Galaxy-galaxy-galaxy lensing: Third-order correlations between the galaxy and mass distributions in the Universe
Galaxy-galaxy-galaxy lensing: Third-order correlations between the galaxy and mass distributions in the Universe
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DOI：
10.1051/0004-6361:20041923
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发表时间：
2005-02
影响因子：
6.5
通讯作者：
P. Watts
中科院分区：
文献类型：
--
作者：
P. Watts
星系-星系透镜（Galaxy-galaxy lensing，GGL）测量星系和宇宙质量之间的2点互相关。在这项工作中，我们试图通过考虑星系和质量之间的三阶相关性来概括这种效应：星系-星系-星系透镜效应。宇宙剪切场中的三阶相关最近在VIRMOS-DESCART和CTIO巡天中得到了报道。这些数据也应该是测量星系-星系-星系透镜效应的理想数据。事实上，这些高阶关联的影响可能已经在最近的星系-星系透镜效应研究中被发现。高阶互相关函数包含关于星系与其质量环境之间关系的宝贵信息，这些信息是GGL单独研究无法检测到的。在本文中，我们奠定了基本关系的三阶互相关和他们的投影，并介绍了一组新的尺度相关的三阶偏置参数。我们定义了三个新的观测量：两个星系切变相关函数G±和一个星系-星系切变相关函数G。我们将这些与各种预计的交叉双谱，并给出实用的估计其测量。我们注意到，这些星系的观测特征仅仅是对前景星系（G±）测量的过量剪切-剪切相关和对前景星系对（G）的平均切向剪切。这些量在剪切中不超过二阶，因此应该比剪切3点相关更容易测量。最后，我们推导出的三阶孔径质量统计的交叉双谱和实空间相关函数的表达式。这样的统计提供了双谱的非常局部化的测量，因此基本上封装了所有可用的三阶信息，同时保持容易从3点互相关函数的观测获得。此外，我们发现，利用孔径统计有进一步的好处，他们只测量三阶相关的连接部分。
Galaxy-galaxy lensing (GGL) measures the 2-point cross-correlation between galaxies and mass in the Universe. In this work we seek to generalise this effect by considering the third-order correlations between galaxies and mass: galaxy-galaxy- galaxy lensing. Third-order correlations in the cosmic shear field have recently been reported in the VIRMOS-DESCART and CTIO surveys. Such data should also be ideal for measuring galaxy-galaxy-galaxy lensing. Indeed, the effects of these higher- order correlations may have already been detected in recent studies of galaxy-galaxy lensing. Higher-order cross-correlation functions contain invaluable information about the relationship between galaxies and their mass environments that GGL studies alone cannot detect. In this paper we lay out the basic relations for third-order cross correlations and their projections and introduce a new set of scale dependent third-order bias parameters. We define three new observables: two galaxy-shear-shear correlation functions, G±, and a galaxy-galaxy-shear correlation, G. We relate these to the various projected cross-bispectra and give practical estimators for their measurement. We note that the observational signature of these correlators is simply the excess shear-shear correlation measured about foreground galaxies (for G±) and the average tangential shear around foreground galaxy pairs (for G). These quantities are no more than second order in the shear and so should be more easily measurable than the shear 3-point correlation. Finally we derive expressions for the third order aperture mass statistics in terms of both the cross-bispectra and the real-space correlation functions. Such statistics provide a very localized measurement of the bispectra, thus encapsulating essentially all of the available third-order information, while remaining easily obtainable from observations of 3-point cross-correlation functions. In addition we find that utilising aperture statistics has the further benefit that they measure only the connected part of the third order correlation.