Polarization radiation with turbulent magnetic fields from X-ray binaries

0.48 MB·

by  Jian-Fu Zhang

Draftversion January16,2017
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
POLARIZATION RADIATION WITH TURBULENT MAGNETIC FIELDS FROM X-RAY BINARIES
Jian-Fu Zhang1, Fu-Yuan Xiang1 and Ju-Fu Lu2
Draft version January 16, 2017
ABSTRACT
We study the properties of polarized radiation in turbulent magnetic fields from X-ray binary jets.
7 These turbulent magnetic fields are composed of large- and small-scale configurations, which result
1 in the polarized jitter radiation when the characteristic length of turbulence is less than the non-
0 relativisticLarmorradius. Onthe contrary,thepolarizedsynchrotronemissionoccurs,corresponding
2 to a large-scaleturbulent environment. We calculate the spectral energy distributions and the degree
of polarization for a general microquasar. Numerical results show that turbulent magnetic field con-
n
figurations can indeed provide a high degree of polarization, which does not mean that a uniform,
a
J large-scalemagneticfieldstructureexists. The modelisappliedtoinvestigatethepropertiesofpolar-
izedradiationofblackholeX-raybinaryCygnusX–1. Undertheconstraintofmultibandobservations
2
of this source, our studies demonstrate that the model can explain the high polarization degree at
1
MeV tail and predict the highly polarized properties at high-energy γ-rayregion, and that the domi-

