We demonstrate the utility and constraining power of a new statistic for investigating galaxy bias: the galaxy-lensing phase difference. The statistic consists in taking the differences of the phases of the harmonic wave modes between the weak lensing convergence field and the galaxy count field. We use dark matter simulations populated with galaxies up to redshift z = 1 to test the performance of this estimator. We find that phase differences are sensitive to the absolute value of the second-order bias (c2 = b2/b1) and demonstrate why this is the case. For a $1500$ deg2 galaxy survey we recover c2 with an error of approximately 0.1 for a wide range of c2 values; current constraints from redshift surveys have errors of 0.1–0.6 depending on redshift. This new statistic is therefore expected to provide constraints for c2 which are complementary and competitive with constraining power by the conventional estimators from the power spectrum and bispectrum. For the Dark Energy Survey (DES), we predict leading measurements of second-order bias.

中文翻译：

---

从星系透镜相位差中获得非线性星系偏差约束

我们展示了研究星系偏差的新统计数据的效用和约束力：星系透镜相位差。该统计包括在弱透镜会聚场和星系计数场之间获取谐波模式的相位差异。我们使用由红移 z = 1 的星系组成的暗物质模拟来测试这个估计器的性能。我们发现相位差对二阶偏置 (c2 = b2/b1) 的绝对值很敏感，并说明了为什么会出现这种情况。对于价值 1500 美元的 deg2 星系调查，我们恢复了 c2，对于大范围的 c2 值，误差约为 0.1；来自红移调查的当前限制具有 0.1-0.6 的误差，具体取决于红移。因此，这个新的统计量有望为 c2 提供约束，这些约束与来自功率谱和双谱的传统估计器的约束功率互补和竞争。对于暗能量调查 (DES)，我们预测二阶偏差的领先测量。