三个不动中心问题的一个三维解

本文对三个不动中心问题的平面解作进一步发展，通过对三个不动中心在四维空间中的定义得到三个不动中心问题的三维解．     

光引力限制性三体问题的平动点

本文研究两个主星体的质量缩减因子ｑ＿，ｑ＿２∈（－∞，１］的光引力限制性三体问题。文中给出一种平动点的个数估计和位置计算的分析方法。结果表明对于不同的ｑ＿１和ｑ＿２可有１～７个平动点。作为应用，文末还讨论了太阳系类似彗尾尘埃物质的运动。     

A THREE-DIMENSIONAL SOLUTION OF THE PROBLEM OF THREE FIXED CENTRES

ＡＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＳＯＬＵＴＩＯＮＯＦＴＨＥＰＲＯＢＬＥＭＯＦＴＨＲＥＥＦＩＸＥＤＣＥＮＴＲＥＳ￥ＱｉｎＹｉｐｉｎｇ（覃一平）ＮｉｅＺｈａｏｍｉｎｇ（聂昭明）（ＹｕｎｎａｎＯｂｓｅｒｖａｔｏｒｙ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｋｕｎ...     

The libration points in photogravitational restricted three-body problem

ＴＨＥＬＩＢＲＡＴＩＯＮＰＯＩＮＴＳＩＮＰＨＯＴＯＧＲＡＶＩＴＡＴＩＯＮＡＬＲＥＳＴＲＩＣＴＥＤＴＨＲＥＥ－ＢＯＤＹＰＲＯＢＬＥＭＺｈｅｎｇＸｕｅ－ｔａｎｇ（郑学塘）ＹｕＬｉ－ｚｈｏｎｇ（郁丽忠）（Ｄｅｐｔ．ｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃｓ,Ｎａｎｊ...     

Supplement to the previous application of the first junction condition to a highly symmetric spacetime

Application of the first junction condition to a highly symmetric spacetime was investigated recently in {\it Chin. Phys. Lett.} B {\bf 546} 189 2006, where a partial differential equation arising from the connection of the Robertson--Walker and the Schwarzschild--de Sitter metrics was presented, but no solutions of the equation were provided. Here we provide a proof to the statement that there exist solutions of the equation. In addition, an example of the solution and some analyses associated with this issue are presented. We find that in connecting the two metrics, there are three conditions which should be satisfied. Of these conditions, one condition constrains the place where the two metrics can take the same value for a local system whose mass is provided which marks the boundary of the system, and the other two constrain the transformation form. In realizing the connection of the two metrics, the latter two conditions are required to be satisfied only at the boundary defined by the former condition.     

A cosmological model with negative energy photons

According to recent investigations of states of quantum fields, we postulate that there exist negative energy photons in the universe. With this assumption, we find a solution of Einstein's equation without introducing the cosmological constant. A new and sizable type Ia supernovae sample is employed to perform a fit with our model and the conventional model. Both models can well account for the current type Ia supernovae observation and they are not distinguishable. With the new model, the cause of the accelerated expansion of the universe and the mechanism of the negative pressure existing in outer space can be explained in ordinary physical terms.     

Applications of the Junction Conditions Connecting the Robertson-Walker Metric and the Metric of a Local System on Our Universe

We investigate how the local and global metrics are connected in an ideal model of spacetime where the local system is assumed to be highly symmetric and the cosmological matter is kept away from the local system and does not disturbed by the local system. A boundary condition arising from the junction conditions is obtained and its implication in our universe is studied. We know that the total mass of a sufficiently large system must be that of the cosmological matter within the region of that size. This requirement is satisfied since it is just a consequence of the boundary condition. The analysis shows that at the very late epoch of the universe, there exists a particular time when the largest symmetric local systems stop growing and the observation of this time can be used to check the cosmological parameters. Adopting the popular values （ΩM, Ωa） = （0.28, 0.72）, we find that particular time would be associated with z = 0.726, the effect of dark matter on the clustering of objects would be insignificant, and the Virgo cluster would be gravitationally bound even if dark matter is ignored.     

Development of the spectrum of gamma-ray burst pulses influenced by the intrinsic spectral evolution and the curvature effect

The spectral evolution of gamma-ray burst pulses assumed to arise from the emission of fireballs is explored. It is found that due to the curvature effect, the integrated flux is well related to peak energy by a power law in the decaying phase of pulses, where the index is about 3, which does not depend on intrinsic emission and the Lorentz factor. The spectra of pulses in the decaying phase are slightly different from each other when different intrinsic spectral evolution patterns are considered, indicating that it is dominated by the curvature effect. In the rising phase, the integrated flux keeps increasing whilst the peak energy remains unchanged when the intrinsic emission bears an unchanged spectrum. Within this phase, the flux decreases with the increase of the peak energy for a hard-to-soft intrinsic spectrum, and for a soft-to-hard-to-soft intrinsic spectrum, the flux generally increases with the increase of the peak energy. An intrinsic soft-to-hard-to-soft spectral evolution within a co-moving pulse would give rise to a pulse-like evolutionary curve for the peak energy.     

Origination of gamma-ray burst pulses associated with the Doppler effect of spherical fireballs or uniform jet

Ryde and Petrosian have pointed out that the rise phases of gamma-ray burst (GRB) pulses originate from the widths of the intrinsic pulses and their decay phases are determined by the curvature effect of the expanding fireball surface based on their simplified formula. In this paper we investigate in detail the issue based on the formula in Ref.[20], which is derived based on a model of highly symmetric expanding fireballs, where the Doppler effect is the key factor to be concerned about, and no terms are omitted in their derivation. Our analyses show that the decay phases of the observed pulses originate from the contributions from both the curvature effect of the expanding fireball and the two timescales of the local pulses, and the rise phases of the observed pulses only come from the two timescales of the local pulses. Associated with a local pulse with both rise and decay portions, the light curve of GRBs in the rise portion is expected to undergo a concave phase and then a convex one, whereas that in the decay portion is expected to evolve by an opposite process. And the ratio of the concave timescale to the convex one in the rise phase of the observed pulse linearly increases with the ratio of the rising timescale to the decay one of the local pulse ($r_{\rm rd}$), whereas the ratio of the convex timescale to the concave timescale in its decay phase linearly decreases with $r_{\rm rd}$. The two correlations are independent of the local pulse forms and the rest-frame radiation forms. But the different forms of local pulses and the different values of $r_{\rm rd}$ gives rise to the diversity of the light curve pulse shapes. We test a sample of 86 GRB pulses detected by the BATSE instrument on board the Compton Gamma Ray Observatory and find that the characteristics do exist in the light curve of GRBs.     

Method of determining cosmological parameter ranges with samples of candles with an intrinsic distribution

In this paper, the effect of the intrinsic distribution of cosmological candles is investigated. We find that in the case of a narrow distribution the deviation of the observed modulus of sources from the expected central value can be estimated within a ceratin range. We thus introduce lower and upper limits of X², X _min² and X_max² to estimate cosmological parameters by applying the conventional minimizing X² method. We apply this method to a gamma-ray burst (GRB) sample as well as to a combined sample including this GRB sample and an SN Ia sample. Our analysis shows that: a) in the case of assuming an intrinsic distribution of candles of the GRB sample, the effect of the distribution is obvious and should not be neglected; b) taking into account this effect would lead to a poorer constraint of the cosmological parameter ranges. The analysis suggests that in the attempt of constraining the cosmological model with current GRB samples, the results tend to be worse than was previously anticipated if the mentioned intrinsic distribution does exist.