Rotation Curves Research Articles

Curves that allow the motion of a regular polygon

AbstractThis paper characterizes curves where a regular polygon of either a variable side length or a constant side length is allowed to rotate during k full revolutions while having its vertices on the curve during the motion. A constructive method to generate these curves is given based on the curve described by the polygon centers (centroids) during the motion and some examples are shown. Moreover, if the regular polygon divides the curve perimeter into parts of equal length, it is proved that the curve is either a rotational symmetric curve in the case of a variable side length or a circle otherwise. Finally, in the case of a regular polygon of constant side length rotating along a curve, a simple relation between the algebraic areas of such a curve and the curve of polygon centers is revisited.

Experimental investigation of countercurrent flow limitation (CCFL) in a 1/19 scale of VVER-1000 geometry

Countercurrent flow limitation (CCFL) has been experimentally considered in a VVER-1000 hot-leg. The proposed test facility consists of a hot-leg pipe, a reactor vessel simulator (RVs), and a steam generator simulator (SGs). It was designed and constructed based on power-to-volume scaling approach by preserving the Froud number in the hot leg. The scaling ratio was considered 1/19 of the Bushehr NPP (VVER-1000) geometry. The hot leg of the proposed facility provides good optical observation of the gas/liquid interface. The SG simulator has also a side view for optical observation. Experimental results were captured at atmospheric pressure with air/water as fluid. CCFL was obtained by analyzing the pressure differences between RV and SG simulators.This CCFL data was compared with empirical data and correlations available in the literature. With increasing liquid superficial velocity, the gas superficial velocity curve is continuously decreased, which is consistent with Navarro's results. In this study, an experimental correlation is proposed and compared to other correlations. It was very close to the Navarro and Richter correlations.The results of experimental investigations clarified the onset of the CCFL phenomenon in a Bushehr NPP (VVER-1000) hot-leg geometry. Moreover, the achieved patterns and behaviors of the air/water mixture would be used in computational fluid dynamics (CFD) code validations.

Photometric and Spectroscopic Analysis of V583 Lyrae, an Algol with a g-mode Pulsating Primary and Accretion Disk

V583 Lyr is an extremely low-mass-ratio Algol-type binary with an orbital period of 11.2580 days. We determined an effective temperature of T eff1 = 9000 ± 350 K from newly observed spectra, which might be an underestimate due to binary mass transfer. The binary mass ratio q = 0.1 ± 0.004 and the orbital inclination i = 85.°5 are determined based on the assumption that the secondary fills its Roche lobe and rotates synchronously. The radial velocity curve is obtained from time series spectra, allowing for improved estimation of stellar masses and radii: M 1 = 3.56 ± 0.5 M ⊙, R 1 = 2.4 ± 0.2 R ⊙; and M 2 = 0.36 ± 0.02 M ⊙, R 2 = 6.9 ± 0.4 R ⊙. The variations in the double-peaked Hα emission indicate the formation of a stable disk during mass transfer. V583 Lyr appears to be a post-mass-reversal system, according to the mass transfer estimated using O − C period analysis. Its orbital period is slowly increasing, from which the rate of mass accretion by the primary star is estimated to be M1̇=3.384 × 10−8 M ⊙ yr−1. The pulsation analysis was conducted on the residuals of the light curve. The primary component was found to be a g-mode pulsating star with 26 frequencies extracted lower than 9 day−1. The frequency groups and rotational splitting properties of the g mode were studied in detail. This study provides compelling evidence for an accretion disk surrounding the g-mode pulsating primary.

Hooks & Bends in the radial acceleration relation: discriminatory tests for dark matter and MOND

ABSTRACT The radial acceleration relation (RAR) connects the total gravitational acceleration of a galaxy at a given radius, atot(r), with that accounted for by baryons at the same radius, abar(r). The shape and tightness of the RAR for rotationally-supported galaxies have characteristics in line with MOdified Newtonian Dynamics (MOND) and can also arise within the cosmological constant + cold dark matter (ΛCDM) paradigm. We use zoom simulations of 20 galaxies with stellar masses of M⋆ ≃ 107–11 M⊙ to study the RAR in the FIRE-2 simulations. We highlight the existence of simulated galaxies with non-monotonic RAR tracks that ‘hook’ down from the average relation. These hooks are challenging to explain in Modified Inertia theories of MOND, but naturally arise in all of our ΛCDM-simulated galaxies that are dark-matter dominated at small radii and have feedback-induced cores in their dark matter haloes. We show, analytically and numerically, that downward hooks are expected in such cored haloes because they have non-monotonic acceleration profiles. We also extend the relation to accelerations below those traced by disc galaxy rotation curves. In this regime, our simulations exhibit ‘bends’ off of the MOND-inspired extrapolation of the RAR, which, at large radii, approach atot ≈ abar/fb, where fb is the cosmic baryon fraction. Future efforts to search for these hooks and bends in real galaxies will provide interesting tests for MOND and ΛCDM.

