arXiv subjects

A. P. Milone

Publications and source records attributed to A. P. Milone.

At least 37 records · Page 2Linked to original sources

arXiv2025

High-Resolution Infrared Spectroscopy of the Dust-Obscured Metal-Poor Open Cluster Trumpler 5

Trumpler 5 is a moderately old, dust-obscured metal-poor open cluster. In this study, high-resolution near-infrared spectroscopic data of seven giant stars from the Trumpler 5 cluster were analyzed to derive chemical abundances for 20 elements and $^{12}C/^{13}C$ ratios. Color-magnitude diagram (CMD) analysis of BV and Gaia photometry has also been performed for a comprehensive study of the cluster. Thanks to the methodology employed, some targets are studied for the first time. Additionally, it provides a detailed color-magnitude diagram analysis using photometric and spectroscopic data. We gathered high-resolution spectra for seven Trumpler 5 red giants in the near-infrared H and K wavelength domains, using the Immersion Grating INfrared Spectrometer (IGRINS). We introduced a method to initially estimate the stellar surface gravity (log g) by using calibrated equivalent widths of the Ti II line at 15873 Å from a large sample. We performed standard spectroscopic analyses to refine the model atmospheric parameters of our targets and determined the chemical abundances primarily through spectrum synthesis. We also performed color-magnitude diagram analyses to extract differential reddening correction to compare cluster parameters both with and without corrections. We derived stellar parameters for seven members of Trumpler 5 with our method and the results are consistent with both the literature and other methods. We also inferred elemental abundances for more than 20 species, along with the $^{12}C/^{13}C$ ratios. The elemental abundances are in good agreement with the literature values for similar targets. Through CMD analysis, we found the reddening value, E(B-V)$\simeq$0.76 and estimated the age of the cluster to be approximately 2.50 Gyr.

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arXiv2025

A JWST project on 47 Tucanae: kinematics, energy equipartition and anisotropy of multiple populations

Recent work with JWST has demonstrated its capability to identify and chemically characterize multiple populations in globular clusters down to the H-burning limit. In this study, we explore the kinematics of multiple populations in the globular cluster 47 Tucanae by combining data from JWST, HST, Gaia, and ground-based telescopes. We analyzed velocity dispersion and anisotropy profiles from the cluster center out to $\sim$10$R_h$. Our findings indicate that while first population (1G) stars' motions are isotropic, second population (2G) stars' motions are significantly radially anisotropic. These results align with the predictions of simulations of the dynamical evolution of clusters where 2G stars are initially more centrally concentrated than 1G stars. Furthermore, we subdivided the 2G population into two subpopulations: $2G_A$ and $2G_B$, with the latter being more chemically extreme. We compared their dynamical profiles and found no significant differences. For the first time, we measured the degree of energy equipartition among the multiple populations of 47 Tucanae. Overall, within the analyzed radial range ($\sim$2-4$R_h$), both populations exhibit a low degree of energy equipartition. The most significant differences between 1G and 2G stars are observed in the tangential velocity component, where 2G stars are characterized by a stronger degree of energy equipartition than 1G stars. In the radial component, the behavior of 1G and 2G stars is more variable, with differences largely dependent on radius. Moreover, our analysis reveals that the ratio of rotational velocity to velocity dispersion is larger for the 2G population. Finally, we found that 1G stars exhibit higher skewness in their tangential proper motions than 2G stars, providing additional evidence of kinematic differences between the two stellar generations.

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arXiv2025

A JWST project on 47 Tucanae. Binaries among multiple populations

Almost all globular clusters (GCs) contain multiple populations consisting of stars with varying helium and light-element abundances. These populations include first-population stars, which exhibit similar chemical compositions to halo-field stars with comparable [Fe/H], and second-population stars, characterized by enhanced He and N abundances along with reduced levels of O and C. Nowadays, one of the most intriguing open questions about GCs pertains to the formation and evolution of their multiple populations. Recent works based on N-body simulations of GCs show that the fractions and characteristics of binary stars can serve as dynamic indicators of the formation period of multiple-population in GCs and their subsequent dynamical evolution. Nevertheless, the incidence of binaries among multiple populations is still poorly studied. Moreover, the few available observational studies are focused only on the bright stars of a few GCs. In this work, we use deep images of the GC 47 Tucanae collected with the JWST and HST to investigate the incidence of binaries among multiple populations of M-dwarfs and bright main-sequence stars. To reach this objective, we use UV, optical, and near infrared filters to construct photometric diagrams that allow us to disentangle binary systems and multiple populations. Moreover, we compared these observations with a large sample of simulated binaries. In the cluster central regions, the incidence of binaries among first-population stars is only slightly higher than that of second-population stars. In contrast, in the external regions, the majority (>85%) of the studied binaries are composed of first population stars. Results are consistent with the GC formation scenarios where the second-population stars originate in the cluster's central region, forming a compact and dense stellar group within a more extended system of first-population stars

