本研究针对低质量星系中大量 $N_{GC}=0$ 的问题，比较 Poisson、NB 及其零膨胀模型，发现普通 NB 已足以描述数据，无需零膨胀。
摘要：
星系的球状星团（GC）族群规模（$N_{GC}$）与星系恒星质量（$M_*$）之间的标度关系通常用连续线性模型描述，但实际上它是一种计数关系，理应据此建模。对于大质量星系，负二项（NB）模型已被证明能很好地描述数据，但在低星系质量端，有相当比例的星系具有 $N_{GC}=0$，该标度关系在这一区间的表现尚不清楚。本研究检验了 Poisson 模型和 NB 模型在描述 $N_{GC}-M_*$ 标度关系低质量端方面的效用。我们引入了这些模型的零膨胀版本，它们允许存在比其他模型预测更大的零值群体（例如没有 GC 的星系）。我们使用多种预测模型比较方法评估模型，包括预测区间、留一交叉验证准则和后验预测比较。我们发现 NB 模型与数据相符，但朴素 Poisson 模型则不然。此外，我们发现无需对模型进行零膨胀即可描述缺少 GC 的低质量星系群体，这表明单一形成与演化过程在所有星系质量上均起作用。在 NB 模型下，许多低质量星系缺少 GC 似乎并无特殊之处；它们只是更大范围 $N_{GC}-M_*$ 标度关系在低质量端的延伸。
英文摘要：
The scaling relation between the size of a galaxy's globular cluster (GC) population ($N_{GC}$) and the galaxy's stellar mass ($M_*$) is usually described with a continuous, linear model, but in reality it is a count relationship that should be modeled as such. For massive galaxies, a negative binomial (NB) model has been shown to describe the data well, but it is unclear how the scaling relation behaves at low galaxy masses where a substantial portion of galaxies have $N_{GC}=0$. In this work, we test the utility of Poisson and NB models for describing the low-mass end of the $N_{GC}-M_*$ scaling relation. We introduce the use of zero-inflated versions of these models, which allow for larger zero populations (e.g. galaxies without GCs) than would otherwise be predicted. We evaluate our models with a variety of predictive model comparison methods, including predictive intervals, leave-one-out cross-validation criterion, and posterior predictive comparisons. We find that the NB model is consistent with our data, but the naive Poisson is not. Moreover, we find that zero inflation of the models is not necessary to describe the population of low-mass galaxies that lack GCs, suggesting that a single formation and evolutionary process acts over all galaxy masses. Under the NB model, there does not appear to be anything unique about the lack of GCs in many low-mass galaxies; they are simply the low-mass extension of the larger $N_{GC}-M_*$ scaling relation.
It is argued that Galactic globular clusters rotating retrograde may originate from prograde globular clusters that change their angular momenturm due to gravitational perturbations from the Magellanic Cloud galaxies. It is shown that those galactic globular clusters with orbits near the Lagrangiane point of the system "Milky Way - Maggellanic Clouds" can change the sign of their angular momentum in few Gyr time scale.
