一种X射线脉冲星自转参数估计新方法

doi:10.7527/S1000-6893.2024.30526

Abstract

Abstract:

The establishment of pulsar parameter database is an important achievement of pulsar observation， and is also the basis for the study of pulsar applications in space. The improvement of the accuracy of pulsar timing model parameters is of great significance for pulsar applications， such as X-ray pulsar navigation， and time reference maintenance in deep space. However， the radio ephemeris of pulsars cannot meet the needs of X-ray timing analysis. In this paper， the PSR B1937+21 observed by NICER detector is taken as the research object， and a method using RANSAC robust fitting to update pulsar’s spin parameters is proposed. The timing results after updating the spin parameters using the least squares fitting algorithm， the Gauss-Newton iteration method and the RANSAC robust fitting algorithm are compared， and the characteristic changes of pulse profile during parameter updating are analyzed. After the spin parameters are updated， the main trend items in timing residuals are deducted， and the timing accuracy and rotation stability within six years are improved significantly.

Key words: pulsar timing, millisecond pulsar, parameter fit, timing residual, stability

CLC Number:

V419

Mengna HAN, Minglei TONG, Yongqiang SHI, Zheyu WANG. A new estimation algorithm for spin parameters of X-ray pulsar[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(3): 630526.

Figures/Tables 15

Fig.1

Fig.2

Table 1

Spin parameters of pulsar obtained by iterative update

迭代次数	$ν 0$ /s^-1	$ν ˙$ /s^-2
0	641.928 233 334 554 4	-4.330 901 553 450×10^-14
1	641.928 233 334 407 0（5.9×10^-15）	-4.330 801 133 739×10^-14（3.7×10^-23）
2	641.928 233 334 402 8（4.3×10^-15）	-4.330 798 161 015×10^-14（2.7×10^-23）

