We present pulse phase-resolved X-ray spectra of the high mass X-ray binary Vela X-1 using the Rossi X-ray Timing Explorer. We observed Vela X-1 in 1998 and 2000 with a total observation time of ~90 ksec. We find an absorption feature at 23.3 +1.3 -0.6 kev in the main pulse, that we interpret as the fundamental cyclotron resonant scattering feature (CRSF). The feature is deepest in the rise of the main pulse where it has a width of 7.6 +4.4 -2.2 kev and an optical depth of 0.33 +0.06 -0.13. This CRSF is also clearly detected in the secondary pulse, but it is far less significant or undetected during the pulse minima. We conclude that the well known CRSF at 50.9 +0.6 -0.7 kev, which is clearly visible even in phase-averaged spectra, is the first harmonic and not the fundamental. Thus we infer a magnetic field strength of B=2.6 x 10^12 G.
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