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arXiv2025

Linking Photometry and spectroscopy: profiling multiple populations in globular clusters

Our understanding of multiple populations in globular clusters (GCs) largely comes from photometry and spectroscopy: appropriate photometric diagrams can disentangle first and second populations (1P and 2P)-1P having chemical signatures similar to field stars, and 2P stars showing unique light-element variations-while spectroscopy enables detailed chemical abundances analyses of these populations. We combine multi-band photometry with extensive spectroscopic data to investigate the chemical composition of multiple populations across 38 GCs, yielding a chemical abundance dataset for stars with precise population tagging. This dataset provides the most extensive analysis of C, N, O, Na, Mg, and Al variations, revealing the largest sample yet of light-element spreads across GCs. GC mass correlates with light-element variations, supporting earlier photometric studies. We investigated iron differences among 1P stars, confirming their presence in 19 GCs, and finding a spread consistent with prediction based on photometry. Notably, in eight of them we detected a correlation between [Fe/H] and the position in iron-sensitive photometric diagrams. More massive GCs display larger lithium depletion among 2P stars, which is consistent with zero at smaller masses. Notably, some 2P stars with the most extreme chemical differences compared to 1P stars still show Li comparable to 1P, suggesting that the 1P polluters have produced some amount of this element. We analyzed the anomalous stars, a population characterized by enrichment in iron, s-process elements, and C+N+O, in ten GCs. NGC1851, NGC5139, NGC6656, and NGC 6715 display light-element inhomogeneities similar to 1P and 2P stars. Iron and barium enrichment varies widely-negligible in some clusters and much larger than errors in others. Generally, these elemental spreads correlate with GC mass.

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arXiv2025

Exploring Multiple Stellar Populations in Globular Clusters with Euclid: A Theoretical Overview and Insights from NGC 6397

We investigate the behavior of multiple stellar populations in globular clusters (GCs) using photometric diagrams constructed with Euclid photometry. By employing synthetic spectra and isochrones that incorporate the chemical differences between first-population (1P) stars, resembling field stars, and second-population (2P) stars, enriched in helium and nitrogen but depleted in carbon and oxygen, we identify, from a theoretical perspective, the color-magnitude diagrams and the chromosome maps most effective at distinguishing these populations within GCs. Euclid photometry proves to be a powerful tool for identifying multiple populations among M-dwarfs, as 1P and 2P stars form distinct sequences in well-chosen photometric diagrams, driven by differences in the strength of oxygen-based molecular features, such as water vapor. To validate our theoretical findings, we analyzed Euclid photometry and astrometry of the GC NGC 6397, complemented by photometric and astrometric data from the Hubble Space Telescope and James Webb Space Telescope, enabling a comprehensive study of its stellar populations across a wide field of view. We find that the 1P constitutes about 30% of the M-dwarfs in NGC 6397, with the fraction of 1P stars remaining consistent across different stellar masses and throughout the entire field of view. 2P stars exhibit an [O/Fe] depletion of about 0.3 dex relative to 1P stars, and both populations display isotropic proper motions. This study represents the first comprehensive analysis of multiple populations among M-dwarfs across a wide field of view, demonstrating that Euclid photometry is a powerful instrument for investigating multiple populations in GCs.

