Baltic Astronomy,
vol. 8, 575-592, 1999.
P H O T O M E T R Y A N D P O L A R I M E T R Y OF ACTIVE
GALACTIC
NUCLEI
V. A. H a g e n - T h o r n a n d S. G. Marchenko
Astronomical Institute, St.-Petersburg State University,
Bibliotechnaya Pl. 2, Petrodvoretz, 198904 St.-Petersburg,
Russia
Received January 10, 2000.
Abstract. A method of analysis of polarimetric and photometric
observations of AGN with the aim to find the spectral energy distribution and polarization parameters of variable sources responsible
for activity is described. Some results of such analyses are given. The
properties of the sources point to their synchrotron nature.
K e y words: galaxies: active galaxies, variability, polarization
1. I N T R O D U C T I O N
This p a p e r is devoted to t h e methods of analysis of photometric a n d polarimetric observations of Active Galactic Nuclei (AGN)
with t h e purpose to establish the properties of the sources responsible for their activity. T h e problem of the activity of extragalactic
objects is of prime importance in current astrophysics. There are
m a n y manifestations of activity, including photometric and polarimetric variability in all spectral regions. T h e sources responsible for
variability are placed in the nearest neighborhood of the central engine. Understanding t h e n a t u r e of these sources might give a way to
solution t h e problem of nuclear activity in general.
Numerous observations, in particular - photoelectric p h o t o m e t r y
with different apertures, as well as direct imaging, show t h a t these
sources are not optically resolved. Unfortunately, the flux of active
point sources is not observable directly, without the confusion of
some flux of t h e underlying galaxy, unresolved accretion disk and
other c o n t i n u u m contributors, as well as sources of narrow and broad
line emission.
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All earlier photometric and polarimetric measurements, made
with photomultipliers, recorded the flux (or polarized flux) within
some aperture of known size. CCD observations give the same situation: the published data are always obtained by summing fluxes
in several (often many) pixels. Despite the higher precision, the situation with CCD observations in some respects is even worse than
in the case of photomultipliers, since CCD observers usually do not
give the aperture diameter. Therefore their results are somewhat
indefinite because of the lack of information which would allow one
to take into account the contribution of the surrounding area. The
situation is complicated by the fact that in different observational
conditions the summing includes a different number of pixels - more
pixels in bad seeing. So in the investigation of variability, a comparison of the data in long sets of observations is problematic even for
the data of the same observer. Later on, however, we consider that
information on the aperture dimensions will be available.
Thus, several components contribute to the observed radiation
and the extraction of the radiation of a variable source is not a
simple task. In various spectral regions the contribution of different
components is different. However in all regions the radiation of active
sources may be extracted in the most reliable way on the basis of
variability studies.
For understanding the nature of active sources, it is most important to know their spectral energy distributions. These distributions
may be found from the analysis of multicolor data on photometric
variability. Another important feature of active sources is the polarization of their radiation. The analysis of the data on polarimetric
variability may give information about polarization properties of the
active sources.
The highest activity among extragalactic objects is observed in
blazars. Therefore blazars are being investigated most extensively
with the purpose to find properties of the variable sources. Other
active extragalactic objects (for instance, Seyfert galaxies) are suitable for such analysis too.
At present the instantaneous spectra of active objects in a wide
frequency range (from radio to X-rays or even 7-rays) are measured
as a result of cooperative work. These spectra are obtained for different brightness levels of the objects, and some correlations between
various observed parameters are studied. However, the success of
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577
such an approach for studying the properties of variable sources is
limited, and conclusions about their n a t u r e are not decisive.
T h e confrontation of variations measured in different spectral regions shows t h a t variable sources seen in these regions are connected
with each other because t h e variations (maybe with the exception
of X-rays) are correlated (sometimes with time lag). However, for
confirmation of t h e identity of these sources we must compare their
spectral and polarization properties.
Now let us consider one simple m e t h o d of obtaining spectral and
polarization properties of variable sources.
