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WIND NEBULAE

Elena Amato INAF-Osservatorio Astrofisico di Arcetri OUTLINE OF PART 1

• INTEREST FOR PHYSICS, ASTROPHYSICS AND ASTROPARTICLE PHYSICS • BITS OF PULSAR THEORY: . CHARGE EXTRACTION, PAIR PRODUCTION, FORMATION OF A WIND • PULSAR WIND NEBULAE . BASIC INFERECES FROM SYNCHROTRON THEORY . EVOLUTIONARY ONE-ZONE MODELS . CHALLENGES • MHD MODELING OF NEBULAE AND THEIR RADIATION . 1-D MHD MODELING OUTLINE OF PART 2

• MHD MODELING OF NEBULAE AND THEIR RADIATION . 2-D MHD MODELING . VARIABILITY • PARTICLE ACCELERATION AT THE MOST RELATIVISTIC SHOCKS IN NATURE • CRAB FLARES • OLD NEBULAE, FAST AND THE ELECTRON-POSITRON EXCESS IN COSMIC RAYS WHY ARE PULSARS INTERESTING?

 MATTER IN EXTREME CONDITIONS

 BEST KNOWN COSMIC CLOCKS

 PRIMARY SOURCES OF ANTIMATTER IN THE GALAXY

 EXCELLENT LABS TO TEST GENERAL RELATIVITY

 AMONG THE FEW SOURCES IN THE GALAXY WITH POTENTIAL DROPS IN EXCESS OF 1 PeV WHY ARE PWNe INTERESTING?

 MOST OF THE PULSAR SPIN-DOWN ENERGY: PULSED EMISSION REALLY IS THE TIP OF THE ICEBERG

 BEST LABORATORIES FOR PHYSICS OF RELATIVISTIC PLASMAS: CLOSE TO C AND CLOSE TO US

 PARTICLE ACCELERATION AT THE HIGHEST SPEED SHOCKS IN NATURE (104<Γ<107 ): A FORMIDABLE CHALLENGE!!!!

 AS MANY POSITRONS AS ELECTRONS: SOMETHING TO DO WITH PAMELA AND AMS02 EXCESS?

 ONLY SOURCES SHOWING DIRECT EVIDENCE FOR PEV PARTICLES THE PERFECT TIME TO STUDY THESE OBJECTS HESS AND Fermi ERA

High Energy Stereoscopic System

Hess Victor ENERGY RANGE: 100 GeV

ENERGY RANGE:

100 MeV < Eγ<300 GeV

Fermi Enrico ANGULAR RESOLUTION: Nobel Prize 1938 ~30’ THE PULSING GeV SKY

Pulses at 1/10th true rate THE NEBULOUS TeV SKY ~ 1/2 OF SOURCES ASSOCIATED WITH PWNe PULSARS DISCOVERY Bell and Hewish 1967

(Nobel 1974)

IMPULSE WITH P≈1.33S LASTING ≈1/100 S…

D

WHITE DWARF? TOO FAST!!!

LGM1!!!!! Chinese and native american records: THE CRAB : “A visiting in Taurus, 4 times bright 6000 lyr FROM US: Venus at its maximum. Visible in daylight REMNANT OF AN EXPLOSION for 23 days and for 2 years at night.” FROM 1054 A.D.

Chaco Canyon Anasazi Painting

CRAB PULSAR PREDICTED 1967 (Pacini)

DETECTED 1968 (Staelin & Reifenstein) OBLIQUE ROTATING MAGNETIC DIPOLE

α

THIS IS ALL IN VACUUM NO VACUUM PHYSICS… STAR IS AN EXCELLENT CONDUCTOR

IF VACUUM OUTSIDE: WHERE

BOUNDARY CONDITION AT STAR SURFACE

FINITE SURFACE CHARGE DENSITY

AND A LARGE FIELD TO EXTRACT IT THE GOLDREICH AND JULIAN MAGNETOSPHERE… CHARGES EXTRACTED UNTIL E-FIELD CONTINUOUS AT STAR SURFACE (Goldreich & Julian, 1969) THE PULSAR DEVELOPS A COROTATING MAGNETOSPHERE

