Galactic Sun's motion in the cold dark matter,MOdified Newtonian Dynamics and modified gravity scenarios

We numerically integrate the equations of motion of the Sun in Galactocentric Cartesian rectangular coordinates for –4.5 Gyr ≤ t ≤ 0 in Newtonian mechanics with two different models for the Cold Dark Matter (CDM) halo, in MOdified Newtonian Dynamics (MOND) and in MOdified Gravity (MOG) without resorting to CDM. The initial conditions used come from the latest kinematical determination of the 3D Sun's motion in the Milky Way (MW) by assuming for the rotation speed of the Local Standard of Rest (LSR) the recent value Θ₀ = 268 km s^–1 and the IAU recommended value Θ₀ = 220 km s^–1; the Sun is assumed located at 8.5 kpc from the Galactic Center (GC). For Θ₀ = 268 km s^–1 the birth of the Sun, 4.5 Gyr ago, would have occurred at large Galactocentric distances (12–27 kpc depending on the model used), while for Θ₀ = 220 km s^–1 it would have occurred at about 8.8–9.3 kpc for almost all the models used. The integrated trajectories are far from being circular, especially for Θ₀ = 268 km s^–1, and differ each other with the CDM models yielding the widest spatial extensions for the Sun's orbital path (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Imprint of Galactic dynamics on Earth's climate

A connection between climate and the Solar system's motion perpendicular to the Galactic plane during the last 200 Myr years is studied. An imprint of galactic dynamics is found in a long‐term record of the Earth's climate that is consistent with variations in the Solar system oscillation around the Galactic midplane. From small modulations in the oscillation frequency of Earth's climate the following features of the Galaxy along the Solar circle can be determined: 1) the mass distribution, 2) the timing of two spiral arm crossings (31 Myr and 142 Myr) 3) Spiral arm/interarm density ratio (ρ _arm/ρ _interarm ≈ 1.5–1.8), and finally, using current knowledge of spiral arm positions, a pattern speed of Ω_P = 13.6 ± 1.4 km s^–1 kpc^–1 is determined. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Galactic Rotation Based on OB Stars from the Gaia DR2 Catalogue

We have studied a sample containing ~6000 OB stars with proper motions and trigonometric parallaxes from the Gaia DR2 catalogue. The following parameters of the angular velocity of Galactic rotation have been found: Ω₀ = 29.70 ± 0.11 km s^-1 kpc^-1, Ω'₀ = -4.035 ± 0.031 km s^-1 kpc^-2, and Ω ₀ = 0.620 ± 0.014 km s^-1 kpc^-3. The circular rotation velocity of the solar neighborhood around the Galactic center is V₀ = 238 ± 5 km s^-1 for the adopted Galactocentric distance of the Sun R₀ = 8.0 ± 0.15 kpc. The amplitudes of the tangential and radial velocity perturbations produced by the spiral density wave are f_θ = 4.4 ± 1.4 kms^-1 and f_R = 5.1 ± 1.2 kms^-1, respectively; the perturbation wavelengths are λ_θ = 1.9 ± 0.5 kpc and λ_R = 2.1 ± 0.5 kpc for the adopted four-armed spiral pattern. The Sun's phase in the spiral density wave is χ_⊙ = -178° ± 12°.

     

Periodic pattern in the residual-velocity field of OB associations

An analysis of the residual-velocity field of OB associations within 3 kpc of the Sun has revealed periodic variations in the radial residual velocities along the Galactic radius vector with a typical scale length of λ = 2.0 ± 0.2 kpc and a mean amplitude of f _R = 7 ± 1 km s^?1. The fact that the radial residual velocities of almost all OB associations in rich stellar-gas complexes are directed toward the Galactic center suggests that the solar neighborhood under consideration is within the corotation radius. The azimuthal-velocity field exhibits a distinct periodic pattern in the 0°<l<180° region, where the mean azimuthal-velocity amplitude is f _θ = 6 ± 2 km s^?1. There is no periodic pattern of the azimuthal-velocity field in the 180°<l<360° region. The locations of the Cygnus arm, as well as the Perseus arm, inferred from an analysis of the radial-and azimuthal-velocity fields coincide. The periodic patterns of the residual-velocity fields of Cepheids and OB associations share many common features.     

