Structures in a class of magnetized scale-free discs

Abstract

We construct analytically stationary global configurations for both aligned and logarithmic spiral coplanar magnetohydrodynamic (MHD) perturbations in an axisymmetric background MHD disc with a power-law surface mass density $\Sigma_0\propto r^{-\alpha}$, a coplanar azimuthal magnetic field $B_0\propto r^{-\gamma}$, a consistent self-gravity and a power-law rotation curve $v_0\propto r^{-\beta}$ where $v_0$ is the linear azimuthal gas rotation speed. The barotropic equation of state $\Pi\propto\Sigma^{n}$ is adopted for both MHD background equilibrium and coplanar MHD perturbations where $\Pi$ is the vertically integrated pressure and $n$ is the barotropic index. For a scale-free background MHD equilibrium, a relation exists among $\alpha$, $\beta$, $\gamma$ and $n$ such that only one parameter (e.g., $\beta$) is independent. For a linear axisymmetric stability analysis, we provide global criteria in various parameter regimes. For nonaxisymmetric aligned and logarithmic spiral cases, two branches of perturbation modes (i.e., fast and slow MHD density waves) can be derived once $\beta$ is specified. To complement the magnetized singular isothermal disc (MSID) analysis of Lou, we extend the analysis to a wider range of $-1/4<\beta<1/2$. As an example of illustration, we discuss specifically the $\beta=1/4$ case when the background magnetic field is force-free. Angular momentum conservation for coplanar MHD perturbations and other relevant aspects of our approach are discussed.Comment: 25 page

Global non-axisymmetric perturbation configurations in a composite disc system with an isopedic magnetic field: relation between dark matter halo and magnetic field

“…In addition, this work can also be understood as a preparation for the following study on MHD density waves in such a composite disc system since all relevant quantities and their relations among each other are presented in this work. In reference to SID models of Shu & Li (1997), Shu et al (2000), Lou & Shen (2003), Lou & Zou (2004, 2006), Shen et al (2005), there exist two classes of solutions for stationary MHD perturbation configurations with in‐phase and out‐of‐phase density perturbations in the two discs. We expect for the case of a scale‐free stellar disc and an isopedically magnetized scale‐free gaseous disc embedded in an axisymmetric dark matter halo that there are also two classes of in‐phase and out‐of‐phase density perturbations.…”

“…Over the past decade, a research area has been developed on the so‐called scale‐free discs and perturbation structures therein (e.g. Syer & Tremaine 1996; Shu et al 2000; Lou & Zou 2004; Shen & Lou 2003, 2004; Shen, Liu & Lou 2005; Lou & Zou 2006; Lou & Bai 2006; Wu & Lou 2006). The scale‐free condition corresponds to a power‐law dependence of all physical quantities on the cylindrical radius r , for example, the background surface mass density is Σ 0 ∝ r −2β−1 with β being a constant scaling index.…”

Dispersal of gaseous circumstellar discs around high-mass stars

“…Secondly, the isothermal condition can be replaced by the more general polytropic approximation (Wang & Lou 2006; Lou & Wang 2006; Lou & Zou 2006). Thirdly, it is of considerable interest to incorporate the effect of a magnetic field (Shen et al 2005; Yu & Lou 2005; Lou & Zou 2004, 2006; Lou & Wu 2005; Wu & Lou 2006; Lou & Gao 2006).…”

“…Following the above procedure by ignoring gravity and centrifugal forces, one can extend these results to a power‐law surface mass density Σ( r ) ∝ r − n where 0 < n ≤ 2 (Shen et al 2005). Similar to the n = 1 case, the downstream behind the shock approaches a uniform density yet with the enclosed mass ∝ t − n and the flow speed becomes linear in radii, viz.…”

“…We start with a specific case of a neutral H i disc carrying a surface mass density Σ∝ r −1 , and then extend the results to different power‐law indices of Σ profiles (Shen & Lou 2004a; Shen, Liu & Lou 2005; Lou & Bai 2006; Wu & Lou 2006) in the limit when the thermal pressure dominates other forces in the shock evolution of an H ii disc. The stellar gravity has weaker effects over distances larger than where a is the sound speed of the H ii gas.…”