Table Of Content1
Abstract. It is shown that linear polarization data can
be used to constrain the composition (normal or pair
plasma) of pc-scale extragalactic jets. A simple criterion,
based on synchrotron and Faraday depolarization prop-
erties, is established. It does not depend on the particle
density and the length of the emitting region along the
line of sight, thus eliminating two physical unknowns.
Key words: galaxies : jet – galaxies : active – radiation
mechanisms : non-thermal – radio continuum : galaxies –
2 polarization – methods : analytical
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A&A manuscript no. ASTRONOMY
(will be inserted by hand later) AND
Your thesaurus codes are: ASTROPHYSICS
missing; you have not inserted them
Linear polarization and composition of VLBI jets
D. Fraix-Burnet
Laboratoire d’AstrophysiquedeGrenoble, BP 53, F-38041 Grenoble C´edex 9, France.
Received November21 2000 /Accepted October 10 2001
1. Introduction 2.1. Synchrotron surface brightness and polarization
Due to their synchrotron emission, extragalactic jets are
Thesynchrotronsurfacebrightnessofapopulationofelec-
known to contain electrons. But what is the positive
trons (or positrons) with an energy distribution spectral
charge population : protons or positrons? This makes a
index p is derived from the standard formulae (i.e. (5.43)
hugedifferenceinthe kinetic energytobe putinthe ejec-
in Ginzburg 1979):
tion process and implies different properties for accelera-
tion and propagationmechanisms. I =K1(p)(Nel+Npo)γmp−in1LB⊥(p+1)/2δ(p+n)/2ν(1−p)/2 (2)
Extractedmatterfromthe accretiondiskis comprised with
ofnormal(electron-proton)plasma.Butacceleratingpro-
K (p)=4.48 10−11 p−1 Γ 3p−1 Γ 3p+19
tsoonmsewtoharteplartoibvliestmicatsicp.eTedhsesmchakemesetohfeaetnweor–gfleutiicdpbluadsgmeat 1 (cid:16)p+1(cid:17) (cid:0) ×12 8(cid:1).40(cid:0)10162(p(cid:1)−1)/2 (3)
(Sol et al. 1989, Pelletier & Marcowith 1998) alleviates in Jy arcsec−2, where Γ(x) is the G(cid:0)amma fu(cid:1)nction, N +
this difficulty by reserving the relativistic speed to a pair el
N the total radiating particle density, γ the mini-
(electron–positron)plasma, while the bulk of the jet, non po min
mum energy of the electron (positron) population, L the
relativistic and non radiating, is made of normal plasma.
column length along the line of sight in centimeters, B⊥
Observationally,therehavebeentwoapproachestode-
the component of the magnetic field which is perpendic-
termine the nature of the radiating plasma: spectroscopic
ular to the line of sight, ν the observational frequency, δ
behavior (Reynolds et al. 1996), and circular polarization
the bulk Doppler factor, n = 3 for a continuous jet and
(Wardleetal.1998).Theresultstendverystronglytoward
n=5 for a single plasmoid (Lind & Blandford 1985).
electron–positron pairs for the radiating component.
Inthispaper,itisshownthatlinearpolarizationcould In the conditions assumed in this paper, the intrin-
also be used to derive the nature of the jet material from sic polarization of the synchrotron emission is given by
very high resolution observations. Based on basic formu- (Ginzburg 1979):
lae presented in Sect. 2, a very simple analytical criterion p+1
Π = (4)
is established in Sect. 3. In Sect. 4, some particular ob- i p+7/3
servational data are discussed before a brief conclusion is
which is ≃69% for p=2 and ≃75% for p=3.
given in Sect. 5.
2. Simple properties of synchrotron radiation 2.2. Faraday depolarization
LetusconsideranelectronpopulationofdensityNel.The The polarized synchrotron radiation emitted by a given
positive charge is assumed to be a mixture of protons set of electrons is affected by Faraday rotation through
(Npr) and positrons (Npo). We have Nel = Npo + Npr other sets of electrons along the line of sight. Integration
and we define: ofthelightcomingfromallthesesets resultsinanappar-
τ =Npo/Nel. (1) entdepolarizationcalledtheFaradaydepolarization.This
A simple homogeneousslabwitha homogeneousmag- is the minimum depolarization that occurs. Any hetero-
netic fieldisassumed.Asexplainedlateron,this assump- geneity (in density or in magnetic field) within the slab
tionisnotrestrictive,butyieldstheminimumdepolariza- increases the observed depolarization.
tion that must be observed in a source. We only consider
Forpositrons,theFaradayrotationisofoppositesign,
the optically thin part of the synchrotronspectrum.
so that there is no Faraday depolarization in a pure
Correspondence to: [email protected] electron–positron plasma.
