A&A 385, 55-61 (2002)
DOI: 10.1051/0004-6361:20020145
V. A. Hagen-Thorn1,2 - E. G. Larionova1 - S. G. Jorstad1,3 - C.-I. Björnsson4 - V. M. Larionov1,2
1 - Astronomical Institute of St. Petersburg State
University, Universitetsky pr. 28, 198504 St. Petersburg, Russia
2 -
Isaac Newton Institute of Chile, St. Petersburg Branch, Russia
3 -
Institute for Astrophysical Research, Boston University,
725 Commonwealth Ave., Boston, MA 02215, USA
4 -
Stockholm Observatory, 13336 Saltsjöbaden, Sweden
Received 29 August 2001 / Accepted 22 January 2002
Abstract
An analysis is performed of polarimetric and
photometric observations of BL Lac carried out in
1969-1991 at the Astronomical Institute of St. Petersburg State
University. The distribution of polarization directions certainly
points to the existence of the preferred direction of polarization
(
)
close to the direction of the jet observed by
VLBI. High polarization degree and colorimetric data are evidence
of the synchrotron nature of the variable source. The relative
Stokes parameters are distributed normally over some mean value.
The correlations between different parameters characterizing the
flux density and polarization of the central point source allow us
to consider that in BL Lac there is a continually acting
source of polarized radiation on which the sources with randomly
distributed polarization directions are superimposed.
Key words: BL Lac objects: individual: BL Lac - techniques: polarimetric
Polarization variability is one of the main properties of blazars. The variations occur on different time scales: from dozens of years to hours and even minutes. The nature of these variations may be diverse. Usually, long-term photometric variability is explained as arising in jets in synchrotron sources. Then polarization variability may give information on the variations of the magnetic field in the jet and other properties of these sources. Rapid variability could be caused by flares in an accretion disk near the central engine. In this case the flares would most likely be of thermal origin and the polarization due to scattering. The polarization variability (if it exists) would then provide information on the geometric parameters of the scattering matter. However, a synchrotron nature of the emission in flares is not excluded. In either case an investigation of the optical polarization variability is very important tool for studying of properties of active galactic nuclei (AGNs) in the regions close to the central engine.
BL Lac is one of the most well-studied blazars. Several international campaigns (e.g. Moore et al. 1982; Brindle et al. 1985) have been organized to investigate its variability. However, polarization data were obtained only in a few of these. It is essential to note that such campaigns give information about variability on short time scales but are less useful for studying the long-term behaviour.
At the Astronomical Institute of St. Petersburg State University polarimetric observations of BL Lac were begun in 1969. The prolonged series of such observations include data for 1969-1991. The results have been published in two papers (Hagen-Thorn et al. 1984, 1994). The preliminary results of the analysis of part of these data may be found in two other papers (Hagen-Thorn et al. 1985, 1986). Here we analyze the entire mass of observational data that include the results of polarimetric observations on 517 dates.
All polarimetric data were obtained with a photoelectric polarimeter at the 48-cm reflecting telescope of the Byurakan station of the Astronomical Institute. A photomultiplier with a multialkaline cathode was used in all observations, usually performed without filters. More details may be found in Hagen-Thorn et al. (1984).
![]() |
Figure 1: The variations with time of several intensity and polarization parameters for point source; the mean values of some of these are shown by dotted lines. |
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The value of polarimetric observations strongly increases when these are accompanied by photometric data. Unfortunately, we have very few simultaneous photoelectric estimations of the brightness of BL Lac; however, the object was intensively observed in our photographic monitoring program of AGNs in B band (Johnson system) with typically 3-5 photographic estimates of BL Lac's brightness per night. The data have been published in a series of papers in Contributions of the Astronomical Observatory of St. Petersburg University (see Hagen-Thorn et al. 1991 and references therein). These data, as well as data taken from the literature, allow us to construct the combined light curve of BL Lac that we use below.
