脉冲星到达时间 Pulsar Timing
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Transcript of 脉冲星到达时间 Pulsar Timing
23/4/22Pulsar Workshop, 2009, NAOC1
脉冲星到达时间Pulsar Timing
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地球的公转:精度 ~0.1秒的小数
平太阳时,恒星时地球自转:精度 ~10 - 8
秒 协调世界时
经 典 计 时
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古 老 方 法
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现 代 计 时
自然界的微观周期运动,以原子 /分子的周期振动制作人工连续计时
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脉冲星——精确自转的天体
0.001s 0.01s 0.1s 1s 10s
已知 1850 颗脉冲星,绝大多数在银河系 周期~ 1s
毫秒脉冲星性质很不相同 (~ 0.003 s)
多数毫秒脉冲星处于双星系统 毫秒脉冲星是再循环的年老脉冲星,自转 非常稳定
PSR J0437-4715 周期为 :
5.757451831072007
0.000000000000008 ms
脉冲星简介
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Pulsar Workshop, 2009, NAOC
PSR B0329+54 的脉冲
T (second)
什么是脉冲星脉冲到达时间
The Vela
The Crab
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Vela
Crab
Pulsar rotate tens or even hundreds of times every
second. Measure the time-of-arrival (TOA) of pulses. Differences between the observed TOAs and a
model are called timing residuals. The predicted rotation pulse phase given by the
basic timing model:
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cos( )cosct A t A: light travel time from
Sun to Eartht: timeλ: ecliptic longitudeβ: ecliptic latitudeω: angular velocity of
Earth位置测量精度的问题:β=90° : highest angular
accuracy of positionβ=0° : poor angular accuracy
of position
位置测量误差导致时间延迟:
地球运动造成的脉冲到达时间延迟:
(假设圆运动)
sin( )cos cos( )sinct A t A t
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需考虑:•地球自转 21ms•椭圆轨道•太阳系惯性质量中心与太阳并不重合:木星等行星的影响•地球在椭圆轨道上的引力势有周年变化,地面钟相对圆形轨道有周年变化•Doppler效应二阶项,与地球的椭圆轨道相关,∝ V2
地球
Roemer延迟 vs. 视差测量•地球轨道上引力势的变化,时空弯曲 ->时间延迟•群延迟:消色散
2 2 2cos cos
2 2
a a
cd c
视差最大延迟示意图:PSRJ0437-4715:2.7μs
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0 2
( , , , 0, ) ( ) ( ,
( , , )
)
, ,R Eb obs C
R b E S A
S
x e P T r
Mt t
s
Dt
参考时刻 测站主钟与标准地面时间的差
太阳系内传播效应时间延迟,和相对论时间改正分别对应:“ Roemer”、“ Einstein”、“ Shapiro”效应
双星系统中传播效应时间延迟,和相对论时间改正,分别对应:“ Roemer”、“ Einstein”、“ Shapiro”效应
光行差效应
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Roemer 改正ob oe es sb r r r r
ˆ.obct c
r s
oe: observer to earth centeres: earth center to sunsb: sun to solar system barycenterob: observer to solar system barycenter
res:天文单位,由地月质心运动和地球本身的运动决定
rob
res
rsb
roe
Pulsar
s
11
1( )
1sb i iiii
mm
r rrsb:太阳系各行星之和:
roe:观测站的高度
JPL星表
时间改正
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广义相对论项改正
1. Time dilation:地球运动及引力红移
S :随地球椭圆轨道公转的地面原子钟时间t :距太阳无限远的原子钟协调时
两个时间系统的微分表达:
2
2d 1 11
d 4
GMt
S r a c
r :日地距离a :地球轨道半长轴
① r= 常数 a : 8d
1.48 10d
t
S
② 变化 r : 10d3.3079 10 cos
d
tf
S
其中 f :地球实时运动与近日点的角距,非均匀变化:真近点角
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原子钟与标准钟之差:
10
0
10 2
3.3079 10 cos d
1 3 13.3079 10 sin sin 2 sin 3 sin
2 8 3
lf l
l e l l e l l
l: 平近点角。,- el 为常数改正,并入所定义的标准钟,其他变化量表示为相对论改正:
2r
1 1 31.66145 (1 )sin sin 2 sin 3
8 2 8t l e l e l
广义相对论项改正
ms
Sin(i)=0.99975±0.00015Sin(i)=0.99975±0.00015
Shapiro Delay 的残差 23/4/2214 Pulsar Workshop, 2009, NAOC
2. Shapiro delay :时空弯曲,太阳系时间延迟为:
广义相对论项改正
S 3
2ln(1 cos )
GM
c
θ :脉冲星 - 太阳 - 地球夹角
太阳附近:最大值 120us木星附近: 200 ns 。行星很小,可忽略
太阳的质量是 1.989133千克,质量使它的四周产生时空扭曲,如果光经过太阳的附近,光发生 1.75“角度的偏转。通过双星系统中的脉冲星也可观测到该现象。
引力作用下的时空扭曲
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Four General Relativistic Effects—by Andrew Lyne
• 1. Periastron Advance: dω/dt– Due to non-radial force arising from finite speed of
gravity
