UPPER LIMIT ON PERIODICITY IN THE 3-DIMENSIONAL LARGE-SCALE DISTRIBUTION OF MATTER

Recently Broadhurst et al. (hereafter BEKS) found that there was '' an apparent regularity ... with a scale of 128 h-1 Mpc'' in the large-scale distribution of galaxies down one line of sight. Here we present a search for large-scale periodicity in the three-dimensional distribution of 268 Mg II QSO absorption systems which are distributed over 60% of the sky, at redshifts 0.1-2.0. We assume that the large-scale distribution of these absorption systems is the same as that of other luminous galaxies because they arise in luminous intervening galaxies similar to those studied by BEKS, they cluster on small scales like galaxies, and the gas in a subset of them makes the same contribution to the mass density of the universe as do stars and gas in contemporary galaxies. We have calculated the scalar three-dimensional comoving separations of all pairs of absorption systems, and seached for peaks in the power spectrum of the distribution of those separations. We have also searched for quasi-periodic signals with power dispersed over a range of frequencies, and considered cosmologies with 0 less-than-or-equal-to q0 less-than-or-equal-to 1. There is no significant periodicity on any scale from 10 to 210 h-1 Mpc. Our 95% confidence limits on the power at any wavelength in this range are factors of 0.1-0.001 below that in the BEKS data at 128 h-1 Mpc, because we remove all clustering on scales of under 20 h-1 Mpc, making each absorber an independent sample of the large-scale distribution, and because we use three-dimensional separations rather than one-dimensional positions. We make extensive use of randomized samples to determine the sensitivity of our data to various periodic and quasi-periodic signals, and we show that we are limited by the random noise associated with the small size of our sample and not by the systematic effects of incompleteness, which means that our inhomogeneous sample should be as good as a homogeneous one of the same size. We find that the structure and power apparent in the BEKS data should have produced a detectable signal in the Mg II absorption system data. Our 95% confidence upper limit on the amplitude of a possible periodic fluctuation in the density of galaxies is between one-fourth and three-fourths of the amplitude implied by the BEKS data, depending on the extent to which the wavelength varies and the phase of the signal drifts down lines of sight. These limits are quite general, and they are not restricted to any specific three-dimensional geometry for the periodicity, so we conclude that the amplitude of the periodicity indicated down the BEKS line of sight is not representative of the average of lines of sight in many directions, from many positions. Our sensitivity is partly due to our much larger sample size. The comoving volume of the universe out to z = 2 can be partitioned into 32,500 cubes, with 128 h-1 Mpc sides. Our main sample has 35,778 three-dimensional separations, with a mean length of 2377 h-1 Mpc, which together pass through each such cube an average of 20 times. The BEKS data samples a volume which is 10(6) times smaller, amounting to only 1% of a single cube. Our analysis also supports the conclusion of Kaiser & Peacock, that the power detected by BEKS is most likely the alias of power arising from small-scale clustering. In appendices we described how QSO absorption systems sample the three-dimensional population of absorbers, how three-dimensional positions can be represented by their scalar separations, and various consistency checks. We also give general descriptions of the form and use of power spectra and the use of randomized samples for the analysis of inhomogeneous samples.