Deep-MOND polytropes
نویسندگان
چکیده
Working within the deep-MOND limit (DML), I describe spherical, self-gravitating systems governed by a polytropic equation of state, $P=\mathcal{K}\rho^\gamma$. As self-consistent structures, such can serve as heuristic models for DML, astronomical systems, dwarf spheroidal galaxies, low-surface-density elliptical galaxies and star clusters, diffuse galaxy groups. They also testing ground various theoretical MOND inferences. In dimensionless form, satisfied radial density profile $\zeta(y)$ is (for $\gamma\not=1$) $[\int_0^y \zeta \bar y^2 d\bar y]^{1/2}=-yd(\zeta^{\gamma-1})/dy$. Or, $\theta^n(y)=y^{-2}[(y\theta')^2]'$, where $\theta=\zeta^{\gamma-1}$, $n\equiv (\gamma-1)^{-1}$. discuss properties solutions, contrasting them with those their Newtonian analogues -- Lane-Emden polytropes. Due to stronger gravity, all DML polytropes have finite mass, $n<\infty$ ($\gamma>1$) radius. (Lane-Emden spheres mass only $n\le 5$.) use study scaling relations. For example, they satisfy universal relation $\mathcal{K}$ $\gamma$) between total $M$, mass-average velocity dispersion $\sigma$: $MGa_0=(9/4)\sigma^4$. However, $M$ other measures dispersion, central, projected one, $\bar\sigma$, does depend on $n$ (but not $\mathcal{K}$), defining `fundamental surface' in $[M,~\bar\sigma,~n]$ space. generalization anisotropic polytropes, which radius $\gamma>1$), above $M-\sigma$ relation. This more extended class exhibits central-surface-densities relation: tight baryonic dynamical central surface densities predicted MOND.
منابع مشابه
Roche Lobe Sizes in Deep-MOND Gravity
MOdified Newtonian Dynamics (MOND) is evolving from an empirical to a decent theory respecting fundamental physics after Bekenstein (2004) showed that lensing and Hubble expansion can be modeled rigourously in a Modified Relativity. The degeneracy of MOND with Dark Matter can be broken if we examine the non-linear MONDian Poisson’s equation in detail. Here we study the effect of tides for a bin...
متن کاملGlobal deep-MOND parameter as a theory discriminant.
Different formulations of modified Newtonian dynamics predict somewhat different rotation curves for the same mass distribution. Here I consider a global attribute of the rotation curve that might provide a convenient discriminant between theories when applied to isolated, pure-disk galaxies that are everywhere deep in the modified Newtonian dynamics regime. This parameter is Q ≡ V(2)/V(∞)(2), ...
متن کاملStability analysis of Newtonian polytropes
We analyze the stability of Newtonian polytropic static fluid spheres, described by the Lane-Emden equation. In the general case of arbitrary polytropic indices the Lane-Emden equation is a non-linear second order ordinary differential equation. By introducing a set of new variables, the Lane-Emden equation can be reduced to an autonomous system of two ordinary differential equations, which in ...
متن کاملStability of Polytropes
This paper is an investigation of the stability of some ideal stars. It is intended as a study in General Relativity, with emphasis on the coupling to matter, eventually aimed at a better understanding of very strong gravitational fields and “Black Holes”. This contrasts with the usual attitude in astrophysics, where Einstein’s equations are invoked as a refinement of classical thermodynamics a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical review
سال: 2021
ISSN: ['0556-2813', '1538-4497', '1089-490X']
DOI: https://doi.org/10.1103/physrevd.103.044043