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Fund. Physics & Astrophysics of Supernova Remnants. Lecture #1 What SNRs are and how are they observed Hydrodynamic evolution on shell-type SNRs Microphysics in SNRs – electron-ion equ Lecture #2 Microphysics in SNRs - shock acceleration Statistical issues about SNRs Lecture #3

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fund physics astrophysics of supernova remnants
Fund. Physics & Astrophysicsof Supernova Remnants
  • Lecture #1
    • What SNRs are and how are they observed
    • Hydrodynamic evolution on shell-type SNRs
    • Microphysics in SNRs – electron-ion equ
  • Lecture #2
    • Microphysics in SNRs - shock acceleration
    • Statistical issues about SNRs
  • Lecture #3
    • Pulsar wind nebulae
order of magn estimates
Order-of magn. estimates
  • SN explosion
    • Mechanical energy:
    • Ejected mass:
      • VELOCITY:
  • Ambient medium
    • Density: Mej~Mswept when:
      • SIZE:
      • AGE:
classical radio snrs

Tycho – SN 1572

“Classical” Radio SNRs
  • Spectacular shell-like morphologies
    • comparedto optical
    • polarization
    • spectral index(~ – 0.5)

BUT

  • Poor diagnostics on the physics
    • featureless spectra (synchrotron emission)
    • acceleration efficiencies ?
slide4

90cm Survey4.5 < l < 22.0 deg(35 new SNRs found;Brogan et al. 2006)

Blue: VLA 90cm Green: Bonn 11cmRed: MSX 8 mm

  • Radio traces both thermal and non-thermal emission
  • Mid-infrared traces primarily warm thermal dust emission

A view of Galactic Plane

snrs in the x ray window
SNRs in the X-ray window
  • Probably the “best” spectral range to observe
    • Thermal:
      • measurement of ambient density
    • Non-Thermal:
      • synchrotron-emitting electrons are near the maximum energy (synchrotron cutoff)
x ray spectral analysis
X-ray spectral analysis
  • Low-res data
    • Overall fit with thermal models
  • High-res data
    • Abundances of elements
    • Single-line spectroscopy!
shell type snr evolution a classical and wrong scenario
Shell-type SNR evolutiona “classical” (and wrong) scenario

Isotropic explosion and further evolution

Homogeneous ambient medium

Three phases:

  • Linear expansion
  • Adiabatic expansion
  • Radiative expansion

Isotropic

Homogeneous

Linear

Adiabatic

Radiative

basic concepts of shocks

r

V

shock

Strong shock

If

Basic concepts of shocks
  • Hydrodynamic (MHD) discontinuities
  • Quantities conserved across the shock
    • Mass
    • Momentum
    • Energy
    • Entropy
  • Jump conditions(Rankine-Hugoniot)
  • Independent of the detailed physics
forward and reverse shocks

Forward

shock

Density

Reverse

shock

Radius

Forward and reverse shocks
  • Forward Shock: into the CSM/ISM(fast)
  • Reverse Shock: into the Ejecta (slow)
dimensional analysis and self similar models
Dimensional analysisand Self-similar models
  • Dimensionality of a quantity:
  • Dimensional constants of a problem
    • If only two, such that M can be eliminated, THEN evolution law follows immediately!
  • Reduced, dimensionless diff. equations
    • Partial differential equations (in r and t) then transform into total differential equations (in a self-similar coordinate).
early evolution
Early evolution
  • Linear expansion only if ejecta behave as a “piston”
  • Ejecta with and
  • Ambient medium with and
  • Dimensional parameters and
  • Expansion law:
a self similar model
A self-similar model

(Chevalier 1982)

  • Deviations from “linear” expansion
  • Radial profiles
    • Ambient medium
    • Forward shock
    • Contact discontinuity
    • Reverse shock
    • Expanding ejecta
evidence from sne
Evidence from SNe
  • VLBI mapping (SN 1993J)
  • Decelerated shock
  • For an r-2 ambient profileejecta profile is derived
the sedov taylor solution
The Sedov-Taylor solution
  • After the reverse shock has reached the center
  • Middle-age SNRs
    • swept-up mass >> mass of ejecta
    • radiative losses are negligible
  • Dimensional parameters of the problem
  • Evolution:
  • Self-similar, analytic solution (Sedov,1959)
the sedov profiles