] nant small-scale turbulent magnetic field plays an important role for explaining the highly polarized
E observationathardX-ray/softγ-raybands. This modelcanbe tested bypolarizationobservationsof
H upcoming polarimeters at high-energy γ-ray bands.
Subject headings: X-rays: binaries - gamma rays: general - polarization - stars: individual: Cygnus
.
h X–1
p
-
o 1. INTRODUCTION esting to study multi-wavelength polarization proper-
r
ties (e.g., Russell & Shahbaz 2014 for a recent work on
t A compact X-ray binary consists of a stellar compan-
s the microquasar Cygnus X–1). Recently, Laurent et al.
a ion and a compact object, such as black hole or neutron
(2011) observed strong polarization, 67 30%, of the
[ star. Among Galactic X-ray binaries detected, there are ±
high-energy radiation of Cygnus X–1, between 400 keV
abouttwentymicroquasarsthatpresenttheextendedrel-
1 and 2 MeV (so-called MeV tail), using the Interna-
ativistic radio jets. It is widely considered that during
v tional Gamma-Ray Astrophysics Laboratory Imager on
the low/hard spectral state, radio through infrared (IR)
7 boardtheIntegralsatellite(INTEGRAL/IBIS).Thisre-
emissions are from synchrotron processes of relativistic
2 sult, i.e., the highly polarized emission at MeV tail,
electrons. However, the origin of both X-ray and γ-ray
5 later was independently confirmed by using the INTE-
emissions still remains open; they may be from the rel-
3 GRAL/SPI instrument, namely, 76 15 % at 0.23–0.85
ativistic jet, hot accretion flow, and/or disk-corona re-
0 MeV (Jourdain et al. 2012). By se±parating the obser-
gion (e.g., Markoff et al. 2001, 2005; Yuan et al. 2005;
.
1 P´eer et al. 2009;Zhang & Xie2013). Asfarasweknow, vations of Cygnus X–1 into hard, soft, and intermedi-
0 itseemstobedifficulttodistinguishthemonlybyfitting ate/transitional spectral states, Rodriguez et al. (2015)
7 confirmedthat in the hardspectral state, where it is ex-
emission spectra. We in this paper study the properties
1 pected to be the presence of the jet, the degree of linear
of polarizationradiationof microquasars. The polarized
: polarization is 75 32% between 0.4 MeV and 2 MeV
v radiation is an intrinsic property of the electromagnetic and the polarizatio±n angle is 40◦.0 14◦.3.
Xi radiation,which carriesimportant informationon astro- Producing such a high polariz±ation at MeV tail
physical sources, such as the geometry and orientation
was claimed as the synchrotron emission of relativis-
r of the magnetic field, radiation mechanism. Therefore,
a tic electrons in the jet due to a uniform (ordered),
polarization study is one of the important methods to
large-scale magnetic field configuration (Laurent et al.
probe an X-ray binary, leading to a better understand-
2011; Jourdain et al. 2012; Russell & Shahbaz 2014;
ing of radiativemechanism, of configurationof magnetic
Rodriguez et al. 2015). Alternatively, it has been pro-
fields, and of matter compositionas well as energetics of
posed that a hot accretion flow, which requires mono-
the jet.
directionmotion ofrelativistic electronsalonghighly or-
The polarization properties of emissions in X-ray bi-
deredmagneticfieldsintheinnerregionsoftheaccretion
naries have been strongly studied at the radio wave-
flow (Veledina et al. 2013), or a hot, highly magnetized
band (e.g., Fender 2006), where a relatively low level
plasma corona around the black hole, where hadronand
of polarization is associated with synchrotron process
lepton interacting with matter and magnetic fields are
in the jet. Similar to the studies for multi-wavelength
invoked, may produce the highly polarized emission at
spectral energy distributions (SEDs), it is more inter-
MeV tail (Romero et al. 2014).
[email protected];[email protected];[email protected] In these works mentioned above, almost all investi-
1Department of Physics, Xiangtan University, Xiangtan gations with regard to a high polarization degree usu-
411105, China;
2Department of Astronomy and Institute of Theoretical ally are considered as the existence of a uniform, large-
Physics and Astrophysics, Xiamen University, Xiamen, Fujian scale magnetic field configuration. In this context, one
361005, China could intuitively understand the polarization properties
2 Zhang et al.
bythefollowingmethods. Inanopticallythinregion,the black hole induce the generation of jets by means of
electric vector of the emitted radiation is perpendicular a magneto-centrifugal mechanism (Blandford & Znajek
to the magnetic field direction and the linear polariza- 1977; Blandford & Payne 1982). Therefore, it is natu-
tiondegreeisgivenbyΠ= p+1 (Rybicki & Lightman ral that when modelling the multi-broadband observa-
p+7/3
tionsofX-raybinaries,theordered,large-scalemagnetic
1979),wherep isthe spectralindexofemittingrelativis-
field configuration is usually assumed in operation in
tic electrons. However, the electric vector of the emit-
many published works. Due to the generation of the
ted radiation is parallel, rather than perpendicular, to
shock waves and compression between them, it is easy
the magnetic field direction in an optically thick region,
where the degree of polarizationis written as Π= 3 to envision that the large-scale magnetic fields could be
6p+13 disturbed or disrupted to bring about random, small-
(Longair 2011). Inthis paper,oneofourmainpurposes
and large-scalefields, which are mixed by some random,
is to suggest that a highly polarized emission does not
small-scale turbulent magnetic fields generated behind
necessarily require that the magnetic field in X-ray bi-
shock fronts by the turbulence. The anisotropy of these
naryjets haveauniform,large-scaleconfiguration,ifthe
turbulentfieldscanbegeneratedbycompressionofshock
configuration of turbulent magnetic fields has a certain
waveswithinthejetorshearatthejetboundarylayerof
anisotropy.
initially chaotic magnetic fields as well as by production
As is known, magnetic turbulence is ubiquitous in as-
of anisotropic turbulence by the shock wave itself. In
trophysicalobjectsandplaysancriticalroleinkeyastro-
this work, anisotropic structures are confined to a lim-
physical processes, such as star formation, acceleration
iting case of the total compression, i.e., a slab geometry
andpropagationofcosmicrays,heattransport,magnetic
(e.g.,Laing 1980),inwhichdirectionsofmagneticfields
reconnection,amplificationofmagneticfields,andaccre-
are parallel to the slab plane.
tionprocesses(seeZhang et al.2016,forabriefreviewin
Inthesehighlyturbulentenvironments,whenthechar-
theintroductionsection). Itisnecessaryfortheexistence
acteristic scale of turbulence λ, which is of the or-
of turbulent magnetic fields to induce a diffusive shock
der of the plasma skin-depth, is greater than the non-
acceleration. Whenparticlescrosssuccessivelytheshock relativistic Larmor radius R = m c2/eB, radiation
L e
front,magneticturbulencewouldtraptheseparticlesand
proceeds in the usual synchrotron regime. Here, B is
results in the particle energy gain. Moreover, particle-
the strength of the magnetic field as a function of the
in-cellsimulationsdemonstratethataWeibelinstability,
height of the jet, and other parameters have a con-
which is a crucial ingredient for amplification of mag-
ventional meaning. On the contrary, λ R , the
L
netic fields and production of collisionless shock waves ≪
emission is referred to as diffusive synchrotron radia-
(e.g.,Spitkovsky 2008;Medvedev et al. 2011),cangen-
tion (Toptygin & Fleishman 1987), or jitter radiation
erate turbulent magnetic fields in the shock waves, and
(Medvedev 2000; Kelner et al. 2013). Below, we first
that a conspicuous anisotropy of the magnetic turbu-
studytheevolutionofrelativisticelectronsinjets,which
lence appears at the saturation stage of field amplifica-
has an isotropic distribution along the jets. Subse-
tion (Medvedev et al. 2011).
quently, the configurations of the magnetic slab and the
We consider that random, turbulent magnetic fields
jet and radiative mechanisms of polarization are pre-
appearinthe jetofblackholeX-raybinaries(seeLaing
sented.
1980; Kelner et al. 2013; Prosekinet al. 2016for theo-
reticalbasics). Thesemagneticfieldsmixedbylarge-and 2.1. Relativistic Electron Evolution
small-scale random structures are confined to a certain
We consider that the evolution of steady-state rel-
plane(slab),i.e.,thelimitingcaseofathree-dimensional
ativistic electrons in a conical jet is formulated as
geometry of the total compression, which results in the
(Zdziarski et al. 2014b; Zhang & Lu 2015; Zhang et al.
polarized synchrotron and jitter emissions. With this
2015)
magnetic field configuration, we explore whether rela-
tivistic electrons in random fields can produce an ex-
1 ∂ ∂ dγ
pected highly polarized emission in the jets of X-ray bi- [Γ βcz2N˜ (γ,z)]+ Γβ cN˜ (γ,z) =Q (γ,z),
z2∂z j j γ ∂γ (cid:20) j j γ dz(cid:21) in
naries.
(1)
The paper is organized as follows. Model descriptions
where the first term denotes spatial advection, corre-
including relativistic electronevolution,modelgeometry
and radiative mechanisms of polarization are presented sponding to the divergence term, ▽ υN˜γ, in a spherical
·
in Section 2. Numerical results of the model are shown coordinate, and the second term energy losses of rela-
in Section 3. Section 4 is an application of the model to tivistic electrons. Qin is called the source term, that is,
Cygnus X–1. Conclusions and discussion are presented the injection rate of relativistic electrons, which has the
in Section 5. dimension erg−1 s−1 cm−3. N˜ is the energy density of
γ
electrons, as a function of the electron energy γ and the
2. MODEL DESCRIPTIONS jet height z from the central compact object. Γ is the
j
We employ a classical geometry of the microquasar bulk Lorentz factor of the jet, and β = Γ2 1/Γ the