Small-Scale Cosmology Independent of the Standard Model

‘Small-scale cosmology’ is a theory designed to incorporate the linear redshift versus distance relation, which is inferred from observations, into the theoretical framework independent of the global Robertson–Walker–Friedman (RWF)-type models. The motivation behind this is that the RWF cosmological models, based on the assumptions of homogeneity and a constant matter density, as well as the concept of expanding space inherent to them are not applicable on the scales of observations from which the linear Hubble law is inferred. Therefore, explaining the Hubble law as the small redshift limit of the RWF model or as an effect of expanding space is inconsistent. Thus, the Hubble linear relation between the redshift of an extragalactic object and its distance should be considered an independent law of nature valid in the range of the distances where the RWF cosmology is not valid. In general, the theory, based on that concept, can be developed in different ways. In the present paper, ‘small-scale cosmology’ is formulated as a theory operating in the (redshift–object coordinates) space, which allows developing a conceptual and computational basis of the theory along the lines of that of special relativity. In such a theory, the condition of invariance of the Hubble law with respect to a change in the observer acceleration plays a central role. In pursuing this approach, the effectiveness of group theoretical methods is exploited. Applying the Lie group method yields transformations of the variables (the redshift and space coordinates of a cosmological object) between the reference frames of the accelerated observers. In this paper, the transformations are applied to studying the effects of the solar system observer acceleration on the observed shape, distribution and rotation curves of galaxy clusters.

Phonon-phason coupling and nonlocal effects on Lamb waves in functionally graded one-dimensional hexagonal quasicrystal nanoplates

Due to the coupled phonon-phason coupling and nonlocal effects, dynamic behaviors of quasicrystal nanostructures are highly complex. Mechanics investigations have mainly focused on the statics, but rarely on dynamics, thus limiting their engineering applications. In the present paper, a fractional order elastodynamics model is proposed to investigate guided waves propagating in functionally graded one-dimensional hexagonal quasicrystal nanoplates in the context of the nonlocal theory. In this model, the fractional order can be flexibly adjusted to describe the role of the phason field accurately. Phase velocity and attenuation curves, as well as stress distributions, are illustrated. The phonon-phason coupling and nonlocal effects on wave characteristics are studied. Some new results are revealed: The fractional order considerably influences phason modes, but weakly affects phonon modes; The phonon-phason coupling and the nonlocal effects promote each other. These results establish a theoretical foundation for designing and optimizing quasicrystal nanostructures.

Testing Yukawa cosmology at the Milky Way and M31 galactic scales

We address the galaxy rotation curves through the Yukawa gravitational potential emerging as a correction of the Newtonian potential in extended theories of gravity. On the one hand, we consider the contribution of the galactic bulge, galactic disk, and the dark matter halo of the Navarro–Frenk–White profile, in the framework of the standard Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model. On the other hand, we use modified Yukawa gravity to show that the rotational velocity of galaxies can be addressed successfully without the need for dark matter. In Yukawa gravity, we recover MOND and show that dark matter might be seen as an apparent effect due to the modification of the law of gravitation in terms of two parameters: the coupling constant α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and the characteristic length λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document}. We thus test our theoretical scenario using the Milky Way and M31 rotation velocity curves. In particular, we place observational constraints on the free parameters of Yukawa cosmology through the Monte Carlo method and then compare our results with the predictions of the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM paradigm by making use of Bayesian information criteria. Specifically, we find that λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document} is constrained to be of the order of kpc, while cosmological data suggest λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document} of the order of Gpc. To explain this discrepancy, we argue that there is a fundamental limitation in measuring λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document} due to the role of quantum mechanics on cosmological scales.

