We used an appropriate combination of high-resolution Hubble Space Telescope observations and wide-field, ground-based data to derive the radial stellar density profiles 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 have been obtained. This collection of data represents the largest homogeneous catalog collected so far of star count profiles and structural parameters derived therefrom. The analysis of the data of our catalog has shown that (1) the presence of the central cusps previously detected in the SB profiles of NGC 1851, M13, and M62 is not confirmed; (2) the majority of clusters in our sample are fit equally well by the King and the Wilson models; (3) we confirm the known relationship between cluster size (as measured by the effective radius) and galactocentric distance; (4) the ratio between the core and the effective radii shows a bimodal distribution, with a peak at ~0.3 for about 80% of the clusters and a secondary peak at ~0.6 for the remaining 20%. Interestingly, the main peak turns out to be in agreement with that expected from simulations of cluster dynamical evolution and the ratio between these two radii correlates well with an empirical dynamical-age indicator recently defined from the observed shape of blue straggler star radial distribution, thus suggesting that no exotic mechanisms of energy generation are needed in the cores of the analyzed clusters.
Classification of the optical spectra of active galactic nuclei (AGN) into different types is currently based on features such as line widths and intensity ratios. Although well founded on AGN ...physics, this approach involves some degree of human oversight and cannot scale to large datasets. Machine learning (ML) tackles this classification problem in a fast and reproducible way, but is often (and not without reason) perceived as a black box. However, ML interpretability and are active research areas in computer science that are providing us with tools to mitigate this issue. We apply ML interpretability tools to a classifier trained to predict AGN types from spectra. Our goal is to demonstrate the use of such tools in this context, obtaining for the first time insight into an otherwise black box AGN classifier. In particular, we want to understand which parts of each spectrum most affect the predictions of our classifier, checking that the results make sense in the light of our theoretical expectations. We trained a support-vector machine on 3346 high-quality, low-redshift AGN spectra from SDSS DR15. We considered either two-class classification (type 1 versus 2) or multiclass (type 1 versus 2 versus intermediate-type). The spectra were previously and independently hand-labeled and divided into types 1 and 2, and intermediate-type (i.e., sources in which the Balmer line profile consists of a sharp narrow component superimposed on a broad component). We performed a train-validation-test split, tuning hyperparameters and independently measuring performance via a variety of metrics. On a selection of test-set spectra, we computed the gradient of the predicted class probability at a given spectrum. Regions of the spectrum were then color-coded based on the direction and the amount by which they influence the predicted class, effectively building a saliency map. We also visualized the high-dimensional space of AGN spectra using t-distributed stochastic neighbor embedding (t-SNE), showing where the spectra for which we computed a saliency map are located. Our best classifier reaches an F-score of 0.942 on our test set (with 0.948 precision and 0.936 recall). We computed saliency maps on all misclassified spectra in the test set and on a sample of randomly selected spectra. Regions that affect the predicted AGN type often coincide with physically relevant features, such as spectral lines. t-SNE visualization shows good separability of type 1 and type 2 spectra. Intermediate-type spectra either lie in-between, as expected, or appear mixed with type 2 spectra. Misclassified spectra are typically found among the latter. Some clustering structure is apparent among type 2 and intermediate-type spectra, though this may be an artifact. Saliency maps show why a given AGN type was predicted by our classifier resulting in a physical interpretation in terms of regions of the spectrum that affected its decision, making it no longer a black box. These regions coincide with those used by human experts, for example relevant spectral lines, and are even used in a similar way; the classifier effectively measures the width of a line by weighing its center and its tails oppositely.
Globular star clusters that formed at the same cosmic time may have evolved rather differently from the dynamical point of view (because that evolution depends on the internal environment) through a ...variety of processes that tend progressively to segregate stars more massive than the average towards the cluster centre. Therefore clusters with the same chronological age may have reached quite different stages of their dynamical history (that is, they may have different 'dynamical ages'). Blue straggler stars have masses greater than those at the turn-off point on the main sequence and therefore must be the result of either a collision or a mass-transfer event. Because they are among the most massive and luminous objects in old clusters, they can be used as test particles with which to probe dynamical evolution. Here we report that globular clusters can be grouped into a few distinct families on the basis of the radial distribution of blue stragglers. This grouping corresponds well to an effective ranking of the dynamical stage reached by stellar systems, thereby permitting a direct measure of the cluster dynamical age purely from observed properties.
