Stellar Velocity Distribution Research Articles

Validation of the Bond et al. (2010) SDSS-derived kinematic models for the Milky Way's disk and halo stars with Gaia Data Release 3 proper motion and radial velocity data

We validate the 2010ApJ...716....1B kinematic models for the Milky Way's disk and halo stars with Gaia Data Release 3 data. Bond et al. constructed models for stellar velocity distributions using stellar radial velocities measured by the Sloan Digital Sky Survey (SDSS) and stellar proper motions derived from SDSS and the Palomar Observatory Sky Survey astrometric measurements. These models describe velocity distributions as functions of position in the Galaxy, with separate models for disk and halo stars that were labeled using SDSS photometric and spectroscopic metallicity measurements. We find that the Bond et al. model predictions are in good agreement with recent measurements of stellar radial velocities and proper motions by the Gaia survey. In particular, the model accurately predicts the skewed non-Gaussian distribution of rotational velocity for disk stars and its vertical gradient, as well as the dispersions for all three velocity components. Additionally, the spatial invariance of velocity ellipsoid for halo stars when expressed in spherical coordinates is also confirmed by Gaia data at galacto-centric radial distances of up to 15 kpc.

Exploring the Origin of Stars on Bound and Unbound Orbits Causing Tidal Disruption Events

Tidal disruption events (TDEs) provide a clue to the properties of a central supermassive black hole (SMBH) and an accretion disk around it, and to the stellar density and velocity distributions in the nuclear star cluster surrounding the SMBH. Deviations of TDE light curves from the standard occurring at a parabolic encounter with the SMBH depend on whether the stellar orbit is hyperbolic or eccentric and the penetration factor (β, the tidal disruption radius to the orbital pericenter ratio). We study the orbital parameters of bound and unbound stars being tidally disrupted by comparison of direct N-body simulation data with an analytical model. Starting from the classical steady-state Fokker–Planck model of Cohn & Kulsrud, we develop an analytical model of the number density distribution of those stars as a function of orbital eccentricity (e) and β. To do so, fittings of the density and velocity distribution of the nuclear star cluster and of the energy distribution of tidally disrupted stars are required and obtained from N-body data. We confirm that most of the stars causing TDEs in a spherical nuclear star cluster originate from the full loss-cone region of phase space, derive analytical boundaries in eccentricity-β space, and find them confirmed by N-body data. Since our limiting eccentricities are much smaller than critical eccentricities for full accretion or the full escape of stellar debris, we conclude that those stars are only very marginally eccentric or hyperbolic, close to parabolic.

Deciphering dark matter: A computational analysis of stellar velocity distributions

This study examines the dark matter density in the Galaxy by fitting recent data on stellar rotational velocities. We employ a model including the disk, the bulge, and the dark matter halo. The disks density is parameterized using a modified Bessel function, and the bulge is modeled using both the De Vaucouleurs and Exponential Sphere functions to better fit large and small radii respectively. The dark halo is modeled using the generalized Navarro-Frenk-White profile, with slope parameters for standard NFW and Moore profiles, and an Isothermal profile for comparison. The fit of the model parameters is established using local Dark Matter density and total Dark Matter mass as boundary conditions, with circular velocities derived via a Newtonian approach. The least chi-square ( 2 ) method is used for rotation curve fitting. Results demonstrate successful fitting of rotational velocity data and significant influence of the DH at large radial distances from the Galactic center.

