关于尘埃星际介质中阿尔芬波传播的研究：在分子云中能否忽略尘埃惯性？
On the propagation of Alfvén waves in the dusty interstellar medium. Can we neglect dust inertia in molecular clouds?
AI总结：
本文解析研究尘埃星际介质中阿尔芬波传播，发现忽略尘埃惯性在长波长下有效，但短波长时失效，考虑惯性后波传播更对称，哨声模式仅在高密度出现。
摘要：
阿尔芬波是基本的磁化模式，在磁化流动（如星际介质）的动力学中发挥着重要作用。在弱电离介质中，其传播不仅关键依赖于电离率，还依赖于电荷载流子，而电荷载流子根据气体密度可以是离子、电子或尘埃颗粒。尤其众所周知，尘埃颗粒对致密星际介质（如坍缩中的致密核）中的磁阻率有重大影响。然而，在大多数计算中，出于数值原因，通常忽略颗粒惯性。我们解析地研究了在单尺寸和多尺寸颗粒介质（如星际介质）中阿尔芬波的传播，并得到了波数作为波频率函数的精确表达式。这些表达式随后在考虑或忽略颗粒惯性的情况下进行解析或数值求解。在大波长条件下，忽略颗粒惯性是一个非常好的近似，但对于短于某一临界值（该值大致与 $1/n$ 成比例，其中 $n$ 为气体密度）的波长，情况则相当不同。更具体地说，当忽略惯性时，波在短波长下不传播，或者由于霍尔效应，仅对一种圆偏振发展出哨声模式，使得 ${\cal R} _e (ω) \propto k^2$，而另一种偏振则具有零群速度，即 ${\cal R} _e (ω) \propto k^0$。当考虑颗粒惯性时，两种偏振的传播趋于更加对称，且哨声模式仅在密度高于 $\simeq 10^8$ cm$^{-3}$ 时才存在。在较低密度下，它被一种具有 ${\cal R} _e (ω) \propto k^{\simeq 1.2}$ 的模式所取代。
英文摘要：
Alfvén waves are fundamental magnetized modes which play an important role in the dynamics of magnetized flows such as the interstellar medium (ISM). In weakly ionised medium, their propagation critically depends on the ionisation rate but also on the charge carriers which, depending on gas density can be ions, electrons or dust grains. The latter in particular are well known to have a drastic influence on the magnetic resistivities in the dense ISM such as collapsing dense cores. Yet, in most calculations, for numerical reasons, the grain inertia is usually neglected. We investigate analytically the propagation of Alfvén waves both in a single-size and multi-size grain medium such as the ISM and we obtain exact expressions giving wavenumbers as a function of wave frequencies. These expressions are then solved analytically or numerically taking into account or neglecting grain inertia. Whereas at large wavelengths, neglecting grain inertia is a very good approximation, the situation is rather different for wavelengths shorter than a critical value, which broadly scales as $1/n$, $n$ being the gas density. More precisely, when inertia is neglected the waves do not propagate at short wavelengths or, due to the Hall effect, develop for one circular polarisation only, a whistler mode such that ${\cal R} _e (ω) \propto k^2$, whereas the other polarisation presents a zero group velocity, i.e. ${\cal R} _e (ω) \propto k^0$. When grain inertia is accounted for, the propagation of the two polarisations tend to be more symmetrical and the whistler mode is only present at density higher than $\simeq 10^8$ cm$^{-3}$. At lower density it is replaced by a mode having ${\cal R} _e (ω) \propto k^{\simeq 1.2}$. Abridged
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