Isochrone Fitting of Galactic Globular Clusters—Ⅵ.High-latitude Clusters NGC 5024 (M53),NGC 5053,NGC 5272 (M3),NGC 5466,and NGC7099 (M30)

We fit various color–magnitude diagrams(CMDs) of the high-latitude Galactic globular clusters NGC 5024(M53),NGC 5053,NGC 5272(M3),NGC 5466,and NGC 7099(M30) by isochrones from the Dartmouth Stellar Evolution Database and Bag of Stellar Tracks and Isochrones for α–enrichment [α/Fe] = +0.4.For the CMDs,we use data sets from Hubble Space Telescope,Gaia,and other sources utilizing,at least,25 photometric filters for each cluster.We obtain the following characteristics with their statistical uncertainties for NGC 5024,NGC 5053,NGC 5272,NGC 5466,and NGC 7099,respectively:metallicities [Fe/H] =-1.93 ± 0.02,-2.08 ± 0.03,-1.60 ± 0.02,-1.95 ± 0.02,and-2.07 ± 0.04 dex with their systematic uncertainty 0.1 dex;ages 13.00 ± 0.11,12.70 ± 0.11,11.63 ± 0.07,12.15 ± 0.11,and 12.80 ± 0.17 Gyr with their systematic uncertainty 0.8 Gyr;distances(systematic uncertainty added) 18.22 ± 0.06 ± 0.60,16.99 ± 0.06 ± 0.56,10.08 ± 0.04 ± 0.33,15.59 ±0.03 ± 0.51,and 8.29 ± 0.03 ± 0.27 kpc;reddenings E(B-V) = 0.023 ± 0.004,0.017 ± 0.004,0.023 ± 0.004,0.023 ± 0.003,and 0.045 ± 0.002 mag with their systematic uncertainty 0.01 mag;extinctions AV= 0.08 ± 0.01,0.06 ± 0.01,0.08 ± 0.01,0.08 ± 0.01,and 0.16 ± 0.01 mag with their systematic uncertainty 0.03 mag,which suggest the total Galactic extinction AV= 0.08 across the whole Galactic dust to extragalactic objects at the North Galactic Pole.The horizontal branch morphology difference of these clusters is explained by their different metallicity,age,mass-loss efficiency,and loss of low-mass members in the evolution of the core-collapse cluster NGC 7099 and loose clusters NGC 5053 and NGC 5466.

A Fermi-LAT Study of Globular Cluster Dynamical Evolution in the Milky Way:Millisecond Pulsars as the Probe

Using archival Fermi-LAT data with a time span of~12 yr,we study the population of Millisecond Pulsars(MSPs)in Globular Clusters(GlCs)and investigate their dependence on cluster dynamical evolution in the Milky Way.We show that theγ-ray luminosity(L_(γ))and emissivity(i.e.,ε_(γ)=L_(γ)/M,with M the cluster mass)are good indicators of the population and abundance of MSPs in GlCs,and they are highly dependent on the dynamical evolution history of the host clusters.Specifically speaking,the dynamically older GlCs with more compact structures are more likely to have larger L_(γ)andε_(γ),and these trends can be summarized as strong correlations with cluster stellar encounter rateΓand the specific encounter rate(Λ=Γ/M),with L_(γ)∝Γ^(0.7±0.11)andε_(γ)∝Λ^(0.73±0.13)for dynamically normal GlCs.However,as GlCs evolve into deep core collapse,these trends are found to be reversed,implying that strong encounters may have lead to the disruption of Low-Mass X-ray Binaries and ejection of MSPs from core-collapsed systems.Besides,the GlCs are found to exhibit largerε_(γ)with increasing stellar mass function slope(ε_(γ)∝10^((0.52±0.1)α)),decreasing tidal radius(ε_(γ)∝R_(t)^(-10±0.22))and distances from the Galactic Center(GC,ε_(γ)∝R_(gc)^(-1.13±0.21)).These correlations indicate that,as GlCs losing kinetic energy and spiral in toward the GC,tidal stripping and mass segregation have a preference in leading to the loss of normal stars from GlCs,while MSPs are more likely to concentrate to cluster center and be deposited into the GC.Moreover,we gaugeε_(γ)of GlCs is~10-1000 times larger than the Galactic bulge,the latter is thought to reside thousands of unresolved MSPs and may be responsible for the GC 7-ray excess,which supports that GlCs are generous contributors to the population of MSPs in the GC.