We present semi-analytical models and simplified N-body simulations with 10 super(4) particles aimed at probing the role of dynamical friction (DF) in determining the radial distribution of blue ...straggler stars (BSSs) in globular clusters. The semi-analytical models show that DF (which is the only evolutionary mechanism at work) is responsible for the formation of a bimodal distribution with a dip progressively moving toward the external regions of the cluster. However, these models fail to reproduce the formation of the long-lived central peak observed in all dynamically evolved clusters. The results of N-body simulations confirm the formation of a sharp central peak, which remains as a stable feature over time regardless of the initial concentration of the system. In spite of noisy behavior, a bimodal distribution forms in many cases, with the size of the dip increasing as a function of time. In the most advanced stages, the distribution becomes monotonie. These results are in agreement with the observations. Also, the shape of the peak and the location of the minimum (which, in most of cases, is within 10 core radii) turn out to be consistent with observational results. For a more detailed and close comparison with observations, including a proper calibration of the timescales of the dynamical processes driving the evolution of the BSS spatial distribution, more realistic simulations will be necessary.
We study the binary fraction of the globular cluster M10 (NGC 6254) as a function of the radius from the cluster core to the outskirts, by means of a quantitative analysis of the color distribution ...of stars relative to the fiducial main sequence. By taking advantage of two data sets, acquired with the Advanced Camera for Survey and the Wide Field Planetary Camera 2 on board the Hubble Space Telescope, we have studied both the core and the external regions of the cluster. The binary fraction is found to decrease from ~14% within the core, to ~1.5% in a region between 1 and 2 half-mass radii from the cluster center. Such a trend and the derived values are in agreement with previous results obtained in clusters of comparable total magnitude. The estimated binary fraction is sufficient to account for the suppression of mass segregation observed in M10, without any need to invoke the presence of an intermediate-mass black hole in its center.
The Alessandrini A+ indicator is a measure of star cluster dynamical evolution based on the mass-segregation of blue straggler stars. A+ is defined as the integral of the cumulative distribution of ...blue stragglers over log radius, minus a term related to the reference population used. In a companion paper I introduced a model of dynamical friction and calculated the A+ indicator analytically. Here I show further properties of the time evolution of A+, focusing on the physical interpretation of its time derivative dA+ /dt. I find that dA+ /dt is the mean of the reciprocal dyamical friction timescale, weighted by the density of blue stragglers. I show that it is non-negative (as expected based on monotonicity) due to the density of blue-stragglers being non-negative and that, for a radially non-decreasing dynamical friction timescale, dA+ /dt is also non-decreasing with time, making A+ a convex function.
Blue straggler stars are more massive than the average star in globular clus- ters, as they originate from the merger of two stars. Consequently, they experience dynamical friction, progressively ...sinking to the cluster center. Recently, several indicators of the degree of dynamical relaxation of a globular cluster have been proposed, based on the observed radial distribution of blue straggler stars. The most successful is the Alessandrini indicator, or A+ for short, which is the integral of the cumulative distribution of the blue straggler stars minus that of a lighter reference population. A+ correlates with the dynamical age of a cluster both in realistic simulations and in observations. Here I calculate the temporal dependence of the A+ indicator analytically in a simplified model of the evolution of the blue straggler star distribution under dynamical friction only.
Context. The globular clusters of our Galaxy have been found to lie close to a plane in the log{R_{e}}, log{\sigma}, {\mathit}_{e} space, on the continuation of the Fundamental Plane that is known to ...characterize the global properties of early-type galaxies. There is no apparent reason why such physically different self-gravitating systems should follow the same scaling law. Aims. We reexamine the issue by focusing on a sample of 48 globular clusters selected with homogeneity criteria for the photometric data available from the literature. Methods. We perform a model-independent analysis of surface brightness profiles and distance moduli, estimating error bars and studying selection effects with robust non-parametric statistical tests. Results. We determine the values of the coefficients that define the Fundamental Plane and their error bars and show that the scatter from the Fundamental Plane relation is likely to be intrinsic, i.e. not due to measurement errors only. Curiously, we find that in the standard Fundamental Plane coordinates the set of points for our sample occupies a rather slim, axisymmetric, cylindrical region of parameter space, which suggests that the relevant scaling relation might be around a line, rather than a plane, confirming results noted earlier. This is likely to be the origin of the difficulties in the fit by a plane, often mentioned in previous investigations. In addition, such a Fundamental Line relation would imply a pure photometric scaling law relating luminosity to the effective radius which might be tested on wider samples and on extra-galactic globular cluster systems. As to the residuals from the Fundamental Plane relation, we find a correlation of the deviations from the plane with the central slope of the surface brightness profile. No other statistically significant correlations are identified. Finally, given the constraint imposed by the virial theorem, we study the distribution of the values of the quantity KV /(M / L) (virial coefficient divided by the relevant mass-to-light ratio); the distribution of the logarithms, reconstructed through kernel density estimation methods, shows evidence for bimodality, which suggests that the galactic globular cluster system may be composed of at least two dynamically different populations. Yet, these populations do not appear to reflect the standard dichotomy between disk and halo clusters.
PDF