THROUGHOUT COROTATION REGION

COROTATION ONLY POSSIBLE UNTIL v

LIGHT CYLINDER PULSARS CANNOT BE SURROUNDED BY VACUUM •A COROTATING MAGNETOSPHERE DEVELOPS

•COROTATION CANNOT EXTEND BEYOND RLC •NOT ALL FIELD LINES CAN BE CLOSED •PARTICLES LEAVE THE STAR ALONG OPEN FIELD LINES

E//=0 EVERYWHERE NOT POSSIBLE WITH ONLY CHARGES FROM STAR SURFACE CHARGE DISTRIBUTION AND GAPS

CHARGE DENSITY

DEPENDING ON BZ/B CHARGE DENSITY IS (SMALLER) LARGER

THAN ηGJ (UN)FAVOURABLY CURVED FIELD LINES POLAR GAPS CREATE POTENTIAL DIFFERENCE

UNSCREENED POTENTIAL ⇒ ACCELERATION TO E»”KNEE”

IN CRAB Emax≈60 PeV

FOR PSRs Φ IS MEASURED DIRECTLY: PAIR PRODUCTION UNSCREENED POTENTIAL ⇒ QUICK ACCELERATION TO RELATIVISTIC ENERGIES

PAIR CASCADE IS INITIATED

MULTIPLICITY K≈103-104 (Hibschman & Arons 01)

Curvature + - e- or γ (Eγ>50 MeV) γ+B→e +e 7 ICS on star X-rays 2-3 γprimary~10 γsecondary~10 γ-RAYS FOLLOW THE

ENERGY γ-RAYS (AND PULSED EMISSION IN GENERAL) IS NOT WHERE THE ENERGY GOES!!!!! • #10 Lradio "10 E R • $2 L" #10 E R

!ON THE OTHER HAND… ! • LPWN " 0.1E R

THE PWN IS WHERE THE ENERGY GOES!!!! ! THE WIND ZONE Spitkovsky 06 ACTS AS SOURCE OF TOROIDAL FIELD:

BT COMPARABLE TO BP AT THE LIGHT CYLINDER

AT LARGER DISTANCES FIELD LINES

ARE OPEN: BP MONOPOLE LIKE

TOROIDAL FIELD BECOMES DOMINANT

~SAME AS FOR OBLIQUE DIPOLE IN VACUUM THE WIND ENERGY • 2 6 4 B0 R0 " r & c r r 3) E R = = dS E $ B + %wind (n± me + ni mi )c c 3 , '( 4# *+

• • $ ' 2 mi E R = " N GJ m± c #wind &1 + )( 1+ *) WE MEASURE IT " m ! % ± ( • DEPENDS ONLY ON 2 2 %GJ 0 32 µ30 '1 N GJ " # R0 $ pc " 3&10 2 s MEASURED e P100 PSR PARAMETERS

! • N CAN BE EVALUATED FROM PWN SYNC. EMISSION " = • KNOWING B N GJ ! 4 6 B2 MUST BE LARGE AT LC: σ≈10 -10 " = PROBABLY SMALL IN THE PWN 4# m n c 2 $2 ! eff eff wind BASED ON MHD MODELING

! OPEN QUESTIONS • • $ ' 2 mi E R = " N GJ m± c #wind &1 + )( 1+ *) % " m± ( •WHAT IS κ? NOTES ON IONS: 6 •WHAT IS σ? •FOR Γwind=10 ! •IS IT IONS WHO CARRY THE THESE WOULD BE PeV RETURN CURRENT? PROTONS OR 30PeV Fe

