Free Access
Volume 520, September-October 2010
Article Number A89
Number of page(s) 12
Section Stellar structure and evolution
Published online 08 October 2010

Online Material

Appendix A: Overview of available RV observations

Table A.1:   Journal of available RV observations.

We reduced and measured two sets of electronic spectra secured at the coudé focus of the 2-m reflector of the Ondrejov Observatory which cover the red spectral region containing the H$\alpha$ and He I 6678 Å lines. These spectra have a linear dispersion of 17.2 Å mm-1and a 2-pixel resolution of 12 700 (11-12 km s-1 per pixel).

In the period 1993-2000, 20 spectra were obtained with a Reticon 1872RF linear detector. They cover the wavelengths from 6305 to 6740 Å and have the S/N between 110 and 900.
A series of 204 spectrograms obtained with a SITe-005 $800\times2000$ CCD detector secured between 2003 and 2010. They cover a slighly longer wavelength region 6255-6765 Å and have S/N between 200 and 880.
There are also four echelle spectra publicly available in the ELODIE archive (Moultaka et al. 2004), which cover the interval from 4000 to 6700 Å. We consulted these spectra but have not used them for RV measurements because of their insufficient number and phase distribution.

The initial reductions of spectra were performed using the IRAF (Ondrejov CCD spectra and SPEFO (Ondrejov Reticon spectra) programs. All subsequent reductions and the RV measurements were carried out using the SPEFO reduction program written by the late Dr. J. Horn and then further developed by Dr. P. Skoda and by (now also late) Mr. J. Krpata (Horn et al. 1996; Skoda 1996). Note that SPEFO displays direct and reverse traces of the line profiles superimposed on the computer screen, and the user can slide them to achieve their exact ovelapping for the studied detail of the profile.

A.1. Radial-velocity data files

We carried out a critical compilation of all available RV measurements from the literature with the known dates of observations. In all cases where the original sources give the dates and times of mid-exposures, we used the program HEC19 to derive heliocentric Julian dates[*]. The journal of all RVs used in this study is in Table A.1.

When the number of measured lines N used to derive the mean RV was given in the original study, we applied internal weighting of individual RVs, assigning weights w = 0.1*N. The only exception are Vienna RVs based on the mean of 11-38 individual lines. Here we used a linear transformation from the interval (11, 38) to (0.5, 1.5).

Comments on some individual files follow:

  • Spg. 1: Potsdam Four very first RVs of ${\sf\delta }$ Orionis were obtained by Vogel & Scheiner (1892) in 1888-1891 and showed no evidence of RV changes. They are based on RV of H$\gamma$ alone. When Deslandres (1900a) discovered the RV variations, Prof. Vogel remeasured the old spectra at the request of Dr. Hartmann. He found out that the last two spectra do show significant RV changes. His revised RVs are published in Hartmann's (1904) paper and should be preferred over the original measurements so are used by us.
  • Spg. 2: Meudon Deslandres (1900a,b) published his discovery RVs giving only the days of observations. Hartmann (1904) republished his RVs with estimated fractions of the days of observations, but later Deslandres (1904) published the actual mid-exposure times of his observations and these are used by us.
  • Spg. 3: Lick Three RVs from 1900 Lick spectra taken with the Mills pectrograph were obtained and measured by Dr. Wright and published by Campbell (1901), again without accurate mid-exposure times. Hartmann (1904) also estimated the times of mid-exposures for these spectra but we use the actual mid-exposure times published by Campbell & Moore (1928), adopting also mean RV from two independent measurements of these spectra for this last publication.
  • Spg. 6: Vienna Hnatek (1921) tabulated mid-exposure times in Central European Mean Time (G.M.T.+1 h) and used this time also for the fractions of his Julian days. We derived and used correct HJDs.
  • Spg. 11: IUE Harvey et al. (1987) analysed the first 44 SWP spectra obtained by the IUE. Their RV measurements were relative and the RVs published in their Table 1 have the zero point artificially shifted in such a way as to give the systemic velocity of 20.4 km s-1, adopted from the study by Curtiss (1915). Harvin et al. (2002) later analysed the complete set of 60 IUE SWP spectra from the final IUE reduction. The derived RVs via cross-correlation, using the spectra of O 9.5V star AB Aur (HD 34078) as a template. Here we adopted their RVs.
  • Spg. 14&15: Kitt Peak and Mt. Stromlo These RVs are solely based on the He I 6678 Å line and were also derived via cross-correlation by Harvin et al. (2002).
  • Spg. 13&16: Ondrejov These RVs are also solely based on the He I 6678 Å line measured in SPEFO via comparison of direct and flipped line profile on the computer screen.

Appendix B: Photometry

After the discovery that ${\sf\delta }$ Orionis is an eclipsing variable by Stebbins (1911, 1915), the binary was measured by several authors: Storer (1930), Skoberla (1935; only times of minima), Worley (1955, who also published measurements by Storer), and Koch & Hrivnak (1981). Then there is the photometry by Hipparcos.

Table B.1:   Photometric data sets used.

Table B.2:   Comparison and check stars used by various photometric observers.

