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Two giant outbursts of V 0332+53 observed with INTEGRAL

In July 2015, the high-mass X-ray binary V 0332+53 underwent a giant outburst, a decade after the previous one. This system hosts a strongly magnetized neutron star. During the 2004--2005 outburst, an anti-correlation between the centroid energy of its fundamental cyclotron resonance scattering features (CRSFs) and the X-ray luminosity was observed. The long ($\approx 100$ d) and bright ($L_{\rm x} \approx 10^{38}$ erg s$^{-1}$) 2015 outburst offered the opportunity to study during another outburst the unique properties of the fundamental CRSF and its dependence on the X-ray luminosity. The source was observed by the INTEGRAL satellite for $\sim 330$ ks. We exploit the spectral resolution at high energies of the SPectrometer on INTEGRAL (SPI) and the Joint European X-ray Monitors to characterize its spectral properties, focusing in particular on the CRSF-luminosity dependence. We complement the data of the 2015 outburst with those collected by SPI in 2004--2005 and left unpublished so far. We find a highly significant anti-correlation of the centroid energy of the fundamental CRSF and the $3-100$ keV luminosity of $E_1 \propto -0.095(8)L_{37}$ keV. This trend is observed for both outbursts. We confirm the correlation between the width of the fundamental CRSF and the X-ray luminosity previously found in the JEM-X and IBIS dataset of the 2004--2005 outburst. By exploiting the RXTE/ASM and Swift/BAT monitoring data we also report on the detection of a $\sim 34$ d modulation superimposed on the mean profiles and roughly consistent with the orbital period of the pulsar. We discuss possible interpretations of such variability.