Study of long-term X-ray variability with sparse light curves -- analysis method

Naoko Iyomoto$^1$,Yuuichiro Ezoe$^2$,Kazuo Makishima$^2$

$^1$ISAS, Sagamihara, Kanagawa, Japan\newline
$^2$University of Tokyo, Bunkyo-ku, Tokyo, Japan

We have developed an analysis method to estimate long-term
power-spectral density (PSD) from sparse and unevenly-sampled light
curves, introducing two key techniques.  The first is the use of
"structure function (SF)", which is mathematically equivalent to the
PSD, and is less affected by data gaps.  The second is "forward
method" with Monte-Carlo simulation: assuming various PSDs, we
generate fake data and compare them with the actual data.  When the
sampling is sparse, even the SF becomes distorted and exhibits large
scatter; therefore we investigate the effect of the sparse sampling
using the forward method.

As an illustration, we apply the method to a low-luminosity AGN
(LLAGN), the M81 nucleus, which has been observed with {\it ASCA} 16
times over 5.5 years.  With 1/8 day binning, more than 99\% of the M81
light curve are data gaps.  When the PSD is assumed to be white below
a "break frequency ($f_{\rm b}$)" and to falls off as $\propto
f^{-\alpha}$ above $f_{\rm b}$, the M81 SF is well described with
1/$f_{\rm b} \ge 800$ days and $\alpha = 1.4 \pm 0.2$, with 90\%
confidence.  The relatively long 1/$f_{\rm b}$ reinforces the view
that LLAGNs have massive black holes in spite of their low
luminosities.


--------  --------  --------  --------  --------  --------  --------
Study of long-term X-ray variability with sparse light curves -- an application to quasars

Yu-ichiro Ezoe$^1$,Naoko Iyomoto$^2$,Kazuo Makishima$^1$,Gunther Hasinger$^3$

$^1$University of Tokyo, Bunkyo-ku, Tokyo, Japan\newline
$^2$ISAS, Sagamihara, Kanagawa, Japan\newline
$^3$Astrophysikalisches Institut Potsdam, Potsdam, Germany\newline


We estimate the X-ray power spectral density (PSD) and black hole mass
of 6 quasar candidates, utilizing our method to estimate PSD from
sparse and unevenly-sampled light curves.  We assume a broken
power-law type PSD with a break frequency $f_{\rm b}$ and adopt a
forward-method approach with extensive Monte-Carlo simulations, in the
same way as described by Iyomoto et al. (this symposium).  For 5
luminous AGNs ($L_x>10^{43.5}$ ergs$^{-1}$ in 0.5--2.0 keV) in the
Lockman field observed with {\it ROSAT} 5 times over 2 years, we
obtained $1/ f_{\rm b}$ 10 to $>700$ days.  For RX~J0957.9 6903
observed with {\it ASCA} 16 times over 5.5 years, we also obtained $1/
f_{\rm b} >500$ days.  These long time scales of variation reinforce
the view that these luminous AGNs really host massive black holes,
which becomes $10^{6-8}~M_\odot$ when scaled with Cygnus X-1.