2. T H E T E C H N I Q U E O F E X T R A C T I N G VARIABLE S O U R C E S
F R O M OBSERVATIONS O F P H O T O M E T R I C AND
P O L A R I Z A T I O N VARIABILITY
Let us suppose t h a t t h e variability within some time interval is
due to a single variable source, and we have multicolor photometric
and polarimetric d a t a distributed within this interval. As was shown
by Choloniewski (1981) for photometric d a t a and by Hagen-Thorn
(1981) for polarimetric d a t a (only linear polarization will be considered), if t h e variability is caused only by flux variations of t h e variable
source, b u t its relative spectral energy distribution (for photometry)
or relative Stokes p a r a m e t e r s Px,viPy,v (for polarimetry) remain unchanged, then in the flux space {F\ , . . . , F n } (for photometry, here n is
the n u m b e r of spectral b a n d s used) or in the space of absolute Stokes
p a r a m e t e r s {I, Q, U} (for polarimetry) the observational points must
lie on a "straight line". T h e direction tangents of this line are t h e
flux ratios of the variable source ( F { / F j ) v , i.e., its relative spectral
energy distribution (for photometry) or relative Stokes parameters
of t h e source (for polarimetry).
Let us show this for polarimetry at first (see Fig. 1). Let I,Q,U
b e t h e observed Stokes parameters, Ic,Qc,Uc - the common Stokes
p a r a m e t e r s of all invariable components and IV,QV,UV - the Stokes
p a r a m e t e r s of t h e variable source. T h e n Qv = IvPx,v> Uv = IvPy,v,
the relative Stokes parameters of the variable source Pz,v and Pytv
being constant.
Because of additive character of Stokes parameters we have:
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I
(IoQcUc)
0
/
Q? /
/
u
i
i'
F i g . 1. Polarization behavior in the space of absolute Stokes parameters.
(1)
After substitution in the second and third equations the value
I v = I — I c , found from the first one, we have:
Q = Px,vl
+ (Qc -
Px,vlc)
U = Py>vI
+ (Uc -
Py,VIC)•
(2)
The system (2) is the equation of straight line in the space of Stokes
parameters {I,Q,U}
and pXtV and pVjV are its direction tangents.
Evidently, we can consider two planes {I, Q} and { / , U} in which
the observed Stokes parameters must follow straight lines with the
slopes equal to pXfV and pViV, respectively.
Let we have n polarimetric observations accompanied by photometry. Usually, the results of polarization measurements are presented as a degree of polarization p and its direction 8q , and the
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Photometry and polarimetry of AGN
Fc
/
Fc
F
F i g . 2 . Polarization behavior in the plane { . F , F p } .
photometric data as a magnitude m. Transforming these values to
the absolute Stokes parameters may be done by equations:
(3)
where const is determined by absolute calibration of the photometric
system used.
Thus, we have n observations (Ik, Qk,Uk)(k = 1, ...n). If in the
planes { I , Q}, { I , U} the observational points within the observational errors lie on straight lines, one can conclude that the model
of single variable source with unchanged relative Stokes parameters
is valid. Then the values pXjV and py<v may be found as the slopes of
the lines by solution of surplus systems of equations (2) by the least
square method. It is better, however, to use the method of orthogonal regression suggested by Wald (1940) for the cases when random
errors exist in both data sets under comparison. Of course, the necessary condition for the relative Stokes parameters, (p x 2 +Py2)1/2
< 1
must be fulfilled.
It should be noted that positions of the observed points on
straight lines is a necessary but not sufficient condition for validity of the model of single variable source with unchanged relative
Stokes parameters.
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Indeed, let us consider the plane {F,Fp} (Fig. 2) where F and
Fp are the total and polarized fluxes, respectively (in the case, when
the observed direction of polarization does not change, this plane is
analogous to the planes {I, Q} or { / , U}). Let the observed points
lie on a straight line, and its equation is
Fp = aF + b.
(4)
In the two-component model, a is the degree of polarization of the
variable component pv (we remind that this is a constant). The intersection of the line with F-axis gives the flux of unpolarized component Fc.
In principle, the flux of the unpolarized component may not be
equal to Fc, being, say Fc. Then one must move from Fc to the
observed points along vectors with different slopes (or varying pv).
But in this case a special dependence between pv and Fv = F — Fc
must exist to bring the observed points on straight line. In fact, we
have Fp = (F — Fc)pv = aF + b, or
pv = a + (aFc
+
b)/Ft
(5)
i.e., the degree of polarization of the variable component must be
inversely proportional to its flux. Because, in general, there are no
physical reasons for fulfilling such a condition, one can conclude that
if the observed points lie in the plane {F, F p } on a straight line, then
the model of variable source with unchanged polarization parameters
is valid. Of course, this is correct for the planes { / , Q} and {I, U}
also.
