Determination of galactic rotation parameters and the solar galactocentric distance R 0 from 73 masers

We have determined the Galactic rotation parameters and the solar Galactocentric distance R ₀ by simultaneously solving Bottlinger’s kinematic equations using data on masers with known line-of-sight velocities and highly accurate trigonometric parallaxes and proper motions measured by VLBI. Our sample includes 73 masers spanning the range of Galactocentric distances from 3 to 14 kpc. The solutions found are Ω₀ = 28.86 ± 0.45 km s^?1 kpc^?1, Ω′₀ = ?3.96 ± 0.09 km s^?1 kpc^?2, Ω″₀ = 0.790 ± 0.027 km s^?1 kpc^?3, and R ₀ = 8.3 ± 0.2 kpc. In this case, the linear rotation velocity at the solar distance R ₀ is V = 241 ± 7 km s^?1. Note that we have obtained the R ₀ estimate, which is of greatest interest, from masers for the first time; it is in good agreement with the most recent estimates and even surpasses them in accuracy.     

Faraday rotation and the turbulent structure of the Galaxy

We extend Jokipii and Lerche's analysis of the turbulent structure of our Galaxy by means of a study of the rotation measure of extragalactic sources. Like them we use a simple, statistically homogeneous and isotropic disc model of the Galaxy and assume that the magnetic field has both an average component and a fluctuating one. We assume that the electron density is proportional to some power of the magnetic field (N _eB ⁿ with 1n2). Using the rotation measure data on 242 extragalactic sources given by Vallée and Kronberg we consider both an exponential and a Gaussian two-point correlation function for the (Gaussian) fluctuating component of the magnetic field with a correlation lengthL. We find reasonable agreement between theory and observations for an average magnetic field of about 3 G, a fluctuating magnetic field component with an amplitude of about 2.6G, an average electron density of about 0.03 cm^–3, a fluctuating density component of about 0.05 cm^–3, and a correlation length of about 300 pc.     

Galactic rotation curve from the space velocities of selected masers

Based on currently available observations of 28 maser sources in 25 star-forming regions with measured trigonometric parallaxes, proper motions, and radial velocities, we have constructed the rotation curve of the Galaxy. Taking different distances to the Galactic center R ₀, we have estimated the peculiar velocity of the Sun, the angular velocity of Galactic rotation, and its three derivatives. For R ₀ = 8 kpc, we have found the circular velocity of the Sun to be V ₀ = 243 ± 16 km s⁻¹, which corresponds to a revolution period of 202 ± 10 Myr. We have obtained the Oort constants A = 16.9 ± 1.2 km s⁻¹ kpc⁻¹ and B = −13.5 ± 1.4 km s⁻¹ kpc⁻¹. Our simulation of the influence of a spiral density wave has shown that the peculiar velocity of the Sun with respect to the local standard of rest and the component (V _⊙)_LSR depend significantly on the Sun’s phase in the spiral wave.     

Determination of the rotation curve for stars of the Gould Belt using bottlinger's formulas

Based on the Hipparcos catalog and the radial velocities of stars published to date, we perform a kinematic analysis of OB stars. Parameters of the general Galactic rotation were determined from distant OB stars. We used the residual velocities of stars corrected for the general Galactic rotation to study the proper rotation of nearby OB stars. Geometrical characteristics of the Gould Belt were estimated by analyzing its kinematic parameters. We obtained parameters of peculiar solar motion as well as parameters of the proper rotation, expansion, and contraction for rotation around both the Galactic z axis and an axis perpendicular to the plane of symmetry of the disk. Kinematic parameters of the proper differential rotation were found for two age groups of nearby OB stars. Almost all of the nearby OB stars were shown to rotate in the same direction as the Galactic rotation. We constructed rotation curves.     

Time resolved images from the center of the Galaxy appear to counter General Relativity

