The Rayleigh Statistic in the Case of Weak Signals — Applications and Pitfalls

Jager, O. C. de; Raubenheimer, Britt; Swanepoel, Jan

doi:10.1007/978-1-4684-5646-2_2

Cited by 138 publications

(154 citation statements)

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“…Involving higher harmonics gives values Z 2 2 = 42.9, Z 2 3 = 43.0 and Z 2 4 = 43.2 at the same frequency f * . These numbers indicate that, according to the H-test suggested by de Jager et al (1989), there is a statistically significant contribution from the second harmonic. A probability to obtain a noise peak of Z 2 2 = 42.9 in one trial is only p = 1.1 × 10 −8 and in N independent trials is p = 5.1 × 10 −4 , that increases the significance of the period detection up to a 3.5σ level.…”

Section: The Temporal Behaviour Of Rx J08064-4123mentioning

confidence: 88%

XMM-Newton observations of the isolated neutron star RX J0806.4-4123

Haberl

Zavlin

2002

A&A

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Abstract. The isolated neutron star RX J0806.4-4123 was observed with XMM-Newton in November 2000. The data from the three EPIC instruments allowed us (i) to derive an improved X-ray position to an accuracy of 2-3 , (ii) to accumulate the first medium-resolution soft X-ray spectra of high statistical quality and (iii) to find a candidate for the neutron star rotation period. Although this period of 11.3714 s is formally detected at a 3.5σ level in the EPIC-pn data, the similar pulse profiles deduced from all three EPIC instruments increase the confidence that the period is real. The pulsed fraction of ∼6% would then be the weakest X-ray flux modulation detected from dim isolated neutron stars. We fitted the X-ray spectra with blackbody and neutron star atmosphere models and discuss the results with respect to the brightness limit placed by optical images. The reduced size of the error circle on the X-ray position should allow deeper searches for an optical counterpart.

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Section: The Temporal Behaviour Of Rx J08064-4123mentioning

confidence: 88%

XMM-Newton observations of the isolated neutron star RX J0806.4-4123

Haberl

Zavlin

2002

A&A

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“…In these circumstances, the favored techniques are unbinned tests for periodic signals. We use the H-test (de Jager et al 1989;de Jager & Büsching 2010), a statistical test for discarding the null hypothesis that a set of photon phases is uniformly distributed. For N γ gamma-rays, the H-test statistic is H ≡ max(Z 2 m − 4 × (m − 1), 1 m 20), with Z 2 m ≡ (2/N γ ) m k=1 α 2 k +β 2 k , and α k and β k the empirical trigonometric coefficients α k ≡ N γ i=1 sin(2πkφ i ) and β k ≡ N γ i=1 cos(2πkφ i ).…”

Section: Pulsation Discoverymentioning

confidence: 99%

THE SECOND FERMI LARGE AREA TELESCOPE CATALOG OF GAMMA-RAY PULSARS

Abdo¹,

Ajello²,

Allafort³

et al. 2013

ApJS

824

1,129

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This catalog summarizes 117 high-confidence 0.1 GeV gamma-ray pulsar detections using three years of data acquired by the Large Area Telescope (LAT) on the Fermi satellite. Half are neutron stars discovered using LAT data through periodicity searches in gamma-ray and radio data around LAT unassociated source positions. The 117 pulsars are evenly divided into three groups: millisecond pulsars, young radio-loud pulsars, and young radio-quiet pulsars. We characterize the pulse profiles and energy spectra and derive luminosities when distance information exists. Spectral analysis of the off-peak phase intervals indicates probable pulsar wind nebula emission for four pulsars, and off-peak magnetospheric emission for several young and millisecond pulsars. We compare the gammaray properties with those in the radio, optical, and X-ray bands. We provide flux limits for pulsars with no observed gamma-ray emission, highlighting a small number of gamma-faint, radio-loud pulsars. The large, varied gamma-ray pulsar sample constrains emission models. Fermi's selection biases complement those of radio surveys, enhancing comparisons with predicted population distributions.

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“…If we apply the H-test developed by de Jager et al (1989);de Jager & Büsching (2010) 3 to the data sets, we identify a second peak in all pointed observations of RX J0720.4−3125 also in different energy bands. Moreover, for some energy bands, they do show a more significant peak corresponding to 0.0596 Hz rather than 0.119 Hz.…”

Section: X-ray Timing Analysismentioning

confidence: 99%

The compactness of the isolated neutron star RX J0720.4−3125

Hambaryan

Suleimanov

Haberl

et al. 2017

A&A

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Aims. To estimate the compactness of the thermally emitting isolated neutron star RX J0720.4−3125, an X-ray spin phase-resolved spectroscopic study is conducted. In addition, to identify the genuine spin-period, an X-ray timing analysis is performed. Methods. The data from all observations of RX J0720.4−3125 conducted by XMM-Newton EPIC-pn with the same instrumental setup in 2000-2012 were reprocessed to form a homogenous data set of solar barycenter corrected photon arrival times registered from RX J0720.4−3125. A Bayesian method for the search, detection, and estimation of the parameters of an unknown-shaped periodic signal was employed as developed by Gregory & Loredo (1992). A number of complex models (single and double peaked) of light curves from pulsating neutron stars were statistically analyzed. The distribution of phases for the registered photons was calculated by folding the arrival times with the derived spin-period and the resulting distribution of phases -approximated with a mixed von Mises distribution -, and its parameters were estimated by using the Expected Maximization method. Spin phase-resolved spectra were extracted, and a number of highly magnetized atmosphere models of an INS were used to fit simultaneously, the results were verified via an MCMC approach. Results. The phase-folded light curves in different energy bands with high S/N ratio show a high complexity and variations depending on time and energy. They can be parameterized with a mixed von Mises distribution, i.e. with double-peaked light curve profile showing a dependence of the estimated parameters (mean directions, concentrations, and proportion) upon the energy band, indicating that radiation emerges from at least two emitting areas. Conclusions. The genuine spin-period of the isolated neutron star RX J0720−3125 derived as more likely is twice of that reported in the literature (16.78s instead of 8.39s). The gravitational redshift of RX J0720.4−3125 was determined to z = 0.205 +0.006 −0.003 and the compactness was estimated to (M/M )/(R/km) = 0.105 ± 0.002.

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The Rayleigh Statistic in the Case of Weak Signals — Applications and Pitfalls

Cited by 138 publications

References 10 publications

XMM-Newton observations of the isolated neutron star RX J0806.4-4123

XMM-Newton observations of the isolated neutron star RX J0806.4-4123

THE SECOND FERMI LARGE AREA TELESCOPE CATALOG OF GAMMA-RAY PULSARS

The compactness of the isolated neutron star RX J0720.4−3125

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