1 / 52

脉冲星到达时间 Pulsar Timing

脉冲星到达时间 Pulsar Timing. 经 典 计 时. 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. 古 老 方 法. 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. 脉冲星 —— 精确自转的天体. 脉冲星简介. 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.

tress
Download Presentation

脉冲星到达时间 Pulsar Timing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 脉冲星到达时间Pulsar Timing Pulsar Workshop, 2009, NAOC

  2. 经 典 计 时 • 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 Pulsar Workshop, 2009, NAOC

  3. 古 老 方 法 Pulsar Workshop, 2009, NAOC

  4. 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 Pulsar Workshop, 2009, NAOC

  5. 脉冲星——精确自转的天体 Pulsar Workshop, 2009, NAOC

  6. 脉冲星简介 • 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 0.001s 0.01s 0.1s 1s 10s PSR J0437-4715 周期为: 5.757451831072007  0.000000000000008 ms Pulsar Workshop, 2009, NAOC

  7. 什么是脉冲星脉冲到达时间 • 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: Vela Crab The Vela PSR B0329+54的脉冲 The Crab T (second) Pulsar Workshop, 2009, NAOC

  8. 地球运动造成的脉冲到达时间延迟： （假设圆运动） A: light travel time from Sun to Earth t: time λ: ecliptic longitude β: ecliptic latitude ω: angular velocity of Earth 位置测量精度的问题： β=90°：highest angular accuracy of position β=0°：poor angular accuracy of position 位置测量误差导致时间延迟： Pulsar Workshop, 2009, NAOC

  9. 视差最大延迟示意图： PSRJ0437-4715:2.7μs • 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 Pulsar Workshop, 2009, NAOC

  10. 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 光行差效应 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 Pulsar Workshop, 2009, NAOC

  11. Roemer改正 Pulsar oe: observer to earth center es: earth center to sun sb: sun to solar system barycenter ob: observer to solar system barycenter roe 时间改正 rob roe：观测站的高度 res：天文单位，由地月质心运动和地球本身的运动决定 res rsb rsb：太阳系各行星之和： JPL星表 Pulsar Workshop, 2009, NAOC

  12. 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： r：日地距离 a：地球轨道半长轴 • r=常数a： • 变化r： 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 Pulsar Workshop, 2009, NAOC

  13. 广义相对论项改正 原子钟与标准钟之差： ms 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： Pulsar Workshop, 2009, NAOC

  14. Sin(i)=0.99975±0.00015 广义相对论项改正 2. Shapiro delay：时空弯曲，太阳系时间延迟为： 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 Shapiro Delay的残差 Pulsar Workshop, 2009, NAOC

  15. 引力作用下的时空扭曲 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。 Pulsar Workshop, 2009, NAOC

  16. Four General Relativistic Effects—by Andrew Lyne • 1. Periastron Advance: dω/dt • Due to non-radial force arising from finite speed of gravity Advance of perihelion of Mercury = 43 arcsec/century = 0.00012 deg/year Advance of periastron of 0737-3039 = 16.88 deg/year Pulsar Workshop, 2009, NAOC

  17. 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 Pulsar Workshop, 2009, NAOC

  18. Small delay Large delay Sin(i)=0.99975±0.00015 Four General Relativistic Effects—by Andrew Lyne • 3. Shapiro Delay: “Range” r and “Shape” s • Radiation travels more slowly through a gravitational well Pulsar Workshop, 2009, NAOC

  19. Four General Relativistic Effects—by Andrew Lyne • 4. Orbital Decay: dPb/dt • Loss of energy through gravitational radiation • Orbital period and size shrink Pulsar Workshop, 2009, NAOC

  20. 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TOA 7、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 Pulsar Workshop, 2009, NAOC

  21. T是换算到太阳系质量中心的时间 自转模型 残差：观测与模型的差别 • 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 Pulsar Workshop, 2009, NAOC

  22. 如何得到TOA 脉冲星PSR B1933+16 Pulsar Workshop, 2009, NAOC

  23. Timing Signal Submitted to MNRAS 周期测量：三次以上的观测 周期导数：几个月 P，Pdot，position，DM Pulsar Workshop, 2009, NAOC

  24. 位置测量需要至少一年的数据，最高精度达到0.001arcs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”： Pulsar Workshop, 2009, NAOC

