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A mo del for TeV binaries: pulsar wind sho ck with pair feedback
E.V. Derishev

Institute of Applied Physics, Nizhny Novgoro d, Russia


Mo del setup and geometry
opacity at TeV energies


1

absorption and further cascading in the massive star's surrounding

opacity at few MeV


10-6

1

no measurable absorption, no cascading

Rarely pro duced secondary pairs picked up by ultrarelativistic pulsar wind, their energy increases by 2 the feedback strength f = 2 >

1


Mo del parameters
Based on LS 5039 and LS I +61 303: · Massive star's luminosity · Mass-loss rate

Ls = 3 в 1038erg/s 0. 01c

M = 10-6M /yr Vw w c Lp = 1036erg/s 103
­ justified later

· Stellar wind velo city · Pulsar wind p ower

· Pulsar wind Lorentz factor · Orbital distance

D = 3 в 1012cm w M c 2 w= Ls

· Pulsar wind energy density fraction · Magnetic energy fraction m

0. 5

1/ 2


Closing the feedback lo op: 1st option
· Feedback efficiency

2NepEep f = Lp 4 3 w1 R 3 E1 w2 c E2
(Eep E1 if E1 E2)

· Pair pro duction rate Nep =

· Soft (synchrotron from secondary pairs) photon field: Eep 2 eB E2 1/2 f w w b , w2 = Es = 4 Es 2 mec2 mec · Hard (inverse Compton from primary pairs) photon field: 2 2 wb 3 R w1 , E1 = 3 2Ts wb = 4 R T ct 0 0 mec2

wb is thermal background energy density Eep is the average total energy of a secondary pair 0 is the Lorentz factor of the pulsar wind in absence of the pair feedback


Closing the feedback lo op: 1st option
· Feedback efficiency

2NepEep f = Lp 4 3 w1 R 3 E1 w2 c E2
(Eep E1 if E1 E2)

· Pair pro duction rate Nep =

· Soft (synchrotron from secondary pairs) photon field: Eep 2 eB E2 1/2 f w w b , w2 = Es = 4 Es 2 mec2 mec · Hard (inverse Compton from primary pairs) photon field: 2 2 wb 3 R w1 , E1 = 3 2Ts wb = 4 R T ct 0 0 mec2 1/2 Ts 1/4 m Lp 3/4 11/4 w Ls


= 3 2

1 4

0

T

D3/2 mec4

2e2

m2c3 e

1/4


Closing the feedback lo op: 1st option
· Feedback efficiency

2NepEep f = Lp 4 3 w1 R 3 E1 w2 c E2
(Eep E1 if E1 E2)

· Pair pro duction rate Nep =

· Soft (synchrotron from secondary pairs) photon field: 2 e (2 Eep 2 eB Ts m w Ls 4 8 Es = = 2 2 mec mec 2 mec2 mec Dc · Hard (inverse Compton from primary pairs) photon field: 2 3 R 2 wb w1 wb = 4 R T , E1 = 3 2Ts ct 0 0 mec2 1/2 Ts 1/4 m Lp 3/4 11/4 w Ls


c)1/2

= 3 2

1 4

0

T

D3/2 mec4

2e2

m2c3 e

1/4


Closing the feedback lo op: 2nd option
· Synchrotron photons from secondary pairs get absorb ed on themselves 1/2 2 e (2 Ts m w Lsc) Es = 8 2 mec2 mec Dc

mec2



=

21/4(mec2)1/2
1/4 Ts

D1/8
1/16

( e)1/8 (2 m w Lsc)

750


Sp ectral comp onents in pair feedback mo del
Emission from primary pairs · synchrotron, p eaked at s E1y

e (2 m w Lsc)1/2 = 2 0.3 eV mec Dc
I E1C = 3 2Ts 5 MeV

· inverse Compton from stellar radiation, p eaked at

Emission from secondary pairs · synchrotron emission, p eaked at s E2y mec2 I E2C = 2mec2 0.3 TeV

· (less efficient) inverse Compton, p eaked at

Recoil-assisted inverse Compton · a broken p ower-law, with the break at

E

raIC

(mec2)2 = 15 GeV 6 Ts


Recoil-assisted inverse Compton

Thomson regime vs Klein-Nishina regime: what we will observe in the slow co oling approximation?


Recoil-assisted inverse Compton
Thomson regime: EIC = 2Eb

LIC 2wb

Klein-Nishina regime (direct): - EIC = mec2 LIC Eb 2wb

Klein-Nishina (recoil-assisted): Eb,2 kick Lorentz factor k = 2mec2
2E 4 Eb,1Eb,2 E EIC = ( k ) b,1 = b,2 4m2c4 e -2 LIC ( k )2wb,1 в -1Eb,2 wb,2 3wb,1wb,2


Recoil-assisted inverse Compton
N E - (scattered in the Klein-Nishina regime) + thermal radiation from the massive companion E1 3 Ts

Background:

p ower-law


distribution over the kick Lorentz factors - N k 1-


k mec2/(6 Ts) k
(Thomson regime)


mec2/(6 Ts)
(Klein-Nishina regime)


F -/2


F -1-