates into variations in the mean mass of between ≈0.2 and 0.55 M⊙. This level of variation is consistent with what is observed for young stellar clusters in the Milky Way and may reflect variations in the physical conditions of the globular cluster progenitor clouds at the time the G1 population formed or may indicate the occurrence of collisions between protostellar embryos before stars settle on the main sequence.

Gaia DR3 in 6D: the search for fast hypervelocity stars and constraints on the galactic centre environment

ABSTRACT The third data release (DR3) of the European Space Agency satellite Gaia provides coordinates, parallaxes, proper motions, and radial velocities for a sample of ∼34 million stars. We use the combined 6D phase space information to search for hypervelocity stars (HVSs), unbound stars accelerated by dynamical processes happening in the Galactic Centre. By looking at the kinematics of Gaia DR3 stars in Galactocentric coordinates and by integrating their orbits in the Galactic potential, we do not identify any HVS candidates with a velocity higher than 700 km s−1 and robustly observed kinematics. Assuming a scenario wherein the interaction between a stellar binary and the massive black hole Sgr A* is responsible for HVS ejections from the Galactic Centre, we derive degenerate limits on the ejection rate of HVSs and the slope of the initial mass function of the primary star among binaries in the Galactic Centre. Our results indicate that the HVS ejection rate is ≲8 × 10−5 yr−1 assuming a Salpeter mass function, and this upper limit becomes progressively smaller for an increasingly top-heavy mass distribution. A fiducial HVS ejection rate of 10−4 yr−1 prefers a mass function slope ≲−2.35, disfavouring previously claimed top-heavy initial mass functions among stars in the Galactic Centre.

A panchromatic view of star cluster formation in a simulated dwarf galaxy starburst

ABSTRACT We present a photometric analysis of star and star cluster (SC) formation in a high-resolution simulation of a dwarf galaxy starburst that allows the formation of individual stars to be followed. Previous work demonstrated that the properties of the SCs formed in the simulation are in good agreement with observations. In this paper, we create mock spectral energy distributions and broad-band photometric images using the radiative transfer code skirt 9. We test several observational star formation rate (SFR) tracers and find that 24 $\mu$m, total infrared and Hα trace the underlying SFR during the (post)starburst phase, while UV tracers yield a more accurate picture of star formation during quiescent phases prior to and after the merger. We then place the simulated galaxy at distances of 10 and 50 Mpc and use aperture photometry at Hubble Space Telescope resolution to analyse the simulated SC population. During the starburst phase, a hierarchically forming set of SCs leads inaccurate source separation because of crowding. This results in estimated SC mass function slopes that are up to ∼0.3 shallower than the true slope of ∼−1.9 to −2 found for the bound clusters identified from the particle data in the simulation. The masses of the largest clusters are overestimated by a factor of up to 2.9 due to unresolved clusters within the apertures. The aperture-based analysis also produces a relation between cluster formation efficiency and SFR surface density that is slightly flatter than that recovered from bound clusters. The differences are strongest in quiescent SF environments.

Bursting Bubbles: Feedback from Clustered Supernovae and the Trade-off Between Turbulence and Outflows

We present an analytic model for clustered supernovae (SNe) feedback in galaxy disks, incorporating the dynamical evolution of superbubbles formed from spatially overlapping SNe remnants. We propose two realistic outcomes for the evolution of superbubbles in galactic disks: (1) the expansion velocity of the shock front falls below the turbulent velocity dispersion of the interstellar medium in the galaxy disk, whereupon the superbubble stalls and fragments, depositing its momentum entirely within the galaxy disk; or (2) the superbubble grows in size to reach the gas scale height, breaking out of the galaxy disk and driving galactic outflows/fountains. In either case, we find that superbubble breakup/breakout almost always occurs before the last Type II SN (≲40 Myr) in the recently formed star cluster, assuming a standard high-end initial mass function slope, and scalings between stellar lifetimes and masses. The threshold between these two cases implies a break in the effective strength of feedback in driving turbulence within galaxies, and a resulting change in the scalings of, for example, star formation rates with gas surface density (the Kennicutt–Schmidt relation) and the star formation efficiency in galaxy disks.

