Vol 44, No 11 (2018)

The various measurements of the linear matter density perturbation amplitude obtained from the observations of the cosmic microwave background (CMB) anisotropy, weak gravitational lensing, galaxy cluster mass function, matter power spectrum, and redshift space distortions are compared. The Planck data on the CMB temperature anisotropy spectrum at high multipoles, ℓ > 1000 (where the effect of gravitational lensing is most significant), are shown to give a measurement of the matter density perturbation amplitude that contradicts all other measurements of this quantity from both Planck CMB anisotropy data and other data at a significance level of about 3.7σ. Thus, at present these data should not be combined together for the calculations of constraints on cosmological parameters. Except for the Planck data on the CMB temperature anisotropy spectrum at high multipoles, all the remaining measurements of the density perturbation amplitude agree well between themselves and give the following constraints: σ₈ = 0.792± 0.006 on the linear matter density perturbation amplitude, Ω_m = 0.287± 0.007 on the matter density parameter, and H₀ = 69.4 ± 0.6 km s⁻¹ Mpc⁻¹ on the Hubble constant. Various constraints on the sum of neutrino masses and the number of neutrino flavors can be obtained by additionally taking into account the data on baryon acoustic oscillations and (or) direct Hubble constant measurements in the local Universe.

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.

The influence of various factors on the statistical properties of the Galactic center distance (R₀) estimate obtained by solving the general problem of determining the geometric parameters of a Galactic spiral arm from its segment with the inclusion of the distance to the spiral pole, i.e., R₀, in the set of parameters has been studied by the Monte Carlo method. Our numerical simulations have been performed for the model segments representing the Perseus and Scutum arms based on masers in high-mass star forming regions. We show that the uncertainty in the present-day parallax measurements for these objects systematically decreases (!) with increasing heliocentric distance, while the relative uncertainty in the parallaxes is, on average, approximately constant. This lucky circumstance increases significantly (by a factor of 1.4–1.7) the accuracy of estimating R₀ from the arm segment traced by masers. Our numerical experiments provide evidence for the consistency of the R₀ estimate from the spiral-segment geometry. The significant biases of the estimate detected only for the Scutum arm are caused mainly by the random parallax errors, the small angular extent of the segment, and the small number of objects representing it. The dispersion of the R₀ estimate depends most strongly on the angular extent of the segment and the parallax uncertainty if the latter, on average, does not depend on the distance. The remaining parameters, except for the pitch angle, exert an equally significant, but weaker influence on the statistical accuracy of the estimate. When the data on 3–8 segments are processed simultaneously, the predicted standard error of the final estimate is σR₀ ≃ 0.5−0.3 kpc, respectively. The accuracy can be improved by increasing the extent of the identified segments and the number of objects belonging to them. The method of determining R₀ from spiral segments has turned out to be operable for a wide set of possible parameters even when using an L-estimator (median). This makes the development of a more complex method based on an M-estimator, which allows one to properly take into account the measuring and natural dispersions of objects relative to the arm center line and, thus, to avoid the biases of the parameter estimates, meaningful.

A method for investigating the differential rotation of the solar corona using the coronal magnetic field as a tracer is proposed. The magnetic field is calculated in the potential approximation from observational data at the photospheric level. The time interval from June 24, 1976, to December 31, 2004, is considered. The magnetic field has been calculated for all latitudes from the equator to ±75◦ with a 5◦ step at distances from the base of the corona 1.0 R_⊙ to 2.45 R_⊙ near the source surface. The coronal rotation periods at 14 distances from the solar center have been determined by the method of periodogram analysis. The coronal rotation is shown to become progressively less differential with increasing heliocentric distance; it does not become rigid even near the source surface. The change in the coronal rotation periods with time is considered. At the cycleminimumthe rotation has been found to bemost differential, especially at small distances from the solar center. The change in coronal rotation with time is consistent with the tilt of the solar magnetic equator. The results from the magnetic field are compared with those obtained from the brightness of the green coronal Fe XIV 530.3 nm line. The consistency between these results confirms the reliability of the proposed method for studying the coronal rotation. Studying the rotation of the coronal magnetic field gives hope for the possibility of using this method to diagnose the differential rotation in subphotospheric layers.