Multi-wavelength Pulsed Emission from Fermi Pulsars:

Vela & Crab ——Annular Gap Model

Reporter: YuanJie Du (NAOC)

Supervisor ： JinLin Han (NAOC)

GuoJun Qiao (PKU)

RenXin Xu (PKU)

Du Y. J., Qiao G. J., Han, J. L., Lee K. J. & Xu R. X. 2010, Du Y. J., Qiao G. J., Han, J. L., Lee K. J. & Xu R. X. 2010, MNRASMNRAS, 406, 2671-2677, 406, 2671-2677

Du Y. J., Han, J. L., Qiao G. J. & Chou C. K. 2011, Du Y. J., Han, J. L., Qiao G. J. & Chou C. K. 2011, ApJApJ,, 731, 2 (Vela) 731, 2 (Vela)

Du Y. J. 2011, Du Y. J. 2011, ApJApJ,, to be submitted (Crab)to be submitted (Crab)

Outline

BackgroundBackground

Annular Gap ModelAnnular Gap Model

SummarySummary

Overview

Vela Fermi observations

Crab multi-wavelength observations

Other models

Our work —— Vela （☻）

Our work —— Crab

Background — Pulsed Emission

Before 2008, only 7 γ-ray pulsars were discovered. 3 candidates

After Fermi launching, about 100 γ-ray pulsars were discovered so far γ-ray selected pulsars, radio selected pulsars millisecond pulsars.

Golden age for pulsar high energy emission studies: opportunity and challenge

Pulsar Emission

Background——Pulsar Emission Physics

Emission Physical Picture

Problems ： Emission Region and Emission Mechanism

Yong Pulsar MSP

J0437-4715

J0218+4232

Background— Fermi telescopeFermi ： LAT and GBM

LAT: a pair conversion telescope

Large effective area: ~ 8000 cm2

Large view of field: ~ 2.4 sr Wide energy band: 0.02GeV to 300 GeV High angular resolution: 0.6o for 1 GeV; 0.1o for 10 GeV

GBM: for gamma-ray burst (not discussed here)

LAT data reduction for pulse profileData collect (based on radio timing

solution)Data selection (Diffuse, 0.1 － 300GeV,

2o, zenith angle<105o)Energy selection Timing each photon → phase information (Tempo2 with Fermi plug-in)Light curves plotting

1.3] ),log10(E 3-max[1.6 GeV

The Vela Pulsar

P1

P3

P2

Du et al. 2011, ApJ, 731, 2

• Two sharp peaks, P1 is narrower than P2

• P1/P2 varies with energy

• A third peak (P3) in the bridge, the location and intensity shift with energy

GeV phase-averaged spectrum for Vela

Hyper-exponential power law cut-off

Multi-wavelength observed light curves for Crab

Two peaks

Bridge

Phase-aligned

Fermi data

Observations of phase-averaged spectrum and phase-resolved spectra for Crab

Ku

iper et al. 2001, A

&A

, 378, 918

Observation hints

• Vela: Two sharp γ-ray peaks with a large separation 0.42 —— high emission height !

• Vela: P1/P2 and P3 varying with energy —— single pole or two pole?

• Vela & Crab: The “radio lag” problem needs to be solved self-consistently —— Outer Gap model?

• Modelings of multi-waveband light curves and phase-resolved spectra are needed for the Crab pulsar —— The Annular Gap model

Outline

BackgroundBackground

Annular Gap ModelAnnular Gap Model

SummarySummary

Other models

Our work —— Vela （☻）

Our work —— Crab

High Energy Emission Models

Outer Gap (Cheng)

Polar Cap (Harding)

Two-pole caustic (Dyks)

Slot Gap (Harding)

Annular Gap (Qiao)

Two separatrix layer

Polar Cap Model for VelaDaugherty & Harding 1996 Emission height: 2-3 Rns Nearly aligned

rotator: αvery small

Outer Gap Model for VelaRomani & Yadigaroglu 1995• Both radio and γshown• γemission is from single

pole, whereas radio comes from the other polar cap.

Comments from Lommen et al. 2007 “Our results imply a connection

between the radio and X-ray emission mechanisms for Vela that is not consistent with outer gap model … It is not clear how a correlation could exist between the radio and high energy regimes in these models”.