Galactic rotation parameters from data on open star clusters

Currently available data on the field of velocities V _r , V _l , V _b for open star clusters are used to perform a kinematic analysis of various samples that differ by heliocentric distance, age, and membership in individual structures (the Orion, Carina-Sagittarius, and Perseus arms). Based on 375 clusters located within 5 kpc of the Sun with ages up to 1 Gyr, we have determined the Galactic rotation parameters ω ₀ = ?26.0 ± 0.3 km s^?1 kpc^?1, ω′₀ = 4.18 ± 0.17 km s^?1 kpc^?2, ω″₀ = ?0.45 ± 0.06 km s^?1 kpc^?3, the system contraction parameter K = ?2.4 ± 0.1 km s^?1 kpc^?1, and the parameters of the kinematic center R ₀ = 7.4 ± 0.3 kpc and l ₀ = 0° ± 1°. The Galactocentric distance R ₀ in the model used has been found to depend significantly on the sample age. Thus, for example, it is 9.5 ± 0.7 and 5.6 ± 0.3 kpc for the samples of young (≤50 Myr) and old (>50 Myr) clusters, respectively. Our study of the kinematics of young open star clusters in various spiral arms has shown that the kinematic parameters are similar to the parameters obtained from the entire sample for the Carina-Sagittarius and Perseus arms and differ significantly from them for the Orion arm. The contraction effect is shown to be typical of star clusters with various ages. It is most pronounced for clusters with a mean age of ≈100 Myr, with the contraction velocity being Kr = ?4.3 ± 1.0 km s^?1.     

Corrections for the Lutz-Kelker bias for Galactic masers

Based on published data, we have collected information about Galactic maser sources with measured distances. In particular, 44 Galactic maser sources located in star-forming regions have trigonometric parallaxes, proper motions, and radial velocities. In addition, ten more radio sources with incomplete information are known, but their parallaxes have been measured with a high accuracy. For all 54 sources, we have calculated the corrections for the well-known Lutz-Kelker bias. Based on a sample of 44 sources, we have refined the parameters of the Galactic rotation curve. Thus, at R ₀ = 8kpc, the peculiar velocity components for the Sun are (U _⊙, V _⊙, W _⊙) = (7.5, 17.6, 8.4) ± (1.2, 1.2, 1.2) km s^?1 and the angular velocity components are ω ₀ = ?28.7 ± 0.5 km s^?1 kpc^?1, ω ₀′ = +4.17 ± 0.10 km s^?1 kpc^?2, and ω₀″ = ?0.87 ± 0.06 km s^?1 kpc^?3. The corresponding Oort constants are A = 16.7 ± 0.6 km s^?1 kpc^?1 and B = ?12.0 ± 1.0 km s^?1 kpc^?1; the circular rotation velocity of the solar neighborhood around the Galactic center is V ₀ = 230 ± 16 km s^?1. We have found that the corrections for the Lutz-Kelker bias affect the determination of the angular velocity ω ₀ most strongly; their effect on the remaining parameters is statistically insignificant. Within themodel of a two-armed spiral pattern, we have determined the pattern pitch angle $i = - 6_.^ \circ 5$ and the phase of the Sun in the spiral wave χ ₀ = 150°.     

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.     