Density

Pressure

Temperature

The Sedov profiles
  • Most of the mass is confined in a “thin” shell
  • Kinetic energy is also confined in that shell
  • Most of the internal energy in the “cavity”
thin layer approximation
Thin-layer approximation
  • Layer thickness
  • Total energy
  • Dynamics

Correct value:1.15 !!!

testing sedov expansion

Deceleration parameter

Tycho SNR (SN 1572) Dec.Par. = 0.47

SN 1006 Dec.Par. = 0.34

Testing Sedov expansion

Required:

  • RSNR/D(angular size)
  • t(reliable only for historical SNRs)
  • Vexp/D(expansion rate, measurable only in young SNRs)
other ways to measure the shock speed
Other ways to “measure”the shock speed
  • Radial velocities from high-res spectra(in optical, but now feasible also in X-rays)
  • Electron temperature from modelling the (thermal) X-ray spectrum
  • Modelling the Balmer line profile in non-radiative shocks (see below)
end of the sedov phase
End of the Sedov phase
  • Sedov in numbers:
  • When forward shock becomes radiative: with
  • Numerically:
beyond the sedov phase

Internal energy

Kinetic energy

Beyond the Sedov phase
  • When t>ttr, energy no longer conserved.What is left?
  • “Momentum-conservingsnowplow” (Oort 1951)
  • WRONG !! Rarefied gas in the inner regions
  • “Pressure-driven snowplow” (McKee & Ostriker 1977)
numerical results

2/5

2/7=0.29

1/4=0.25

Numerical results

(Blondin et al 1998)

0.33

ttr

Blondin et al 1998

an analytic model
An analytic model

Bandiera & Petruk 2004

  • Thin shell approximation
  • Analytic solution

H either positive (fast branch)

limit case: Oort or negative (slow branch)

limit case: McKee & Ostriker

H,K from initial conditions

inhomogenous ambient medium
Inhomogenous ambient medium
  • Circumstellar bubble (ρ~ r -2)
    • evacuated region around the star
    • SNR may look older than it really is
  • Large-scale inhomogeneities
    • ISM density gradients
  • Small-scale inhomogeneities
    • Quasi-stationary clumps (in optical) in young SNRs (engulfed by secondary shocks)
    • Thermal filled-center SNRs as possibly due to the presence of a clumpy medium
collisionless shocks
Collisionless shocks
  • Coulomb mean free path
    • Collisional scale length (order of parsecs)
    • Larmor radius is much smaller (order of km)
  • High Mach numbers
    • Mach number of order of 100
  • MHD Shocks
    • B in the range 10-100 μG
  • Complex related microphysics
    • Electron-ion temperature equilibration
    • Diffusive particle acceleration
    • Magnetic field turbulent amplification
electron ion equilibration

(Cargill and Papadopoulos 1988)

(Spitzer 1978)

Electron & Ion equilibration
  • Naif prediction, for collisionless shocks
  • But plasma turbulence may lead electrons and ion to near-equilibrium conditions
  • Coulomb equilibration on much longer scales
optical emission in sn1006
Optical emission in SN1006
  • “Pure Balmer” emissionin SN 1006
  • Here metal lines are missing (while they dominate in recombination spectra)
    • Extremely metal deficient ?
non radiative emission
“Non-radiative” emission
  • Emission from a radiative shock:
    • Plasma is heated and strongly ionized
    • Then it efficiently cools and recombines
    • Lines from ions at various ionization levels
  • In a “non-radiative” shock:
    • Cooling times much longer than SNR age
    • Once a species is ionized, recombination is a very slow process
  • WHY BALMER LINES ARE PRESENT ?
the role of neutral h
The role of neutral H

(Chevalier & Raymond 1978, Chevalier, Kirshner and Raymond 1980)

  • Scenario: shock in a partially neutral gas
  • Neutrals, not affected by the magnetic field, freely enter the downstream region
  • Neutrals are subject to:
    • Ionization (rad + coll)[LOST]
    • Excitation (rad + coll)Balmer narrow
    • Charge exchange (in excited lev.)Balmer broad
  • Charge-exchange cross section is larger at lower vrel
  • Fast neutral component more prominent in slower shocks
h alpha profiles

(Kirshner, Winkler and Chevalier 1987)

(Hester, Raymond and Blair 1994)

