False-alarm probability in relation to over-sampled power spectra, with application to Super-Kamiokande solar neutrino data

The term "false-alarm probability" denotes the probability that at least one out of M independent power values in a prescribed search band of a power spectrum computed from a white-noise time series is expected to be as large as or larger than a given value. The usual formula is based on the assumption that powers are distributed exponentially, as one expects for power measurements of normally distributed random noise. However, in practice one typically examines peaks in an over-sampled power spectrum. It is therefore more appropriate to compare the strength of a particular peak with the distribution of peaks in over-sampled power spectra derived from normally distributed random noise. We show that this leads to a formula for the false-alarm probability that is more conservative than the familiar formula. We also show how to combine these results with a Bayesian method for estimating the probability of the null hypothesis (that there is no oscillation in the time series), and we discuss as an example the application of these procedures to Super-Kamiokande solar neutrino data

Analysis of Super-Kamiokande 5-day Measurements of the Solar Neutrino Flux

Data in 5-day bins, recently released by the Super-Kamiodande Consortium, has been analyzed by a likelihood procedure that has certain advantages over the Lomb-Scargle procedure used by the consortium. The two most prominent peaks in the power spectrum of the 10-day data were at 9.42 y-1 and 26.57 y-1, and it was clear that one was an alias of the other caused by the regularity of the binning. There were reasons to believe that the 9.42 y-1 peak was an alias of the 26.57 y-1 peak, but analysis of the 5-day data makes it clear that the reverse is the case. In addition to a strong peak near 9.42 y-1, we find peaks at 43.72 y-1and at 39.28 y-1. After comparing this analysis with a power-spectrum analysis of magnetic-field data, we suggest that these three peaks may be attributed to a harmonic of the solar rotation rate and to an r-mode oscillation with spherical harmonic indices l = 2, m = 2.Comment: Accepted for publication in Astrophysical Journa

Time-Series Analysis of Super-Kamiokande Measurements of the Solar Neutrino Flux

The Super-Kamiokande Consortium has recently released data suitable for time-series analysis. The binning is highly regular: the power spectrum of the acquisition times has a huge peak (power S > 120) at the frequency (in cycles per year) 35.98 (period 10.15 days), where power measurements are such that the probability of obtaining a peak of strength S or more by chance at a specified frequency is exp(-S). This inevitably leads to severe aliasing of the power spectrum. The strongest peak in the range 0 - 100 in a power spectrum formed by a likelihood procedure is at 26.57 (period 13.75 days) with S = 11.26. For the range 0 - 40, the second-strongest peak is at 9.42 (period 38.82 days) with S = 7.3. Since 26.57 + 9.42 = 35.99, we conclude that the weaker peak at 9.42 is an alias of the stronger peak at 26.57. We note that 26.57 falls in the band 26.36 - 27.66, formed from twice the range of synodic rotation frequencies of an equatorial section of the Sun for normalized radius larger than 0.1. Oscillations at twice the rotation frequency, attributable to "m = 2" structures, are not uncommon in solar data. We find from the shuffle test that the probability of obtaining a peak of S = 11.26 or more by chance in this band is 0.1 %. This new result therefore supports at the 99.9% confidence level previous evidence, found in Homestake and GALLEX-GNO data, for rotational modulation of the solar neutrino flux. The frequency 25.57 points to a source of modulation at or near the tachocline.Comment: 15 pages, 8 figure

Rapid fluctuations in solar flares

Study of rapid fluctuations in the emission of radiation from solar flares provides a promising approach for probing the magneto-plasma structure and plasma processes that are responsible for a flare. It is proposed that elementary flare bursts in X-ray and microwave emission may be attributed to fine structure of the coronal magnetic field, related to the aggregation of photospheric magnetic field into magnetic knots. Fluctuations that occur on a subsecond time-scale may be due to magnetic islands that develop in current sheets during magnetic reconnection. The impulsive phase may sometimes represent the superposition of a large number of the elementary energy-release processes responsible for elementary flare bursts. If so, the challenge of trying to explain the properties of the impulsive phase in terms of the properties of the elementary processes must be faced. Magnetic field configurations that might produce solar flares are divided into a number of categories, depending on: whether or not there is a filament; whether there is no current sheet, a closed current sheet, or an open current sheet; and whether the filament erupts into the corona, or is ejected completely from the Sun's atmosphere. Analysis of the properties of these possible configurations is compared with different types of flares, and to Bai's subdivision of gamma-ray/proton events

Uncertainty in estimates of the number of extraterrestrial civilizations

An estimation of the number N of communicative civilizations is made by means of Drake's formula which involves the combination of several quantities, each of which is to some extent uncertain. It is shown that the uncertainty in any quantity may be represented by a probability distribution function, even if that quantity is itself a probability. The uncertainty of current estimates of N is derived principally from uncertainty in estimates of the lifetime of advanced civilizations. It is argued that this is due primarily to uncertainty concerning the existence of a Galactic Federation which is in turn contingent upon uncertainty about whether the limitations of present-day physics are absolute or (in the event that there exists a yet undiscovered hyperphysics) transient. It is further argued that it is advantageous to consider explicitly these underlying assumptions in order to compare the probable numbers of civilizations operating radio beacons, permitting radio leakage, dispatching probes for radio surveillance for dispatching vehicles for manned surveillance

A theory of theories

Theory comparisons with facts obtained by reduction of observed dat