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Context: The Rossiter-McLaughlin (RM) effect, a rotational effect ineclipsing systems, provides unique insight into the relative orientation ofstellar spin axes and orbital axes of eclipsing binary systems.  Aims: Our aim is to develop a robust method to analyze the RM effect in aneclipsing system with two nearly equally bright components. This gives accessto the orientation of the stellar rotation axes and may shed light on questionsof binary formation and evolution.  Methods: High-resolution spectra have been obtained both out of eclipse andduring the primary and secondary eclipses in the V1143Cyg system, using thehigh-resolution Hamilton Echelle Spectrograph at the Lick Observatory. TheRossiter-McLaughlin effect is analyzed in two ways: (1) by measuring the shiftof the line center of gravity during different phases of the eclipses and (2)by analysis of the line shape change of the rotational broadening functionduring eclipses.  Results: The projected axes of both stars are aligned with the orbital spinwithin the observational uncertainties, with the angle of the primary rotationaxis beta_p=0.3+-1.5 deg, and the angle of the secondary rotation axisbeta_s=-1.2+-1.6 deg, thereby showing that the remaining difference between thetheoretical and observed apsidal motion for this system is not due to amisalignment of the stellar rotation axes. Both methods utilized in this paperwork very well, even at times when the broadening profiles of the two starsoverlap.[abridged]

The spin axes orbital alignment of both stars within the eclipsing binary system V1143Cyg using the Rossiter-McLaughlin effect