标题： 一个用于星团强恒星风联合外流的广义半解析模型 显示英文标题

标题： A generalized semi-analytic model for the combined outflow from a cluster of stars with strong stellar winds

摘要： 我们推导了密集恒星团中由热驱动的累积外流的半解析解，该恒星团由大量具有强恒星风的恒星组成，在关键假设下，它们的质量和能量沉积可以被视为热化风物质的连续源。 我们的方法提供了流动临界半径和声速的显式解析形式，这使得可以从临界半径向内/向外积分以获得完整解。 应用于先前假设质量沉积为幂律或指数形式的模型，可以直接比较它们的速度解。 我们随后得到了新的模型解，这些模型的质量沉积具有高斯形式或Plummer和Elson所推导的经验形式。 比较表明，当以临界半径缩放的半径表示时，整体速度定律非常相似，渐近地趋近于能量平均的恒星风速度$V_w$，并固定通过一个共同的临界/音速$v_c = V_w/2$。 通过推导外流密度和温度的相关变化，我们得到了预期X射线发射的标度形式，并表明辐射冷却通常只是对绝热膨胀假设冷却的小修正。 对不完全风热化的初步分析表明，这同样会对密集星团的整体外流产生较小的影响。 这里提出的简化半解析方法可以很容易地应用于其他质量沉积情况，从而为解释年轻恒星团外流的详细数值模拟结果提供基础。 显示英文摘要

摘要： We derive semi-analytic solutions for the thermally driven cumulative outflow from a dense stellar cluster that consists of a large number of stars with strong stellar winds, under the key assumption that their mass and energy deposition can be treated as a continuous source of thermalized wind material. Our approach provides explicit analytic forms for the flow critical radius and sound speed, which then allows for full solution by inward/outward integration from this critical radius. Application to previous models that assume either a power-law or exponential mass deposition allows a direct comparison of their velocity solutions. We then obtain solutions for new models that have mass depositions with a gaussian or the empirically motivated forms derived by Plummer and Elson. Comparisons show that, when cast in terms of the radius scaled by the critical radius, the overall velocity laws are all quite similar, asymptotically approaching the energy-averaged stellar wind speed $V_w$, and anchored to passing through a common critical/sonic speed $v_c = V_w/2$. By deriving associated variations in outflow density and temperature, we obtain scaling forms for the expected X-ray emission, and show that radiative cooling generally represents only a small correction to the assumed cooling from adiabatic expansion. An initial analysis of incomplete wind thermalization suggests this should likewise have modest effect on the overall outflow in dense clusters. The simplified semi-analytic method presented here can be readily applied to alternative mass depositions and so form a basis for interpreting results from detailed numerical simulations of outflows from young stellar clusters.