We investigated the dependence of the parameters of the segments of spiral arms of the Galaxy on the age of classical Cepheids. The catalog of Cepheids (Mel'nik et al. 2015) was divided into two samples-relatively young (P > 9 d ) and relatively old (P < 9 d ) objects. The parameters of the spiral structure were determined both for two samples separately and jointly for the combination of two systems of segments traced by young and old objects. For most of the segments, their parameters for young and old objects differ significantly. Taking into account the difference between the two segment systems, we obtained the estimate R 0 equal to 7.23 +0.19 −0.18 kpc, which in the modern LMC calibration corresponds to the value of R 0 = 8.08 +0.21 −0.20 | stat. +0.38−0.36 | cal. kpc. It is shown that the displacement between the segments is not reduced to the effect of differential rotation only. To interpret this displacement for objects of Perseus and Sagittarius-2 segments we carried out a dynamic modeling of the change in the position of the segment points when moving in the smooth gravitational field of the Galaxy. At the angular velocity of rotation of the spiral pattern Ω p = 25.2 ± 0.5 km s −1 kpc −1 (Dambis et al. 2015) the observed displacement between segments on young and old objects can be explained by the amplitude of spiral perturbations of the radial velocity of u = 10 ± 1.5 km s −1 . For the constructed double system of spiral segments, it is demonstrated that the assumption of constancy of the pitch angles within each segment and the assumption that the pole of the spiral pattern is in the direction of the nominal center of the Galaxy do not contradict the data within the range of uncertainty.
We consider the problem of determining the geometric parameters of a Galactic spiral arm from its segment by including the distance to the spiral pole, i.e., the distance to the Galactic center (R 0 ). The question about the number of points belonging to one turn of a logarithmic spiral and defining this spiral as a geometric figure has been investigated numerically and analytically by assuming the direction to the spiral pole (to the Galactic center) to be known. Based on the results obtained, in an effort to test the new approach, we have constructed a simplified method of solving the problem that consists in finding the median of the values for each parameter from all possible triplets of objects in the spiral arm segment satisfying the condition for the angular distance between objects. Applying the method to the data on the spatial distribution of masers in the Perseus and Scutum arms (the catalogue by Reid et al. (2014)) has led to an estimate of R 0 = 8.8 ± 0.5 kpc. The parameters of five spiral arm segments have been determined from masers of the same catalogue. We have confirmed the difference between the spiral arms in pitch angle. The pitch angles of the arms revealed by masers are shown to generally correlate with R 0 in the sense that an increase in R 0 leads to a growth in the absolute values of the pitch angles.
The influence of various factors on the statistical properties of the Galactic center distance (R 0 ) 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., R 0 , 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 R 0 from the arm segment traced by masers. Our numerical experiments provide evidence for the consistency of the R 0 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 R 0 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 σ R 0 ≃ 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 R 0 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 new approach to determining the solar galactocentric distance, R 0 , from the geometry of spiral-arm segments is proposed. Geometric aspects of the problem are analyzed and a simplified three-point method for estimating R 0 from objects in a spiral segment is developed in order to test the proposed approach. An estimate of R 0 = 8.44 ± 0.45 kpc is obtained by applying the method to masers with measured trigonometric parallaxes, and statistical properties of the R 0 estimation from spiral segments are analyzed.
1 Санкт-Петербургский государственный университет, 2 Главная (Пулковская) астрономическая обсерватория РАН В работе представляется программный комплекс обработки двумерных функций распределения статистических выборок на основе нового самосогласованного метода вейвлет-анализа.
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