Constraining the geometry of the neutron star RX J1856.5−3754

RX J1856.5−3754 is one of the brightest, nearby isolated neutron stars (NSs), and considerable observational resources have been devoted to its study. In previous work, we found that our latest models of a magnetic, hydrogen atmosphere match well the entire spectrum, from X-rays to optical (with best-fitting NS radius   R ≈ 14  km, gravitational redshift   z _g∼ 0.2  , and magnetic field   B ≈ 4 × 10¹²  G). A remaining puzzle is the non-detection of rotational modulation of the X-ray emission, despite extensive searches. The situation changed recently with XMM–Newton observations that uncovered 7-s pulsations at the     level. By comparing the predictions of our model (which includes simple dipolar-like surface distributions of magnetic field and temperature) with the observed brightness variations, we are able to constrain the geometry of RX J1856.5−3754, with one angle <6° and the other angle     , though the solutions are not definitive, given the observational and model uncertainties. These angles indicate a close alignment between the rotation and the magnetic axes or between the rotation axis and the observer. We discuss our results in the context of RX J1856.5−3754 being a normal radio pulsar and a candidate for observation by future X-ray polarization missions such as Constellation-X or XEUS .     

用化石天长计算地球年龄的方法及意义——如何理解地球年龄

天长（一天时长）是地球自转速度的直接反映。古生代-中生代化石记录的天长数据表明,古生代-中生代期间的天长随时间呈线性增加。根据角动量守恒定律,这意味着同时段地球自转速度呈线性衰减。如果把这个趋势应用于地球历史的全过程,计算结果为4.519～4.495 Ga,与目前公认的地球绝对年龄4.54 Ga一致。这意味着,从这个时间点起,地球有一种自转速度衰减的总趋势。地球自转速度衰减年龄等值于地球年龄说明：1）所测量的陨石样本生成的时间（表征地球年龄）与地球受月球吸引形成自转减速的时间几乎相同。这意味着地-月体系形成之前的地球比该陨石表征的地球年龄更为古老。2）地球、月球、自转速度衰减时长,三者的年龄呈现等值状态,因而此结果与月球起源于大碰撞的假说可以匹配。     

Non-linear hydrodynamical evolution of rotating relativistic stars: numerical methods and code tests

We present numerical hydrodynamical evolutions of rapidly rotating relativistic stars, using an axisymmetric, non-linear relativistic hydrodynamics code. We use four different high-resolution shock-capturing (HRSC) finite-difference schemes (based on approximate Riemann solvers) and compare their accuracy in preserving uniformly rotating stationary initial configurations in long-term evolutions. Among these four schemes, we find that the third-order piecewise parabolic method scheme is superior in maintaining the initial rotation law in long-term evolutions, especially near the surface of the star. It is further shown that HRSC schemes are suitable for the evolution of perturbed neutron stars and for the accurate identification (via Fourier transforms) of normal modes of oscillation. This is demonstrated for radial and quadrupolar pulsations in the non-rotating limit, where we find good agreement with frequencies obtained with a linear perturbation code. The code can be used for studying small-amplitude or non-linear pulsations of differentially rotating neutron stars, while our present results serve as testbed computations for three-dimensional general-relativistic evolution codes.     

Influence of the r-mode instability on hypercritically accreting neutron stars

We have investigated the influence of the r-mode instability on hypercritically accreting neutron stars in close binary systems during their common envelope phases, based on the scenario proposed by Brown et al. On the one hand, neutron stars are heated by the accreted matter at the stellar surface, but on the other hand they are also cooled down by the neutrino radiation. At the same time, the accreted matter transports its angular momentum and mass to the star. We have studied the evolution of the stellar mass, temperature and rotational frequency.
The gravitational-wave-driven instability of the r-mode oscillation strongly suppresses spinning up of the star, the final rotational frequency of which is well below the mass-shedding limit, in fact typically as low as 10 per cent of that of the mass-shedding state. On a very short time-scale the rotational frequency tends to approach a certain constant value and saturates there, as long as the amount of accreted mass does not exceed a certain limit to collapse to a black hole. This implies that a similar mechanism of gravitational radiation to that in the so-called 'Wagoner star' may work in this process. The star is spun up by accretion until the angular momentum loss by gravitational radiation balances the accretion torque. The time-integrated dimensionless strain of the radiated gravitational wave may be large enough to be detectable by gravitational wave detectors such as LIGO II.     

A numerical study of the r-mode instability of rapidly rotating nascent neutron stars

The first results of numerical analysis of classical r-modes of rapidly rotating compressible stellar models are reported. The full set of linear perturbation equations of rotating stars in Newtonian gravity is solved numerically without the slow rotation approximation. A critical curve of gravitational wave emission induced instability, which restricts the rotational frequencies of hot young neutron stars, is obtained. Taking the standard cooling mechanisms of neutron stars into account, we also show the 'evolutionary curves' along which neutron stars are supposed to evolve as cooling and spinning down proceed. Rotational frequencies of 1.4-M_⊙ stars suffering from this instability decrease to around 100 Hz when the standard cooling mechanism of neutron stars is employed. This result confirms the results of other authors, who adopted the slow rotation approximation.     

