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The galactic rotation curve is an essential tool for understanding the dynamics, evolution, and formation of the Milky Way galaxy. We can study the mass distribution of the galaxy via the rotation curve. However, the galactic rotation curve, especially for the outer region, has not been accurately determined due to distance uncertainties of Galactic objects. Our target source is IRAS 06469+0333, a star-forming region located near a galactic plane in the outer region of the galaxy. To observe the star-forming region, we use the Very Long Baseline Interferometry (VLBI) technique to get the highest accuracy of the position and distance of the source. Thus, we can provide additional data on rotation velocity for accurately constructing the Milky Way outer rotation curve. We collected data from the Outer Rotation Curve of the galaxy with the VLBI Exploration of Radio Astrometry (VERA) project observing water maser at 22 GHz from January 2013 to October 2014. We also used the National Radio Astronomy Observatory (NRAO) Astronomical Image Processing System (AIPS) software to make data reduction. We have finished data reductions for five epochs. Double peak spectra for the water masers are found in four epochs, and the V lsr varies between 29 km/s and 31 km/s. A parallax of 0.618 ± 0.166 milliarcsecond (mas) corresponding to a distance of 1.62 + - 0 0 .. 5 3 9 4 kpc is obtained, and proper motions are -1.15 ± 0.07 mas/yr and -0.09 ± 0.61 mas/yr for right ascension and declination directions, respectively. The galactocentric distance and galactic rotation velocity of the source are 9.44 + - 0 0 .. 5 3 4 1 kpc and 187.21 ± 3.94 km/s, respectively. Based on the observational results, the rotation curve is constructed to examine the mass distribution of the Milky Way galaxy. The accuracy of results from this current work will be evaluated based on the comparison with the previous studies.

The general theory of relativity (GR) is symmetric under smooth coordinate transformations, also known as diffeomorphisms. The general coordinate transformation group has a linear subgroup denoted as the Lorentz group of symmetry, which is also maintained in the weak field approximation to GR. The dominant operator in the weak field equation of GR is thus the d’Alembert (wave) operator, which has a retarded potential solution. Galaxies are huge physical systems with dimensions of many tens of thousands of light years. Thus, any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects are neglected in the present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper, we will show that, by taking general relativity seriously without neglecting retardation effects, one can explain the radial velocities of galactic matter in the M33 galaxy without postulating dark matter. It should be stressed that the current approach does not require that velocities v are high; in fact, the vast majority of galactic bodies (stars, gas) are substantially subluminal—in other words, the ratio of vc≪1. Typical velocities in galaxies are 100 km/s, which makes this ratio 0.001 or smaller. However, one should consider the fact that every gravitational system, even if it is made of subluminal bodies, has a retardation distance, beyond which the retardation effect cannot be neglected. Every natural system, such as stars and galaxies and even galactic clusters, exchanges mass with its environment, for example, the sun loses mass through solar wind and galaxies accrete gas from the intergalactic medium. This means that all natural gravitational systems have a finite retardation distance. The question is thus quantitative: how large is the retardation distance? For the M33 galaxy, the velocity curve indicates that the retardation effects cannot be neglected beyond a certain distance, which was calculated to be roughly 14,000 light years; similar analysis for other galaxies of different types has shown similar results. We demonstrate, using a detailed model, that this does not require a high velocity of gas or stars in or out of the galaxy and is perfectly consistent with the current observational knowledge of galactic and extra galactic material content and dynamics.

The standard proposal within the context of General relativity and its weak field Newtonian limit for the nature of dark matter is that it consists of dark matter particles of unknown type. In the present work and specifically for spiral galaxy rotation curves, an alternative possibility is explored, in the form of an axially symmetric vortex mass distribution of finite extent threading the centre of the galaxy and perpendicular to its disk. Some general considerations are developed and characteristic properties are identified, pointing to the potential interest of such an alternative to be studied in earnest.

Based on Cepheids located near the solar circle, we have determined the Galactocentric distance of the Sun and the Galactic rotation velocity at the solar distance . For our analysis we used a sample of 200 classical Cepheids from the catalogue by Skowron et al. (2019), where the distances to them were determined from the period–luminosity relation. For these stars the proper motions and line-of-sight velocities were taken from the Gaia DR3 catalogue. The values of found lie within the range 7.8–8.3 kpc, depending on the heliocentric distance of the sample stars, on the adopted solar velocity relative to the local standard of rest, and on whether or not the perturbations caused by the Galactic spiral density wave are taken into account. The dispersion of the estimates is 2 kpc. Similarly, the values of lie within the range 240–270 km s with a dispersion of the estimates of 70–90 km s . We consider the following estimates to be the final ones: kpc and km s found by taking into account the perturbations from the Galactic spiral density wave.

We searched for a resolution of the flat galactic rotation curve problem from geometry instead of assuming the existence of dark matter. We observed that the scale independence of the rotational velocity in the outer region of galaxies could point out to a possible existence of local scale symmetry and therefore the gravitational phenomena inside such regions should be described by the unique local scale symmetric theory, namely Weyl’s theory of gravity. We solved field equations of Weyl gravity and determined the special geometry in the outer region of galaxies. In order to understand the effective description of gravitational phenomena, we compared individual terms of so called Einstein–Weyl theory and concluded that while the outer region of galaxies are described by the Weyl term, the inner region of galaxies are described by the Einstein-Hilbert term.

