Pulsar timing observations with Haoping Radio Telescope

We report pulsar timing observations carried out in L-band with NTSC’s 40-meter Haoping Radio Telescope(HRT),which was constructed in 2014.These observations were carried out using the pulsar machine we developed.Timing observations toward millisecond pulsar J0437–4715 obtain a timing residual(r.m.s.)of 397 ns in the time span of 284 days.Our observations successfully detected Crab pulsar’s glitch that happened on 2019 July 23.

Wiener Filtration Algorithm of an Ensemble Pulsar Timescale Based on a Power-law Model of Pulsar Power Spectrum

An ensemble pulsar timescale derived from the traditional Wiener filtration still contains some high level noise.To improve this situation we developed a Wiener filtration algorithm of the ensemble pulsar timescale based on a power-law model of power spectrum for pulsars.Our algorithm has three strengths:(1)mitigating spectral leakage between frequency bins for Fourier techniques;(2)using a power-law model for power spectrum;(3)signal realization in original residuals of data set by the power-law model.According to improved algorithm we constructed an ensemble pulsar timescale EPT-TAI using timing data with respect to International Atomic Time(TAI)about 16 yr time span of ten pulsars from International Pulsar Timing Array second data release(version A).The results show that EPT-TAI detected correctly the differences TT(BIPM2015)-TAI between terrestrial time TT(BIPM2015)and TAI.Fractional frequency stabilityσzanalysis shows that EPT-TAI does not indicate red noise for 16 yr time interval,and fractional frequency stability for 8 yr and longer time intervals is slightly better than that of TT(BIPM2015)-TAI.Stability for short time intervals of TT(BIPM2015)-TAI is better than that of EPT-TAI,but TT(BIPM2015)-TAI shows red noise for longer time intervals.Using the same algorithm we also derived an ensemble pulsar timescale EPT-TT(BIPM2015)with respect to TT(BIPM2015).The fractional frequency stability curve of EPT-TT(BIPM2015)shows similar characteristics as that of EPT-TAI but with slightly lower values.

Imprints of relic gravitational waves on pulsar timing

Relic gravitational waves （RGWs）, a background originating during inflation, would leave imprints on pulsar timing residuals. This makes RGWs an important source for detection of RGWs using the method of pulsar timing. In this paper, we discuss the effects of RGWs on single pulsar timing, and quantitatively analyze the timing residuals caused by RGWs with different model parameters. In principle, if the RGWs are strong enough today, they can be detected by timing a single millisecond pulsar with high precision after the intrinsic red noises in pulsar timing residuals are understood, even though simultaneously observing multiple millisecond pulsars is a more powerful technique for extracting gravitational wave signals. We correct the normalization of RGWs using observations of the cosmic microwave background （CMB）, which leads to the amplitudes of RGWs being reduced by two orders of magnitude or so compared to our previous works. We obtained new constraints on RGWs using recent observations from the Parkes Pulsar Timing Array, employing the tensor-to-scalar ratio r = 0.2 due to the tensor-type polarization observations of CMB by BICEP2 as a reference value, even though its reliability has been brought into question. Moreover, the constraints on RGWs from CMB and Big Bang nucleosynthesis will also be discussed for comparison.

Pulsar timing residuals due to individual non-evolving gravitational wave sources

The pulsar timing residuals induced by gravitational waves from non- evolving single binary sources are affected by many parameters related to the relative positions of the pulsar and the gravitational wave sources. We will analyze the various effects due to different parameters. The standard deviations of the timing residuals will be calculated with a variable parameter fixing a set of other parameters. The or- bits of the binary sources will be generally assumed to be elliptical. The influences of different eccentricities on the pulsar timing residuals will also be studied in detail. We find that the effects of the related parameters are quite different, and some of them display certain regularities.

The application of co-integration theory in ensemble pulsar timescale algorithm

Employing multiple pulsars and using an appropriate algorithm to establish ensemble pulsar timescale can reduce the influences of various noises on the long-term stability of pulsar timescale,compared to a single pulsar.However,due to the low timing precision and significant red noises of some pulsars,their participation in the construction of ensemble pulsar timescale is often limited.Inspired by the principle of solving non-stationary sequence modeling using co-integration theory,we put forward an algorithm based on co-integration theory to establish an ensemble pulsar timescale.It is found that this algorithm can effectively suppress some noise sources if a co-integration relationship between different pulsar data exists.Different from the classical weighted average algorithm,the co-integration method provides the chance for a pulsar with significant red noises to be included in the establishment of an ensemble pulsar timescale.Based on data from the North American Nanohertz Observatory for Gravitational Waves(NANOGrav),we found that the co-integration algorithm can successfully reduce several timing noises and improve the long-term stability of the ensemble pulsar timescale.

Neighbor Sum Distinguishing Chromatic Index of Sparse Graphs via the Combinatorial Nullstellensatz

Let Ф ： E（G）→ {1, 2,…, k}be an edge coloring of a graph G. A proper edge-k-coloring of G is called neighbor sum distinguishing if ∑eЭu Ф（e）≠∑eЭu Ф（e） for each edge uv∈E（G）.The smallest value k for which G has such a coloring is denoted by χ＇Σ（G） which makes sense for graphs containing no isolated edge（we call such graphs normal）. It was conjectured by Flandrin et al. that χ＇Σ（G） ≤△（G） ＋ 2 for all normal graphs,except for C5. Let mad（G） = max{（2｜E（H）｜）/（｜V（H）｜）｜HЭG}be the maximum average degree of G. In this paper,we prove that if G is a normal graph with△（G）≥5 and mad（G） 〈 3-2/（△（G））, then χ＇Σ（G）≤△（G） ＋ 1. This improves the previous results and the bound △（G） ＋ 1 is sharp.