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arXiv2025

Exploring the formation environment of multiple stellar populations in Globular Clusters through binary systems

Globular Clusters (GCs) are known to host distinct stellar populations, characterized by different chemical compositions. Despite extensive research, the origin of these populations remains elusive. According to many formation scenarios, the second population (2P) originated within a compact and denser region embedded in a more extended first population (1P) system. As a result, 2P binaries should be disrupted at a larger rate than 1P binaries. For this reason, binary systems offer valuable insight into the environments in which these stellar populations formed and evolved. In this research, we analyze the fraction of binaries among 1P and 2P M dwarfs in the outer region of NGC 288 using Hubble Space Telescope data. We combine our results with those from a previous work, where we inferred the fraction of 1P and 2P binaries in the cluster center. In the outer region, we find a predominance of 1P binaries ($97^{+1}_{-3}\%$) compared to 2P binaries ($3\pm1\%$) corresponding to an incidence of binaries with a mass ratio (i.e., the ratio between the masses of the primary and secondary star) greater than 0.5 equal to $6.4\pm 1.7\%$ for the 1P population and $0.3\pm 0.2\%$ for the 2P population. These binary fractions and incidences differ from those found in the cluster$'$s central region, where the 1P and 2P populations exhibit similar binary incidences and fractions. These results are in general agreement with the predictions of simulations following the evolution of binary stars in multiple-population GCs, starting with a dense 2P subsystem concentrated in the central regions of a 1P system.

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arXiv2025

Mass loss along the red giant branch of the intermediate stellar populations in NGC6752 and NGC2808

The morphology of the Horizontal Branch (HB) in Globular Clusters (GC) is among the early evidences that they contain multiple populations of stars. Indeed, the location of each star along the HB depends both on its initial helium content (Y) and on the global average mass loss along the red giant branch ($μ$). In most GCs, it is generally straightforward to analyse the first stellar population (standard Y), and the most extreme one (largest Y), while it is more tricky to look at the "intermediate" populations (mildly enhanced Y). In this work, we do this for the GCs NGC6752 and NGC2808; wherever possible the helium abundance for each stellar populations is constrained by using independent measurements present in the literature. We compare population synthesis models with photometric catalogues from the Hubble Space Telescope Treasury survey to derive the parameters of these HB stars. We find that the location of helium enriched stars on the HB is reproduced only by adopting a higher value of $μ$ with respect to the first generation stars in all the analysed stellar populations. We also find that $μ$ correlates with the helium enhancement of the populations. This holds for both clusters. This finding is naturally predicted by the model of ''pre-main sequence disc early loss'', previously suggested in the literature, and is consistent with the findings of multiple-populations formation models that foresee the formation of second generation stars in a cooling flow.

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arXiv2025

New perspective on the multiple population phenomenon in Galactic globular clusters from a wide-field photometric survey

Wide-field photometry of Galactic globular clusters (GCs) has been investigated to overcome limitations from the small field of view of the Hubble Space Telescope in the study of multiple populations. In particular, 'chromosome maps' (ChMs) built with ground-based photometry were constructed to identify the first and second generation stars (1G and 2G) over the wide-field of view. The ChMs allow us to derive the fraction of distinct populations in an analyzed field of view. We present here the radial distribution of the 2G fraction in 29 GCs. The distributions show that all the GCs either have a flat distribution or more centrally concentrated 2G stars. Notably, we find that the fraction of 1G stars outside the half-light radius is clearly bifurcated across all mass range. It implies that a group of GCs with lower 1G fractions (hereafter Group II) have efficiently lost their 1G stars in the outermost cluster regions. In fact, in connection with the trends of the radial distribution, most GCs of Group II have spatially mixed populations, while only less massive GCs in Group I (a group with higher 1G fraction) show that feature. Lastly, we investigate links between these two groups and host cluster parameters. We find that most GCs of Group II are distributed along a broader range of galactocentric distances with smaller perigalactic distances < 3.5 kpc. Besides, by using the Gaia data, it is observed that Group II GCs have higher energy on the integrals of motion diagrams than Group I GCs.

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arXiv2024

oMEGACat V: Helium Enrichment in $ω$ Centauri as a Function of Metallicity

Constraining the helium enhancement in stars is critical for understanding the formation mechanisms of multiple populations in star clusters. However, measuring helium variations for many stars within a cluster remains observationally challenging. We use Hubble Space Telescope photometry combined with MUSE spectroscopic data for over 7,200 red-giant branch stars in \omc\ to measure helium differences between distinct groups of stars as a function of metallicity separating the impact of helium enhancements from other abundance variations on the pseudo-color (chromosome) diagrams. Our results show that stars at all metallicities have subpopulations with significant helium enhancement ($ΔY_{min} \gtrsim$ 0.11). We find a rapid increase in helium enhancement from low metallicities ($\rm{[Fe/H] \simeq -2.05}$ to $\rm{[Fe/H] \simeq -1.92})$, with this enhancement leveling out at \deltay\ $= 0.154$ at higher metallicities. The fraction of helium-enhanced stars steadily increases with metallicity ranging from 10\% at $\rm{[Fe/H] \simeq -2.04}$ to over $90\%$ at $\rm{[Fe/H] \simeq -1.04}$. This study is the first to examine helium enhancement across the full range of metallicities in \omc{}, providing new insight into its formation history and additional constraints on enrichment mechanisms.

