Download Radiative Processes in Astrophysics. Radio Polarization

Radiative Processes in Astrophysics.
Radio Polarization
Cormac Reynolds
May 24, 2010
Radio Polarization
Topics
Description of the polarized state – Stokes parameters. (TMS §4.8)
Why are radio sources polarized? (RL §6.5, L §18.1.6)
Faraday rotation. (L §17.3.4)
Polarization calibration. (TMS §4.8)
Bibliography
TMS: Interferometry and Synthesis in Radio Astronomy (Second Edition), Thompson, Moran
and Swenson. Wiley Interscience
RL: Rybicki and Lightman, Radiative Processes in Astrophysics. Wiley Interscience
L: Longair, High Energy Astrophysics (Second Edition). Cambridge University Press
Describing the Polarized Wave – Stokes Parameters
The polarized state of a wave can be described in terms of 4 parameters, known as Stokes
parameters.
I – gives the total energy flux or the ‘total intensity’
Q, U – give the linear polarization.
V – gives the circular polarization. V ∼ 0 intrinsically for synchrotron radiation.
The complex polarization, P, is then given as
P = Q + iU = mIe2iχ = pe2iχ
(1)
where m is the fractional polarization, p is the polarized flux density and χ is the polarization
position angle (= electric vector position angle, EVPA).
We may also note:
p
p = Q2 + U 2 + V 2
m = p/I
(2)
1
U
χ = tan−1
2
Q
The Poincaré sphere provides a means for visualising the
Stokes parameters. The point P represents a given polarization state and lies on the surface of the sphere whose
radius is the total polarized power.
1
Relating the Stokes Parameters to Interferometry
The elements of radio interferometers are equipped with either linearly or circularly polarized
feeds. The correlations formed between the orthogonal modes are related to the Stokes
parameters by:
Circularly polarized feeds (most common in VLBI)
Measure right circular polarization (RCP or R) and left circular polarization (LCP or L). The
correlations that can be formed between antennas j and k are
Rj Rk∗ = I + V
Lj L∗k = I − V
Rj L∗k = Q + iU
(3)
Lj Rk∗ = Q − iU
Linearly polarized feeds (e.g. Westerbork, ATCA)
Measure two perpendicular modes, p and q
pj pk∗ = I + Q cos 2χ + U sin 2χ
qj qk∗ = I − Q cos 2χ − U sin 2χ
pj qk∗
qj pk∗
= I − Q sin 2χ + U cos 2χ + iV
(4)
= I − Q sin 2χ + U cos 2χ − iV
2
Why Radio Sources are Polarized
The radio emission from most bright radio sources arises from Synchrotron Radiation ⇒ linearly
polarized.
The radiation from a single relativistic e− gyrating around a magnetic field is elliptically polarized.
For an ensemble of e− ’s with a smooth distribution of pitch angles the opposite senses of the
elliptical polarization will cancel out resulting in linearly polarized radiation. If the e− ’s have a
power law distribution the fractional polarization (m) in the presence of a uniform magnetic field is
given by:
α+1
(5)
m=
α + 5/3
where α is the spectral index of the source. E.g. if α = 0.5 (typical of synchroton emitting
sources), m = 0.7.
Real radio sources generally have m < 0.1 ⇒ tangled magnetic fields, cellular depolarization,
Faraday depolarization, etc. Higher m can be seen as the result of ‘repolarization’.
3
Depolarization
Radio sources show low polarization compared with simple synchrotron models.
Cellular depolarization
The magnetic fields in the sources are not uniform but have small scale structures. Consider a
source composed of many cells in each of which the magnetic field is randomly orientated
(Figure 2). The polarization contribution
from each cell adds vectorially. If there are N cells within
√
the telescope beam, m → m/ N.
Cellular depolarization. Arrows represent the dominant magnetic field direction in the cell.
Radio sources can also be affected by Faraday depolarization which we will return to later.