Cygnus Loop

H-alpha profiles
  • MEASURABLE QUANTITIES
  • Intensity ratio
  • Displacement (not if edge-on)
  • FWHM of broad component (Ti !!)
  • FWHM of narrow component
  • (T 40,000 K – why not fully ionized?)
snr 1e 0102 2 7219

Optical

X-rays

Radio

SNR 1E 0102.2-7219

(Hughes et al 2000, Gaetz et al 2000)

  • Very young and bright SNR in the SMC
  • Expansion velocity (6000 km s-1, if linear expansion)measured in optical (OIII spectra) and inX-rays (proper motions)
  • Electron temperature~ 0.4-1.0 keV, whileexpected ion T ~ 45 keV
  • Very smallTe/Ti, orTimuch less than expected?Missing energy in CRs?
lectures 2 3
Lectures #2 & #3
  • Shock acceleration
    • The prototype: SN 1006
    • Physics of shock acceleration
    • Efficient acceleration and modified shocks
  • Pulsar Wind Nebulae
    • The prototype: the Crab Nebula
    • Models of Pulsar Wind Nebulae
    • Morphology of PWN in theory and in practice
    • A tribute to ALMA
the strange case of sn1006

Tycho with ASCA

Hwang et al 1998

The “strange case” of SN1006

“Standard”X-ray spectrum

thermal non thermal
Thermal & non-thermal
  • Power-law spectrum at the rims
  • Thermal spectrum in the interior
diffusive shock acceleration

shock

flow speed

X

Diffusive shock acceleration
  • Fermi acceleration
    • Converging flows
    • Particle diffusion(How possible, in acollisionless plasma?)
  • Particle momentum distributionwhere r is the compression ratio (s=2, if r = 4)
  • Synchrotron spectrum
  • For r = 4, power-law index of -0.5
  • Irrespectively of diffusion coefficient

(in the shock reference frame)

the diffusion coefficient
The diffusion coefficient
  • Diffusion mean free path(magnetic turbulence)(η > 1)
  • Diffusion coefficient
and its effects
…and its effects
  • Acceleration time
  • Maximum energy
  • Cut-off frequency
    • Naturally located near the X-ray range
    • Independent of B
basics of synchrotron emission
Basics of synchrotron emission
  • Emitted power
  • Characteristic frequency
  • Power-law particle distribution
  • If then
  • Synchrotron life time
sn 1006 spectrum
SN 1006 spectrum
  • Rather standard( -0.6)power-law spectrum in radio(-0.5 for a classical strong shock)
  • Synchrotron X-rays below radio extrapolationCommon effect in SNRs(Reynolds and Keohane 1999)
  • Electron energy distribution:
  • Fit power-law + cutoff to spectrum:

“Rolloff frequency”

measures of rolloff frequency
Measures of rolloff frequency
  • SN 1006 (Rothenflug et al 2004)
  • Azimuthal depencence of the breakChanges in tacc? or in tsyn? ηof order of unity?
dependence on b orientation
Dependence on B orientation?
  • Highly regular structure of SN 1006.Barrel-like shape suggested (Reynolds 1998)
  • Brighter where B is perpendicular to the shock velocity?

Direction of B ?

radio x ray comparison
Radio – X-ray comparison

(Rothenflug et al 2004)

  • Similar pattern (both synchrotron)
  • Much sharper limb in X-rays (synchrotron losses)
slide44

(Rothenflug et al 2004)

  • Evidence for synchrotron losses of X-ray emitting electrons
  • X-ray radial profile INCONSISTENT with barrel-shaped geometry (too faint at the center)
3 d geometry polar caps

Ordered magnetic field

(from radio polarization)

3-D Geometry. Polar Caps?

