4. Visibility measurements
Since our observations are limited by detector noise, we can still apply the reduction method developed for the FLUOR experiment (Coude du Foresto et al. 1997) to the L band data. Due to the effect of uncorrected atmospheric piston, object phase and spectral information are lost. The unbiased observable calculated by this method is the squared modulus of the coherence factor, derived from the energy measured in the power spectrum of the interferograms, in the frequency range of the fringes. The only difference with respect to the K band comes from the "shape factor" of the observed source in the L band (Coude du Foresto et al. 1997). The shape factor F is given by the square of the normalized source spectrum B(), integrated over the optical bandpass of the system, and is closely related to the effective wavelength of observation =1/, given by:
In practice F is mostly sensitive to the optical bandwidth, and to possible strong absorption features in the stellar atmosphere. It is otherwise roughly independent of the stellar effective temperature, and cancels out in the reduction process for objects and references of close temperatures or spectral types.
Using the transmission curve of our L band filter (m, m), and a low resolution spectrum (Strecker et al. 1979) of Arcturus, we find F=2.4 cm, which is the value used for the absolute determination of in Sect. 3.2.3., and an effective wavelength of 3.75 µm. We present here the results and statistical error bars provided by this reduction method, when applied to the interferometric data obtained on Arcturus and Her.
4.1. Using Arcturus as a calibrator
The value of the instrumental transfer function is derived from the data obtained on Arcturus, used as a calibrator. In the K band, FLUOR/IOTA observations (Perrin et al. 1998) show that the uniform disk and limb darkened diameter of Arcturus already match within 3%. In the L band the limb darkening effect is expected to be still smaller, because the blackbody emission of the 4300 K star is less affected by a given thermal gradient in the stellar photosphere. Furthermore, Arcturus is very partially resolved at the spatial frequency of operation, so that taking limb darkening effects into account, the theoretical visibility departs very little from the one computed using uniform disk approximation.
Table 2. Theoretical visibilities () and measured fringe contrasts on Arcturus. S (in cycles/arcsec) is the spatial frequency at the effective wavelength of observation. The adopted uniform disk diameter of Arcturus is 20.20 0.08 mas. First 3 batches are for the night of April 2 1998, the fourth one corresponds to April 3. Error bars correspond to the 1 level.
To compute the expected theoretical visibility at the spatial frequency of observation, we can then neglect the limb darkening effect in a first approximation, and we use the uniform disk diameter of 20.20 0.08 mas measured in the K band by the FLUOR instrument. Measured fringe contrasts on Arcturus are given in Table 3. First three batches correspond to the night of April 2, the fourth one was observed on the following night.
Table 3. Observed fringe contrasts , and corresponding visibility measurements on Her as a function of the spatial frequency S. For the 3 batches, the interferometric transfer function used is 0.516 +/- 0.008, from most recent observations of Arcturus.
4.2. Deriving an angular diameter of Her in the L band
Her was observed 3 times in one and a half hour during the night of April 2 1998. These 3 batches have been analyzed independently using the sky estimation described above, and the closest most recent available value of the transfer function deduced from the observations of Arcturus (=0.516 0.011).
Individual visibility measurements are given in Table 3. The relative dispersion of visibility measurements is about 10% rms. Since the estimation of the thermal background causes an rms error of 1% at the worst (Sect. 3.1.2), we conclude that most of the observed variations probably arise from the lack of injected flux monitor and not from unsampled background fluctuations.
These three independent measurements - assumed to be of equal quality - are used to provide a single visibility data at the mean spatial frequency of observation (minimizing a functional). Corresponding error bar is determined so that .
Fitting this data point with a uniform disk model, we derive a uniform disk diameter for Her of 32.8 0.7 mas in the L band (Fig. 7).
Uniform disk diameters found in the K band by the FLUOR experiment and by the infrared Michelson array IRMA (Benson et al. 1991) are respectively: 30.90 0.02 mas and 32.2 0.8 mas. Favoring the more accurate results found with FLUOR, our L band measurements would then indicate a 6% increase in the photosphere diameter with respect to K observations.
© European Southern Observatory (ESO) 1999
Online publication: May 6, 1999