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张力 张力 2003 年 10 月 21 日于北京 2003 年 10 月 21 日于北京 Gamma-ray Luminosity...
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Transcript of 张力 张力 2003 年 10 月 21 日于北京 2003 年 10 月 21 日于北京 Gamma-ray Luminosity...
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张力 张力 20032003 年年 1010 月月 2121 日于北京日于北京
Gamma-ray Luminosity and Death Lines of Pulsars with Outer Gaps
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OutlineOutlineIntroduction The Outer Gap Model Magnetospheric Geometry
X-ray Field in the Magnetosphere
The Fractional Size of an Outer Gap
High-Energy Gamma-ray LuminosityThe Death lines of Pulsars with Outer
GapsConclusion and Discussion
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1.Introduction1) Observations of High-Energy Emission from Rot
ation-Powered Pulsars
History: SAS 2, COSB(1970’s-1980’s). EGRET (1990’s)
Coming satellite: GLAST
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The Observations of Gamma-ray Pulsars
The OSSE/EGRET experiments have detected pulsed signals from eight rotation-powered pulsars.
Nolan et al. 1993, ApJ 409, 697 Crab Matz et al. 1994, ApJ 434, 288 B1509-58*
Kanbach et al. 1994, A&A 289, 855 Vela Mayer-Hasselwander et al. 1994, ApJ 421, 276 Geminga
Ramanamurthy et al. 1995, ApJ 447, L109 B1951+32 Thompson et al. 1996, ApJ 465, 385 B1706-44 Fierro et al. 1998, ApJ 494, 734 Crab, Vela, Geminga Thompson et al. 1999, ApJ 516, 297 B1055-52 Kaspi et al. 2000, ApJ 528, 445 B1046-58
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Pulses at multi-wavebands
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Energy spectra of gamma-ray pulsars
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2) Models for High-Energy Emission from 2) Models for High-Energy Emission from PulsarPulsar
There are two kinds of models for high-energy emission from pulsars:(1) polar cap models (Harding et al. 1978, ApJ 225, 226; Daugherty & Harding 1982 ApJ 252, 337;1996 ApJ 458, 278; Zhang & Harding, 2000, ApJ; Sterner et al. 1995, ApJ 445, 736).(2) Outer gap models(Cheng, Ho, Ruderman ,1986, ApJ 300, 500; 300, 522; Chiang & Romani 1994, ApJ 436, 754;Romani, 1996, ApJ 470, 469, Zhang & Cheng 1997, ApJ 487 370; Hirotani & Shibata 2001, MNRAS 325, 1228)
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Schematic geometry of polar and outer gaps. Dark solid regions are thin gaps of younger pulsars. Hatched regions are thick gaps of older pulsars
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3) Outer gaps:charge density
surrounds a rotating NS with B and . The plasma is corotating with the NS within RL=c/ . In the corotating
region, E||= EB/B ~0. But, the flows of the plasma along open field lines will results in some plasma void regions (where 0) in the vicinity of null charge surfaces ( B=0). In such charge deficient regions, which are called outer gaps, E|| 0 is sustained,e-/e+ can be accelerated to relativistic energies and the subsequent high-energy -ray emission and pair production can maintain the current flow in the magnetosphere.
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5)Motivations:Observation indicates (Thompson et al. 2001): L L ½ sd .New polar gap models (e.g. Zhang &Harding 2000; Harding et al. 2002): L L ½ sd for Lsd > Lbreak sd, L L sd for Lsd < Lbreak sd,where Lbreak sd,= 5 x 1033 P-1/2 erg/s.For previous outer gap models: L ~ f3 L sd f B -13/20 P33/20 (CHR II) f B -4/7 P26/21 (ZC97)ZC97 model predicts L (B/P) 0.3, e.g, the ratio of (B/P) 0.3 for PSR B1055-52 to that for Geminga is~ 0.9. But, the observed ratio ~8 (Kaspi et al. 2000). Therefore, other physics quantities shouldbe taken into account in order to explain the observed data.
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We re-study the gamma-ray emission from the outer gaps of the rotation-powered pulsars. We take the magnetosphere geometry into account and show that the fractional size of the outer gap is a function of period, magnetic field, radial distance to the neutron star and magnetic inclination angle.
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2. The Outer Gap Modele+ and e- are accelerated by E||
Relativistic e+/e- emit gamma-rays viaSynchro-curvature, and IC processes
Soft X-rays from stellar surface are produced by the collision of return current with NS. Gamma-rays collide with these soft photons to materialize as pairs in the accelerator to maintain the outer gap.
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Based on ZC97 model, 2D and 3D models were developed
CrabCrab
The spectra of Crab
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Emission projection and pulseprofile for Geminga parameter.Panel A: Photon emission from thepulsar as a function of phase.Panel B: Pulse profile.
Phase-resolved and phase-averaged gamma-ray spectra of the Geminga pulsar
Geminga Geminga
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Magnetospheric Geometry
For an oblique magnetic dipole rotator with an angular velocity and the magnetic moment vector , let its spin axis be along the Oz axis, be in the plane xOz and be the angle between and .
= BpR3/2.