4
Repolarization
Repolarization by field compression
Compression of an initially random magnetic field (e.g. by a shock) modifies components of the
field perpendicular to the direction of compression. A random field viewed along the axis of
compression will still appear to be random. If a random field is compressed into a plane and is
viewed in that plane, it will appear indistinguishable from an ordered field and will produce
polarization at the level given by equation 5. If the field is only partially compressed or is viewed at
some angle to the plane of compression, then the observed polarization will be less than this.
Compression of a cube containing an initially random magnetic field (Laing 1980, MNRAS).
5
Repolarization
The observed polarization for a compressed, initially random field is given by:
m=
α+1
(1 − k 2 ) cos2 α + 5/3 2 − (1 − k 2 ) cos2 (6)
where the first term on the RHS is the same as equation 5, k is the compression factor (k = 1 ⇒
full compression) and is the viewing angle measured in the frame of the source (relativistic
aberration is important for AGN jets).
Repolarization by field shear
Shear layers result from the interaction between the surface of an expanding source and the
surrounding medium. Essentially, a component of magnetic field gets ‘stretched out’ along the
direction of motion in a boundary layer resulting in the development of a uniform component of
magnetic field, with direction parallel to the direction of motion.
6
Faraday Rotation I
For synchrotron radiation, the rest-frame polarization position angle can be used to infer the
direction of the magnetic field. For optically thin emission, the EVPA is perpendicular to the
magnetic field, for optically thick emission it is parallel. However, interpretation of the observed
EVPA is complicated by the presence of Faraday rotation. Faraday rotation is a rotation of the
angle of polarization and occurs when electromagnetic radiation propagates through an ionised
plasma containing cold (thermal) electrons and a magnetic field.
Linearly polarized radiation can be decomposed into a superposition of a right circularly polarized
(RCP) wave and a left circularly polarized (LCP) wave. Consider 2 orthogonal states of the
electric field
Ex = îE0 cos(kz − ωt)
Ey = ĵE0 sin(kz − ωt)
(7)
⇒ E(z, t) = E0 [î cos(kz − ωt) + ĵ sin(kz − ωt)]
LCP.mp4
rcp.mp4
RCP: the electric field vector rotates counter-clockwise when viewed with the wave approaching
the observer. LCP: rotates clockwise.
7
Faraday Rotation II
Similarly one can have a wave described by
E(z, t) = E0 [î cos(kz − ωt) − ĵ sin(kz − ωt)]
(8)
which is left circularly polarized (LCP). The superposition of an LCP and RCP state gives plane
(linear) polarization if the amplitudes of the LCP and RCP states are equal. The resultant of the
superposition is
E(z, t) = (E0 + E0 )[î cos(kz − ωt)+
(E0 − E0 )ĵ sin(kz − ωt)]
(9)
⇒ E = 2E0 î cos(kz − ωt)
which is a plane polarized wave.
As the plane wave propagates through an ionised medium, the force on an e− in the gas is
e(E + (v × B)) where E is the wave electric field and this force will be balanced by the centripetal
force of the electron (cf. dipole moment of e− ):
e(E + Bωr ) = −me r ω 2
(10)
The e− displacement is given by:
−e
r =
m
"
#
1
E
e
ω2 ± m
Bω
(11)
8
Faraday Rotation III
The ± in this equation is because the e− ’s rotation can be either in the same or the opposite
direction as the LCP and RCP mode respectively. Now, the relative permittivity of the plasma () is
given by:
"
#
ne e2
1
=1−
(12)
0 me ω 2 1 ± eB
ωme
Noting that the plasma frequency (νp ) is
νp2 = (ne e2 )/(4π 2 0 m)
(13)
and ω = 2πν we find
=1−
νp2
ν2
"
1
1±
#
eB
ωme
(14)
and so the relative permittivity has 2 values depending on the direction of the e− ’s motion. For
one of the fundamental modes (RCP and LCP) it will√be in the same direction, for the other it will
be in the opposite. The wave velocity is given by c/ .
