Multi-order TODCOR: Application to observations taken with the CORALIE echelle spectrograph - I. The system HD 41004

This paper presents an application of the TwO- Dimensional CORrelation ( TODCOR) algorithm to multi- order spectra. The combination of many orders enables the detection and measurement of the radial velocities of very faint companions. The technique is first applied here to the case of HD41004, where the secondary is 3 : 68 mag fainter than the primary in the V band. When applied to CORALIE spectra of this system, the technique measures the secondary velocities with a precision of 0.6 km s(-1) and facilitates an orbital solution of the HD41004 B subsystem. The orbit of HD41004 B is nearly circular, with a companion of a 19 M-J minimum mass. The precision achieved for the primary is 10 m s(-1), allowing the measurement of a long- term trend in the velocities of HD41004 A.