A Possible γ-Ray Pulsation from PSR J1740-5340B in the Globular Cluster NGC 6397

Recently, a new radio millisecond pulsar(MSP) J1740-5340B, hosted in the globular cluster(GC) NGC 6397,was reported with a 5.78 ms spin period in an eclipsing binary system with a 1.97 days orbital period. Based on a modified radio ephemeris updated by tool tempo2, we analyze the ~15 yr γ-ray data obtained from the Large Area Telescope on board the Fermi Gamma-ray Space Telescope and detect PSR J1740-5340B's γ-ray pulsation at a confidence level of ~4σ with a weighted H-test value of ~26. By performing a phase-resolved analysis, the γ-ray luminosity in on-pulse interval of PSR J1740-5340B is L_(γ)~ 3.8 × 10^(33) erg s^(-1) using NGC 6397's distance of 2.48 kpc. And γ-rays from the on-pulse part of PSR J1740-5340B contribute ~90% of the total observed γ-ray emissions from NGC 6397. No significant γ-ray pulsation of another MSP J1740-5340A in the GC is detected.Considering that the previous four cases of MSPs in GCs, more data in γ-ray, X-ray, and radio are encouraged to finally confirm the γ-ray emissions from MSP J1740-5340B, especially starving for a precise ephemeris.

Classifying Globular Clusters and Applying them to Estimate the mass of the Milky Way

We combine the kinematics of 159 globular clusters(GCs) provided by the Gaia Early Data Release 3(EDR3) with other observational data to classify the GCs,and to estimate the mass of the Milky Way(MW).We use the agemetallicity relation,integrals of motion,action space and the GC orbits to identify the GCs as either formed in situ(Bulge and Disk) or ex situ(via accretion).We find that 45.3% have formed in situ,while 38.4% may be related to known merger events:Gaia-Sausage-Enceladus,the Sagittarius dwarf galaxy,the Helmi streams,the Sequoia galaxy and the Kraken galaxy.We also further identify three new sub-structures associated with the Gaia-Sausage-Enceladus.The remaining 16.3% of GCs are unrelated to the known mergers and thought to be from small accretion events.We select 46 GCs which have radii 8.0 <r<37.3 kpc and obtain the anisotropy parameter β=0.315_(-0.049)^(+0.055),which is lower than the recent result using the sample of GCs in Gaia Data Release 2,but still in agreement with it by considering the error bar.By using the same sample,we obtain the MW mass inside the outermost GC as M(<37.3 kpc)=0.423_(-0.02)^(+0.02)×10^(12)M_(⊙),and the corresponding M_(200)=1.11_(-0.18)^(+0.25)×10^(12)M_(⊙).The estimated mass is consistent with the results in many recent studies.We also find that the estimated β and mass depend on the selected sample of GCs.However,it is difficult to determine whether a GC fully traces the potential of the MW.

The Analyses of Globular Cluster Pulsars and Their Detection Efficiency

Up to 2022 November,267 pulsars had been discovered in 36 globular clusters(GCs).In this paper,we present our studies on the distribution of GC pulsar parameters and the detection efficiency.The power law relation between average dispersion measure(■)and dispersion measure difference(ΔDM)of known pulsars in GCs is lgΔDM∝1.52lg■.The sensitivity could be the key to finding more pulsars.As a result,several years after the construction of a large radio telescope facility,the number of known GC pulsars will likely be increased accordingly.We suggest that currently GCs in the southern hemisphere could have higher possibilities for finding new pulsars.

Age and chemical composition of the globular cluster NGC 6652

We present the results of determination of the age,helium mass fraction(Y),metallicity([Fe/H]),and abundances of the elements C,N,O,Na,Mg,Ca,Ti,C and Mn for the Galactic globular cluster NGC 6652.We use its medium-resolution integrated-light spectrum from the library of Schiavon and our population synthesis method to fulfill this task.We select the evolutionary isochrone and stellar mass function for our analysis,which provide the best approximation to the shapes and intensities of the observed Balmer line profiles.The determined elemental abundances,age and metallicity are characteristic of stellar populations in the Galactic Bulge.

A binary study of color-magnitude diagrams of 12 globular clusters

Binary stars are common in star clusters and galaxies, but the detailed ef- fects of binary evolution are not taken into account in some color-magnitude diagram （CMD） studies. This paper studies the CMDs of twelve globular clusters via binary- star stellar populations. The observational CMDs of the star clusters are compared to those of binary-star populations, and then the stellar metallicities, ages, distances and reddenings of these star clusters are obtained. The paper also tests the different effects of binary and single stars on CMD studies. It is shown that binaries can better fit the observational CMDs of the sample globular clusters compared to single stars. This suggests that the effects of binary evolution should be considered when modeling the CMDs and stellar populations of star clusters and galaxies.

