Possible Distance indicators in Gamma-ray Pulsars

Wei Wang( 王 伟 )

May 11 2011 NOAC Beijing

Outline• Distance information for pulsars• Gamma-ray emission efficiency (η) versus pulsa

r parameters: P, age, magnetic field at light cylinder (BLC)

• Efficiency versus generation order parameters (GOP)

• Good correlation between η-GOP, η-BLC are distance indicators for gamma-ray pulsars

• Distances of 25 gamma-selected pulsars are estimated

Distance information for pulsars

• Trigonometric parallax measurements

only available for nearby pulsars, <0.4 kpc

mainly for some millisecond pulsars

• dispersion measurement (DM) distances for radio pulsars combined with electron density distribution model

NE2001 model

Distance for pulsars• kinematic models:

the distance of possible associated objects (SNR, PWNe, star clusters, HII regions) could be measured from Doppler shift of absorption or emission lines in HI spectrum together with the rotation curve model of the Galaxy

• Estimators according to thermal X-ray spectra or Lx-Edot, Lx-Γ relations

Beck & Truemper 1997

Gotthelf 2003

One-year observations:

Gamma-ray all-sky map> 100 MeV

>1400 gamma-ray point sources!!!

EGRET: 270

Gamma-ray pulsar family in Fermi/LAT era

• Near 100 gamma-ray pulsars

• 30 radio young pulsars• 25 gamma-selected pul

sars• 13+34 MSPs

Gamma-ray pulsar family in Fermi/LAT era

21 radio-selected young pulsars

17 gamma-selected young pulsars (most have no any distance information!)

8 millisecond pulsars

The first gamma-ray pulsar catalog by Fermi/LAT (2010)

L- Edot relation : EGRET pulsars L∝ Edot 0.5 (Thompson 2001) In FERMI/LAT Era, not simple case! very large scattering

If we fit the data of 21 radio young pulsars, we find a relation of

L Edot∝ 0.7(0.2)

But for MSPs, L 0.1 Edot∝

Our aims• Find a possible better correlation in gamma-ray pulsars,

connecting Lγ and pulsar parameters

• Considering Gamma-ray emission efficiency η• η = Lγ/Edot• L γ=4πd2 f Fγ, Fγ is the flux of LAT (>100 MeV)• f is beaming factor, model dependent; could be obtained

using pulse profile information, f ～ 1 for 8 gamma-ray pulsars estimated by Watters et al. (2009).

• For simplicity, f =1 in this work• We show the relations between η and three well-known p

arameters: P, age and BLC and generation order parameters (GOPs)

• 21 radio-selected young gamma-ray pulsars with distance information in the first gamma-ray pulsar catalog (Abdo et al. 2010) are used in the analysis.

no correlation σ= 1.63 σ=1.56 p-value 1.04 e-4 2.90e-5

Age=P/2Pdotmagnetic field at light cylinder

G

Generation order parameters • describe pair cascade processes in gamma-ray pulsars ba

sed on the RS model (Ruderman & Sutherland 1975; Lu & Shi 1990; Zhao et al. 1989)

• The first generation photon with very high energy

• The primary photon will be absorbed in magnetosphere, into e-/e+ pairs, the production condition is:

• The e-/e+ can emit the second-generation gamma-ray photons, if the energy is high enough. In the similar conditions, the photon will be absorbed again, converted into e-/e+, to emit third-generation photons.

• Then pair cascade processes occur

Generation order parameters

• Three GOPs defined by:• Absorbed through electron fields (Lu et al. 1994)

• Absorbed through magnetic and electron fields (Wei et al. 1997)

• Absorbed through magnetic fields (Wang & Zhao 2004)

GOPs describe gamma-ray properties of pulsars

Main gamma-ray photon (first generation) must be produced:

so GOPs must >1, then gamma-rays can be emitted.

For gamma-ray pulsars, GOPs >1

Larger values of GOPs, more generations of photons, then photon energy become lower, even to X-ray bands

The correlation of GOPs and photon index in gamma-rays are found based on EGRET pulsars

Then lager GOPs, softer in gamma-ray bands,

i.e., given a total emitting rate, larger GOPs imply a smaller gamma-ray efficiency !

Better correlation for η-ζ3 implies the magnetic fields dominate the absorption in pair cascade processes.

In all correlations, η-ζ3 are the best one (σ, p-value smallest), η-BLC correlation is also acceptable.

No correlation σ= 1.69 σ=1.34

Possible distance indicators• Two fundamental parameters P and Pdot are relatively easily obtain

ed

• ζ3 and BLC: the functions of P and Pdot

• Good correlations between η-ζ3 and η-BLC exist for radio-selected young gamma-ray pulsars

• η depends on pulsar distance• With known P and Pdot, and detected gamma-ray flux, pulsar distan

ce will be evaluated• 17 gamma-selected pulsars in the first gamma-ray pulsar catalog (A

bdo et al. 2010), 8 new gamma-selected pulsars in blind search (Saz Parkinson et al. 2010): most of they have no any distance information

• Distances of 25 gamma-selected pulsar are estimated

Distance estimate for 25 gamma-selected pulsarsζ3 BLC

Distance indicators of gamma-selected pulsars

• Geminga: d=0.25+0.12_0.06 kpc from trigonometric parallax on possible optical counterpart

Our prediction: d=0.19±0.07 kpc• Many gamma-selected pulsars have too large (non-physi

cal) emission efficiency, e.g.η>1 from other distance estimation.

• Like PSR J2021+4026, d=1-2 kpc from kinematics model on possible association , η=100-400%.

Our prediction: d=0.4±0.1 kpc, η=16%.

Millisecond pulsars ?

• In parameter spaces of P, τ, MSPs are quite different from young pulsars; and ζ1 and ζ2 of MSPs is below 1 or near 1, may be not suitable for gamma-ray MSPs

• But in parameter spaces of BLC and ζ3, MSPs and young pulsars are still similar

MSPs may have constant efficiency of 10%; though they still follow behavior: larger BLC and ζ3 induce smaller η,

Distance distribution of three classes of gamma-ray pulsars

The large population of nearby gamma-ray radio-quiet pulsars (or MSPs) could significantly contribute to e-/e+ background flux and diffuse gamma-ray background.

Summary• Good correlations between η-ζ3 and η-BLC are found

• Gamma-ray luminosity of pulsars depends on two fundamental parameters: P and Pdot

• The relations would be the distance indicators for gamma-ray pulsars, specially radio-quiet pulsars

• Gamma-selected pulsars are closer to us compared to radio-selected young pulsars

• Our GOPs models are originally proposed based on polar-cap scenario, the possible GOPs applied in outer-gap or slot-gap models may be more complicated, which can be studied furthermore.