Estimating Distances from Parallaxes. VI. A Method for Inferring Distances and Transverse Velocities from Parallaxes and Proper Motions Demonstrated on Gaia Data Release 3

The accuracy of stellar distances inferred purely from parallaxes degrades rapidly with distance. Proper motion measurements, when combined with some idea of typical velocities, provide independent information on stellar distances. Here, I build a direction- and distance-dependent model of the distribution of stellar velocities in the Galaxy, then use this together with parallaxes and proper motions to infer kinegeometric distances and transverse velocities for stars in Gaia DR3. Using noisy simulations, I assess the performance of the method and compare its accuracy to purely parallax-based (geometric) distances. Over the whole Gaia catalog, kinegeometric distances are on average 1.25 times more accurate than geometric ones. This average masks a large variation in the relative performance, however. Kinegeometric distances are considerably better than geometric ones beyond several kpc, for example. On average, kinegeometric distances can be measured to an accuracy of 19% and velocities () to 16 km s−1 (median absolute deviations). In Gaia DR3, kinegeometric distances are smaller than geometric ones on average for distant stars, but the pattern is more complex in the bulge and disk. With the much more accurate proper motions expected in Gaia DR5, a further improvement in the distance accuracy by a factor of (only) 1.35 on average is predicted (with kinegeometric distances still 1.25 times more accurate than geometric ones). The improvement attained from proper motions is limited by the width of the velocity prior, in a way that the improvement from better parallaxes is not limited by the width of the distance prior.

Resonant Effects of a Bar on the Galactic Disk Kinematics Perpendicular to Its Plane

Detailed analysis of kinematics of the Milky Way disk in the solar neighborhood based on the GAIA DR3 catalog reveals the existence of peculiarities in the stellar velocity distribution perpendicular to the galactic plane. We study the influence of resonances—the outer Lindblad resonance and the outer vertical Lindblad resonance—of a rotating bar with stellar oscillations perpendicular to the plane of the disk, and their role in shaping the spatial and the velocity distributions of stars. We find that the Z and VZ distributions of stars with respect to LZ are affected by the outer Lindblad resonance. The existence of bar resonance with stellar oscillations perpendicular to the plane of the disk is demonstrated for a long (large semi-axis 5 kpc) and fast rotating bar with Ωb=60.0kms−1kpc−1. We show also that, in the model with the long and fast rotating bar, some stars in the 2:1 OLR region deviate far from their original places, entering the bar region. A combination of resonance excitation of stellar motions at the 2:1 OLR region together with strong interaction of the stars with the bar potential leads to the formation of the group of ‘escapees’, i.e., stars that deviate in R and Z—directions at large distances from the resonance region. Simulations, however, do not demonstrate any noticeable effect on VZ-distribution of stars in the solar neighborhood.

Evolution in the orbital structure of quiescent galaxies from MAGPI, LEGA-C, and SAMI surveys: direct evidence for merger-driven growth over the last 7 Gyr

ABSTRACT We present the first study of spatially integrated higher-order stellar kinematics over cosmic time. We use deep rest-frame optical spectroscopy of quiescent galaxies at redshifts z = 0.05, 0.3, and 0.8 from the SAMI, MAGPI, and LEGA-C surveys to measure the excess kurtosis h4 of the stellar velocity distribution, the latter parametrized as a Gauss-Hermite series. Conservatively using a redshift-independent cut in stellar mass ($M_\star = 10^{11}\, \mathrm{M_\odot }$) and matching the stellar-mass distributions of our samples, we find 7σ evidence of h4 increasing with cosmic time, from a median value of 0.019 ± 0.002 at z = 0.8 to 0.059 ± 0.004 at z = 0.06. Alternatively, we use a physically motivated sample selection based on the mass distribution of the progenitors of local quiescent galaxies as inferred from numerical simulations; in this case, we find 10σ evidence. This evolution suggests that, over the last 7 Gyr, there has been a gradual decrease in the rotation-to-dispersion ratio and an increase in the radial anisotropy of the stellar velocity distribution, qualitatively consistent with accretion of gas-poor satellites. These findings demonstrate that massive galaxies continue to accrete mass and increase their dispersion support after becoming quiescent.