Influence of Shallow Foundations on the Response of Steel Wind Towers

The objective of this study, concerning the soil–structure interaction of shallow reinforced concrete foundations of wind towers with circular cross-sections, was determination in a closed form of the monotonic moment–rotation curve of the soil–foundation complex. This study was based on elastic and plastic analyses of shallow rigid foundations assuming a Winkler soil type including the flexibility of the foundation in the elastic range and the nature of the soil (cohesive and non-cohesive types) through corrective factors of the constant of the Winkler model. The flexibility of the foundations influences the moment–rotation response through the initial rotational stiffness with a coefficient between 1 and 0.7 for a width-to-span ratio between 5 and 2. The nature of the soil is considered through corrective factors of 0.75 and 1.3 of the Winkler constant for cohesive and non-cohesive soil, respectively. Analyses carried out stressed that a possible design valued to be adopted in a steel wind tower with shallow foundations is a diameter of the steel tube 1/15 of the height of the tower, a diameter of foundation 0.75 of the length, and a depth of foundation 1/10 of the diameter and thickness of steel tower ratio diameter equal to 1/10. In this range it was observed that the effects of the soil-to-foundation interaction in the elastic range influences the critical length in the stability of the steel wind tower, with values between 2.5 and 2 (column fixed at the base) in a range of Winkler constant between 0.1 and 1 daN/cm3. Finally, an experimental validation of the proposed model was carried out with the data available from the literature.

Spectroscopic Follow-up on Potential Magnetic Cataclysmic Variables

Spectroscopic observations of nine cataclysmic variables that have been postulated to contain magnetic white dwarfs were obtained to further characterize their classifications, orbital parameters, inclinations, and/or accretion properties. Zwicky Transient Facility (ZTF) and Transiting Exoplanet Survey Satellite (TESS) data were also used when available. This information enables these systems to be useful in global population and evolution studies of close binaries. Radial velocity curves were constructed for eight of these systems, at various states of accretion. High-state spectra of ZTF0548+53 reveal strong He ii emission, large radial velocity amplitudes, as well as cyclotron harmonics yielding a magnetic field strength of 50 MG, confirming this as a polar system. Analysis of TESS data reveals an orbital period of 92.1 minutes. High-state spectra of SDSS0837+38 determine a period of 3.18 hr, removing the ambiguity of periods found during the low state, and showing this is a regular polar and not a pre-polar system. The ZTF light curve of CSS0026+24 shows a total eclipse with a period of 122.9 minutes, and features indicative of two accretion poles. A new, remarkably large spin-to-orbit ratio is found for ZTF1631+69 (0.61), making it, along with 2011+60 (=Romanov V48), likely stream-accreting intermediate polars. ZTF data reveal the presence of ∼2 mag low states in ZTF1631+69, and along with McDonald Observatory 2.1 m and TESS light curves, confirm a grazing eclipse that is deepest at a narrow subset of beat phases. The TESS data on PTF12313+16 also indicate a partial eclipse. Analysis of ZTF data on SDSS1626+33 reveals a period of 3.17 hr and suggests the presence of a partial eclipse.

Magnetized heat transfer visualization through computational modeling of third-grade fluid via exponentially stretching cylinder

The steady MHD boundary-layer axis-symmetric flow of a third-grade fluid passing through an exponentially expanded cylinder in the vicinity of a magnetic field is investigated in this study. The problem is mathematically modeled. Suitable similarity transformations are carried out to convert the partial differential equations into nonlinear ordinary differential equations. The Runge–Kutta fourth-order shooting technique is used to solve the transmuted system of nonlinear ODEs. Graphical representations of numerical findings are used to examine the effects of various physical factors on the velocity and temperature profiles. The influence of fluid variables on the velocity curve, such as third-grade parameters, second-grade parameters, and Reynolds number, is illustrated and explored. The skin-friction coefficient expression is computed and given. The widths of the velocity and momentum boundary layers are revealed to be increasing functions of the curvature parameter. It is found that the third-grade fluid has a higher velocity profile than Newtonian and second-grade fluids. Also, the stretched cylinders cause a more progressive shift in heat and mass pattern for flow than flat plates do.

Thermal and solutal transport by Cattaneo-Christov model for the magnetohydrodynamic Williamson fluid with joule heating and heat source/sink

