================================================================================ The orbits of visual double and multiple stars obtained by the Apparent Motion Parameters method during the last 40 years. Romanenko L.G., Kiyaeva O.V., Izmailov I.S., Shakht N.A., Gorshanov D.L. Publications of the Pulkovo Observatory, N 227, p.146-158 (2022). ================================================================================ ADC_Keywords: Binaries, visual ; Orbits; Stars Keywords: visual double stars; orbits; AMP method Abstract: Summed many years of work at Pulkovo, the orbits of 67 wide pairs of visual double and multiple stars (included in 64 systems) which were obtained by the Apparent Motion Parameters (AMP) method are presented. This short arc determination orbit method is based on the most reliable astrometric and astrophysical data corresponding to one instant of time. The rest of the observations accumulated in the world serve to control the quality of the orbit and refine some parameters. All early determined AMP-orbits were compared with new observations, some of them were recalculated, new ones were added. For the stars of Pulkovo program of observations with a 26-inch refractor, the Gaia DR2 data were analised. Based on these data, the orbits of 16 stars were calculated. In 20 cases from 67, the quasi-instant motion according to the Gaia DR2 data at the instant 2015.5 contradicts the motion according to all-world observations. A possible reason is the presence of inner subsystems. The orientation of the obtained orbits in the galactic coordinate system is also given. Description: In the TABL1 - Common data about the stars: number one after another, Hipparcos number, ADS number, Components, WDS number (coordinates), magnitudes and spectral classes of components according to WDS, spectral classes of components according to Teff from the catalog Gaia DR2, the time interval and the number of observations in WDS (version 2016), the time interval and the number of photographic and CCD observations with Pulkovo 26-inch refractor, number of solutions, any flags and references. In the TABL2 - Initial data for AMP orbit determinations. In the TABL3 - The AMP orbits and their uncertainties for 50 pairs with 1, 2 or 4 solutions, comparison with observations and also we give coordinates of the Pole and Periastron directions in the Galaxy frame. Orbital element uncertainties are determined by the total effect of initial data errors, but they are asymmetrical with respect to the calculated values of the orbital elements, therefore we give two values of uncertainties: positive (pos, with sign "+") and negative (neg, with sign "-"). In the TABL4 - The Families of AMP orbits for 17 pairs corresponding to special solutions, their comparison with observations and also we give coordinates of orbital Pole and Periastron directions in the Galactic frame. File Summary: -------------------------------------------------------------------------------- FileName Lrecl Records Explanations -------------------------------------------------------------------------------- ReadMe 80 . This file TABL1.txt 146 67 Description of data on stars TABL2.txt 185 134 Initial data for orbits of 67 pair of stars ) TABL3.txt 315 122 Results for 50 double stars TABL4.txt 167 95 Results for 17 double stars (Family) -------------------------------------------------------------------------------- Byte-by-byte Description of file: TABL1.txt -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 3 I3 --- I Number one after another 6- 11 A6 --- HIP1 Hipparcos catalog number of a primary star 12 A1 --- / Dividing sign 13- 18 A6 --- HIP2 Hipparcos catalog number of a secondary star 21- 25 A5 --- ADS ADS catalog number 29- 32 A4 --- Cmp Components of the pair 34- 43 A10 --- WDS WDS catalog number (J2000.0) 45- 49 F5.2 mag Mag1 Magnitude of a primary star according to WDS 52- 56 F5.2 mag Mag1 Magnitude of a secondary star according to WDS 60- 67 A8 --- Sp1WDS Spectral class of a primary star according to WDS 68- 73 A6 --- Sp2WDS Spectral class of a secondary star according to WDS 74- 80 A7 --- Sp1Gaia Spectral class of a primary star according to Teff Gaia DR2 (1) 82- 87 A6 --- Sp2Gaia Spectral class of a secondary star according to Teff Gaia DR2 (1) 89- 92 I4 year t1WDS Beginning of