Different higher order kinematics between star-forming and quiescent galaxies based on the SAMI, MAGPI, and LEGA-C surveys

ABSTRACT We present the first statistical study of spatially integrated non-Gaussian stellar kinematics spanning 7 Gyr in cosmic time. We use deep, rest-frame optical spectroscopy of massive galaxies (stellar mass $M_\star \gt 10^{10.5} \, \mathrm{M_\odot }$) at redshifts z = 0.05, 0.3, and 0.8 from the SAMI, MAGPI, and LEGA-C surveys, to measure the excess kurtosis h4 of the stellar velocity distribution, the latter parametrized as a Gauss–Hermite series. We find that at all redshifts where we have large enough samples, h4 anticorrelates with the ratio between rotation and dispersion, highlighting the physical connection between these two kinematic observables. In addition, and independently from the anticorrelation with rotation-to-dispersion ratio, we also find a correlation between h4 and M⋆, potentially connected to the assembly history of galaxies. In contrast, after controlling for mass, we find no evidence of independent correlation between h4 and aperture velocity dispersion or galaxy size. These results hold for both star-forming and quiescent galaxies. For quiescent galaxies, h4 also correlates with projected shape, even after controlling for the rotation-to-dispersion ratio. At any given redshift, star-forming galaxies have lower h4 compared to quiescent galaxies, highlighting the link between kinematic structure and star-forming activity.

The initial spin distribution of B-type stars revealed by the split main sequences of young star clusters

Spectroscopic observations of stars in young open clusters have revealed evidence for a dichotomous distribution of stellar rotational velocities, with 10−30% of stars rotating slowly and the remaining 70−90% rotating fairly rapidly. At the same time, high-precision multiband photometry of young star clusters shows a split main sequence band, which is again interpreted as due to a spin dichotomy. Recent papers suggest that extreme rotation is required to retrieve the photometric split. Our new grids of MESA models and the prevalent SYCLIST models show, however, that initial slow (0−35% of the linear Keplerian rotation velocities) and intermediate (50−65% of the Keplerian rotation velocities) rotation are adequate to explain the photometric split. These values are consistent with the recent spectroscopic measurements of cluster and field stars, and are likely to reflect the birth spin distributions of upper main-sequence stars. A fraction of the initially faster-rotating stars may be able to reach near-critical rotation at the end of their main-sequence evolution and produce Be stars in the turn-off region of young star clusters. However, we find that the presence of Be stars up to two magnitudes below the cluster turnoff advocates for a crucial role of binary interaction in creating Be stars. We argue that surface chemical composition measurements may help distinguish these two Be star formation channels. While only the most rapidly rotating, and therefore nitrogen-enriched, single stars can evolve into Be stars, slow pre-mass-transfer rotation and inefficient accretion allows for mild or no enrichment even in critically rotating accretion-induced Be stars. Our results shed new light on the origin of the spin distribution of young and evolved B-type main sequence stars.

A correlation between accreted stellar kinematics and dark-matter halo spin in the artemis simulations

ABSTRACT We report a correlation between the presence of a Gaia-Sausage-Enceladus (GSE) analogue and dark-matter (DM) halo spin in the artemis simulations of Milky Way-like galaxies. The haloes which contain a large population of accreted stars on highly radial orbits (like the GSE) have lower spin on average than their counterparts with more isotropic stellar velocity distributions. The median modified spin parameters λ′ differ by a factor of ∼1.7 at the present day, with a similar value when the haloes far from virial equilibrium are removed. We also show that accreted stars make up a smaller proportion of the stellar populations in haloes containing a GSE analogue, and are stripped from satellites with stellar masses typically ∼4 times smaller. Our findings suggest that the higher spin of DM haloes without a GSE-like feature is due to mergers with large satellites of stellar mass ∼1010 M⊙, which do not result in prominent radially anisotropic features like the GSE.

