The statistical properties of astrophysical transients: The importance of solar flares for coronal heating and the distances to gamma ray burst sources

Two important unsolved problems in astrophysics are the source of heating of the solar corona and the distances to cosmic gamma-ray bursts. These seemingly disparate phenomena are linked by the use of statistical distributions to reveal some of their properties.; The idea that solar coronal heating may be related to solar flares is investigated by examining how the power in flares relates to their X-ray intensity distributions. It is shown that a simple extrapolation of the flare distribution to lower ("nanoflare") energies cannot explain coronal heating unless correlations among certain flare properties exist. Evidence for at least one such correlation is shown to exist by the examination of the relationship between hard and soft X-ray flare distributions. Some suggestions for integrating "nanoflare" heating theories with avalanche models are given. Because of the nature of the observations, special statistical techniques are used to extract the distributions of interest.; These techniques are also used to find the distributions of gamma-ray burst fluxes and durations to test the homogeneity of the burst spatial distribution. These techniques also for the first time allow fluence distributions to be accurately obtained from the data, which is especially important if the distribution of burst total energy is narrower than the distribution of peak energy release rate. Correlations between burst duration and some "standard candle" measures are used in tests of the cosmological time dilation hypothesis. Although as a result of the new statistical techniques more data was utilized than in previous tests, the tests are still inconclusive.