We study the phase shifts of propagating slow magnetoacoustic waves in solar coronal loops invoking the effects of thermal conductivity, compressive viscosity, radiative losses, and heating–cooling imbalance. We derive the general dispersion relation and solve it to determine the phase shifts of density and temperature perturbations relative to the velocity and their dependence on the equilibrium parameters of the plasma such as the background density [\(\rho _{0}\)] and temperature [\(T_{0}\)]. We estimate the phase difference [\(\Delta \phi \)] between density and temperature perturbations and its dependence on \(\rho _{0}\) and \(T_{0}\). The role of radiative losses, along with the heating–cooling imbalance for an assumed specific heating function [\(H(\rho , T) \propto \rho ^{-0.5} T^{-3}\)], in the estimation of the phase shifts is found to be significant for the high-density and low-temperature loops. Heating–cooling imbalance can significantly increase the phase difference (\(\Delta \phi \approx 140^{\circ }\)) for the low-temperature loops compared to the constant-heating case (\(\Delta \phi \approx 30^{\circ }\)). We derive a general expression for the polytropic index [\(\gamma _{\rm eff}\)] using the linear MHD model. We find that in the presence of thermal conduction alone, \(\gamma _{\rm eff}\) remains close to its classical value \(5/3\) for all the considered \(\rho _{0}\) and \(T_{0}\) observed in typical coronal loops. We find that the inclusion of radiative losses (with or without heating–cooling imbalance) cannot explain the observed polytropic index under the considered heating and cooling models. To make the expected \(\gamma _{\rm eff}\) match the observed value of \(1.1 \pm 0.02\) in typical coronal loops, the thermal conductivity needs to be enhanced by an order of magnitude compared to the classical value. However, this conclusion is based on the presented model and needs to be confirmed further by considering more realistic radiative functions. We also explore the role of different heating functions for typical coronal parameters and find that although the \(\gamma _{\rm eff}\) remains close to \(5/3\), but the phase difference is highly dependent on the form of the heating function.

我们研究了在太阳日冕环中传播慢磁声波的相移，这引起了热导率、压缩粘度、辐射损失和加热-冷却不平衡的影响。我们推导出一般色散关系并求解它以确定密度和温度扰动相对于速度的相移及其对等离子体平衡参数（例如背景密度 [ \(\rho _{0}\) ] ]的依赖性和温度 [ \(T_{0}\) ]。我们估计密度和温度扰动之间的相位差 [ \(\Delta \phi \) ] 及其对\(\rho _{0}\)和\(T_{0}\) 的依赖. 辐射损失的作用，以及假设的特定加热函数 [ \(H(\rho , T) \propto \rho ^{-0.5} T^{-3}\) ]的加热-冷却不平衡，在发现相移的估计对于高密度和低温回路很重要。与恒定加热情况相比，加热-冷却不平衡可以显着增加低温回路的相位差（\(\Delta \phi \approx 140^{\circ }\)）（\(\Delta \phi \approx 30^{\circ }\) )。我们使用线性 MHD 模型推导出多变指数 [ \(\gamma _{\rm eff}\) ]的一般表达式。我们发现，在单独存在热传导的情况下，\(\gamma _{\rm eff}\)对于在典型日冕环中观察到的所有考虑的\(\rho _{0}\)和\(T_{0}\)，仍然接近其经典值\(5/3\)。我们发现包含辐射损失（有或没有加热-冷却不平衡）不能解释在考虑的加热和冷却模型下观察到的多方指数。为了使预期的\(\gamma _{\rm eff}\)匹配观察值\(1.1 \pm 0.02\)在典型的日冕环中，与经典值相比，热导率需要提高一个数量级。然而，这个结论是基于所提出的模型，需要通过考虑更现实的辐射函数来进一步证实。我们还探索了不同加热函数对典型日冕参数的作用，发现虽然\(\gamma _{\rm eff}\)仍然接近\(5/3\)，但相位差高度依赖于加热函数的形式。