From ridges to manifolds: 3D characterization of the moving groups in the Milky Way disc

Context. The details of the effect of the bar and spiral arms on the disc dynamics of the Milky Way are still unknown. The stellar velocity distribution in the solar neighbourhood displays kinematic substructures, which are possibly signatures of these processes and of previous accretion events. With the Gaia mission, more details of these signatures, such as ridges in the Vϕ − R plane and thin arches in the Vϕ − VR plane, have been revealed. The positions of these kinematic substructures, or moving groups, can be thought of as continuous manifolds in the 6D phase space, and the ridges and arches as specific projections of these manifolds. Aims. Our aim is to detect and characterize the moving groups along the Milky Way disc, sampling the galactocentric radial and azimuthal velocities of the manifolds through the three dimensions of the disc: radial, azimuthal, and vertical. Method. We developed and applied a novel methodology to perform a blind search for substructure in the Gaia EDR3 6D data, which consists in the execution of the wavelet transform in independent small volumes of the Milky Way disc, and the grouping of these local solutions into global structures with a method based on the breadth-first search algorithm from graph theory. We applied the same methodology to simulations of barred galaxies to validate the method and for comparison with the data. Results. We reveal the skeleton of the velocity distribution, uncovering projections that were not possible before. We sample nine main moving groups along a large region of the disc in configuration space, covering up to 6 kpc, 60 deg, and 2 kpc in the radial, azimuthal, and vertical directions, respectively, extending significantly the range of previous analyses. In the radial direction we find that the groups deviate from the lines of constant angular momentum that one would naively expect from an epicyclic approximation analysis of the first-order effects of resonances. We reveal that the spatial evolution of the moving groups is complex and that the configuration of moving groups in the solar neighbourhood is not maintained along the disc. We also find that the azimuthal velocity of the moving groups that are mostly detected in the inner parts of the disc (Arcturus, Bobylev, and Hercules) is non-axisymmetric. For Hercules we measure an azimuthal gradient of −0.50 km s−1 deg−1 at R = 8 kpc. We detect a vertical asymmetry in the azimuthal velocity for the Coma Berenices moving group, which is not expected for structures originating from a resonance of the bar, supporting the previous hypothesis of the incomplete vertical phase mixing of the group. In our simulations we extract substructures corresponding to the outer Lindblad resonance and the 1:1 resonances and observe the same deviation from constant angular momentum lines and the non-axisymmetry of the azimuthal velocities of the moving groups in the inner part of the disc. Conclusions. This data-driven characterization is a starting point for a holistic understanding of the moving groups. It also allows for a quantitative comparison with models, providing a key tool to comprehend the dynamics of the Milky Way.

The two phases of core formation – orbital evolution in the centres of ellipticals with supermassive black hole binaries

ABSTRACT The flat stellar density cores of massive elliptical galaxies form rapidly due to sinking supermassive black holes (SMBHs) in gas-poor galaxy mergers. After the SMBHs form a bound binary, gravitational slingshot interactions with nearby stars drive the core regions towards a tangentially biased stellar velocity distribution. We use collisionless galaxy merger simulations with accurate collisional orbit integration around the central SMBHs to demonstrate that the removal of stars from the centre by slingshot kicks accounts for the entire change in velocity anisotropy. The rate of strong (unbinding) kicks is constant over several hundred Myr at $\sim 3 \ \mathrm{ M}_\odot\, \rm yr^{-1}$ for our most massive SMBH binary (MBH = 1.7 × 1010 M⊙). Using a frequency-based orbit classification scheme (box, x-tube, z-tube, rosette), we demonstrate that slingshot kicks mostly affect box orbits with small pericentre distances, leading to a velocity anisotropy of β ≲ −0.6 within several hundred Myr as observed in massive ellipticals with large cores. We show how different SMBH masses affect the orbital structure of the merger remnants and present a kinematic tomography connecting orbit families to integral field kinematic features. Our direct orbit classification agrees remarkably well with a modern triaxial Schwarzschild analysis applied to simulated mock kinematic maps.