It is interesting to note that because of the possible existence
of the constant polarized component even in the simplest case of
a single variable source of polarized radiation with constant polarization parameters many types of correlations between the observed
brightness and polarization parameters may exist. The degree of polarization may either increase or decrease with growing brightness.
In the case of varying observed direction of polarization, a rise of
polarization degree with brightness can lead to its decrease and vice
versa.
It is obvious that the necessary condition for explanation of the
polarization variability in such a simple model is the location of the
observed points in the plane of relative Stokes parameters {p x ,py}
on a straight line. This fact has to be verified at the very beginning.
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F i g . 3 . Photometry behavior in three-dimensional flux space.
Now let us appeal to photometry (more details can be found in
the paper of Hagen-Thorn (1997). Because there are no principal
differences between considering both photometric and polarimetric
data, we begin from a three-dimensional case (as in polarimetry).
Following Choloniewski (1981), let us consider the three-dimensional
space of the observed fluxes {FU, FB, FY} (Fig. 3). Let F y , F g , F y
are the fluxes of all constant components and JFyar, FGAR,FYAR are
the fluxes of the variable component, the ratios
/ jpvar
*u
Tpvar
¡bv
rpvar
/1rivar
%B
=
a„
uv
„
l*V
'
~aBV
being constant.
Evidently,
' FU=F[R
+
F™R
< FB = FG + FGAR
rpc-\r
i rrrvar
rJ7iv — ry
tv .
(7)
Substituting FJ}AR and FGAR in the first two equations of this system
through FYAR found from (6) and then eliminating FYAR by using the
third equation, one can find
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Fjj = AUVFV + {FU ~
a
Fb
aBVF£).
= AByFv
+ (Fg
-
uvFy)
S. G.
Marchenko
(8)
System (8) is the equation of straight line in the space {Fu, F b ,
Fy}. Each equation of the system is the equation of a projection
of the line to the corresponding coordinate plane. Therefore, in the
following we will consider only the two-dimensional case, bearing in
mind that the consideration may be generalized to n dimensions.
In the two-dimensional case, instead of (6) we have ( F j / F i ) v a r =
aji (aji is constant) and instead of (8) we have
Fj =
ajiFi
+ (F/ - djiFf).
(9)
This is the equation of a straight line in the plane {Fi,Fj}.
Thus, for the variable component of the invariable energy distribution the points that correspond to the observed fluxes lie in the
plane {Fi,Fj} along the straight line (9). Eq. (9) shows that the
point which corresponds to the constant component lies on this line
closer to the origin of coordinates than the point which corresponds
to the minimum observed flux.
In the analysis of observational data we have to solve the inverse
problem, because all that we can do is to compare the observed fluxes
F^Fj
(k = 1 ,...,iV, where N is the number of observations). Assume that the points corresponding to the observed fluxes lie (within
the limits of measurement errors) along the straight line
Fj — ajiFi
~f~ bji
(10)
The coefficients aji and bji should be determined by the orthogonal
regression method.
Let us consider possible interpretations for the fact that the
points lie along the straight line in terms of a two-component model
(constant component + single variable source).
(i) Energy distribution of the variable source is invariable. In
this case the coefficient a,ji is the flux ratio of the variable component ( F j / F i ) v a r in the compared bands (in other words, the color
index of the variable component). If there are observations in n photometric passbands, the relative spectral energy distribution of the
variable component over the spectral range covered by these passbands is determined. The important fact is that this information can
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of AGN
be obtained without knowledge of its contribution to the observed
flux.
It is necessary to note that the relative spectral energy distribution found by such a method is the observed, one, and it should be
corrected (if needed) for reddening in the Galaxy. To do this we have
to know the interstellar reddening law and the value of extinction in
one of the passbands used. The correction may be done either at
the very beginning, before the construction of "flux-flux" diagrams
(then we obtain corrected ratios directly), or after determination of
the flux ratios because the observed and corrected values of these
ratios differ from each other by a factor which may be easily found.
In addition, the point corresponding to the constant component
is known to lie on the straight line (10). If there is additional information about the color of the constant component, we can determine
the contribution of the constant and variable components to the total
(observed) light. We shall consider the possibilities later.
(ii) Interpretation (i) formally is not the only possible. T h e
reason for this is trivial and exactly the same as in case of polarimetry. One can assume that the point (F°,Fj), corresponding to constant component, does not lie on the straight line (10). From this
point we have to reach the observed point (lying on the straight
line) by the vector whose projections are F^ar ^ FJar. In this case
the ratio ( F j / F i ) v a r will obviously vary with varying F^ar.