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arXiv2024

Exploring Simple-Population and Multiple-Population Globular Clusters in the Outer Galactic Halo using the Hubble Space Telescope

The pseudo two-color diagram, known as chromosome map (ChM), is a valuable tool for identifying globular clusters (GCs) that consist of single or multiple stellar populations (MPs). Recent surveys of Galactic GCs using the ChM have provided stringent observational constraints on the formation of GCs and their stellar populations. However, these surveys have primarily focused on GCs at moderate distances from the Galactic center and composed of MPs. In this paper, we present the first detailed study of the stellar composition of four GCs in the outer halo of the Milky Way: Arp 2, Ruprecht 106, Terzan 7, and Terzan 8. Our analysis is based on high-precision photometry obtained from images collected with the Hubble Space Telescope in the F275W, F336W, F438W, F606W, and F814W bands. We find that Ruprecht 106 and Terzan 7 are composed solely of a single stellar population, whereas Arp 2 and Terzan 8 host both first- and second-population stars. In these clusters, the second population comprises about half and one-third of the total number of GC stars, respectively. The results from this paper and the literature suggest that the threshold in the initial GC mass, if present, should be smaller than approximately 10^5 M$_{\odot}$. The first-population stars of Arp 2 and Terzan 8, along with the stars of the simple-population GCs Ruprecht 106 and Terzan 7, exhibit intrinsic F275W - F814W color spreads, likely indicative of [Fe/H] variations of approximately 0.05 -- 0.30 dex. This suggests that star-to-star metallicity variations are a common feature of star clusters, regardless of the presence of MPs.

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arXiv2024

Spectro-Photometry and Radial Distribution of Multiple Stellar Populations in Globular Clusters from Gaia XP Spectra

Understanding the formation of multiple populations in globular clusters (GCs) represents a challenge for stellar population studies. Nevertheless, the outermost cluster regions, likely to hold clues about the initial configuration of GC stars, remain underexplored. We use synthetic spectra reflecting the chemical compositions of first- and second-population (1P, 2P) stars in 47Tucanae to identify spectral regions sensitive to these populations. This led us to define new photometric bands that effectively distinguish 1P and 2P giant stars using Gaia XP spectra. Testing these filters, we constructed the pseudo two-color diagrams dubbed chromosome maps (ChMs) and, for the first time, identified 1P and 2P stars in the cluster's outermost regions and beyond its tidal radius. We constructed similar diagrams for NGC3201, NGC6121, NGC6752, and NGC6397, thus exploring GCs with different metallicities. The ChMs effectively distinguished multiple populations in the outer regions of all clusters, except for the metal-poor NGC6397. Our findings, together with literature results from more-internal regions, show that the 2P stars of 47Tucanae are more-centrally concentrated than the 1P. A similar pattern is seen for 2P stars with extreme chemical composition of NGC3201. The multiple populations of NGC6121, and NGC6752 share the same radial distributions. These radial behaviors are consistent with the GC formation scenarios where 2P stars originate in the central regions. Noticeably, results on NGC3201 are in tension with the conclusion from recent work that its 1P is more centrally concentrated than the 2P and might form with more central concentration.

