利用Crab脉冲星X射线观测校准星载原子钟频率

doi:10.7527/S1000-6893.2022.26566

Abstract

Abstract:

To improve the long-term time-keeping ability of a spaceborne atomic clock and improve its autonomy， this paper proposes a method for steering the frequency of the spaceborne atomic clock by using the Crab pulsar data observed by XPNAV-1 satellite. In the X-ray pulsar timing processing， we use the Gaussian kernel regression method to smooth the pulsar profile， which can effectively improve the Signal-to-Noise Ratio （SNR） of the pulsar profile and timing precision. By simulating the frequency deviation of the reference clock recording the photon arrival times， the influence of the frequency deviation of the reference clock on pre-fit timing residuals is analyzed. Based on this， a method for frequency calibration of the spaceborne atomic clock is given. For the spaceborne clock with frequency deviation of order 10^－11， the frequency calibration accuracy with relative error of about 40% can be obtained from the Crab Pulsar data for about one month. It is expected that the frequency calibration accuracy of spaceborne clock can be further improved by using the pulsar timing data with a longer time span.

Key words: pulsar, atomic clock, X-ray pulsar timing, frequency steering, timing residual

CLC Number:

V419

Minglei TONG, Mengna HAN, Tinggao YANG, Chengshi ZHAO, Xingzhi ZHU. Correcting frequency of a spaceborne atomic clock using X-ray observations of Crab pulsar[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(3): 526566-526566.

Figures/Tables 11

Table 1

Spin parameters of Crab pulsar

参数	P1数值	P2数值
参考历元（TDB）t₀/s	57 715×86 400+0.016 934	57 737×86 400+0.024 934
$ν 0$ /s^-1	29.6 478 547 456	29.647 153 432 3
$ν ˙$ /s^-2	-368 970.96×10^-15	-368 942.90×10^-15
$ν ¨$ /s^-3	9.183 772 012 612 545×10^-21	9.182 592 438 173 919×10^-21

Table 1

Fig. 1

Table 2

Signal-to-noise ratio of integrated pulse profile folded by different number of sub-phase intervals

子相位间隔数 $N$	SNR
64	3 840.68
128	1 959.79
256	981.64
512	515.77
1 024	270.36
4 096	81.80

Table 2

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Table 3

Estimates of frequency deviations corresponding to different sub-phase intervals and their relative errors

$N$	$y c$ /10^-10	$δ y c$	$y s$ /10^-10	$δ y s$
64	2.659 3	-0.012 9	2.654 0	-0.014 9
128	2.629 0	-0.024 2	2.671 8	-0.008 3
192	2.651 2	-0.015 9	2.698 7	0.001 7
256	2.628 9	-0.024 2	2.685 8	-0.003 1
320	2.656 4	-0.014 0	2.685 4	-0.003 2
384	2.711 6	0.006 5	2.685 2	-0.003 3
448	2.738 1	0.016 3	2.669 0	-0.009 3
512	2.747 0	0.019 6	2.664 8	-0.010 8
576	2.493 2	-0.074 6	2.654 5	-0.014 7
640	1.924 8	-0.285 5	2.654 1	-0.014 8
704	1.789 6	-0.335 7	2.654 3	-0.014 8
768	0.828 3	-0.692 5	2.673 5	-0.007 6
832	1.154 3	-0.571 5	2.663 3	-0.011 4
896	0.413 8	-0.846 4	2.659 7	-0.012 8
960	0.623 1	-0.768 7	2.669 8	-0.009 0
1 024	0.009 8	-1.003 6	2.654 0	-0.014 9