At this point we make some important remarks:
The histogram for observed directions of polarization (the
preferred direction of the electric vector)
is presented
in Fig. 2a. Here we use the data for all 517 nights of
the polarimetric observations (the number of nights with
simultaneous estimates of the total intensity and polarization
parameters is reduced to 451 because the brightness estimates are
not available for some nights). We see that the bulk of data lies
near
.
Comparison with Fig. 1
shows that this is not due to uneven temporal spacing of the
observations. Therefore, we assert that BL Lac has a
preferred direction of polarization in the optical region.
![]() |
Figure 2: The distributions of observed polarization directions a) and relative Stokes parameters b), c). |
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The histogram of observed values of
has a narrow maximum
near
and wings reaching to
.
Figures 2b,c give the histograms of the relative
Stokes parameters
,
.
Use of
the
-test reveals that both distributions may be
represented (at a significance level of 5%) by normal
distributions (these are also given in Figs. 2b,c). The
parameters of the normal distributions are as follows:
,
;
,
,
.
We have verified whether the results are similar for the central
point source only. Again the -test shows that the
distributions are normal with parameters
,
,
,
,
(
.
The location of all 451 points for
the central source in the plane
is shown in Fig. 3 (dots). The point
(
)
is indicated by
the black square. The errors in the relative Stokes parameters are
less than 2% (the cross in the upper-left corner). The strong
polarization variability is stressed by the fact that the
dispersion is much higher than the errors.
![]() |
Figure 3:
The plane
![]() ![]() |
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The first panel of Fig. 1 shows that flux variations are characterized by numerous outbursts. The time scales of these outbursts are different: from an entire season to several days, the minimum timescale to which our observations are sensitive. Such behaviour in the flux variations of BL Lac has been described many times (e.g., Webb et al. 1988; Hagen-Thorn et al. 1997).
Visual inspection of panels 2 and 3 of Fig. 1 shows that
contrary to the behaviour of the parameter I, the Stokes
parameters Q and U that describe the polarization behaviour
are much less variable. With the exception of several points, all
others lie near the median level. The relationship between these
absolute Stokes parameters is shown in Fig. 4. Here the
dotted lines give the mean values of the parameters Q (
)
and U (
= 0.090), and the solid lines represent
the results of the least square fits. The slopes of the lines are
,
.
Their distinctions with respect to the 0-slope
are not significant. Therefore, on average the Stokes
parameters Q and U are independent of I.
![]() |
Figure 4: The connection between the absolute Stokes parameters for the entire data. |
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One can see that the scatter of the values Q and U relative to mean is higher for high values of I. This is due primarily to the fact that I is included as a factor when finding Q and U from an observation. Hence, the same errors in the observed polarization parameters lead to higher scatter when I is higher.
Since the variations of the parameters Q and U are small while
the total flux I is strongly variable, the degree of
polarization should depend on the total flux. Figure 5
confirms this: the highest degree of polarization occurs at lower
flux levels, although this is only an average tendency. For
example, in four cases (out of six) when mJy the degree
of polarization is quite high (between 12% and 20%). As
expected, the same behaviour as in Fig. 5 is seen in the
dependence of the relative Stokes parameters px and
py on I (Fig. 6).
![]() |
Figure 5: The dependence of the degree of polarization on flux. |
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![]() |
Figure 6: The dependencies of the relative Stokes parameters on flux. Dotted lines give the mean values of the Stokes parameters. |
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It is evident from Fig. 3 that there must be a
dependence between the degree of polarization and its direction:
the strongest polarization has to occur when the position angle is
near the preferred value. Figure 7 shows that this is
indeed the case: the distribution of degree of polarization is
almost symmetric with respect to the preferred direction of
.
(Note that some points for
may be transported to the right in the region
of
by adding
).
