Detection of kilosecond hard lags in the new pulsating ULX candidate NGC 7456 ULX-1

Abstract: Context. Ultraluminous X-ray sources (ULXs) are thought to be powered, in many cases, by super-Eddington accretion onto compact objects. While soft X-ray lags have been detected in several ULXs, hard lags remain rare and poorly understood. Aims. We investigate the temporal and energy dependence of X-ray lags in NGC 7456 ULX-1 to constrain their physical origin and probe the super-Eddington accretion flow. Methods. We analyzed the two deepest XMM-Newton observations, taken in 2018 and 2023. Hard (1-10 keV) and soft (0.3-1 keV) light curves were cross-correlated using adaptive-binning techniques optimized for Poissonian low-count data. We measured lags over consecutive 10 ks intervals and investigated their energy dependence. Spectra were modeled using thermal and Comptonization models. Results. We detect significant hard X-ray lags in both observations, with the hard emission delayed by $\sim 10<sup>3$ s during phases of rapid flux variability. The delays are primarily driven by the lowest-energy photons. Spectral modeling indicates a Comptonization-dominated flow comprising a cooler, extended outer region and a hotter, compact inner flow embedded in an optically thick wind. We interpret the delays as the combined effect of inward propagation of accretion-rate fluctuations and photon diffusion within the dense outflow. Fluctuations first enhance the soft-emitting outer regions and then propagate toward the hotter inner flow, where photons undergo stronger Comptonization before escaping with a kilosecond delay. The small inferred inner emitting radius disfavors an intermediate-mass black hole accretor. Conclusions. The sign, amplitude, and energy dependence of the delays disfavor standard reverberation. Propagation-driven variability coupled with radiative transfer in optically thick winds appears to play a major role in shaping the timing properties of super-Eddington accretion flows.