A theoretical basis for modifying Newtonian dynamics on a galactic scale can be obtained by postulating that cosmic rays interact with graviton exchanges between distant masses. This assumes that these charged particles move under the influence of local electromagnetic fields rather than the weak gravitational fields of distant matter. It leads to an enhancement of graviton exchanges between distant masses via an additional gravitational force term inversely proportional to distance. At planetary and local interstellar distances this predicts an extremely small additional gravitational force, but it can become significant on a galactic scale. The model is used here to predict rotational velocities in a wide range of galaxies including the Milky Way, Andromeda (M31) and some galaxies in the THINGS study. Results are obtained assuming a galactic cosmic ray density consistent with observations in the solar system. This approach is compared with the dark matter hypothesis and with Modified Newtonian Dynamics (MOND), the two primary postulates used to explain the constant rotational velocities observed in most galaxies.

The extreme astrophysical processes and conditions that characterize the early Universe are expected to result in young galaxies that are dynamically different from those observed today 1 – 5 . This is because the strong effects associated with galaxy mergers and supernova explosions would lead to most young star-forming galaxies being dynamically hot, chaotic and strongly unstable 1 , 2 . Here we report the presence of a dynamically cold, but highly star-forming, rotating disk in a galaxy at redshift 6 z  = 4.2, when the Universe was just 1.4 billion years old. Galaxy SPT–S J041839–4751.9 is strongly gravitationally lensed by a foreground galaxy at z  = 0.263, and it is a typical dusty starburst, with global star-forming 7 and dust properties 8 that are in agreement with current numerical simulations 9 and observations 10 . Interferometric imaging at a spatial resolution of about 60 parsecs reveals a ratio of rotational to random motions of 9.7 ± 0.4, which is at least four times larger than that expected from any galaxy evolution model at this epoch 1 – 5 but similar to the ratios of spiral galaxies in the local Universe 11 . We derive a rotation curve with the typical shape of nearby massive spiral galaxies, which demonstrates that at least some young galaxies are dynamically akin to those observed in the local Universe, and only weakly affected by extreme physical processes. A strongly lensed galaxy at redshift 4.2 appears to be a dynamically cold disk galaxy, similar to spiral galaxies in the local neighbourhood and weakly affected by extreme physical processes.

In a recent galactic survey, Bizyaev et. al. (2021) modeled the rotation curves for 153 ultra-faint, edge-on galaxies using the 3.5 m telescope at the Apache Point Observatory. One of the interesting features of this survey was that the majority of the distances for the galaxies were inferred using the Tully Fisher Relation. Although there is nothing new about surveys using Tully Fisher for distance estimates, these authors reported drastically different scale lengths for some of these galaxies within a one year time frame. Since rotation curve modeling for any theory is most sensitive to the distance, an opportunity arises in this survey to begin to try to shed some light on how galactic rotation curves are derived for any theory. However, the preliminary analysis shows that this survey may not hold the key to unraveling some of these mysteries, but can provide insight into the methods for a more standard fit for rotation curve physics.

Based on the measurements performed in the first 14 months of Gaia operation, we have solved the problem of obtaining the systematic differences between the stellar positions and proper motions of the TGAS (Tycho–Gaia Astrometric Solution) and Tycho-2 catalogues. By dividing the common stars from the TGAS and Tycho-2 catalogues into three G -magnitude groups for mean values of 10 m ˙ 5 , 11 m ˙ 5 , a n d 13 m ˙ 0 , we have obtained the systematic differences between the stellar equatorial coordinates and proper motions of both catalogues in the form of a decomposition into vector spherical harmonics by taking into account the magnitude equation. The systematic components have been extracted from the individual differences with a probability of 0.977–0.999. The constructed model of systematic differences allows any position measurements performed using Tycho-2 as a reference catalogue to be transformed to the TGAS frame. An important fact is the existence of a magnitude equation in the systematic differences: when passing from bright ( G = 10 m ) to faint ( G = 13 m ) stars, the systematic position differences change within the range from approximately −40 to 15 mas, while the systematic proper motion differences change from −3 to 3 mas yr −1 . The orientation and mutual rotation parameters of the Tycho-2 and TGAS frames have also been found to be different for stars of different magnitudes: when passing from bright to faint stars, the rotation angle of the Tycho-2 frame relative to TGAS changes from 3.51 to 5.63 mas, while the angular velocity of rotation changes from 0.35 to 1.22 mas yr −1 . Based on the developed method that allows the extent to which the systematic errors in the equatorial propermotions of stars affect the results of a kinematic analysis of the Galactic proper motions to be estimated within the Ogorodnikov–Milne model, we have shown that the slope of the Galactic rotation curve and the Oort parameter C are most sensitive to the transition from the Tycho-2 frame to the TGAS one. Their relative changes after the transformation to the TGAS frame reach 56 and 100%, respectively. At the same time, the changes in the estimates of the Oort parameters A and B as well as the linear velocity of the Sun relative to the Galactic center, the Galactic rotation period, the ratio of the epicyclic frequency to the angular velocity of Galactic rotation, and the mass of the Galaxy within the Galactocentric distance of the Sun are not so large, being 2−10%.

We show that, contrary to some recent claims, relativistic effects cannot mimic dark matter in the galactic rotation curves and gravitational lensing.