The
necessary variation law can be determined. Since the point with
the coordinates (F? + Ftvar,Ff + Ffar) falls on line (10), we have
Ff + Ffar = aji(Ff + Ftvar) + bji. From this the dependence of
(.Fj/Fi)var
o n F?ar
is given b y
= aji + (inFf
+ b3i - F<)/Fr.
(11)
An alternative interpretation, therefore, requires a special form of
the dependence in which the difference between the current ratio
(Fj/Fi)var
and the observed slope a,ji of the straight line is inversely
proportional to the current flux of the variable component in one
passband. It is rather difficult (if at all possible) to justify physically
this dependence. This prompts us to accept the first interpretation.
Let us note one important circumstance. If we are interested
only in the ratio ( F j / F i ) v a r we may compare the fluxes in different
measuring apertures. For this is necessary that all measurements
in each passband were made through the same aperture. Differences in aperture sizes will result in parallel shift of the straight
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line in the plane {Fi,Fj}, enabling us to compare simultaneous (or
quasi-simultaneous) d a t a obtained by different observers in different passbands through different apertures; this is vital for "joining"
the spectra of the variable components obtained in different spectral
regions (IR, optical, UV, etc.) into a single spectrum.
This method is, of course, not universal and should be applied
with caution. T h e main limitations are related to the following two
fundamental factors: the multicomponent structure of the variable
component and the limited lifetime of individual components. In
essence, this method can be used to establish colors of the variable
component which determines the photometric behavior of the object on a given time interval. When a new variable subcomponent
appears, the behavior of the points in the {Fi, Fj} plane may change.
There may be several variable components in the total light with
different time scales of variability and different amplitudes. The variations of a slowly varying component can be frequently neglected in
the analysis of fast variations (flares), because they are small on short
time scale of flares, even though the total amplitude of the variability of these smoothly varying components exceeds the amplitude of
the flare component. On the other hand, fast small-amplitude variations can sometimes be ignored in the analysis of smooth variability
because they will only increase the scatter of points in the plots of
the flux Fj versus Ft due to random errors. Moreover, it is possible in such analysis to compare the data averaged over some time
interval (for example, to take the means for a season or a synodic
month). In particular, this makes it possible to "join" together the
spectra obtained in different wavelength regions when the time of
observations do not coincide "day-to-day" but the relative positions
of points on straight lines in each region suggests that the colors of
the variable component are invariable over the entire time interval
under consideration.
The limited lifetime of the variable components severely complicates the analysis because this parameter is not known in advance.
Still, some information can be obtained by examining the light curve
of the object if it is fairly detailed.
If the colors of the newly appearing and previously existed variable components differ considerably from each other, this difference
can be seen rather clearly in the plots in which the fluxes F{ and
Fj are compared. If, however, energy distributions of the two components differ only slightly then the systematic differences can be
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of AGN
camouflaged by random errors. Consequently, it is inadmissible to
combine all observations of the object together and plot the d a t a
in the plane {Fi, Fj} without individual analysis of each d a t a point.
This may result in significant errors. Some examples are given in
Hagen-Thorn (1997).
Before going to the next item, we once more stress that this technique has two advantages. First, the information about the spectral
energy distribution of the variable source may be obtained without
knowledge of its contribution to the total flux. Second, for the construction of the relative spectral energy distribution of the variable
source in a wide spectral range it is not necessary to have simultaneous observations in all wavelengths. For instance, the variable source
may be extracted in IR and optical ranges separately, and then these
spectra may be connected by a comparison of the simultaneous d a t a
in only two spectral passbands (e.g. K and B).
T h e limitation of this technique is obvious: it is applicable in the
case when at given time range the single variable source determines
the behavior of the AGN, and variability is due to variations of its
flux level only. Often this is the case, however.
3. D E T E R M I N A T I O N O F T H E CONTRIBUTION O F T H E
C O M P O N E N T S T O T H E TOTAL FLUX
Usually the constant component is identified with the underlying
galaxy. Let us return to the space {Fu, FB, Fv} (Fig. 3). Here the
point labeled as "gal" corresponds to the constant component. Our
goal is to find its coordinates. Because it lies on straight line (8), in
accordance with (10) we have
j F f j = ajjvFy
+
{F9B
+
= aBvF^
buv
bBv,
(12)
where coefficients ajjv-, flsv, buv, i>flv are known.
