## 4. The structure function of the variable optical fluxes of the NGC 1275 nucleus## 4.1. The structure function propertiesPress (1978) suggested that the variability in quasars is caused by a process aliased as "noise". The power spectrum of the simplest of them has a form g() . The compact variable AGNs exhibit three types of noise: white-noise ( = 0), flicker-noise ( = 1), and shot-noise ( = 2) (see Terebizh, 1993). Such processes are easily revealed by the technique of SF analysis. In application to AGNs it was discussed by Hufnagel & Bregman (1992); Hughes et al. (1992); Lainela & Valtaoja (1993) and others. The first-order SF is defined as: F(t) being the flux at time t, and dt being the time delay (lag)
between observations of fluxes F(t) and F(t+dt), the angular brackets
denote an ensemble average. The SF of an "ideal" stationary random
process on a logarithmic scale consists of three components: a slope b
= d log(SF)/ d logdt, which is located between two plateaus. For short
time scales, the plateau is just twice the variance of the measurement
noise, because it has a zero correlation time scale. The longest
correlation time scale - T There is a simple correspondence between the power spectrum of the
Fourier analysis and the SF analysis: if
SF(dt) dt ## 4.2. Structure function analysis realizationThe Structure Function analysis was done using a special program package by S.G.Sergeev. The program package used was tested using the optical observations of the quasar 3C 273 during 1887-1967, reduced in a common system by Kunkel (1967). The light curve of 3C 273 in arbitrary units was given by Fahlmann & Ulrich (1975). Data are averaged over 100 days intervals. This light curve was investigated with a correlation method and
power spectra analysis by Kunkel (1967), Terrell & Olsen (1970),
Terebizh (1993) and others. According to these investigations, the
power spectrum of the variable flux of the quasar is
g()
Fig. 4 shows SFs for the variable flux of NGC 1275 in 1982-1987 and 1987-1994. One can see that there is no SF of a simple "ideal" one - process form with one slope for all time lags. The slopes "b" of SFs for the intranight and years variations are essentially different. We examine these SFs on the intranight time-scale and on the months - years timescale separately.
## 4.3. The structure function of the intranight variability of the nucleus of NGC 1275. MicrovariabilityFig. 4 shows that the intranight part of all SFs does not contain a
well-defined first plateau, caused by the observational errors. All
logarithmic slopes are restricted only by T
The data in Table 2 show that the slopes of SFs of the
low-level microvariations of the nucleus of NGC 1275 were in the
range 0.25 b
0.66, and T One can see that the slope "b" for
5200 Å in 1982-1987 and for V band in 1989-1994 was 0.25-0.35 -
just the same within the limits of errors. Obtained data show that the
low-level microvariability of NGC 1275 in 1982-1994 was caused by
a mixed process of flicker-noise and shot-noise. The character of the
microvariability does not change with time, but T Table 3 contains the SF parameters of the high-level flux
microvariations. The logarithmic slopes of the SFs are in the range
0.66-1.19, and T
Comparison of the slope "b" for 5200 Å in 1982-1987 and for the V band in 1989-1994 shows that it decreased from 1.14 to 0.66. The difference is insignificant, because it is equal to about 2.5. The data of Fig. 4, Tables 2 and 3 show that the SF of the microvariability of the optical flux of the NGC 1275 nucleus in the period 1982-1994 shows the presence of two types of intranight process with different time scales. A mixed process of flicker-noise and shot-noise dominates on time scales less than 4 hours, and a shot-noise type process - on time scales more than 4 hours. The maximum time scale of the correlated flux variations is equal to 8.6 hours. The slopes of the SFs obtained for the observations in the UBVRI system are not equal each to other. The highest slopes of the SF are calculated for the U and I bands: 0.42-0.66 against 0.35 in the V band for low level variations, and 1.19-1.04 against 0.66 in the V band for high level variations. The excess for the I band amounts to 0.66-0.35=0.31 (about 2.5) and 1.04-0.66= 0.38 (more than 3). The excess in the slopes of the SF in the U and I bands compared to the slope in the V band can be interpreted as an elevated activity of the nucleus in the ultraviolet and near-infrared regions of the galaxy spectrum compare to the visual region, but the differences are at a low confidence level. ## 4.4. Structure function of the optical flux of the NGC 1275 nucleus for time lags from 1 day to several yearsTable 4 contains the SF parameters of the variability of the optical flux of the NGC 1275 on a time scale of years. The columns are the same as for Tables 2 and 3. Both Table 4 and Fig. 4 demonstrate that the SF for the 1982-1994 observations on time scales of more than one day exhibits the slope b 0.06-0.14 with a confidence level of the correlation of up to 0.99. The second plateau of SFs is not clearly present. It is possible that in the NGC 1275 nucleus in 1982-1994 a weak flicker-noise type process was present on time lags more than 4 years, or entirely absent.
Fig. 4 exhibits several minima and maxima in SFs on time lags of days, months and years. Such peculiarities of SFs are usually interpreted as the evidence of cyclic processes or individual flares in active nuclei. Cyclic processes must be shown by SFs for both periods of observations. One can see that there is only one short interval of time lags with a common minimum for all SFs: -0.3 log dt +0.4, or 0.9 dt 2.5 days. In this interval of time lags one can look for the cyclic variability of the optical flux of the NGC 1275 nucleus. All other maxima and minima are caused by noncorrelated individual flares. © European Southern Observatory (ESO) 1999 Online publication: November 2, 1999 |