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arXiv2024

Hubble Space Telescope survey of Magellanic Cloud star clusters. Binaries among the split main sequences of NGC 1818, NGC 1850, and NGC 2164

Nearly all star clusters younger than ~600 Myr exhibit extended main sequence turn offs and split main sequences (MSs) in their color-magnitude diagrams. Works based on both photometry and spectroscopy have firmly demonstrated that the red MS is composed of fast-rotating stars, whereas blue MS stars are slow rotators. Nevertheless, the mechanism responsible for the formation of stellar populations with varying rotation rates remains a topic of debate. Potential mechanisms proposed for the split MS include binary interactions, early evolution of pre-main sequence stars, and the merging of binary systems, but a general consensus has yet to be reached. These formation scenarios predict different fractions of binaries among blue- and red-MS stars. Therefore, studying the binary populations can provide valuable constraints that may help clarify the origins of the split MSs. We use high-precision photometry from the Hubble Space Telescope (HST) to study the binaries of three young Magellanic star clusters exhibiting split MS, namely NGC 1818, NGC 1850, and NGC 2164. By analyzing the photometry in the F225W, F275W, F336W, and F814W filters for observed binaries and comparing it to a large sample of simulated binaries, we determine the fractions of binaries within the red and the blue MS. We find that the fractions of binaries among the blue MS are higher than those of red-MS stars by a factor of ~1.5, 4.6, and ~1.9 for NGC 1818, NGC 1850, and NGC 2164, respectively. We discuss these results in the context of the formation scenarios of the split MS.

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arXiv2024

oMEGACat III. Multi-band photometry and metallicities reveal spatially well-mixed populations within $ω$ Centauri's half-light radius

$ω$ Centauri, the most massive globular cluster in the Milky Way, has long been suspected to be the stripped nucleus of a dwarf galaxy that fell into the Galaxy a long time ago. There is considerable evidence for this scenario including a large spread in metallicity and an unusually large number of distinct sub-populations seen in photometric studies. In this work, we use new MUSE spectroscopic and HST photometric catalogs to investigate the underlying metallicity distributions as well as the spatial variations of the populations within the cluster up to its half-light radius. Based on 11,050 member stars, the [M/H] distribution has a median of $ (-1.614 \pm 0.003)$ dex and a large spread of $\sim$ 1.37 dex reaching from $ -0.67$ dex to $ -2.04$ dex for 99.7 % of the stars. In addition, we show the chromosome map of the cluster, which separates the red giant branch stars into different sub-populations, and analyze the sub-populations of the metal-poorest component. Finally, we do not find any metallicity gradient within the half-light radius, and the different sub-populations are well mixed.

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arXiv2024

A JWST project on 47 Tucanae. NIRSpec spectroscopy of multiple populations among M dwarfs

We present the first spectroscopic estimates of the chemical abundance of M dwarf stars in a globular cluster (GC), namely 47 Tucanae. By exploiting NIRSpec on board the James Webb Space Telescope (JWST) we gathered low-resolution spectra for 28 stars with masses in the range ~0.4-0.5 solar masses. The spectra are strongly affected by the H2O water vapour bands which can be used as indicators of the oxygen abundance. The spectral analysis reveals that the target stars feature a different O abundance, with a difference of ~0.40 dex between first and the most-polluted second population. The observed range is similar to that observed among red giant stars. This result reinforces previous findings based on the analysis of photometric diagrams, including the ``chromosome maps'', providing a first, and more direct, evidence of light element variations in the M dwarfs' mass regime. The observation that the multiple populations, with their variations in light elements, exhibit the same patterns from the lower main sequence all the way to the red giant branch further strengthens the notion that multiple stellar populations in globular clusters formed in a series of bursts of star formation.

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arXiv2024

On the original composition of the gas forming first-generation stars in clusters: insights from HST and JWST

Globular cluster (GC) stars composed of pristine material (first-generation, 1G, stars) are not chemically homogeneous, as they exhibit extended sequences in the "Chromosome Map" (ChM). Recent studies characterized 1G stars within the center of 55 Galactic GCs, revealing metallicity variations. Despite this progress, several unanswered questions persist, particularly concerning the link between the 1G metallicity spread and factors such as the radial distance from the cluster center or the host GC parameters. Additionally, it remains unclear whether the extended 1G sequence phenomenon is exclusive to old Galactic GCs with multiple populations. This work addresses these open issues, examining 1G stars in different environments. First, we combine Hubble Space Telescope (HST) and James Webb Space Telescope photometry of the GC 47 Tucanae to study 1G stars at increasing distances from the cluster center. We find that metal-rich 1G stars are more centrally concentrated than metal-poor ones, suggesting a metallicity radial gradient. Additionally, the two groups of 1G stars share similar kinematics. Since our analysis focuses on giant stars in the cluster center and M dwarfs in external fields, we discuss the possibility that the metallicity distribution depends on stellar mass. Subsequently, we analyze HST multi-band photometry of two simple-population clusters, NGC 6791 and NGC 1783, revealing elongated sequences in the ChM associated with metallicity variations. Finally, we investigate the 1G color distribution in 51 GCs, finding no connections with the host cluster parameters. These results shed light on the complex nature of 1G stars, providing insights into the GC formation environment.