in which dipole jets are launched from the inner re- j q j − j
bulk velocity. In order to make Equation (1) more com-
gions of an accretion disk, perpendicular to the or-
pact and numericalcalculation convenient,we introduce
bital plane of binary system. Thanks to collision in-
teractions between the ejected matter, shock waves are a symbol Nγ, then let Nγ(γ,z)=N˜γπRj2etΓjβjc with di-
generated in the bulk motion of the jets. Theoreti- mension erg− s−1. R = ztanδ is the radius of the
jet
cal works suggested that the ordered, large-scale mag- jet, where δ is a half-opening angle of the jet. In this
netic fields anchored in an accretion disk or a rotating way, Equation (1) is rewritten as the following compact
Polarizationradiation from X-ray binaries 3
form(seealso,Moderski et al. 2003;Zhang & Lu 2015; (1)Theangleθbetweenthejetdirectionj andtheline
Zhang et al. 2015), ofsight n. Their scalarproduct is givenby cosθ =j n.
·
(2) The angle θ between the projection of the jet
pos
∂Nγ(γ,z) + ∂ N (γ,z)dγ =πR2 Q (γ,z), (2) jproj on the sky plane and the direction to the North
∂z ∂γ (cid:20) γ dz(cid:21) jet in celestial pole. Here, j = (j cosθn)/j cosθn is
proj − | − |
the unit 2-D vector for the projection of the jet vector
where, the energy loss rate of relativistic electrons along
j on the sky plane and eˆ is the unit vector on the sky
the jet is N
plane pointing to North. Further, we have cos(θ ) =
dγ 1 dγ 2γ pos
dz = cβjΓj (cid:18)dt′(cid:19)rad− 3z. (3) jjeptr.oj·eˆN, where θpos is called the position angle of the
(3) The angle ϕ between the normal to the slab s and
Thetotalradiativelossratesofelectrons,(dγ/dt′)rad,in- the line of sight n. Two unit vectors’ scalar product is
cludesynchrotronandjitteremissions,andComptoniza- cosϕ = s n = σ. The symbol σ is here introduced for
tionofthephotonsfromthecompanion. Inthiswork,we ·
thesakeofcompactnesswhenwritingradiativeformulae.
neglect synchrotronself-Compton scattering and Comp-
(4)Theangleϕ betweenprojectionofthenormalto
pos
tonizationofthephotonsfromaccretiondiskandcorona the slab s and the North. s = (s cosϕn)/s
proj proj
components, on the basis of the studies of Zhang et al. cosϕn is the unit 2-D vector for the pro−jection of|th−e
(2014). The secondterm of the right-handside ofEqua- norma|l vector s to the slab on the sky plane. Thus, we
tion (3) indicates the adiabatic loss of relativistic elec- have cos(ϕ ) = s eˆ , where ϕ is the position
pos proj N pos
trons due to an adiabatically expanding jet. ·
angle of the slab.
Theinjectionoftheacceleratedelectronsisconsidered
(5) The angle α between projection of the normal
pos
as to the slab s and the projection of the jet j . The
Q (γ,z)=Q γ−pexp( γ/γ ), (4) proj proj
in 0 cut scalar product is cos(α )=j s .
− pos proj· proj
wherepandγ arethespectralindexandbreakenergy (6) The polarization angle Φ between the polarization
cut
ofthe relativisticelectrons,respectively. The normaliza- vector e and the North.
tion constant of relativistic electrons, Q , is determined (7) The angle Ψ between polarization(electric) vector
0
by ofthe radiatione onthe skyplane andprojectionofthe
zmax γmax normaltotheslabsproj. Ψwouldappearintheradiation
L =π dz dγR2 Q (γ,z)γ, (5) formulaeofbothsynchrotronandjitterprocesses. Inthe
rel Zz0 Zγmin jet in case of linearly polarizedradiation, if Ψ=90◦, radiative
flux is P = I Q for jitter radiation and P =
where Lrel = ηrelηjetLacc is the power of injection elec- I Qjit forjsityn−chrjoittron radiation, whereas if Ψsy=n 0,
trons, and L = M˙ c2 is the accretion power of the syn− syn
acc acc P =I +Q forjitterradiationandP =I +Q
jit jit jit syn syn syn
system via stellar wind outflows of the companion star.
for synchrotron radiation (see also Eqs. (12) and (22)).
Here, M˙acc 10−8M⊙yr−1 is the mass accretion rate Thismeansthatthefluxislargerinthedirectionparallel
∼
for a high-mass system. The power of relativistic elec- to s . Therefore, the polarization vector e is parallel
proj
trons, Lrel = ηrelLjet, is a fraction of the jet power of to sproj.
Ljet = ηjetLacc, where ηjet is set as 0.1 and ηrel is an Letuswritej =sinθcosθposeˆN+sinθsinθposeˆE+cosθeˆn,
adjustable parameter. γmin and γmax(∼ 107) are mini- s = sinϕcosϕposeˆN +sinϕsinϕposeˆE +cosϕeˆn, and n =
mumandmaximumenergiesofthe relativisticelectrons, eˆ ,whereeˆ isthe unitvectorontheskyplanepointing
n E
respectively. to East. Once the polarizationangle Φ is determined by
observation, one can obtain ϕ in terms of the angle
pos
2.2. Model Geometry relation ϕ = Φ. Furthermore, provided that θ and ϕ
pos
are fixed, as well as the position angle of the jet θ on
Inordertodeterminethepositionsofboththeslaband pos
theskyplaneisknownbyobservation,wecanderivethe
the jet on the sky plane, and formulate the subsequent
angle α and the angle ϑ between j and s.
polarizationradiativeprocesses,weinFigure1providea pos
schematic illustration for the model geometry. The def-
inition of the position angles of both the jet and slab is
2.3. Polarization Processes
associated with the angles on the sky plane relative to
the North celestialpole, and these angles are counted to 2.3.1. Polarization of Synchrotron Emission
theEast,i.e.,counter-clockwise. Asshown,thedirection
Wepresentthesomemainformulaerelatedtothecur-
of the line of sight is denoted as the unit vector n that
rentwork,onthebasisofProsekin et al. (2016)’sworks.
is perpendicular to the sky plane, the direction of the
Thepowerspectrumofsynchrotronradiationofrelativis-
jet as the unit 3-D vector j, and the normal directionto
tic electrons in the tensor form is expressed as
the slab of turbulent magnetic fields as the unit vector
s. In the three-dimensional coordinate reference frame
√3e2
constituted by both the sky plane and the observer line Psyn = [I δ Q (δ 2s s )], (6)
of sight, s also is a unit 3-D vector. It should be no- ik 4πR syn ik− syn ik− proj,i proj,k
L
ticed that generally three vectors n, j, and s are not
coplanar except for in the particular space position; the where, δ is the two-dimensional Kronecker delta per-
ik
2-Dprojectionvectorsontheskyplaneofthetwolatters pendicular to the direction n. I and Q correspond
syn syn
are indicated as j , and s , respectively. Now we to the prefactor to the Stokes parameters I and Q, re-
proj proj
distinguish the following completely different angles: spectively. They are given by
4 Zhang et al.
whereK (ζ)andK (x)arethemodifiedBesselfunc-
5/3 2/3
tions. The power spectrum in some particular direction
e, i.e., the position of electric vector in the plane per-
Jet axis pendicular to n, is written as
j √3e2
North Observer Psyn =Piskyneiek = 4πR [Isyn−Qsyn(1−2cos2Ψ)]. (12)
L
n
Using Equations (7) and (8), the degree of polarization
ofsynchrotronemissionofelectronpopulationis written
as
pos
s Q (ω)
jproj Πsyn(ω)= syn . (13)
I (ω)
syn
o
pos pos Integrating the power spectrum Psyn over the frequency
ω,wecanobtainthepolarizationdegreeofthetotalsyn-
chrotronradiation to be
Q (ω)dω 3 1 σ2
syn
sproj Πsyn = R I (ω)dω = 4(cid:18)1−+σ2(cid:19). (14)
syn
R
East As shown below, jitter radiation has the same polariza-
Fig. 1.— A schematic illustration of the positions for the slab
tion degree for its total radiation intensity.
(withthe unit normalvector s) ofturbulent magnetic fields com-
pressed by shock waves and for the jet (a unit 3-D vector j), as
wellasoftheskyplaneperpendicular tothelineofsight,n. The 2.3.2. Polarization of Jitter Emission
2-D projections on the sky plane of the 3-D vectors j and s are
denotedasjprojandsproj,respectively. Notethatthreevectorsj, The power spectrum of jitter radiation of relativistic
n,ands arenotcoplanarexceptforthecaseofaparticularspace
electrons in the tensor form is written as
position.
e4 B2
Pjit = ss [I δ Q (δ 2s s )], (15)
ik m(cid:10)2c4(cid:11) jit ik− jit ik− proj,i proj,k
where B is the strength of small-scale turbulent mag-
ss
netic field in the jet. The paper assumes that B has
ss
zmax γmax the same spatial distribution along the jet as the large-
I (ω)=π dz dγN˜ (γ,z)Imon(ω)R2 (z),
syn Z Z γ syn jet scale magnetic field, i.e., Bss = ςBls, where, ς is the ra-
z0 γmin tio factor. The functions I and Q correspond to the
(7) jit jit
prefactoroftheStokesparametersI andQ,respectively.
zmax γmax
Q (ω)=π dz dγN˜ (γ,z)Qmon(ω)R2 (z). They are determined by
syn Z Z γ syn jet
z0 γmin zmax γmax
(8) I (ω)=π dz dγN˜ (γ,z)Imon(ω)R2 (z),
Here the functions Imon and Qmon arise from a jit Z Z γ jit jet
syn syn z0 γmin
monoenergetic electron emission, and are written as (16)
(Prosekin et al. 2016) zmax γmax
Q (ω)=π dz dγN˜ (γ,z)Qmon(ω)R2 (z),
2 π/2 jit Zz0 Zγmin γ jit jet
Imon(ω)= χF(ξ/χ)dφ , (9) (17)
syn π Z0 B where the functions Imon and Qmon are given by (see
jit jit
Prosekinet al. 2016)
2 π/2 2(χ2 σ2) 1
Qmon(ω)= − χ2 G(ξ/χ)dφ ,
syn π Z0 (cid:20) 1−σ2 − (cid:21)χ (B10) Ijmiton(ω)= 4π12 (cid:18)2γω2c(cid:19)2Z 1 η13̟(2γω2cη)̥1(η,σ)dη,
where χ = [1 (1 σ2)cos2φ ]1/2, ξ = ω/ω , ω = 2πν, 0
B c (18)
− −
ω = 3γ2ω being the critical frequency of the syn-
c 2 B 1 ω 2 1 1 ω
chrotron emission, and ωB = eBmlsc(z) = c/RL being the Qmjiton(ω)= 4π2 (cid:18)2γ2c(cid:19) Z η3̟(2γ2cη)̥2(η,σ)dη.
cyclotron frequency of electrons. Here, B (z) is the 0
ls
(19)
large-scale turbulent magnetic field in the jet, which is
Here, the functions ̥ (η,σ) and ̥ (η,σ) are
considered as B (z) = B z /z, and B is the mag- 1 2
ls ls,0 0 ls,0
netic field strength at the starting position z of a dissi-
0 2σ 1 1
pation region. In Equations (9) and (10), the functions ̥ (η,σ)= +(2 )η2+ 1 η3 η(1+lnσ)
F(x) and G(x) are expressed as 1 (cid:20) 3 − σ (cid:18)3σ2 − (cid:19) − (cid:21)
∞ Θ(σ η)+η(2η η2 1 lnη)Θ(η σ),
− − − − −
F(x)=x K (ζ)dζ, G(x)=xK (x), (11) (20)
5/3 2/3
Z
x
Polarizationradiation from X-ray binaries 5