D. Fraix-Burnet:Linear polarization and composition of VLBI jets 3
Forprotons,theFaradayrotationisnegligibleanddoes
not compensate for that of the electrons. Hence, the ob-
served polarization Π is constrained by:
obs
sin(ψ) 1
Πobs ≤Πi ≤Πi (5) 1
ψ ψ
TheFaradayrotationangleψ isgivenby(Burn1966):
ψ =2.35 104(N −N )B Lν−2δ2 (6)
el po // log b
whereB isthecomponentofthemagneticfieldwhich 0
//
is parallel to the line of sight.
3. Combining surface brightness and polarization –1
informations
0.2 0.4 cos v 0.6 0.8 1
3.1. Principle
BothI andψareincreasingfunctionsofdensity,B andL.
Thebrightestcomponentsshouldthenbelesspolarizedin
thecaseofanormalplasma.Inprinciple,thiscouldbean
observationaltestfordeterminingthecompositionofajet. Fig.1. Function log(b(p,v)) for p = 2 (solid line) and
However,this is only a statistical argument,based on the p=3 (dotted line) vs cosv.
improbableassumptionthatallparametersareequal,par-
ticularly the level of homogeneity of the emitting region.
3.3. Numerical value for pc-scale jets
Isthereanotherwayoftranslatingtheincompatibilitybe-
tween high surface brightness and high polarization for a
The determination of the physical parameters in extra-
normal plasma?
galactic jets is a major problem. We now re-write equa-
Weproposetousetheratiobetweenthesurfacebright- tion (12) in a convenient form to numerically apply it to
nessI andthe Faradaydepolarizationψ.Ascalculatedin jets.
the next section, its notable property is that it does not As suggested by the observations, p is somewhat be-
dependonNel andLforanormalplasma,eliminatingthe tween 2 and 3: K2(2) = 0.103 and K2(3) = 0.074. Even
indetermination regarding these two parameters. if it is a somewhat uncertain guess, a typical value for
the magnetic field appears to be B ≈10−2 G. γ seems
min
3.2. Definition of the Brightness Faraday Ratio to be more constrained at about 102 (see discussion in
Reynoldset al.1996).The allowedvariationsofthese two
Using equations (2) and (6), we define the “Brightness parametersareprobablynotmuchhigherthanafactorof
Faraday Ratio” as: 10 in most cases.
BFR= I =K (p)ǫν(5−p)/2γp−1B⊥(p+1)/2δ(p+n−4)/2 (7) Defining:
where ψ 2 min B// ν10 =(cid:16)101ν0Hz(cid:17) , γ100 =(cid:16)γ1m0i2n(cid:17) , B−2 =(cid:18)10−B2G(cid:19),
K (p)=K (p)/2.35 104, (8) we obtain:
in2Jy arcsec1−2rad−1, and BFRp=2 = 4.06 104ǫb(2,v)δ(n−2)/2ν130/2 γ100B−1/22,
ǫ= ((NNel−+NNpo)) = 11−+ττ. (9) BFRp=3 = 1.29 104ǫb(3,v)δ(n−1)/2ν10 γ1200B−2. (13)
el po
Thefunctionǫessentially≈1,exceptforanearlypure
Since BFR is intended to test the normal plasma hy-
pairplasmainwhichcaseitcanbe muchhigher.Letv be pothesis, one can assume ǫ≈1 (see Sect. 3.2).
the anglebetweenthemagneticfieldandthe line ofsight.
Thevalueforndependsonthegeometryofthesource
It becomes:
(see Sect. 2.1). However, jets are characterized by a com-
B(p+1)/2
⊥ =B(p−1)/2b(p,v) (10) plex continuous structure so that most probably: n = 3.
B// This makes a relativelysofter dependance onthe Doppler
with factor than for n=5.
(sinv)(p+1)/2 This Doppler factor is known from apparent motions
b(p,v)= . (11)
cosv in quite a lot of jets. It seems to be rarely higher than
The function b(p,v) is plotted on Fig. 1. It is smaller
about 10 (i.e. Zensus 1997).
than 0.1 for v ≤15◦ and is higher than 10 for v ≥85◦.
The most uncertain parameter in the expression of
Finally, BFR can be written in the following way:
BFR is undoubtly the angle v which cannot be easily
BFR=K2(p)ǫb(p,v)ν(5−p)/2γmp−in1B(p−1)/2δ(p+n−4)/2(12) determined from the observations. However, as said pre-
4 D. Fraix-Burnet:Linear polarization and composition of VLBI jets
viously (see Fig. 1), b(p,v) is higher than 10 only when v of the criterion presented in this paper when applied to
◦ ◦
is larger than 85 (and b(p,v)>5 when v >80 ), that is very high resolution data.