Effects of Inclination angle is not included in ZC97 model
New modelNew model:
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It is believed that the outer gap is extended from its inner boundary to the light cylinder (CHR I). For the oblique magnetic dipole rotator, outer boundary is determined by (Kapoor & Shukre 1998)
Inner boundary:
The Goldreich-Julian current
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X-ray Field in the Magnetosphere
Observed X-ray spectra: soft (thermal) + hard (non-thermal) X-rays thermal X-rays.
Thermal X-ray emission from neutron star cooling
Zhang & Harding (2000)
Hibschman & Arons (2001)
X-ray emission from polar cap heating
Harding and Muslimov (2001)
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X-ray emission from outer gap heating
In the outer gap models, part of the relativistic particles from the outer gap will collide the stellar surface, producing the thermal X-rays. These relativistic inflowing particles from the outer gap radiate away much of their energy before reaching the polar cap (Zhang & Cheng 1997, Zhu et al. 1997; Wang et al. 1998; Cheng & Zhang 1999).
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Average energy of X-rays
Two possible cases:NS cooling+ pc heating; og heating
Assuming these X-ray can be approximated as the black-body, their spectrum can be expressed as
NS cooling + pc heating:
Outer gap heating
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The Fractional Size of an Outer Gap
In two dimensional geometry, the parallel electric field in the outer gap can be approximated as (ZC97)
Lesch et al. 1998
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Typical energy of the gamma-rays in the outer gap :
Inside the outer gap, pair production condition :
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X-rays are produced by the NS cooling and pc heating:
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X-rays are produced by the outer gap heating:
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In order to explain the average properties of high-energy photon emission from the outer gap, we assume that high-energy emission at a average radius <r> represents the typical emission of high-energy photons from a pulsar. The average radius is given by
Corresponding fractional size is
where f0 (P, B) = 5.5 P 26/21 B -4/712 is the fractional
size of outer gap by ignoring the effect of inclination angle (Zhang & Cheng 1997)
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Fig.1 Variation of the fractional size of the outer gap with the magnetic inclination angle for some typical pulsar parameters.
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3. High-Energy Gamma-ray Luminosity
In our model, L for each gamma-ray pulsar depends on P, B and . However, values are not known well. Once f(<r>,P,B) for a pulsar is estimated, L is
We find out statistically the relation between L and Lsdfor the canonical pulsars using Monte Carlo method. The details of this Monte Carlo method is given by Cheng & Zhang (1998) and Zhang et al. (2000).
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Fig.2 The change of L with Lsd in the simulated -ray pulsar. In our simulation, we have used the EGRET threshold as the minimumdetectable -ray energy flux. Open circles and shaped circles are the model radio-quiet and radio-loud -ray pulsars respectively.
Radio-loud : L L 0.30 sd
Radio-quiet : L L 0.38 sd
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Fig.3 L /L 0 versus L in the -ray pulsar population predicted by our outer gap model. We have used the EGRET threshold as the
minimum detectable -ray energy flux. Open circles are the expected data and solid line is the best fit. For comparison, we show the result given by Zhang & Cheng (1997) as a dashed line.
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Fig. 4 L versus Lsd. Solid circles with error bar are the observed data given by Thompson et al. (2001).
Solid line:lg L 20.42+0.38lg Lsd
Dashed line: lg L 3.25+0.30lg Lsd
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4. The Death lines of Pulsars with Outer Gaps
We now consider the condition which the outer gap of a pulsar exists. If the fractional size of the outer gap at rinis larger than unity, then the outer gap would not exist, I.e. f(rin)=1 give the death lines.
NS cooling+pc heating (Zhang & Harding 2000)
A1= 12.87-3.16lg Gpc ()A2= 12.92-1.17lg Gpc ()
Outer gap heating:
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It was generally believed that the parent distribution of the magnetic inclinations satisfy an uniform distribution (Gunn & Ostriker 1970; Gil & Han 1996). But recent study by using polarization data of the radio pulsarsindicate that the parent distribution of the magnetic inclinations satisfies a cosine-like distribution (Tauris & Manchester 1998). Therefore, we estimate the average value of f(rin) in these two possible parent distributions of the magnetic inclinations, i.e.
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For the uniform distribution, <Gpc()>~ 0.43 and <G()=0.38.
For cosine distribution,
NS+pc
NS+pc
OG
OG
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Fig.5 Death lines of the pulsars with outer gaps. It is assumed that X-rays are produced by the neutron star cooling and polar cap heating. Two cases of the inclination angle distributions are considered: (i)an uniform distribution and (ii)a cosine distribution.
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Fig.6 Death lines of the pulsars with self-sustained outer gaps. The observed data are taken from see website http://www.atnf.csiro.au/research/catalogue/.
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4. Conclusion and Discussion
We studied the outer gap size, gamma-ray luminosity and death lines of gamma-ray emission of the pulsars with outer gaps when the geometry of dipole magnetic field is taken into account.f(P, B, <r>()) is not only the function of P and B, but also the function of <r>, which depends on . The outer gap will not exist if f(r, ) > 1. For all gamma-ray pulsars with self-sustained outer gaps simulated by using Monte Carlo method, L L sd , where the value of ~0.38 for EGRET sensitivity . The death lines of the pulsars with outer gaps in the two possible X-ray fields are given and thecomparison with the observed data are considered.
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谢谢!谢谢!