Direct detection of pulsations of the Cepheid star ζ Gem and an independent calibration of the period–luminosity relation


Cepheids are a class of variable (pulsating) stars whose absolute luminosities are related in a simple manner to their pulsational periods. By measuring the period and using the ‘period–luminosity’ relationship, astronomers can use the observed visual brightness to determine the distance to the star. Because these stars are very luminous, they can be observed in other galaxies, and therefore can be used to help determine the expansion rate of the Universe1 (the Hubble constant). Calibration of the period–luminosity relation is a necessary first step, but the small number of sufficiently nearby Cepheids has forced the use of a number of indirect means, with associated systematic uncertainties. Here we present a distance to the Cepheid ζ Geminorum, determined using a direct measurement (by an optical interferometer) of its changes in diameter as it pulsates. Within our uncertainty of 15 per cent, our distance is in agreement with previous indirect determinations. Planned improvements to the instrument will allow us to calibrate directly the period–luminosity relation to better than a few per cent.

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Figure 1: The uniform-disk (UD) angular diameter of ζ Gem as measured by PTI.
Figure 2: The UD angular diameter of ζ Gem as a function of pulsational phase with a model based on radial velocity data.


  1. 1

    Mould, J. R. et al. The Hubble Space Telescope key project on the extragalactic distance scale. XXVIII. Combining the constraints on the Hubble constant. Astrophys. J. 529, 786– 794 (2000).

    ADS  Article  Google Scholar 

  2. 2

    Wesselink, A. J. Surface brightnesses in the U, B, V system with applications of M V and dimensions of stars. Mon. Not. R. Astron. Soc. 144, 297–311 ( 1969).

    ADS  Article  Google Scholar 

  3. 3

    Krockenberger, M., Sasselov, D. D. & Noyes, R. W. Radii and distances of Cepheids. I. Method and measurement errors. Astrophys. J. 479, 875– 885 (1997).

    ADS  Article  Google Scholar 

  4. 4

    Tanvir, N. R. in Post-Hipparcos Cosmic Candles 17–35 (Kluwer, Dordrecht, 1999).

    Google Scholar 

  5. 5

    Mourard, D. et al. The mean angular diameter of δ Cephei measured by optical long-baseline interferometry. Astron. Astrophys. 317 , 789–792 (1997).

    ADS  Google Scholar 

  6. 6

    Kervella, P. et al. in Working on the Fringe: Optical and IR Interferometry from Ground and Space 22–27 (ASP Conf. Ser. 194, Astronomical Society of the Pacific, San Francisco, 1999).

    Google Scholar 

  7. 7

    Nordgren, T. et al. Astrophysical quantities of Cepheid variables measured with the NPOI. (in the press).

  8. 8

    Szabados, L. Northern Cepheids: Period update and duplicity effects. Commun. Konkoly Observatory, Hungary 96, 123– 244 (1991).

    ADS  Google Scholar 

  9. 9

    Laney, C. D. & Stobie, R. S. The radii of galactic Cepheids. Mon. Not. R. Astron. Soc. 274, 337– 360 (1995).

    ADS  Article  Google Scholar 

  10. 10

    Perryman, M. A. C. et al. The HIPPARCOS Catalogue. Astron. Astrophys. 323, L49–L52 (1997).

    ADS  Google Scholar 

  11. 11

    Colavita, M. M. et al. The Palomar Testbed Interferometer. Astrophys. J. 510, 505–521 ( 1999).

    ADS  Article  Google Scholar 

  12. 12

    Colavita, M. M. Fringe visibility estimators for the Palomar Testbed Interferometer. Publ. Astron. Soc. Pacif. 111, 111– 117 (1999).

    ADS  Article  Google Scholar 

  13. 13

    Boden, A. F. et al. An interferometric search for bright companions to 51 Pegasi. Astrophys. J. 504, L39– L42 (1998).

    ADS  Article  Google Scholar 

  14. 14

    Bersier, D., Burki, G., Mayor, M. & Duquennoy, A. Fundamental parameters of Cepheids. II. Radial velocity data. Astron. Astrophys. 108, 25–39 ( 1994).

    ADS  Google Scholar 

  15. 15

    Hindsley, R. & Bell, R. A. An investigation of photoelectric radial-velocity spectrometers as used in the analysis of Cepheid variables. Publ. Astron. Soc. Pacif. 98, 881– 888 (1986).

    ADS  CAS  Article  Google Scholar 

  16. 16

    Ridgway, S. T. et al. Angular diameters by the lunar occultation technique. IV—Alpha Leo and the Cepheid Zeta Gem. Astron. J. 87, 680–684 (1982).

    ADS  Article  Google Scholar 

  17. 17

    Gieren, W. P., Barnes, T. G. & Moffett, T. J. The period-radius relation for classical Cepheids from the visual surface brightness technique. Astrophys. J. 342, 467–475 (1989).

    ADS  Article  Google Scholar 

  18. 18

    Gieren, W. P., Barnes, T. G. & Moffett, T. J. The Cepheid period-luminosity relation from independent distances of 100 galactic variables. Astrophys. J. 418, 135–146 (1993).

    ADS  Article  Google Scholar 

  19. 19

    McAlister, H. A. et al. Progress on the CHARA array. Proc. SPIE 3350, 947–950 (1998).

    ADS  Article  Google Scholar 

  20. 20

    Cohen, M. et al. Spectral irradiance calibration in the infrared. X. A self-consistent radiometric all-sky network of absolutely calibrated stellar spectra. Astron. J. 117, 1864–1889 (1999).

    ADS  Article  Google Scholar 

  21. 21

    Welch, D. L. Near-infrared variant of the Barnes-Evans method for finding Cepheid distances calibrated with high-precision angular diameters. Astron. J. 108, 1421–1426 (1999).

    ADS  Article  Google Scholar 

  22. 22

    Claret, A., Diaz-Cordoves, J. & Gimenez, A. Linear and non-linear limb-darkening coefficients for the photometric bands R I J H K. Astron. Astrophys. 114, 247–252 (1995).

    ADS  Google Scholar 

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We thank R. Akeson, T. Armstrong, A. Bouchez, M. Colavita, T. Nordgren, M. Nunez and D. Sasselov for valuable comments. Part of the work described in this paper was performed at the Jet Propulsion Laboratory under contract with the National Aeronautics and Space Administration. This research has made use of the Simbad database, operated at Centre de Données astronomiques de Strasbourg, Strasbourg, France. B.F.L. gratefully acknowledges the support of NASA through the Michelson fellowship programme. B.F.L. acknowledges the support of NASA and the NSF.

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Correspondence to S. R. Kulkarni.

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Lane, B., Kuchner, M., Boden, A. et al. Direct detection of pulsations of the Cepheid star ζ Gem and an independent calibration of the period–luminosity relation. Nature 407, 485–487 (2000).

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