Galactic kinematics from data on open star clusters from the MWSC catalogue

Open star clusters from the MWSC (Milky Way Star Clusters) catalogue have been used to determine the Galactic rotation parameters. The circular rotation velocity of the solar neighborhood around the Galactic center has been found from data on more than 2000 clusters of various ages to be V ₀ = 236 ± 6 km s^?1 for the adopted Galactocentric distance of the Sun R ₀ = 8.3 ± 0.2 kpc. The derived angular velocity parameters are Ω ₀ = 28.48 ± 0.36 km s^?1 kpc^?1, Ω’₀ = ?3.50 ± 0.08 km s^?1 kpc_?2, and Ω″₀ = 0.331 ± 0.037 km s^?1 kpc^?3. The influence of the spiral density wave has been detected only in the sample of clusters younger than 50 Myr. For these clusters the amplitudes of the tangential and radial velocity perturbations are f ^θ = 5.6 ± 1.6 km s^?1 and f _R = 7.7 ± 1.4 km s^?1, respectively; the perturbation wavelengths are λ _θ = 2.6 ± 0.5 kpc (i _θ = ^?11? ± 2?) and λ _R = 2.1 ± 0.5 kpc (i _R = ?9? ± 2?) for the adopted four-armed model (m = 4). The Sun’s phase in the spiral density wave is (χ_⊙)_θ = ?62? ± 9? and (χ_⊙)_R = ?85? ± 10? from the residual tangential and radial velocities, respectively.     

Kinematics of the Gould Belt based on open clusters

We have redetermined the kinematic parameters of the Gould Belt using currently available data on the motion of nearby young (log t < 7.91) open clusters, OB associations, and moving stellar groups. Our modeling shows that the residual velocities reach their maximum values of ?4 km s^?1 for rotation (in the direction of Galactic rotation) and +4 km s^?1 for expansion at a distance from the kinematic center of ≈300 pc. We have taken the following parameters of the Gould Belt center: R ₀ = 150 pc and l ₀ = 128°. The whole structure is shown to move relative to the local standard of rest at a velocity of 10.7 ± 0.7 km s^?1 in the direction l = 274° ± 4° and b = ?1° ± 3°. Using the derived rotation velocity, we have estimated the virial mass of the Gould Belt to be 1.5 × 10⁶ M _⊙.     

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.     

Testing the Distance Scale of the Gaia TGAS Catalogue by the Kinematic Method

We have studied the simultaneous and separate solutions of the basic kinematic equations obtained using the stellar velocities calculated on the basis of data from the Gaia TGAS and RAVE5 catalogues. By comparing the values of Ω'₀ found by separately analyzing only the line-of-sight velocities of stars and only their proper motions, we have determined the distance scale correction factor p to be close to unity, 0.97 ± 0.04. Based on the proper motions of stars from the Gaia TGAS catalogue with relative trigonometric parallax errors less than 10% (they are at a mean distance of 226 pc), we have found the components of the group velocity vector for the sample stars relative to the Sun (U, V,W)_⊙ = (9.28, 20.35, 7.36) ± (0.05, 0.07, 0.05) km s^?1, the angular velocity of Galactic rotation Ω⁰ = 27.24 ± 0.30 km s?1 kpc?1, and its first derivative Ω'₀ = ?3.77 ± 0.06 km s^?1 kpc^?2; here, the circular rotation velocity of the Sun around the Galactic center is V₀ = 218 ± 6 km s^?1 kpc (for the adopted distance R₀ = 8.0 ± 0.2 kpc), while the Oort constants are A = 15.07 ± 0.25 km s^?1 kpc^?1 and B = ?12.17 ± 0.39 km s^?1 kpc^?1, p = 0.98 ± 0.08. The kinematics of Gaia TGAS stars with parallax errors more than 10% has been studied by invoking the distances from a paper by Astraatmadja and Bailer-Jones that were corrected for the Lutz–Kelker bias. We show that the second derivative of the angular velocity of Galactic rotation Ω'₀ = 0.864 ± 0.021 km s^?1 kpc^?3 is well determined from stars at a mean distance of 537 pc. On the whole, we have found that the distances of stars from the Gaia TGAS catalogue calculated using their trigonometric parallaxes do not require any additional correction factor.     

