Constraining the pulsar power in gamma-ray binaries through thermal X-ray emission V´ ıctor Zabalza in collaboration with V. Bosch-Ramon and J.M. Paredes Departament d’Astronomia i Meteorologia, Institut de Ci` encies del Cosmos (ICC), Universitat de Barcelona (IEEC-UB) HEPRO III , Barcelona, 28 June 2011
Gamma-ray binaries (Mirabel 2006) Microquasar Pulsar binary V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 2 / 18
Gamma-ray binaries (Mirabel 2006) Microquasar Pulsar binary V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 2 / 18
Pulsar gamma-ray binaries shocked stellar wind ▸ Acceleration of particles in pulsar shocked pulsar wind wind reverse shock stellar wind ▸ Synchrotron → X-ray ∼ 10 33 ergs − 1 ▸ IC with stellar photons → GeV, TeV pulsar wind star pulsar 0.5 1.0 1.5 2.0 2. Szostek & Dubus (2011) V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 3 / 18
Pulsar gamma-ray binaries shocked stellar wind ▸ Acceleration of particles in pulsar shocked pulsar wind wind reverse shock stellar wind ▸ Synchrotron → X-ray ∼ 10 33 ergs − 1 ▸ IC with stellar photons → GeV, TeV pulsar wind ▸ Thermal X-ray emission from star pulsar shocked stellar wind: 0.5 1.0 1.5 2.0 2. ▸ Not detected in X-ray spectra of gamma-ray binaries. ▸ Upper limits provide information on: ▸ Interaction region shape → L sd ▸ Stellar wind: v ( r ⋆ ) = v ∞ ( 1 − R ⋆ / r ⋆ ) β ; β = 0 . 8 Szostek & Dubus (2011) V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 3 / 18
Estimate of thermal X-ray luminosity Making the following assumptions: ▸ L X ≃ 1 2 L sh kin , ▸ the CD has a conical shape, ▸ the stellar wind dominates over the pulsar wind ( η ∞ ≪ 1), V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 4 / 18
Estimate of thermal X-ray luminosity Making the following assumptions: ▸ L X ≃ 1 2 L sh kin , ▸ the CD has a conical shape, ▸ the stellar wind dominates over the pulsar wind ( η ∞ ≪ 1), the X-ray luminosity is related to L sd and ˙ M as L X ≈ 1 . 2 × 10 32 [ 2 − 1 10 36 ergs − 1 ] [ 10 − 7 M ⊙ / yr ] ˙ L sd M ergs − 1 . V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 4 / 18
Estimate of thermal X-ray luminosity Making the following assumptions: ▸ L X ≃ 1 2 L sh kin , ▸ the CD has a conical shape, ▸ the stellar wind dominates over the pulsar wind ( η ∞ ≪ 1), the X-ray luminosity is related to L sd and ˙ M as L X ≈ 1 . 2 × 10 32 [ 2 − 1 10 36 ergs − 1 ] [ 10 − 7 M ⊙ / yr ] ˙ L sd M ergs − 1 . On the other hand, if η ∞ → 1, L X ≈ 3 × 10 34 [ ˙ 10 − 7 M ⊙ / yr ] ergs − 1 . M V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 4 / 18
Shape of contact discontinuity y ⃗ r ⋆ θ ⋆ ⃗ r p θ p x Star Pulsar D p ⋆⊥ = p p ⊥ V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 5 / 18
Shape of contact discontinuity y ⃗ r ⋆ θ ⋆ ⃗ r p θ p x Star Pulsar D ˙ sin 2 θ ⋆ = L sd / c Mv ( r ⋆ ) sin 2 θ p 4 πr 2 4 πr 2 p ⋆ V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 5 / 18
Shape of contact discontinuity y η ∞ = 0 . 3 η ∞ = 0 . 04 ⃗ r ⋆ θ ⋆ ⃗ r p η ∞ = 0 . 003 θ p x Star Pulsar D p sin 2 θ ⋆ r 2 ˙ sin 2 θ ⋆ = L sd / c sin 2 θ p ⇒ = ≡ η ( x , y ) Mv ( r ⋆ ) L sd / c ⋆ sin 2 θ p 4 πr 2 4 πr 2 r 2 ˙ Mv ( r ⋆ ) p ⋆ V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 5 / 18
Emission model details ▸ Strong shock: ρ 0 / ρ w = v w ⊥ / v 0 = 4 ▸ Post-shock temperature: keV ≈ 1 . 4 × 10 7 [ 2 2 kT 0 = 3 w ≈ 1 . 21 [ 1000km / s ] 1000km / s ] v w ⊥ v w ⊥ 16 µm p v 2 K ▸ Competing energy-loss mechanisms in the post-shock region: ▸ Escape losses: t esc ≃ r p v 0 ▸ Radiative losses: t rad ≃ kT 0 n 0 ∆ ( T 0 ) V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 6 / 18
Emission model details ▸ Strong shock: ρ 0 / ρ w = v w ⊥ / v 0 = 4 ▸ Post-shock temperature: keV ≈ 1 . 4 × 10 7 [ 2 2 kT 0 = 3 w ≈ 1 . 21 [ 1000km / s ] 1000km / s ] v w ⊥ v w ⊥ 16 µm p v 2 K ▸ Competing energy-loss mechanisms in the post-shock region: ▸ Escape losses: t esc ≃ r p v 0 ▸ Radiative losses: t rad ≃ kT 0 n 0 ∆ ( T 0 ) ▸ Kinetic luminosity converted to X-ray luminosity: t − 1 L X = rad L kin t − 1 esc + t − 1 rad V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 6 / 18
Emission model details To compute the cumulative X-ray spectrum: 1 Compute contact discontinuity shape V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 7 / 18