Understanding the Velocity Distribution of the Galactic Bulge with APOGEE and Gaia

Abstract We revisit the stellar velocity distribution in the Galactic bulge/bar region with Apache Point Observatory Galactic Evolution Experiment DR16 and Gaia DR2, focusing in particular on the possible high-velocity (HV) peaks and their physical origin. We fit the velocity distributions with two different models, namely with Gauss–Hermite polynomials and Gaussian mixture models (GMMs). The result of the fit using Gauss–Hermite polynomials reveals a positive correlation between the mean velocity ( ) and the “skewness” (h 3) of the velocity distribution, possibly caused by the Galactic bar. The n = 2 GMM fitting reveals a symmetric longitudinal trend of ∣μ 2∣ and σ 2 (the mean velocity and the standard deviation of the secondary component), which is inconsistent with the x 2 orbital family predictions. Cold secondary peaks could be seen at ∣l∣ ∼ 6°. However, with the additional tangential information from Gaia, we find that the HV stars in the bulge show similar patterns in the radial–tangential velocity distribution (V R–V T), regardless of the existence of a distinct cold HV peak. The observed V R–V T (or V GSR–μ l ) distributions are consistent with the predictions of a simple Milky Way bar model. The chemical abundances and ages inferred from ASPCAP and CANNON suggest that the HV stars in the bulge/bar are generally as old as, if not older than, the other stars in the bulge/bar region.

Birth sites of young stellar associations and recent star formation in a flocculent corrugated disc

ABSTRACT With backwards orbit integration, we estimate birth locations of young stellar associations and moving groups identified in the solar neighbourhood that are younger than 70 Myr. The birth locations of most of these stellar associations are at a smaller galactocentric radius than the Sun, implying that their stars moved radially outwards after birth. Exceptions to this rule are the Argus and Octans associations, which formed outside the Sun’s galactocentric radius. Variations in birth heights of the stellar associations suggest that they were born in a filamentary and corrugated disc of molecular clouds, similar to that inferred from the current filamentary molecular cloud distribution and dust extinction maps. Multiple spiral arm features with different but near corotation pattern speeds and at different heights could account for the stellar association birth sites. We find that the young stellar associations are located in between peaks in the radial/tangential (UV) stellar velocity distribution for stars in the solar neighbourhood. This would be expected if they were born in a spiral arm, which perturbs stellar orbits that cross it. In contrast, stellar associations seem to be located near peaks in the vertical phase-space distribution, suggesting that the gas in which stellar associations are born moves vertically together with the low-velocity dispersion disc stars.

The Stellar Velocity Distribution Function in the Milky Way Galaxy

Abstract The stellar velocity distribution function in the solar vicinity is reexamined using data from the Sloan Digital Sky Survey Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey’s DR16 and Gaia DR2. By exploiting APOGEE’s ability to chemically discriminate with great reliability the thin-disk, thick-disk, and (accreted) halo populations, we can, for the first time, derive the three-dimensional velocity distribution functions (DFs) for these chemically separated populations. We employ this smaller but more data-rich APOGEE+Gaia sample to build a data-driven model of the local stellar population velocity DFs and use these as basis vectors for assessing the relative density proportions of these populations over the 5 < R < 12 kpc and −1.5 < z < 2.5 kpc range as derived from the larger, more complete (i.e., all-sky, magnitude-limited) Gaia database. We find that 81.9% ± 3.1% of the objects in the selected Gaia data set are thin-disk stars, 16.6% ± 3.2% are thick-disk stars, and 1.5% ± 0.1% belong to the Milky Way stellar halo. We also find the local thick-to-thin-disk density normalization to be ρ T (R ⊙)/ρ t (R ⊙) = 2.1% ± 0.2%, a result consistent with, but determined in a completely different way from, typical star-count/density analyses. Using the same methodology, the local halo-to-disk-density normalization is found to be ρ H (R ⊙)/(ρ T (R ⊙) + ρ t (R ⊙)) = 1.2% ± 0.6%, a value that may be inflated due to the chemical overlap of halo and metal-weak thick-disk stars.

