Temporal Variations of the Power-Law Distribution of Low-Chromospheric Bright Points in a Solar Active Region

The power-law distribution of the energy of flares and microflares is an important character of solar activities. Investigating its attributes and temporal variations helps to study the transmission of energy and the heating of the solar corona. In this observation, we study the temporal variations of the frequency distribution of low-chromospheric bright points (BPs), and probe the pattern of energy release in low solar atmospheres. We utilize Ca Ⅱ H λ3968.5 monograms of NOAA AR 10930 acquired by Hinode/SOT and recognize BPs with a two-dimensional region-labelling algorithm. On the time sequence with a time span of 124h and a field-of-view of 202″.4×85″.3, a sample of 2.99×10⁵ BPs is identified, with a numerical density of 24.15±6.34 per square arcminute.The main results are summarized as follows: (1) The instantaneous frequency distribution of BP's scale (L=L_xL_y) virtually observes the power-law and self-similarity. (2) The value and signal-to-noise ratio of BP's production decrease with the increase of BP's scale. Numerous small-scale BPs could be a valid source of energy for the heating of upper atmosphere. For instance, BPs with a scale smaller than 4″ share approximately 53.23% of the sample's total light flux budget. (3) As the active region decays, the numerical density of small-scale BPs also decreases. (4) The distribution of the sample set's scale observes the power-law, with a dispersion index σ The power-law distribution of the energy of flares and microflares is an important character of solar activities. Investigating its attributes and temporal variations helps to study the transmission of energy and the heating of the solar corona. In this observation, we study the temporal variations of the frequency distribution of low-chromospheric bright points (BPs), and probe the pattern of energy release in low solar atmospheres. We utilize Ca Ⅱ H λ3968.5 monograms of NOAA AR 10930 acquired by Hinode/SOT and recognize BPs with a two-dimensional region-labelling algorithm. On the time sequence with a time span of 124h and a field-of-view of 202″.4×85″.3, a sample of 2.99×10⁵ BPs is identified, with a numerical density of 24.15±6.34 per square arcminute.The main results are summarized as follows: (1) The instantaneous frequency distribution of BP's scale (L=L_xL_y) virtually observes the power-law and self-similarity. (2) The value and signal-to-noise ratio of BP's production decrease with the increase of BP's scale. Numerous small-scale BPs could be a valid source of energy for the heating of upper atmosphere. For instance, BPs with a scale smaller than 4″ share approximately 53.23% of the sample's total light flux budget. (3) As the active region decays, the numerical density of small-scale BPs also decreases. (4) The distribution of the sample set's scale observes the power-law, with a dispersion index σ(ζ) of 4%. The power-law index γ of the observed and low-noise (L≤8″) samples are respectively 1.97 and 2.12. (5) However, within the observation time, the overall power-law index γ does not converge. The relationship between the power-law index and the time-span of observation is serrated: in quiet times γ gradually increases, while in active moments γ decreases sharply. (6) The instantaneous γ is reversely proportional to the instantaneous total light flux. Even after filtering large-scale BPs (L > 8″), the low-noise sample, which contains only middle- and small-scale BPs, still shows such correlation. This quashes our initial suspicion that the numerical calculation of γ is rigged by the injection of few large BPs into the sample pool; the observed relationship between large events and the dropping of γ is intrinsic. Solar activities not only produces middle and large scale BPs, but also changes the entire pattern of BP's distribution and hence lowers γ.(ζ) of 4%. The power-law index γ of the observed and low-noise (L≤8″) samples are respectively 1.97 and 2.12. (5) However, within the observation time, the overall power-law index γ does not converge. The relationship between the power-law index and the time-span of observation is serrated: in quiet times γ gradually increases, while in active moments γ decreases sharply. (6) The instantaneous γ is reversely proportional to the instantaneous total light flux. Even after filtering large-scale BPs (L > 8″), the low-noise sample, which contains only middle- and small-scale BPs, still shows such correlation. This quashes our initial suspicion that the numerical calculation of γ is rigged by the injection of few large BPs into the sample pool; the observed relationship between large events and the dropping of γ is intrinsic. Solar activities not only produces middle and large scale BPs, but also changes the entire pattern of BP's distribution and hence lowers γ.