The right and left circularly polarized components of the linearly polarized wave will therefore
propagate at different speeds through the plasma as they will experience different refractive
9
Faraday Rotation IV
indices and this leads to a rotation of the angle of linear polarization. We can calculate the
difference in the speeds (∆v ).
v12 − v22 = (v2 + ∆v )2 − v22 ∼ 2v2 ∆v
ff

1
1
⇒ 2v2 ∆v = c 2
−
1
2
⇒ 2v2 ∆v ∼
Substituting for (eqn 14) and assuming
eB
mω
(15)
c 2 (2
− 1 )
2
<< 1
2v2 ∆v =
2c 2
` νp ´2
c2
` νp ´2
⇒ ∆v =
ν
2
eB
mω
eB
ν
mω
2 v2
(16)
Since v2 ∼ c and ∼ 1
∆v = c
“ ν ”2 eB
p
ν
mω
(17)
10
Faraday Rotation V
Finally substituting νp (eqn 13)
∆v ∼
ne e2
eB
c
4π0 m 2πmν 3
ne B
⇒ ∆v ∝ 3
ν
⇒ ∆v ∝ ne Bλ3
(18)
Consider again our 2 circularly polarized modes, now propagating with speeds v1 and v2
respectively. In one period of oscillation (τ ) the relative phase difference (φ = 2πl
) between the
λ
two modes is 2π∆v τ /λ. Since τ = ν1 = λc , the angle of rotation of the polarization plane (Θ) per
oscillation period is then given by 2Θ = 2π∆v /c. For a given frequency the total rotation angle (θ)
is proportional to the distance travelled by the wave (D) divided by λ.
Z
π D ∆v
(19)
θ=
ds
λ 0 c
We know ∆v from eqn 18 and with appropriate choice of units we get
Z D
θ = 8.1 × 103 λ2
ne Bk ds
(20)
0
11
Faraday Rotation VI
where θ is measured in rads, ne is in m−3 , λ is in m, Bk is the line of sight magnetic field in Tesla
and D is in parsecs. This equation is normally written as
θ = RM λ2
(21)
where
RM = 8.1 × 103
D
Z
ne Bk ds
(22)
0
is the rotation measure in units of rad m−2 .
Faraday rotation is characterised by a wavelength dependence of the degree of rotation. In the
simplest case of a resolved, homogeneous foreground Faraday screen the observed EVPA is
related to the rest-frame EVPA by
χobs = χ0 + RM λ2
(23)
where χobs is the observed EVPA and χ0 is the rest-frame EVPA.
Faraday rotation can arise as a result of thermal gas either (i) within the volume of material that is
emitting the radiation, or (ii) external to the emitting material. The former situation is known as
internal Faraday rotation, the latter as external Faraday rotation.
12
External Faraday Rotation
For a resolved external Faraday screen located between the synchrotron emitting plasma and the
observer, equation 23 completely describes the effect of the screen on the source polarization.
The situation is somewhat complicated if the Faraday screen is not resolved and there is a
distribution of Faraday depths within a single beam of the telescope. Radiation from a source with
uniform polarization position angle will pass through different Faraday depths and thus the electric
vectors will be rotated by different amounts. Since linear polarization is a complex quantity, the
telescope effectively does a vector sum of the polarizations within the beam. Thus, if there are
fluctuations in the Faraday depth across the beam then this results in a departure from the simple
λ2 law given by equation 23 and leads to depolarization (a decrease in the percentage
polarization with increasing wavelength).
13
Internal Faraday Rotation
Faraday rotation can occur within the ionised plasma responsible for the observed synchrotron
radiation. Since a single electron’s contribution to the Faraday rotation is inversely proportional to
the square of the electron’s effective mass (equation 18), relativistic electrons such as those
responsible for synchrotron radiation do not give rise to significant Faraday rotation. However, a
population of thermal (cold) electrons within the synchrotron emitting plasma can produce internal
Faraday rotation. Internal Faraday rotation can often be distinguished from external Faraday
rotation. Internal Faraday rotation tends to induce depolarization and a departure from a simple
λ2 rotation as a result of the different path length through the Faraday screen which is traversed
by radiation from the front and back of the source. For realistic geometries, internal Faraday
rotation cannot produce a rotation greater than π/2 rads. This constraint is even tighter for a
spherical geometry where the maximum rotation is ∼ π/4 rads.
