Between the base of the solar corona at $r=r_\textrm {b}$ and the Alfvén critical point at $r=r_\textrm {A}$ , where $r$ is heliocentric distance, the solar-wind density decreases by a factor $ \mathop > \limits_\sim 10^5$ , but the plasma temperature varies by a factor of only a few. In this paper, I show that such quasi-isothermal evolution out to $r=r_\textrm {A}$ is a generic property of outflows powered by reflection-driven Alfvén-wave (AW) turbulence, in which outward-propagating AWs partially reflect, and counter-propagating AWs interact to produce a cascade of fluctuation energy to small scales, which leads to turbulent heating. Approximating the sub-Alfvénic region as isothermal, I first present a brief, simplified calculation showing that in a solar or stellar wind powered by AW turbulence with minimal conductive losses, $\dot {M} \simeq P_\textrm {AW}(r_\textrm {b})/v_\textrm {esc}^2$ , $U_{\infty } \simeq v_\textrm {esc}$ , and $T\simeq m_\textrm {p} v_\textrm {esc}^2/[8 k_\textrm {B} \ln (v_\textrm {esc}/\delta v_\textrm {b})]$ , where $\dot {M}$ is the mass outflow rate, $U_{\infty }$ is the asymptotic wind speed, $T$ is the coronal temperature, $v_\textrm {esc}$ is the escape velocity of the Sun, $\delta v_\textrm {b}$ is the fluctuating velocity at $r_\textrm {b}$ , $P_\textrm {AW}$ is the power carried by outward-propagating AWs, $k_\textrm {B}$ is the Boltzmann constant, and $m_\textrm {p}$ is the proton mass. I then develop a more detailed model of the transition region, corona, and solar wind that accounts for the heat flux $q_\textrm {b}$ from the coronal base into the transition region and momentum deposition by AWs. I solve analytically for $q_\textrm {b}$ by balancing conductive heating against internal-energy losses from radiation, $p\,\textrm {d} V$ work, and advection within the transition region. The density at $r_\textrm {b}$ is determined by balancing turbulent heating and radiative cooling at $r_\textrm {b}$ . I solve the equations of the model analytically in two different parameter regimes. In one of these regimes, the leading-order analytic solution reproduces the results of the aforementioned simplified calculation of $\dot {M}$ , $U_\infty$ , and $T$ . Analytic and numerical solutions to the model equations match a number of observations.

中文翻译：

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日冕加热与太阳风加速耦合问题的近似解析解

在日冕底部之间 $r=r_\textrm {b}$ 和 Alfven 临界点 $r=r_\textrm {A}$ ， 在哪里 $r$ 是日心距离，太阳风密度降低了一个因子 $ \mathop > \limits_\sim 10^5$ ，但等离子体温度的变化只有几个因素。在本文中，我证明了这种准等温演化 $r=r_\textrm {A}$ 是由反射驱动的 Alfvén 波 (AW) 湍流驱动的外流的一般特性，其中向外传播的 AW 部分反射，而反向传播的 AW 相互作用以产生小尺度的波动能量级联，从而导致湍流加热. 将亚阿尔芬区域近似为等温区域，我首先提出一个简短的简化计算，表明在由 AW 湍流驱动的太阳能或恒星风中，传导损耗最小， $\dot {M} \simeq P_\textrm {AW}(r_\textrm {b})/v_\textrm {esc}^2$ , $U_{\infty } \simeq v_\textrm {esc}$ ， 和 $T\simeq m_\textrm {p} v_\textrm {esc}^2/[8 k_\textrm {B} \ln (v_\textrm {esc}/\delta v_\textrm {b})]$ ， 在哪里 $\点 {M}$ 是质量流出率， $U_{\infty }$ 是渐近风速， $T$ 是日冕温度， $v_\textrm {esc}$ 是太阳的逃逸速度， $\delta v_\textrm {b}$ 是波动速度在 $r_\textrm {b}$ , $P_\textrm {AW}$ 是向外传播的 AW 携带的功率， $k_\textrm {B}$ 是玻尔兹曼常数，并且 $m_\textrm {p}$ 是质子质量。然后，我开发了一个解释热通量的过渡区域、日冕和太阳风的更详细模型 $q_\textrm {b}$ 从日冕底部到过渡区域和 AWs 的动量沉积。我解析解决 $q_\textrm {b}$ 通过平衡传导加热与辐射造成的内能损失， $p\,\textrm {d} V$ 工作和过渡区域内的平流。密度为 $r_\textrm {b}$ 由平衡湍流加热和辐射冷却决定 $r_\textrm {b}$ . 我在两种不同的参数状态下解析地求解模型方程。在其中一种方案中，前导解析解再现了上述简化计算的结果 $\点 {M}$ , $U_\infty$ ， 和 $T$ . 模型方程的解析和数值解与许多观察结果相匹配。