The tidal tails of globular cluster Palomar 5 based on the neural networks method

The sixth Data Release （DR6） of the Sloan Digital Sky Survey （SDSS） provides more photometric regions, new features and more accurate data around globular cluster Palomar 5. A new method, Back Propagation Neural Network （BPNN）, is used to estimate the cluster membership probability in order to detect its tidal tails. Cluster and field stars, used for training the networks, are extracted over a 40 × 20 deg^2 field by color-magnitude diagrams （CMDs）. The best BPNNs with two hidden layers and a Levenberg-Marquardt （LM） training algorithm are determined by the chosen cluster and field samples. The membership probabilities of stars in the whole field are obtained with the BPNNs, and contour maps of the probability distribution show that a tail extends .5.42° to the north of the cluster and another tail extends 3.77° to the south. The tails are similar to those detected by Odenkirchen et al., but no more debris from the cluster is found to the northeast in the sky. The radial density profiles are investigated both along the tails and near the cluster center. Quite a few substructures are discovered in the tails. The number density profile of the cluster is fitted with the King model and the tidal radius is determined as 14.28＇. However, the King model cannot fit the observed profile at the outer regions （R 〉 8＇） because of the tidal tails generated by the tidal force. Luminosity functions of the cluster and the tidal tails are calculated, which confirm that the tails originate from Palomar 5.

p-capture reaction cycles in rotating massive stars and their impact on elemental abundances in globular cluster stars: A case study of O, Na and Al

Elemental abundance patterns of globular cluster stars can provide important clues for understanding cluster formation and early chemical evolution.The origin of the abundance patterns,however,still remains poorly understood.We have studied the impact of p-capture reaction cycles on the abundances of oxygen,sodium and aluminium considering nuclear reaction cycles of carbon-nitrogenoxygen-fluorine,neon-sodium and magnesium-aluminium in massive stars in stellar conditions of temperature range 2×107to 10×107K and typical density of 102gm cc-1.We have estimated abundances of oxygen,sodium and aluminium with respect to Fe,which are then assumed to be ejected from those stars because of rotation reaching a critical limit.These ejected abundances of elements are then compared with their counterparts that have been observed in some metal-poor evolved stars,mainly giants and red giants,of globular clusters M3,M4,M13 and NGC 6752.We observe an excellent agreement with[O/Fe]between the estimated and observed abundance values for globular clusters M3 and M4 with a correlation coefficient above 0.9 and a strong linear correlation for the remaining two clusters with a correlation coefficient above 0.7.The estimated[Na/Fe]is found to have a correlation coefficient above 0.7,thus implying a strong correlation for all four globular clusters.As far as[Al/Fe]is concerned,it also shows a strong correlation between the estimated abundance and the observed abundance for globular clusters M13 and NGC 6752,since here also the correlation coefficient is above 0.7 whereas for globular cluster M4 there is a moderate correlation found with a correlation coefficient above 0.6.Possible sources of these discrepancies are discussed.

Possible Streams of the Globular Clusters in the Galaxy

We aim to retrieve ghost streams under the assumption that all the globular clusters in our Galaxy were formed in very early merge events. Our results are based on two speculations： that the specific energy and angular momentum of the globular clusters after merge are not changed in the course of evolution and that the globular clusters with a common origin would stay in the same orbit plane as the parent galaxy. After taking into account the apogalacticum distance of the orbits, we suggest with some Confidence five possible streams. The number of streams is consistent with the previous results. Three of the four well established members of the Sagittadus stream were found to be in one of our streams. Several other globular clusters in our result were also thought to come from accretion by previous researchers. The orbital parameters of the streams are derived, which provide a way to test whether these streams are true with the help of more accurate measurement of proper motions of the globular clusters.

A proper motion study of the globular cluster M12(NGC 6218)

Using astrometric techniques developed by Anderson et al., we determine proper motions （PMs） in the ~ 14.60 × 16.53 arcmin^2 area of the kinematically ＂thick-disk＂ globular cluster M 12. The cluster＇s proximity and sparse nature makes it a suitable target for ground-based telescopes. Archive images with time gap of ~ 11.1 years were observed with the wide-field imager （WFI） mosaic cam-era mounted on the ESO 2.2m telescope. The median value of PM error in both components is 0.7masyr^-1 for the stars having V ≤ 20mag. PMs are used to determine membership probabil-ities and to separate field stars from the cluster sample. In electronic form, a membership catalog of 3725 stars with precise coordinates, PMs and BVRI photometry is being provided. One of the possible applications of the catalog is demonstrated by gathering the membership information of the variable stars, blue stragglers and X-ray sources reported earlier in the cluster＇s region.