1 1 σ (1+σ)2η3
̥ (η,σ)= − +σ Θ(σ η)+
2 3(cid:18)1+σ(cid:19)(cid:20) 2σ2 (cid:21) − -1 s] 32
1−1σ2 (cid:20)1+2σ2(1−η2)η− 2σ32(1−η3)(cid:21)Θ(η−σ), L [erg 30
where Θ is the Heaviside step function. The radia(t2io1n) Log 10 28
intensity in the direction e is expressed as
e4 B2 e 1.0
Pjit =Pijkiteiek = m(cid:10)2cs4s(cid:11)[Ijit−Qjit(1−2cos2Ψ)]. (22) egre 0.8
D
Therefore, the degree of polarization of jitter radiation n
o 0.6
per angular frequency is given by ati
z
Q (ω) ari 0.4
Π (ω)= jit . (23) ol
jit I (ω) P 0.2
jit
After integratingthe powerspectrumPjit overthe angu- 0.0
larfrequencyω,wecanimmediatelyobtainthepolariza- 10 12 14 16 18 20 22 24 26
tion degree of the total jitter radiation
Log10 [Hz]
Q (ω)dω 3 1 σ2 Fig. 2.—TheSEDs(upperpanel)andthedegreeofpolarization
Π = jit = − . (24) (lower panel) of jitter radiation as a function of the frequency at
jit R I (ω)dω 4(cid:18)1+σ2(cid:19) ϕ = 80◦, for the different turbulence spectral indices α =2, 5/3,
jit
and3/2.
R
Thus, it can be seen that the polarization degree is con-
sistentwiththatofthesynchrotronradiation. Thefunc-
tion ̟ included in the integrand of Equations (18) and
(19)describesthedistributionofturbulence,andiswrit- general high-mass X-ray binary, i.e., microquasar. The
ten as typicalvaluesofthissystemaregivenasfollows: ablack
Kαλ3 hole mass of MBH = 20M⊙, a distance of d = 2 kpc, an
̟(κ)= . (25) effective surface temperature of the stellar companionof
(1+λ2κ2)1+α/2
T = 104 K, a radius of the companion of Rco = 20R⊙,
The derivationof the normalizationcoefficient Kα satis- anorbitalradiusofbinary systemofRorb ∼1012 cm, an
fies the non-divergentcondition of the magnetic field. It opening angleof the jet of5 degrees,anda bulk Lorentz
is expressed as factor of the jet of Γj =1.5.
RegardingnumericalprocedurestosolveEquation(2),
3 Γ(1+α/2) interested readers are referred to Zhang et al. (2014),
Kα =8π2 , (26)
Γ[(α 1)/2] in which we have studied in detail the evolution of rel-
−
ativistic electrons along the jet. The model parameters
where Γ is the gamma function.
are: the starting point of the dissipation region z ; the
As seen in Equation (25), jitter radiation depends on 0
terminalpositionofthedissipationregionz ;thespec-
thecorrelationscale,λ,ofaturbulentmagneticfieldand max
tral index of relativistic electrons p; the break energy of
the spectral index of turbulence α. The famous Kol-
electrons γ ; the minimum Lorentz factor of electrons
mogorov spectrum presents the index α = 5/3, describ- cut
γ ; the characteristiclength ofturbulence λ; the angle
ing the turbulence in hydrodynamics. However, mag- min
ϕ between the normal to the slab and the line of sight,
netohydrodynamical (MHD) turbulence is more com-
and the magnetic field strength B . These parameter
plex than the hydrodynamical one. In the case of ls,0
valuesarelistedinTable1foreachfigurethroughoutthe
incompressible turbulence, Goldreich & Sridhar (1995)
paper. In the studies of this section, the viewing angle
claimed that spectral index is compatible with hydro- of an observer is set as 30◦.
dynamical scenario. Simulations of compressible MHD
Wefirstexplorehowmagneticturbulenceinfluenceson
turbulence showed that turbulent fluctuations are di-
the properties of polarization and SEDs of jitter radia-
videdintothreetypes(Cho & Lazarian2002): (1)Alfv´en
tion. For our purposes, the ratio factor ς is set as 1, and
wave, which has a Kolmogorov-typespectrum, α=5/3; theangleϕas80◦. InFigure2,weplottheSEDsandpo-
(2) slowmode, which followsthe spectrum of the Alfv´en
larizationdegree of the jitter radiation,with α=2, 5/3,
mode, α=5/3; (3) fast mode, which corresponds to the
and 3/2. At low frequencies, i.e., below the peak fre-
spectrumofacousticturbulence with the index α=3/2.
quency, the change of turbulence index almost does not
In the case of shock environment, turbulence spectrum
affecttheSEDsandpolarizationdegreeofthejitterradi-
is expected to give rise to a steeper spectralindex α 2
∼ ation,andthe SEDshapeis associatedwiththe spectral
(Padoan et al. 2009; Chepurnov at al. 2010).
index of emitting relativistic electrons, which is similar
to spectral behaviors of synchrotron emission. Above
3. NUMERICAL RESULTS
the peak frequency, the turbulence index determines the
In this section, we explore the properties of polariza- shape of SEDs that becomes steeper with increasing the
tion and SEDs by using some typical parameters for a index α. As seen in the lower panel, a large value of
6 Zhang et al.
lower panel. It is evident that the degrees of polariza-
tion of both jitter and synchrotron emissions decrease