Table 3

Fig. 6

Table 4

Fig. 7

References 30

1	LORIMER D R， KRAMER M. Handbook of pulsar astronomy［M］. Cambridge： Cambridge University Press， 2005
2	吴鑫基，乔国俊，徐仁新. 脉冲星物理［M］. 北京：北京大学出版社， 2018： 42-43， 83-87.
	WU X J， QIAO G J， XU R X. Pulsar physics［M］. Beijing： Peking University Press， 2018： 42-43， 83-87 （in Chinese）.
3	HULSE R A， TAYLOR J H. Discovery of a pulsar in a binary system［J］. The Astrophysical Journal Letters， 1975， 195： L51.
4	BACKER D C， KULKARNI S R， HEILES C， et al. A millisecond pulsar［J］. Nature， 1982， 300（5893）： 615-618.
5	WOLSZCZAN A， FRAIL D A. A planetary system around the millisecond pulsar PSR1257 + 12［J］. Nature， 1992， 355（6356）： 145-147.
6	帅平，李明，陈绍龙. X射线脉冲星导航系统原理与方法［M］. 北京：中国宇航出版社， 2009： 11-20.
	SHUAI P， LI M， CHEN S L. Principle and method of X-ray pulsar navigation system［M］. Beijing： China Aerospace Press， 2009： 11-20 （in Chinese）.
7	HOBBS G， COLES W， MANCHESTER R N， et al. Development of a pulsar-based time-scale［J］. Monthly Notices of the Royal Astronomical Society， 2012， 427（4）： 2780-2787.
8	HOBBS G， GUO L， CABALLERO R N， et al. A pulsar-based time-scale from the international pulsar timing array［J］. Monthly Notices of the Royal Astronomical Society， 2020， 491（4）： 5951-5965.
9	ZHANG Z H， TONG M L， ZHAO C S， et al. The influence of the observational strategies of pulsar timing on the properties of pulsar clocks［J］. Research in Astronomy and Astrophysics， 2020， 20（12）： 135-141.
10	QIAN G. LM-11 successfully launched XPNAV-1［J］. Aerospace China， 2016， 17（4）： 61.
11	黄良伟，帅平，张新源，等. 脉冲星导航试验卫星时间数据分析与脉冲轮廓恢复［J］. 中国空间科学技术， 2017， 37（3）： 1-10.
	HUANG L W， SHUAI P， ZHANG X Y， et al. XPNAV-1 Satellite timing data analysis and pulse profile recovery［J］. Chinese Space Science and Technology， 2017， 37（3）： 1-10 （in Chinese）.
12	帅平，张新源，黄良伟，等. 脉冲星导航试验卫星科学观测数据分析［J］. 空间控制技术与应用， 2017， 43（2）： 1-6.
	SHUAI P， ZHANG X Y， HUANG L W， et al. X-ray pulsar navigation test satellite science data analysis［J］. Aerospace Control and Application， 2017， 43（2）： 1-6 （in Chinese）.
13	帅平，刘群，黄良伟，等. 首颗脉冲星导航试验卫星及其观测结果［J］. 中国惯性技术学报， 2019， 27（3）： 281-287.
	SHUAI P， LIU Q， HUANG L W， et al. Pulsar navigation test satellite XPNAV-1 and its observation results［J］. Journal of Chinese Inertial Technology， 2019， 27（3）： 281-287 （in Chinese）.
14	北斗网. 脉冲星试验01星在轨试验数据［EB/OL］. （2017-05-09）［2020-06-01］. .
	Website Beidou. On-orbit test data of XPNAV-1［EB/OL］. （2017-05-09）［2020-06-01］. （in Chinese）.
15	朱鸿旭，童明雷，杨廷高，等. XPNAV-1卫星先期发布数据的计时分析［J］. 宇航学报， 2019， 40（12）： 1492-1500.
	ZHU H X， TONG M L， YANG T G， et al. Timing analysis of pre-released data for XPNAV-1 satellite［J］. Journal of Astronautics， 2019， 40（12）： 1492-1500 （in Chinese）.
16	韩孟纳，童明雷，朱鸿旭，等. X射线脉冲星TOA数量对计时精度和导航的影响分析［J］. 时间频率学报， 2021， 44（1）： 66-76.
	HAN M N， TONG M L， ZHU H X， et al. Analysis of the influences of TOA number on timing precision and navigation［J］. Journal of Time and Frequency， 2021， 44（1）： 66-76 （in Chinese）.