observations in WDS version 2016 94- 97 I4 year t2WDS Ending of observations in WDS version 2016 101-103 I3 --- NWDS Number of WDS observations 107-110 I4 year t1Pul Beginning of Pulkovo 26-inch refractor observations 113-116 I4 year t2Pul Ending of Pulkovo 26-inch refractor observations 119-121 I3 --- Nphoto Number of photographic observations 124-126 I3 --- NCCD Number of CCD observations 130 A1 --- Flag1 Number of orbit solutions (2) 134-141 A8 --- CVWGMO Feature of the star (3) 142-146 A5 --- ref References (4) -------------------------------------------------------------------------------- Note (1): Spectral class we estimated according to Teff in Gaia DR2 if the star is dwarf (see Agekian, 1981), else it is given in brackets (2): If there is family of orbits Flag1=F (3): : Signs corresponding to the features of the star are as follows: C - There is curvature from basis observations. In brackets, if it is seen according to all observations only. V - There is a radial velocity from observations, else it is given in brackets. W - Wide star, a>100A.U. G - Orbit is determined on the basis of Gaia DR2 observations. M - There is inner subsystems. In brackets, if it is our assumption. O - AMP orbit is corrected by the program ORBITX (Tokovinin, 1992). (4): If the orbit is published for the first time ref=[0], else ref=code: [1] = (Kiyaeva et al., 2017) [2] = (Kiyaeva et al., 2020) [3] = (Kiyaeva et al., 2001) [4] = (Romanenko, Izmailov, 2021) [5] = (Kiyaeva, Izmailov, 2018) [6] = (Shakht et al., 2007) [7] = (Kiyaeva, Romanenko, 2020) [8] = (Shakht et al., 2020) [9] = (Romanenko, Kiselev, 2014) [10] = (Romanenko, 2018) [11] = (Grosheva, 2006b) [12] = (Kiselev et al., 2000) [13] = (Kiselev et al., 2009) [14] = (Romanenko, 2017) [15] = (Kiyaeva, Gorynya, 2015) [16] = (Shakht et al., 2017) [17] = (Grosheva, 2006a) [18] = (Kiyaeva et al., 2021). ----------------------------------------------------------------------------- Byte-by-byte Description of file: TABL2.txt ----------------------------------------------------------------------------- Bytes Format Units Label Explanations ----------------------------------------------------------------------------- 1- 10 A10 --- WDS WDS catalog number (J2000.0) 11 A1 --- * Flag1 (1) 13- 16 A4 --- Cmp Components of the pair 19- 23 A5 --- Bas Identification of the basis observations (2) 26- 29 I4 year Tb_1 Beginning of Basis observations 30 A1 --- - Dividing sign 31- 34 I4 year Tb_2 Ending of Basis observations 36- 38 I3 --- Nb Number of Basis observations 39- 40 A2 --- ** Flag2 (3) 43- 48 F6.1 year T_0 Instant 51- 59 F9.5 arcsec Rho Separation between components 62- 67 F6.5 arcsec e_Rho Error in Rho 72- 80 F9.5 degree Theta Positional Angle (equinox: 2000.0) 83- 88 F6.5 degree e_Theta Error in Theta 91- 96 F6.2 mas/yr mu Relative motion in the sky plane 99-102 F4.2 mas/yr e_mu Error in mu 105-110 F6.2 degree Psi Positional Angle of a direction of relative motion 113-117 F5.2 degree e_Psi Error in Psi 121-125 F5.2 arcsec Rc Radius of curvature 128-131 F4.2 arcsec e_Rc Error in Rc 134 A1 --- ( left bracket (4) 135-139 F5.2 km/c dVr Relative radial velocity 140 A1 --- ) right bracket 143 A1 --- ( left bracket 144-147 F4.2 km/c e_dVr Error in dVr 148 A1 --- ) right bracket 151-156 F6.2 mas pt Parallax 160-163 F4.2 mas e_pt Error in pt 168-171 F4.2 M_Sun M Sum of component masses in mass of the Sun 174-178 F5.1 mas S_r Dispersion in radial direction 181-185 F5.1 mas S_t Dispersion in tangential direction -------------------------------------------------------------------------------- Note (1): * - Different initial data are used. For ADS 48 - different basis, for ADS 15600 - different masses. (2): Bas=WDS - WDS observations PUL - Pulkovo 26-inch photographic observations CCD - Pulkovo 26-inch CCD observations G-DR2 - Gaia DR2 observations PCCD - Pul+CCD WPUL - WDS+PUL SPUL - The first Struve observations+PUL SCCD - The first Struve observations+CCD Keck - Published uniform Keck1 observations for the star WDS 04220+1932 (T Tauri NS) *** - Ephemeries of the AMP orbit corrected with ORBITX for two stars: WDS02433+0314 and WDS 06555+3010 (3): ** - set of observations was smoothed previously (4): If there are no radial velocity observations, the adopted values are presented in brackets. Byte-by-byte Description of file: TABL3.txt -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 3 I3 --- I Number one after another 5 I1 --- k The orbital solution number 7- 16 A10 --- WDS WDS catalog number (J2000.0) 18- 21 A4 --- Cmp Components of the pair 24- 27 F4.0 deg beta Angle BETA 32- 37 F6.0 year P Orbital period 42- 47 F6.0 year +er_P Period uncertainty positive (pos) 48 A1 --- * Flag (1) 51- 56 F6.0 year -er_P Period uncertainty negative (neg) 60- 66 F7.3 arcsec a Semi-major axis of orbit 71- 76 F6.3 arcsec +er_a Semi-major axis uncertainty (pos) 79- 84 F6.3 arcsec -er_a Semi-major axis uncertainty (neg) 87- 91 F5.1 deg i Inclination of the orbit 94- 97 F4.1 deg +er_i Inclination uncertainty (pos) 100-103 F4.1 deg -er_i Inclination uncertainty (neg) 106-110 F5.1 deg Node Longitude of ascending node 102-116 F5.1 deg +er_Node Longitude of ascending node uncertainty (pos) 118-122 F5.1 deg -er_Node Longitude of ascending node uncertainty (neg) 125-129 F5.0 year Tp Time of periastron passage 132-136 F5.0 year +er_Tp Time of periastron passage uncertainty (pos) 138-142 F5.0 year -er_Tp Time of periastron passage uncertainty (neg) 146-149 F4.3 --- e Eccentricity 151-154 F4.3 --- +er_e Eccentricity uncertainty (pos) 156-159 F4.3 --- -er_e Eccentricity uncertainty (neg) 162-166 F5.1 deg w Longitude of periastron 168-172 F5.1 deg +er_ w Longitude of periastron uncertainty (pos) 174-178 F5.1 deg -er_w Longitude of periastron uncertainty (neg) 181-184 F4.0 deg lQ Galactic longitude of Pole 187-189 F3.0 deg +er_lQ Galactic longitude of Pole uncertainty (pos) 192-194 F3.0 deg -er_lQ Galactic longitude of Pole uncertainty (neg) 197-200 F4.0 deg bQ Galactic latitude of Pole 203-205 F3.0 deg +er_bQ Galactic latitude of Pole uncertainty (pos) 208-210 F3.0 deg -er_bQ Galactic latitude of Pole uncertainty (neg) 213-216 F4.0 deg lP Galactic longitude of Periastron 219-221 F3.0 deg +er_lP Gal. longitude of Periastron uncertainty (pos) 224-226 F3.0 deg -er_lP Gal. longitude of Periastron uncertainty (neg) 229-232 F4.0 deg bP Galactic latitude of Periastron 235-237 F3.0 deg +er_bP Gal. latitude of Periastron uncertainty (pos) 240-242 F3.0 deg -er_bP Gal. latitude of Periastron uncertainty (neg) 246-253 F8.3 year T_1 Instant of the first observation 255-262 F8.3 year T_2 Instant of the last observation 265-267 I3 --- N Number of all observations 270-275 F6.2 mas S_r RMS in radial direction 278-283 F6.2 mas S_t RMS in tangential direction 286-291 F6.2 mas S_xy RMS in the sky plane 293-299 F7.2 mas (O-C)rG (O-C) in radial direction for Gaia DR2 obs. 301-307 F7.2 mas (O-C)tG (O-C) in tangential direction for Gaia DR2 obs. 309-315 F7.2 mas (O-C)xyG (O-C) in the sky plane for Gaia DR2 obs. -------------------------------------------------------------------------------- Note (1): * - for the star WDS 01055+1523 we have great errors of orbital elements due to great errors of radial velocity observations in Gaia DR2. Byte-by-byte Description of file: TABL4.txt -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 2 I2 --- I Number one after another 4 I1 --- k The orbital solution number 6- 15 A10 --- WDS WDS catalog number (J2000.0) 16- 19 A4 --- Cmp Components of the pair 21- 24 F4.0 deg beta Angle BETA 26- 31 F6.2 arcsec a Semi-major axis of orbit in arcsec 33- 39 F7.1 AU a1 Semi-major axis of orbit in AU 41- 48 F8.0 year P Orbital period 50- 52 F3.2 --- e Eccentricity 54- 58 F5.1 deg w Longitude of periastron 60- 64 F5.1 deg i Inclination 66- 70 F5.1 deg Node Longitude of ascending node 72- 78 F7.0 year Tp Time of periastron passage 80- 83 F4.0 deg lQ Galactic longitude of Pole 85- 88 F4.0 deg bQ Galactic latitude of Pole 90- 93 F4.0 deg lP Galactic longitude of Periastron 95- 98 F4.0 deg bP Galactic latitude of Periastron 100-107 F8.3 year T_1 Instant of the first observation 109-116 F8.3 year T_2 Instant of the last observation 119-121 I3 --- N Number of all observations 123-128 F6.2 mas S_r RMS in radial direction 130-135 F6.2 mas S_t RMS in tangential direction 138-143 F6.2 mas S_xy RMS in the sky plane 145-151 F7.2 mas (O-C)rG (O-C) in radial direction for Gaia DR2 obs. 153-159 F7.2 mas (O-C)tG (O-C) in tangential direction for Gaia DR2 obs. 162-167 F6.2 mas (O-C)xyG (O-C) in the sky plane for Gaia DR2 obs. ------------ --------------------------------------------------------------------