14
Polarization Calibration in VLBI
The polarization calibration of any radio interferometer is in principle the same. However, the high
resolution of VLBI introduces some additional practical problems. Nonetheless, most of what
follows is equally applicable to connected-element interferometers as to VLBI arrays.
In previous lectures you have seen the calibration technique required to produce total intensity
maps from interferometer data – a priori amplitude calibration, fringe-fitting, self-calibration and
deconvolution. The calibration of polarization data is largely similar but with a few extra steps
required to produce well-calibrated cross-hand visibilities (i.e. the RL and LR correlations which
provide the Stokes Q and U parameters).
15
Instrumental Polarization
In real observations using dual polarized feeds the signal measured on one polarization is
corrupted by “leakage” from the orthogonal sense. As the typical polarization of radio sources is
also only a few percent this must be removed before reliable polarization maps can be made. The
instrumental response of an antenna to the radiation field can be written as
R = GR [ER e−iφ + DR EL eiφ ]
L = GL [EL eiφ + DL ER e−iφ ]
(24)
where R and L are the measured RCP and LCP signals respectively, GR and GL are the antenna
gains in RCP and LCP respectively, ER and EL are the true RCP and LCP electric fields from the
source respectively, DR and DL are the fraction of the orthogonal sense that leaks through to RCP
and to LCP respectively, and φ is the parallactic angle (PA).
The PA is the angle between
the lines on the celestial
sphere joining the source to
the north celestial pole and
the source to the antenna’s
zenith, which measures the
orientation of the feed with
respect to the source.
Diagram illustrating the parallactic angle (φ) and how it changes as a
source moves across the sky.
16
Instrumental Polarization
The correlations in equation 3 can then be rewritten in terms of the R and L instrumental
responses, e.g.
∗
∗
Rj Rk = GRj GRk
“
”
“
”
∗ −i φj −φk
∗
∗ −i φj +φk
ERj ERk e
+ DRk ERj ELk e
+
"
“
”
“
”#
∗ i φj +φk
∗
∗ i φj −φk
DRj ELj ERk e
+ DRj DRk ELj ELk e
∗
∗
Rj Lk = GRj GLk
“
”
“
”
∗ −i φj +φk
∗
∗ −i φj −φk
ERj ELk e
+ DLk ERj ERk e
+
(25)
"
“
”
“
”#
∗ i φj −φk
∗
∗ i φj +φk
DRj ELj ELk e
+ DRj DLk ELj ERk e
.
Ignoring terms of higher order than D 2 and cross-hand terms and assuming V = 0 (so that
hERj i ≈ hELj i) , the ratio of the cross- to parallel-hand terms can be written as e.g.
"
∗
∗ i
GRj GLk
hERj ELk
Rj L∗k
=
e−2iφj
∗
∗
∗
Lj Lk
GLj GLk hELj ERk i
i
∗ 2i(φk −φj )
+DRj + DLk
e
(26)
where the angle brackets indicate quantities that have been time averaged by the correlator.
17
Instrumental Polarization
The first term inside the square brackets in equation 26 is the source polarization and can be set
to zero if unpolarized sources are observed, giving:
∗ h
i
GRj GLk
Rj L∗k
∗ 2i(φk −φj )
(27)
e
=
DRj + DLk
∗
∗
Lj Lk
GLj GLk
This is the equation of a circle of radius |DLk | centred on DRj (see Figure 6).
