Title: Constraints on halo formation from cross-correlations with correlated variables Show Chinese title

Title: 与相关变量的交叉相关性对晕形成的影响约束

Abstract: Cross-correlations between biased tracers and the dark matter field encode information about the physical variables which characterize these tracers. However, if the physical variables of interest are correlated with one another, then extracting this information is not as straightforward as one might naively have thought. We show how to exploit these correlations so as to estimate scale-independent bias factors of all orders in a model-independent way. We also show that failure to account for this will lead to incorrect conclusions about which variables matter and which do not. Morever, accounting for this allows one to use the scale dependence of bias to constrain the physics of halo formation; to date the argument has been phrased the other way around. We illustrate by showing that the scale dependence of linear and nonlinear bias, measured on nonlinear scales, can be used to provide consistent estimates of how the critical density for halo formation depends on halo mass. Our methods work even when the bias is nonlocal and stochastic, such as when, in addition to the spherically averaged density field and its derivatives, the quadrupolar shear field also matters for halo formation. In such models, the nonlocal bias factors are closely related to the more familiar local nonlinear bias factors, which are much easier to measure. Our analysis emphasizes the fact that biased tracers are biased because they do not sample fields (density, velocity, shear, etc.) at all positions in space in the same way that the dark matter does. Show Chinese abstract

Abstract: 有偏示踪剂与暗物质场之间的互相关编码了描述这些示踪剂的物理变量的信息。 然而，如果感兴趣的物理变量彼此相关，那么提取这些信息并不像人们最初认为的那样直接。 我们展示了如何利用这些相关性，以一种与模型无关的方式估计所有阶数的尺度无关的偏差因子。 我们还表明，未能考虑这一点会导致关于哪些变量重要哪些不重要的错误结论。 此外，考虑到这一点可以使人们利用偏差的尺度依赖性来约束晕形成物理机制；到目前为止，这一论点是反过来表述的。 我们通过展示在非线性尺度上测量的线性和非线性偏差的尺度依赖性可以用来提供关于晕形成临界密度如何依赖于晕质量的一致估计来说明这一点。 我们的方法即使在偏差是非局部和随机的情况下也有效，例如，除了球对称平均密度场及其导数外，四极剪切场也对晕形成有影响时。 在这样的模型中，非局部偏差因子与更熟悉的局部非线性偏差因子密切相关，后者更容易测量。 我们的分析强调了一个事实，即有偏示踪剂之所以有偏，是因为它们并不像暗物质那样以相同的方式在空间所有位置采样场（密度、速度、剪切等）。