Pulse frequency variations and timing noise of MXB 0656–072 during the 2007–2008 type I outbursts and implications for its magnetic field

Aims. We aim to explore the properties of the Be/X-ray binary system MXB 0656–072 from a timing analysis perspective through an investigation of the RXTE/PCA and Fermi/GBM data during its 2007–2008 type I outbursts.Methods. We applied two new techniques, for the first time, along with the conventional Deeter method to produce higher-resolution power density spectra (PDS) of the torque fluctuations. We also investigated the spin frequency evolution of the source by utilising a pulse timing technique.Results. The PDSs show a red noise pattern, with a steepness of Γ ∼ −2 and a saturation timescale of ∼150 d, indicating that MXB 0656–072 is a disc-fed source. With the obtained long term spin frequency evolution, we reveal the torque–luminosity correlation of MXB 0656–072 for the first time. We also demonstrate that the frequency evolution is largely consistent with the Ghosh–Lamb model. In the RXTE/PCA observations, the pulsed emission disappears below ∼5 × 10^{35 erg s−1, while the profiles remain stable above this value in our analysis time frame. We show that the magnetic field strength deduced from the torque model is compatible with the field strength of the pulsar derived from the cyclotron resonance scattering feature. Utilising the new distance of MXB 0656–072 measured by Gaia, we show that the spectral transition of MXB 0656–072 occurs at a luminosity that matches the expected theoretical transition from the subcritical to supercritical accretion regime.}