Let
(13)
Replacing Fjj and Fg in (12) by Fy from (13) we obtain
- auv)
Fy(a
- asv
=
=
buv
bBv-
(14)
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Eliminating Fy we obtain the dependence of (3 on a :
¡3 = ( b u v / b B v ) < x + aBV[
1 - (buV/bBv)}.
(15)
Returning to (13) one can see that a and ¡3 are in fact the observed color indices of the underlying galaxy. For normal galaxies
there is an empirical dependence between color indices B-V and
U-V. If underlying galaxy is normal, the dependence is valid for it.
This gives another equation between a and ¡3:
13 = tp(a),
(16)
where <p is known function. Solving the system (15)—(16) one can
find a and f3.
This consideration suggests that the values a and b in (14) are
those obtained for fluxes corrected for reddening in our Galaxy and
in Eq. (16) the K-corrections are taken into account in accordance
with the redshift of the object under investigation which has to be
known.
Now, using (14) we find Fy and then Fg and Fjj from (13).
Thus, the problem is solved after accepting only one assumption
- about the normality of the color indices of the underlying galaxy.
Furthermore, after finding its color indices we may specify its Hubble
type. As a rule, the underlying galaxy is a giant elliptical.
If we have observations in only two spectral passbands, say B
and V, the problem may be solved with one more supposition. Let
us note that all galaxies with the same colour index B-V must lie
in the plane {Fv,FB}
at the ray which goes from the coordinate
origin with the slope a = Fg/Fy. After postulating the Hubble type
of underlying galaxy (usually, giant elliptical) and, hence, its color
index (and the value a ) , and taking into account the K-correction
(the redshift of the object under investigation must be known) one
can find the values Fy and Fg by solving the system
F% = agyFy
F9b =
+
bBV
*Fgy.
If the redshift is unknown, we have only the first equation of
(17). The less we know the more we have to suppose. As was shown
by Hagen-Thorn & Marchenko (1989), in this case we must postulate
the Hubble type of the host galaxy (its color index), its absolute magnitude in one of the spectral passbands, say
, within the isophote
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26 m a g / D " and curve of light growth with aperture in the galaxy.
Under these conditions one can calculate a table giving the observed
magnitude B9ohs for aperture used in observations in dependence on
redshift. Then by iterations one can find the redshift 2 and fluxes
Fg and Fy. Indeed, let us take any value of z ^ and consequently
Bg0^\
find B
For this value of redshift we can solve the system (17) and
g
o^\
If this value is not equal to B 9 o f®\ the table gives us
the value z ^ to calculate B 9 ' ^ and so on. Usually, after two or
three iterations we reach the goal. This method was developed in
the paper of Hagen-Thorn & Marchenko (1989), where the redshift
for the object OQ 530 was found. Later this value of redshift has
been confirmed by direct spectral observations.
4. RESULTS
T h e technique of extracting the variable sources described above
was used by the authors and their colleagues many times (it was used
also by Winkler et al. (1992)).
T h e most detailed investigations made by us are for the blazars
3C 345 (Hagen-Thorn & Mikolaichuk 1988, Hagen-Thorn k Yakovleva 1994, Hagen-Thorn et al. 1996), OJ 287 (Hagen-Thorn 1980,
Hagen-Thorn & Gataullina 1991, Hagen-Thorn et al. 1994, 1998)
and BL Lac (Hagen-Thorn et al. 1985, 1986). In these works and
in Hagen-Thorn et al. (1992) one can find many examples confirming the constancy of polarization parameters and spectral energy
distributions of variable sources responsible for photometric and polarization behavior of blazars. Here we give some illustrations from
these articles.
Fig. 4 shows the "flux-flux" diagram for OJ 287 in the outburst
of 1994-95 (Hagen-Thorn et al. 1998). One can see that the spectral
energy distribution of the variable source was unchanged. In Fig. 5
the absolute Stokes parameters are compared for polarization burst
of OJ 287 in 1984. Evidently, the relative Stokes parameters of the
variable source were constant.
Fig. 6 shows the "flux-flux" diagram for Sy 2 galaxy NGC 1275
(Hagen-Thorn et al. 1999). The d a t a are from Lyuty (1972, 1977).
The time range of the observations is several years. We see that the
points lie on straight lines quite well. This means that the spectral shape of the variable source was unchanged. The shifted points
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V. A. Hagen-Thorn, S. G. Marchenko
Fig. 4. A comparison of the optical fluxes for OJ 287 in 1994-95
event.