Polar cap geometry:

electrons accelerated

in regions with quasi-parallel field

(as expected from the theory)

statistical analysis
Statistical analysis

(Fulbright & Reynolds 1990)

Expected morphologies in radio

Polar cap SNR

(under variousorientations)

Barrel-like SNR

(under variousorientations)

the strength of b
The strength of B ?
  • Difficult to directly evaluate the value of the B in the acceleration zone.νrolloffis independent of it !
  • “Measurements” of B must rely on some model or assumption
b from limb sharpness
B from limb sharpness

(Bamba et al 2004)

Profiles of resolved non-thermal X-ray

filaments in the NE shell of SN 1006

Length scales 1” (0.01 pc) upstream20” (0.19 pc) downstream

Consistent withB ~ 30 μG

a diagnostic diagram

rolloff

tsync> tacc

 > Bohm

A diagnostic diagram
  • Acceleration timetacc = 270 yr
  • Derivation of the diffusioncoefficients:u=8.9 1024 cm2s-1d=4.2 1025 cm2s-1(Us=2900 km s-1)to compare withBohm=(Emaxc/eB)/3
non linear shock acceleration
Non-linear shock acceleration
  • Such high values of B are not expected in the case of pure field compression(3-6 μG in the ISM, 10-20 μG in the shock – or even no compression in parallel shocks)
  • Turbulent amplification of the field?
  • Possible in the case of efficient shock acceleration scenario: particles, streaming upstream, excite turbulence

(e.g. Berezhko; Ellison; Blasi)

shock modification

Dynamical effects of theaccelerated particles ontothe shock structure(Drury and Voelk 1981)

Shock modification
  • Intrinsically non linear
  • Shock precursor
  • Discontinuity (subshock)
  • Larger overall compression factor
  • Accelerated particle distribution is no longer a power-law
deviations from power law

Blasi Solution

Thermal

Deviations from Power-Law
  • In modified shocks,acc. particles withdifferent energiessee different shockcompression factors.Higher energy Longer mean free path Larger compress.factor Harder spectrum
  • Concavity in particledistribution.(also for electrons)

Standard PL

gamma ray emission

Synchrotron

νFν

IC

γ-ray

Radio

X-ray

Gamma-ray emission
  • Measurement of gamma-ray emission, produced by the same electrons that emit X-ray synchrotron, would allow one to determine the value of B.
slide55

(Ellison et al 2000)

  • On the other hand, there is another mechanism giving Gamma-ray emission
    • accelerated ions
    • p-p collisions
    • pion production
    • pion decay (gamma)
  • Lower limit for B
  • Need for “targets”(molecular cloud?)
  • Efficiency in in accelerating ions?(The origin of Cosmic rays)
tev telescopes generation
TeV telescopes generation
  • H.E.S.S. Cherenkov telescopes
  • Observations :
  • RX J0852.0-4622(Aharonian et al 2005)
  • Upper limits on SN 1006(Aharonian et al 2005)
  • RX J1713.7-3946(Aharonian et al 2006)
observ of rx j0852 0 4622
Observ. of RX J0852.0-4622
  • Good matching between X-rays and gamma-rays
  • CO observation show the existence of a molecular cloud
  • Pion-decay scenario slightly favoured. Nothing proved as yet
indirect tests on the crs

(Blondin and Ellison 2001)

(Decourchelle et al 2000)

Indirect tests on the CRs
  • Some “model-dependent” side effects of efficient particle acceleration
  • Forward and reverse shock are closer, as effect of the energy sink
  • HD instabilities behavior depends on the value of eff
shock acceleration efficiency
Shock acceleration efficiency
  • Theory predicts (~ high) values of the efficiency of shock acceleration of ions.
  • Little is known for electrons
  • Main uncertainty is about the injection process for electrons
    • Shock thickness determined by the mfp of ions (scattering on magnetic turbulence)
    • Electrons, if with lower T, have shorter mfps
    • Therefore for them more difficult to be injected into the acceleration process
the d relationship
The Σ–D Relationship
  • Empirical relation
    • SNR surface brightness, in radio
    • SNR diameter
    • Any physicalreason forthis relation ?

(Case & Bhattacharya 1998)

a basic question
A basic question
  • Is the correlation representative of the evolution of a “typical object”?
  • Or is, instead, the convolution of the evolution of many different objects?
  • Theorists attempts to reproduce it.

Berezhko & Voelk 2004

dependence on ambient density
Dependence on ambient density

(Berkhuijsen 1986)

  • Primary correlations are D-n, and Σ-n
  • Diff. ISM conditions
the prototype
The Crab Nebula

Optical

Thermal filaments

Amorphous compon.

Radio

Filled-center nebula

No signs of shell

X-rays

More compact neb.

