Polarization in Pulsar Wind Nebulae Delia Volpi In collaboration with: L. Del Zanna - E. Amato - N....
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Transcript of Polarization in Pulsar Wind Nebulae Delia Volpi In collaboration with: L. Del Zanna - E. Amato - N....
S
Polarization in Pulsar Wind Nebulae
Delia Volpi
In collaboration with: L. Del Zanna - E. Amato - N. Bucciantini
Dipartimento di Astronomia e Scienza dello Spazio-Università degli Studi di Firenze-Italy
Observations: optical and X-ray Continnum emission
Jet-torus structure
Crab Nebula
PWN
Optical (Hubble)
X-ray (CHANDRA)
Vela PSR 1509-58 G 54.1+0.3
RELATIVISTIC MHD Models
Analytical 1-D models (Kennel & Coroniti ,1984 -- Emmering and Chevalier,1987): no jet-torus structure.
Analytical 2-D models (Bogovalov & Khangoulian, 2002 -- Lyubarsky, 2002): anisotropic Poynting+kinetic energy flux torus and oblate TS. Jets collimated by hoop stresses downwards TS.
RMHD simulations (Komissarov and Lyubarsky, 2003 – Del Zanna et al., 2004) solve 2-D hyperbolic equations and confirm jet-torus morphology theories
Lyubarsky, 2001
IDEAL RMHD EQUATIONS
€
∂ ργ( )∂t
+∇ • ργr v ( ) = 0 continuity equation
∂r S
∂t+∇ •
r T = 0 equation of the momentum conservation
∂U∂t
+ c2∇ •r S = 0 equation of the energy conservation
∂r B
∂t−∇×
r v ×
r B ( ) = 0 Faraday induction equation
r S =
w
c2γ 2r
v +1
4πc
r E ×
r B
r T =
w
c2γ 2 r
v r v −
14π
r E
r E +
r B
r B ( ) + P + uem( )I U = wγ 2 − P + uem
w = ρc2 +Γ
Γ −1P Γ =
43
uem =E2 + B2
8π
r E = -
r v ×
r B
c Ohm law
Adiabatic equation of state
ECHO: GRMHD 3-D VERSION (Del Zanna et al., 2007, A&A, 473, 11)
Numerical model• 2-D (axysimmetric) RMHD shock capturing code in spherical coordinates (Del
Zanna et al., 2002, 2003, 2004) • Initial cold ultrarelativistic Pulsar Wind with v radial and r-2 +SNR+ISM Lorentz factor (conservation of energy along streamlines) :
Anisotropic energy flux:
Toroidal field:
• Space and time evolution of RMHD equations+ maximum particle energy (Lorentz factor) equation with adiabatic and synchrotron losses averaged on the pitch angle:
€
γ θ( )=γ0α
0+ 1−α
0( )sin 2 θ( ) γ 0= 100 α
0= 0.1 anisotropy parameter
€
F0 r,θ( ) = F0r0r
⎛ ⎝ ⎜
⎞ ⎠ ⎟2
α 0 + 1− α 0 +σ( )sin2 θ[ ] σ =B2
4πwγ 2= magnetization parameter
€
B r,θ( ) = B0r0r
⎛ ⎝ ⎜
⎞ ⎠ ⎟sinθ tanh b
π2
−θ ⎛ ⎝ ⎜
⎞ ⎠ ⎟
⎡
⎣ ⎢ ⎤
⎦ ⎥ b = width of striped wind region
(b =/2)
w=c2+4p
€
d
dt'lnε
∞=
d
dt'ln n1/3 +
1
ε∞
dε∞
dt'
⎛
⎝ ⎜
⎞
⎠ ⎟sync
dε
∞dt'
⎛
⎝ ⎜
⎞
⎠ ⎟sync
= −4e4
9m3c5 B'2ε∞
2
Synchrotron emission recipes
• Emitting particles’ isotropic distribution function at termination shock (TS = 0)
(Kennel & Coroniti, 1984b):
• Post-shock distribution function (obtained from conservation of particles’number along streamlines and under condition of 0.5):
€
f0(ε0 ) =A
4πε0
−(2α +1) ε 0min≤ ε0 ≤ ε0
max A = Knn0 = Kpp0
mc2
€
f (ε ) =K
p
4π
p
mc2ε −(2α +1) ε <ε
∞ K
p= constant
spectral index
Synchrotron emission recipes
• Emission coefficient in observer’s fixed frame:
Relativistic corrections:
• Cut-off frequency for synchrotron burn-off (evolved in the code from the maximum particle energy):
€
jν(ν , ˆ n )∝Cp
r B ' × ˆ n '
α +1
Dα + 2ν −α ν∞
≥ ν
jν(ν , ˆ n ) = 0 ν
∞< ν
D =1
γ (1−r β • ˆ n )
= Doppler boosting factor r β =
r v
c
ˆ n ' = D ˆ n +γ 2
γ +1
r β • ˆ n −γ
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟r β
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
r B ' =
1
γ
r B +
γ 2
γ +1
r β •
r B ( )
r β
⎡
⎣ ⎢
⎤
⎦ ⎥
€
ν ∞ =D3e
4πmc
r B ' × ˆ n ' ε
∞
2
observer direction versor
optical or X-ray frequency of observation
Synchrotron emission recipes• Surface brightness:
• Stokes parameters (linear polarization):
• Polarization fraction () and polarization direction (P):
• Spectral index () for two frequencies (1, 2) and integrated spectra (F):
€
Iν (ν ,Y ,Z) = jν−∞
+∞
∫ (ν , X,Y ,Z)dX X = line of sight Y, Z = plane of sky
€
Qν (ν ,Y ,Z) =α +1
α + 5/3jν
−∞
+∞
∫ (ν , X,Y ,Z) cos 2χ( )dX
Uν ν ,Y ,Z( ) =α +1
α + 5/3jν
−∞
+∞
∫ (ν , X,Y ,Z) sin 2χ( )dX local polarization position anglebetween emitted electric field and Z
€
Πν =Q
ν
2+U
ν
2
Iν
r P
ν= Π
νsin χ( ) ˆ x + cos χ( ) ˆ y ( )
€
αν ν1,ν
2,Y ,Z( ) = −
