1. Timing noise in pulsars
Yuan Jianping XAO

2. Outline Pulsar timing and timing noise Power spectrum of timing noise
Our work in preparation
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

3. 1 Pulsar timing and timing noise
Lighthouse
Spin down. P: 1.3 ms – 12 s, Pdot：1.1 × 10–21 – 5.4 × 10– 10
Rotation powered.
Magnetic dipole radiation
Rotation Model:
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

4. 1 Pulsar timing and timing noise
Pulsar timing: time of arrival,
Spin, ISM, proper motion, orbit, relativity
Timing residual: Tobs – Tpre
Non-zero (not white) :
proper motion
precession
Companion
Glitch: sudden increase in the rotation rate.
GWB
...
Timing noise
2019/1/14
FPS3, 2-4 July, 2014, Shanghai
(Yuan et al. 2010)

5. 1 Pulsar timing and timing noise
Spin fluctuation
gradual
low frequency, Red noise,
Quasi-Sine
Hobbs 2010
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

6. 1 Pulsar timing and timing noise
braking index
n = 3 for magnetic dipole radiaton model
Crab: n = 2.51 (Lyne 1993), Measered n ≠ 3, why ?
n for Crab has changed – Wind braking
(Ω=2πf)
(Wang, Tong et al. 2012)
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

7. 1 Pulsar timing and timing noise
RMS of timing residual (Cordes, Helfand 1980)
f2, (Arzoumanian et al ) 1994)
timing noise on various time scale (Matsakis et al. 1997)
Hobbs 2010
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

8. 1 Pulsar timing and timing noise
Origin of low frequency noise
Magnetospheric model (Cheng 1987 a, b)
co-rotating vortex ( Jones 1990)
Random process ( Groth（1971)
Chaos (Harding et al. 1990）
GW background. …
No one is able to explain all the observations.
The mechanisms responsible for pulsar timing is not fully clear.
Help us to understand the interior of pulsar.
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

9. 1 Pulsar timing and timing noise
Groth (1971): phase noise (PN), spin noise (F Noise), slow-down noise.
Boynton et al. 1972: Crab 2 yr timing, random walk in f.
Cordes & Downs 1985: random walk model is too simple.
D’Alessandro 1997, 18 PSRs, model may need to be modified.
Hobbs 2010, Time-scales > 10 yr, large sample of 366 PSRs:
timing noise exist normally.
Inversely correlated with pulsar age.
The structure in the timing noise vary with data span.
Timing noise in the young pulsar with age < 100 kyr is mainly caused by the recovery from the previous glitch.
...
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

10. 2. Power spectra of timing noise
D’Alessandro et al. 1997
Power spectrum: power-law
Alpha = −2, −4, −6, random walk in phase, spin , and spindown rate.
Could not simply be modelled as walk random in phase, f0, f1 Hobbs et al
Provide valuable information about the theoretical models responsible for the timing noise
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

11. 2. Power spectra of timing noise
Standard Fourier method. （Boynton 1972）
spectrum leakage
uneven observations 。
Non-uniform data quality。
Orthonormal polynomials （Groth 1975 Cordes & Helfand 1980 Deeter ）
Boynton et al. 1972
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

12. 2. Power spectra of timing noise
CLEAN technique (Deshpande et al D’Alessandro 1997)
D’Alessandro et al. 1997
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

13. 2. Power spectra of timing noise
Cholesky method, Coles 2011
-- -- spectralModel plugin in the TEMPO2 package
low freqeuncy noise + high frequency noise
exponential smoothing function:
DFT of original residual, the DFT of the interpolated data.
consisted  Obtaining the Covariance function directly
not consisted，  pre-whitening, obtaine the Covariance function
Covariance matrix：Cholesky decomposition  whiting matrix
Whiting the data, obtianed the spectrum.
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

14. 2. Power spectra of timing noise
Coles 2011
Residuals
covariance function of the residuals
Power Spectrum of the residuals whitened and normalize with Cholesky transformation
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

15. Coles 2011 Residuals 平滑的低频噪声，一阶差分白化得到的频谱 平滑后的低频噪声，乔勒斯基Cholesky变换后得到的频谱
Power Spectrum of the residuals whitened and normalize with Cholesky transformation
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

16. 2. Power spectra of timing noise
Shannon et al Science
Black lines: Power Spectra
purple lines: model of PS
Purple = Gray (white c) + pink (GWB c), +(red for PSR J1713) lines: model of PS
Green: PS in the presence of Gaussian GWB
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

17. 3. Our work in preparation
25 m dish, AFB+DFB
pulsar timing since 2000,
~ 300 pulsars, including 9 MSP
~ year data span
At least 50 glitches detected from 2000 to (Zou 2005, 2008, Yuan 2010, Wang 2012)
Zou et al. 2008
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

18. 3. Our work in preparation
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

19. 3. Our work in preparation
~ 100 sources
Study the power spectral.
In progress
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

20. 3. Our work in preparation
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

21. 3. Our work in preparation
2019/1/14
FPS3, 2-4 July, 2014, Shanghai

22. Summary Timing noise exist normally in pulsars.
Which is not full understood.
Could not simply be modelled as walk random.
The power spectrum of timing noise in most pulsars obey the power low.
Cholesky mothod provides an excellent power spectral estimate.
Could constraint the theoretical models of pulsar timing noise.
XAO have long data span for the study of power spectral of pulsar timing noise.
Started to work on it.
2019/1/14
FPS3, 2-4 July, 2014, Shanghai