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6. Application to real data


Preliminary results obtained with the technique in its standard version were already presented elsewhere (Carbillet et al. 1996b). We give here a more accurate application of the technique in its two versions to three binary stars for which the observing conditions are reported in Table2. All the data reduced in this section consist of high-light level speckle frames of tex2html_wrap_inline2395 pixels. We give in what follows a detailed description of the analysis for each object.

Figure 6: Top: linear gray-level representation of tex2html_wrap_inline2347 a) and tex2html_wrap_inline2357 c), together with plots of the corresponding radial integrations-- b) and d) --for the binary tex2html_wrap_inline1895Del. Middle: Q a) and tex2html_wrap_inline2201 c), and the corresponding radial integrations-- b) and d) --for the binary Moaï 1. Bottom: the same as in Top for the binary tex2html_wrap_inline1899Per


star name r.a. 2000.0 dec. 2000.0 mR Telescope tex2html_wrap_inline2689 <r0> tex2html_wrap_inline2693 Date
tex2html_wrap_inline1895Del tex2html_wrap_inline2697 tex2html_wrap_inline2699 3.2 2m BLT 6580/425 tex2html_wrap_inline2701 cm 20 ms 11/09/94
Moaï 1 tex2html_wrap_inline2703 tex2html_wrap_inline2705 6 2m BLT 6500/700 tex2html_wrap_inline2191 cm 20 ms 12/12/95
tex2html_wrap_inline1899Per tex2html_wrap_inline2711 tex2html_wrap_inline2713 2.3 4.2m WHT 6580/425 tex2html_wrap_inline2701 cm 25 ms 19/01/95
Table 2: Observation table of the three sets of data processed in Sect. 6. The right ascension, the declination and the combined magnitude in the red ( mR ) are given, together with the telescope used (WHT = WilliamHershellTelescope, LaPalma, Spain-- BLT = BernardLyotTelescope, PicduMidideBigorre, France), the observing wavelength /bandwidth in Å, the approximate average value of the Fried's parameter r0 , the exposure time and the date of observation

6.1. tex2html_wrap_inline1895Del

The subgiant tex2html_wrap_inline1895Del is a close binary of 26.6 years of period given as a standard star for binary-star interferometry by McAlister & Hartkopf (1983). The latest orbit is computed by Hartkopf et al. (1989). The reference star observed was tex2html_wrap_inline2723Del from which we used 410 frames, and 324 for the binary.

The separation angle d and the PA from which we derived an estimation of tex2html_wrap_inline1927 were computed from the classical calculation of the visibility function, founding: tex2html_wrap_inline2729 and tex2html_wrap_inline2731.

Figure 6 (click here), first row, shows both the quantities tex2html_wrap_inline2347 and tex2html_wrap_inline2357, with their radial integrations tex2html_wrap_inline2319 and tex2html_wrap_inline2577, derived from the twofold PDFs of the binary and of the reference star computed for the space-lag vector tex2html_wrap_inline2029, and from the twofold PDF of the binary computed for tex2html_wrap_inline2217. From these quantities, we could deduce the value of tex2html_wrap_inline2157 for which they are extrema by the procedure described in Sect. 5 (click here). So we have: tex2html_wrap_inline2747 using the standard version; or: tex2html_wrap_inline2749 using the reference-less version. The exact value of the intensity ratio, giving then both the orientation and a relative photometry of the binary system, is found to be tex2html_wrap_inline2751 (or tex2html_wrap_inline2753), that corresponds to a magnitude difference tex2html_wrap_inline2755 (or tex2html_wrap_inline2757). This is in agreement with the value given by Couteau (1962)-- i.e. 0.9 --if one considers that tex2html_wrap_inline2759 is roughly similar to tex2html_wrap_inline2761 for this object. Moreover, since we found an intensity ratio smaller than 1, we can assume, given the orientation of the frames and tex2html_wrap_inline1981, that PA is 288tex2html_wrap2657 and not 108tex2html_wrap2657. This is anyway what was expected from the orbit cited before.

It is interesting to note that the two versions of the method give, for these data, an equivalent result, even if the relevant ridge seems to be better defined using the reference star data.

6.2. Moaï 1

The close double star Moaï 1 (SAO12917) was discovered during the observation from which the data used in this section are extracted. The approximate period evaluated by Carbillet et al. (1996c) is tex2html_wrap_inline2781 years. The separation vector tex2html_wrap_inline1927 was deduced from this last paper using the cross-correlation technique (Aristidi et al. 1996). This corresponds to: tex2html_wrap_inline2785 and tex2html_wrap_inline2787. The reference star observed was SAO12929 from which we used 2617 frames, and 2619 for the binary.

Figure 6 (click here), second row, shows both the quantities Q and tex2html_wrap_inline2201, with their radial integrations IQ and tex2html_wrap_inline2511. The value of tex2html_wrap_inline2157 derived from these quantities is: tex2html_wrap_inline2799-- or tex2html_wrap_inline2801. The deduced value of tex2html_wrap_inline1947 is then: tex2html_wrap_inline2805 (or tex2html_wrap_inline2807), that corresponds to a magnitude difference: tex2html_wrap_inline2809 (or tex2html_wrap_inline2811). This is in agreement with the value computed in the paper cited before and using both the cross-correlation technique and the fork algorithm (Bagnuolo 1988)-- tex2html_wrap_inline2813 and tex2html_wrap_inline2815. The position angle is then confirmed to be: tex2html_wrap_inline2787 and the magnitude difference between the companion and the primary star in the red: tex2html_wrap_inline2819.

We can say that, here again, the method seems to take advantage of its use with the data of the reference star, the reference-less method giving anyway an acceptable value of the intensity ratio.

6.3. tex2html_wrap_inline1899Per

tex2html_wrap_inline1899Per is a giant eclipsing binary star of 17.8 years period whose orbit can be found in Hartkopf et al. (1996). The reference star observed was tex2html_wrap_inline1947Per from which we used 752 frames, and 443 for the binary. The separation and position angle computed from the visibility function were: tex2html_wrap_inline2835 and tex2html_wrap_inline2837.

Figure 6 (click here), third row, shows both the quantities tex2html_wrap_inline2347 and tex2html_wrap_inline2357, with their radial integrations tex2html_wrap_inline2319 and tex2html_wrap_inline2577. The value of tex2html_wrap_inline2157 derived from these quantities is: tex2html_wrap_inline2849-- or tex2html_wrap_inline2851. The deduced value of the intensity ratio is then: tex2html_wrap_inline2853 (or tex2html_wrap_inline2855), that corresponds to a magnitude difference: tex2html_wrap_inline2857 (or tex2html_wrap_inline2859). This first shows that the right position angle is 62tex2html_wrap2657 and not 242tex2html_wrap2657. Moreover, the absolute value of tex2html_wrap_inline2865 found is in agreement with the early speckle interferometric measurement of Labeyrie et al. (1974) that estimated a tex2html_wrap_inline2865 of 1-2 mag for a wavelength of tex2html_wrap_inline2871Å. More precisely, McAlister et al. (1982) estimated tex2html_wrap_inline2865 in the red to be at least greater than 1.4 mag, the estimated tex2html_wrap_inline2759.

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