•WHAT IS Γwind? •IF κ

DETAILED MODELING OF PWNE REQUIRED FOR QUANTITATIVE ANSWERS PULSAR WIND NEBULAE

Plerions:  Remnants with a center filled morphology

Flat radio spectrum (αR<0.5) Very broad non-thermal emission spectrum (from radio to X-ray and even γ-rays) (~15 objects at TeV energies)

Kes 75 (Chandra)

(Gavriil et al., 2008) “THE” PULSAR WIND NEBULA

PRIMARY EMISSION MECHANISM: BY RELATIVISTIC PARTICLES IN AN INTENSE

(>FEW X 100 BISM) ORDERED (HIGH DEGREE OF RADIO )

SOURCE OF BOTH MAGNETIC FIELD AND PARTICLES: SUGGESTED BEFORE PULSAR DISCOVERY (Pacini 67) BASIC PICTURE OF A PWN ELECTROMAGNETIC BRAKING OF MAGNETIZED FAST-SPINNING MAGNETIZED NS RELATIVISTIC WIND

IF WIND IS STAR ROTATIONAL ENERGY VISIBLE AS EFFICIENTLY CONFINED NON-THERMAL EMISSION OF THE BY SURROUNDING SNR MAGNETIZED RELATIVISTIC

RN

pulsar wind RTS

Synchrotron bubble

(from Gaensler & Slane 06) MODELING OF PWNe

•BASIC ARGUMENTS •1-ZONE MODELING •1-D MAGNETOHYDRODYNAMICAL MODELING •2-D AXISYMMETRIC MHD MODELING SYNCHROTRON RADIATION SPECTRUM SINGLE PARTICLE SPECTRUM POWER-LAW

2 2 PARTICLE DISTRIBUTION P" (#) = a1# B $(" %" s(#)) 2 " s(#) = a2# B

SYNCHROTRON RADIATION SPECTRUM

sync a (#$1) # +1 $# p #1 ! S (") = 1 a k B " " = " 2 2 2

IN ORDER TO ESTIMATE K AND γ WE NEED TO KNOW B ! ! EQUIPARTITION 1 2 # p $ # ' N(") = k " " min < " < " max " 0 = & ) % c2B( 2 % B # max 2 ( Wtot = V ' + $ N(#)mc # d#* 2 EQUATIONS FOR & 8" # min ) 2 UNKNOWNS: k & B ! ! c1 (#$1) # +1 $# 2S" $(# +1) # S" (") = c2 k B " % k = (#$1) B " 2 c1c2 ! 2 & B %3 / 2 ) Wtot = V ( + #$ B + IN ξν ONLY OBSERVED QUANTITIES ! ' 8" *

MINIMUM ENERGY: "Wtot 2 / 7 = 0 # Bmin = (6$%& ) "B ! 2 / 7 EQUIPARTITION: WB = W part " Beq = (8#$% )

! CAVEATS!!!!

! EQUIPARTITION FIELD IN PWNe TYPICAL VALUES: 10 µG< B

IN CRAB:

RADIO EMITTING PARTICLES HAVE

THEIR EMISSION CORRESPONDS TO

IF PART OF THE PSR WIND:

NOTE: IN THIS CASE, EVEN IF IONS ARE THERE, THEY CANNOT BE ENERGETICALLY DOMINANT

BUT RADIO PARTICLES COULD BE FOSSILE…. 1-ZONE EVOLUTIONARY MODELS EVERYTHING IS SPATIALLY HOMOGENEOUS BUT TIME-DEPENDENT (Pacini & Salvati 73): CHANGING PULSAR INPUT, SYNCHROTRON AND ADIABATIC LOSSES OF PARTICLES AND FIELD ARE INCLUDED

INJECTION SPECTRUM PER UNIT "# TIME AND ENERGY INTERVAL: J(E,t) = k(t) E

k(t)←

CONSERVATION OF PARTICLE! NUMBER dN(E,t) dE = J(E i,ti )dtidE i

E max "ti RELATION NEEDED N(E,t) = # J[E i;ti (E i,E,t)] dE i E "E BETWEEN E, Ei, ti !

