The LISA telescope will provide the first opportunity to probe the scenario of a first-order phase transition happening close to the electroweak scale. In thermal transitions, the main contribution to the GW spectrum comes from the sound waves propagating through the plasma. Current estimates of the GW spectrum are based on numerical simulations of a scalar field interacting with the plasma or on analytical approximations — the so-called sound shell model. In this work we present a novel setup to calculate the GW spectra from sound waves. We use a hybrid method that uses a 1d simulation (with spherical symmetry) to evolve the velocity and enthalpy profiles of a single bubble after collision and embed it in a 3d realization of multiple bubble collisions, assuming linear superposition of the velocity and enthalpy. The main advantage of our method compared to 3d hydrodynamic simulations is that it does not require to resolve the scale of bubble wall thickness. This makes our simulations more economical and the only two relevant physical length scales that enter are the bubble size and the fluid shell thickness (that are in turn enclosed by the box size and the grid spacing). The reduced costs allow for extensive parameter studies and we provide a parametrization of the final GW spectrum as a function of the wall velocity and the fluid kinetic energy.

LISA 望远镜将提供第一个机会来探测发生在电弱尺度附近的一阶相变场景。在热转变中，引力波谱的主要贡献来自通过等离子体传播的声波。当前对 GW 频谱的估计基于与等离子体相互作用的标量场的数值模拟或基于解析近似值——所谓的声壳模型。在这项工作中，我们提出了一种新的设置来计算声波的 GW 谱。我们使用混合方法，该方法使用 1d 模拟（具有球对称性）来演化碰撞后单个气泡的速度和焓分布，并将其嵌入到多个气泡碰撞的 3d 实现中，假设速度和焓是线性叠加的。与 3d 流体动力学模拟相比，我们的方法的主要优点是它不需要解析气泡壁厚的尺度。这使我们的模拟更加经济，并且输入的唯一两个相关物理长度尺度是气泡尺寸和流体壳厚度（它们依次被框尺寸和网格间距包围）。降低的成本允许进行广泛的参数研究，我们提供了最终 GW 谱的参数化，作为壁速度和流体动能的函数。这使我们的模拟更加经济，并且输入的唯一两个相关物理长度尺度是气泡尺寸和流体壳厚度（它们依次被框尺寸和网格间距包围）。降低的成本允许进行广泛的参数研究，我们提供了最终 GW 谱的参数化，作为壁速度和流体动能的函数。这使我们的模拟更加经济，并且输入的唯一两个相关物理长度尺度是气泡尺寸和流体壳厚度（它们依次被框尺寸和网格间距包围）。降低的成本允许进行广泛的参数研究，我们提供了最终 GW 谱的参数化，作为壁速度和流体动能的函数。