100
PLot file version 1 created 11-NOV-2002 17:43:03
Imag vs Real for 3C84 1.7G.MULTI.1 FG # 1
IF 1 CHAN 1 STK RL/RR
100
LA - PT ( 5 - 9 )
80
80
60
60
40
40
LA - PT ( 5 - 9 )
20
Ratio x 1000
Ratio x 1000
20
PLot file version 2 created 11-NOV-2002 17:43:09
Imag vs Real for 3C84 1.7G.MULTI.1 FG # 1
IF 1 CHAN 1 STK RL/RR
0
0
-20
-20
-40
-40
-60
-60
-80
-80
-100
-100
-100
-100
-50
0
Ratio x 1000
50
100
-50
0
Ratio x 1000
50
100
The plot on the left shows the cross- to parallel-hand ratio (cf. equation 26) for 2 VLBA antennas
at 1.7 GHz, for the bright unpolarized source 3C 84 after the source has been self-calibrated but
before the instrumental D-terms have been corrected. The D-terms trace a circle due to rotation
with parallactic angle. The plot on the right shows the same but with the D-term correction applied.
18
Polarization position angle calibration
The complex gains GR and GL of the antennae are determined during self-calibration. This is
done relative to a reference antenna whose gain phases are arbitrarily set to zero. Although this
has no serious consequences for total intensity mapping (apart from the loss of absolute position
information) it results in the introduction of an arbitrary phase offset (equal to the RL phase
difference at the reference antenna) to the RL and LR correlations which produces a
corresponding rotation of χ in the polarization map.
The polarization position angle of connected-element interferometers such as the VLA can easily
be calibrated by observations of sources with known integrated EVPA. Unfortunately no such
sources are known on VLBI scales. Instead, we observe a source with compact polarization
structure simultaneously with the VLBI array and with a single dish/connected-element
interferometer.
If the source has sufficiently compact polarization structure then all the polarized flux detected by
the low resolution instrument (e.g. VLA) should also be present in the VLBI observation. As a
result, the integrated polarization position angle in the VLBI observation should be the same as
that of the VLA. It is important that the time between the two observations be as short as possible
as many compact polarized sources are variable on timescales of days or less.
19
Matrix Formulation
A more elegant mathematical description of polarimetry is given by the matrix formulation of
Hamaker, Bregman and Sault (see TMS §4.8).
„
«
EL
~ =
The EM field can be described by a complex vector E
ER
~
Any linear effect can be described in terms of a 2 × 2 (Jones) matrix, thus E~0 = Jn Jn−1 . . . J1 E
An interferometer measures coherencies (E) between the EM field at the individual elements
(j, k), giving a visibility matrix V:
„
«
ERR ERL
~j E
~ †i =
(28)
Vjk = hE
k
ELR ELL
The Jones matrices describing all the signal propagation effects are cumulative and may be
multiplied to give a single Jones matrix (Jj ) for each antenna, so
~ k E)
~ † i = Jj hE
~E
~ † iJ†
Vjk = hJj E(J
k
(29)
The true source coherency (B, or source brightness) is then related to the measured visibility by:
Vjk = Jj BJ†k
(30)
and this is known as the Measurement Equation.
20
Matrix Formulation
Some Jones matrices describing typical propagation effects are:
„
«
exp(iθ)
0
Jrotn =
0
exp(−iθ)
„
«
1
DR
Jleakage =
DL
1
„
«
GR
0
Jgain =
0
GL
(31)
The simple form of the Jones matrices for describing most effects and the fact that polarization
effects are intrinsically accounted for makes this a very attractive formalism for describing radio
instruments. casa already incorporates a modified version of the Hamaker ‘Measurement
Equation’ but older (and more widely used) packages do not (hence the brief treatment here).
21
Where’s the Science?
A few highlights:
Laing-Garrington effect
Magnetic field alignments in quasar cores and lobes – helical fields?
Faraday rotation as a probe of thermal gas content
Kinematic constraints for parsec-scale jets
Circular polarization has implications for jet composition – difficult to measure but may
answer some important questions
Polarization gives us information about the magnetic field orientation in the sources, the degree of
ordering in the magnetic fields and the thermal gas content – much of this information cannot be
obtained in any other way.
Can help us distinguish between thermal and non-thermal emission mechanisms – thermal
emission is not generally polarized.
22
Laing-Garrington Effect
The cause of the one-sidedness in the jets of otherwise
symmetrical extragalactic radio sources was a subject of
some controversy for many years.
