Radio Emission from 3D Relativistic Hydrodynamic Jets: Observational Evidence of Jet Stratification

Abstract

We present the first radio emission simulations from high resolution three dimensional relativistic hydrodynamic jets, which allow for a study of the observational implications of the interaction between the jet and external medium. This interaction gives rise to a stratification of the jet where a fast spine is surrounded by a slow high energy shear layer. The stratification, and in particular the large specific internal energy and slow flow in the shear layer largely determines the emission from the jet. If the magnetic field in the shear layer becomes helical (e.g., resulting from an initial toroidal field and an aligned field component generated by shear) the emission shows a cross section asymmetry, in which either the top or the bottom of the jet dominates the emission. This, as well as limb or spine brightening, is a function of the viewing angle and flow velocity, and the top/bottom jet emission predominance can be reversed if the jet changes direction with respect to the observer, or presents a change in velocity. The asymmetry is more prominent in the polarized flux, because of field cancellation (or amplification) along the line of sight. Recent observations of jet cross section emission asymmetries in the blazar 1055+018 can be explained assuming the existence of a shear layer with a helical magnetic field. Comment: 6 pages, 5 figures, 1 latex style file, ApJL accepted

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arXiv:astro-ph/9911153v1 9 Nov 1999
DRAFT VERSION FEBRUARY 1, 2008
Preprint typeset using LATEX style emulateapj
RADIO EMISSION FROM 3D RELATIVISTIC HYDRODYNAMIC JETS: OBSERVATIONAL EVIDENCE
OF JET STRATIFICATION
MIGUEL-ANGEL ALOY1, JOSÉ-LUIS GÓMEZ2, JOSÉ-MARÍA IBÁÑEZ1, JOSÉ-MARÍA MARTÍ1AND EWALD MÜLLER3
Draft version February 1, 2008
ABSTRACT
We present the first radio emission simulations from high resolution three dimensional relativistic hydrody-
namic jets, which allow fora study ofthe observationalimplications of the interactionbetween the jet andexternal
medium. This interaction gives rise to a stratification of the jet where a fast spine is surrounded by a slow high
energy shear layer. The stratification, and in particular the large specific internal energyand slow flow in the shear
layer largely determines the emission from the jet. If the magnetic field in the shear layer becomes helical (e.g.,
resulting from an initial toroidal field and an aligned field component generated by shear) the emission shows a
cross section asymmetry, in which either the top or the bottom of the jet dominates the emission. This, as well as
limb or spine brightening, is a function of the viewing angle and flow velocity, and the top/bottom jet emission
predominance can be reversed if the jet changes direction with respect to the observer, or presents a change in
velocity. The asymmetry is more prominent in the polarized flux, because of field cancellation (or amplification)
along the line of sight. Recent observations of jet cross section emission asymmetries in the blazar 1055+018 can
be explained assuming the existence of a shear layer with a helical magnetic field.
Subject headings: galaxies: jets – hydrodynamics– radiation mechanisms: non-thermal – methods: numerical –
relativity
1. INTRODUCTION
The development of high-resolution multidimensional rela-
tivistic hydrodynamic codes has provided a tool which allows
to simulate the (synchrotron) radio emission from parsec-scale
relativistic jets (Gómez et al. 1995, 1997; Komissarov & Falle
1996, 1997; Mioduszewski, Hughes & Duncan 1997), obtain-
ing a better understanding of the physics involved in the jets
of active galactic nuclei and their enviroments. It has also
been used to successfully explain the structure of particular
sources (e.g., 3C 120, Gómez et al. 1998a,b; 3C 454.3,Gómez,
Marscher & Alberdi 1999).
In this Letter we study, for the first time, the radio emis-
sion properties of three-dimensional relativistic hydrodynamic
jet models. In particular, we focus on the observational con-
sequences of the interaction between the relativistic jet and
the surrounding medium, which leads to the development of a
shear layer. Suchshear layers(withdistinct kinematicalproper-
ties and magnetic field configuration) appear naturally in some
models of jet formation(Sol, Pelletier, & Asseo 1989)and have
been invoked in the past by several authors (Komissarov 1990,
Laing 1996, Laing et al. 1999)in order to account for a number
of observational characteristics of FRI radio sources. However,
the physical nature of the shear layer is still largely unknown.
Recently, Swain, Bridle & Baum (1998) have found evidence
of shear layers in FRII radio galaxies (3C353), and Attridge,
Roberts & Wardle (1999)have inferreda two-componentstruc-
ture in the parsec scale jet of the source 1055+018.