Measuring the mass of the supermassive black hole of the lenticular galaxy NGC 4546

ABSTRACT Most galaxies with a well-structured bulge host a supermassive black hole (SMBH) in their centre. Stellar kinematics models applied to adaptive optics (AO) assisted integral field unit observations are well-suited to measure the SMBH mass (MBH) and also the total mass-to-light ratio [(M/L)TOT] and possible anisotropies in the stellar velocity distribution in the central region of galaxies. In this work, we used new AO assisted Near-Infrared Integral Field Spectrometer (NIFS) observations and also photometric data from the Hubble Space Telescope Legacy Archive of the galaxy NGC 4546 in order to determine its SMBH mass. To do this, we applied the Jeans Anisotropic Modelling (JAM) method to fit the average second velocity moment in the line of sight $(\overline{v^2_{\mathrm{ los}}})$ of the stellar structure. In addition, we also obtained (M/L)TOT and the classical anisotropy parameter βz = 1-(σz/σR)2 for this object within a field of view of 200 × 200 pc2. Maps of the stellar radial velocity and of the velocity dispersion were built for this galaxy using the penalized pixel fitting (ppxf) technique. We applied the Multi Gaussian Expansion procedure to fit the stellar brightness distribution. Using JAM, the best-fitting model for $\overline{v^2_{\mathrm{ los}}}$ of the stellar structure was obtained with (M/L)TOT = 4.34 ± 0.07 (Johnson’s R band), MBH = (2.56 ± 0.16) × 108 M⊙ and βz = −0.015 ± 0.03 (3σ confidence level). With these results, we found that NGC 4546 follows the MBH × σ relation. We also measured the central velocity dispersion within a radius of 1 arcsec of this object as σc = 241 ± 2 km s−1.

Capture of interstellar objects: a source of long-period comets

ABSTRACT We simulate the passage through the Sun–Jupiter system of interstellar objects (ISOs) similar to 1I/‘Oumuamua or 2I/Borisov. Capture of such objects is rare and overwhelmingly from low incoming speeds on to orbits akin to those of known long-period comets. This suggests that some of these comets could be of extrasolar origin, in particular inactive ones. Assuming ISOs follow the local stellar velocity distribution, we infer a volume capture rate of $0.051\, \mathrm{au}^3\, \mathrm{yr}^{-1}$. Current estimates for orbital lifetimes and space densities then imply steady-state captured populations of ∼102 comets and ∼105 ‘Oumuamua-like rocks, of which 0.033 per cent are within 6 au at any time.

Constraining scatter in the stellar mass–halo mass relation for haloes less massive than the Milky Way

ABSTRACT Most galaxies are hosted by massive, invisible dark matter haloes, yet little is known about the scatter in the stellar mass–halo mass relation for galaxies with host halo masses Mh ≤ 1011M⊙. Using mock catalogues based on dark matter simulations, we find that two observable signatures are sensitive to scatter in the stellar mass–halo mass relation even at these mass scales; i.e. conditional stellar mass functions and velocity distribution functions for neighbouring galaxies. We compute these observables for 179,373 galaxies in the Sloan Digital Sky Survey (SDSS) with stellar masses M* > 109 M⊙ and redshifts 0.01 < z < 0.307. We then compare to mock observations generated from the Bolshoi-Planck dark matter simulation for stellar mass–halo mass scatters ranging from 0 to 0.6 dex. The observed results are consistent with simulated results for most values of scatter (<0.6 dex), and SDSS statistics are insufficient to provide firm constraints. However, this method could provide much tighter constraints on stellar mass–halo mass scatter in the future if applied to larger data sets, especially the anticipated Dark Energy Spectroscopic Instrument Bright Galaxy Survey. Constraining the value of scatter could have important implications for galaxy formation and evolution.

