The effects of dust temperature and radiative heat-loss functions on the instability of selfgravitating homogeneous viscoelastic dusty plasma have been studied using the modified GH model. A general dispersion relation representing the dust temperature, radiative heat-loss functions, magnetic field, thermal conductivity and relaxation time parameters are obtained using the normal mode analysis method in the linearized perturbation equations system. Jeans criteria that represent the onset of instability of selfgravitating medium are obtained under the limits; when the medium behaves like a viscous liquid (strongly coupled limit) and a Newtonian liquid (weakly coupled limit) for some limiting cases. The effects of various parameters on the Jeans instability criteria and on the growth rate of selfgravitating viscoelastic dusty plasma have been discussed. It is found that the dust temperature and radiative heat-loss functions modify the instability criterion by reducing the critical wave number.

中文翻译：

---

尘埃温度和辐射热损失函数对粘弹性尘埃等离子体磁引力不稳定性的影响

使用修正的GH模型研究了尘埃温度和辐射热损失函数对自引力均匀粘弹性尘埃等离子体不稳定性的影响。在线性化微扰方程系统中使用常模分析方法获得了表示灰尘温度、辐射热损失函数、磁场、热导率和弛豫时间参数的一般色散关系。代表自引力介质不稳定性开始的 Jeans 标准是在限制下获得的；当介质在某些极限情况下表现为粘性液体（强耦合极限）和牛顿液体（弱耦合极限）时。已经讨论了各种参数对 Jeans 不稳定性标准和自引力粘弹性尘埃等离子体的增长率的影响。发现灰尘温度和辐射热损失函数通过减少临界波数来修改不稳定性准则。