Gravitational Lensing of Fermion Stars

We discuss the fermion stars, the self-gravitating systems of Fermi gases, as possible gravitational lenses. It is supposed that the fermions interact with themselves and other particles only by gravity, so they are the candidates of dark matter. We calculate Einstein deflection angles, study the image configurations, and calculate the magnification factors for a number of fermion stars that range from strong relativistic configurations to nonrelativistic ones. We find that typically there are three images, one Einstein ring and one radial critical curve for both cases. Two of the images are within the Einstein ring, and the other is outside, which may be very far. All these lensing characteristics can help to identify fermion stars as potential lensing objects, thus might give direct evidence that dark fermion stars exist in the universe.     

The possible equation of state of dark matter in low surface brightness galaxies

The observed rotation curves of low surface brightness (LSB) galaxies play an essential role in studying dark matter, and indicate the existence of a central constant density dark matter core. However, the cosmological N-body simulations of cold dark matter predict an inner cusped halo with a power-law mass density distribution, and cannot reproduce a central constant-density core. This phenomenon is called cusp-core problem. When dark matter is quiescent and satisfies the condition for hydrostatic equilibrium, the equation of state can be adopted to obtain the density profile in the static and spherically symmetric space-time. To address the cusp-core problem, we assume that the equation of state is independent of the scaling transformation. Its lower order approximation for this type of equation of state can naturally lead to a special case, i.e., \begin{document}$p=\zeta\rho+2\epsilon V_{\rm rot}^{2}\,\rho$\end{document}, where p and \begin{document}$\rho$\end{document} represent the pressure and density, respectively, \begin{document}$V_{\rm rot}$\end{document} depicts the rotation velocity of galaxy, and \begin{document}$\zeta$\end{document} and \begin{document}$ \epsilon$\end{document} are positive constants. It can obtain a density profile that is similar to the pseudo-isothermal halo model when \begin{document}$\epsilon$\end{document} is approximately 0.15. To obtain a more universally used model, let the equation of state include the polytropic model, i.e. \begin{document}$p= \frac{\zeta}{\rho_{0}^{s}}\rho^{1+s}+ 2\epsilon V_{\rm rot}^{2}\,\rho$\end{document}, from which we can obtain other types of density profiles, such as the profile that is nearly same as the Burkert profile, where s and \begin{document}$\rho_{0}$\end{document} are positive constants.     

Interpretation of Rotation Curves of Spiral Galaxies in Modified Teleparallel Gravity

There is a significant difference between the calculation based on the theory of general relativity and observation of rotation curves of spiral galaxies. To describe this discrepancy, two distinct theories have been proposed so far： existence of dark matter and modification of underlying gravitational theory. In the absence of dark matter, it is assumed that the theory of general relativity on galactic scales needs to be modified. This letter is devoted to explaining this difference in a modified teleparMIeI gravity. We show that modified teleparallel gravity favors flatness of rotation curves of spiral galaxies much in the same way as observation shows.     

暗物质粒子的质量与物态

讨论一类与宇宙超大尺度结构有关的、稳定的弱作用暗物质粒子,它们很可能是处在简并态的费米子(也可能处在近高温态)和处在近高温态的玻色子,其质量均为～10^－1eV,而其化学势的绝对值均远小于10^－1eV,这个结果与超高能原初宇宙线能谱在～10¹⁵eV及～10¹⁸eV附近出现拐折的现象不相矛盾.     

Interpretation of Rotation Curves of Spiral Galaxies in Modified Teleparallel Gravity

There is a significant difference between the calculation based on the theory of general relativity and observation of rotation curves of spiral galaxies. To describe this discrepancy, two distinct theories have been proposed so far: existence of dark matter and modification of underlying gravitational theory. In the absence of dark matter, it is assumed that the theory of general relativity on galactic scales needs to be modified. This letter is devoted to explaining this difference in a modified teleparallel gravity. We show that modified teleparallel gravity favors flatness of rotation curves of spiral galaxies much in the same way as observation shows.     