from 86% to 0%, with decreasing angle ϕ, that is,
1.0
e jitter from 9∼0◦ (observed edge-on) to 0◦ (observed face-on),
e
gr 0.8 respectively. Similar to jitter case (see the lower panel
e
D synchrotron of Figure 2), synchrotronpolarizationdemonstrates also
on 0.6 a sharp increase at radio frequencies, but this increase
ati 0.4 appears at the lower radio bands. In general, these po-
z
ari total larization distributions present plateau features at low
Pol 0.2 frequencies,thenincreaseslowlynearpeakfrequency. As
forthe sameangleϕ, thepolarizedsynchrotronemission
0.0
34 90 10 has a slight larger polarization degree than jitter radi-
-1 L [erg s] 32 863000 0 jitter star IC atphtrieeosnet.nottTaslhaeenmdeiixssstpirooibnnusentiitno-cnlilkuoedfifntohgremndoaengt-rpheoeiglahorfizfpreeodqlauIreCinzacpiterioso.nceosIstf
og 1030 sphoolaurlidzabteiomnednetgiroeneedatthhaigtha-frsehqaurpenccuytoliffmiotfissynacnhuromterorin-
L
synchrotron cal artifact because the relation Π = Qsyn/Isyn remains
finite.
28
10 12 14 16 18 20 22 24 26 As shown in the lower panel of Figure 3, both jit-
Log10 [Hz] terandsynchrotronemissionshavesignificantlydifferent
spectralshapesathigh-frequencylimit. Thesynchrotron
Fig.3.— The degrees of polarization (upper panel) and SEDs emission decreases exponentially over a break frequency
(lower panel) of both the synchrotron and jitter radiation as a ν = 3eB γ2 /4πm c, whereas the jitter radiation
function of the frequency, with a ratio factor, ς =1, of turbulent cut ls cut e
spectrumbeyondthe breakfrequencyν R /λpresents
magneticfieldstrengths,andtheturbulenceindexofα=5/3. Dif- cut L
ferentcurvesindicateindividualcomponents correspondingtothe a long power-law tail, which depends on the turbulence
angle values ϕ as labeled in the legend. The degree of polariza- index α but is independent of a distribution of emitting
tion of the total radiation isshown inthe upper panel. The SED
electrons (see also Figure 2). This unique feature of jit-
of Comptonization of non-polarized soft photons from companion
starisplottedinthelowerpanel. terradiationimplies direct,model-independent informa-
tion about the properties of turbulence spectrum. How-
ever, synchrotron emission can provide information on
energy spectral shapes of emitting relativistic electrons,
turbulence index givesriseto ahighpolarizationdegree. which is associated with different acceleration mecha-
Thelargevalueoftheturbulenceindeximpliesthatmore nisms(seealsoKelner et al. 2013,formorediscussions).
turbulence energiesareconcentratedata larger-scalere- Withdecreasingtheangleϕ,intensitiesofbothjitterand
gion of turbulence (corresponding to small wavenumber synchrotronradiationincrease,whichareanti-correlated
regime). Therefore, the turbulent magnetic field with with their linear polarization degrees.
a large-scale configuration results in a higher polarized Below, we investigate how relative strengths between
radiation at high frequency bands. large-andsmall-scaleturbulentmagneticfieldsinfluence
Itisnoticedthatthepolarizationdegreefirstincreases onthe polarizedjitter andsynchrotronemissionsas well
sharply with increasing frequency at radio wavebands, as IC scattering spectrum of the surrounding compan-
and tends to be slow in the 1012 - 1019 Hz range, then ion. Here, we fix ϕ = 80◦ and α = 5/3, but change the
becomesfasternearthepeakfrequency( 1021 Hz). Af- ratio factor ς. Figure 4 presents the resulting polariza-
∼
ter the peak frequency, the distribution of polarization tiondistributions(upperpanel)andSEDs(lowerpanel).
degree tends to form a plateau, i.e., close to a constant The SEDs of Comptonization of non-polarized soft pho-
polarization degree. In our calculation, we also test the tonsfromcompanionstarareplotted inthe lowerpanel,
influence of different correlation lengths of small-scale whichdependsontherelativestrengthofturbulentmag-
magnetic fields on both SEDs and polarization of jit- netic fields. It is easy to understand this phenomenon
ter radiation. The results demonstrate that the peak because the evolution of injected electrons is related to
frequency of jitter radiation shifts to higher frequencies jitter,synchrotron,IClossesbyEquation(2). Thevaria-
with decreasing the value λ. A change of distributions tionsofthefactorς wouldresultinthechangeofspectral
ofpolarizationdegreeisrelatedinthe samewaytojitter distributionsofemittingrelativisticelectrons,producing
SEDs as those of Figure 2. differentphotonspectralfeatures. Asshowninthelower
We now study how the angle between the line of sight panel, when small-scale magnetic field dominates, i.e.,
and the normalto the slab of chaotic magnetic fields in- ς >1,jitter radiationdominatesemissionoutput. When
fluencesonthepolarizationdegreeandSEDsofbothjit- ς 1,synchrotroncomponentsdominatebelowthechar-
terandsynchrotronemissions. Here,wefirstfixα=5/3 ac≤teristic frequency of the jitter radiation (about 1021
and ς = 1, then change the angle values in order to ob- Hz). At high-frequency limit, jitter radiation is domi-
serve their behaviors. We in Figure 3 plot the degree nant component due to its typical spectral feature rele-
of polarization (upper panel) and SEDs (lower panel) of vant to turbulence nature (see the previous discussions
both the synchrotron and jitter radiation as a function related to Figure 3). With decreasing the value ς, two
of the frequency. Meanwhile, the non-polarized inverse component losses including both jitter and synchrotron
Compton (IC) scattering of the companion star, which decrease compared to IC losses of star, the reason why
is independent of the angle ϕ, is also included in the star IC fluxes increase. As seen in the upper panel, the
Polarizationradiation from X-ray binaries 7
stellar companion (Orosz et al. 2000). The mass of the
former is measured to be 16M⊙, but the mass of the
latter remains relatively uncertain and here is consid-
1.0
e synchrotron ered as 27M⊙ (e.g., Zdziarski et al. 2016). The sys-
e
gr 0.8 tem is located at a distance of 1.86 kpc (Reid et al.
e
D 2011; Xiang et al. 2011), which has a separation dis-
on 0.6 jitter tance, 3.2 1012 cm, between two components, with an
zati 0.4 orbital per×iod of 5.6 days. The parameters related to
ari the companion star are its effective surface temperature
Pol 0.2 Total of 2.8 104 K, and its radius of 16R⊙, which im-
med∼iately×gives the monochromatic luminosity 1038
34 jitter erg s−1, according to the Stefan-Boltzmann law∼. The