Table 1

Fig.3

Table 2

Changes in parameters of pulse profile during spin parameters updating

迭代次数	$χ 2$	FWHM
0	1.422 1	0.015 6
1	1.422 4	0.007 8
2	1.422 4	0.007 8

Table 2

Fig.4

Fig.5

Table 3

Estimated values of spin parameters obtained by three estimation methods

方法

ν 0

/s^-1

ν ˙

/s^-2

最小二乘算法

641.928 233 334 407 0（641.928 233 334 409 9）

-4.330 801 133 739×10^-14

（-4.330 802 843 865 259×10^-14）

高斯-牛顿迭代法

641.928 233 334 407 0（641.928 233 334 409 9）

-4.330 801 133 815 196 6×10^-14（-4.330 802 843 939 356 4×10^-14）

RANSAC抗差拟合算法

641.928 233 334 407 2

-4.330 799 512 645 931×10^-14

Table 3

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

References 27

1	SUN H F， SUN X， FANG H Y， et al. Building X-ray pulsar timing model without the use of radio parameters［J］. Acta Astronautica， 2018， 143： 155-162.
2	GENDREAU K C， ARZOUMANIAN Z， OKAJIMA T. The Neutron star Interior Composition ExploreR （NICER）： An explorer mission of opportunity for soft X-ray timing spectroscopy［C］∥Space Telescopes and Instrumentation 2012： Ultraviolet to Gamma Ray. Bellingham： SPIE， 2012： 844313.
3	GENDREAU K C， ARZOUMANIAN Z， ADKINS P W， et al. The Neutron star Interior Composition Explorer （NICER）： Design and development ［C］∥Space Telescopes and Instrumentation 2016： Ultraviolet to Gamma Ray. Bellingham： SPIE， 2016： 99051H.
4	BACKER D C， KULKARNI S R， HEILES C， et al. A millisecond pulsar［J］. Nature， 1982， 300： 615-618.
5	VIVEKANAND M. The 31 yr rotation history of the millisecond pulsar J1939+2134 （B1937+21）［J］. The Astrophysical Journal， 2020， 890（2）： 143-154.
6	RAWLEY L A， TAYLOR J H， DAVIS M M， et al. Millisecond pulsar PSR 1937+21： A highly stable clock［J］. Science， 1987， 238（4828）： 761-765.
7	SHEMAR S， FRASER G， HEIL L， et al. Towards practical autonomous deep-space navigation using X-Ray pulsar timing［J］. Experimental Astronomy， 2016， 42（2）： 101-138.
8	DENEVA J S， RAY P S， LOMMEN A， et al. Large high-precision X-ray timing of three millisecond pulsars with NICER： Stability estimates and comparison with radio［J］. The Astrophysical Journal， 2019， 874（2）： 160-172.
9	SUN H F， YAO D K， SHEN L R， et al. Estimating 5-year rotation stability of PSR B1937+21 using NICER observations［J］. Acta Astronautica， 2023， 210： 141-150.
10	杨廷高，高玉平，童明雷，等. 计时观测测量脉冲星参数的数学模型与精度估计［J］. 天文学报， 2015， 56（4）： 370-377.
	YANG T G， GAO Y P， TONG M L， et al. Mathematical model for measuring pulsar parameters and precision estimation with pulsar timing observations［J］. Acta Astronomica Sinica， 2015， 56（4）： 370-377 （in Chinese）.
11	周庆勇，刘思伟，郝晓龙，等. 空间X射线观测确定脉冲星星历表参数精度分析［J］. 物理学报， 2016， 65（7）： 079701.
	ZHOU Q Y， LIU S W， HAO X L， et al. Analysis of measurement accuracy of ephemeris parameters for pulsar navigation based on the X-ray space observation［J］. Acta Physica Sinica， 2016， 65（7）： 079701 （in Chinese）.
12	SUN H F， SU J Y， ZHAO L， et al. Building the crab pulsar timing model with XPNAV-1 observations［C］∥Lecture Notes in Electrical Engineering China Satellite Navigation Conference （CSNC） 2018 Proceedings. Singapore： Springer Singapore， 2018： 897-907.
13	陈师. X射线脉冲星计时模型参数估计方法研究［D］. 西安：西安电子科技大学， 2022： 35-39.
	CHEN S. Study on parameter estimation method of X-ray pulsar timing model［D］.Xi’an： Xidian University， 2022： 35-39 （in Chinese）.
14	LENTATI L， HOBSON M P， ALEXANDER P. Bayesian estimation of non-Gaussianity in pulsar timing analysis［J］. Monthly Notices of the Royal Astronomical Society， 2014， 444（4）： 3863-3878.
15	SAMAJDAR A， SHAIFULLAH G M， SESANA A， et al. Robust parameter estimation from pulsar timing data［J］. Monthly Notices of the Royal Astronomical Society， 2022， 517（1）： 1460-1468.
16	EDWARDS R T， HOBBS G B， MANCHESTER R N. TEMPO2， a new pulsar timing package-II. The timing model and precision estimates［J］. Monthly Notices of the Royal Astronomical Society， 2006， 372（4）： 1549-1574.
17	TAYLOR J H. Pulsar timing and relativistic gravity［J］. Philosophical Transactions of the Royal Society of London Series A， 1992， 341（1660）： 117-134.
18	HOBBS G B， EDWARDS R T， MANCHESTER R N. TEMPO2， a new pulsar-timing package–I. An overview［J］. Monthly Notices of the Royal Astronomical Society， 2006， 369（2）： 655-672.
19	杨成伟，郑建华. 脉冲星X射线数据处理与分析［J］. 深空探测学报， 2018， 5（3）： 219-225.
	YANG C W， ZHENG J H. X-ray pulsar data processing and analysis［J］. Journal of Deep Space Exploration， 2018， 5（3）： 219-225 （in Chinese）.
20	FISCHLER M A， BOLLES R C. Random sample consensus： A paradigm for model fitting with applications to image analysis and automated cartography［J］. Communications of the ACM， 1981， 24（6）： 381-395.
21	杨元喜，吴富梅. 临界值可变的抗差估计等价权函数［J］. 测绘科学技术学报， 2006， 23（5）： 317-320， 324.
	YANG Y X， WU F M. Modified equivalent weight function with variable criterion for robust estimation［J］. Journal of Geomatics Science and Technology， 2006， 23（5）： 317-320， 324 （in Chinese）.
22	周庆勇，魏子卿，雷耀虎，等. 面向脉冲星深空基准建立的X射线望远镜及发展设想［J］. 航空学报， 2023， 44（3）： 526608.
	ZHOU Q Y， WEI Z Q， LEI Y H， et al. X-ray telescope for pulsar deep space reference and its development vision［J］. Acta Aeronautica et Astronautica Sinica， 2023， 44（3）： 526608 （in Chinese）.
23	童明雷，韩孟纳，杨廷高，等. 利用Crab脉冲星X射线观测校准星载原子钟频率［J］. 航空学报， 2023， 44（3）： 526566.
	TONG M L， HAN M N， YANG T G， et al. Correcting frequency of a spaceborne atomic clock using X-ray observations of Crab pulsar［J］. Acta Aeronautica et Astronautica Sinica， 2023， 44（3）： 526566 （in Chinese）.
24	王禹淞，王奕迪，郑伟.基于实测星载原子钟数据的脉冲星守时方法［J］. 导航定位与授时， 2023， 10（6）： 10-16.
	WANG Y S， WANG Y D， ZHENG W. Pulsar timing method based on measured spaceborne atomic clock data［J］. Navigation Positioning and Timing， 2023， 10（6）： 10-16 （in Chinese）.
25	HAN M N， TONG M L， LI L S， et al. Frequency steering of spaceborne clocks based on XPNAV-1 observations［J］. Chinese Journal of Aeronautics， 2023， 36（6）： 266-278.
26	MATSAKIS D N， TAYLOR J H， EUBANKS T M. A statistic for describing pulsar and clock stabilities［J］. Astronomy and Astrophysics， 1997， 326（3）： 924-928.
27	李孝辉，杨旭海，刘娅，等. 时间频率信号的精密测量［M］. 北京：科学出版社， 2010： 17-19.
	LI X H， YANG X H， LIU Y， et al. Precise measurement of time-frequency signal［M］. Beijing： Science Press， 2010： 17-19 （in Chinese）.

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A new estimation algorithm for spin parameters of X-ray pulsar

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