The fractions of post-binary-interaction stars and evolved blue straggler stars on the red giant branch of globular clusters

The red giant branch(RGB)of globular clusters(GCs)is home to some exotic stars,which may provide clues on the formation of multiple stellar populations in GCs.It is well known that binary interactions are responsible for many exotic stars.Thus,it is important to understand what fraction of stars on the RGB of GCs is the result of binary interactions.In this paper,we performed a binary population synthesis study to track the number of post-binary-interaction(post-BI)stars that appear on the RGB,with particular emphasis on the evolved blue straggler stars(E-BSSs).Assuming an initial binary fraction of nearly 50%,we find that about half of the objects on the RGB(called giants)underwent the binary interactions,and that E-BSSs account for around 10%of the giants in our standard simulation.We also compare the properties of post-BI giants that evolved from different channels.We find that the initial orbital period and mass ratio distributions significantly affect the fraction of post-BI giants.Our results imply that the non-standard stars from binary interactions provide a non-negligible contribution to the RGB stars in GCs,which should be considered in future investigations of the origin of multiple stellar populations.

Orbits of 152 globular clusters of the Milky Way galaxy constructed from Gaia DR2

We present orbits and their properties for 152 globular clusters of the Milky Way galaxy obtained using average Gaia DR2 proper motions and other astrometric data from the list of Vasiliev. For orbital integration we have applied the axisymmetric model of the Galactic potential based on the Navarro-Frenk-White dark halo, and modified by Bajkova & Bobylev utilizing circular velocities of Galactic objects in a wide region of Galactocentric distances(up to 200 kpc) from the Bhattacharjee et al. catalog. Based on the analysis of the obtained orbits, we have modified the composition of the subsystems of globular clusters presented in Massari et al..

Milky Way globular cluster dynamics:are they preferentially co-rotating?

The motion of baryonic components of the Milky Way is governed by both luminous and dark matter content of the Galaxy.Thus,the dynamics of Milky Way globular clusters(GCs)can be used as tracers to infer the mass model of the Galaxy up to a large radius.In this work,we apply the directly observable line-of-sight velocities to test if the dynamics of the GC population are consistent with an assumed axisymmetric gravitational potential of the Milky Way.For this,we numerically compute the phase space distribution of the GC population where the orbits are either oriented randomly or co-/counter-rotating with respect to the stellar disk.Then we compare the observed position and line-of-sight velocity distribution of^150 GCs with those of the models.We found that,for the adopted mass model,the co-rotating scenario is the favored model based on various statistical tests.We do the analysis with and without the GCs associated with the progenitors of early merger events.This analysis can be extended in the near future to include precise and copious data to better constrain the Galactic potential up to a large radius.

Probing dark contents in globular clusters with timing effects of pulsar acceleration

We investigate pulsar timing residuals due to the coupling effect of the pulsar transverse acceleration and the Romer delay.The effect is relatively small and usually negligible.Only for pulsars in globular clusters,it is possibly important.The maximum residual amplitude,which is from the pulsar near the surface of the core of the cluster,is about tens of nanoseconds,and may hardly be identified for most globular clusters currently.However,an intermediate-mass black hole in the center of a cluster can apparently increase the timing residual magnitudes.Particularly for pulsars in the innermost core region,their residual magnitudes may be significant.The high-magnitude residuals,which are above critical lines of each cluster,are strong evidence for the presence of a black hole or dark remnants of comparable total mass in the center of the cluster.We also explored the timing effects of line-of-sight accelerations for the pulsars.The distribution of measured line-of-sight accelerations are simulated with a Monte Carlo method.Two-dimensional Kolmogorov-Smirnov tests are performed to reexamine the consistency of distributions of the simulated and reported data for various values of parameters of the clusters.It is shown that the structure parameters of Terzan 5 can be constrained well by comparing the distribution of measured lineof-sight accelerations with the distributions from Monte Carlo simulations.We find that the cluster has an upper limit on the central black hole/dark remnant mass of~6000 M⊙.