This article scrutinizes the 2-dimensional and boundary layer flow of magnetohydrodynamic Williamson fluid flowing on a stretchable surface with variable viscosity. The thermal and solutal rates are examined through the Cattaneo-Christov model with Joule heating, heat source/sink, and chemical reaction. The authors are motivated to conduct this study because of its practical and scientific significance in various processes, including polymer processing, textile industries, food industries, solar energy, biomedical science, wind turbine blades, oil spill clean-up, metal rolling, and forging. With the mentioned assumptions, the partial differential equations are achieved by using the basic governing laws, including momentum law, energy law, and concentration law. This non-linear system of equations is transmuted into ordinary differential equations by taking similarity transformations. The main novelty behind the conduction of this work is the numerical technique, namely the ‘Adams-Milne (Predictor-Corrector)’ method along with the Runge-Kutta technique on Matlab software, which has not previously been studied by any researcher in the literature. The analytical solution of the determined equations is not possible due to their highly non-linear nature; therefore the multistep numerical method namely the ‘Adams-Milne (Predictor-Corrector)’ method, along with the Runge-Kutta technique is used to determine the numerical results. The outcomes are noted due to numerous parameters for velocity, temperature, and concentration profiles. The explanation of graphical and numerical results is discussed here. The graphical impression of the Williamson parameter reveals that the velocity and temperature curves diminish for higher inputs of this parameter. The movement of fluid shows the declining behavior for the Hartmann number and viscosity parameter. The solutal and thermal findings due to Cattaneo-Christov heat and mass relaxation coefficients mark the reducing behaviour in respective field. The rise in reaction coefficient decreases the mass distribution. The analyses of comparison of results are also presented here.

Modelling Einstein cluster using Einasto profile

We demonstrate a general relativistic approach to model dark matter halos using the Einstein cluster, with the matter stress-energy generated by collisionless particles moving on circular geodesics in all possible angular directions and orbital radii. Such matter, as is known, allows an anisotropic pressure profile with non-zero tangential but zero radial pressure. We use the Einasto density profile for the Einstein cluster. Analytical studies on its properties (metric functions) and stability issues are investigated. Further, to establish this model (with the Einasto profile) as one for a dark matter halo,we use the SPARC galactic rotation curve data and estimate the best-fit values for the model parameters. General relativistic features (beyond the Keplerian velocities) such as the tangential pressure profile, are quantitatively explored. Thus, Einstein clusters with the Einasto profile, which tally well with observations, may be considered as a viable model for dark matter halos.

XookSuut: A BAYESIAN TOOL FOR MODELING CIRCULAR AND NON–CIRCULAR FLOWS ON 2D VELOCITY MAPS

We present XookSuut, a Python implementation of the DiskFit algorithm, optimized to perform robust Bayesian inference on parameters describing models of circular and noncircular rotation in galaxies. XookSuut surges as a Bayesian alternative for kinematic modeling of 2D velocity maps; it implements effcient sampling methods, specifically Markov Chain Monte Carlo (MCMC) and Nested Sampling (NS), to obtain the posteriors and marginalized distributions of kinematic models including circular motions, axisymmetric radial flows, bisymmetric flows, and harmonic decomposition of the LoS velocity. In this way, kinematic models are obtained by pure sampling methods, rather than standard minimization techniques based on the Χ2. All together, XookSuut represents a sophisticated tool for deriving rotational curves and to explore the error distribution and covariance between parameters.

Discovery of the Longest-period Classical Cepheid in the Milky Way

We report the discovery of the classical Cepheid OGLE-GD-CEP-1884 (= GDS_J1535467-555656) with the longest pulsation period known in our Galaxy. The period of 78.14 days is nearly 10 days longer than that of the previous record-holding Cepheid, S Vulpeculae, and thus, OGLE-GD-CEP-1884 can be categorized as the first ultra-long-period Cepheid in the Milky Way. This star is present in the ASAS-SN and Gaia DR3 catalogs of variable stars, but it has been classified as a long-period variable in those catalogs. Based on more than 10 yr of the photometric monitoring of this star carried out by the OGLE project in the I and V bands and a radial velocity curve from the Gaia Focused Product Release, we unequivocally demonstrate that this object is a fundamental-mode classical Cepheid. By employing the mid-infrared period–luminosity relation, we determine the distance to OGLE-GD-CEP-1884 (4.47 ± 0.34 kpc) and place it on the Milky Way map, along with about 2400 other classical Cepheids. We also discuss the potential of finding additional ultra-long-period Cepheids in our Galaxy.