! MAGNETIC FIELD EVOLUTION 4" 3 dWB WB dV V(t) = R(t) = "B L(t) # 3 dt 3V(t) dt 2 B (t) 4" 3 WB (t) = R(t) 8" 3 t 2 4 2 4 B R " B0 R0 = 6#B $ L(t)R(t)dt ! t0 •EXPANSION WITH CONSTANT! VELOCITY •CONSTANT ENERGY SUPPLY: t<<τ " R(t) vt 2 1/ 2 != 2 6&B L0vt # 6"B L0 & 1 # % B = 4 4 B(t) = % 3 ( $ L(t) = L0 v t $ v ' t

2 •EXPANSION WITH CONSTANT BR =cost VELOCITY % 2 (1 / 2 ! ! 6"B L0# 1 •DECAYING ENERGY SUPPLY: t>>τ B(t) = ' 3 * 2 & ($ -1)($ - 2)v ) t

! SINGLE PARTICLE EVOLUTION SYNCHROTRON dE 2 2 E 1 dV = "c1B (t)E " AND dt 3 V (t) dt ADIABATIC LOSSES

INTEGRATE TO OBTAIN SEEKED RELATION BETWEEN E,Ei,ti IN YOUNG PWNe (CONSTANT EXPANSION & ENERGY SUPPLY) 1/ 2 ! . ( 2 " %+ 2" %5 1 Et 0 E i E 0 E R(t)=vt ti = /1 + *1 + 4 $1 + '- 3$ 1 + ' 2E i 0 ) EEb (t)# 2E b (t)&, 0# 2E b (t)& B(t)∝t-1 1 4 # &) 1 # &) 1 "ti E iti E i E i E it = 2 %1 + ( = 2 %1 + ( BREAK ENERGY: "E E $ E b (ti )' E ti $ E b (t)ti ' SYNCHROTRON! AND ADIABATIC LOSSES EQUAL •BREAK WAS ONCE AT VERY LOW ENERGY 1 ! •INITIAL RADIO PARTICLES E b (t) = 2 " t c1B (t)t CANNOT HAVE SURVIVED

! LOW ENERGY LIMIT

1/ 2 . ( 2 " %+ 2" %5 1 Et 0 E i E 0 E ti = /1 + *1 + 4 $1 + '- 3$ 1 + ' 2E EE (t) 2E (t) 2E (t) i 10 ) b # b &, 40# b &

# &) 1 # &) 1 "ti E iti E i E i E it 1 = %1 + ( = %1 + ( E b (t) = " t "E E 2 E (t ) E 2t E (t)t c B2 (t)t ! $ b i ' i $ b i ' 1

E<

E max "ti "# N(E,t) = J[E i;ti (E i,E,t)] dE i J(E,t) = k(t) E #E E ! ! " t Emax N(E,t) = k E "# dE % ktE "# E $E i i ! !

! HIGH ENERGY LIMIT

1/ 2 . ( 2 " %+ 2" %5 1 Et 0 E i E 0 E ti = /1 + *1 + 4 $1 + '- 3$ 1 + ' 2E EE (t) 2E (t) 2E (t) i 10 ) b # b &, 40# b &

# &) 1 # &) 1 "ti E iti E i E i E it 1 = %1 + ( = %1 + ( E b (t) = " t "E E 2 E (t ) E 2t E (t)t c B2 (t)t ! $ b i ' i $ b i ' 1

Eb<

E max "ti "# N(E,t) = J[E i;ti (E i,E,t)] dE i J(E,t) = k(t) E !# E E ! " #$ #1 SPECTRUM STEEPENS BY -1 N(E,t) " ktEb E RADIATION SPECTRUM BY -1/2 ! !