Fig. 5. A comparison of the absolute Stokes parameters in the polarization burst of OJ 287 in JD 2445782-794.
belong to one outburst of 100 days duration (J.D. 2441218-321).
Arrows show its temporal development. The points move exactly
along the straight lines both at flux rise and flux decrease. This is a
very important result because we must reject any variability mechanism resulting in changes of spectral shape of the variable source. In
particular, if the radiation is of synchrotron nature (see below) we
do not see the influence of synchrotron losses in this spectral range.
One can often find in the literature that observed reddening of the
spectrum in decreasing part of the outburst is due to synchrotron
losses in active point source. This is not the case.
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40
FB
30
20
0
10
20
30
40
50
FUt iV (mJy)
Fig. 6. The "flux-flux" diagram for the Sy 2 galaxy NGC 1275.
Usually t h e sources in t h e IR and optical ranges are extracted
separately and t h e n the spectrum in the whole spectral interval is
built by a comparison of t h e K and B fluxes. As a rule, in the
composite s p e c t r u m neither shift nor break exist. This means t h a t
the same source acts in b o t h regions.
T h e relative spectral energy distributions obtained for variable
sources are f o u n d to be well represented by the spectrum of homogeneous synchrotron source with or without high-frequency cutoff
(Hagen-Thorn & Yakovleva 1994, Hagen-Thorn et al. 1994, 1998).
Fig. 7 gives, as a n example, t h e derived spectrum of the variable
source (points with error bars) and the calculated one (curved solid
line) for O J 287 in 1984-85.
If there are no temporal changes of the relative spectral energy
distribution in t h e region of the high-frequency cutoff, the only reason for flux variability is the variation in the number of relativistic
electrons in t h e source (Hagen-Thorn et al. 1992).
O n t h e other h a n d , some flattening of the spectrum in the I R
region (but not in the optical) at the very top of the o u t b u r s t s of
1983-84 and 1994-95 was found for OJ 287 (Hagen-Thorn et al.
1994, 1998). T h e most probable explanation of this fact is synchrotron self-absorption.
T h e results of extracting the sources of polarized radiation on
different variability time scales are given in Table 1. T h e polarization
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Fig. 7. The observed spectrum of the variable source of OJ 287 in
1984-85 and the calculated one for the homogeneous synchrotron source.
Table 1. The sources of polarized radiation.
OJ 287
Interday:
Interday:
(#pref = 82°)
40 % < P < 50 %
P = 43%
BL Lac
Interday:
Long-term:
( 0 p r e f = 20°)
P = 27%
P= 5 6 %
P= 2 3 %
0o = 3°
J . D . 2443017-022
J . D . 2443786-789
1972
3C 345
Long-term:
P= 5 3 %
0o = 15°
Febr.-July 1983
00 = 101°
Oo = 73°
00 = 27°
March 15,1972
J . D . 2441803-808
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of AGN
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degree found for individual sources may be as high as 50%.
confirms their synchrotron nature.
This
3. CONCLUSIONS
T h e main results may be formulated as follows.
(a) In many cases the photometric behavior of AGN on different
time scales and in different spectral ranges may be explained by
the existence of a single variable source which has variable flux but
unchanged spectral energy distribution. In particular, this concerns
to the behavior during the flares. As a rule, the spectral shape in
the optical and UV regions is the same from the very beginning to
the end of each event.
(b) The distributions are well represented by the spectrum of
homogeneous synchrotron source with or without a high-frequency
cutoff. In some cases, at the top of the light curve in the outburst
synchrotron self-absorption may exist.
(c) The spectral shape constancy excludes all variability mechanisms resulting in a change of the spectral energy distributions (for
instance, fading because of synchrotron losses). Probably, the variability within each event is due to a variation in the number of relativistic electrons in the source.
(d) The polarization behavior is determined by a single variable
source very rarely; but if it is the case, the polarization degree for
the source can be as high as 50%. This may be considered as an
evidence of its synchrotron nature.
A C K N O W L E D G M E N T S . The authors are grateful for the support from the Nordic Research Academy for the Nordic-Baltic Advanced Research Course and from the NATO Scientific and Environmental Affairs Division linkage grant, computer network supplement
which made the connection possible. This work was partly supported
by the Russian Fund of Basic Researches under grant 98-02-16609.
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