包含暗物质的强子夸克混合星

研究了含有暗物质的夸克核心混合星的观测属性。用相对论平均场理论和有效质量口袋模型分别描述夸克核心的混合星物质内强子相和夸克相,用Gibbs相平衡条件描述强子-夸克混合相,研究了由于包含强、弱相互作用的费米子暗物质对混合星质量、半径、引力红移、自转频率和转动惯量等整体观测属性的影响。结果表明,在强、弱相互作用下,暗物质粒子质量大于等于0.5 GeV时暗物质会使混合星的状态方程比无暗物质时有一定软化,相应的混合星最大质量减少。当调节暗物质粒子质量研究表明,随着暗物质粒子质量的增大,夸克核心的混合星物质的状态方程变软,混合星的质量、半径变小,并且引力红移、自转频率和转动惯量等整体观测属性也明显依赖于暗物质粒子的质量。当暗物质粒子质量0.1 GeV时,包含强、弱作用暗物质的混合星质量达到2.0 M_⊙和2.8 M_⊙（其中M_⊙为太阳质量）,说明大质量脉冲星PSR J1859-0131和J1931-01可能是包含小质量暗粒子暗物质的强子夸克的混合星。整体观测属性的计算结果均在中子星的天文观察数据范围内,也说明强子夸克的混合星内可能包含暗物质。The observational properties of quark core hybrid star contain dark matter are studied. The influences of containing of strongly or weakly interacting dark matter to global observational features of hybrid stars, mass, radius, gravitational red-shift, rotational period and moment of inertia are studied by using relativistic mean field theory to describe hadron phase, effective mass bag model to quark phase, and Gibbs phase equilibrium conditions to hadron-quark mixed phase respectively. Our results indicate that, both in the strong and weak interacting case, the equation of state for hybrid star matter contain dark matter become softer than that of without dark matter while the mass of dark matter particles larger than 0.5 GeV, which leads to the decrease of the mass and corresponding radius of hybrid star. With the increase of the dark matter particle mass, the equation of state for hybrid star matter become softer, this cause the decrease of the mass and radius of hybrid star obviously. The gravitational red-shift and the rotational period, obviously increase of the moment of inertia of the hybrid stars are influenced by the dark matter particle mass. When the dark matter particle mass is equal to 0.1 GeV, the masses of the star with strong and weak interacting dark matter reach to 2.0 M_⊙ and 2.8 M_⊙(M_⊙ is the solar mass), this result indicates that the giant mass PSR, J1859-0131 and J1931-01, can be a hadron-quark hybrid star and containing dark matter with small dark particle mass. The computational results of all above global observational features of hybrid stars are in the range of astronomical observation data, these also indicate that hybrid star with quark core may contains dark matter.     

A naive toy model of dark matter:Fermion sea

A naive toy model that the fermion sea offers the dark matter density is discussed here.If the fermion sea fills the total space and the temperature equals the temperature of CMB,we can get the mass of the fermion is about 4.7×10 38 kg (0.026 eV).     

Dark Energy and Global Rotation of the Universe

We discuss the problem of universe acceleration driven by global rotation. The redshift-magnitude relation is calculated and discussed in the context of SN Ia observation data. It is shown that the dynamics of considered problem is equivalent to the Friedmann model with additional non-interacting fluid with negative pressure. We demonstrate that the universe acceleration increase is due to the presence of global rotation effects, although the cosmological constant is still required to explain the SN Ia data. We discuss some observational constraints coming from SN Ia imposed on the behaviour of the homogeneous Newtonian universe in which matter rotates relative local gyroscopes. In the Newtonian theory _r,0 can be identified with ^,0 (only dust fluid is admissible) and rotation can exist with _r,0 =^,0 0. However, the best-fit flat model is the model without rotation, i.e., ^,0 =0. In the considered case we obtain the limit for ^,0>-0.033 on the confidence level 68.3. We are also beyond the model and postulate the existence of additional matter which scales like radiation matter and then analyse how that model fits the SN Ia data. In this case the limits on rotation coming from BBN and CMB anisotropies are also obtained. If we assume that the current estimates are _m,0 ~ 0.3, _r,0 ~ 10^-4, then the SN Ia data show that ^,0 -0.01 (or ₀ > 2.6 · 10^-19 rad/s). The statistical analysis gives us that the interval for any matter scaling like radiation is _r,0 ( - 0.01, 0.04).     

Scalar Soliton in Newtonian Gravity Modelling Dark Matter Halos

Within standard Newtonian gravity, galactic dark matter is modelled by a scalar field in order to effectively modify Kepler's law. In particular, we show that a solvable toy model with a self-interaction U() borrowed from non-topological solitons produces already qualitatively correct rotation curves. Although relativistic effects in the halo are very small, we indicate corrections arising from the general relativistic formulation.     