Intense observations of the galactic center since 1992 have revealed the presence of a supermassive object located there, some 26 000 light years from Earth. The mass of the galactic center was determined using time resolved astrometry over a time span of 13 years, from 1992 to present. The observations clearly show that the stars in the immediate vicinity of the supermassive galactic center, denoted as Sagittarius A* (Sgr A*), move along purely Keplerian orbits around Str A*. Observation of the rapidly moving stars permitted astrophysicists to determine a mass for the galactic center of around 3.6 million solar masses. Time resolved images of the Keplerian motions of these stars has exhibited to date no evidence of distortions in the images due to gravitational light bending effects, as predicted by General Relativity. In this paper, a well known tool commonly used by astrophysicists for estimating the effect of gravitation on light rays was examined. The results reveal flaws in the understanding of fundamental principles in mathematical physics applied to gravitational effects on rays of light, as predicted by General Relativity, at the site of a point‐like gravitating masses such as the galactic center mass. Application of the Gauss Law to point‐like gravitating masses shows that a requirement for the colinear alignment of the light source, the lensing and the observer is not necessary for an observation of gravitational lensing as predicted by General Relativity. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Sun’s distance from the center and the shape of the inner halo in the Galaxy: Gaia EDR3, HST and literature globular clusters

A statistical method is used to derive both the Sun’s distance $r_0$ from the Galactic Center (GC) and the 3D geometry of the inner ($<$ 25 kpc) halo. The spatial distribution of the 138 Gaia EDR3 globular clusters (GCs) with distances established on a combination of HST and literature data of Baumgardt and Vasiliev (2021) is explored. An estimate by using these ancient objects of the pressure-supported subsystem of the Galaxy with newly derived distances leads to the mean $r_0=7.81\pm 0.14$ kpc. The distribution of GCs within 25 kpc is almost spherically symmetric, and has the shape of an ellipsoid with a major axis of its symmetry slightly elongated toward the Sun and two minor axes of almost the same length. The obtained scale-length ratio of the major axis to the minor axis in the plane and to the vertical axis of the ellipsoid is $\approx$ 1:0.8:0.7. Based on the papers of a series, for practical use we argue to employ the following Sun’s distances from the GC and the plane: $r_0=8.15\pm 0.15$ kpc and $z_0=15\pm 5$ pc.     

General magnetic field and rotation of the outer layers of the sun

We investigate how the rotation of the outer layers of the sun will be influenced by a variable general magnetic field. Applying the resulting formulae to the spectroscopic observations of the velocity of rotation at the solar limb in middle and high latitudes, the variation of the rotational velocity during the cycle 1901–1912 as found by Newall and by Halm can be made to agree with modern views on the general magnetic field.Mitteilung des Astronomischen Instituts der Universität Tübingen, Nr. 117.     

NGC 3741: the dark halo profile from the most extended rotation curve

We present new H  i observations of the nearby dwarf galaxy NGC 3741. This galaxy has an extremely extended H  i disc, which allows us to trace the rotation curve out to unprecedented distances in terms of the optical disc: we reach 42 B -band exponential scalelengths or about 7 kpc. The H  i disc is strongly warped, but the warp is very symmetric. The distribution and kinematics are accurately derived by building model data cubes, which closely reproduce the observations. In order to account for the observed features in the data cube, radial motions of the order of 5–13 km s⁻¹ are needed. They are consistent with an inner bar of several hundreds of pc and accretion of material in the outer regions.
The observed rotation curve was decomposed into its stellar, gaseous and dark components. The Burkert dark halo (with a central constant density core) provides very good fits. The dark halo density distribution predicted by the Λ cold dark matter (CDM) theory fails to fit the data, unless NGC 3741 is a 2.5σ exception to the predicted relation between concentration parameter and virial mass and at the same time a high value of the virial mass (though poorly constrained) of  10¹¹ M_⊙  . Noticeably, modified Newtonian dynamics (MOND) seems to be consistent with the observed rotation curve. Scaling up the contribution of the gaseous disc also gives a good fit.     

银河系自转曲线的测定

银河系自转曲线研究有着重要的天体物理意义.自转曲线可以利用多种星族Ⅰ示踪天体来加以测定,如经典造父变星、行星状星云、碳星、疏散星团、OB型星,以及中性氢巡天等.相关研究表明,在太阳圈之外,银河系自转曲线大致保持为平坦状,甚至略有抬高,从而为大质量暗晕的存在提供了有力的观测证据.     