Palomar 5 is one of the sparsest star clusters in the Galactic halo and is best-known for its spectacular tidal tails, spanning over 20 degrees across the sky. With N-body simulations we show that both distinguishing features can result from a stellar-mass black hole population, comprising ~20% of the present-day cluster mass. In this scenario, Palomar 5 formed with a `normal' black hole mass fraction of a few per cent, but stars were lost at a higher rate than black holes, such that the black hole fraction gradually increased. This inflated the cluster, enhancing tidal stripping and tail form…
The formation of globular clusters (GC), with their multiple stellar generations, is still an unsolved puzzle. Thus, interest is rising on the possibility to detect their precursors at high redshift, hence directly witnessing their formation. A simple set of assumptions are empirically justified and then used to predict how many such precursors formed between redshift 3 and 10 could actually be detected by the NIRCam instrument on board of JWST. It is shown that the near power-law shape of the rest-frame UV continuum of young globular cluster precursors (GCP) implies that both colours and lumi…
We used a proper combination of high-resolution HST observations and wide-field ground based data to derive the radial star density profile of 26 Galactic globular clusters from resolved star counts (which can be all freely downloaded on-line). With respect to surface brightness (SB) profiles (which can be biased by the presence of sparse, bright stars), star counts are considered to be the most robust and reliable tool to derive cluster structural parameters. For each system a detailed comparison with both King and Wilson models has been performed and the most relevant best-fit parameters hav…
We present core radii for 54 Milky Way globular clusters determined by fitting King-Michie models to cumulative projected star count distributions. We find that fitting star counts rather than surface brightness profiles produces results that differ significantly due to the presence of mass segregation. The sample in each cluster is further broken down into various mass groups, each of which is fit independently, allowing us to determine how the concentration of each cluster varies with mass. The majority of the clusters in our sample show general agreement with the standard picture that more …
We present results of a search for objects with H-alpha excess, such as cataclysmic variables (CVs) and chromospherically active binaries (ABs), as counterparts to X-ray sources detected with Chandra satellite observatory in six Galactic globular clusters (GCs): M4, M28, M30, M71, M80, NGC 6752. Binary systems play a critical role in the evolution of GCs, serving as an internal energy source countering the tendency of GC cores to collapse. Theoretical studies predict dozens of CVs in the cores of some GCs (e.g., 130 for M28, 40 for M30). A number of such binaries is also expected outside the c…
We present Hubble Space Telescope imaging of two ultra diffuse galaxies (UDGs) with measured stellar velocity dispersions in the Coma cluster. The galaxies, Dragonfly 44 and DFX1, have effective radii of 4.7 kpc and 3.5 kpc and velocity dispersions of $47^{+8}_{-6}$ km/s and $30^{+7}_{-7}$ km/s, respectively. Both galaxies are associated with a striking number of compact objects, tentatively identified as globular clusters: $N_{\rm gc}=74\pm 18$ for Dragonfly 44 and $N_{\rm gc}=62\pm 17$ for DFX1. The number of globular clusters is far higher than expected from the luminosities of the galaxies…
The formation of purely baryonic globular clusters with no gravitationally bound dark matter is still a theoretical challenge. We show that these objects might form naturally whenever there is a relative stream velocity between baryons and dark matter. The stream velocity causes a phase shift between linear modes of baryonic and dark matter perturbations, which translates to a spatial offset between the two components when they collapse. For a 2sigma (3sigma) density fluctuation, baryonic clumps with masses in the range 1e5 - 2.5e6 Msun (1e5 - 4e6 Msun) collapse outside the virial radii of the…
We have derived accurate distances to Galactic globular clusters by combining data from the Gaia Early Data Release 3 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-seque…
We present the broadest and most precise empirical investigation of red giant branch bump (RGBB) brightness and number counts ever conducted. We implement a new method and use data from two \textit{Hubble Space Telescope (HST)} globular cluster (GC) surveys to measure the brightness and star counts of the RGBB in 72 GCs. The brightness is measured to a precision better than 0.01 mag while the precision in number counts reaches 10%. The position of the main-sequence turnoff (MSTO) and the number of horizontal branch (HB) stars are used as comparisons where appropriate. Several independent scien…
