4 Discussion

4.1 Summary account

The analysis of Structure Functions calculated for the UBVRI bands variations of the NGC 4151 nucleus during its extraordinary brightening in 1989-1996 using the observational data of 1516 flux measurements in each spectral band led to the following main results:

1. The logarithmic slopes of SFs for all periods of observations were different for intranight and extranight variability: 0.81-0.96 and 0.44-0.60, respectively. The durations of observed $T_{\max}$ were different, too, being 1 hour and 4.2 years. This indicates that the processes acting on time-scales of hours and years were different: almost pure shot-noise for intranight variations, and mixed shot-noise and flicker-noise for variations on a time-scale of years.

2. The logarithmic slopes of SFs for 10-150 days flares are higher than the SF slopes for the whole period of observations. The difference is highest (factor 2) for the slopes observed during period I.

3. The evolution of the SF slopes with time was revealed. It developed in different directions for intranight and extranight variations. Intranight processes evolved over 7.3 years from flicker-noise to shot-noise while extranight processes developed in the opposite directions. Flux variations on a time-scale of years became weaker; pulses became less steep when the nucleus brightness increased. At the same time, events on time-scales of less than one day became stronger with time and pulses became steeper and shorter when the nucleus brightening increased. This result shows that intranight and extranight variations are caused by different sources acting in the nucleus.

4. The first period of brightening differs from the three others in the most pronounced dependence of SF slopes on wavelength, both for intranight and for extranight flux variations, being essentially higher for the U band and decreasing to the I band.

4.2 Discussion

SF analysis indicates that during the period of 7.3 years brightening (1989-1996) of the NGC 4151 nucleus, different processes acted on different time-scales. There was evolution of the processes and this evolution was in different directions for intranight and extranight variations. These data indicate that the sources causing the intranight and extranight variations in the NGC 4151 nucleus are different. We discuss the obtained results for intranight and extranight variations separately.

 

 

Table 4: Structure Function parameters for yearly (b, $T_{\max}$ and k) and monthly (b₁ and k₁) variability of the NGC 4151 nucleus.

Period	Spectral	b	$T_{\max}$,	k	b1	k1
of observ.	region		years
1	2	3	4	5	6	7
I	U	$1.086 \pm 0.122$	1.65	0.833	$2.108 \pm 0.404$	0.793
I	B	$1.041 \pm 0.122$	1.65	0.884	$1.781 \pm 0.442$	0.710
I	V	$0.939 \pm 0.084$	1.65	0.884	$1.223 \pm 0.340$	0.668
I	R	$0.833 \pm 0.084$	1.65	0.858	$1.511 \pm 0.259$	0.825
I	I	$0.716 \pm 0.119$	1.65	0.714	$1.294 \pm 0.275$	0.762
II	U	$0.672 \pm 0.117$	1.4	0.686	$0.483 \pm 0.310$	0.363
II	B	$0.573 \pm 0.121$	1.4	0.615	$0.500 \pm 0.275$	0.414
II	V	$0.440 \pm 0.106$	1.4	0.562	$0.376 \pm 0.258$	0.342
II	R	$0.246 \pm 0.101$	1.4	0.372	$0.550 \pm 0.253$	0.478
II	I	$0.394 \pm 0.088$	1.4	0.594	$0.593 \pm 0.247$	0.515
III	U	$0.826 \pm 0.215$	1.83	0.661	$1.265 \pm 0.398$	0.692
III	B	$0.882 \pm 0.233$	1.83	0.655	$1.306 \pm 0.450$	0.659
III	V	$0.784 \pm 0.219$	1.83	0.634	$1.056 \pm 0.400$	0.622
III	R	$0.698 \pm 0.215$	1.83	0.598	$0.963 \pm 0.318$	0.674
III	I	$0.585 \pm 0.240$	1.83	0.488	$0.563 \pm 0.464$	0.343
IV	U	$0.514 \pm 0.065$	1.97	0.795	$0.267 \pm 0.201$	0.307
IV	B	$0.524 \pm 0.057$	1.97	0.838	$0.366 \pm 0.172$	0.458
IV	V	$0.488 \pm 0.054$	1.97	0.833	$0.469 \pm 0.144$	0.619
IV	R	$0.391 \pm 0.045$	1.97	0.824	$0.545 \pm 0.099$	0.800
IV	I	$0.443 \pm 0.049$	1.97	0.838	$0.704 \pm 0.080$	0.907

