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Polytropic wind solutions via the Complex Plane Strategy
Astronomy and Computing ( IF 2.5 ) Pub Date : 2021-08-11 , DOI: 10.1016/j.ascom.2021.100491
Vasileios Karageorgopoulos 1 , Konstantinos N. Gourgouliatos 1 , Vassilis Geroyannis 1
Affiliation  

Solar-type stars generate spherical winds, which are pressure driven flows, that start subsonic, reach the sound speed at the sonic point and transition to supersonic flows. The sonic point, mathematically corresponds to a singularity of the system of differential equations describing the flow. In the problem of an isothermal wind, the Parker solution provides an exact analytical expression tuned appropriately so that the singularity does not affect the solution. However, if the wind is polytropic it is not possible to find an analytical solution and a numerical approach needs to be followed. We study solutions of spherical winds that are driven by pressure within a gravitational field. The solutions pass smoothly from the critical point and allow us to study the impact of the changes of the polytropic index to these winds. We explore the properties of these solutions as a function of the polytropic index and the boundary conditions used. We apply the Complex Plane Strategy (CPS) and we obtain numerically solutions of polytropic winds. This allows us to avoid the singularity appearing in the equations through the introduction complex variables and integration on the complex plane. Applying this method, we obtain solutions with physical behaviour at the stellar surface, the sonic point and at large distances from the star. We further explore the role of the polytropic index in the flow and the effect of mass-loss rate and temperature on the solution. We find that the increase of polytropic index as well as the decrease of flow parameter both yield to a smoother velocity profile and lower velocities and shifts the transition point from subsonic to supersonic behaviour further from the star. Finally, we verify that the increasing of coronal temperature yields higher wind velocities and a weaker dependence on polytropic index.



中文翻译:

通过复平面策略的多方风解决方案

太阳型恒星产生球形风,这是压力驱动的流动,开始亚音速,在音速点达到声速并过渡到超音速流动。声波点在数学上对应于描述流动的微分方程系统的奇点。在等温风问题中,Parker 解提供了一个精确的解析表达式,经过适当调整,奇点不会影响解。但是,如果风是多方的,则不可能找到解析解,需要遵循数值方法。我们研究由重力场内的压力驱动的球形风的解决方案。解从临界点顺利通过,使我们能够研究多方指数的变化对这些风的影响。我们将这些解的性质作为多方指数和所使用的边界条件的函数进行探索。我们应用复平面策略 (CPS) 并获得多方风的数值解。这使我们可以通过在复平面上引入复变量和积分来避免方程中出现奇点。应用这种方法,我们获得了在恒星表面、声波点和远离恒星的物理行为的解。我们进一步探讨了多方指数在流动中的作用以及质量损失率和温度对溶液的影响。我们发现多方指数的增加以及流动参数的减少都会产生更平滑的速度剖面和更低的速度,并将过渡点从亚音速转变为离恒星更远的超音速行为。最后,我们验证了日冕温度的增加会产生更高的风速和更弱的对多方指数的依赖性。

更新日期:2021-08-20
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