Models predict that the well-studied mass–radius relation of white dwarf stars depends on the temperature of the star, with hotter white dwarfs having larger masses at a given radius than cooler stars. In this paper, we use a catalog of 26,041 DA white dwarfs observed in Sloan Digital Sky Survey Data Releases 1–19. We measure the radial velocity, effective temperature, surface gravity, and radius for each object. By binning this catalog in radius or surface gravity, we average out the random motion component of the radial velocities for nearby white dwarfs to isolate the gravitational redshifts for these objects and use them to directly measure the mass–radius relation. For gravitational redshifts measured from binning in either radius or surface gravity, we find strong evidence for a temperature-dependent mass–radius relation, with warmer white dwarfs consistently having greater gravitational redshifts than cool objects at a fixed radius or surface gravity. For warm white dwarfs, we find that their mean radius is larger and mean surface gravity is smaller than those of cool white dwarfs at 5.2σ and 6.0σ significance, respectively. Selecting white dwarfs with similar radii or surface gravities, the significance of the difference in mean gravitational redshifts between the warm and cool samples is >6.1σ and >3.6σ for measurements binned in radius and surface gravity, respectively, in the direction predicted by theory. This is an improvement over previous implicit detections, and our technique can be expanded to precisely test the white dwarf mass–radius relation with future surveys.

中文翻译：

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白矮星质-半径关系与引力红移的温度依赖性检测


模型预测，经过充分研究的白矮星的质量-半径关系取决于恒星的温度，在给定半径内，较热的白矮星比较冷的恒星具有更大的质量。在本文中，我们使用了在斯隆数字巡天数据版本 1-19 中观察到的 26,041 颗 DA 白矮星的目录。我们测量每个物体的径向速度、有效温度、表面重力和半径。通过在半径或表面重力中对这个星表进行分档，我们平均了附近白矮星的径向速度的随机运动分量，以隔离这些物体的引力红移，并使用它们直接测量质量-半径关系。对于通过半径或表面重力分箱测量的引力红移，我们发现了与温度相关的质量-半径关系的有力证据，在固定半径或表面重力下，较暖的白矮星始终比冷天体具有更大的引力红移。对于暖白矮星，我们发现它们的平均半径大于冷白矮星，平均表面重力小于冷白矮星，分别为 5.2σ 和 6.0σ。选择具有相似半径或表面重力的白矮星，暖样本和冷样本之间平均引力红移差异的显著性分别为>6.1σ和>3.6σ，分别在理论预测的方向上按半径和表面引力进行分档测量。这是对以前隐式探测的改进，我们的技术可以扩展为精确测试白矮星质量-半径与未来巡天的关系。