We present NuSTAR observations of Vela X-1 , a persistent , yet highly variable , neutron star high-mass X-ray binary ( HMXB ) .
Two observations were taken at similar orbital phases but separated by nearly a year .
They show very different 3–79 keV flux levels as well as strong variability during each observation , covering almost one order of magnitude in flux .
These observations allow , for the first time ever , investigations on kilo-second time-scales of how the centroid energies of cyclotron resonant scattering features ( CRSFs ) depend on flux for a persistent HMXB .
We find that the line energy of the harmonic CRSF is correlated with flux , as expected in the sub-critical accretion regime .
We argue that Vela X-1 has a very narrow accretion column with a radius of around 0.4 km that sustains a Coulomb interaction dominated shock at the observed luminosities of L _ { \text { x } } \sim 3 \times 10 ^ { 36 } erg s ^ { -1 } .
Besides the prominent harmonic line at 55 keV the fundamental line around 25 keV is clearly detected .
We find that the strengths of the two CRSFs are anti-correlated , which we explain by photon spawning .
This anti-correlation is a possible explanation for the debate about the existence of the fundamental line .
The ratio of the line energies is variable with time and deviates significantly from 2.0 , also a possible consequence of photon spawning , which changes the shape of the line .
During the second observation , Vela X-1 showed a short off-state in which the power-law softened and a cut-off was no longer measurable .
It is likely that the source switched to a different accretion regime at these low mass accretion rates , explaining the drastic change in spectral shape .