Simultaneous NuSTAR and XMM-Newton 0.5-80 keV spectroscopy of the Narrow Line Seyfert 1 galaxy SWIFT J2127.4+5654

We present a broad band spectral analysis of the joint XMM-Newton and NuSTAR observational campaign of the Narrow Line Seyfert 1 SWIFT J2127.4+5654, consisting of 300 ks performed during three XMM-Newton orbits. We detect a relativistic broadened iron K$\alpha$ line originating from the innermost regions of the accretion disc surrounding the central black hole, from which we infer an intermediate spin of $a$=$0.58^{+0.11}_{-0.17}$. The intrinsic spectrum is steep ($\Gamma=2.08\pm0.01$) as commonly found in Narrow Line Seyfert 1 galaxies, while the cutoff energy (E$_{\rm c}=108^{+11}_{-10}$ keV) falls within the range observed in Broad Line Seyfert 1 Galaxies. We measure a low-frequency lag that increases steadily with energy, while at high frequencies, there is a clear lag following the shape of the broad Fe K emission line. Interestingly, the observed Fe K lag in SWIFT J2127.4+5654 is not as broad as in other sources that have maximally spinning black holes. The lag amplitude suggests a continuum-to-reprocessor distance of about $ 10-20\ r_{\mathrm{g}}$. These timing results independently support an intermediate black hole spin and a compact corona.