Astron. Astrophys. 360, 399-410 (2000)

Polaris: astrometric orbit, position, and proper motion

R. Wielen, H. Jahreiß, C. Dettbarn, H. Lenhardt and H. Schwan

Astronomisches Rechen-Institut, Moenchhofstrasse 12-14, 69120 Heidelberg, Germany

Received 14 February 2000 / Accepted 22 April 2000

Abstract

We derive the astrometric orbit of the photo-center of the close pair UMi AP (= UMi Aa) of the Polaris multiple stellar system. The orbit is based on the spectroscopic orbit of the Cepheid UMi A (orbital period of AP: 29.59 years), and on the difference between the quasi-instantaneously measured HIPPARCOS proper motion of Polaris and the long-term-averaged proper motion given by the FK5. There remains an ambiguity in the inclination i of the orbit, since cannot distinguish between a prograde orbit and a retrograde one . Available photographic observations of Polaris favour strongly the retrograde orbit. For the semi-major axis of the photo-center of AP we find about 29 milliarcsec (mas). For the component P, we estimate a mass of 1.5 and a magnitude difference with respect to the Cepheid of 6.5 mag. The present separation between A and P should be about 160 mas.

We obtain the proper motion of the center-of-mass of UMi AP with a mean error of about 0.45 mas/year. Using the derived astrometric orbit, we find the position of the center-of-mass at the epoch 1991.31 with an accuracy of about 3.0 mas. Our ephemerides for the orbital correction, required for going from the position of the center-of-mass to the instantaneous position of the photo-center of AP at an arbitrary epoch, have a typical uncertainty of 5 mas. For epochs which differ from the HIPPARCOS epoch by more than a few years, a prediction for the actual position of Polaris based on our results should be significantly more accurate than using the HIPPARCOS data in a linear prediction, since the HIPPARCOS proper motion contains the instantaneous orbital motion of about 4.9 mas/year = 3.1 km/s. Finally we derive the galactic space motion of Polaris.

Key words: astrometry stars: binaries: general stars: variables: Cepheids

Send offprint requests to: R. Wielen (wielen@ari.uni-heidelberg.de)

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Contents

• 1. Introduction
• 2. Overview of the Polaris system
  • 2.1. The Cepheid UMi A
  • 2.2. The spectroscopic-astrometric binary UMi AP
  • 2.3. The visual binary UMi (AP) - B
  • 2.4. UMi C and UMi D
• 3. Astrometric orbit of UMi AP
  • 3.1. The determination of
    • 3.1.1. The proper motion of the center-of-mass of AP
    • 3.1.2. The HIPPARCOS proper motion
    • 3.1.3. The observed value of
    • 3.1.4. The photo-center of UMi AP
    • 3.1.5. The predicted value of
    • 3.1.6. The problem of and of
  • 3.2. The astrometric orbit
    • 3.2.1. Determination of the inclinationi
    • 3.2.2. Determination of the nodal length
    • 3.2.3. The ambiguity problem ofi
    • 3.2.4. Resulting orbits of UMi AP
    • 3.2.5. Derived physical properties of UMi P
• 4. Proper motion and position of Polaris
  • 4.1. Center-of-mass of UMi AP
  • 4.2. Orbital corrections for the photo-center of UMi AP
  • 4.3. Comparison of positions
  • 4.4. Space velocity of Polaris
• References

© European Southern Observatory (ESO) 2000

Online publication: July 27, 2000
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