17	LYNE A G， PRITCHARD R S， GRAHAM-SMITH F. Jodrell bank Crab pulsar monthly ephemeris［EB/OL］. （2021-05-21）［2021-06-01］. .
18	SHANG L H， DU Y J， CUI X Q， et al. Long-term variations of X-ray pulse profiles for the Crab pulsar： Data analysis and modeling［J］. Science China Physics， Mechanics & Astronomy， 2020， 63（10）： 109511.
19	杨廷高，童明雷，赵成仕，等. Crab脉冲星X射线计时观测数据处理与分析［J］. 天文学报， 2018， 59（2）： 10-16.
	YANG T G， TONG M L， ZHAO C S， et al. Process and analysis of X-ray timing data for crab pulsar［J］. Acta Astronomica Sinica， 2018， 59（2）： 10-16 （in Chinese）.
20	易韦韦，偶晓娟，许静文，等. 脉冲星导航试验卫星观测数据处理与分析［J］. 深空探测学报， 2018， 5（3）： 241-245， 261.
	YI W W， OU X J， XU J W， et al. Processing and analysis of X-ray pulsar-based navigation test satellite observation data［J］. Journal of Deep Space Exploration， 2018， 5（3）： 241-245， 261 （in Chinese）.
21	TAYLOR J H. Pulsar timing and relativistic gravity［J］. Philosophical Transactions of the Royal Society of London Series A： Physical and Engineering Sciences， 1992， 341（1660）： 117-134.
22	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.
23	YAN L L， GE M Y， YUAN J P， et al. Phase evolution of the crab pulsar between radio and X-ray［DB/OL］. arXiv preprint： 1708.05898，2017.
24	朱鸿旭，童明雷，周庆勇，等. XPNAV-1卫星首批公开数据中光子能量对计时精度影响的统计分析［J］. 时间频率学报， 2020， 43（1）： 29-40.
	ZHU H X， TONG M L， ZHOU Q Y， et al. Statistical analysis of the influences of photon energy on timing accuracy in the first public data release of XPNAV-1 satellite［J］. Journal of Time and Frequency， 2020， 43（1）： 29-40 （in Chinese）.
25	李孝辉，杨旭海，刘娅. 时间频率信号的精密测量［M］. 北京：科学出版社， 2010： 15-17.
	LI X H， YANG X H， LIU Y. Precise measurement of time frequency signal［M］. Beijing： Science Press， 2010： 15-17 （in Chinese）.
26	陈洪卿，王振伟. GPS系统时间及其与其他时间的关系［J］. 时间频率学报， 2012， 35（4）： 201-204， 234.
	CHEN H Q， WANG Z W. GPS system time and its relation with other time［J］. Journal of Time and Frequency， 2012， 35（4）： 201-204， 234 （in Chinese）.
27	PETIT G. From atomic clocks to coordinate times［J］. Proceedings of the International Astronomical Union， 2006， 2（14）： 478.
28	International Astronomical Union. IAU 2006 Resolution B3［EB/OL］. （2020-03-12）［2020-06-01］. .
29	International Astronomical Union. IAU 2000 Resolution B1［EB/OL］. （2020-03-12）［2020-06-01］. .
30	FUKUSHIMA T. Time ephemeris and general relativistic scale factor［J］. Proceedings of the International Astronomical Union， 2009， 5（S261）： 89-94.

相对频率偏差设定值	相对频率偏差估计值	相对误差
2.694 1×10^-10	2.685 8×10^-10	-0.003 066 79
2.694 1×10^-11	1.575 26×10^-11	-0.415 301 23
2.694 1×10^-12	-3.506 1×10^-13	-1.130 141 66

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Correcting frequency of a spaceborne atomic clock using X-ray observations of Crab pulsar

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