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

The hard X-ray spectral index of some 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 {\it NuSTAR} observation of Ark 564 in 3--50 keV band, revealed the presence of one of the coolest coronae with temperature $kT_e \sim 15$ keV in the time-averaged spectrum. Here, we re-analyse the data and examined the spectra in four flux levels. Our analysis shows that the coronal temperature decreased from $\sim 17$ to $\sim 14$ keV as the flux increased. The high energy photon index $\Gamma \sim 2.3$ varied by less than $0.1$, implying that the optical depth of the corona increased by about 10\% as the flux increased. This first reporting of coronal temperature variation with flux shows that further long observation by {\it NuSTAR} of this and other sources would shed light on the geometry and dynamics of the inner regions of the accretion flow.