γ-ray emissions from wind of black widow

Jumpei Takata (The University of Hong Kong)

Collaborators; K.S. Cheng & E. Wu (The university of Hong Kong)

Black Widow Pulsars  Subclass of millisecond pulsars (MSPs).

Pulsar  A binary pulsar composed of millisecond radio pulsar and very low < 0.1푀⊙. Companion  The eclipse of the radio emissions around inferior conjunction. -- Evidence of intra-binary matter.

PSR  MSP stripes mass off a closed companion by intense radiation, and eventually ablates away the companion. -- Evolutionary stage to solitary MSPs. http://www.daviddarling.info/encyclopedia/B/Black_Widow_Pulsar.html  Before Fermi , only three black widow pulsars were known in Galactic field.

 Follow up radio observations of Fermi unidentified sources discovered many new millisecond pulsars in binary system. --22 black widow pulsars (Roberts, 2013)

 More new systems will be discovered by further analysis of the Fermi unidentified source.

Black widow pulsar vs. γ-ray binary

Black Widow pulsars PSR B1259-63  Spin down power 1034−35 erg/s ~1036 erg/s

 System size ~0.01AU ~1 − 10 AU

4  Shock distance from 4 ~0.1AU~10 푅푙푐 at ~0.01AU~10 푅푙푐 the pulsar periastron

 Soft photon energy ~2erg cm−3 ~3erg cm−3 density (T～6000K) (T～30000K)

 Magnetic energy density ~0.6 − 6 erg cm−3 ~0.6 erg cm−3 (equipartition) PSR B1957+20

 First black widow pulsar Observed rotation period (Fruchter et al. 1988, Nature). 11 -- 푃표푏~9.2 ℎ푟, 푎~1.7 × 10 cm. -- 푀푐~0.022푀⨀, 35 -- 퐿푠푝~1.1 × 10 erg/s, 푃푠푝~1.61ms

 Pulsed X-ray and γ-ray emissions from the magnetosphere (Guillemot et al. 2012)

Orbital phase  Eclipse of radio emissions around INFC。

Radio eclipse (INFC) Orbital modulation of the optical emission  A large orbital modulation of the optical emissions from the companion. 19 -- Illumination by pulsar radiation. -- Un-illuminated side , 푇~2900 퐾 -- Illuminated side, 푇~8300 퐾 (Reynolds et al. 2007) 24  Eclipsing light-curve model (Orosz & Hauschildt 2000) provides an inclination angle 𝑖~65 deg. Phase  The non-thermal X-ray emissions could be produced by the intra-binary shock Non-pulsed X-ray light curve between the pulsar wind and the outflow from companion (Arons & Tavani 1993, ApJ).

 Un-pulsed and non-thermal X-ray emissions (Stappers et al. 2003, Sci.).

−13 −2 −1  퐹푋 0.3 − 8푘푒푉 ~10 erg cm s and 훼~1.96 ±0.02

Inferior conjunction (radio eclipse region)  Orbital modulation of the non-thermal X-ray emissions (Huang et al. 2012).

Searching orbital modulating γ-ray emissions (Wu et al. 2012)

 3yr Fermi data  First, we looked orbital light curve with all data (>100MeV) Companion Phase 2 -- No orbital modulation. Phase 1 (INFC) --Magnetospheric emission dominates. (SUPC) PSR  Divided the data into two parts -- Phase1, half orbit centered at superior conjunction (SUPC). -- Phase2, half orbit centered at inferior conjunction (INFC).

 In Phase 1, the spectral shape is fitted well by power law + exponential cut-off. typical pulsar spectrum

 In Phase2, an additional component is required >2.7 GeV with a −12 −2 −1 flux 퐹>2.7퐺푒푉~5 × 10 푒푟𝑔 푐푚 푠 .

TS-map (>2.7GeV) Phase 1 Phase 2 (SUPC) (INFC) Phase 1 Phase 2

10−1

Typical pulsar spectrum 10−2 25 55 1 10 1 10 Energy (GeV)  In Phase 1, the spectral shape is fitted well by power law + exponential cut-off. typical pulsar spectrum

 In Phase2, an additional component is required >2.7 GeV with a −12 −2 −1 flux 퐹>2.7퐺푒푉~5 × 10 푒푟𝑔 푐푚 푠 .

TS-map (>2.7GeV) Phase 1 Phase 2 (SUPC) (INFC) Phase 1 Phase 2

10−1

Typical pulsar spectrum 10−2 25 55 1 10 1 10 Energy (GeV)  Light curve >2.7 GeV has a peak at around inferior conjunction.

 Emissions above 2.7 GeV is probably modulating with orbital phase. -- emissions from the inter-binary space.

 It is unlikely the inverse-Compton INFC (radio eclipse emission from the inter-binary shock region) 푈 퐹 -- 푝ℎ ≈0.7 ≪ >2.7퐺푒푉 ~50 푈퐵 퐹푋 Cold relativistic Pulsar Wind model  The cold relativistic pulsar wind in up-stream region scatters off the stellar photon fields and produces γ-rays.

 Pulsar wind particles approaching toward the observer contribute to the emissions. -- Anisotropic inverse-Compton process 2 -- Power (Thomson regime) ∝ (1 − cos 휃푐)  Around SUPC (Phase 1), tail-on like collision, cos 휃푐 > 0  Around INFC (Phase 2), head-on like collision, cos 휃푐 < 0 Earth Earth

PSR PSR Phase 1 : I.C. is less efficient Phase 2 : I.C. is high efficient 1

𝑖 = 80deg. 60deg. 40deg. 20deg.

