(i.e. dominated by Poisson fluctuations)
One of the best data sets to show this is from the Sloan Digital Sky Survey (SDSS). Selecting galaxies more luminous than -21.3, in r-band absolute magnitude, provides a 'volume-limited sample' of 54620 galaxies over a volume corresponding to 150 Mpc by 410 Mpc by 700 Mpc.
The top-left plot below shows this distribution of galaxies collapsed along the shortest dimension, i.e., a 2D distribution over 410 Mpc by 700 Mpc. The top-middle plot shows this distribution after moving each galaxy in a random direction and with a root-mean-square (rms) distance of 20 Mpc. The top-right plot shows this distribution after moving each galaxy with an rms distance of 147 Mpc.
The bottom plots show the same distributions, and smoothed distributions, except where each square represents the number of galaxies in 15 Mpc by 15 Mpc from zero (white) to three times the average or more (black). The average number in each square is 44 so the expected Poisson standard deviation (σ) is 6.6. The measured σ is given below each plot, with an estimate of the structure contribution after subtracting the Poission contribution.
Click on the left plots or here to see an animated gif of the smoothing. The rms distance of moving the galaxies is shown by the length of the blue lines. The structural, as opposed to Poission, fluctuations drop below 10% after smoothing the galaxy distribution over scales greater than about 100 Mpc.
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| σmeasured=24.4 σstructure=23.5 | σmeasured=15.7 σstructure=14 | σmeasured=6.8 σstructure=2
(i.e. dominated by Poisson fluctuations) |
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