Detection of the Farthest Globular Cluster NGC 6715 and Two Other GCs in Gamma-Rays with Fermi-LAT

In this paper,~12 yr long-term Pass 8 data from Fermi Large Area Telescope for the 157 globular clusters are carefully re-analyzed.Besides the 31 globular clusters reported in the fourth Fermi Large Area Telescope catalog Data Release 2,NGC 1851 is identified as a gamma-ray emitter and the significant gamma-ray emissions from NGC 6715 and NGC 6723 are detected.Especially NGC 6715 is located at a distance of 26.8 kpc,so far it is the farthest globular cluster detected in gamma-rays.A detailed analysis for these three globular clusters has been performed,but their gamma-ray pulsation emissions or flux variabilities are not found.The numbers of millisecond pulsars(MSPs)in these globular clusters are estimated under the assumption that each MSP inside globular clusters emits a similar amount of gamma-rays.Some possible origins of gamma-ray emission from globular clusters,such as MSPs,pulsar binary systems and/or dark matter,are discussed.

Self-similar orbit-averaged Fokker-Planck equation for isotropic spherical dense clusters(iii)Application to Galactic globular clusters

Fitting parametric models to globular clusters’structural profiles has been essential for the study of stellar dynamics.It provides their important structural parameters,such as the concentrations and core radii of the clusters.However,existing parametric models can apply only to non-collapsing-core clusters in the early relaxation-evolution stage.Hence,a single parametric model cannot provide globular clusters’structural parameters in both the early and late evolution stages.We have recently found an accurate spectral solution for the self-similar orbit-averaged Fokker-Planck(OAFP)equation to model collapsingcore clusters at the late evolution stage.The present work establishes a new parametric model by combining the self-similar OAFP-and polytropic-models.Although it is a single-mass and isotropic model,the new model applies to at least fifty-five Galactic globular clusters with resolved cores in all the evolution stages.As a main result,we show the characteristics of the relaxation times against the concentrations of the clusters.We also affirm that the structures of low-concentration clusters are polytropic in the Milky Way.

Radio Emission from Globular Clusters

Radio emission of globular clusters is studied by analyzing the VLA radio survey data of the NVSS and FIRST. We find that 13 clusters have radio sources within their half-mass radii of clusters. Sources detected previously in NGC 7078 and NGC 6440 are identified. Pulsars in NGC 6121, NGC 6440 and NGC 7078 cannot be detected because of the insufficient survey sensitivity and resolution. There may be a pulsar in the core of Terzan 1. The nature of the extended radio source near the core of NGC 6440 remains unclear. In the core of a globular cluster, there may be many neutron stars or an intermediate mass black hole, but this cannot be clarified with the current radio observations.

Two particular EA-type binaries in the globular cluster ω Centauri

We analyzed the B and V light curves of two EA-type binaries V211 and NV358 for the first time using the Wilson-Devinney code. Our analysis shows that V211 is a typical Algol-type binary and NV358 is a well detached binary system. As the two binaries are definite members of ω Centauri due to their proper motion, we estimated their physical parameters, obtaining M1 = 1.13 4±0.03 M⊙, R1 = 0.98±0.01 R⊙, M2 = 0.33 ±0.01 M⊙ and R2 = 0.92 ±0.01 R⊙ forV211; M1 = 1.304-0.05 M⊙, R1 = 1.03±0.01 R⊙, M2 = 0.58±0.02 M⊙ and R2 = 0.78±0.01 R⊙ for NV358. On the color-magnitude diagram of ω Centauri, V211 is located in the faint blue straggler region and its primary component is more massive than a star at the main-sequence turnoff. Therefore, V211 is a blue straggler and was formed by mass transfer from the secondary component to the primary. The age of NV358 is less than 1.93 Gyr, indicating that it is much younger than the first generation of stars in ω Centaufi. Like NV364 in ω Centaufi, NV358 should be a second-generation binary.

Detections of Gamma-Rays from Globular Clusters ESO 452-SC11, NGC 6380, Palomar 6 and UKS 1 with Fermi-LAT

The events from 157 globular clusters(GCs)are analyzed by using 12 yr long-term Pass 8 data from Fermi Large Area Telescope.Besides the 34 GCs reported in previous literatures,four additional GCs(ESO 452-SC11,NGC6380,Palomar 6 and UKS 1)in the Milky Way are detected as gamma-ray GC candidates.Especially for UKS 1,these are known as the faintest GCs in long-wavelength bands.Further data analysis has been performed for the four GCs.While no pulsars are determined in radio and/or X-ray wavelengths so far,their gamma-ray pulsation emissions are not found,and no significant gamma-ray flux variability is detected.The numbers of MSPs within the four GCs are estimated based on the assumption that the MSPs within each GC emit similar amounts of gamma-rays.The gamma-ray results reported here could help us better understand the nature of gamma-ray emission origins for GCs.