Two-pole caustic model for VelaDyks & Rudak 2003

Static dipole fieldrmax< 0.95RLC

Caustics in water

A REVISIT OF THE TWO-POLE CAUSTIC MODEL

Fang & Zhang 2010, ApJ

Retarded dipole field

Yu, Fang & Jiang 2009

Two-layer outer gap model（ Wang, Takata, Cheng 2011, arXiv: 1102.4474 ）

α=57◦ ， ζ=80◦

Annular Gap Model —— Our work Vela (Fermi Gamma-ray studies)

Concepts & Methods Light curve Phase-averaged spectrum Phase-resolved spectra

Crab (Multi-wavelength studies) Light curve Phase-averaged spectrum Phase-resolved spectra

Annular Gap + Core Gap

The open field line region is divided into core gap and annular gap regions by the critical field line.

The annular gap radius is much larger for pulsars with short spin periods, and can be a excellent accelerator for pulsar γ-ray emission.

Ruderm

an & S

utherland 1975

Primary particles and pairs Primary particles are accelerated

to ultra-relativistic energy with γ~ 107 by the induced acceleration electric field.

Three modes of pairs: CR, thermal ICS and resonant ICS.

Thermal ICS induced pairs usually have larger Lorentz factors up to γth~ 105 .

Radio emssion comes from pairs. High energy emission comes from

primary particles.

Electric field

Pair production

Zhang, Qiao & Han 1997, 491, 891

Light curve modeling thread

(0)rλ)κ (1)(rλκ )(r NNs ψψ

α,ψ

Re (α,ψ)

θnull (α,ψ)

rN (0)

rN (ψ)

CentralEmission height

Gaussian distribution

]2

)(exp[),(

2

20

2

llI Io

Aberration retardation

Project onto the sky

I(φ0,ζ0)256 bins of φandζ

I(φ,ζ)

View angle

Light Curve Modeling Steps (Vela)

Dividing polar cap

Projected intensity

Emissiom direction

Emission phase

Light curve

Step : Dividing polar capⅠDividing polar cap

Projected intensity

Emissiom direction

Emission phase

Light curve plotting

Magnetic inclination angle α: 70 deg Viewing angle ζ: 64 deg Critical field line θN (ψ)

Last open field line θP (ψ)

Footpoint in each open field line 40 rings for both core and annular gap

Core Gap

Annular Gap

Torus fitting

ζ

(Ng & Romani 2008)

PA fittingα β(Johnston 2005)

Step Ⅱ： Projected intensity

Two types of Gaaussian emission intensities are assumed, i.e.,

• A Gaussian distribution on a field line (parameter: κ,λ,σarc_AG,σarc_CG, ratio, I1, I2 , ICG)

• Another Gaussian distribution between field lines with same magnetic azimuthal (ψ)

(parameter: σpeak_AG,σpeak_CG)

• Model parameters are different between core and annular gap.

Dividing polar cap

Projected intensity

Emissiom direction

Emission phase

Light curve plotting

nspin in the spin frame

Emission direction of each emission spot nB in the magnetic frame

Step : Emission directionⅢDividing polar cap

Projected intensity

Emissiom direction

Emission phase

Light curve plotting

nobserver = {nx, ny, nz} in the observer frame

Matrix Tα

Aberration

)/narctan(n xy0 )nnn/arccos(n 2z

2y

2xz0

Step : Emission phaseⅣ

• “Retardation effect” is needed for the final photon emission phase φ.

• A phase shift Δφret retardation is because of the photon flight time at a certain emission height.

This leads to photon generated at higher height comes to the Earth earlier.

• Finally, φ= φ0 -Δφret

Dividing polar cap

Projected intensity

Emissiom direction

Emission phase

Light curve plotting

LCret Rr /)cos( Wang et al. 2006

Step : Light curve plottingⅤ• Observations (red solid

lines in 256 bins) versus similations (thick black solid lines in 128 bins) in the framework of Annular + Core gap model.

• P1 and P2 originate from the annular gap region.

• P3 and bridge emission come from the core gap region

Dividing polar cap

Projected intensity

Emissiom direction

Emission phase

Light curve plotting

Du et al. 2011, ApJ, 731, 2

Radio lag

• A radio lag ~0.13 is shown.

• Radio emission originates from high altitude and narrow regions in the annular gap.

• Single-pole annular and core gap model is favored for Vela.