-1 s] star IC parameters related to the jet are the bulk Lorentz fac-
og L [erg 103302 t22oo00fr11t44ho;aef,ZΓj2dej0tz1i=ao6rf)s.10k..i2I5n5e◦ta((aZSdldtd.izirtil2iaio0nrn1gs,k6ei)at,enatanlia.ndlc.lt2ihn02ea00t1h1i;oa4Znlaf;d-oozZfpihaetranhsniekngigneeoattrnmaaglla..lel
L
synchrotron to the orbital plane with respect to the line of sight is
28 29◦ (Orosz et al. 2000; Zi´ol kowski 2014).
10 12 14 16 18 20 22 24 26 As discussed in the introduction section, the origin of
Log10 [Hz] MeV tailemission andpolarizationis still an open ques-
tion. Ourworksfocusonunderstandingthepropertiesof
Fig.4.— The degrees of polarization (upper panel) and SEDs itsradiationandpolarizationinaturbulentenvironment
(lowerpanel)ofbothsynchrotronandjitterradiationasafunction
ofthefrequency,withϕ=80◦ andα=5/3,fordifferentvaluesof mixing large- and small-scale magnetic fields. Based on
theratiofactorς labeledinthelegend. Thedegreeofpolarization the relative strength between large-scale turbulent mag-
of the total radiation is shown in the upper panel. The SEDs of netic field and small-scale one, we explore three scenar-
thenon-polarizedICscatteringarealsoshowninthelowerpanel. ios: (1) the case of a dominant small-scale turbulent en-
vironment (ς > 1), jitter radiation contributing to ra-
dio, MeV tail and Fermi LAT (to low frequency bands,
change of the ratio factor ς almost does not influence
<1023 Hz) observations;(2)anequipartitionscenarioof
on the degrees of polarization from individual jitter and
the strength between two turbulent fields (ς = 1), syn-
synchrotron emissions. But, due to the presence of the
chrotronemissionreproducingradioflux,andjitterradi-
non-polarized IC component, the degree of polarization
ation dominating Fermi LAT (< 1023 Hz) observations;
of the total emissions demonstrates a trough feature at
(3) the case of dominant large-scale fields (ς < 1), syn-
high frequency bands.
chrotron radiation emitting radio flux, as well as both
In the above studies, the viewing angle, that is, the
jitter and synchrotron emissions contributing to Fermi
angle between the line of sight and the jet axis is set
as θ = 30◦, which gives a constant Doppler factor via LAT (<1023 Hz) observations.
Under the condition of dominant small-scalemagnetic
D =1/Γ(1 βcosθ). For relativistic motion of the jet,
j − j fields,weinFigure5presentthefittingofmultibandob-
the variationof the angle θ would only effect onthe am-
servationsandthedegreeofpolarizationforCygnusX–1.
plitude of radiation fluxes rather than the SED shape.
In this case, our main purpose is to study the properties
Meanwhile, the change of the viewing angle does not re-
of MeV tail emission and its polarization. The same pa-
sult inthe changeof the polarizationdegree due to both
rametersusedineachpanelarelistedinTable1. Inorder
the jitter and synchrotron emissions, for the same value
to obtain a self-consistent result, we in this set of fitting
oftheangleϕ. However,anincreaseoftheviewingangle
changeonlytheanglesϕbetweenthelineofsightandthe
θ would lead to the decrease in the angle ϑ between the
normal to the plane of turbulent magnetic fields, which
jet axis j and the normal to the slab of magnetic fields
are ϕ = 90◦ (left upper panel), 80◦ (right upper), 70◦
s via the relation cosϑ=j s.
· (leftlower),and60◦ (rightlower),respectively. Itisseen
Similar to a common procedure adopted in studies of
from the figure that jitter radiation reproduces observa-
extragalacticAGN and Galactic jets, the relatednumer-
tions at radio, MeV tail, and γ-ray (about < 1023 Hz)
ical calculations of radiation processes in this study are
bands. The synchrotron component in each panel pro-
carried out in the co-moving frame of the jet, then the
vides a low, negligible flux throughout the wide wave-
results are transformed to the reference frame of the ob-
band, except it has a slight flux contribution at radio
servertoreproduceobservations. Alternatively,provided
bands, for the case of ϕ=90◦ (see upper-left panel). IC
that the calculation is performed in the observer’s ref-
processes of the companion can well explain Fermi LAT
erence frame, and some structures of the slabs in the
observations above 1023 Hz. Take notice that the to-
jet reference frame can be determined, one should re-
tal emission fluxes at radio bands become stronger with
calculate all the directions of slabs taking into account
decreasing the value ϕ, because a smaller observational
relativistic aberration, via the transformation relation,
tanϕ′ =sinϕ/Γ(sinϕ β ). angle results in higher jitter and synchrotron emission
j − j intensities (see also Figure 3).
As shownin eachpanel of Figure 5, synchrotronemis-
4. APPLICATION TO CYGNUS X–1
sion presents an exponent-like cutoff appearing at lower
Cygnus X-1 is a high-mass X-ray binary, in which the frequencies than that of Figure 3; this is because that
centralblackhole identified is accretingmatter from the
8 Zhang et al.