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.     

Galactic kinematics from a sample of young massive stars

Based on published sources, we have created a kinematic database on 220 massive (> 10 M _⊙) young Galactic star systems located within ≤3 kpc of the Sun. Out of them, ≈100 objects are spectroscopic binary and multiple star systems whose components are massive OB stars; the remaining objects are massive Hipparcos B stars with parallax errors of no more than 10%. Based on the entire sample, we have constructed the Galactic rotation curve, determined the circular rotation velocity of the solar neighborhood around the Galactic center at R ₀ = 8kpc, V ₀ = 259±16 km s^?1, and obtained the following spiral density wave parameters: the amplitudes of the radial and azimuthal velocity perturbations f _R = ?10.8 ± 1.2 km s^?1 and f _θ = 7.9 ± 1.3 km s^?1, respectively; the pitch angle for a two-armed spiral pattern i = ?6.0° ± 0.4°, with the wavelength of the spiral density wave near the Sun being λ = 2.6 ± 0.2 kpc; and the radial phase of the Sun in χ _⊙ = ?120° ± 4°. We show that such peculiarities of the Gould Belt as the local expansion of the system, the velocity ellipsoid vertex deviation, and the significant additional rotation can be explained in terms of the density wave theory. All these effects decrease noticeably once the influence of the spiral density wave on the velocities of nearby stars has been taken into account. The influence of Gould Belt stars on the Galactic parameter estimates has also been revealed. Eliminating them from the kinematic equations has led to the following new values of the spiral density wave parameters: f _θ = 2.9 ± 2.1 km s^?1 and χ _⊙ = ?104° ± 6°.     

Kinematics of the Galaxy from OB Stars with Data from the Gaia DR2 Catalogue

We have selected and analyzed a sample of OB stars with known line-of-sight velocities determined through ground-based observations and with trigonometric parallaxes and propermotions from the Gaia DR2 catalogue. Some of the stars in our sample have distance estimates made from calcium lines. A direct comparison with the trigonometric distance scale has shown that the calcium distance scale should be reduced by 13%. The following parameters of the Galactic rotation curve have been determined from 495 OB stars with relative parallax errors less than 30%: (U, V,W)_⊙ = (8.16, 11.19, 8.55)± (0.48, 0.56, 0.48) km s^?1, Ω₀ = 28.92 ± 0.39 km s^?1 kpc^?1, Ω'₀ = ?4.087 ± 0.083 km s^?1 kpc^?2, and Ω″ ₀ = 0.703 ± 0.067 km s?1 kpc^?3, where the circular velocity of the local standard of rest is V0 = 231 ± 5 km s^?1 (for the adopted R₀ = 8.0 ± 0.15 kpc). The parameters of the Galactic spiral density wave have been found from the series of radial, V_R, residual tangential, ΔV_circ, and vertical, W, velocities of OB stars by applying a periodogram analysis. The amplitudes of the radial, tangential, and vertical velocity perturbations are f_R = 7.1± 0.3 km s^?1, f_θ = 6.5 ± 0.4 km s^?1, and f_W = 4.8± 0.8 km s^?1, respectively; the perturbation wavelengths are λ_R = 3.3 ± 0.1 kpc, λ_θ = 2.3 ± 0.2 kpc, and λ_W = 2.6 ± 0.5 kpc; and the Sun’s radial phase in the spiral density wave is (χ_⊙)_R = ?135? ± 5?, (χ_⊙)θ = ?123? ± 8?, and (χ_⊙)_W = ?132? ± 21? for the adopted four-armed spiral pattern.     

Scale length of the galactic thin disk

This paper presents an analysis of the first 2MASS (The Two Micron All Sky Survey) sampler data as observed at lower Galactic latitude in our Galaxy. These new near-infrared data provide insight into the structure of the thin disk of our Galaxy, The interpretation of star counts and color distributions of stars in the near-infrared with the synthetic stellar population model, gives strong evidence that the Galactic thin disk density scale length,h _R , is rather short (2.7 ± 0.1 kpc).     