4.2.1 Extranight variations

The logarithmic slopes of the SF (Table 2 and Fig. 2) obtained for extranight UBVRI variations of the NGC 4151 nucleus for the whole sample of 1989-1996 observations are equal to 0.44-0.60, and are near to those of monthly and yearly optical variations of AGNs obtained by other authors. Hufnagel & Bregman (1992) analyzed flux density variations in the optical (4400 Å) obtained for the five best observed variable AGNs. The nature of the variability is determined using Structure Function analysis. The logarithmic slopes of SF were in the range of 0.3-0.5. The authors showed that the optical variations are similar for all objects, and are a combination of flicker and shot noise.

Kawaguchi et al. (1998) obtained a SF parameter $b\sim0.35$ for $2\leq\log~{\rm d}t\leq500$ days for the optical variations of the object 0957+561 A/B. The calculations led to logarithmic slopes of SFs equal to 0.41-0.49, which permit them to conclude that the observational slopes of SFs of AGNs favored the disk instability model (DI model) .

The nature of weekly, monthly and yearly optical continuum variations of AGNs was discussed by Ulrich et al. (1997) from other point of view. The authors concluded that the continuum flux variability in the optical and UV wavelengths on time-scales from one week to several months observed in low-luminosity AGNs are incompatible with a model wherein this variable component is emitted through viscous effects in an accretion disk. Because the amplitude of the variations at 1400 Å on time-scales of weeks is more than a factor of 2, at least half of the blue bump luminosity is involved.

The results of the NGC 4151 nucleus observations in the UV favor the point of view of Ulrich et al. (1997). A high amplitude of the extrahigh UV variations of the NGC 4151 nucleus was obtained by several authors: Edelson et al. (1996), Kaspi et al. (1996). Paltani & Walter (1996) analyzed the IUE observations of NGC 4151 complete up to 1991. The UV spectral slope varied considerably, with $\Delta\alpha_{\rm pl} = 1.4$. The authors concluded that neither an accretion disk, nor the optically thin emission model can explain these variations.

The UBVRI light curves of NGC 4151 given by Merkulova et al. (1999a) showed that the greatest amplitude of brightening of the nucleus in 1989-1996 was observed in the U band. The amplitude of flux variability of the NGC 4151 nucleus during the 7.3 years of our observations in an aperture D=20'' amounts to 2 $.\!\!^{\rm m}$2, 1 $.\!\!^{\rm m}$5, 0 $.\!\!^{\rm m}$9, 0 $.\!\!^{\rm m}$8 and 0 $.\!\!^{\rm m}$7 in the UBVRI bands, respectively. Reduced to an aperture D=5'', the amplitude of the V flux varied by a factor more than 9 and the U flux - by a factor more than 50. The reduction was made using the UBV multiaperture observations of NGC 4151 according to Doroshenko et al. (1998). One may suppose that the yearly brightening was connected with new activity of a variable source of high ultraviolet emission and a high degree of variation. This supposition is supported by our data on the strong shot-noise process revealed in the UBV bands in the first period of the nucleus brightening.

Some alternative models for DI variations in AGNs have been discussed. Daltabuit & Cox (1972) considered the processes involving the conversion of large-scale kinetic energy to electromagnetic radiation at or near a pair of shock fronts between dense colliding gas clouds.

Shock-in-jet (SJ) models for AGN variability have recently been developed. Marscher (1980) interpreted the radio through optical, and possible X-ray, emission of QSOs and radio weak AGNs in terms of a relativistic jet containing high-energy particles and magnetic field. Marscher & Gear (1985) presented models including the effects of synchrotron, Compton, and expansion losses as well as variable injection of relativistic electrons and the magnetic field. The observed behavior of AGNs is obtained in a more natural way in a model in which the outburst is due to a shock wave passing through an adiabatic, conical, relativistic jet. The minimum time-scale of variability can be as short as $\sim$1 day.