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Advance of perihelion of Mercury = 43 arcsec/century
= 0.00012 deg/year
Advance of periastron of 0737-3039 = 16.88 deg/year
Advance of perihelion of Mercury = 43 arcsec/century
= 0.00012 deg/year
Advance of periastron of 0737-3039 = 16.88 deg/year
Four General Relativistic Effects —by Andrew Lyne
• 2. Gravitational Redshift and Time Dilation: γ– Clocks run slow in a gravitational well
e.g. Clocks on Earth run slow and fast by ± 0.0016 sec e.g. Clocks on Earth run slow and fast by ± 0.0016 sec
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Four General Relativistic Effects —by Andrew Lyne
• 3. Shapiro Delay: “Range” r and “Shape” s– Radiation travels more slowly through a
gravitational well
Small delay
Large delay
Small delay
Large delay
Sin(i)=0.99975±0.00015Sin(i)=0.99975±0.00015
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Four General Relativistic Effects —by Andrew Lyne
• 4. Orbital Decay: dPb/dt
– Loss of energy through gravitational radiation– Orbital period and size shrink
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射电脉冲星实测关键技术 & 数据库脉冲星脉冲到达时间观测是基本观测1 、获得观测起始时刻2 、获得观测时间的视周期3 、数据采样:足够的时间、频率分辨率4 、观测积分折叠5 、消色散(射电观测)提高脉冲轮廓信噪比6 、脉冲轮廓相关,获得 TOA7 、太阳系星历表 TOA归算到惯性系8 、分析,改进的脉冲星自转模型,其他
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3200 6
1
2
1)( TTTT
自转模型T 是换算到太阳系质量中心的时间
影响脉冲到达时间的因素 :• 脉冲星自转变化 • 脉冲星位置变化和误差• 色散延迟• 散射• 相对论效应 • 双星系统的轨道运动 • 地球运动• 其他未知因素
1 20 0 0 0 0 0 0 0
1 1( ) ( ) ( ) [ ( )] [ ( )] ......
2 6t t t t t t A t t B t t
残差:观测与模型的差别
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如何得到 TOA
脉冲星 PSR B1933+16
Timing Signal
P , Pdot , position , DM
Submitted to MNRAS
周期测量:三次以上的观测周期导数:几个月
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位置测量需要至少一年的数据,最高精度达到 0.001arcs自行测量则需要几年的数据,收到达时间噪声影响,若需精确测定PM一般用 VLBI技术
位置位差与自行误差的“ Timing signal”:
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PSR J2150+5247 的残差
噪声小的脉冲星,其自转参数、位置、自行等参数的测量也准确
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The Shklovsky effect – secular acceleration
对于脉冲星横向速度 V 较大的情形, Doppler 效应造成视周期的变化,甚至可以抵消 slow-down ,时间延迟可表示为:
2 2 2
2 2
a V t
dc dc
观测现象表现为周期导数的变化:21P V
P c d
设 d=1 kpc,V=100km s-1
113.4 10P
P
yr
脉冲星的内禀周期导数与 Shklovsky 效应不易区分,除非自行与距离精确已知对于长周期脉冲星,该效应不明显,毫秒脉冲星则不同
secular acceleration for MSPs:PSR J0437-4715:
12(5.3 0.9) 10bP
a :轨道半场轴, d :脉冲星距离
2Obs Int
b b
b b
P P V
P P c d
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Gravitational acceleration
obs
aP P
cP
a: 视线方向加速度
考虑银河系引力场、球状星团、伴星中,脉冲星在视线方向被加速,观测到得脉冲星周期导数为:
球状星团中的脉冲星加速明显,甚至表现为脉冲星在加速自转:
球状星团 M15 中的 MSPs PSR B2127+11A 和 PSR B2127+11D :
位于星团的远端,朝着中心运动,可用来估计星团中心的质量
16obs 2 10P P
脉冲星的摇摆(进动)导致其自转轴随时间的运动轨迹为圆形;就象陀螺的脉冲星的摇摆(进动)导致其自转轴随时间的运动轨迹为圆形;就象陀螺的顶部的运动一样。所以我们就从不同的角度观测锥形辐射束,导致观测到的顶部的运动一样。所以我们就从不同的角度观测锥形辐射束,导致观测到的脉冲形状和脉冲到达时间的变化。脉冲形状和脉冲到达时间的变化。
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自由进动
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自由进动
1. 旋转的物体会表现出自由进动,自转轴与角动量矢量不重合2. 自转轴与磁轴夹角的周期变化 3. 表现为自转速率的长期、准周期变化,可观测到周期导数的变化4. 还会表现为脉冲轮廓的变化5. 进动幅度:对应 0.5—1deg的进动角6. 进动角速度:
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Pulsar ages
角频率 Ω ,磁偶极矩 M⊥ 时辐射能量为
磁偶极辐射主导,粒子流。辐射损失角动能21
2I
2 4 32
3M c
2
2 2 4 3
1d( ) 22 sin
d 3
II M c
t
α:磁倾角
19 1 23.2 10 ( ) gaussSB PP 磁赤道表面磁场:
磁极表面磁场: 2Bs2 8 2 1 2
0 ,12( ) ( 3.15 10 )sP t P B t 周期为 P0 的脉冲星周期演化:
假设脉冲星减慢遵循指数变化:n
1 1
( 1) ( 1)
P
n n P
积分上式,得脉冲星特征年龄
n: braking index
