Analysis of Bimodality in Histograms Formed from GALLEX and GNO Solar Neutrino Data

Abstract

Abstract.A histogram display of the solar neutrino capture-rate measurements made by the GALLEX experiment appears to be bimodal, but that of the follow-on GNO experiment does not. To assess the significance of these results, we introduce a "bimodality index" based on the probability-transform procedure. This confirms that the GALLEX measurements are indeed bimodal (at the 99.98 percent confidence level), and that the GNO measurements are not. Tracking the bimodality index as a function of time shows that the strongest contribution to bimodality comes from runs 42 to 62, i.e. from the time interval 1995.1 to 1996.9. The bimodality index for the first half (runs 1 through 33) is 2.56, whereas that for the second half (runs 33 through 65) is 7.05. Power-spectrum analysis shows a similar distinction: the peaks in the power spectrum formed from the second half are stronger than those in the power spectrum formed from the first half, suggesting that bimodality and rotational modulation are related.2

Reexamination of Possible Bimodality of GALLEX Solar-Neutrino Data

“…It has been known for some time that the published capture-rate measurements derived from the GALLEX solar neutrino experiment are bimodal in the sense that the histogram formed from these data has two distinct peaks (Sturrock and Scargle, 2001). We recently introduced a "bimodality index" to provide an objective measurement of bimodality (Sturrock, 2008). This analysis confirmed that the published capture rate measurements for the GALLEX experiment are indeed bimodal, but those for the GNO experiment are not.…”

“…In order to assign a significance level to the bimodality of a histogram, we have recently introduced a "bimodality index" B (Sturrock, 2008). This index has the property that, if the neutrino flux is constant, we expect that B will be distributed exponentially so that the probability of obtaining the value B or more is e −B .…”

An Asymmetric Bimodal Double Regression Model

“…However, fitting data can be difficult when their distribution is bimodal, which occurs commonly in practice: in astrophysics, the metallicity of the globular cluster system in the Milky Way (see [1]); in ecology, the tree cover of moist savanna and tropical forest ecosystems (see [2]); in genetics, gene expression measurements (see [3]). Other practical examples of bimodality in data can be seen in [4][5][6]. In the literature, there are many proposals discussing bimodal distributions; e.g., the works of [7][8][9][10][11][12].…”