Hufnagel & Bregman (1992) obtained that the slopes of SF for the optical (4400 Å) variations of the best observed variable AGNs were inside 0.3-0.5 exhibiting a mixed shot-noise and flicker-noise process. For the radio region (4.8-14.5 GHz), the flux density variations of these objects revealed a strong shot-noise process $(b\geq1)$. They explained these results in the framework of models of an inhomogeneous jet of blazars in which shocks propagate along the jet. These models reproduce individual radio outbursts, and may also hold promise to explain optical variations as well. They indicated that the optical and radio emitting regions are physically related, exist on distinct size scales, and excite their synchrotron emitting plasmas differently.

Hufnagel & Bregman (1992) and other authors pointed out that the flatness of the SF and a decrease of the time-scale of variability from radio to optics are characteristic. It is a common opinion that the process causing the optical variability of AGNs is mixed shot-noise and flicker-noise and is weaker than the process causing the radio variability of AGNs. Our SF analysis showed that the process causing the optical fluxes of the NGC 4151 nucleus variability depends on the phase of nucleus activity (see Fig. 4). It was a strong shot-noise type at the beginning of the nucleus brightening (slopes of SF $b\geq1$, and for flares they were equal $\sim$2). At this time, the process was near to a process being characteristic for radio flux variations of AGNs. But from the beginning to the end of the NGC 4151 nucleus brightening, the process evolved to a mixed shot-noise and flicker-noise. At the end of our observations the process approached flicker-noise, when the nucleus brightness increased: $b \sim 0.4{-}0.5$. These events have not been observed for other AGNs because, as a rule, their optical variability was considered for long time periods as a whole, but not for fixed active or nonactive periods. In this case, processes acting at different periods cannot be revealed. Existing phases of a strong shot-noise process for the active period of the NGC 4151 nucleus in the optical region indicated that this process was near to that acting in the radio region of AGNs, and favored the SJ model for its optical flux variability during 1989-1996.

As a rule, SJ models are proposed for blazars and related objects, which show the specific behavior of variations of their spectra. Brown et al. (1989a,b) discussed the continuum variability of blazars from radio to ultraviolet. They obtained that for some of them the correlation between flux level and spectral index, in the sense that the near infrared spectrum flattens when the J band flux density increases. The behavior observed was explained naturally in terms of a single synchrotron component which experienced recurrent bursts of injection, or reacceleration. The steepening of the near-infrared spectrum accompanied by a decrease of flux is attributable to radiative energy losses which affect the higher energy electrons before affecting the lower energy electrons. Quirrenbach et al. (1991) argued that 1-7 days optical variable emission of the object 0716+714 originates in the jet region. It would be a small jet at a considerable distance from the central engine. Camenzind & Krockenberger (1992) discussed radio and optical variability in blazars in terms of shocks propagating in collimated relativistic flows.

Hagen-Thorn et al. (1998) analyzed data of the UBVRI 1993-1996 observations of the object OJ 287. They found that the variable sources have the same power-law spectrum in the optical ( $F_\nu \sim \nu^{-1.5}$) irrespective of flux level. In the IR region the spectrum flattens during the flare. Comparison of the outburst of 1994 with those of 1971 and 1983 shows that there is a clear correlation between the power of the outburst and the color indices of the variable component in each event: if the outburst is stronger, the variable source is bluer. At the same time the energy spectrum of relativistic electrons is flatter for a stronger outburst. Hagen-Thorn et al. (1998) suspected a synchrotron self-absorption mechanism for the observed events.

During the brightening of the NGC 4151 nucleus in 1989-1996 the increase of the spectral indices $\alpha _{\rm pl}$ with time indicated the flattening of the optical spectrum with increasing luminosity of the variable source (Merkulova et al. 1999a). This result is in accordance with the results obtained for blazars by Brown et al. (1989b) and by Hagen-Thorn et al. (1998). A variable optical source of synchrotron emission in the NGC 4151 nucleus was suspected by Babadzhanjants et al. (1972), Thompson et al. (1979) and Schmidt & Miller (1980). Observed significant variations in the degree of polarization and its wavelength dependence were among the reasons for this supposition. They obtained that the continuum polarization of the variable source of NGC 4151 varies smoothly throughout the visible, from a value of approximately 1.2% in the red to approximately 2.5% at lambda 4000A being consistent with the presence of an uniformly polarized synchrotron component. Qualitatively the same wavelength dependence has been observed in other polarized Seyferts. According to Schmidt & Miller (1980), the observed NGC 4151 continuum can be represented by a combination of a power-law component and a galactic stellar population in proportions approximately 1:1 at visual wavelengths.

