RHESSI microflare statistics.: I.: Flare-finding and frequency distributions

We present the first in-depth statistical survey of all X-ray microflares observed by RHESSI between 2002 March and 2007 March, a total of 25,705 events, an order of magnitude larger then previous studies. These microflares were found using a new flare-finding algorithm designed to search the 6-12 keV count rate when RHESSI's full sensitivity was available in order to find the smallest events. The peak and total count rate are automatically obtained along with count spectra at the peak and the microflare centroid position. Our microflare magnitudes are below GOES C class, on average GOES A class (background subtracted). They are found to occur only in active regions, not in the quiet'' Sun, and are similar to large flares. The monthly average microflaring rate is found to vary with the solar cycle and ranges from 90 to 5 flares a day during active and quiet times, respectively. Most flares are found to be impulsive (74%), with rise times shorter than decay times. The mean flare duration is similar to 6 minutes with a 1 minute minimum set by the flare-finding algorithm. The frequency distributions of the peak count rate in the energy bands, 3-6, 6-12, and 12-25 keV, can be represented by power-law distributions with a negative power-law index of 1.50 +/- 0.03, 1.51 +/- 0.03, and 1.58 +/- 0.02, respectively. We find that these power-law indices are constant as a function of time. The X-ray photon spectra for individual events can be approximated with a power-law spectrum [dJ/d(hv) similar to (hv)(-gamma)]. Using the ratio of photon fluxes between 10-15 and 15-20 keV, we find 4 < gamma < 12, with an average of 7.4. Based on these values, the nonthermal power is calculated. The microflare occurrence frequency varies with the rate of energy release consistent with a power law with an exponent of -1.7 +/- 0.1. We estimate the total energy flux deposited in active regions by microflare-associated accelerated electrons (> 10 keV) over the five years of observations to be, on average, below 1026 erg s(-1).