when the magnetic field is nearly exactly in the plane of
the sky. In practice, by comparing a given set of several
4.2. 3C273
structureswithinajetand/orindifferentsources,itwould
certainly be possible to restrain v to a reasonable range InLister&Smith(2000),bothsurfacebrightnessandpo-
where the function b(p,v) can be given a representative larization of several components in different sources are
upper limit. compiled. For component G of the jet in 3C273 we de-
Finally, the choiceofp between2or3 mightnotbe so rive a surface brightness of about 5 105 Jy arcsec−2 and
critical. a rather low polarization of 4%. However, this still yields
at 22 GHz (resolution of 0.97 mas×0.38 mas):
I Π
3.4. A criterion for the composition of jets obs obs ≈3 106.
Π
i
In components C and D, we have a surface brightness
For a given set of physical parameters, BFR is the max-
of about 4 105 Jy arcsec−2 with about 21% polarization.
imum value allowed for I/ψ in the case of an electron–
This yields:
proton plasma. Combining equations (5) and (7) the
I Π
scheme is therefore very simple: obs obs ≈105.
Π
I Π i
obs obs >BFR⇒normal plasma excluded (14) These high observed ratios require, for a normal
Π
i plasma, high values of the parameters (i.e. n = 5, large
where I is the observed surface brightness.
obs
Doppler factor, high value for b(p,v)...).
Toavoidthecontributionofsmearingintheobserving
One way to reduce some uncertainties on the parame-
beam that can particularly affect the observed polariza-
ters would be to compute the above ratio in every struc-
tionandalsotheintensity,thehighestspatialresolutionis
ture of the jet. For instance, it would be hard to believe
recommended. As a consequence, the VLBI observations
thatvisthesameeverywhereinthejet,henceitwouldbe
are expected to provide the most interesting data.
possible to put a global upper limit on b(p,v). Note also
Notethatcriterion(14)canbeusedwithothercriteria
thatthe compositionofthe radiatingmaterialiscertainly
likethoseinReynoldsetal.(1996)toreduceuncertainties
the same everywhere in a given jet.
on parameters.
4.3. 3C279
4. Comparison with observations
Fromthe same paper (Lister & Smith 2000), we find that
In this section, we illustrate the use of the BFR criterion componentFinthejetof3C279,ataboutthesameresolu-
with observations.A concreteapplicationofthe proposed tion,hasasurfacebrightnessofabout1.4107 Jyarcsec−2
criterion requires a thorough study of individual cases or and 18% polarization. This yields:
of a statistically significant sample, in order to determine I Π
obs obs ≈3.6 106.
the most appropriate values for the parameters in BFR. Π
i
This again shows that our criteria provide interest-
ing constraints on the parameters in equation (13) if one
4.1. M87
wishes to assume a normal plasma. The fact that the ra-
We start with the example of knot A in the jet of M87 at tio found in knot F of 3C279 is close to that for knot G
0.14arcsecresolutionand15GHzasobservedbyOwenet in 3C273is undoubtly pure chance,but comparingvalues
al.(1989).Thesurfacebrightnessfromtheirmapisfound foundinseveraljets isanotherwayto usetheBFR crite-
to be about 15 Jy arcsec−2 with a ≈ 30% polarization. rion and find hints for the composition of jets in general.
This yields:
I Π
obs obs ≈6.5 5. Conclusion
Π
i
In this case, it is not possible to draw conclusions Thepresentstudyhasbeeninitiatedfromthesynchrotron
about the composition of the jet, but at this resolution, emission simulations (Despringre & Fraix-Burnet 1997,
beam smearing is quite certain and the use of the cri- Fraix-Burnetinprep.)inwhichitappearsnearlyimpossi-
terion is somewhat hopeless. Taking the observations by ble to reproduce both surface brightness and polarization
Junor et al. (1999) at 43 GHz and 0.33 mas×0.12 mas of typical VLBI jets. We have then devised a simple tool,
resolution,we obtain a surfacebrightness ofabout106 Jy presented in this paper,to constrainthe compositionof a
arcsec−2.Assumingapolarizationof10%,thiswouldgive jet with linear polarization data.
I Π /Π ≈ 1.4 105. Preserving a normal plasma hy- It is based on the Faraday depolarization which is
obs obs i
pothesis would put some interesting contraintsonthe pa- the minimum depolarization that occurs from a normal
rameters in equation (13). This illustrates the usefulness plasma. This yields a criterion, easily computed from the
D. Fraix-Burnet:Linear polarization and composition of VLBI jets 5
observations, that does not depend on the length of the
emitting plasma along the line of sight nor on density of
the emitting particles. These two parameters are always
very difficult to estimate.
Still,thereareafewuncertainparametersinthecrite-
rion,butfromafewillustrativeexamplespresentedinthis
paper, it already appears that they should be pushed to
high values if one assumes a normal plasma. A complete
statistical study of severaljets or a very detailed study of
a well-observed jet is necessary to reach more significant
conclusions.Thisisbeyondthescopeofthepresentpaper.
Our criterion is not valid in the self–absorbed part of
thespectrum.Itiscertainlynotaproblemforfrequencies
above10GHzinthejets,butitshouldbeappliedtocores
only with caution.
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