Classical color fields as a dark matter candidate

A model of Dark Matter is proposed where the Dark Matter is a classical color field. The color fields are invisible as they may interact with colored elementary particles like the ’t Hooft-Polyakov monopole only. Comparison with the Universal Rotation Curve is carried out.      

Anisotropic Stars: Exact Solutions

We study the effects of anisotropic pressure on the properties of spherically symmetric, gravitationally bound objects. We consider the full general-relativistic treatment of this problem and obtain exact solutions for various forms of the equation of state connecting the radial and tangential pressures. It is shown that pressure anisotropy can have significant effects on the structure and properties of stellar objects. In particular, the maximum value of 2M / R can approach unity (2M / R < 8/9 for isotropic objects) and the surface redshift can be arbitrarily large.     

Anisotropic Stars II: Stability

We investigate the stability of self-gravitating spherically symmetric anisotropic spheres under radial perturbations. We consider both the Newtonian and the full general-relativistic perturbation treatment. In the general-relativistic case, we extend the variational formalism for spheres with isotropic pressure developed by Chandrasekhar. We find that, in general, when the tangential pressure is greater than the radial pressure, the stability of the anisotropic sphere is enhanced when compared to isotropic configurations. In particular, anisotropic spheres are found to be stable for smaller values of the adiabatic index .     

利用密度相关的相对论平均场理论对核物质与中子星的研究(英文)

研究和详细地比较了RMF理论中不同的有效相互作用强度的密度依赖性, 并且讨论了这种密度依赖性对于核物质和中子星性质的影响. 对于核物质, 不同的参数组给出的对称核物质的饱和点非常接近, 基本都在经验值的范围内. 对于中子星, 考虑超子后不同参数组给出的质量极限的范围为1.52—2.06 M☉, 半径为10.24—11.38 km.The density dependencies of various effective interaction strengths in the relativistic mean field and their influences on the properties of nuclear matter and neutron stars are studied and carefully compared. The differences of saturation properties given by various effective interactions are subtle in symmetric nuclear matter. The Oppenheimer Volkoff mass limits of neutron stars calculated from different equations of state are 1.52—2.06 M☉, and the radii are 10.24—11.38 km with hyperons included.     

Generalized Lane–Emden Equation and the Structure of Galactic Dark Matter

Starting from the collisionless Boltzmann equation and the Plummer's distribution function, the Lane–Emden (LE) equation is derived and applied to the problem of galactic dark halos. Some generalizations of the LE equation are considered and their implications for the structure of dark halos are investigated. The relevance of a relativistic scalar field to the problem under investigation is also discussed.     

Quadratic interaction effect on the dark energy density in the universe

In this study, we deal with the holographic model of interacting dark components of dark energy and dark matter quadratic case of the equation of state parameter(Eo S). The effective equations of states for the interacting holographic energy density are derived and the results are analyzed and compared with the solution of the linear form in the literature.The result of our work shows that the value of interaction term between dark components affects the fixed points at far future in the DE-dominated universe in the case of quadratic Eo S parameter; it is a different result from the linear case in the theoretical results in the literature, and as the Quintom scenario the equations of state had coincidence at the cosmological constant boundary of -1 from above to below.     

A complete calculation for direct detection of Wino dark matter

In the anomaly-mediated supersymmetry (SUSY) breaking scenario, neutral gaugino of SUL₍₂₎$\mathit{SU}{(2)}_L$ multiplet, Wino, can be the lightest SUSY particle and become a candidate for dark matter. We calculated scattering cross section of Wino dark matter with nucleon, which is responsible for direct detection of the dark matter, on the assumption that the SUSY particles and the heavier Higgs bosons have masses of the order of the gravitino mass in the SUSY standard model. In such a case, the Wino–nucleon coupling is generated by loop processes. We have included two-loop contribution to Wino–gluon interaction in the calculation, since it is one of the leading contributions to the Wino–nucleon coupling. It was found that the spin-independent scattering cross section with proton is ^{10−(46–48)} cm²${10}^{-(46\text{–}48)}{\text{cm}}^2$. While it is almost independent of the Wino mass, the result is quite sensitive to the Higgs boson mass due to the accidental cancellation.     

理解暗能量和暗物质之间的相互作用

从热力学角度研究了暗能量和暗物质之间的相互作用. 假设相互作用是平衡态上的涨落并考虑此涨落导致的熵的修正, 导出了相互作用的物理表述, 把我们模型和观测结果作了比较.