log Iν
ν2,Y ,Z( ) / I
νν
1,Y ,Z( )[ ]
log ν2/ν
1( )
Fν
ν( ) =1
d 2I
νν ,Y ,Z( )∫∫ dYdZ d=distance of emitting object
Wind magnetization Runs with effective=0.02
(averaged over ) A (=0.025, b=10) B (=0.1,
b=1)
Results: flow structure maps
• RunA: a) Stronger pinching forces smaller wind zone; b) Equipartition near TS; c) Larger magnetized region • particles loose most of their energy nearer to TS; d) Less complex magnetization map.• Supersonic jets and equatorial outflow: v 0.5-0.7c (as in Crab Nebula-Hester-2002, Vela-Pavlov 2003).
=0.025, b=10 narrow striped wind region
=0.1, b=1 large striped wind region
Results: surface brightness maps
• Optical and X emitting particles: = 0.6 (Veron-Cetty & Woltjer,1993)
• Cut-off frequencies: =5364 Å in optical maps (V.C.1993) h=1keV in X maps (Chandra)
• Angles (Weisskopf, 2000): inclination of symmetry axis:300
rotation respect to North: 480
• I normalized respect to maximum value, logarithmic scales
• Larger emitting regions in optical than in X bandsynchrotron burn-off• Internal regions: system of rings (connected to external vortices), brighter arch (inner ring), a central knot (connected to polar cusp region) due to Doppler boosting (very strong near TS, vc)• Stronger emission near TS where magnetization and velocity are higher
=0.025, b=10 narrow striped wind region
=0.1, b=1 large striped wind region
HIGH RESOLUTION POLARIZATION MAPS TOY MODEL
UNIFORM EMITTING TORUS WITH B TOROIDAL AND V RADIAL : ANGLE SWING INCREASES WITH V AND BIGGER IN THE FRONTv=0.2C θ=90° - - v=0.5c θ=75° -- v=0.8c θ=60°=>INFORMATION ABOUTFLOW VELOCITYPOLARIZATION FRACTION=>MAXIMUM EVERYWHERE
SAME EFFECT WITH A KC FLOW
Results: optical polarization maps Synchrotron emission
linear polarization
Polarization fraction: Bpoloidal
• Normalization against (+1)/(+5/3)70%• Along polar axis: higher polarized fraction (projected B line of sight)• Outer regions: depolarization (opposite signs of projected B along line of sight)
Polarization direction: vflow
• Ticks: ortogonal to B, lenght proportional to Π (Schmidt, 1979)• Polarization angle swing (deviation of vector direction) in brighter arcs, v c, strong Doppler boost Bigger effect in the front side Origin of the knot????? RunB: more complex structure slow velocity
=0.1, b=1 large striped wind region
=0.025, b=10 narrow striped wind region
Results: X-ray polarization maps=0.025, b=10 narrow striped wind region
=0.1, b=1 large striped wind region
Results: spectral index maps
• Values of Crab Nebula• Optical maps obtained with: 1=5364Å, 2=9241Å (Veron-Cetty & Woltjer, 1993)• X-ray maps obtained with: h1=0.5keV, h2=8keV (Mori et al., 2004)• Spectral index grows from inner to outer regions• RunA: X-ray simulated spectral index maps similar to ones of Crab Nebula (Mori et al, 2004)
= + 1
=0.025, b=10 narrow striped wind region
=0.1, b=1 large striped wind region
Observations: gamma-ray• MAGIC Telescope (J.Albert et al., Arxiv:0705.3244v1, 2007)
• Crab Nebula: gamma-ray standard candle → target of new instruments
• Emission: accelerated electrons+target photons (CMB+FIR+sync)
• HESS: TeV frequencies; GLAST: 20MeV-300GeV
• Disantangle magnetic field and distribution function+adronic component
Synchrotron and IC emission recipes
• Primordial isotropic radio-emitting population (A&A,1996):
• Accelerated wind population at TS (A&A,1996):
• Evolved distribution function (Del Zanna et al., 2006):
• Integration between spectral power per unit of frequency and distribution function:
synchrotron=> monochromatic frequency
IC => respect to ε and ν, total differential cross section, 3 targets (FIR, CMB, SYNC) (Blumenthal and Gould, 1970)
€
fr(ε) =Ar4π
ε−(2αr +1)
e(−ε /ε*r)
€
fTS
(εTS
) =A
TS4π
(ε +εTS
)−(2α
w+1)
e(−ε
TS/ε*
w ) ε
TS= ε
ρ TSρ
⎛
⎝ ⎜
⎞
⎠ ⎟
1/31
1 -ε
ε∞
€
fw(ε) = ρρTS
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
4/3εTS
ε
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
2fTS(εTS)
€
νc = 0.293
4πe
mcB⊥
'ε 2 critical frequency
Results: IC
Multislopes Disconnetted areas in maximum particle energyIC emission in excessEnergy map: Compression around TS of B.Parameter? Distribution function?