  25. Pulsar Workshop, 2009, NAOC

  26. 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 Pulsar Workshop, 2009, NAOC

  27. 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： a：轨道半场轴，d：脉冲星距离 观测现象表现为周期导数的变化： 设d=1 kpc,V=100km s-1 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: Pulsar Workshop, 2009, NAOC

  28. Gravitational acceleration 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： a: 视线方向加速度 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 Pulsar Workshop, 2009, NAOC

  29. 自由进动 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，导致观测到的脉冲形状和脉冲到达时间的变化。 Pulsar Workshop, 2009, NAOC

  30. 自由进动 • 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 • 自转轴与磁轴夹角的周期变化 • 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 • 还会表现为脉冲轮廓的变化 • 进动幅度：对应0.5—1deg的进动角 • 进动角速度： Pulsar Workshop, 2009, NAOC

  31. 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 即： α：磁倾角 磁赤道表面磁场： 磁极表面磁场：2Bs 周期为P0的脉冲星周期演化： n: braking index 假设脉冲星减慢遵循指数变化： 积分上式，得脉冲星特征年龄 磁偶极n=3，星表特征年龄为： Pulsar Workshop, 2009, NAOC

  32. Pulsar ages • 1. 验证脉冲星磁偶极模型 • 脉冲星与超新星遗迹，验证恒星演化 • Crab的验证：1054年超新星爆发 Crab脉冲星的周期三阶导数可测，并与偶极 辐射理论一致！ The braking index 对 求导， • 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 PSR B0531+21 n=2.515±0.005 (Crab) PSR B1509－58 n=2.837±0.001 PSR B0540－69 n=1.81±0.07 PSR J1119－6127 n=3.0±0.1 PSR B0835－45 n=1.4±0.2 (Vela) PSR J1846－0258 n=2.65±0.1 (AXP) Pulsar Workshop, 2009, NAOC

  33. Pulsar clock clock • 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. Matsakis, Taylor & Eubanks, 1997, A&A Pulsar Workshop, 2009, NAOC

  34. 13 Years of Timing of PSR B1259-63 N. Wang S. Johnston R. N. Manchester Pulsar Workshop, 2009, NAOC

  35. 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*) Pulsar Workshop, 2009, NAOC

  36. 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 Pulsar Workshop, 2009, NAOC

  37. PSR B1259-53 Wex DM Pulsar Workshop, 2009, NAOC

  38. What’s Pulsar Timing? It measures the pulse arrival time: PSR B0329+54 T (second) Pulsar Workshop, 2009, NAOC

  39. A rotational model is fitted to data: T is the time at the solar system barycenter • 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: Pulsar Workshop, 2009, NAOC

  40. Residual of position error Residual of p and pdot error Pulsar Workshop, 2009, NAOC

  41. 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 Pulsar Workshop, 2009, NAOC

  42. Steps at second periastron Pulsar Workshop, 2009, NAOC

  43. Earlier Timing Solution by Wex et al. (1998): Data up to end of 1996, cover 1990 and 1994 periastrons. Three Solutions: 1. Timing noise 2. Spin-orbital coupling:Precession of the orbit Pulsar Workshop, 2009, NAOC

  44. Observations and Analysis 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 18 443 1997.5－2000.9 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 Pulsar Workshop, 2009, NAOC

  45. ●Standard profiles ●Pulse profile evolution Differing spectral index ●Alignment of profiles Outer edge Pulsar Workshop, 2009, NAOC

  46. DM variation • 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. Pulsar Workshop, 2009, NAOC

  47. 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: Pulsar Workshop, 2009, NAOC

  48. Keplerian • 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 Spin-orbital coupling Mass accretion Orbital jump Pulsar Workshop, 2009, NAOC

  49. Discussion 1. Timing noise: jitter in the pulse arrival times 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 Pulsar Workshop, 2009, NAOC

  50. Discussion 2. Steps in Rotational Parameters 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 Pulsar Workshop, 2009, NAOC

More Related