MiMO: Mixture Model for Open Clusters in Color–Magnitude Diagrams

We propose a mixture model of open clusters (OCs) in color–magnitude diagrams (CMDs) to measure the OC properties, including isochrone parameters (age, distance, metallicity, and dust extinction), stellar mass function (MF), and binary parameters (binary fraction and mass-ratio distribution), with high precision and reliability. The model treats an OC in the CMD as a mixture of single and binary member stars and field stars in the same region. The cluster members are modeled using a theoretical stellar model, mass function, and binary properties. The field component is modeled nonparametrically using a separate field-star sample in the vicinity of the cluster. Unlike conventional methods that rely on stringent member selection, ours allows us to use a sample of more complete cluster members and attendant field stars. The larger star sample reduces the statistical error and diminishes the potential bias by retaining more stars that are crucial for age estimation and MF measurement. After validating the method with 1000 mock clusters, we measured the parameters of 10 real OCs using Gaia EDR3 data. The best-fit isochrones are consistent with previous measurements in general but with more precise age estimates for several OCs. The inferred MF slope is −2.7 to −1.6 for clusters younger than 2 Gyr, while older clusters appear to have significantly flatter MFs. The binary fraction is 30%–50%. The photometric and astrometric distances agree well.

A dynamical evolution study of the open clusters: Berkeley 10, Berkeley 81, Berkeley 89 and Ruprecht 135

By utilizing Gaia EDR3 photometric/astrometric data, we studied the dynamical evolution from the obtained astrophysical, structural and dynamical parameters of the open clusters (OCs), Berkeley10 (Be 10), Berkeley81 (Be 81), Berkeley89 (Be 89), and Ruprecht135 (Ru 135). The Gaia EDR3 photometric distances from the isochrone fitting method are smaller than the ones of Gaia EDR2. The relaxation times of four OCs are smaller than their ages, in this regard, they are dynamically relaxed. Their steep overall mass function slopes mean that their low mass stars outnumber their massive ones. Their large τ/relatively small trlx values imply an advanced mass segregation. Therefore, they seem to have lost their low-mass stars much to the field. Be 89’s outer parts indicate an expansion with time. However, Be 10 and Be 81 show the relatively shrinkage core/cluster radii due to dynamical evolution. Ru 135 (1.0 Gyr) may have a primordial origin, instead of shrinking in size and mass with time. Be 89’s tidal radius is less than its cluster radius. This means that its member stars lie within its tidal radius, in the sense it is gravitationally bound to the cluster. For the rest OCs, the cluster members beyond their tidal radii are gravitationally unbound to the clusters, which are more influenced by the potential of the Galaxy.

A Deep Investigation of Two Poorly Studied Open Clusters Haffner 22 and Melotte 71 in the Gaia era

This paper presents a deep investigation of two open clusters, Haffner 22 and Melotte 71, using astrometric and photometric data from Gaia EDR3. We identified 382 and 597 most probable cluster members with membership probability higher than 50%. Mean proper motions in R.A. and decl. are estimated as (−1.631 ± 0.009, 2.889 ± 0.008) and (−2.398 ± 0.004, 4.210 ± 0.005) mas yr−1 for Haffner 22 and Melotte 71, respectively. A comparison of observed CMDs with the theoretical isochrones leads to an age of 2.25 ± 0.25 and 1.27 ± 0.14 Gyr for these clusters. The distances 2.88 ± 0.10 and 2.28 ± 0.15 kpc based on the parallax are comparable with the values derived by the isochrone fitting method. Five and four blue straggler stars (BSS) are identified as cluster members in Haffner 22 and Melotte 71. Based on the relative number of high-velocity (binary) and single stars, we inferred binary fractions for both clusters in the range of ∼10% ≤ f bin ≤ 14%, for both core and o?-core regions. We found binary content is larger in the core region. Mass function slope is in good agreement with the Salpeter’s value for Melotte 71 (x = 1.23 ± 0.38 within mass range 1–3.4 M ⊙) while it is quite a flat slope for Haffner 22 (x = 0.63 ± 0.30 within mass range 1–2.3 M ⊙). Evidence for the existence of mass-segregation effect is observed in both clusters. Using the Galactic potential model, Galactic orbits are derived, indicating that both clusters follow a circular path around the Galactic center, evolving slowly.