The MASSIVE Survey XIII. Spatially Resolved Stellar Kinematics in the Central 1 kpc of 20 Massive Elliptical Galaxies with the GMOS-North Integral Field Spectrograph

Abstract We use observations from the GEMINI-N/GMOS integral field spectrograph (IFS) to obtain spatially resolved stellar kinematics of the central ∼1 kpc of 20 early-type galaxies (ETGs) with stellar masses greater than 1011.7 M ⊙ in the MASSIVE survey. Together with observations from the wide-field Mitchell IFS at McDonald Observatory in our earlier work, we obtain unprecedentedly detailed kinematic maps of local massive ETGs, covering a scale of ∼0.1–30 kpc. The high (∼120) signal-to-noise ratio of the GMOS spectra enables us to obtain two-dimensional maps of the line-of-sight velocity and velocity dispersion σ, as well as the skewness h 3 and kurtosis h 4 of the stellar velocity distributions. All but one galaxy in the sample have σ(R) profiles that increase toward the center, whereas the slope of σ(R) at one effective radius (R e ) can be of either sign. The h 4 is generally positive, with 14 of the 20 galaxies having positive h 4 within the GMOS aperture and 18 having positive h 4 within 1R e . The positive h 4 and rising σ(R) toward small radii are indicative of a central black hole and velocity anisotropy. We demonstrate the constraining power of the data on the mass distributions in ETGs by applying Jeans anisotropic modeling (JAM) to NGC 1453, the most regular fast rotator in the sample. Despite the limitations of JAM, we obtain a clear χ 2 minimum in black hole mass, stellar mass-to-light ratio, velocity anisotropy parameters, and circular velocity of the dark matter halo.

From ridges in the velocity distribution to wiggles in the rotation curve

Abstract Recently, the Gaiadata release 2 (DR2) showed us the richness in the kinematics of the Milky Way disc. Of particular interest is the presence of ridges covering the stellar velocity distribution, Vϕ–R; as shown by others, it is likely that these ridges are the signature of phase mixing, transient spirals, or the bar. Here, with a Galactic model containing both, bar and spirals, we found the same pattern of ridges extending from the inner to the outer disc. Interestingly, ridges in the Vϕ–R plane correlate extremely well with wiggles in the computed rotation curve (RC). Hence, although the DR2 reveals (for the first time) such substructures in a wide spatial coverage, we notice that we have always seen such a pattern of ridges, but projected into the form of wiggles in the RC. The separation and amplitude of the wiggles strongly depend on the extension and layout of ridges in the Vϕ–R plane. This means that within the RC are encoded the kinematic state of the disc and information about the bar and spiral arms. The amplitude of the wiggles suggests that similar features currently observable in external galaxies' RCs have similar origins, triggered by spirals and bars.

A method to deconvolve stellar rotational velocities

Aims. The study of accurate methods to estimate the distribution of stellar rotational velocities is important for understanding many aspects of stellar evolution. From such observations we obtain the projected rotational speed (v sin i) in order to recover the true distribution of the rotational velocity. To that end, we need to solve a difficult inverse problem that can be posed as a Fredholm integral of the first kind. Methods. In this work we have used a novel approach based on maximum likelihood (ML) estimation to obtain an approximation of the true rotational velocity probability density function (PDF) expressed as a sum of known distribution families. In our proposal, the measurements have been treated as random variables drawn from the projected rotational velocity PDF. We analyzed the case of Maxwellian sum approximation, where we estimated the parameters that define the sum of distributions. Results. The performance of the proposed method is analyzed using Monte Carlo simulations considering two theoretical cases for the PDF of the true rotational stellar velocities: (i) an unimodal Maxwellian probability density distribution and (ii) a bimodal Maxwellian probability density distribution. The results show that the proposed method yielded more accurate estimates in comparison with the Tikhonov regularization method, especially for small sample length (N = 50). Our proposal was evaluated using real data from three sets of measurements, and our findings were validated using three statistical tests. Conclusions. The ML approach with Maxwellian sum approximation is a accurate method to deconvolve the rotational velocity PDF, even when the sample length is small (N = 50).