We present a far-ultraviolet (FUV) study of the globular cluster M30 (NGC 7099). The images were obtained using the Advanced Camera for Surveys (ACS/SBC, F150LP, FUV) and the Wide Field Planetary Camera 2 (WFPC2, F300W, UV) on board the Hubble Space Telescope (HST). We compare the catalogue of FUV objects to ten known X-ray sources and find six confident matches of two cataclysmic variables (CVs), one RS CVn, one red giant with strong FUV emission and two sources only detected in the FUV. We also searched for variable sources in our dataset and found a total of seven blue stragglers (BSs), fou…
The motion of the baryonic components of the Milky Way is governed by both luminous and dark matter content of the Galaxy. Thus, the dynamics of the Milky Way globular clusters can be used as tracers to infer the mass model of the Galaxy up to a large radius. In this work, we use the directly observable line-of-sight velocities to test if the dynamics of the globular cluster population is consistent with an assumed axisymmetric gravitational potential of the Milky Way. For this, we numerically compute the phase space distribution of the globular cluster population where the orbits are either o…
We report the discovery of the likely white dwarf companions to radio millisecond pulsars 47 Tuc Q and 47 Tuc S in the globular cluster 47 Tucanae. These blue stars were found in near-ultraviolet images from the Hubble Space Telescope for which we derived accurate absolute astrometry, and are located at positions consistent with the radio coordinates to within 0.016 arcsec (0.2sigma). We present near-ultraviolet and optical colours for the previously identified companion to millisecond pulsar 47 Tuc U, and we unambiguously confirm the tentative prior identifications of the optical counterparts…
Globular clusters produce many exotic stars due to a much higher frequency of dynamical interactions in their dense stellar environments. Some of these objects were observed together with several hundred thousands other stars in our MUSE survey of 26 Galactic globular clusters. Assuming that at least a few exotic stars have exotic spectra, that means spectra that contain emission lines, we can use this large spectroscopic data set of over a million stellar spectra as a blind survey to detect stellar exotica in globular clusters. To detect emission lines in each spectrum, we model the expected …
We investigate archival Hubble Space Telescope ACS/SBC F140LP observations of NGC~1399 to search for evidence of multiple stellar populations in extragalactic globular clusters. Enhanced FUV populations are thought to be indicators of He-enhanced second generation populations in globular clusters, specifically extreme/blue horizontal branch stars. Out of 149 globular clusters in the field of view, 58 have far ultraviolet (FUV) counterparts with magnitudes brighter than 28.5. Six of these FUV-deteced globular clusters are also detected in X-rays, including one ultraluminous X-ray source ($L_X >…
We present an observational far-UV (FUV) and near-UV (NUV) study of the core region of the globular cluster NGC 6397. The observations were obtained with the Space Telescope Imaging Spectrograph (STIS, FUV), and the Wide Field Camera 3 (WFC3, NUV) on board the Hubble Space Telescope. Here, we focus on the UV bright stellar populations such as blue stragglers (BSs), white dwarfs (WDs) and cataclysmic variables (CVs). We present the first FUV-NUV color-magnitude diagram (CMD) for this cluster. To support our classification of the stellar populations, we compare our FUV-NUV CMD with optical data …
We present a combination of high-resolution Hubble Space Telescope and wide-field ground-based and Galaxy Evolution Explorer data of the Galactic Globular Cluster M10 (NGC6254). By using this large data-set we determined the center of gravity of the cluster and we built its density profile from star counts over its entire radial extension. We find that the density profile is well reproduced by a single-mass King model with structural parameters c=1.41 and r_c=41". We also studied the Blue Straggler Star population and its radial distribution. We count a total number of 120 BSS within the tidal…
One of the key questions in Astrophysics concerns the issue of whether there exists an upper-mass limit to stars, and if so, what physical mechanism sets this limit, which might also determine if the upper-mass limit is metallicity (Z) dependent. We argue that mass loss by radiation-driven winds mediated by line opacity is one of the prime candidates setting the upper-mass limit. We present mass-loss predictions (dM/dt_wind) from Monte Carlo radiative transfer models for relatively cool (Teff = 15kK) inflated very massive stars (VMS) with large Eddington Gamma factors in the mass range 100-100…
