Figure 1 VINCI observations of the pulsation of L Car, of period 35.5 days. The points are the interferometric measurements, and the curve is the fit derived from the time integration of radial velocity along the cycle.

Thanks to the very high spatial resolution of the VLTI interferometer, (The Very Large Telescope Interferometer — VLT), a team of french astronomers has measured directly the change of apparent size of four southern bright Cepheids, during their pulsation cycle. For that, they used the recombination instrument VINCI, designed and buit by Paris Observatory (LESIA), under contract with the European Southern Observatory (ESO). The difficutly of these observations is the very small apparent size of these stars, comparable to that of a 1 euro coin at a distance of 2000 km. The angular size measurement of the brightest Cepheid in the sky, L Carinae (Fig. 1) shows clearly its variation along its period of 35.5 days. The mean size of three other stars was also measured.

Figure 2 The two observations which must be combined to obtain the distance are: left the measurement of velocity by spectroscopy, along a pulsation cycle, and right, the measurement by interferometry of the variation of angular size of the star, along the same cycle. After time integration, the velocity measurement gives the variation in linear size (in metres). The ratio between linear and angular sizes gives the distance of the Cepheid. Click on the image to enlarge it By combining the interferometric observations with spectroscopic measurements of the radial velocity of the surface of these stars (shift of the spectral lines by Doppler effect), it is possible to obtain their distance in a quasi-geometrical way, and thus calibrate the P-L relation. Indeed, measurements of angular diameter give the amplitude of the angular size variation of the star in the sky plane, whereas the velocity measurements integrated over the period of pulsation give the amplitude of its linear size variation. The ratio of these two amplitudes (linear/angular) gives the distance of the star (fig. 2). The new calibration of the P-L relation obtained thanks to VLTI interferometric measurements does not show significant bias compared to previous estimates obtained by other methods (fig. 3). This result will be refined in the years to come thanks to the new interferometric instrument AMBER.

Figure 3 Period-Luminosity relation in the V band, derived from interferometric observations of Cepheids, and the HST parallax measurement of Delta Cep. The green line is the fitted P-L relation, assuming the slope from Gieren et al (1998, ApJ 496, 17). The agreement is excellent, in particular with the very precise measurements of L Car and Delta Cep.

### References

- Kervella P., Nardetto, N., Bersier, D., Mourard, D., CoudÃ© du Foresto, V., "Cepheid distances from infrared long-baseline interferometry. I. VINCI/VLTI observations of seven Galactic Cepheids", Astronomy & Astrophysics 416, 941 Kervella P., Bersier, D., Mourard, D., Nardetto, N., CoudÃ© du Foresto, V. "Cepheid distances from infrared long-baseline interferometry. II. Calibration of the period-radius and period-luminosity relations", 2004, Astronomy & Astrophysics 423, 327 Kervella P., Bersier D., Mourard D., Nardetto N., FouquÃ© P., CoudÃ© du Foresto V. "Cepheid distances from infrared long-baseline interferometry - III. Calibration of the surface brightness-color relations", 2004, Astronomy & Astrophysics, in press Kervella P., FouquÃ© P., Storm J., Gieren W. P., Bersier D., Mourard D., Nardetto N., CoudÃ© du Foresto V. "The angular size of the Cepheid L Car: a comparison of the interferometric and surface brightness techniques", 2004, Astrophysical Journal 604, L113

Last update on 3 November 2016