磁偶极 n=3 ,星表特征年龄为: Myr2c
P
P
即:
1, in
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PSR B0531+21 n=2.515±0.005 (Crab)PSR B1509 - 58 n=2.837±0.001PSR B0540 - 69 n=1.81±0.07PSR J1119 - 6127 n=3.0±0.1PSR B0835 - 45 n=1.4±0.2 (Vela)PSR J1846 - 0258 n=2.65±0.1 (AXP)
The braking index
1. 验证脉冲星磁偶极模型2.脉冲星与超新星遗迹,验证恒星演化3.Crab 的验证: 1054 年超新星爆发
n 求导, 2 2 22
PPn
P
• 仅对六颗年轻脉冲星,测得n :• 大部分脉冲星受周期噪声影响n 测量值没有物理意义
对
Crab 脉冲星的周期三阶导数可测,并与偶极辐射理论一致! 3
2
(2 1)n n
Pulsar ages
clock
Matsakis, Taylor & Eubanks, 1997, A&A
• T(1937) and T(1855) are the timescales based on the pulsars PSR B1937+21 and PSR B1855+09, respectively.
• TT96 is a terrestrial atomic timescale. TA(A.1)
• TA(PTB) are free running atomic timescales from the U.S. Naval Observatory and Germany.
Pulsar clock
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13 Years of Timing of PSR B1259-63
N. Wang S. Johnston R. N. Manchester
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Brief Introduction of PSR B1259-63:
• Discovered in a large-scale high frequency survey of
the Galactic plane (Johnston et. al, 1992a)
• It is the only known pulsar that has a young, massive,
non-degenerate, Be star companion (Johnston et. al,
1992b)
• Characteristic age: ~330 kyr
Period: ~48 ms
Orbital period: ~1237 days -- longest so far
Eccentricity: ~0.87 -- largest known
Periastron: 24 stellar radii (R*)
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Companion:
• SS 2883, B2e main sequence star
• 10 solar mass, 6 solar radii
• Equatorial velocity vsin(i) = 280 km/s and runaway
velocity of 80 km/s
• A hot, tenuous polar wind: loss ~10-6 solar mass/yr
• A cooler, high density, equatorial disk:
108—1010cm-3 near the star surface, falls off as power-law
Hα emission at 20 R*, just inside the pulsar orbit (Johnston
et al., 1994 )
Highly tilted with respect to the pulsar orbital plane
PSR B1259-63 eclipse for ~40 days 23/4/2236 Pulsar Workshop, 2009, NAOC
PSR B1259-53
DM
Wex
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What’s Pulsar Timing?It measures the pulse arrival time:
PSR B0329+54
T (second)
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A rotational model is fitted to data:
3200 6
1
2
1)( TTTT
T is the time at the solar system barycenter
)]([)]([])(6
1)(
2
1)[( 00
20000
100 ttBttAtttttt
Factors that effect pulse arrival time:• pulsar rotation • pulsar position change• dispersion smearing• scattering• relativistic effect • orbital motion in binary system • earth movement
The observed residuals:
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Residual of position error Residual of p and pdot error
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Interactions of PSR B1259-63 with its surroundings
• Frictional drag from the disk: • Mass accretion: spins-up or slows-down the pulsar, depends on the relative size of Alfven radius and corotation radius • Spin-orbital coupling: spin induced oblateness of the star implies additional 1/r3
gravitational potential (quadrulpole gravitational moment ), introduces precession of the orbital plane
• Tidal effects with the main sequence B2e star: Pb, e, i
ePb ,,
x ,
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217105 s
Steps at second periastron19105 s
14 deg102 yr
121015 x
03.0
sx 01.0
6104 e
sPb 30
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Earlier Timing Solution by Wex et al. (1998):
Data up to end of 1996, cover 1990 and 1994 periastrons.