38 38
Obs. data INTEGRAL Obs. data INTEGRAL
-1 erg s] 3346 JSiyttne.r rraadd.. COMPFTeErmLi LAT -1 erg s] 3346 JSiyttne.r rraadd.. COMPFTeErmLi LAT
L [ L [
g 10 32 Radio Star IC g 10 32 Radio Star IC
o o
L 30 Total Spec. L 30 Total Spec.

1.0 1.0
e e
e e
gr 0.8 gr 0.8
e e
D D
n 0.6 n 0.6
o o
zati 0.4 Jitter polarization zati 0.4 Jitter polarization
ari Syn. polarization ari Syn. polarization
Pol 0.2 Total polarization Pol 0.2 Total polarization
0.0 0.0
10 12 14 16 18 20 22 24 26 10 12 14 16 18 20 22 24 26
Log10 [Hz] Log10 [Hz]

38 38
Obs. data INTEGRAL Obs. data INTEGRAL
-1 erg s] 3346 JSiyttne.r rraadd.. COMPFTeErmLi LAT -1 erg s] 3346 JSiyttne.r rraadd.. COMPFTeErmLi LAT
L [ L [
g 10 32 Radio Star IC g 10 32 Radio Star IC
o o
L 30 Total Spec. L 30 Total Spec.

1.0 1.0
e e
e e
gr 0.8 gr 0.8 Jitter polarization
e e
D D Syn. polarization
on 0.6 on 0.6 Total polarization
ati ati
z 0.4 z 0.4
ari Jitter polarization ari
Pol 0.2 Syn. polarization Pol 0.2
Total polarization
0.0 0.0
10 12 14 16 18 20 22 24 26 10 12 14 16 18 20 22 24 26
Log10 [Hz] Log10 [Hz]
Fig. 5.— The fitting of multiband observations and the degree of polarization for Cygnus X–1, in the case of dominant small-scale
turbulentmagneticfield. Theplottedobservations areradiodatafromFenderetal.(2000),hardX-raydatapointsfromZdziarskietal.
(2012)byINTEGRAL,softγ-raydatafromMcConnelletal. (2011)byCOMPTEL,FermiLATobservationsfromZdziarskietal. (2016).
ThelowerlimitofIRemissionobserved,whichhasahighfluxandisusuallyexplainedastheblackbodyradiationofthestellarcompanion,
ismarkedas‘K’glyph. TheupperlimitsofMAGICismarkedapproximatelyonthefigureaccordingtoAlbertetal. (2007). Theangles
betweenthelineofsightandthenormaltotheslabofturbulentmagneticfieldsareϕ=90◦ (leftupperpanel),80◦ (rightupper),70◦ (left
lower), and 60◦ (right lower), respectively. Different curves indicate individual and total polarization and radiation spectral components
aslabeledinthelegend.
TABLE 1
The ModelParameters Used inthe Study.
Case ς λ[RL] α z0[Rorb] zmax[Rorb] Bls,0[G] ηrel p γmin γcut ϕ
Fig. 2 1 0.1 X 0.01 50 100 0.3 2 50 5×106 80◦
Fig. 3 1 0.1 5/3 0.01 50 100 0.3 2 50 5×106 X
Fig. 4 X 0.1 5/3 0.01 50 100 0.3 2 50 5×106 80◦
Fig. 5 12 0.03 2 0.07 1 420 0.06 1 1 6×104 X
Fig. 6 1 0.3 5/3 0.05 15 60 0.3 2 60 8×106 X
* Note. Symbolindicatingς: ratioofsmall-tolarge-scalemagneticfield;λ: coherencelengthof
magnetic field; α: turbulence spectral index; z0: onset of dissipation; zmax: end of dissipation;
Bls,0: magnetic field strength; ηrel: transform factor of electrons; p: electron spectral index;
γmin: electronminimumenergy;γcut: electronbreakenergy;RL: non-relativisticLarmorradius;
Rorb: orbitalradiusofbinarysystem;ϕ: theanglebetweenthenormaltotheslabandtheline
ofsight;X:indicatingthechangeofcorrespondingparameters.
Polarizationradiation from X-ray binaries 9

38 38
Obs. data INTEGRAL Obs. data INTEGRAL
-1 erg s] 3346 JSiyttne.r rraadd.. COMPFTeErmLi LAT -1 erg s] 3346 JSiyttne.r rraadd.. COMPFTeErmLi LAT
L [ L [
g 10 32 Radio Star IC g 10 32 Radio Star IC
o o
L 30 Total Spec. L 30 Total Spec.

1.0 1.0
e e
e e
gr 0.8 gr 0.8
e e
D D
n 0.6 n 0.6
o o
zati 0.4 Jitter polarization zati 0.4 Jitter polarization
ari Syn. polarization ari Syn. polarization
Pol 0.2 Total polarization Pol 0.2 Total polarization
0.0 0.0
10 12 14 16 18 20 22 24 26 10 12 14 16 18 20 22 24 26
Log10 [Hz] Log10 [Hz]

38 38
Obs. data INTEGRAL Obs. data INTEGRAL
-1 erg s] 3346 JSiyttne.r rraadd.. COMPFTeErmLi LAT -1 erg s] 3346 JSiyttne.r rraadd.. COMPFTeErmLi LAT
L [ L [
g 10 32 Radio Star IC g 10 32 Radio Star IC
o o
L 30 Total Spec. L 30 Total Spec.

