(e) Structure Function

Long-term X-ray variability of the low-luminosity active galactic nucleus of M81 was studied, using 16 ASCA observations spanning 5.5 years. The object exhibits a factor three variation over the 5.5 years. The source intensity was relatively constant within each observation which lasted typically for one day, but intra-day variability by 30% was detected on the 15th observation. The power-spectral density (PSD) was estimated in “forward” manner, over a frequency range of 10–10 Hz (period range of 1/4 day–5.5 years), by utilizing structure function and extensive Monte-Carlo simulations in order to overcome the very sparse and uneven data samplings. When the PSD is assumed to be white below a “break frequency” fb and falls off as ∝ f −α above fb, where f is frequency and α is a positive parameter, the M81 light curve is well described with 1/fb ≥ 800 days and α = 1.4± 0.2.