Numerical theory of rotation of the deformable Earth with the two-layer fluid core. Part 1: Mathematical model

Improved differential equations of the rotation of the deformable Earth with the two-layer fluid core are developed. The equations describe both the precession-nutational motion and the axial rotation (i.e. variations of the Universal Time UT). Poincaré’s method of modeling the dynamical effects of the fluid core, and Sasao’s approach for calculating the tidal interaction between the core and mantle in terms of the dynamical Love number are generalized for the case of the two-layer fluid core. Some important perturbations ignored in the currently adopted theory of the Earth’s rotation are considered. In particular, these are the perturbing torques induced by redistribution of the density within the Earth due to the tidal deformations of the Earth and its core (including the effects of the dissipative cross interaction of the lunar tides with the Sun and the solar tides with the Moon). Perturbations of this kind could not be accounted for in the adopted Nutation IAU 2000, in which the tidal variations of the moments of inertia of the mantle and core are the only body tide effects taken into consideration. The equations explicitly depend on the three tidal phase lags δ, δ _c, δ _i responsible for dissipation of energy in the Earth as a whole, and in its external and inner cores, respectively. Apart from the tidal effects, the differential equations account for the non-tidal interaction between the mantle and external core near their boundary. The equations are presented in a simple close form suitable for numerical integration. Such integration has been carried out with subsequent fitting the constructed numerical theory to the VLBI-based Celestial Pole positions and variations of UT for the time span 1984–2005. Details of the fitting are given in the second part of this work presented as a separate paper (Krasinsky and Vasilyev 2006) hereafter referred to as Paper 2. The resulting Weighted Root Mean Square (WRMS) errors of the residuals dθ, sin θd for the angles of nutation θ and precession are 0.136 mas and 0.129 mas, respectively. They are significantly less than the corresponding values 0.172 and 0.165 mas for IAU 2000 theory. The WRMS error of the UT residuals is 18 ms.     

An interpretation of the variations of the magnetic core-mantle coupling torques and the core drift rate

The influence of recently computed axial magnetic core-mantle coupling torques on the Earth's rotation was investigated. These torques derived from poloidal geomagnetic field within the mantle and at the core-mantle boundary are retarding torques. An accelerating torque due to the action of unknown parts of the core field was estimated by inverse solution of the equation of the mantle rotation for the periodic variations of the quantities of the magnetic field and the length of day. The variations of the drift rate of the Earth's core were compared with those of the mantle rotation velocity for a force-free Earth. The time constants of the coupling process were estimated and discussed in connection with the magnetic coupling of the mantle with an upper core layer. Der Einfluß kürzlich berechneter axialer Kern-Mantel-Kopplungsmomente auf die Erdrotation wurde untersucht. Diese Lorentz-Drehmomente, abgeleitet vom poloidalen geomagnetischen Feld im Mantel und an der Kern-Mantel-Grenze, sind retardierende Momente. Ein beschleunigendes Drehmoment, das der Wirkung unbekannter Feldanteile zugeordnet wird, wurde durch inverse Lösung der Mantelrotationsgleichung für die periodischen Variationen der Magnetfeldgrößen und der Tageslänge abgeschätzt. Die Variationen der Kerndriftgeschwindigkeit wurden mit denen der Mantelrotationsgeschwindigkeit für eine kräftefreie Erde verglichen. Die Zeitkonstanten des Kopplungsprozesses wurden ermittelt und im Zusammenhang mit der magnetischen Kopplung des Mantels mit einer oberen Kernschicht diskutiert.     

Spin rate distribution of small asteroids

The spin rate distribution of main belt/Mars crossing (MB/MC) asteroids with diameters 3-15 km is uniform in the range from f=1 to 9.5 d⁻¹, and there is an excess of slow rotators with f<1 d⁻¹. The observed distribution appears to be controlled by the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. The magnitude of the excess of slow rotators is related to the residence time of slowed down asteroids in the excess and the rate of spin rate change outside the excess. We estimated a median YORP spin rate change of ≈0.022 d⁻¹/Myr for asteroids in our sample (i.e., a median time in which the spin rate changes by 1 d⁻¹ is ≈45 Myr), thus the residence time of slowed down asteroids in the excess is ≈110 Myr. The spin rate distribution of near-Earth asteroids (NEAs) with sizes in the range 0.2-3 km (∼5 times smaller in median diameter than the MB/MC asteroids sample) shows a similar excess of slow rotators, but there is also a concentration of NEAs at fast spin rates with f=9-10 d⁻¹. The concentration at fast spin rates is correlated with a narrower distribution of spin rates of primaries of binary systems among NEAs; the difference may be due to the apparently more evolved population of binaries among MB/MC asteroids.