Emission model details To compute the cumulative X-ray spectrum: 1 Compute contact discontinuity shape 2 Compute kT 0 , t esc , t rad and L X for different region on the CD V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 7 / 18
Emission model details To compute the cumulative X-ray spectrum: 1 Compute contact discontinuity shape 2 Compute kT 0 , t esc , t rad and L X for different region on the CD 3 Obtain intrinsic thermal spectrum through MEKAL code V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 7 / 18
Emission model details To compute the cumulative X-ray spectrum: 1 Compute contact discontinuity shape 2 Compute kT 0 , t esc , t rad and L X for different region on the CD 3 Obtain intrinsic thermal spectrum through MEKAL code 4 Compute photoelectric opacity owing to stellar wind V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 7 / 18
Emission model details To compute the cumulative X-ray spectrum: 1 Compute contact discontinuity shape 2 Compute kT 0 , t esc , t rad and L X for different region on the CD 3 Obtain intrinsic thermal spectrum through MEKAL code 4 Compute photoelectric opacity owing to stellar wind 5 Add all absorbed spectra to obtain cumulative spectrum V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 7 / 18
Caveats of the model Some effects can only be taken into account through hydrodynamical simulations V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 8 / 18
Caveats of the model Some effects can only be taken into account through hydrodynamical simulations, e.g.: ▸ Instabilities of the contact discontinuity owing to ▸ Thin shell instabilities ▸ Stellar wind clumping ▸ Shocked layer properties in adiabatic limit ( t esc < t rad ) V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 8 / 18
Application to LS 5039 Name Compact object Star Orbital period PSR B1259 − 63 pulsar O8.5Ve 3.4 years HESS J0632+057 ? B0pe ∼ 320 days LS I +61 303 ? B0Ve 26.5 days 1FGL J1018.6 − 5856 ? O6V 16.6 days LS 5039 ? O6.5V 3.9 days Only gamma-ray binary with powerful, radial stellar wind. Observed non-thermal X-ray luminosity: L nt , X ≈ 10 33 ergs − 1 V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 9 / 18
Pulsar and stellar winds in LS 5039 Pulsar spin-down luminosity ▸ L sd ≳ 3 × 10 36 ergs − 1 from energetic constrains ▸ Upper limit unknown V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 10 / 18
Pulsar and stellar winds in LS 5039 Pulsar spin-down luminosity ▸ L sd ≳ 3 × 10 36 ergs − 1 from energetic constrains ▸ Upper limit unknown Stellar mass-loss rate ▸ From lack of orbital variability of X-ray absorption (Bosch-Ramon et al., 2007; Szostek & Dubus, 2011) : M ≤ 5 × 10 − 8 M ⊙ / yr ▸ For a point-like source: ˙ M ≤ 1 . 5 × 10 − 7 M ⊙ / yr ▸ For an extended source: ˙ ▸ From H α direct measurement (Sarty et al., 2011) : M = ( 3 . 7–4 . 8 ) × 10 − 7 M ⊙ / yr ˙ V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 10 / 18
Pulsar and stellar winds in LS 5039 Pulsar spin-down luminosity ▸ L sd ≳ 3 × 10 36 ergs − 1 from energetic constrains ▸ Upper limit unknown Stellar mass-loss rate ▸ From lack of orbital variability of X-ray absorption (Bosch-Ramon et al., 2007; Szostek & Dubus, 2011) : M ≤ 5 × 10 − 8 M ⊙ / yr ▸ For a point-like source: ˙ M ≤ 1 . 5 × 10 − 7 M ⊙ / yr ▸ For an extended source: ˙ ▸ From H α direct measurement (Sarty et al., 2011) : M = ( 3 . 7–4 . 8 ) × 10 − 7 M ⊙ / yr ˙ ▸ Terminal wind velocity: v ∞ = 2400 km s − 1 V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 10 / 18
Shape of contact discontinuity P Star A to observer η ∞ = [ 0 . 0025 , 0 . 025 , 0 . 25 ] V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 11 / 18
Synthetic X-ray spectra 10 35 10 34 Luminosity E d L / d E [erg/s] 10 33 M = 2 . 65 × 10 − 7 M ⊙ / yr 10 32 ˙ L sd = [ 0 . 3 , 3 , 30 ] × 10 36 ergs − 1 10 31 10 30 Periastron 10 29 10 28 0.4 0.6 0.8 1 2 4 6 8 10 Energy [keV] 10 35 10 34 Luminosity E d L / d E [erg/s] 10 33 10 32 10 31 10 30 Apastron 10 29 10 28 0.4 0.6 0.8 1 2 4 6 8 10 Energy [keV] V´ ıctor Zabalza (ICC-UB) Thermal X-rays from pulsar gamma-ray binaries 12 / 18
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