Jet-torus structure

X-rays

Crab Nebula - radio

Crab Nebula – Ha + cont

The “Prototype”
the crab nebula spectrum

-0.8

-1.1

-1.5

-0.3

The Crab Nebula spectrum

(apart from optical filaments and IR bump)

Synchrotron emission

  • Radio
  • Optical
  • Soft X-rays
  • Hard X-rays
some basic points
Some basic points
  • Synchrotron efficiency
    • 10-20% of pulsar spin-down power
  • Powered by the pulsar
  • High polarizations (ordered field)
  • No signs of any associated shell.
basics of synchrotron emission67
Basics of synchrotron emission
  • Emitted power
  • Characteristic frequency
  • Power-law particle distribution
  • If then
  • Synchrotron life time
simple modelling
Simple modelling

(Pacini & Salvati 1973)

  • Homogeneous models (no info on structure)
  • Magnetic field evolution
    • Early phases (constant pulsar input)
    • Later phases (most energy released)
slide69
Power-law injection

With upper energy cutoff

Continuum injection

link to the pulsar spin down

Particle evolution (adiabatic vs synchrotron losses)

Evolutionary break

Adiabatic regime

(-0.3 in radio)

Synchrotron-dominated regime

(-0.8 in optical)

kennel coroniti model 1984

Pulsar magnetosphere

ISM

Pulsar wind

Stellarejecta

Termination shock

Pulsar Wind Nebula

Kennel & Coroniti model (1984)

Basics of “Pulsar Wind Nebula” scenario

  • Pulsar magnetosphere
  • Pulsar wind
  • Termination shock
  • Pulsar Wind Nebula
  • Interface with theejecta (CD, FS)
  • Stellar ejecta
  • Interface with theambient medium(RS, CD, FS)
  • Ambient medium (either ISM or CSM)
the ingredients
The ingredients
  • Pulsar wind
    • super-relativistic
    • magnetized(toroidal field)
    • isotropic
  • Termination shock
    • mass conservation
    • magnetic flux cons.
    • momentum cons.
    • energy cons.

where (specific enthalpy)

large and small limits
Large and small σ limits
  • Large σ
    • weak shock
    • flow stays super-relativistic
    • neither field, nor density jump
    • inefficient in converting kinetic into thermal energy
  • Small σ
    • strong shock
    • flow braked to mildly relativistic speed
    • both field and density increase
    • kinetic energy efficienly converted
mhd evolution in the nebula
MHD evolution in the nebula
  • Steady solution (flow timescale << SNR age)
    • number flux cons. - magnetic flux cons.
    • momentum cons. - energy cons.
  • Asymptotic velocity !!!
    • no solution for V∞=0
    • outer expansion Vext~1500 km s-1 (for the Crab Nebula)
    • then σ~3 10-3
    • size of termination shock, from balance of wind ram pressure and nebular pressure

Rn~10 arcsec

(wisps region)

radial profiles
Radial profiles
  • Inner part with:
  • Outer part with:
  • Equipartition in the outer part:
do we expect what observed
Do we expect what observed?
  • Injected particles
    • power-law, between a min and a max energy
    • only 1 free parameter (n2 and p2 from the jump conditions at the termination shock)
    • plus wind parameters (L, σ and γ1 )
  • Energy evolution during radial advection
best fit solution
Best-fit solution
  • Parameters:
  • Fit to:
problems ia
Problems -Ia
  • The sigma paradox
    • A value is required, in order to get an effective slowing-down of the flow, and a high (10-20 %) synchrotron conversion efficiency
    • BUT the (magnetically driven) pulsar wind cannot have been produced with a low σ .
    • With a normal MHD evolution, the value of σ must keep constant from the acceleration region till the termination shock.
problems ib
Problems - Ib
  • A POSSIBLE WAY OUT
    • A tilted pulsar generates a striped wind.
problems ic
Problems -Ic
  • Magnetic reconnection in the wind zone (if possible) would dissipate the field.(Coroniti 1990)
  • Reconnection in the wind zone does not efficiently destroy the field. Reconnection at the termination shock is more effective.