Estimation of the solar galactocentric distance and galactic rotation velocity from near-solar-circle objects

We have tested the method of determining the solar Galactocentric distance R ₀ and Galactic rotation velocity V ₀ modified by Sofue et al. using near-solar-circle objects. The motion of objects relative to the local standard of rest has been properly taken into account. We show that when such young objects as star-forming regions or Cepheids are analyzed, allowance for the perturbations produced by the Galactic spiral density wave improves the statistical significance of the estimates. The estimate of R ₀ = 7.25 ± 0.32 kpc has been obtained from 19 star-forming regions. The following estimates have been obtained from a sample of 14 Cepheids (with pulsation periods P > 5 ^d ): R ₀ = 7.66 ± 0.36 kpc and V ₀ = 267 ± 17 km s^?1. We consider the influence of the adopted Oort constant A and the character of stellar proper motions (Hipparcos or UCAC4). The following estimates have been obtained from a sample of 18 Cepheids with stellar proper motions from the UCAC4 catalog: R ₀ = 7.64 ± 0.32 kpc and V ₀ = 217 ± 11 km s^?1.     

Determination of Galaxy Members in Clusters

A new empirical procedure is introduced to determine the confirmed galaxy members of a cluster. The method depends on both the projected distances of galaxies in the cluster field from the cluster centre and their radial velocities. Galaxies of the main body of the cluster are selected first, then the method works iteratively by increasing the standard values of the relative radial distance and velocity until all galaxies belong to the cluster are included. The general apparent shape of the cluster will result from the distribution of the celestial coordinates of the cluster members. This revised version was published online in July 2006 with corrections to the Cover Date.     

Galactic rotation curve and spiral density wave parameters from 73 masers

Based on kinematic data on masers with known trigonometric parallaxes and measurements of the velocities of HI clouds at tangential points in the inner Galaxy, we have refined the parameters of the Allen-Santillan model Galactic potential and constructed the Galactic rotation curve in a wide range of Galactocentric distances, from 0 to 20 kpc. The circular rotation velocity of the Sun for the adopted Galactocentric distance R ₀ = 8 kpc is V ₀ = 239 ± 16 km s^?1. We have obtained the series of residual tangential, ΔV _θ , and radial, V _R , velocities for 73 masers. Based on these series, we have determined the parameters of the Galactic spiral density wave satisfying the linear Lin-Shu model using the method of periodogram analysis that we proposed previously. The tangential and radial perturbation amplitudes are f _θ = 7.0±1.2 km s^?1 and f _R = 7.8±0.7 km s^?1, respectively, the perturbation wave length is λ = 2.3±0.4 kpc, and the pitch angle of the spiral pattern in a two-armed model is i = ?5.2° ±0.7°. The phase of the Sun ζ _⊙ in the spiral density wave is ?50° ± 15° and ?160° ± 15° from the residual tangential and radial velocities, respectively.     

The estimate of the deceleration in the earth's rotation due to the sun

The tidal long-term decrease in the angular velocity of the Earth's rotation has been estimated on the basis of the angular momentum tidal balance in the Earth-Moon-Sun system. The observed (LLR) tidal long-term decrease in the Moon's mean motion, the apparent secular acceleration in the mean longitude of the Sun and the long-term decrease in the 2nd degree zonal geopotential parameter were used.Presented at the XXth General Assembly of the I.A.G., Vienna, August 15, 1991.     

The peculiar rotation curve of NGC 157

We present the results of a new H i , optical, and Hα interferometric study of the nearby spiral galaxy NGC 157. Our combined C- and D-array observations with the VLA show a large-scale, ring-like structure in the neutral hydrogen underlying the optical disc, together with an extended, low surface density component going out to nearly twice the Holmberg radius. Beginning just inside the edge of the star-forming disc, the line of nodes in the gas disc commences a 60° warp, while at the same time, the rotation velocity drops by almost half its peak value of 200 km s⁻¹, before levelling off again in the outer parts. While a flat rotation curve in NGC 157 cannot be ruled out, supportive evidence for an abrupt decline comes from the ionized gas kinematics, the optical surface photometry, and the global H i profile. A standard 'maximum-disc' mass model predicts comparable amounts of dark and luminous matter within NGC 157. Alternatively, a model employing a disc truncated at 2 disc scalelengths could equally well account for the unusual form of the rotation curve in NGC 157.     

Active longitudes of the sun: The rotation period and statistical significance

Using data from the Greenwich catalog, we determined the nonuniformity of the longitudinal distribution of sunspot groups as a function of the rotation period taken for the longitude determination. We estimated the statistical significance of the active longitudes found. A fairly high significance was achieved only for sunspot groups of the Northern Hemisphere and odd activity cycles and only for a synodic rotation period close to 28 days. In this case, one interval of active longitudes was found. The active longitudes are assumed to be associated with the fossil magnetic field frozen in the uniformly rotating radiative zone of the Sun.     

