强引力透镜在何种尺度下能可靠约束低质量扰动体的质量分布？
On what scales does strong lensing robustly constrain the mass profile of low-mass perturbers?
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中文总结 AI 辅助
本文基于费舍尔信息矩阵定义强引力透镜约束低质量扰动体质量分布的可靠半径，揭示其与弧像素加权几何均值的关系，该定义可推广至子暗晕与视线暗晕，体现数据分辨率和信噪比的影响。
中文摘要 AI 辅助
星系-星系强引力透镜是一种已确立的探测和表征低质量暗晕的方法，这类暗晕因过暗而无法被直接观测。近期分析从经验上表明，存在一个特征半径，在该半径内可以可靠测量这些暗晕的投影 enclosed mass（投影 enclosed mass 可保留英文术语）。本文基于费舍尔信息矩阵，给出了该可靠半径的物理和数学上的定义。我们证明，对于任何具有至少两个自由参数的球对称平滑分布，存在一个 pivot radius（pivot radius 保留英文），在该半径处，投影质量的估计值会与局部对数斜率去相关，且相对不确定性最小。因此，在该半径内的投影质量可被任何足够拟合数据的分布一致地恢复。该可靠半径在一阶近似下与扰动体的弧像素距离的加权几何均值重合，其中权重取决于扰动体偏转角、宏模型（macro-model 保留英文）放大率以及源面亮度梯度。超出一阶近似，修正项为弧的加权对数宽度量级。研究表明，数据对暗晕分布振幅之外的局部性质的约束能力，取决于弧相对于扰动体的径向杠杆作用，以及扰动体偏转角在高信噪比像素上的印记。本文的定义可推广到子暗晕和视线方向暗晕，自然涵盖了该问题的重要物理方面，以及数据分辨率和信噪比的影响。
英文摘要
Galaxy-galaxy strong gravitational lensing is an established method to detect and characterise low-mass haloes, which are otherwise too faint to be directly observed. Recent analyses have shown empirically that there exists a characteristic radius within which the projected enclosed mass of these haloes can be robustly measured. Here we provide a physically and mathematically motivated definition of this robust radius based on the Fisher information matrix. We show that for any spherically symmetric smooth profile with at least two free parameters, there exists a pivot radius at which estimates of the projected mass become decorrelated from the local logarithmic slope and have minimum relative uncertainty. As a result, the projected mass within this radius can be recovered consistently by any profile that fits the data well enough. This robust radius coincides, to leading order, with the weighted geometric mean of the arc pixel distances from the halo, where the weights depend on the perturber deflection angle, the macro-model magnification, and the source surface brightness gradient. Beyond leading order, corrections are of order the weighted log-width of the arc. The data constraining power on the local properties of the halo profile beyond amplitude is shown to depend on the radial leverage of the arc around the perturber, and on the imprint of the perturber deflection angle on high signal-to-noise-ratio pixels. Our definition generalises to both subhaloes and line-of-sight haloes and naturally captures the important physical aspects of the problem and the effect of the data resolution and signal-to-noise ratio.
