NuSTAR observation of Ark 564 reveals the variation of coronal temperature with flux

The hard X-ray spectral index of some active galactic nuclei (AGN) has been observed to steepen with the source flux. This has been interpreted in a Comptonization scenario, where an increase in the soft flux decreases the temperature of the corona, leading to steepening of the photon index. However, the variation of the coronal temperature with flux has been difficult to measure due to the presence of complex reflection component in the hard X-rays and the lack of high-quality data at that energy band. Recently, a 200 ks Nuclear Spectroscopic Telescope Array(NuSTAR) observation of Ark 564 in 3-50 keV band revealed the presence of one of the coolest coronae with temperature kT_e ∼ 15 keV in the time-averaged spectrum. Here, we reanalyse the data and examined the spectra in four flux levels. Our analysis shows that the coronal temperature decreased from ∼17 to ∼14 keV as the flux increased. The high energy photon index Γ ∼ 2.3 varied by less than 0.1, implying that the optical depth of the corona increased by about 10 per cent as the flux increased. This first reporting of coronal temperature variation with flux shows that further long observation by NuSTAR of this and other sources would shed light on the geometry and dynamics of the inner regions of the accretion flow.