We obtained new $U\!B{}V$ observations using the automated photoelectric photometer attached to the 0.65-m reflector of the Hvar Observatory. The data were transformed to the standard $U\!B{}V$ system via non-linear transformation (see Harmanec et al. 1994, for details).

The reductions were carried out with the latest version 16.1 of the HEC22 program (Harmanec & Horn 1998), which permits extinction variations to be modelled in the course of the night. To be able to also transform the old Stebbins (1915) photometry to the V magnitude, we also observed his comparison star $\varepsilon $ Ori regularly during the first season.

The new observations were combined with several existing photometric data sets that we critically compiled from the literature. Basic information about all data sets used is summarized in Table B.1. Table B.2 summarizes the $U\!B{}V$ magnitudes of all comparison stars used by different observers. Hvar mean all-sky magnitudes were added to all magnitude differences ${\sf\delta }$ Orionis - comparison whenever these differences were known.

A few comments on individual data sets follow:

  • Stebbins (1915): magnitude differences ${\sf\delta }$ Orionis - $\epsilon$ Ori, secured with the Lick 12-inch refractor, were transformed toJohnson V following Holmgren et al. (1999) and Harmanec & Bozic (2001). The mean Hvar all-sky V magnitude of $\epsilon$ Ori, 1 $^{\rm m}\!\!.$695 $\pm$ 0 $^{\rm m}\!\!.$019 was then added to the transformed magnitude differences to get Stebbins' observations on the standard Johnson V magnitude. Note, however, that $\epsilon$ Ori is a known variable star (see Fig. B.1), so these early data must be treated with some caution.
  • Storer (1930) and Worley (1955): Both these authors published their observations only in a graphical form. Their observations were also secured with the Lick 12-inch refractor, but no details about the photometer used by Storer are known. Worley used an EMI 5659 photomultiplier and Corning filters 3385 and 5543, which very closely match the B and V magnitudes of the Johnson system. He obtained about 300 yellow and 250 blue observations and formed 112 running means of them. Storer observed in the years 1926-1928 relative to $\eta$ Ori (V = 3 $^{\rm m}\!\!.$36) and only showed plots of magnitude differences from several observed eclipses. They range from about 0 $^{\rm m}\!\!.$1 to 0 $^{\rm m}\!\!.$2; apparently the integral parts of the ordinate scale of his plot should be -1 instead zero. Worley (1955) obtained Storer's individual observations but he published them along with his own observations only in the form of a phase diagram, forming the normal points from the original Storer's observations. We therefore reconstructed these two sets of observations from his plot and assigned them ``artificial'' Julian dates corresponding to the mean times of observations of the respective data sets applying the ephemeris that Worley probably used: HJD 2419068.20 + 5 $.\!\!^{\rm d}$732476 $\times\ E$[*]. This ephemeris is still close to the present ephemeris for the primary minimum. For the data by Storer (1930) and Worley (1955), the magnitude zero point is unknown, because Worley regrettably did not mention which comparison star he used. Since the colours of the comparison stars that were probably used are quite similar to those of $\delta$ Ori, we treat these data as yellow magnitudes in the photometric solutions.
  • Johnson et al. (1966): we derived heliocentric Julian dates for these standard all-sky $U\!B{}V$ observations.
\end{figure} Figure B.1:

    A time plot of the Hvar V observations of $\varepsilon $ Ori, the star used as the comparison by Stebbins. Mild light variations are clearly seen.

  • Koch & Hrivnak (1981): these authors obtained about 350 individual observations using a photoelectric photometer with an RCA 4509 tube attached to the 0.38-m refractor of the Flower and Cook Observatory and green and blue filters; however, they only published magnitude differences for 64 green and 62 blue normal points. We converted their JDs to HJDs again. The primary comparison they used,HD 36840 = HIP 26149, is a seldom studied G5 star ($V~\sim$ = 6 $^{\rm m}\!\!.$25), and we found no way how to transform their observations to the Johnson V and B magnitudes. We therefore simply added estimated green and blue magnitudes of HD 36840, 6 $^{\rm m}\!\!.$53, and 7 $^{\rm m}\!\!.$15 to the published magnitude differences.
  • Perryman & ESA (1997) These Hipparcos $H_{\rm p} $ observations were transformed to the standard V magnitude following Harmanec (1998) and assuming the mean all-sky Hvar colour indices for $\delta$ Ori: $B\!-\!V$= -0 $^{\rm m}\!\!.$219, and $U\!-\!B$ = -1 $^{\rm m}\!\!.$040 .

As a quality check, it is also useful to add a few comments on possible light variations on other time scales. All photometric observers of ${\sf\delta }$ Orionis have concluded that the object is exhibiting cycle-to-cycle and, possibly also, hour-to-hour changes. The inspection of Fig. 1 indeed reveals a rather large scatter in virtually all visual light curves, although most of them are based on averaged data. A word of caution is appropriate, however, because Stebbins' and Storer's (if not also Worley's) observations were obtained using mildly variable comparison stars. As Hvar observations show, the scatter outside minima is comparable to what is observed for the check star and can to some extent be attributed to the fact that the star could only be observed at relatively high air masses.

What can be suspected, however, is the different height of the maxima between the two eclipses, which might also vary secularly. Only more systematic observations from a good site can decide whether it is indeed so.

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