10−3

10−5

INFC SUPC Calculation for PSR B1957+20

35  Pulsar wind carries the spin-down power 퐿푠푑~1.1 × 10 erg/s. 2 -- But, 퐿푊 ∝ sin 휉 (휉, angle measured from the pulsar’s rotation axis). -- Pulsar wind particles have a mono-energetic distribution. 4 -- Observed emissions ～3GeV implies Γ푊 = 4 × 10 .

 Temperature of the heated surface of the companion, 푇∗~8300퐾 (Raynolds 2007)

 The outer gap model for the magnetospheric emissions (Takata et al. 2010).

Ω Earth (𝑖~67deg) 휉 = 80 deg

Orbital plane PSR Phase 1 Phase 2 (SUPC) (INFC)

Outer gap

I.C.

 The inverse-Compton of the pulsar wind provides a possible explanation for the orbital modulating γ-rays.

 PSR B1957+20 may be the first binary pulsar that shows γ-ray emissions from both magnetosphere and intra-binary space. -- direct measurement of the emissions from cold relativistic pulsar wind of millisecond pulsars.

Discussion

The averaged flux  How about others? --Model prediction vs. inclination angle 0.06  Inclination angle for most system are unknown.

 The flux averaged over one orbital phase 0.01 depends on the inclination angle, but not so sensitive. 0 90 Inclination angle 𝑖 -- Calculation of model flux averaged over one period with midley inclined system, 𝑖 = 60 deg.

 The isotropic pulsar wind

 Pulsar wind carries the spin down luminosity.

4 -- Mono energetic distribution of the particles, Γ푊 = 4 × 10 .

 The temperature of the heated side of the companion is estimated by 4 휎푆퐵푆∗푇 = Ω퐿푠푑 4휋

-- 푆∗; Irradiated surface area of the companion -- Ω; Solid angle of the companion measured from the pulsar

List of bright sources

PSR 푳풔풅,ퟑퟒ 푫풌풑풄 푴풄 Observed flux by Fermi Predicted I.C. flux (>100MeV) (푴⨀) averaged over phase 10−10erg cm−2 s−1 J1023+0038 5 0.6 0.2 0.05 0.26 J2256-1024 5.2 0.6 0.034 0.1 0.083 J1301+0833 6.8 0.7 0.02 0.08 0.07 J2129-0429 4 0.9 0.4 0.09 0.067 B1957+20 11 2 0.02 0.13 0.023 (this work) J2215+5135 6.2 3 0.32 0.1 0.019 J2241-5236 2.5 0.5 0.012 0.3 0.018 J1816+4510 5.2 2.4 0.16 0.15 0.012 J1311-3430 5 1.4 0.01 0.6 0.011 Summary  Many black widow pulsars have been discovered at Fermi un-identified sources.  The black widow pulsars are very similar binary system to γ-ray binary PSR B1259-63.  PSR B1957+20 shows the orbital modulating γ-ray emissions above 2.7 GeV.  Inverse-Compton of the cold relativistic pulsar wind provides a possible explanation for the orbital modulating γ-rays.  Many black widow pulsars may have orbital modulating gamma-rays above ～3GeV, where magnetospheric emissions is less important.  Black widow pulsars could be the binary pulsars that show gamma-ray emissions from both magnetosphere and the intra-binary space. 4 Isotropic pulsar wind, 𝑖 = 60 푑푒𝑔., Γ푊 = 4 × 10

PSR 푳풔풅,ퟑퟒ 푫풌풑풄 푴풄 Averaged flux (푴 ) (ퟏퟎ−ퟏퟎ퐞퐫퐠 /퐜퐦ퟐ s) ⨀ (>100MeV) J1023+0038 5 0.6 0.2 0.26

J2256-1024 5.2 0.6 0.034 0.083

J1301+0833 6.8 0.7 0.02 0.07

J2129-0429 4 0.9 0.4 0.067

B1957+20 11 2 0.02 0.023

J2215+5135 6.2 3 0.32 0.019

J2241-5236 2.5 0.5 0.012 0.018

J1816+4510 5.2 2.4 0.16 0.012

J1311-3430 5 1.4 0.01 0.011

(if 𝑖 = 90deg.)  It is unlikely the emissions from the intra-binary shock. -- Observed spectrum does not extend beyond 5GeV 1/2 5퐺푒푉 4  Γ푚푎푥~ ~8 × 10 푘퐵푇 -- Equi-partition between the particle energy and the magnetic energy implies 퐵푃푊~20Gauss  퐸푠푦푛 Γ푚푎푥 ~2푘푒푉

4 휎푆퐵푇 푈푝ℎ 푐 퐹>2.7퐺푒푉 -- = 2 ≈0.7 ≪ ~50 푈퐵 퐵푃푊 퐹푋 8휋  Before Fermi , only three black widow MSPs were known in Galactic field.

 Many new radio millisecond pulsars in binary system are discovered at the Fermi unidentified sources. --22 sources in the list of Roberts (2013)

 PSR J1311-3430; the first black widow pulsar found from gamma-ray observations -- More news systems will be discovered by further analysis of the Fermi unidentified source.

Roberts (2011) if 𝑖 = 90deg.