Three Solutions:
10
1
10)3(15.0
deg)8(000184.0
x
yrw
10
1
10)4(40.2
deg)9(000396.0
x
yrw
PPPP ,,,
1. Timing noise
2. Spin-orbital coupling: Precession of the orbit
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Details of the observation data spans.
Data Preceding T+ T - No. of span Periastron (MJD) (d) (d) TOAs ----------------------------------------------------------------------------------------------------1990.1 - 1990.7 - - 107 18 1990.7 - 1994.0 48124 171 20 187 1994.0 - 1997.5 49361 24 18 4431997.5 - 2000.9 50597 16 52 237 2000.9 - 2003.5 51834 19 - 146
Altogether 1031 independent observations, obtained on 0.66, 1.4, 2.4, 4.8, 8.4, 13.6 GHz
Observations and Analysis
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● Standard profiles
● Pulse profile evolution Differing spectral index
● Alignment of profiles Outer edge
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• Dispersion measure variations from 13 years of timing observation.
• The offset is measured relative to the value of 146.8 pc cm-3.
• A mean offset of - 0.2±0.1 pc cm-3 from T+43 of 2000 periastron.
DM variation windISMe DMDMdlnDM
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Timing Results
A glitch near MJD 50691 (1997, August 30), 94 days after
1997 periastron.
A glitch is a sudden jump in pulsar spin rate, with relative
amplitude △ν/ν~10-9 - 10-6
Exponential decay with a assumed time scale of 100 days,
we have:
19
19
10)122(
10)167(
s
s
d
g
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(a)fitting for and the five Keplerian orbital parameters. Plus the addition of:
(b)
(c)jumps in at each periastron;
(d)jumps in x at each periastron.
Residual:4.3, 4.7, 0.78, 0.46 ms
,,
x ,
,
Keplerian
Spin-orbital coupling
Mass accretion
Orbital jump
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Discussion
1. Timing noise: jitter in the pulse arrival times
1.210
)6
||log(
88
3
st
tt
Close to the value of other pulsars with similar frequency derivatives, so the long term timing noise is reasonably well removed
n= - 36.7
Reflect the high level of timing activity in this young pulsar
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Problems:
△ν does not have a constant sign at each periastron
Accretion: X-ray obs. show bow shock well outside the
pulsar magnetosphere (Hirayama et al. 1999), require
high density and/or high outflow velocity
Require jumps in frequency derivative
Discussion
2. Steps in Rotational Parameters
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Take △x~ 60ms,Kepler’s third law Pb2∝a3 implying large value of
△Pb ~ 0.08d, has to be △i=7″
• Spin-orbital coupling
Pb~3yr, similar to time scale of typical timing noise
Timing noise may mask the true period variation• Frictional drag from the disk
magnitude too small: △Pb =-0.002s, △e=-3X10-13
(Manchester et al. 1995, Wex et al. 1998) The highly inclined disk with respect to the orbit may tilt the orbit with △i=7″• Tidal effects with the main sequence B2e star Depends on the separation of two objects,
PSR J0045-7319: 4R*, PSR B1259-63: 24R*
Enhanced by resonance of the oscillation modes of star
Discussion
3. Changes in Orbital Parameters
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sinx a i
Summary
1. We’ve obtained 13 years of timing data for PSR B1259-63, including 4 periastrons.
2. Timing of PSR B1259-63 is complicated: ● Eclipse ● Timing noise ● Glitch ● DM changes ● Interaction with its companion3. Spin-orbital coupling: failed in predicting the latest two orbits 4. Best model: jumps in inclination angle5. Physics implication not clear: tidal effects is the possible
mechanism responsible for the observed period veriation.
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