The evidence for bulk relativistic motion suggested that the
one-sidedness could simply be the result of Doppler
boosting of the approaching jet, and Doppler diminution of
the receding jet but this was hard to confirm. Alternative
models such as the ‘flip-flop’ model could not be ruled out.
Laing, Garrington et al. observed a sample of double-lobed
FR II sources with asymmetric jets and showed that the
lobe on the jet side was less depolarized than the
counterjet side in almost all cases (see the example).
Most obvious explanation is that the depolarization is
caused by differential Faraday rotation through the ionised
medium surrounded the radio source. The side with the jet
is closer to us and therefore seen through a smaller depth
of depolarizing medium.
© 1988 Nature Publishing Group
Best evidence yet that the asymmetries in jet sidedness
are due to relativistic Doppler boosting.
23
Faraday Rotation
Faraday rotation measurements require simultaneous observations at at least 3 frequencies to fit
for the λ2 dependence. High resolution is important because polarization is a complex quantity –
multiple components within the telescope beam can cancel each other out. Also must be wary of
optical depth effects (electric vector ⊥ to B for optically thin emission, k for optically thick ⇒ 90◦
rotation).
Recent multi-frequency VLBI observations of quasars have revealed non-uniform Faraday rotation
on parsec scales. The rotation measures (RM) can be very high close to the core (associated with
the active galactic nucleus) but quickly decrease along the jet (see Figure 22). At distances of
more than a few tens of parsecs from the core, the RM is generally consistent with the RM of our
own Galaxy.
24
Faraday Rotation
Rotation measure map of the weak emission line blazar BL Lac
made using VLBA observations at 5, 8 and 15 GHz. The contours
are the 5 GHz total intensity. The RM in the core (northernmost
component) is enhanced with respect to the jet. This is a little
surprising as BL Lac has very weak emission lines (indicating a lack
of thermal gas on scales < 0.1 pc) yet appears to have similar gas
content on scales of ∼ 1 pc as some strong emission line quasars
(Reynolds et al. 2001 MNRAS 327, 1071).
Plot of χ Vs λ2 for the core and 3 jet components.
25
Faraday Rotation
Local regions of enhanced Faraday rotation are sometimes seen near bends and bright regions in
the jet (see Figure 8). This is evidence that the jet bends and brightness enhancements are
caused by an impact with the intergalactic medium, rather than, say, a hydrodynamic instability.
Nan et al. 1999
On the left is total intensity contours with degree of polarization in gray-scale. On the right is
a close-up of the region where the jet brightness is enhanced showing the RM. There is a RM
gradient across the bright component. Nan et al. A&A 344, 402.
26
Faraday Rotation
Faraday rotation can be used to constrain the quantities of thermal gas located close to the core,
which may have implications for unified schemes (see the cartoon in Fig 9). However, sources
must be compared using observations with the same linear resolution to account for the steep RM
gradients near the core.
Cartoon model of the environment around an AGN (Taylor 2000, ApJ)
27
Faraday Rotation
Faraday rotation measurements are important for interpreting magnetic field alignments at all but
the highest radio frequencies. RMs of 5 × 103 rad m−2 have been measured in quasar cores ⇒
rotation of > 40◦ even at 22 GHz.
When Faraday rotation is observed, the interpretation depends on whether the Faraday screen is
resolved or not. If the Faraday screen is not resolved, a situation similar to the cellular
depolarization illustrated earlier occurs. Even with just two regions of differing RM this leads to a
departure from a simple λ2 rotation. For this reason, good agreement with a λ2 law is often taken
as proof that the Faraday screen is resolved and the whole Faraday screen within the telescope
beam can be well described by a single RM.
28
Faraday Rotation
However, over a limited (but sometimes quite large) range in wavelength the departure from a λ2
law may not be apparent. Figure 10 shows an example of the integrated RM that would be
produced by 2 components with very different intrinsic RMs, but which are not resolved from each
other. Using observations at 5, 8 and 15 GHz (the most popular for RM measurements) the
departure from the λ2 law would not be detectable even if the EVPA was determined to an
accuracy of 3◦ (which is quite good for VLBI). Beware!