Rotation curve and mass distribution in the Galaxy from the velocities of objects at distances up to 200 kpc

Three three-component (bulge, disk, halo) model Galactic gravitational potentials differing by the expression for the dark matter halo are considered. The central (bulge) and disk components are described by the Miyamoto–Nagai expressions. The Allen–Santillán (I), Wilkinson–Evans (II), and Navarro–Frenk–White (III) models are used to describe the halo. A set of present-day observational data in the range of Galactocentric distances R from 0 to 200 kpc is used to refine the parameters of thesemodels. For the Allen–Santillán model, a dimensionless coefficient γ has been included as a sought-for parameter for the first time. In the traditional and modified versions, γ = 2.0 and 6.3, respectively. Both versions are considered in this paper. The model rotation curves have been fitted to the observed velocities by taking into account the constraints on the local matter density ρ _⊙ = 0.1 M _⊙ pc^?3 and the force K _z =1.1/2πG = 77 M _⊙ pc^?2 acting perpendicularly to the Galactic plane. The Galactic mass within a sphere of radius 50 kpc, M _G (R ≤ 50 kpc) ≈ (0.41 ± 0.12) × 10¹² M _⊙, is shown to satisfy all three models. The differences between the models become increasingly significant with increasing radius R. In model I, the Galactic mass within a sphere of radius 200 kpc at γ = 2.0 turns out to be greatest among the models considered, M _G (R ≤ 200 kpc) = (1.45 ±0.30)× 10¹² M _⊙, M _G (R ≤ 200 kpc) = (1.29± 0.14)× 10¹² M _⊙ at γ = 6.3, and the smallest value has been found in model II, M _G (R ≤ 200 kpc) = (0.61 ± 0.12) × 10¹² M _⊙. In our view, model III is the best one among those considered, because it ensures the smallest residual between the data and the constructed model rotation curve provided that the constraints on the local parameters hold with a high accuracy. Here, the Galactic mass is M _G (R ≤ 200 kpc) = (0.75 ± 0.19) × 10¹² M _⊙. A comparative analysis with the models by Irrgang et al. (2013), including those using the integration of orbits for the two globular clusters NGC 104 and NGC 1851 as an example, has been performed. The third model is shown to have subjected to a significant improvement.     

Kinematic parameters of young subsystems and the galactic rotation curve

We analyze the space velocities of blue supergiants, long-period Cepheids, and young open star clusters (OSCs), as well as the H I and H II radial-velocity fields by the maximum-likelihood method. The distance scales of the objects are matched both by comparing the first derivatives of the angular velocity Ω′ determined separately from radial velocities and proper motions and by the statistical-parallax method. The former method yields a short distance scale (for R₀=7.5 kpc, the assumed distances should be increased by 4%), whereas the latter method yields a long distance scale (for R₀=8.5 kpc, the assumed distances should be increased by 16%). We cannot choose between these two methods. Similarly, the distance scale of blue supergiants should be shortened by 9% and lengthened by 3%, respectively. The H II distance scale is matched with the distance scale of Cepheids and OSCs by comparing the derivatives Ω′ determined for H II from radial velocities and for Cepheids and OSCs from space velocities. As a result, the distances to H II regions should be increased by 5% in the short distance scale. We constructed the Galactic rotation curve in the Galactocentric distance range 2–14 kpc from the radial velocities of all objects with allowance for the difference between the residual-velocity distributions. The axial ratio of the Cepheid+OSC velocity ellipsoid is well described by the Lindblad relation, while σ_u≈σ_v for gas. The following rotation-curve parameters were obtained: Ω₀=(27.5±1.4) km s^?1 kpc^?1 and A=(17.1±0.5) km s^?1 kpc^?1 for the short distance scale (R₀=7.5 kpc); and Ω₀=(26.6±1.4) km s^?1 kpc^?1 and A=(15.4±0.5) km s^?1 kpc^?1 for the long distance scale (R₀=8.5 kpc). We propose a new method for determining the angular velocity Ω₀ from stellar radial velocities alone by using the Lindblad relation. Good agreement between the inferred Ω₀ and our calculations based on space velocities suggests that the Lindblad relation holds throughout the entire sample volume. Our analysis of the heliocentric velocities for samples of young objects reveals noticeable streaming motions (with a velocity lag of ～7 km s^?1 relative to the LSR), whereas a direct computation of the perturbation amplitudes in terms of the linear density-wave theory yields a small amplitude for the tangential perturbations.