Disturbance Observer-Based Tracking Control of High-Speed Trains Under Adhesion Dynamics

As the anti-skid control and speed tracking control of high-speed trains (HSTs) are interrelated and mutually constrained, it is very challenging to achieve simultaneous tracking of speed and slip ratio. In this paper, it is proposed for the first time that when the traction braking force has been limited to a reasonable range by the adhesion anti-skid condition, the high-precision tracking of the position and velocity curves of HSTs can be achieved, and the tracking error of the slip ratio is acceptable. Firstly, a novel modelling of the adhesion dynamics of HSTs under realistic gusts of wind disturbance is developed, and a model based on strict feedback is obtained by linearising the feedback for high-order non-linear systems. Then, this paper first presents the design scheme of fast terminal sliding mode controller based on disturbance observer for HSTs, which can ensure the anti-disturbance performance and accurate tracking of HSTs. Finally, an example is used to verify the validity of the results. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The actual traction/braking force of HSTs is provided by adhesion, and the existing literature on slip ratio tracking essentially sacrifices the tracking performance of the traction/braking system to meet the anti-skid requirements, while considering velocity and position tracking alone may leave the train in an undesired condition such as “idling” or “skidding”. This paper seeks to achieve high accuracy tracking of velocity and position profiles of HSTs under restricting the slip ratio to a reasonable range, which is expected to be an effective method for train tracking controller design. To avoid discomfort to passengers, nonlinearities dynamics are considered and an anti-disturbance controller is designed to compensate the impact of natural wind disturbances. To enhance the practicality, feedback linearization is introduced to reduce the complexity of the controller implementation. The designed fast terminal sliding mode controller also avoids jitter and singularity problems and obtains finite time stability. The stability analysis and numerical simulation have confirmed the effectiveness of the proposed scheme, which still needs to be verified by experiments in the future.

The orbital parameters of the δ Cep inner binary system determined using 2019 HARPS-N spectroscopic data

Context. An inner companion has recently been discovered orbiting the prototype of classical Cepheids, δ Cep, whose orbital parameters are still not fully constrained. Aims. We collected new precise radial velocity measurements of δ Cep in 2019 using the HARPS-N spectrograph mounted at the Telescopio Nazionale Galileo. Using these radial velocity measurements, we aimed to improve the orbital parameters of the system. Methods. We considered a template available in the literature as a reference for the radial velocity curve of the pulsation of the star. We then calculated the residuals between our global dataset (composed of the new 2019 observations plus data from the literature) and the template as a function of the pulsation phase and the barycentric Julian date. This provides the orbital velocity of the Cepheid component. Using a Bayesian tool, we derived the orbital parameters of the system. Results. Considering priors based on already published Gaia constraints, we find for the orbital period a maximum a posteriori probability of Porb = 9.32−0.04+0.03 years (uncertainties correspond to the 95% highest density probability interval), and we obtain an eccentricity e = 0.71−0.02+0.02, a semimajor axis a = 0.029−0.003+0.002 arcsec, and a center-of-mass velocity V0 = −17.28−0.08+0.08 km s−1, among other parameters. Conclusions. In this short analysis we derive the orbital parameters of the δ Cep inner binary system and provide a cleaned radial velocity curve of the pulsation of the star, which will be used to study its Baade–Wesselink projection factor in a future publication.

The Descartes Code (Spin Orbital Rotation of Photons)–IV. The Harress-Sagnac Color Excess in the Rotation Curves of Galaxies

In 1933, Zwicky formulated the significant bifurcation point in the history of astrophysics. Zwicky postulated an unknown dark matter in order to explain the color excess in the observed Doppler effect in the rotation curves of galaxies. However, until now we have not detected these dark matter particles. In this contribution, we propose to come back to this bifurcation point and to interpret the observed color excess as the Harress-Sagnac effect known in the rotating interferometers. We have described photon properties in those rotating interferometers based on the old color theory of Descartes—rotating light globules (spin-orbital rotation of photons). Therefore, the color excess observed in the rotation curves of galaxies can be interpreted as the additional color excess of photons emitting from distant rotating stars. Formulae for these color excesses are given for different locations of the rotating galaxy inspired by Zwicky’s core-shell model of galaxies. A part of Zwicky’s enigma is an unknown influence of the Solar gravitational field at 1 AU on the distant photon properties. From the forgotten Gerber’s retarded potential formula we have derived an expression for the acceleration of distant photons towards the Sun at 1 AU as ax = 1.171 × 10⁻¹⁰ ms⁻². This is a very surprising coincidence with the Milgrom empirical value a0 = (1.2 ± 0.1) × 10⁻¹⁰ ms⁻². Therefore, we propose to test this new formula at the surface of Mercury and Mars in order to reveal if our gravitational models are universal or “geocentric”, valid for the surroundings of the Earth only.