A sub-sampled deconvolution technique for crowded field photometry with the HST WFPC2 instrument was proposed by Butler (2000) and applied to search for optical counterparts to pulsars in globular clusters (Golden et al. 2001). Simulations showed that the method, which takes account of the point-spread function (PSF) spatial variation, can provide better star detection and recovers the resolution lost to aberrations and poor sampling. The original emphasis was on precision photometry in crowded fields. In the present work, we have extended this technique to determine proper motions of stars in…
We present a new identity card for the cluster NGC 6440 in the Galactic Bulge. We have used a combination of high-resolution Hubble Space Telescope images, wide-field ground-based observations performed with the ESO-FORS2, and the public survey catalog Pan-STARRS, to determine the gravitational center, projected density profile and structural parameters of this globular from resolved star counts. The new determination of the cluster center differs by ~ 2" (corresponding to 0.08 pc) from the previous estimate, which was based on the surface brightness peak. The star density profile, extending o…
Color-magnitude diagrams (CMDs) derived from Hubble Space Telescope (HST) Advanced Camera for Surveys F606W,F814W photometry of 6 globular clusters (GCs) are presented. The six GCs form two loose groupings in Galactocentric distance (Rgc): IC 4499, NGC 6426, and Ruprecht 106 at ~15-20 kpc and NGC 7006, Palomar 15, and Pyxis at ~40 kpc. The CMDs allow the ages to be estimated from the main sequence turnoff in every case. In addition, the age of Palomar 5 (Rgc ~ 18 kpc) is estimated using archival HST Wide Field Planetary Camera 2 V,I photometry. The age analysis reveals the following: IC 4499, …
The MAVERIC survey is the first deep radio continuum imaging survey of Milky Way globular clusters, with a central goal of finding and classifying accreting compact binaries, including stellar-mass black holes. Here we present radio source catalogs for 25 clusters with ultra-deep Karl G. Jansky Very Large Array observations. The median observing time was 10 hr per cluster, resulting in typical rms sensitivities of 2.3 and 2.1 uJy per beam at central frequencies of 5.0 and 7.2 GHz, respectively. We detect nearly 1300 sources in our survey at 5 sigma, and while many of these are likely to be bac…
Blue (metal-poor) globular clusters are observed to have half-light radii that are ~20% larger than their red (metal-rich) counterparts. The origin of this enhancement is not clear and differences in either the luminosity function or in the actual size of the clusters have been proposed. I analyze a set of dynamically self-consistent Monte Carlo globular cluster simulations to determine the origin of this enhancement. I find that my simulated blue clusters have larger half-light radii due to differences in the luminosity functions of metal-poor and metal-rich stars. I find that the blue cluste…
We use deep, high quality colour magnitude diagrams obtained with the Hubble Space Telescope to compute a simplified version of the Mironov index [SMI; B/(B+R)] to parametrize the horizontal branch (HB) morphology for 23 globular clusters in the M31 galaxy (Sample-A), all located in the outer halo at projected distances between 10 kpc and 100 kpc. This allows us to compare them with their Galactic counterparts, for which we estimated the SMI exactly in the same way, in the SMI vs. [Fe/H] plane. We find that the majority of the considered M31 clusters lie in a significantly different locus, in …
In this paper, the third in a series illustrating the power of generalized linear models (GLMs) for the astronomical community, we elucidate the potential of the class of GLMs which handles count data. The size of a galaxy's globular cluster population $N_{\rm GC}$ is a prolonged puzzle in the astronomical literature. It falls in the category of count data analysis, yet it is usually modelled as if it were a continuous response variable. We have developed a Bayesian negative binomial regression model to study the connection between $N_{\rm GC}$ and the following galaxy properties: central blac…
Intermediate mass black holes play a critical role in understanding the evolutionary connection between stellar mass and super-massive black holes. However, to date the existence of these species of black holes remains ambiguous and their formation process is therefore unknown. It has been long suspected that black holes with masses $10^{2}-10^{4}M_{\odot}$ should form and reside in dense stellar systems. Therefore, dedicated observational campaigns have targeted globular cluster for many decades searching for signatures of these elusive objects. All candidates found in these targeted searches…