=0.025, b=10 narrow striped wind region
Results: IC
Size reduction with increasing frequency: along y-axisJet and torus visible for radio electron distribution, no observational counterpart
=0.025, b=10 narrow striped wind region
Results: IC
Time-variability: gamma-rays similar to X-rays.
=0.025, b=10 narrow striped wind region
Conclusions• Spectra: well reproduced from radio to X-ray. Excess in gamma-ray due to
compression of B around TS (flux vortices).
• Brightness maps: jet-torus structure in gamma-rays as in X-rays (high resolution). Observed dimensions.
• Gamma-ray (as X-ray) time-variability is well reproduced by MHD motions.
COMPLETE SET OF DIAGNOSTIC TOOLS FOR PWNe AND OTHER EMITTING SOURCES (AGN, GRB)
• Future work: direct evolution of the distribution function; investigation of the parameter space; applications to other PWNe (different evolution stages) and other non-thermal emitting sources (AGN, GRB).
• Paper: Simulated synchrotron emission from Pulsar Wind Nebulae (L.Del Zanna, D.Volpi, E.Amato, N.Bucciantini, A&A, 453, 621-633, 2006)
• Paper: Non-thermal emission from relativistic MHD simulations of pulsar wind nebulae: from synchrotron to inverse Compton, D.Volpi, L. Del Zanna, E. Amato, N. Bucciantini, A&A, 2008, 485, 337
WHICH KIND OF CONTINUUM EMISSION FROM RADIO TO SOFT-GAMMA ?
CRAB NEBULA: SAME FRACTION AND POSITION ANGLE OF POLARIZATIONFROM RADIO TO X-RAYS=> SIGNATURE OF SYNCHROTRON EMISSIONOPTICAL (SHKLOVSKY, 1952- DOMBROVSKY, 1954)
SYNCHROTRON EMISSION=> LINEAR POLARIZATION WITH A MAXIMUMOF ≈ 80%
IMPORTANCE OF POLARIZATION: 1) GEOMETRY OF THE SOURCE (PULSAR WIND)2) PROPERTIES OF THE SOURCE=>MAGNETIC FIELD STRENGHT AND DIRECTION3) ACCELERATION OF PARTICLES
OBTAIN SYNTHETIC MAPS FROM NUMERICAL SIMULATIONS AND COMPAREWITH OBSERVATIONS: STUDY OF POLARIZATION
IC emission recipes
Integration between distribution function (primordial and wind) and power per unit of frequency respect to ε and ν(Blumenthal&Gould, 1970)
Incident photon density per unit of frequency: IC from CMB target
IC from FIR target
IC from SYN target
€
nνIC−CMB = 8π
c3νt
2
ehνt /kBT
−1 blackbody formula → T= 2.7K
€
nνIC−FIR = 1
chνt
LνFIR
4πR2 Lν → uniformly emitting region of blackbody radiation
€
nνIC−SYN r
r ,νt( ) = 1chνt
jνsyn r
r ',νt ⎛ ⎝ ⎜
⎞ ⎠ ⎟
r r ' −
r r
∫ dV ' integration over the entire nebula
€
Qν (ν ,Y ,Z ) =α +1
α + 5/3jν (ν ,X ,Y ,Z )cos2χdX
−∞
∞
∫
Uν (ν ,Y ,Z ) =α +1
α + 5/3jν
−∞
∞
∫ (ν ,X ,Y ,Z )sin2χdX
r ′ e ∝
r ′ n ×
r ′ B emitted electric field in the comoving frame
r ′ b =
r ′ n ×
r ′ e radiated magnetic field
r e = γ
r ′ e -
γγ +1
r ′ e •
r β ( )
r β −
r β ×
r ′ b
⎡
⎣ ⎢
⎤
⎦ ⎥ Lorentz transformation
r e ∝
r n ×
r q in the plane of the sky
r q =
r B +
r n ×
r β ×
r B ( )
qY = 1− βX( )BY + βY BX qZ = 1− βX( )BZ + βZBX
cos2χ =qY
2 − qZ2
qY2 + qZ
2 sin2χ = -
2qYqZ
qY2 + qZ
2