Retarded Gravity in Disk Galaxies

Disk galaxies have a typical dimension of a few tens of kiloparsecs. It follows from the theory of general relativity that any signal originating from the galactic center will be noticed at the outskirts of the galaxy only tens of thousands of years later. This retardation effect, however, is absent in modelling used to calculate rotation curves throughout entire galaxies and their external gas. The considerable differences between Newtonian predictions and observed velocities are currently removed either by assuming dark matter or by suggesting various modifications to the laws of gravity, MOND being a long standing alternative to Newtonian gravity. In previous papers we have shown that by applying general relativity in a rigorous fashion, without neglecting retardation, one can explain the rotational velocities of galactic matter without modifying gravity or adding dark matter. Moreover, it was shown that dark matter effects, as they appear in gravitational lensing, the Tully-Fisher relation, and mass estimations based on the virial theorem could also be explained as retarded-gravity effects. It must be noted, however, that the proposed theory relies on the existence of a mass flow (of a changing rate) into the galaxy; a requirement that was not directly observed. In the original paper on the subject only one galaxy (M33) was analysed in detail. This was later amended with a published study of eleven galaxies. Here we give a more comprehensive retardation analysis of 143 galaxies of different types from the SPARC Galaxy collection. We show that in most cases we obtain very accurate fits to the data.

Radial and azimuthal gradients of the moving groups in Gaia DR3: The slow and fast bar degeneracy problem

The structure and dynamics of the central bar of the Milky Way (MW) are still under debate whilst being fundamental ingredients for the evolution of our Galaxy. The recent Gaia DR3 offers an unprecedented detailed view of the 6D phase space of the MW, allowing for a better understanding of the complex imprints of the bar on the phase space. We aim to identify and characterise the dynamical moving groups across the MW disc, and use their large-scale distribution to help constrain the properties of the Galactic bar. We used 1D wavelet transforms of the azimuthal velocity ($V_ distribution in bins of radial velocity to robustly detect the kinematic substructure in the Gaia DR3 catalogue. We then connected these structures across the disc to measure the azimuthal (phi ) and radial ($R$) gradients of $V_ of the moving groups. We simulated thousands of perturbed distribution functions using backward integration, sweeping a large portion of parameter space of feasible Galaxy models that include a bar, in order to compare them with the data and to explore and quantify the degeneracies. The radial gradient of the Hercules moving group ($ V_ R$ = 28.1pm 2.8 $) cannot be reproduced by our simple models of the Galaxy that show much larger slopes both for a fast and a slow bar. This suggests the need for more complex dynamics (e.g. a different bar potential, spiral arms, a slowing bar, a complex circular velocity curve, external perturbations, etc.). We measured an azimuthal gradient for Hercules of $ V_ = -0.63pm $deg$^ $ and find that it is compatible with both the slow and fast bar models. Our analysis points out that in using this type of analysis, at least two moving groups are needed to start breaking the degeneracies. We conclude that it is not sufficient for a model to replicate the local velocity distribution; it must also capture its larger-scale variations. The accurate quantification of the gradients, especially in the azimuthal direction, will be key for the understanding of the dynamics governing the disc.

Geometry-driven and dark-matter-sustained Milky Way rotation curves with Gaia DR3

ABSTRACT Thanks to Gaia DR2, we proved for the first time that a general relativistic Milky Way rotation curve is statistically indistinguishable from its state-of-the-art dark matter analogue. Those results supported the ansatz that gravitational dragging can explain the observed flatness of the Milky Way rotation curve with a consistent radial matter density profile. To challenge again such a scenario, we select 719 143 young disc stars within |z| &amp;lt; 1 kpc and up to R ≃ 19 kpc from Gaia DR3 providing a much larger sample of high-quality astrometric and spectrophotometric data of unprecedented homogeneity. This sample comprises 241 918 OBA stars, 475 520 RGB giants, and 1705 Cepheides that we use to fit, as with DR2, both a classical velocity profile model, i.e. with a dark matter halo, and a general relativistic analogue derived from a dust disc-scale metric. Once more, further corroborating our earlier findings, both models are found to explain, with similar statistical quality, the new observed rotational velocities derived from different combinations of the selected sets of stars belonging to the disc of our Galaxy. The geometrical effect is found to drive the velocity profile from 10 kpc outwards, while being responsible for ∼30–37 per cent of this profile already at the Sun distance, similarly to the halo contribution in the classical model. This confirms our previous results on the contribution of Einstein’s geometry and pushes to further investigate the role of General Relativity in tracing the Milky Way rotation curve; notably, the origin of this gravitational dragging remains undetermined, necessitating a dedicated in-depth exploration.