SJ models include collimated relativistic beaming. As a rule, AGNs of moderate radio emission do not contain such events. However, the data of several observations permit us to suppose that relativistic beaming is possible inside the NGC 4151 central region. Ulvestad et al. (1998) obtained VLBI images of the NGC 4151 central region at wavelengths 6 cm and 18 cm, achieving a resolution of $\sim$2 mas and $\sim$5 mas ($\sim$0.16 pc and $\sim$0.40 pc), respectively. They revealed an elongated structure in $\rm PA \sim20$-75 degrees, similar to that of the 3 $.\!\!^{\prime\prime}$5 radio jet and narrow-line region. The nuclear radio structure at 6 cm has a length of $\sim$13 mas (1.0 pc) and a length/width ratio of $\geq$4 and therefore fulfills one of the classical criteria for a radio jet. However, its radio luminosity is only $\sim$10³⁸ ergs/s, several orders of magnitude less than the parsec-scale jets in radio galaxies. Penston et al. (1990), Robinson et al. (1996), Winge et al. (1997) and others showed that the ionization structure of the extended and inner 10 pc narrow line regions of the NGC 4151 nucleus is broadly consistent with photoionization by the AGN radiation field in "an ionization cone'' with an opening angle $\sim$120$^{\circ}$. They proposed a model of anisotropic emission because relativistic beaming now remains one of the most tenable possibilities.

Pedlar et al. (1993) argued that the UV and milliarcsecond radio structure are collimated along PA 50$^{\circ}$ on scales $\sim$1 pc and the radio jet is subsequently bent to PA 77$^{\circ}$ on a scale of 10 pc. Bicknell et al. (1998) considered radio jets of four Seyfert galaxies, and NGC 4151 is among them. They proposed that "dynamically, Seyfert jets resemble FR1 jets which appear to be initially supersonic and relativistic and to then undergo a transition to turbulent transonic flow. At this transition FR 1 jets are mildly relativistic with ${\beta} = v/c = 0.6{-}0.7$''. If this is the case, the polarized variable optical flux of the nucleus which arises in the inner region of relativistic jet can be partly depolarized by turbulent transonic flow.

These data permit us to speculate that extranight variations of the optical continuum flux of the NGC 4151 nucleus may be caused by instabilities in a shock-in-jet event.

4.2.2 Intranight variations

Intranight optical variability is a conventional picture for blazars. There is a strong consensus that activity in a relativistic jet is the best explanation for microvariability and related activity in blazars on time-scales of a few hours (Gonsález-Pérez et al. 1996). Object OJ 287 is one of a few blazars with a very high degree of microvariability which is supposed to be due to the development of a shock and its instabilities (Marscher et al. 1992, Camenzind & Krockenberger 1992). Wagner et al. (1996), discussing the rapid variability of object S5 0716+714 across the electromagnetic spectrum, supposed that the flickering is connected with the plasma processes of particle acceleration.

Analysis of the variability of the NGC 1275 nucleus by Pronik et al. (1999a,b) using observations obtained from 1989-1994 revealed high and low level intranight flares with $SD/F\leq 3\%$ and $SD/F\geq 3\%$, where SD is the standard deviation and F is the average flux obtained for each night.

There is now evidence for intranight variation of several Seyfert 1 galaxies, too. Miller & Noble (1994) observed rapid optical variations of the Seyfert 1 galaxy Akn 120 on a time-scale shorter than an hour. These variations are the most rapid which have been detected for any Seyfert galaxy and clearly demonstrate that radio-quiet AGNs exhibit the phenomenon of microvariability. The authors suggest that these variations are independent of the radio properties of these objects and are thus unlikely to be associated with any disturbance in a relativistic jet. Gopal-Krishna et al. (1995) supposed that optical microvariability for radio-moderate QSO seems to favor models where flares on accretion discs are responsible for the microvariability.