2. JET STRATIFICATION: BEAM AND SHEAR LAYER
To study the emission properties of relativistic jets we have
used the high resolution three dimensional relativistic hydrody-
namic jet model of Aloy et al. (1999a, hereafter A99). The
model is characterized by a beam-to-external proper rest-mass
density ratio η = 0.01, a beam Mach number Mb= 6.0, and a
beam flow speed vb= 0.99c (c is the speed of light) correspond-
ing to a beam Lorentz factor of Γ ∼ 7. Non-axisymmetry was
triggeredby means of a helical velocity perturbationof 1% am-
plitude and with a period of 3.0 Rb/c (where Rbis the initial
beam radius) imposed at the nozzle. We refer the reader to
Aloy et al. (1999b) where a detailed description of the hydro-
dynamical code can be found.
The jet model is characterized by a two-componentstructure
(Fig.1) with a fast (Γ ∼ 7) inner jet and a slower (Γ ∼ 1.7)
shear layer with high specific internal energy. The shear layer
is defined as the region where the beam particle fraction is be-
tween 0.2 and 0.95. As discussed in A99, the formation of the
shear layer is dominated by the numerical viscosity inherent
to the hydrodynamic code and not by the turbulent shear. In-
spite of this fact, the computed jet models still allow to study
the physics of shear layers in relativistic jets and their observa-
tional consequences. As shown in A99, the axial component of
the momentum of the beam particles decreases by 30% within
the first 60 Rb. This loss of momentum causes a decrease of the
Lorentz factor in the inner jet with values ∼ 5.8, 5.3, and 4.8 at
z = 25, 50, and 68 Rb, respectively.
3. EMISSION PROPERTIES
The emission properties of large scale jets in AGNs can
be studied by computing the radio (synchrotron) emission
from relativistic hydrodynamic jet models (see Gómez et al.
1995,1997 and references therein for a complete description of
the model). For this, we assume that the particle and energy
density of the non-thermal electrons is a constant fraction of
1Departamento de Astronomía y Astrofísica, Universidad de Valencia, 46100 Burjassot (Valencia), Spain. miguel.a.aloy@uv.es; jose.m.ibanez@uv.es; Jose-
Maria.Marti@uv.es
2Instituto de Astrofísica de Andalucía, CSIC, Apartado 3004, 18080 Granada, Spain. jlgomez@iaa.es
3Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany. ewald@mpa-garching.mpg.de
1

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the simulated thermal gas. No significant variations from this
proportionality are expected to be found within the jet, since
the radiative loses and particle accelerations in our model are
small. The internal energy among the relativistic non-thermal
electrons is distributed following a power law. The magnetic
energyis set to be locally proportionaland significantly smaller
than the particle energy density, hence being dynamically neg-
ligible. Different ad hoc distributions of the magnetic field in
the jet spine and shear layer can therefore be considered. In our
model we assume that the magnetic field of the jet consists of
two components. A toroidal field present both in the jet spine
and the shear layer, and a second component (in equipartition
with the toroidal field) aligned in the shear layer and radial in
the jet spine. The aligned component in the shear layer could
arise from the shear between the jet and the external medium,
while the radial field in the jet spine may be due to transverse
shocks (i.e., Attridge, Roberts & Wardle 1999). The resulting
projected magnetic field is aligned in the shear layer and is per-
pendicularin the jet spine, as suggested by several observations
(Laing 1996; Swain, Bridle & Baum 1998; Attridge, Roberts
& Wardle 1999). An extra randomly oriented magnetic field
component (containing 60% of the total magnetic field energy)
is assumed both for the shear layer and jet spine.
The Stokes parameters that determine the emission are cal-
culated by integrating the synchrotron transfer equations along
columnsparallelto thelineofsightaccountingfortheappropri-
ate relativistic effects, such as Doppler boosting and light aber-
ration. Light–travel time delays have been ignored assuming
that the jet is stationary. Since only the jet material is expected
to radiate,the energydensity computedwith the hydrocodehas
been weighted with the beam particle fraction. In addition, we
ignore the emission from the jet cocoon and hot spot by limit-
ingthecalculationstovaluesofthebeamparticlefractionlarger
than 0.2 and to the inner 68Rb.
3.1. Total and polarized emission as a function of the viewing
angle
Because of the highly relativistic speeds in the jet, the emis-
sion is mainly determined by the observing viewing angle, θ,
throughthe Dopplerfactor and light aberration. Figures 2 and3
show the computed emission from the hydrodynamic model of
A99 corresponding to a viewing angle of 50◦and 10◦, respec-
tively. Theemissionis computedforanopticallythin observing
frequency, and spectral index of the electrons of 2.4.
