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.

Merging strangeon stars

The state of supranuclear matter in compact stars remains puzzling, and it is argued that pul- sars could be strangeon stars. What would happen if binary strangeon stars merge？ This kind of merger could result in the formation of a hyper-massive strangeon star, accompanied by bursts of gravitational waves and electromagnetic radiation （and even a strangeon kilonova explained in the paper）. The tidal polarizability of binary strangeon stars is different from that of binary neutron stars, because a strangeon star is self-bound on the surface by the fundamental strong force while a neutron star by the gravity, and their equations of state are different. Our calculation shows that the tidal polarizability of merging bi- nary strangeon stars is favored by GW170817. Three kinds of kilonovae （i.e., of neutron, quark and strangeon） are discussed, and the light curve of the kilonova AT 2017gfo following GW170817 could be explained by considering the decaying strangeon nuggets and remnant star spin-down. Additionally, the energy ejected to the fireball around the nascent remnant strangeon star, being manifested as a gamma-ray burst, is calculated. It is found that, after a prompt burst, an X-ray plateau could follow in a timescale of 102 - 103 s. Certainly, the results could be tested also by further observational synergies between gravitational wave detectors （e.g., Advanced LIGO） and X-ray telescopes （e.g., the Chinese HXMT satellite and eXTP mission）, and especially if the detected gravitational wave form is checked by peculiar equations of state provided by the numerical relativistical simulation.

SWIFT J1749.4-2807: A neutron or quark star?

We investigate a unique accreting millisecond pulsar with X-ray eclipses, SWIFT J1749.4-2807 （hereafter J1749）, and try to set limits on the binary system by various methods including use of the Roche lobe, the mass-radius relations of both main sequence （MS） and white dwarf （WD） companion stars, as well as the measured mass function of the pulsar. The calculations are based on the assumption that the radius of the companion star has reached its Roche radius （or is at 90%）, but the pulsar＇s mass has not been assumed to be a certain value. Our results are as follows. The companion star should be an MS one. For the case that the radius equals its Roche one, we have a companion star with mass M ≈ 0.51 Me and radius Rc ≈ 0.52 R⊙, and the inclination angle is i ≈ 76.5°; for the case that the radius reaches 90% of its Roche one, we have M ≈ 0.43M⊙, Rc ≈ 0.44R⊙ and i ≈ 75.7°. We also obtain the mass of J1749, Mp ≈ 1 M⊙, and conclude that the pulsar could be a quark star if the ratio of the critical frequency of rotation-mode instability to the Keplerian one is higher than - 0.3. The relatively low pulsar mass （about - M⊙） may also challenge the conventional recycling scenario for the origin and evolution of millisecond pulsars. The results presented in this paper are expected to be tested by future observations.

Research career of an astronomer who has studied celestial mechanics

Celestial mechanics has been a classical field of astronomy. Only a few astronomers were in this field and not so many papers on this subject had been published during the first half of the 20th century. However, as the beauty of classical dynamics and celestial mechanics attracted me very much, I decided to take celestial mechanics as my research subject and entered university, where a very famous professor of celestial mechanics was a member of the faculty. Then as artificial satellites were launched starting from October 1958, new topics were investigated in the field of celestial mechanics. Moreover, planetary rings, asteroids with moderate values of eccentricity, inclination and so on have become new fields of celestial mechanics. In fact I have tried to solve such problems in an analytical way. Finally, to understand what gravitation is I joined the TAMA300 gravitational wave detector group.

Toward an Understanding of the Periastron Puzzle of PSR B1259-63

Efforts are made to understand the timing behaviors （e.g., the jumps in the projected pulsar semimajor axis at the periastron passages） observed in the 13-year monitoring of PSR B1259-63. Planet-like objects are suggested to orbit around the Be star, which may gravitationally perturb the （probably low mass） pulsar when it passes through periastron. An accretion disk should exist outside the pulsar＇s light cylinder, which creates a spindown torque on the pulsar due to the propeller effect. The observed negative braking index and the discrepant timing residuals close to periastron could be related to the existence of a disk with a varying accretion rate. A speculation is presented that the accretion rate may increase on a long timescale in order to explain the negative braking index.