The spectroscopic binary star beta Aurigae

Manfred Rudolf

Spectroscopy with the Dados slit spectrograph:
Determination of the radial velocity of the spectroscopic binary star beta Aurigae.

Just to recall: spectroscopic binary stars orbiting around their common center of gravity are usually too close to be resolved visually. These systems reveal their double nature by their spectrum.

In certain phases of their orbit, one of the components moves towards the observer (O) while the other one recedes (left image): In such case, the approaching component shows a shift of the wavelengths of its spectral lines towards blue, whereas in the receding component, a shift towards red can be observed (Doppler effect).

If the components move transversally only with respect to the observer (right image), there is no radial movement, and therefore no wavelength shift is observed.

Since the amount of wavelength shift is some ångstroms only, the Dados spectrograph has been equipped with a grating having 1200 lines per mm to achieve higher resolution. The spectrum of beta Aurigae was recorded with a ST10 CCD camera, in a 10 minutes' exposure through a C11 telescope.

A reference spectrum was recorded with the same equipment. The reference star was epsilon UMa which has the same spectral class (A0) as beta Aur.

In the image below, the upper spectrum is that of the reference star epsilon UMa, and the lower spectrum is from beta Aur, obtained on April 3, 2009, at 21h UT. Near the right end of the spectrum, one can see the dark H-alpha absorption line at 6563 Ångstrom which is a single line in the upper reference spectrum but split into two lines because of the Doppler shift in the spectrum of beta Aur (perhaps you need to scroll to the right in your browser's window).

Even farther to the right, starting at ca. 6867 Ångstrom, there is an intense absorption band of molecular oxygen originating from light absorption in the Earth's atmosphere. These lines obviously are not splitted and appear the same in both spectra because of their terrestrial origin.

The image below is the same as above, but contrast has been adjusted to make better visible the fainter absorption lines. The hydrogen alpha line and the telluric oxygen bands are then severely overexposed:
It can be seen that not only the H-alpha line is split into two, but also many further lines. Find for example in the above reference spectrum the lines of Si II at 6347 and 6371 Ångstrom and see their splitting in the lower spectrum. Similarly, the lines of iron Fe II at 6238, 6247, 6417, and 6456 Å are also split.

A number of lines between 5900-5980, 6276-6310 and 6470-6590 Å originate from atmospheric water vapour and oxygen, and again are seen in both spectra without splitting.

Now let us try to estimate the radial velocities of the components of beta Aur from its spectrum: The splitting between the "two" H-alpha lines in the spectrum of beta Aur is about 8 pixels and is rather symmetric relative to the reference line. Thus one line is shifted about 4 pixels towards blue with respect to the unshifted line, and the other one is shifted 4 pixels towards red. As one pixel in the above spectrum corresponds to a difference in wavelength of 0.58 Ångstrom, the shift of the H-alpha line is 4x0.58 = 2,32 Å.

The radial velocity can be calculated from the following formula
wherein delta-Lambda is the wavelength shift as determined above, Lambda the unshifted wavelength, v the radial velocity to be calculated, and c is the speed of light. Using in the above formula the values for the shift of 2.32 Å, 6563 Å for the wavelength of the H-alpha line, and 300.000 km/s for the speed of light, we obtain a value for the radial velocity of 106 km/s. This matches perfectly with the values found in the literature of 107.5 and 111.5 km/s (cf. A. H. Batten et al., Eighth Catalogue of the Orbital Elements of Spectroscopic Binary Systems).

Recently, the beta Aurigae system has also been resolved interferometrically. Its angular separation is about 3 milli-arcseconds.