For relatively large viewingangles (Fig.2) the jet emission is
limb brightened. This is in part due to the higher specific inter-
nal energy in the shear layer, resulting in a larger synchrotron
emission coefficient. On the other hand, the Doppler factor
can either enhance or cancel the limb brightening depending
on the value of the viewing angle θ. Because of the jet veloc-
ity stratification (see Fig. 1), for relatively large viewing angles
the fast jet spine suffers a larger amount of dimming than the
shear layer, enhancing the limb brightening. For our jet model,
with a mean Γ ∼ 7 in the jet spine, this effect is maximized for
θ ∼ 50◦, for which the shear layer emission is boosted while
the jet spine is dimmed (see the panel with the Doppler factor
in Fig.2). Cross section profiles of the jet emission at different
viewing angles are plotted in Fig.4, where the limb brightening
effectcanbeobservedmoreeasily. Forsmallviewingangles,as
correspondingto Fig.3, the jet spine emission is boosted, while
the shear layer emission appears dimmed. Details of the jet
spine can be observed, as for instance two recollimation shocks
located at 26Rband 50Rb. The jet emission then becomes spine
brightened, instead of limb brightened, as observed in Figs.3
and 4.
The same arguments apply to the polarized flux. As a re-
sult of the helical field in the shear layer, the apparent orien-
tation of the magnetic field at the jet edges is parallel to the
jet axis. For the jet spine, the toroidal and radial components
of the magnetic field yield a net polarization perpendicular to
the jet axis. As shown in Figs.2 and 4, for relatively large
angles the aligned component of the helical magnetic field in
the shear layer projects into the jet spine partially canceling its
field, yielding a smaller net polarization, thereby stressing the
limb brightening. Rails of low polarization can be observed
where the apparent magnetic field rotates between being paral-
lel (in the shear layer) to being perpendicular to the jet axis, as
observed in 3C 353 (Swain, Bridle & Baum 1998).
Some of the kinematic and physical properties of the jet can
be deducedby analyzingthe jet/counterjet emission ratio, plot-
ted in Fig.5 for the jet model of Fig.2. The jet deceleration
is apparent from a progressively decrease in the total flux ra-
tio along the jet axis. The velocity stratification across the jet
is also visible as a decrease of the flux ratio close to the jet
edges, that is, in the shear layer. This is visible in the inner
jet region, while further down the jet, when the jet spine and
shear layer velocities are more similar (due to the jet decelera-
tion), the jet/counter jet flux ratio is more uniformly distributed
acrossthejet. Theslowervelocityinthe shearlayerandits high
emission coefficient result in a smaller integrated flux ratio be-
tween the jet and counter jet than for the case of a “naked” high
velocity jet spine (see also Komissarov 1990). This is because
the shear layer emission is less affected by the viewing angle
through the Doppler factor.
3.2. Jet cross section emission asymmetry
Because of the helical magnetic field structure in the shear
layer,an asymmetryin the emission appearsacross the jet. This
asymmetry is more pronounced in the polarized emission, and
isafunctionoftheviewingangle,asshowninFig.4. Inorderto
understand this effect we need to study the variation across the
jet of the angle between the magnetic field and the line of sight
in the fluid frame, ϑ. The synchrotron radiation coefficients
are a function of the sine of this angle, and asymmetries in the
distribution of ϑ will be translated into the emission maps. In
order to compute ϑ we need to Lorentz transform the line of
sight from the observer’s to the fluid’s frame (see e.g., Rybicki
& Lightman 1979)
sinθ′=
sinθ
Γ(1−βcosθ)
,
cosθ′=
cosθ−β
(1−βcosθ)
where θ′is the viewing angle in the fluid frame. Consider a he-
lical magnetic field with a pitch angle φ, measured with respect
to the jet axis. The angles ϑtand ϑb(where superscriptst and b
refer to the top and bottom of the jet, respectively)add 2φ (note
that ϑt,bis always defined as positive). Therefore, as long as
φ is different from zero or π/2, i.e. the field is neither purely
aligned nor toroidal, the factor sinϑt,bin the synchrotron radi-
ation coefficients will introduce an asymmetry in the jet emis-
sion. This asymmetry will reach a maximum value for a helical
magnetic field with φ = π/4, as the one considered here. How-
ever, independently of the helix pitch angle, the predominance
between sinϑtand sinϑbwill reverse at θ′= π/2, which corre-
sponds to a viewing angle in the observer’s frame of cosθr= β.

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For a helical field oriented clockwise as seen in the direction of
flow motion (i.e., the aligned component of the field is parallel
to the jet flow), and for θ′<π/2 the bottom of the jet will show
larger emission, while for θ′> π/2 the top of the jet will be
brighter (the opposite is true for a helical field orientedcounter-
clockwise, i.e. φ>π/2). The maximumasymmetrywill be ob-
tained for θ′= φ and θ′= π−φ, and the fastest transition (with
changing θ′) between top/bottom emission predominance will
be obtained for φ close to π/2, i.e. when little aligned field is
present.
