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 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.

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 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.

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.

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..

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⊙.

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.

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.

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.

Wide-bandwidth drift-scan pulsar surveys of globular clusters:application to early science observations with FAST

The Five-hundred-meter Aperture Spherical Telescope （FAST） will begin its early-science oper- ations during 2016. Drift-scan pulsar surveys will be carried out during this period using an ultra-wide-band receiver system （covering - 270 to 1620 MHz）. We describe a method for accounting for the changes in the telescope beam shape and the pulsar parameters when searching for pulsars over such a wide bandwidth. We applied this method to simulated data sets of pulsars in globular clusters that are visible to FAST and found that a representative observation would have a sensitivity of -40 ply. Our results showed that a sin- gle drift-scan （lasting less than a minute） is likely to find at least one pulsar for observations of four globular clusters. Repeated observations will increase the likely number of detections. We found that pulsars in - 16 clusters are likely to be found if the data from 100 drift-scan observations of each cluster are incoherently combined.

Spectroscopic study of globular clusters in the halo of M31 with the Xinglong 2.16 m telescope Ⅱ: dynamics, metallicity and age

In Paper I, we performed spectroscopic observations on 11 confirmed glob- ular clusters （GCs） in M31 with the Xinglong 2.16 m telescope. We mainly focused on the fitting method and the metallicity gradient for the M31 GC sample. Here, we analyze and further discuss the dynamics, metallicity and age, and their distributions, as well as the relationships between these parameters. In our work, eight more con- firmed GCs in the halo of M31 were observed, most of which lack previous spectro- scopic information. These star clusters are located far from the galactic center at a projected radius of ~ 14 to ~ 117 kpc, which is more spatially extended than that in the previous work. Firstly, we measured the Lick absorption-line indices and the ra- dial velocities. Then the ages and metallicity values of [Fe/H] and [a/Fe] were fitted by comparing the observed spectral feature indices and the Single Stellar Population model of Thomas et al. in the Cassisi and Padova stellar evolutionary tracks, respec- tively. Our results show that most of the star clusters in our sample are older than 10 Gyr except B290, which is ~ 5.5 Gyr, and most of them are metal-poor with metallicity [Fe/H] 〈 - 1, suggesting that these clusters were born at the early stage of the galaxy＇s formation. We find that the metallicity gradient for the outer halo clusters with rp 〉 25 kpc may have an insignificant slope of -0.005 ＋ 0.005 dex kpc-1 and if the outliers G001 and H11 are excluded, the slope does not change significantly, with a value of -0.002 ~ 0.003 dex kpc-1. We also find that the metallicity is not a function of age for the GCs with age 〈 7 Gyr, but for the old GCs with age 〉 7 Gyr, there seems to be a trend that the older ones have lower metallicity. Additionally, we plot metallicity distributions with the largest sample of M31 GCs so far and show the bimodality is not significant, and the number of metal-poor and metal-rich groups be- comes comparable. The spatial distributions show that the metal-rich group is more centrally concentrated but the metal-poor group occupies a more extended halo. In ad- dition, the young population is centrally concentrated but the old population is more spatially extended towards the outer halo.

Development of Multilayer Models of Globular Star Clusters and Study of Their Evolution

Usually, models of globular star clusters are created by analyzing their luminosity and other observation parameters. The goal of this work is to create stable models of globular clusters based on the laws of mechanics. It is necessary to set the coordinates, velocities and masses of the stars so that as a result of their gravitational interaction the globular cluster is not destroyed. This is not an easy task, and it has been solved in this paper. Using an exact solution of the axisymmetric gravitational interaction of N-bodies, single-layer spherical structures were created. They are combined into multilayer models of globular clusters. An algorithm and a program for their creation is described. As a result of solving the problem of gravitational interaction of N bodies, evolution of 5-, 10-, and 15-layer structures was studied. During the inter-body interaction, there proceeds a transition from the initial specially organized structure to a structure with bodies, uniformly distributed in space. The number of inter-body collisions decreases, and the globular cluster model passes into the stable form of its existence. The collisions of bodies and the acquisition of rotational motion and thermal energy by them are considered. As a result of the passage to scaled dimensions, the results were recalculated to the conditions of globular star clusters. The periods of rotation and the temperatures of merged stars are calculated. Attention is paid to a decreased central-body mass in the analyzed models of globular star clusters.

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.

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.

Searching for Multiple Populations in Star Clusters Using the China Space Station Telescope

Multiple stellar populations(MPs) in most star clusters older than 2 Gyr, as seen by lots of spectroscopic and photometric studies, have led to a significant challenge to the traditional view of star formation. In this field, spacebased instruments, in particular the Hubble Space Telescope(HST), have made a breakthrough as they significantly improved the efficiency of detecting MPs in crowded stellar fields by images. The China Space Station Telescope(CSST) and the HST are sensitive to a similar wavelength interval, but the CSST covers a field of view which is about 5–8 times wider than that of HST. One of its instruments, the Multi-Channel Imager(MCI),will have multiple filters covering a wide wavelength range from NUV to NIR, making the CSST a potentially powerful tool for studying MPs in clusters. In this work, we evaluate the efficiency of the designed filters for the MCI/CSST in revealing MPs in different color–magnitude diagrams(CMDs). We find that CMDs made with MCI/CSST photometry in appropriate UV filters are powerful tools to disentangle stellar populations with different abundances of He, C, N, O and Mg. On the contrary, the traditional CMDs are blind to multiple populations in globular clusters(GCs). We show that CSST has the potential of being the spearhead instrument for investigating MPs in GCs in the next decades.

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.

Fractions of Compact Object Binaries in Star Clusters:Theoretical Predictions

The binary population in field stars and star clusters contributes to the formation of gravitational wave(GW)sources.However,the fraction of compact-object binaries(CBs),which is an important feature parameter of binary populations,is still difficult to measure and very uncertain.This paper predicts the fractions of important CBs and semi-compact object binaries(SCBs) making use of an advanced stellar population synthesis technique.A comparison with the result of N-body simulation is also presented.It is found that most CBs are formed within about 500 Myr after the starburst.The fractions of CBs and SCBs are demonstrated to correlate with stellar metallicity.The higher the metallicity becomes,the smaller the fraction of black hole binaries(BHBs),neutron star binaries(NSBs) and SCBs.This suggests that the GW sources of BHBs and NSBs are more likely to form in metal-poor environments.However,the fraction of black hole-neutron star binaries is shown to be larger for metalrich populations on average.

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.