论文标题
深色多层
Deep-MOND polytropes
论文作者
论文摘要
在深限极限（DML）中工作，我描述了由状态多阵容方程式控制的球形，自我磨损系统，$ p = \ nathcal {k}ρ^γ$。作为自一致的结构，此类系统可以用作DML的启发式模型，天文系统，例如矮球星系，低表面密度椭圆星系和星形簇以及弥漫性星系组。它们还可以作为各种理论推断的测试基础。在无量纲的形式中，径向密度曲线满足的方程$ζ（y）$ is（对于$γ\ not = 1 $）$ [\ int_0^yζ\ bar y^2 d \ bar y]^{1/2} = -yd（ζ^{γ-1}）/dy $。或者，$θ^n（y）= y^{ - 2} [（yθ'）^2]'$，其中$θ=ζ^{γ-1} $和$ n \ equiv（γ-1）^{ - 1} $。我讨论了解决方案的属性，将它们与牛顿类似物的泳道偏多型物的属性进行了对比。由于MOND重力较强，所有DML多层都具有有限的质量，并且对于$ n <\ infty $（$γ> 1 $），均具有有限的半径。 （车道填充球的质量仅适用于5 $。）我使用DML多型研究DML缩放关系。例如，他们满足总质量，$ m $和质量平均速度分散$σ$：$ mga_0 =（9/4）σ^4 $之间的通用关系（对于所有$ \ MATHCAL {K} $和$γ$）。但是，$ m $与速度分散的其他度量之间的关系，例如中央，预测的，$ \barσ$，确实取决于$ n $（但不取决于$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \barσ，〜n] $空间。我还描述了对各向异性多型的概括，这些多层型也有有限的半径（$γ> 1 $），并且都满足了上述通用$ M-σ$关系。这种更扩展的模型表现出中央表面密度的关系：MOND预测的Baryonic和动态中央表面密度之间的紧密关系。
Working within the deep-MOND limit (DML), I describe spherical, self-gravitating systems governed by a polytropic equation of state, $P=\mathcal{K}ρ^γ$. As self-consistent structures, such systems can serve as heuristic models for DML, astronomical systems, such as dwarf spheroidal galaxies, low-surface-density elliptical galaxies and star clusters, and diffuse galaxy groups. They can also serve as testing ground for various theoretical MOND inferences. In dimensionless form, the equation satisfied by the radial density profile $ζ(y)$ is (for $γ\not=1$) $[\int_0^y ζ\bar y^2 d\bar y]^{1/2}=-yd(ζ^{γ-1})/dy$. Or, $θ^n(y)=y^{-2}[(yθ')^2]'$, where $θ=ζ^{γ-1}$, and $n\equiv (γ-1)^{-1}$. I discuss properties of the solutions, contrasting them with those of their Newtonian analogues -- the Lane-Emden polytropes. Due to the stronger MOND gravity, all DML polytropes have a finite mass, and for $n<\infty$ ($γ>1$) all have a finite radius. (Lane-Emden spheres have a finite mass only for $n\le 5$.) I use the DML polytropes to study DML scaling relations. For example, they satisfy a universal relation (for all $\mathcal{K}$ and $γ$) between the total mass, $M$, and the mass-average velocity dispersion $σ$: $MGa_0=(9/4)σ^4$. However, the relation between $M$ and other measures of the velocity dispersion, such as the central, projected one, $\barσ$, does depend on $n$ (but not $\mathcal{K}$), defining a `fundamental surface' in the $[M,~\barσ,~n]$ space. I also describe the generalization to anisotropic polytropes, which also all have a finite radius (for $γ>1$), and all satisfy the above universal $M-σ$ relation. This more extended class of models exhibits the central-surface-densities relation: a tight relation between the baryonic and the dynamical central surface densities predicted by MOND.