In the model we are considering, the shear layer has a mean
Γ ∼ 1.7, and therefore θr∼ 36◦. Smaller angles will show bot-
tom jet dominance in emission, while for larger values the top
of the jet will appear brighter. This is more clearly visible in
Fig.4. Note also that for the counter jet the helical field rotates
opposite to the main jet, and therefore the jet asymmetry emis-
sion reverses. This is particularly well observed in the plot of
the polarized emission ratio between the jet and counter jet of
Fig.5.
Although the sinϑ factor affects both the total and the po-
larized emission, the asymmetry is more clearly present in the
polarized flux (see Figs.2, 4 and 5). This is due to: i) The pres-
ence of a randomly oriented magnetic field component, which
renders the magnetic field distribution more homogeneous in
the jet and diminishes the asymmetry. ii) Smaller values of ϑ,
independently whether present at the top or the bottom of the
jet, always represent a larger variation of the magnetic field ori-
entation along the line of sight. In practice this represents a
larger degree of randomness in the magnetic field along the in-
tegration columns, decreasing the net polarization.
It is interesting to note that for θ ∼ θr, small changes in
the jet velocity or the viewing angle will produce a flip in the
top/bottom jet emission dominance. For fast jets, θrwill be ac-
cordingly small, and we will be biased towards observing jets
with top emission predominance (as long as the helical field
rotates clockwise as seen in the direction of flow motion).
An interpretation of the polarization observations of the
blazar 1055+018 by Attridge, Roberts & Wardle (1999) can be
obtained in terms of the model presented here. For that, we
need to assume that 1055+018 is oriented close to θr, and con-
tains a shear layer with a helical field. If the helical field is
oriented clockwise, the polarized emission observed at the top
of the jet in inner regions would require that initially θ > θr,
or θ′> π/2. To obtain the opposite situation further down
the jet, θ′has to become smaller than π/2, and for that either
θ decreases, or θrincreases, which requires that β decreases.
A third less plausible possibility is that the helical field in the
shear layer changes orientation, i.e. the pitch angles becomes
larger that π/2. Therefore, we can successfully explain the flip
in the top/bottom orientation of the polarization asymmetry in
1055+018 if the jet bends towards the observer, or if it deceler-
ates. Attridge, Roberts & Wardle (1999,andreferencestherein)
report the existence of bends in the jet of 1055+018. This sup-
ports our hypothesis, but at the location of the flip in the po-
larization emission asymmetry the jet spine emission decreases
abruptly, contrary to what would be expected in the case of a
bend towards the observer which should increase the jet spine
emission by differential Doppler boosting. Attridge, Roberts
& Wardle (1999) obtained significantly larger apparent veloci-
ties for components closer to the core suggesting a deceleration
along the jet. Therefore, this suggests our hypothesis of jet de-
celerationas themost plausibleforthe suddenchangeinthe po-
larization predominance between the top and bottom of the jet
in 1055+018,since a jet deceleration will decrease the Doppler
boosting, and hence the jet spine emission as observed. A rela-
tively small aligned field (helical pitch angle close to π/2) will
helptoobtainsuchafastflipinthepolarizationasymmetrywith
a relatively small jet deceleration.
This research was supported by Spain’s Dirección Gen-
eral de Enseñanza Superior (DGES) grants PB97-1164 and
PB97-1432. MAA expresses his gratitude to the Conselleria
d’Educaciói Ciència dela GeneralitatValencianafora research
fellowship. We thank A. Alberdi for comments that improved
the manuscript.
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FIG. 1.— Cuts of theLorentzfactor(tophalfpanel)andspecific internalenergy(bottomhalf panel)distributionsofthe hydrodynamic
model along the plane y = 0. White contours representing constant values of the beam particle fraction (0.95 for the innermost
contour, 0.2 for the outermost one) are used to characterize the shear layer. The two panels at the right show the average (along lines
x =constant) of the corresponding distributions across the jet.
FIG. 2.— From top to bottom the panels show the total intensity, the polarized intensity, the degreeof polarization,and mean Doppler
factor for a jet viewed at an angle of 50◦(right panels) and its counter jet (left panels). Averages along the line of sight for each
pixel, using the emission coefficient as a weight, have been used to plot the Doppler factor. The total and polarized intensities (in
units normalized to the maximum of the main jet total intensity) are plotted on a square root scale. The bars in the polarized intensity
panels show the direction of the magnetic field.

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FIG. 3.— Same as Fig. 2, but for a viewing angle of 10◦.
FIG. 4.— Logarithm of the integrated total (left) and polarized (right) intensity across the jet for different viewing angles. Lines are
plotted in intervals of 10◦between an angle of 10◦(top line in both plots) and 90◦(showing a progressive decrease in emission).
Dashed (dot dashed) lines correspondto an observing angle of -130◦(-170◦). Positive beam radii correspondto the top in the images
of Figs.2 and 3. Units are normalized to the maximum total intensity.