EVPA as a function of λ2 for an unresolved source with 2 components of the Faraday screen. The
RM of one component is −550 rad m−2 , the RM of the other is −100 rad m−2 . The integrated
RM is −204 rad m−2 . The dotted line is the EVPA derived for the 2 component model. The
triangles mark the EVPA at 5, 8 and 15 GHz with an error bar of ±3◦ and the dashed line is the
best fit straight line to the EVPA at these three points. Observations of this component at these 3
frequencies would not detect a departure from a λ2 law and could lead to the incorrect assumption
that the screen was resolved.
29
Magnetic Field Alignments in Blazar Jets
The rest-frame EVPA is perpendicular to the magnetic field for optically thin synchrotron emission,
and parallel for optically thick synchrotron emission.
The jets in blazars are optically thin (except very close to the core).
Polarization studies suggest that blazars can have magnetic fields which are either aligned with
the jet direction or perpendicular to the jet direction.
Perpendicular magnetic fields can be given by shock compression (see earlier) or by a toroidal
magnetic field. Parallel magnetic fields could be due to a uniform longitudinal magnetic field or a
shear interaction with the surrounding medium.
The weak-lined objects (BL Lacs) tend to have perpendicular magnetic field directions, the
strong-lined objects (OVV quasars) tend to have parallel magnetic fields.
Suggests that the quasars are dominated by a uniform longitudinal component of magnetic field,
while BL Lacs have a tangled magnetic field which is enhanced by compression due to shocks.
30
Magnetic Field Alignments in Blazar Jets
Evidence for Helical Magnetic Fields
Helical magnetic fields can give both parallel and perpendicular electric vectors depending on the
pitch angle of the magnetic field. Figure 11 shows the RM gradient across the jet in 3C 273. The
variation in RM across the jet is consistent with a helical magnetic field (in fact it is hard to explain
by any other mechanism). The variation in RM is due to changes in the parallel component of the
magnetic field (Bk ) as the magnetic field lines wrap around the jet.
Good lateral resolution of a jet is rare, but such signatures may provide the key to determining
how common helical magnetic fields are in blazars. Also note that if the B-field helix is wound up
by the accretion disk, the orientation of the RM gradient gives the direction of rotation of the
accretion disk.
The change in RM across the jet is consistent with Bk changing due to the presence of a helical
magnetic field (Asada et al. 2002, PASJ 54, L39).
31
Magnetic Field Alignments in Blazar Jets
Evidence for Shear Interactions and Differential Speeds
VLBI polarization images of 1055+018 by Attridge et al. (1999) show a jet with a two-component
magnetic field structure (see attached Figure). The spine of the jet has compact knots with
longitudinal electric vectors (k B-field) while the edge of the jet has transverse electric vectors,
such as would be expected from a sheath formed by a shear interaction with the surrounding
medium. In the simplest picture the sheath is more slowly moving than the spine, and therefore it’s
beaming cone is different. The jet angle to the line of sight then determines whether the spine or
the sheath emission dominates your image. (Attridge et al. 1999, ApJ)
Fig. 1a
Fig. 1b
32
Magnetic Field Alignments in Blazar Jets
The Importance of High Resolution
Many of the reported misalignments between EVPA and structural position angle can probably be
explained by resolution effects. The polarization is often confined to small regions, and the jet
structure can change on very small scales. Even if the polarization is well-aligned with the
structure, small scale wiggles in the jets, combined with insufficient resolution can smear out the
structural changes such that the polarization and structural position angles appear misaligned
(e.g. Figure 12).
The map on the left is 1803+784 at 5 GHz observed with the VLBA. The contours are of total
intensity and the overlaid sticks indicate the polarized intensity and EVPA. The map on the right
uses the same data, but with the addition of (v. long) baselines to the orbiting VLBI antenna
HALCA. The improved resolution given by the space baselines allow one to see that the electric
vectors very neatly follow the bend in the jet with no evidence for misalignments (Gabuzda 1999,
NewAR, 43, 695).
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