! SYNCHROTRON BREAK PARTICLE SPECTRUM RADIATION SPECTRUM N(E,t) " ktE #$ E < E $(% $1)/ 2 b S" (",t) #" " < " b N(E,t) " ktE E #$ #1 E > E $% / 2 b b S" (",t) #" " > " b $ ' 2 2 1 c2 1 " b # c2BEb = c2B& 2 ) * " b = 2 3 2 % c1B t ( c1 B t ! ! MAGNETIC FIELD IN A SOURCE OF KNOWN AGE # &1 / 3 c2 1 *3 *2 / 3 *1/ 3 ! B = % 2 2 ( = 8 )10 G t [kyr]" b [GHz] $ c1 t " b '

ISSUES: •!FOR KYR OLD SOURCES νb TYPICALLY IN OPTICAL/IR •OFTEN MORE THAN 1 BREAK OR Δα>1/2 EXAMPLE CASE: CRAB

TWO BREAKS BETWEEN 0.3 RADIO AND GAMMA-RAYS: 0.6-0.8 WHICH ONE IS SYNCHROTRON AND WHICH IS AGE? 1.2 8mG B = 2 1/ 3 (t [kyr]" b [GHz])

BOTH CONSISTENT ! WITH EQUIPARTITION WITHIN THE UNCERTAINTIES

HOWEVER UNCERTAINTY ON BREAK POSITION IS TELLING US SOMETHING: MORE DETAILED MODELING REQUIRED!!!! 1-ZONE MODELS FOR THE PWN EVOLUTION CHANGING PULSAR INPUT EVOLUTION OF PARTICLES AND MAGNETIC FIELD

Crab 3C58

γ ~5x104 4 w γw~3x10 γ ~7x105 5 c γc~10

Bucciantini, Arons, Amato 2012 HOW TO MAKE PROGRESS •1-ZONE MODELS SUGGEST HIGH MULTIPLICITIES •THEY CANNOT BE CONSIDERED CONCLUSIVE: ASSUMPTIONS ON WIND EVOLUTION MIGHT BE FLAWED •THEY ONLY PROVIDE INFO ON AVERAGE QUANTITIES •THEY DO NOT REALLY PROVIDE INFO ON σ

DETAILED MHD MODELING WHEN POSSIBLE MHD MODELS OF PWNe: ASSUMPTIONS 1-D STEADY-STATE HD (Rees & Gunn 74) 1-D STEADY-STATE MHD (Kennel & Coroniti 84) 1-D SELF-SIMILAR MHD (Emmering & Chevalier 87) 2-D STATIC MHD (Begelman & Li 92)

RN GENERAL ASSUMPTIONS .COLD ISOTROPIC MHD WIND .STRONG PERP. REL. SHOCK pulsar .SUBSONIC FLOW IN THE NEBULA wind R TS .PARTICLE ACCELERATION AT THE TS .SYNCHROTRON LOSSES THEREAFTER Synchrotron bubble

MAIN FREE PARAMETERS •WIND MAGNETIZATION σ= B2/(4πnmc2Γ2) •LORENTZ FACTOR Γ •PARTICLE SPECTRAL INDEX α THE KENNEL AND CORONITI MODEL

(Kennel & Coroniti, 1984a, 1984b) FREE PARAMETERS WIND MAGNETIZATION σ= B2/(4πnmc2Γ2) LORENTZ FACTOR Γ SPECTRAL INDEX α RELATIVISTIC MHD EQUATIONS IN SPHERICAL SYMMETRY

1 " " r2 n u 0 CONSERVATION OF = 0 2 ( ) = "t r "r PARTICLE NUMBER 1 " $ ruB' & ) = 0 INDUCTION r "r % # ( EQUATION ! ! + 2 2 . 1 " % B % u (( 2p -r 2' w u2 + p + 1+ *0 1 = 0 MOMENTUM 2 ' ' 2 ** r "r - & 8# & $ )) 0 r ,! / CONSERVATION 1 " + % B2 u(. ENERGY r2 w u 0 2 - ' # + *0 = CONSERVATION ! r "r , & 4$ # )/