Intranight optical variations of the NGC 4151 nucleus were first revealed by Lyuty et al. (1989) using observations at minimum nucleus brightness in 1987 and 1988. They registered V brightness variations of a variable source with $\Delta V\sim 10\%$ from 15$^{\rm m}$- 30$^{\rm m}$ and noticed that rapid variations are independent of the level of the nucleus brightness averaged over the night. Merkulova (2000) showed that the two types of intranight flares revealed for the NGC 1275 nucleus by Pronik et al. (1999a,b) also act in the NGC 4151 nucleus. We observed the evolution of the process causing intranight variability of the nucleus with time during the extraordinary brightening of the nucleus from 1989-1996. At the beginning of the nucleus brightening, the SF slopes on time-scales less than one day were rather low (0.0-0.4) showing that the powering process did not touch the nucleus regions causing the intranight variations. Then evolution of the process was observed from flicker-noise to shot-noise (see Table 3 and Fig. 4), indicating that the powering of the intranight variations was in accordance with the brightening of the nucleus.

Heidt & Wagner (1996) obtained parameters of SFs for 34 radio selected BL Lacertae objects in the optical R band; the slopes of the SFs are within the range $0\leq b \leq 2.5$, with a mean value of 0.8 and a dispersion of 0.6. The typical time-scale lies in the range from 0.5 to 5 days. Our data on microvariability of the optical flux of the NGC 4151 nucleus gave $0 \leq b \leq 1.16$, and do not contradict the results of Heidt & Wagner (1996), being explained by the standard model where shocks are propagating down a relativistic jet: the SJ model. There will be a high degree of microvariability if the jets are bent and turbulent: the scenario of shocks propagating within the jet entering a turbulent region (Marsher & Gear 1985; Marscher & Travis 1991; Wagner 1991). The time-scales observed are close to the lower limit of this model (1 day). From the above mentioned information, there are signs of relativistic beaming in the NGC 4151 central regions (Ulvestad et al. 1998; Penston et al. 1990; Robinson et al. 1996; Winge et al. 1997).

4.2.3 Extraordinary optical brightening of the NGC 4151 nucleus from 1989-1996 in the framework of the relativistic jet model

The investigations of the NGC 4151 nucleus variability during its extraordinary brightening between February 1990 and June 1996 by Merkulova et al. (1999a,b) exhibited the characteristics of radio loud AGNs:

1. an energy distribution in the optical flux excesses both in the 1.5-2.0 years variations and in flares with duration 10-150 days showed a power law form: $F_\nu \sim\nu^{\alpha_{\rm pl}}$;

2. an increase in the spectral indices $\alpha _{\rm pl}$ with time from the beginning to the end of the nucleus brightening indicated a flattening of the optical spectrum;

3. the logarithmic SF slopes of the UBVRI flux variations during the active period were in the range $0.8\leq b \leq 1.1$, and for 10-150 day flares equal to 2.2, exhibiting the extreme shot-noise process characteristic for radio variable flux of blazars which were interpreted in the framework of SJ models (Hughes et al. 1992; Lainela & Valtaoja 1993);

4. high luminosity of ultraviolet emission and a high degree of variation in this emission are revealed. The increase of the nucleus brightening over 7.3 years in the U band reduced to an aperture D=5'' was by a factor of more than 50.

The obtained data were discussed in the framework of a model where the increase of the nucleus brightening is caused by the clouds of synchrotron radiation ejected from the nucleus during its active period from 1989-1996.

Figure 5 shows the relation between the slope $\alpha _{\rm pl}$ of spectral energy distribution in the flux excess during each of four periods of nucleus brightening (from Table 1) and the variable SF parameter "b'' for extranight U variations (from Table 4). One can see an inverse correlation of these values. The increase of the spectral index $\alpha _{\rm pl}$ was proposed as resulting from increase of the optical depth of the clouds of relativistic electrons, or the accumulation of higher energy electrons. The decrease of the SF parameter "b'' can be caused by the same: increasing optical depth of the emission region, or the accumulation of electrons of higher energy leading to smoothing of pulses of light variability.

Figure 5: Inverse correlation of the spectral slopes $\alpha _{\rm pl}$ with the SF slopes "b''.