1.0 1.0
e e
e e
gr 0.8 gr 0.8 Jitter polarization
De De Syn. polarization
n 0.6 n 0.6 Total polarization
o o
zati 0.4 Jitter polarization zati 0.4
ari Syn. polarization ari
Pol 0.2 Total polarization Pol 0.2
0.0 0.0
10 12 14 16 18 20 22 24 26 10 12 14 16 18 20 22 24 26
Log10 [Hz] Log10 [Hz]
Fig. 6.— The fitting of multiband observations and the degree of polarization for Cygnus X–1, in the case of equipartition turbulent
magneticfield. Theanglesbetweenthelineofsightandthenormaltotheslabofturbulentmagneticfieldsareϕ=90◦ (leftupperpanel),
80◦ (rightupper),70◦ (leftlower),and60◦ (rightlower),respectively. Theother components plottedarethesameasthoseofFigure5.
10 Zhang et al.
in our fitting the low break energy γ = 6 104 is γ = 60 and γ = 107. The fitting results show that
cut min cut
×
required. The synchrotronprocess provides a higher po- the radio fluxes are from the synchrotron emission, and
larization degree than the polarized jitter radiation, but Fermi LATfluxestolowfrequencybands(<1023Hz)are
due to low synchrotron emission fluxes it is not promis- acombinationofjitterandsynchrotronemissions. Fermi
ing to detect such a synchrotron polarization signal. As LAT fluxes to highfrequency bands(>1023 Hz) aredue
expected, the jitter radiation at MeV tail can provide to non-polarized IC processes of the surrounding com-
a high polarization degree. The integrated polarization panion. We do not include these figures in the paper for
degrees at soft γ-ray bands (MeV tail: 0.4–2 MeV) are a conciseness, but they, generally speaking, are similar
81% for ϕ = 90◦, 78% for ϕ = 80◦, 69% for to that of Figure 6. The integrated polarization degrees
ϕ∼ = 70◦, and 55%∼for ϕ = 60◦, respecti∼vely. The we obtain are 61% at radio band due to synchrotron
∼ ∼
polarization observations demonstrated that the degree polarization, 75% at Fermi energy region from both
∼
of polarization is 67 30% between 400 keV and 2 jitter and synchrotron polarizations, for the case of the
MeV(Laurent et al.20±11), 76 15% at0.23–0.85MeV angle ϕ= 90◦. In the same way, we have the degrees of
±
(Jourdain et al. 2012), or 75 32% between 0.4 MeV polarization: 53% at radio and 72% at Fermi ener-
and 2 MeV (Rodriguez et al. 2±015). Hence, our theoret- gies( 1023 H∼z)forϕ=80◦; 41∼%atradioand 61%
ical works can constrain the angle ϕ up to about 75◦, atFer≤mi energies for ϕ=70◦∼; as wellas 29%at∼radio
in which the integrated polarization degrees are 75% and 46% at Fermi energies for ϕ=60◦∼.
∼ ∼
at MeV tail (0.4–2 MeV), 79% at Fermi LAT energy The fitting procedures used above are similar to those
∼
regime (between 1022 and 1023 Hz), and 30% at radio presentedinZhang et al. (2014),inwhichwehavestud-
bands (between 2 109 and 2 1011 Hz∼).The position iedtheoriginofmultibandemissioninacertainregionof
angle value of the C×ygnus X–1 j×et, whichis slightly time the jet. Here, we simply express the motivations for the
dependent, is about 21◦ to 24◦ counted from North to parameter choice. Based on the studies in Zhang et al.
East (Stirling et al. 2001). Noticing ϕ = 75◦ (the an- (2014), in which the MeV tail emissions are produced
gle between s and n) and θ = 29◦ (the angle between inside the binary system and the GeV band emissions
j and n), as well as the observationalpolarizationangle are from the distance close to the binary system scales,
Φ 40◦, we obtain the angle ϑ 47◦ between j and s, we thus fix zmax = Rorb (see Figure 5) and 15Rorb (see
an≈dthe angleα 16◦ between≈j ands ,onthe Figure 6) for fitting MeV tail plus Fermi LAT data and
pos ≈ proj proj for only Fermi LAT data, respectively. Then, we ad-
basis of Section 2.2.
just magnetic field strength B and z to calculate
Our purpose is not to fit the radio emission or ex- ls,0 min
radiative fluxes due to jitter, synchrotron and IC scat-
plain the corresponding polarization feature. The radio
tering processes. Noticing competition between jitter,
data we have plotted on the figure is to provide a con-
synchrotronandICradiationlosses,wefurtherchangeς,
straint for an upper limit of theoretical SEDs. These
whichisdirectlyassociatedwithcompetitionbetweenjit-
radio emissions are usually considered to originate from
ter and synchrotron emissions, and indirectly influences
the regionof large-scalejets. Observationally,the polar-
on the IC spectra (ς in Figure 5 is adjusted to 12 due to
ization degree in this waveband is less than 10 per cent
this reason). Besides, it should be noticed that the pa-
(Stirling et al. 2001). In general, it needs to consider
rametersz andγ wouldimpactonemissionfluxes
self-absorptionprocessesoflowfrequencyradioemissions max min
in the radio frequency band.
inthiscase,whichwoulddecreasethedegreeofpolariza-
From the above fittings, we find that SED fittings ex-
tionpredictedinthispaper,butthisisbeyondthescope
ist relatively large degeneracy. For instance, as for the
of the paper.
change of the angle ϕ, the model can provide a good fit-
Now, we consider an equipartition scenario (ς = 1) of
ting,butthedegreeofpolarizationdistinctfromSEDsis
strengths between turbulent magnetic fields. The fitting
very sensitive to the angle values. It is necessary for the
resultsofmultibandobservationsofCygnusX–1andthe
presenceofthe dominantsmall-scaleturbulentmagnetic
corresponding polarization degree are plotted in Figure
fields to explain the highly polarized hard X-ray/soft γ-
6, in whichthe fitting parametersused in eachpanelare
rayemissions,i.e.,MeVtailpolarizedradiation. Thus,it
listed Table 1. As shown in this figure, the synchrotron
can be seen that the study of polarization radiation is a
emission can reproduce radio observationsand the jitter
robust method to uncover the origin of multiband emis-
radiation provides emission fluxes at high-energy bands
(< 1023 Hz). The integrated polarization degrees are sions,thestructureofmagneticfields,andtheproperties
∼ of turbulence.
59%atradiobandmainlyfromsynchrotronpolarization,
76% at Fermi energy region from the combination of 5. CONCLUSIONS AND DISCUSSION
∼
both jitter and synchrotron polarization radiation, for
the case of the angle ϕ = 90◦. Similarly, the integrated In this paper, we have studied the properties of po-
larized radiation from X-ray binaries, by assuming the
polarizationdegreesaregivenasfollows: 53%atradio
bands (between 2 109 and 2 1011 Hz)∼and 71% at existence of the turbulent magnetic field environment in
Fermi energies (be×tween 1022 a×nd 1023 Hz) for∼ϕ=80◦; the jet. These turbulent fields are composed of large-
40%atradioand 60%atFermi energiesforϕ=70◦; andsmall-scalemagneticfieldstructures,whichresultin
a∼s well as 29% at∼radio and 46% at Fermi energies a polarized jitter radiation when the correlation length
for ϕ=60∼◦. ∼ of turbulence is less than the non-relativistic Larmorra-
dius, i.e., λ R , or a polarized synchrotron emission
We study here the case of dominant large-scale fields ≪ L
when λ > R . We calculate numerically the SEDs and
(ς = 0.6). We first fit multiband observations using L
thedegreeofpolarizationforageneralmicroquasar. The
the following parameters: λ = 0.3R , α = 5/3, z =
L 0 resultsshowthatturbulentmagneticfieldconfigurations
0.05R , z =15R , B =60 G, η =0.3, p=2,
orb max orb ls,0 rel can indeed provide a high polarization degree. Then,