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arXiv2024

A JWST project on 47 Tucanae. Overview, photometry and early spectroscopic results of M dwarfs, and observation of brown dwarfs

The James Webb Space Telescope (JWST) observations have been demonstrated to be efficient in detecting globular clusters' (GCs) multiple stellar populations in the low mass regime of M dwarfs. We present an overview, and first results, of different projects that can be explored by using the JWST observations gathered under the GO2560 for 47 Tucanae, a first program entirely devoted to the investigation of multiple populations in very low mass stars, which includes spectroscopic data for the faintest GC stars for which spectra are available. Our color-magnitude diagram (CMD) shows some substructures for ultracool stars, including gaps and breaks in slope. In particular, we observe both a gap and a minimum in the F322W2 luminosity function less than one magnitude apart, and discuss which one could be associated with the H-burning limit. We detect stars fainter than this minimum, very likely the brown dwarfs. We corroborate the ubiquity of the multiple populations across different masses, from ~0.1 solar masses up to red giants (~0.8 solar masses). The oxygen range inferred from the M dwarfs, both from the CMD and from the spectra of two M dwarfs associated with different populations, is similar to that observed in giants. We have not detected any difference between the fractions of stars in distinct populations across stellar masses >~0.1 solar masses. This work demonstrates the JWST's capability in uncovering multiple populations within M dwarfs and illustrates the possibility to analyse very low-mass stars in GCs approaching the H-burning limit and the brown-dwarf sequence.

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arXiv2023

GN-z11: witnessing the formation of second generation stars and an accreting massive black hole in a massive star cluster

We explore the possibility that the N-rich young proto-galaxy GN-z11 recently observed at z=10.6 by the James Webb Space Telescope is the result of the formation of second generation stars from pristine gas and Asymptotic Giant Branch (AGB) ejecta in a massive globular cluster or nuclear star cluster. We show that a second generation forming out of gas polluted by the ejecta of massive AGB stars and mixed with gas having a standard composition accounts for the unusually large N/O in the GN-z11 spectrum. The timing of the evolution of massive (4-7.5M$_{\odot}$) AGBs also provides a favourable environment for the growth of a central stellar mass black hole to the Active Galactic Nucleus stage observed in GN-z11. According to our model the progenitor system was born at an age of the Universe of $\simeq 260 - 380$Myr, well within the pre-reionization epoch.

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arXiv2023

oMEGACat I: MUSE spectroscopy of 300,000 stars within the half-light radius of $ω$ Centauri

Omega Centauri ($ω$ Cen) is the most massive globular cluster of the Milky Way and has been the focus of many studies that reveal the complexity of its stellar populations and kinematics. However, most previous studies have used photometric and spectroscopic datasets with limited spatial or magnitude coverage, while we aim to investigate it having full spatial coverage out to its half-light radius and stars ranging from the main sequence to the tip of the red giant branch. This is the first paper in a new survey of $ω$ Cen that combines uniform imaging and spectroscopic data out to its half-light radius to study its stellar populations, kinematics, and formation history. In this paper, we present an unprecedented MUSE spectroscopic dataset combining 87 new MUSE pointings with previous observations collected from guaranteed time observations. We extract spectra of more than 300,000 stars reaching more than two magnitudes below the main sequence turn-off. We use these spectra to derive metallicity and line-of-sight velocity measurements and determine robust uncertainties on these quantities using repeat measurements. Applying quality cuts we achieve signal-to-noise ratios of 16.47/73.51 and mean metallicity errors of 0.174/0.031 dex for the main sequence stars (18 mag $\rm < mag_{F625W}<$22 mag) and red giant branch stars (16 mag $<\rm mag_{F625W}<$10 mag), respectively. We correct the metallicities for atomic diffusion and identify foreground stars. This massive spectroscopic dataset will enable future studies that will transform our understanding of $ω$ Cen, allowing us to investigate the stellar populations, ages, and kinematics in great detail.

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