! JUMP CONDITIONS AT A RELATIVISTIC SHOCK + 2 2 . 1 " 1 " % B % u (( 2p 1 r2 n u = 0 3 -r 2' w u2 + p + 1+ *0 1 = 0 ( ) 2 ( ) ( ) 2 ' ' 2 ** r "r r "r ,- & 8# & $ )) /0 r + 2 . 1 " % ruB( 1 " 2% B u( (2) ' * = 0 (4) 2 -r ' w$ u + *0 = 0 r "r & $ ) r "r , & 4# $ )/

SHOCK IS ASSUMED STEADY STATE INTEGRATE EQUATIONS ACROSS THE SHOCK: Δx→0 !

u1B1 u2B2 n1u1 = n2u2 = "1 " 2 w B2 $ u2 ' B2 $ u2 ' µ = n u2 p 1 1 1 n u2 p 2 1 2 n µ1 1 1 + 1 + & + 2 ) = µ2 2 2 + 2 + & + 2 ) 8# % "1 ( 8# % " 2 ( B2 u B2 u µ n u " + 1 1 = µ n u " + 2 2 1 1 1 1 4# " 2 2 2 2 4# " ! 1 2

! THE SHOCK JUMP ASSUMPTIONS: 1 u •HIGHLY RELATIVISTIC SHOCK "1 >> # 1 $ "1 p 1 " 0, µ " mc 2 •UPSTREAM FLUID IS COLD 2 1 n1mc

* 2 . 2 1 , 8" 2 +10" +1 # 8" 2 +10" +1& " 2 , B1 u2 " = 2 = + ± % ( ) / 2 2!, 8(1+ ") $ 8(1+ ") ' 2(1+ ") , 4#n1u1$1mc - ! 0

IMPOSING POSITIVE DOWNSTREAM PRESSURE ALLOWS TO SELECT CORRECT! SOLUTION ! * 2 . 1 , 8" 2 +10" +1 # 8" 2 +10" +1& " 2 , u2 = + ± % ( ) / 1 = 1+ u2 2 2 8(1+ ") 8(1+ ") 2(1+ ") 2 2 -, $ ' 0, 2 # & 5 p2 1 1 2 1 2 B2 1 2 2 2 = 41 + "%1 ) ( ) 7 = n1mc 11 4u21 2 3 $ u2 ' 11 6 B1 u2

! LARGE AND SMALL σ

* 2 . 1 , 8" 2 +10" +1 # 8" 2 +10" +1& " 2 , u2 = + ± % ( ) / 1 = 1+ u2 2 2 8(1+ ") 8(1+ ") 2(1+ ") 2 2 -, $ ' 0, 2 # & 5 p2 1 1 2 1 2 B2 1 2 2 2 = 41 + "%1 ) ( ) 7 = n1mc 11 4u21 2 3 $ u2 ' 11 6 B1 u2

IF B-FIELD DOMINATES " # 0 ! " # $ DYNAMICS: 2 1+ 9" 2 1 1 u2 # u2 # " + + 8 8 64" •FLUID DOES NOT SLOW 9 DOWN AT SHOCK 2 2 9 1 $ 2 # (1+ ") % 2 # " + + 8 8 64" •PRESSURE STAYS LOW p 2 p 1 1 (LITTLE DISSIPATION) 2 # 1% 7" 2 # & 2 2 ( ) 2 2 2 n1mc $1 3 n1mc %1 8" 32" •B-FIELD FURTHER B N B N 1 INCREASES EVEN IF LITTLE 2 = 2 # 3%12" 2 = 2 #1+ B1 N1 B1 N1 2"

! ! IN FIGURES….