Du et al. 2011, ApJ, 731, 2

Phase-averaged spectrum for Vela

3 Components （ P1 、 P2 and P3 ） Emission position ： P1: 0.62RLC, ψ=-110° P2: 0.75RLC, ψ=131° P3: 0.28RLC, ψ=-104° 3 free parameters ： γmin 、 γmax 、 Ω

GeV emission is generated from Synchro-curvature radiation from primary particles and synchrotron radiation from secondaries (pairs)

Du et al. 2011, ApJ, 731, 2

• P1 and P2 ： located in AG region ， larger pitch angle, synchrotron is important for

< 1 GeV band

• P3 ： located in CG region ， pitch angle, CR dominated

Phase-resolved spectra

Du et al. 2011, ApJ, 731, 2

P1 P2

P3 low-energy P3 high-energy

Dependencies of flux and emission heightEmission intensities are not uniform along an open field line. They are likely to have a gaussian distribution near the peak position.

Du et al. 2011, ApJ, 731, 2

Annular Gap Model —— Our work Vela (Fermi Gamma-ray studies)

Concepts & Methods Light curve Phase-averaged spectrum Phase-resolved spectra

Crab (Multi-wavelength studies) Light curve Phase-averaged spectrum Phase-resolved spectra

AG multi-wavelength results for the Crab pulsar

• Light curves

• Phase-averaged spectrum

• Phase-resolved spectra

Outer Gap for Crab Tang et al. 2008, ApJ, 676, 562

Slot Gap for CrabHarding et al. 2008, ApJ, 680, 1378

Outer Gap for CrabLi & Zhang 2010, ApJ, 725, 2225

Phase-averaged spectrum

Photon sky-map

Brief Introduction to the AG work

• This is a fast work mainly focusing on the light curve simulations for millisecond and young pulsars.

• Concepts and methods are announced in details for our annular gap model, although the results are rough.

Du et al. 2010, MNRAS, 406, 2671

年轻脉冲星 Du et al. 2010, MNRAS, 406, 2671

毫秒脉冲星 Du et al. 2010, MNRAS, 406, 2671

Outline

BackgroundBackground

Annular Gap Annular Gap

ModelModel

SummarySummary

Summary• Under our self-consistent annular gap model, multi-

wavelength light curves and phase-averaged and phase-resolved spectra for the Vela pulsar and the Crab pulsar are well reproduced with comparison of the observations.

• The features (spectra and light curves) of P3 for Vela are well described by our model.

• Our model explains the radio lag problem for Vela and Crab, and they are different.

• Existence of both annular and core gaps could be verified by the Vela pulsar and the Crab pulsar.

谢谢各位老师和同学！

Crab

Vela

补充材料

• MSP J0437-4715

• Crab

Both the simulated radio and γ-ray light curves for millisecond pulsar J0437-4715. The radio lag problem can be well solved by our model.

MSP J0437-4715

One part of Poster for 38th Cospar conference in Bremen

Crab 脉冲轮廓

Fermi 观测到的毫秒脉冲星

E‖计算结果

• 粒子数守恒和磁通量守恒

• 泊松方程：

环间隙加速电场 (E‖) 产生

• 产生的原因：在光速圆柱半径附近，磁流管中的带电粒子由于不能随中子星共转而逃逸出磁层。为了保持整个系统的电中性，中子星必须补偿所逃逸的带电粒子，当这些粒子流动时，由于偏离了当地的 GJ电荷密度，故平行与磁力线方向的电场因此而产生。

• 电流回路闭合 : 环区和核区输出电荷符号相反的带电粒子。

E‖计算微磁流管（ beamlet ）

逃逸高度： r1 = RLC

逃逸粒子的电荷密度 :

RLC

Ω

)()( 1 LCGJb Rr

确定辐射高度 P1：高度分布范围小

P3 + bridge：高度分布范围广

P2：高度分布范围广，但由于光性差效应和辐射高度差效应被压缩

引言——脉冲星奇妙的脉冲星： ① 集四大力为一身的天然实验室 ② 宇宙中的灯塔

两次获得诺贝尔物理学奖： Ⅰ 1974年， Hewish，第一颗脉冲星的发现 Ⅱ 1993年， Hulse & Talor, PSR J1913+16

Faster Reaction!

引言——脉冲星• 约 2000 颗脉冲星

类 致密星

• 种类多： 正常脉冲星 毫秒脉冲星 AXP 、 SGR磁星 DTN 、 CCO 、 RRAT

• Fermi 发现将近70

颗伽玛射线脉冲 星，其中包括 29

颗 毫秒脉冲星