(Lyubarski & Kirk 1991)

problems iia
Problems - IIa
  • The unexpected radio emission
    • Predicted radio flux is far lower (a factor ~100) than observed.
    • No easy way to cure it. Little freedom on the particle number. Total power is fixed: more particles mean a lower γ1.
    • Radio emitting electrons as a relict. Was the Crab much more powerful in the past? Ad hoc. All PWNe are radio emitters.
problems iib
Problems IIb
  • Can it be “Diffusive synchrotron radiation”?(Fleishman & Bietenholz 2007)Turbulence spectral index ν.
  • Theory only for a fully turbulent field
    • Total spectrumis reproduced
    • But observedpolarization isnot explained
non spherical structure
Non-spherical structure

(Begelman & Li 1992)

  • Particle, moving passively along field lines (flow motion assumed to be irrotational)
  • Axisymmetric nebular field structure
  • Steady state solutions
slide84

pulsar axis

van der Swaluw 2003

3C 58

MHD simulations

elongated structures of pwne

pulsar spin

Elongated structures of PWNe

3C 58

G5.4-0.1

G11.2-0.3

Crab Nebula

details of the structure

counter-jet

torus

knot

inner ring

jet

Details of the structure

Crab Nebula

Vela

jet sizes

4’ = 6 pc

40” =

0.4 pc

Crab Nebula (Weisskopf et al 2000)

PSR B1509-58 (Gaensler et al 2002)

13” = 0.2 pc

80” = 0.8 pc

3C 58 (Slane et al. 2004)

Vela Pulsar (Pavlov et al. 2003)

Jet sizes
simulating pwne
Simulating PWNe

(Komissarov, 2006; Del Zanna et al 2004, 2006)

  • Relativistic MHD codes
  • Modelling a PWN like the CrabVelocity Magnetization Max Energy
surface brightness maps
Surface brightness maps

Jet-Torus structure

ingredients
Ingredients
  • Wind parameters
    • magnetization (still small, but not too much)σ~0.02 – 0.1aaa
    • wind anisotropy ( γeq~10 γpol )
    • “filling” the jets (since B = 0)
pwn ejecta interaction

Reverse Shock

PWN Shock

Forward Shock

Pulsar

Termination

Shock

Pulsar Wind

Unshocked Ejecta

Shocked Ejecta

Shocked ISM

PWN

ISM

PWN-ejecta interaction
  • PWNe are confined by the associated shell-like SNR
  • Not only the SNR is detectable (like in the Crab)
  • In the Crab NebulaUV emissionassociated with aslow shock (againstthe SN ejecta)
a tribute to alma
A TRIBUTE TO ALMA
  • SNRs and PWNs are mostly non-thermal in that spectral range.
    • no use of spectral capabilities
    • use of high spatial resolution, + wide field, + photometric stability (extended sources)
  • Is mm-submm a “new band” for SNRs, or just an extension of the radio range?
  • A study of the Crab Nebula(extension of a former work, Bandiera et al 2002)
what has been done already

-0.28

-0.20

Spectral map

230 GHz map

What has been done already
  • Comparison of 1.3 mm (230 GHz) images (with IRAM 30-m telescope, 10” res) and radio (20 cm, VLA) maps
a further emission component
A further emission component
  • Radio spectral index: -0.27
  • Concave spectral index from radio to mmReal effector artifact?(absolutephotometry)
  • Evidence foran additionalemission component
component b
Component B
  • Image obtained optimizing the subtraction of amorphous part, and filaments, of radio image (PSF matched), with best-fit weights.
the subtracted components
The subtracted components
  • Amorphous component: consistent with an extension of the spectrum to mm, with the radio spectral index (-0.27).
  • Filaments: consistent with spectral bending (νb~80 GHz).
  • Morphologically, component B resembles more the Crab in the optical than in the radio (ALTHOUGH, in the mm range, electrons of Component B do not lose energy significantly by synchrotron).
the integrated spectrum
The integrated spectrum
  • Radio comp (A)
  • Component B,with low freqcutoff.
  • Evidence higherthan from theerror bar.
  • Components Aand B coexistin the optical.
physical scenario
Physical scenario
  • Number of particles in Component B:Ntot~ 2 1048.
  • Consistent with Kennel & Coroniti)
  • Filament magnetic fields ~6times higher than the rest AND particle do not diffuse in/out of filaments (κ<100 κB).
with alma
With ALMA
  • The same analysis, with a resolution 100 times higher.
  • Detailed mapping of Component B.
  • Separation of comp A and B also through differences in the polarization patterns.
  • Analysis of the spectral bending in individual filaments, and possibly even across the filament (B estimates).
  • Mapping B in filaments (aligned? ordered?)
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