QUANTITIES NORMALIZED TO UPSTREAM TOTAL ENERGY DENSITY NEBULAR DYNAMICS + 2 2 . 1 " 1 " % B % u (( 2p 1 r2 n u = 0 3 -r 2' w u2 + p + 1+ *0 1 = 0 ( ) 2 ( ) ( ) 2 ' ' 2 ** r "r r "r ,- & 8# & $ )) /0 r + 2 . 1 " % ruB( 1 " 2% B u( (2) ' * = 0 (4) 2 -r ' w$ u + *0 = 0 r "r & $ ) r "r , & 4# $ )/

" $ p ' $ B2 ' ! & ) = 0 & µ" + ) = cost "r % n# ( % 4#n" ( " p µ = mc 2 + " #1 n ! ! 2 2 uBr u2B2rs nur = n2u2rs = ! " " 2 & 2 ) & 2 ) p p2 2 # p B 2 # p2 B2 # = # "( mc + + 2 + = " 2( mc + + 2 + n n2 ' # $1 n 4%n" * ' # $1 n2 4%n2" 2 *

! TERMINAL VELOCITY

# u# % ' " # $ % &$ #1 u" = "# = = ( 1+ 2# $# % +1 )" # 0 % &$ # "

! ! !

FOR LARGE σ TERMINAL VELOCITY STAYS RELATIVISTIC

IN CRAB vN=1000km/s e σ=vN/c=0.003 MAGNETIC FIELD

FOR SMALL σ B PEAKS AT AROUND WHERE EQUIPARTITION IS REACHED SPECTRAL EVOLUTION " p INJECTION SPECTRUM AT SHOCK: f2 (E 2 ) = KE 2

CONSERVATION OF PARTICLE NUMBER

2 2 1 $E2 4"r cuf (E,z)dE = 4"rS cf2(E 2)dE 2 # f (E,z) = 2 f 2[E 2(E,z)] ! vz $E

E 2(E,z) = ? dE E dV dE d c = " c B2 E 2 # u = Eu lnn1/ 3 " 1 B2 E 2 ! dt 3V (t) dt 1 dr dr c uBr u!B r B = 2 2 s # B = 2 " " 2 vz n ! nur2 = n u r2 " n = 2 2 2 s vz2 p 2 " p $ '( " ) ! KE E E (z) MAXIMUM PARTICLE f (E,z) = 2 p / 3 &1 " ) ∞ 2 ( + ) E (z) (vz ) % # ( ENERGY AT ANY PLACE !

! NEBULAR SIZE

CRITICAL FREQUENCY FORM FACTORS

zN 2 J" (z)z I" (z# ) = 2 dz % ( % E z ( $ 2 2 3 eB2 1 # ( ) z z z # ( % # ) "#(z) = ' * ' 2 * 4$ & mc ) vz & mc ) NEBULAR SIZE DECREASES !WITH INCREASING OBS. FREQUENCY ! INTEGRATED SPECTRUM

INTEGRATED SPECTRUM SHOWS STEEPENING DUE TO DECREASING NEBULAR VOLUME WITH INCREASING FREQUENCY MHD MODELS OF PWNe: PREDICTIONS

INTEGRATED EMISSION SPECTRUM FROM OPTICAL TO X-RAYS AND EVEN γ-RAYS (de Jager & Harding 92; Atoyan & Aharonian 96) NO EXPLANATION FOR RADIO ELECTRONS: MAYBE PRIMORDIAL (Atoyan 99)…

SIZE SHRINKAGE WITH FREQUENCY ELONGATION BASIC PARAMETERS AND QUESTIONS LEFT OPEN 1/2 9 10 RTS~RN(VN/c) ~10 -10 RLC FROM PRESSURE BALANCE (e.g. Rees & Gunn 74)

In Crab RTS ~0.1 pc: ~boundary of underluminous (cold wind) region ~“wisps” location (variability over months)

Wind parameters

-3 At r~R : σ~104 Γ~102 σ~ VN/c ~3 x 10 LC (pulsar and pulsar wind theories) from basic dynamics σ-paradox!

4 7 Γ~3x106 At RTS: σ«1(!?!) Γ∈(10 -10 ) from radiation properties (PWN theory and observations)

α~2.2 Just right for Fermi I THEN CAME CHANDRA!

G11.2

3C58