我們研究雙星系統有不同方式質量流失的動力學，對於當質量流失完之後，這個系
統是否能維持束縛狀態還是變成自由狀態的問題感到非常有興趣。我們研究兩種狀
況，第一種是只考慮雙星系統，其中一顆星在有限的時間內有質量流失的現象。第
二種是雙星系統在分子雲 (或雲核) 裡而分子雲 (或雲核) 會隨著時間擴張或質量流
失。

對於只考慮雙星系統的例子，我們考慮三種不同的系統:(1) 主星質量遠大於伴
星，然後研究質量流失分別是 (a) 主星流失 (b) 伴星流失，(2) 兩顆雙星質量一
樣，其中一顆星流失 (3) 兩顆星總質量不變，其中一顆星的質量吸積到另一顆星
上。他們大部分擁有相似的結果，像是當流失越多質量的話，這個系統越會變得自
由。或者是對於固定的質量流失，當流失時間變長的話，系統似乎會傾向於束縛狀
態，但是隨著不同的流失時間，系統會在束縛和自由間轉換。

對於分子雲裡的雙星系統，我們提出兩種模型去描述雲 (或雲核) 的擴散。我
們發現當初始半徑和初速越大或雲氣質量越大，系統傾向為自由狀態。擴散時間對
系統的作用依照不同的環境密度會有不同的影響，當環境密度較小時，擴散時間對
系統有很大的影響，對於環境密度較大時，不同的擴散時間會讓此系統處於束縛和
自由間轉換。

We study the dynamics of a binary system under different mass loss scenarios. We
are particularly interested in the conditions under which the system remains bound
or not when the mass loss process is stopped. We study two cases. The first one is
the binary system is an isolated system and one of the stars change its mass for a
finite time. The second one is the binary system is embedded in molecular cloud (or
cloud core) and the cloud (or cloud core) is dispersing or losing mass.

For the isolated binary system, we consider three different systems. (1) The host
star is much heavier than the companion star, and we study mass loss by (a) host
star (b) companion star. (2) Both stars has similar mass, and mass loss by one star
(3) the total mass is unchanged, mass transfer from one star to the other. Most of
them have similar results. For example, the system is more likely to be unbound
if the mass loss is large. Also there is a general trend that for a fix mass loss, the
longer is the time interval of mass loss, the more likely is the system remains bound.
However, this trend is not necessary monotonic. It may happen that the system may
alternate between bound and unbound destiny when the time interval of mass loss
increases within a certain range.

For embedded the binary system, we propose two models for cloud dispersion. We
find that the binary system is more likely to be unbound if the initial position is
larger, or initial velocity is faster, or the mass of cloud is larger. The dependence of
dispersion time is complicated. When the density of interstellar medium is small, the
time of dispersion has a great impact on system. When the density of interstellar
medium is large, the increase in dispersion time may cause the system to alternate
between bound and unbound destiny

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