A. T. Bajkova

Galactic Rotation Curve and the Effect of Density Waves from Data on Young Objects

Based on currently available data on the three-dimensional field of space velocities of young (≤50 Myr) open star clusters and the radial velocities of HI clouds and star-forming (H II) regions, we have found the Galactic rotation curve in the range of Galactocentric distances 3 kpc < R < 12 kpc using the first six terms of the Taylor expansion of the angular velocity of Galactic rotation in Bottlinger’s equations. The Taylor terms found at the Galactocentric distance of the Sun R0 = 7.5 kpc are: ω0 = −27.7 ± 0.6 km s−1 kpc−1, ω01 = 4.13 ± 0.07 km s−1 kpc−2, ω02 = −0.912 ± 0.065 km s−1 kpc−3, ω03 = 0.277 ± 0.036 km s−1 kpc−4, ω04 = −0.265 ± 0.034 km s−1 kpc−5, ω05 = 0.104 ± 0.020 km s−1 kpc−6. In this case, the Oort constants are A = 15.5 ± 0.3 km s−1 kpc−1 and B = −12.2 ± 0.7 km s−1 kpc−1. We have established that the centroid of the sample moves relative to the local standard of rest along the Galactic Y axis with a velocity of −6.2 ± 0.8 km s−1. A Fourier spectral analysis of the velocity residuals from the derived rotation curve attributable to density waves reveals three dominant peaks with wavelengths of 2.5, 1.4, and 0.9 kpc and amplitudes of 4.7, 2.6, and 3.6 km s−1, respectively. These have allowed us to estimate the distances between the density wave peaks, 1.9, 2.4, and 3.2 kpc as R increases, in agreement with the description of the density weave as a logarithmic spiral. The amplitude of the density wave perturbations is largest in the inner part of the Galaxy, ≈9 km s−1, and decreases to ≈1 km s−1 in its outer part. A spectral analysis of the radial velocities of young open star clusters has confirmed the presence of periodic perturbations with an amplitude of 5.9 ± 1.1 km s−1 and a wavelength λ = 1.7 ± 0.5 kpc. It shows that the phase of the Sun in the density wave is close to −π/2 and the Sun is located in the interarm space near the outer edge of the Carina-Sagittarius arm.

Redetermination of galactic spiral density wave parameters based on spectral analysis of masers radial velocities

To redetermine the Galactic spiral density wave parameters, we have performed a spectral (Fourier) analysis of the radial velocities for 44 masers with known trigonometric parallaxes, proper motions, and line-of-sight velocities. The masers are distributed in awide range of Galactocentric distances (3.5 kpc < R < 13.2 kpc) and are characterized by a wide scatter of position angles θ in the Galactic XY plane. This has required an accurate allowance for the dependence of the perturbation phase both on the logarithm of the Galactocentric distances and on the position angles of the objects. To increase the significance of the extraction of periodicities from data series with large gaps, we have proposed and implemented a spectrum reconstruction method based on a generalized maximum entropy method. As a result, we have extracted a periodicity describing a spiral density wave with the following parameters from the maser radial velocities: the perturbation amplitude fR = 7.7−1.5+1.7 km s−1, the perturbation wavelength λ = 2.2−0.1+0.4 kpc, the pitch angle of the spiral density wave i = −5−0.9°+0.2°, and the phase of the Sun in the spiral density wave χ⊙ = −147−17°+3°.

The generalization of maximum entropy method for reconstruction of complex functions

Abstract The Maximum Entropy Method is widely used for reconstruction of real non-negative functions, such as images (intensity distributions) in optics and astronomy. The problem of reconstruction exists not only for real non-negative functions: in radio holography, for example, it is often necessary to reconstruct a coherent source field distribution described by a complex function. In this paper the Generalization of Maximum Entropy Method for reconstruction of functions of different types (real non-negative as well as real with alternating signs and complex ones) is suggested. Though this problem is considered for two-dimensional functions it is evident that the generalization obtained can be applied for functions of different dimensions. Numerical simulation results show high quality of reconstruction of complex functions and stability of the algorithm in the presence of measurement errors.

The OSACA database and a kinematic analysis of stars in the solar neighborhood

We transformed radial velocities compiled from more than 1400 published sources, including the Geneva-Copenhagen survey of the solar neighborhood (CORAVEL-CfA), into a uniform system based on the radial velocities of 854 standard stars in our list. This enabled us to calculate the average weighted radial velocities for more than 25000 HIPPARCOS stars located in the local Galactic spiral arm (Orion arm) with a median error of ±1 km/s. We use these radial velocities together with the stars’ coordinates, parallaxes, and proper motions to determine their Galactic coordinates and space velocities. These quantities, along with other parameters of the stars, are available from the continuously updated Orion Spiral Arm Catalogue (OSACA) and the associated database. We perform a kinematic analysis of the stars by applying an Ogorodnikov-Milne model to the OSACA data. The kinematics of the nearest single and multiple main-sequence stars differ substantially. We used distant (-r ≈ 0.2 kpc) stars of mixed spectral composition to estimate the angular velocity of the Galactic rotation, ωo = −25.7 ± 1.2 kms−1 kpc−1, and the vertex deviation, l = 13° ± 2°, and detected a negative K effect. This negative K effect is most conspicuous in the motion of A0–A5 giants and is equal to K = −13.1 ± 2.0 kms−1 kpc−1.

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 R0 = 8 kpc is V0 = 239 ± 16 km s−1. We have obtained the series of residual tangential, ΔVθ, and radial, VR, 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 fθ = 7.0±1.2 km s−1 and fR = 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 rotation parameters from data on open star clusters

Currently available data on the field of velocities Vr, Vl, Vb 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 ω0 = −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 R0 = 7.4 ± 0.3 kpc and l0 = 0° ± 1°. The Galactocentric distance R0 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.

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 R0 = 8kpc, V0 = 259±16 km s−1, and obtained the following spiral density wave parameters: the amplitudes of the radial and azimuthal velocity perturbations fR = −10.8 ± 1.2 km s−1 and fθ = 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: fθ = 2.9 ± 2.1 km s−1 and χ⊙ = −104° ± 6°.

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 R0 = 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 fR = −6.8 ± 0.7 and fθ = 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 Ωp − 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 |Ωp − Ω0| = 10 ± 1stat ± 3syst 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 fr0 = 0.04 ± 0.01.

Searching for possible siblings of the sun from a common cluster based on stellar space velocities

We propose a kinematic approach to searching for the stars that could be formed with the Sun in a common “parent” open cluster. The approach consists in preselecting suitable candidates by the closeness of their space velocities to the solar velocity and analyzing the parameters of their encounters with the solar orbit in the past in a time interval comparable to the lifetime of stars. We consider stars from the Hipparcos catalog with available radial velocities. The Galactic orbits of stars have been constructed in the Allen-Santillan potential by taking into account the perturbations from the spiral density wave. We show that two stars, HIP 87382 and HIP 47399, are of considerable interest in our problem. Their orbits oscillate near the solar orbit with an amplitude of ≈250 pc; there are short-term close encounters to distances <10 pc. Both stars have an evolutionary status and metallicity similar to the solar ones.

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, R0 = 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 |V0| = 252 ± 14 km s−1); (3) the spiral density wave parameters, namely: the perturbation amplitudes for the radial and azimuthal velocity components, respectively, fR = −12.5±1.1 km s−1 and fϑ = 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°.