什么时候是恒星形成期？一个时滞微分方程负反馈模型
When is star formation episodic? A delay differential equation negative feedback model
摘要：
我们介绍了一个微分方程的恒星形成的星系，包括负反馈的延迟。当反馈是瞬时的时，解接近自限平衡态。当存在时滞时，即使反馈是负的，解也可以表现出循环解和情景解。我们发现，只有当两个条件得到满足时，周期性或偶发性的恒星形成才会发生。首先，延迟时间尺度必须超过云消费时间尺度。第二，反馈必须有力。这种说法在数量上等同于要求接近平衡的时间尺度大于云消费时间尺度的大约两倍。预测的振荡周期约为延迟时间尺度的4倍。振荡的幅度随着反馈强度和延迟时间的增加而增加。讨论了延迟微分方程（DDE）模型在以云密度为变量的星系恒星形成中的应用。DDE模型最适用于循环气体且仅缓慢从系统中移除气体的系统。我们提出了可能的延迟机制的基础上的要求，即延迟时间与观测估计的时间之间的事件。提出的延迟时间尺度可以解释类似于P10 Myrs周期的星系中心、P100 Myrs周期的不规则星系和P2 Gyr周期的银河系盘的幕式恒星形成，分别是大质量恒星形成后的激发湍流、气体被推入晕中返回并与盘相互作用以及螺旋密度波演化的延迟时间尺度。
英文摘要：
We introduce a differential equation for star formation in galaxies that incorporates negative feedback with a delay. When the feedback is instantaneous, solutions approach a self-limiting equilibrium state. When there is a delay, even though the feedback is negative, the solutions can exhibit cyclic and episodic solutions. We find that periodic or episodic star formation only occurs when two conditions are satisfied. Firstly the delay timescale must exceed a cloud consumption timescale. Secondly the feedback must be strong. This statement is quantitatively equivalent to requiring that the timescale to approach equilibrium be greater than approximately twice the cloud consumption timescale. The period of oscillations predicted is approximately 4 times the delay timescale. The amplitude of the oscillations increases with both feedback strength and delay time. We discuss applications of the delay differential equation (DDE) model to star formation in galaxies using the cloud density as a variable. The DDE model is most applicable to systems that recycle gas and only slowly remove gas from the system. We propose likely delay mechanisms based on the requirement that the delay time is related to the observationally estimated time between episodic events. The proposed delay timescale accounting for episodic star formation in galaxy centers on periods similar to P 10 Myrs, irregular galaxies with P 100 Myrs, and the Milky Way disk with P~ 2Gyr, could be that for exciting turbulence following creation of massive stars, that for gas pushed into the halo to return and interact with the disk and that for spiral density wave evolution, respectively.
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