The process of bar formation, evolution and destruction is still a controversial topic regarding galaxy dynamics. Numerical simulations show that these phenomena strongly depend on physical and numerical parameters. In this work, we study the combined influence of the softening parameter, $\epsilon$ and disc mass fraction, $m_{\mathrm{d}}$ on the formation and evolution of bars in isolated disc-halo models via $N$-body simulations with different particle resolutions. Previous studies indicate that the bar strength depends on $m_{\mathrm{d}}$ as $\propto m_{\mathrm{d}}^{-1}$, which is seen as a delay in bar formation. However, the distorsion parameter, $\eta$, which measures the bar's momentum through time, shows that an increase in $m_{\mathrm{d}}$ does not always induce a delay in bar formation. This suggests that $\epsilon$ interact to either enhance or weaken the bar. Moreover, numerical heating dominates in models with small softening values, creating highly accelerated particles at the centre of discs, regardless of $m_{\mathrm{d}}$ or resolution. These enhanced particle accelerations produce chaotic orbits for $\epsilon \leq 5\,$pc, resulting in bar suppression due to collisional dynamics in the centre. In our high resolution models ($N \approx 10^{7}$), small softening values are incapable of reproducing the bar instability. The role of disc mass is as follows: increasing $m_{\mathrm{d}}$ for moderate $\epsilon$ ($\geq 10\,$pc) reduces the amount of drift in the acceleration profile, without affecting the bar's behaviour. Models with lower $m_{\mathrm{d}}$ values coupled with small softening values, have an excess of highly accelerated particles, introducing unwanted effects into otherwise reliable simulations. Finally, we show that the evolution of the disc's vertical acceleration profile is a reliable indicator of numerical heating introduced by $\epsilon$ and the bar.

翻译：棒结构的形成、演化与瓦解过程仍是星系动力学中具有争议的课题。数值模拟表明这些现象强烈依赖于物理参数与数值参数。本研究通过采用不同粒子分辨率的N体模拟，系统探究了软化参数$\epsilon$与盘质量分数$m_{\mathrm{d}}$对孤立盘-晕模型中棒结构形成与演化的耦合影响。既往研究指出棒结构强度与$m_{\mathrm{d}}$呈$\propto m_{\mathrm{d}}^{-1}$依赖关系，这通常表现为棒形成的延迟现象。然而，通过时间维度测量棒动量传输的畸变参数$\eta$显示：$m_{\mathrm{d}}$的增加并不总是导致棒形成延迟。这表明$\epsilon$会通过相互作用增强或削弱棒结构。此外，在采用较小软化值的模型中，数值加热效应占主导地位，无论$m_{\mathrm{d}}$或分辨率如何，都会在盘中心产生高度加速的粒子。当$\epsilon \leq 5\,$pc时，这些增强的粒子加速度将产生混沌轨道，导致中心区域碰撞动力学引发的棒结构抑制。在我们的高分辨率模型（$N \approx 10^{7}$）中，较小的软化值无法再现棒不稳定性。盘质量的作用表现为：在中等$\epsilon$值（$\geq 10\,$pc）条件下增加$m_{\mathrm{d}}$可减少加速度剖面的漂移量，且不影响棒结构行为。较低$m_{\mathrm{d}}$值与较小软化值结合的模型会产生过量高速粒子，给原本可靠的模拟引入非物理效应。最后我们证明，盘垂直加速度剖面的演化可作为$\epsilon$与棒结构引入数值加热效应的可靠指示器。