arXiv 1303.36632013-03astro-ph.CO

星系团的引力红移测量

Measuring Gravitational Redshifts in Galaxy Clusters

Nick Kaiser

备注：: accepted for publication in MNRAS
DOI：: 10.1093/mnras/stt1370

摘要：

Wojtak { \it et al}在红移空间中叠加了来自SDSS调查的7，800个星团。他们发现，相对于最亮的星系团星系，星系团星系的净蓝移很小，这与GR. Zhao { \it et al.}已经指出，除了引力红移之外，人们还期望看到横向多普勒（TD）红移，并且这两种效应通常具有相同的量级。在这里，我们表明，还有其他的修正，也是相同的数量级。我们在过去的光锥上观察星系的事实导致了一种偏差，使得在星系团的框架中，更多的星系远离我们而不是向我们移动。这导致观测到的平均红移为$\langle δz \rangle = -\langle Φ\rangle + \langle β^2 \rangle / 2 + \langle β_x^2 \rangle$，其中$β_x$是视线速度。也就是说，如果我们对具有相同权重的星系进行平均。如果每个星系团中的星系都被它们的注量加权，或者等价地，如果我们不分辨运动的源，并且对每个光子给予相等的权重，对平均红移进行平均，那么观测到的红移就与通常的横向多普勒效应相反。在WHH实验中，由于光谱样品中包含物的通量限制，加权是一个阶梯函数，其结果也是不同的，并取决于光度函数和星系的SED的细节。包括这些效应实质上修改了蓝移曲线。我们表明，在相关范围内的碰撞参量，但变得重要的更大的尺度上的下降和流出有非常小的影响。

英文摘要：

Wojtak {\it et al} have stacked 7,800 clusters from the SDSS survey in redshift space. They find a small net blue-shift for the cluster galaxies relative to the brightest cluster galaxies, which agrees quite well with the gravitational redshift from GR. Zhao {\it et al.} have pointed out that, in addition to the gravitational redshift, one would expect to see transverse Doppler (TD) redshifts, and that these two effects are generally of the same order. Here we show that there are other corrections that are also of the same order of magnitude. The fact that we observe galaxies on our past light cone results in a bias such that more of the galaxies observed are moving away from us in the frame of the cluster than are moving towards us. This causes the observed average redshift to be $\langle δz \rangle = -\langle Φ\rangle + \langle β^2 \rangle / 2 + \langle β_x^2 \rangle$, with $β_x$ is the line of sight velocity. That is if we average over galaxies with equal weight. If the galaxies in each cluster are weighted by their fluence, or equivalently if we do not resolve the moving sources, and make an average of the mean redshift giving equal weight per photon, the observed redshift is then opposite to the usual transverse Doppler effect. In the WHH experiment, the weighting is a step-function because of the flux-limit for inclusion in the spectroscopic sample and the result is different again, and depends on the details of the luminosity function and the SEDs of the galaxies. Including these effects substantially modifies the blue-shift profile. We show that in-fall and out-flow have very small effect over the relevant range of impact parameters but become important on larger scales.

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