![]() |
Figure 7: The connection between the degree and direction of polarization. |
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![]() |
Figure 8: The connection between the direction of polarization and total flux. |
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The last dependence which we consider in this section is that
between the polarization direction and total flux
(Fig. 8). Although there is considerable scatter, one
can see that the points corresponding to lower fluxes group more
closely around the preferred direction than do the higher flux
points. To illustrate this we construct the distributions of
for two intensity intervals:
mJy and
mJy (Fig. 9). The difference in the shape of the
distributions is evident.
![]() |
Figure 9: The difference in the shape of the distributions of position angle for two intervals of flux. |
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In previous section we discussed the gross variability properties
of the BL Lac's central point source. In this section we
consider the behaviour on shorter time scales. As is apparent in
Fig. 1, the behaviour of the variable source is
different for different observational seasons. For example the
difference between the seasons of 1989 and 1990 is striking. In
the first one the flare in I is accompanied by variations in the
parameters Q and U, in the second there are no noticeable
variations in Q and U while a flare in total flux is evident.
Sometimes we see correlated variations between the absolute Stokes
parameters: in 1973 (JD 2441860-2442014) there is a visible
correlation between I and Q, and in 1975 (JD 2442626-2442723)
- between I and U. The absolute Stokes parameters for these
seasons are compared in Figs. 10a,b.
![]() |
Figure 10: The dependencies of Q and U on I for two seasons: 1973 a) and 1975 b); r - correlation coefficients, the lines are drawn by least squares method. |
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The correlation coefficients and the best straight-line fit to the
data (found by least squares method) are given in
Fig. 10. The equations of the straight lines are as
follows:
Q=![]() |
|
U=![]() |
(1) |
Q=![]() |
|
U=![]() |
(2) |
There are seasons when no correlation exists between the
parameters I and Q or U. As an example, in Fig. 11
the data are given for 1980 (JD 2444456-2444583). Here we see the
same behaviour as found in the previous section for all the data:
when the flux increases the degree of polarization becomes lower
while the parameters Q and U, on average, do not change. The
equations of the best-fit straight lines are as follows:
Q=![]() |
|
U=![]() |
(3) |
![]() |
Figure 11: The same as in Fig. 10 but for 1980 (two lower panels); additionally the dependence of the degree of polarization on the total flux is given (upper panel). |
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The rapid optical variability, power-law spectrum, (Hagen-Thorn et
al. 1992, 2000), strong and highly variable
optical polarization of BL Lac point to synchrotron
nature of the variable sources. In this case the presence of a
preferred direction of polarization indicates a preferred
direction of the underlying magnetic field in the region where the
radiation comes into existence. For BL Lac this direction
(
)
is nearly orthogonal to the direction of the
movement of VLBI components in the 1980s,
(Mutel et al. 1990). Furthermore, the magnetic field is
even closer to perpendicular to the jet axis on 1-2 milliarsecond
scales of
(Denn et al. 2000) as
one can expect if the optical radiation arises in shocks in the
jet relatively close to the central engine (Marscher &
Gear 1985).
Such behaviour of the polarization at radio wavelengths is not
unusual and can be explained by models involving transverse shocks
moving along the jet (Hughes et al. 1985). For
example, Aller et al. (1996) report a preferred
direction of polarization for BL Lac at centimeter
wavelengths of about
in 1980's and note, however,
considerable variations of the direction of polarization which
they explain by oblique shock model. In general, the behaviour of
polarization in the optical and centimeter wavelengths is similar
though the data are perhaps related to the different regions of
the jet. On the other hand, this similarity shows that the
underlying magnetic field is stable, on average, on large scales.
Figures 2 b,c and 3 formally allow one to
explain the variability of polarization direction for
BL Lac by a model in which components with randomly
distributed polarization directions are superimposed on a
long-lived underlying source of polarized radiation with
.
Such a model has been suggested by
Hagen-Thorn (1980) to explain polarization variability of
the blazar OJ 287.
