Timing noise in pulsars Yuan Jianping XAO

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

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

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)

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

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

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

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

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

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. 2010 Provide valuable information about the theoretical models responsible for the timing noise 2019/1/14 FPS3, 2-4 July, 2014, Shanghai

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 1982 1984.） Boynton et al. 1972 2019/1/14 FPS3, 2-4 July, 2014, Shanghai

2. Power spectra of timing noise CLEAN technique (Deshpande et al. 1996 D’Alessandro 1997) D’Alessandro et al. 1997 2019/1/14 FPS3, 2-4 July, 2014, Shanghai

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

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

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

2. Power spectra of timing noise Shannon et al. 2013 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

3. Our work in preparation 25 m dish, AFB+DFB pulsar timing since 2000, ~ 300 pulsars, including 9 MSP ~ 12 -- 14 year data span At least 50 glitches detected from 2000 to 2013. (Zou 2005, 2008, Yuan 2010, Wang 2012) Zou et al. 2008 2019/1/14 FPS3, 2-4 July, 2014, Shanghai

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

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

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

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

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