Estimation of the galactic spiral pattern speed from Cepheids

To study the peculiarities of the Galactic spiral density wave, we have analyzed the space velocities of Galactic Cepheids with propermotions from the Hipparcos catalog and line-of-sight velocities from various sources. First, based on the entire sample of 185 stars and taking R ₀ = 8 kpc, we have found the components of the peculiar solar velocity (u _⊙, v _⊙) = (7.6, 11.6) ± (0.8, 1.1) km s^?1, the angular velocity of Galactic rotation Ω₀ = 27.5 ± 0.5 km s^?1 kpc^?1 and its derivatives Ω′₀ = ?4.12 ± 0.10 km s^?1 kpc^?2 and Ω″₀ = 0.85 ± 0.07 km s^?1 kpc^?3, the amplitudes of the velocity perturbations in the spiral density wave f _R = ?6.8 ± 0.7 and f _θ = 3.3 ± 0.5 km s^?1, the pitch angle of a two-armed spiral pattern (m = 2) i = ?4.6° ± 0.1° (which corresponds to a wavelength λ = 2.0 ± 0.1 kpc), and the phase of the Sun in the spiral density wave χ_⊙ = ?193° ± 5°. The phase χ_⊙ has been found to change noticeably with the mean age of the sample. Having analyzed these phase shifts, we have determined the mean value of the angular velocity difference Ω _p ? Ω, which depends significantly on the calibrations used to estimate the individual ages of Cepheids. When estimating the ages of Cepheids based on Efremov’s calibration, we have found |Ω _p ? Ω₀| = 10 ± 1_stat ± 3_syst km s^?1 kpc^?1. The ratio of the radial component of the gravitational force produced by the spiral arms to the total gravitational force of the Galaxy has been estimated to be f _r0 = 0.04 ± 0.01.     

Galactic kinematics from OB3 stars with distances determined from interstellar Ca II lines

Based on data for 102 OB3 stars with known proper motions and radial velocities, we have tested the distances derived by Megier et al. from interstellar Ca II spectral lines. The internal reconciliation of the distance scales using the first derivative of the angular velocity of Galactic rotation Ω′₀ and the external reconciliation with Humphreys’s distance scale for OB associations refined by Mel’nik and Dambis show that the initial distances should be reduced by ≈20%. Given this correction, the heliocentric distances of these stars lie within the range 0.6–2.6 kpc. A kinematic analysis of these stars at a fixed Galactocentric distance of the Sun, R ₀ = 8 kpc, has allowed the following parameters to be determined: (1) the solar peculiar velocity components (u _⊙, v _⊙, ω _⊙) = (8.9, 10.3, 6.8) ± (0.6, 1.0, 0.4) km s⁻¹; (2) the Galactic rotation parameters Ω₀ = −31.5 ± 0.9 km s⁻¹ kpc⁻¹, Ω′₀ = +4.49 ± 0.12 km s⁻¹ kpc⁻², Ω″₀ = −1.05 ± 0.38 km s⁻¹ kpc⁻³ (the corresponding Oort constants are A = 17.9 ± 0.5 km s⁻¹ kpc⁻¹, B = −13.6 ± 1.0 km s⁻¹ kpc⁻¹ and the circular rotation velocity of the solar neighborhood is |V ₀| = 252 ± 14 km s⁻¹); (3) the spiral density wave parameters, namely: the perturbation amplitudes for the radial and azimuthal velocity components, respectively, f _R = −12.5±1.1 km s⁻¹ and f _ϑ = 2.0 ± 1.6 km s⁻¹; the pitch angle for the two-armed spiral pattern i = −5.3° ± 0.3°, with the wavelength of the spiral density wave at the solar distance being λ = 2.3 ± 0.2 kpc; the Sun’s phase in the spiral wave x _⊙ = −91° ± 4°.