In this model the general photometric and polarization behaviour depends on the number and properties of superimposed components. The analysis of the short-term variability (not considered in this paper) shows that as many as tens of variable components may act simultaneously (Brindle et al. 1985) and that the degree of polarization of some of these may be as high as 50%, with different polarization directions (Hagen-Thorn et al. 1986).
A consideration of the observed dependencies between flux level, degree of polarization and its direction confirms the reality of the model and allow us to specify some properties of the underlying source.
The concentration of polarization angles near the preferred
direction (
)
at low and moderate brightness levels
(Figs. 8, 9) reveals a significant
contribution of the underlying source to the total flux compared
with that of variable components. The underlying source dominates
at low brightness levels (I<1 mJy), as indicated by the small
scatter of the position angle of polarization near
.
At low brightness levels (corresponding to a small number of
variable components), the appearance of a new, highly polarized
component with
results in higher observed
polarization along the preferred direction (the highest degrees of
polarization in Figs. 5, 7). On the other
hand, a new polarized component with position angle of
polarization perpendicular to the preferred direction cancels the
polarization of the underlying source, causing low observed
polarization. This explains why Fig. 5 shows a
significant scatter of the degree of polarization when the flux is
low.
A large number of randomly polarized components with similar fluxes result in moderate (even low) variability of the polarized flux, since polarizations with different position angles cancel each other. The brightness, in contrast, can vary more widely due to the linear dependence on the number of components (panels 1-3 in Fig. 1, Fig. 4). Newly born polarized components can cause a decrease in the observed polarization despite the rise in total flux. Such an inverse dependence of the degree of polarization on the flux is apparent in Fig. 5. When the number of randomly polarized components is large the contribution of the underlying source weakens and the shape of the distribution of the position angle of polarizaton changes relative to that at low brightness levels (see Figs. 8, 9).
At high brightness levels (I>3 mJy), Fig. 8 shows
uniform scattering of
within
.
Therefore, one
expects the brightness variability of underlying source to be
moderate such that the source can not dominate when the flux is
high. It is most likely that a newly born bright component is
responsible for the photopolarimetric behaviour of the object at
high brightness levels.
As was shown previously (for details see Hagen-Thorn &
Marchenko 1999), when the variability is due to a single
dominant component with constant relative Stokes parameters and
variable flux, the dependence of the absolute Stokes parameters
Q and U on I must be linear with the slope of the dependence
giving the relative Stokes parameters of the variable component.
Figure 10 shows the dependence of Q and U on I for
two seasons. Though the correlation coefficients are not very
high, the straight lines represent the dependence sufficiently
well. One may conclude that the general behaviour of the object
can be represented by the existence of components with the
relative Stokes parameters determined by the slopes of the
corresponding dependence. For seasons 1973 and 1975 we obtain from
(1) and (2), respectively,
,
,
,
and
,
,
,
.
Note that in both cases the polarization direction does
not coincide with the preferred angle. However, these values must
be considered only as average ones since in reality the
behaviour at each moment is determined by the combined action of
several short-lived variable components. These must be very high
polarized because the combined polarization is quite high (more
than 10%).
In conclusion, the model of a continually acting, underlying source of polarized radiation plus components with randomly distributed polarization directions and high degrees of polarization explains quite well the observational data. Future combined high-frequency VLBI polarimetric imaging and optical-IR polarization monitoring will allow a closer examination of the relationship between the relativistic jet and the magnetic field in the most compact regions of blazars.
In the near future we plan to analyse the temporal behaviour of BL Lac on time scales shorter than those considered in present work.
Acknowledgements
This work was supported by Federal Program "Integration'' (grants A0007 & K0232) and Russian Fund of the Basic Researches (grant 98-02-16609). V.A.H.-Th. thanks the Stockholm Observatory for hospitality. S.G.J. was supported by US National Science Foundation grant AST-9802941. The authors thank Alan Marscher for a constructive discussion.