Solar Physics

, 292:48 | Cite as

Analysis of the Flux Growth Rate in Emerging Active Regions on the Sun

  • V. I. Abramenko
  • A. S. Kutsenko
  • O. I. Tikhonova
  • V. B. Yurchyshyn


We studied the emergence process of 42 active regions (ARs) by analyzing the time derivative, \(R(t)\), of the total unsigned flux. Line-of-sight magnetograms acquired by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) were used. A continuous piecewise linear fitting to the \(R(t)\)-profile was applied to detect an interval, \(\Delta t_{2}\), of nearly constant \(R(t)\) covering one or several local maxima. The magnitude of \(R(t)\) averaged over \(\Delta t_{2}\) was accepted as an estimate of the maximum value of the flux growth rate, \(R_{\mathrm{MAX}}\), which varies in a range of \((0.5\,\mbox{--}\,5)\times10^{20}~\mbox{Mx}\,\mbox{hour}^{-1}\) for ARs with a maximum total unsigned flux of \((0.5\,\mbox{--}\,3)\times 10^{22}~\mbox{Mx}\). The normalized flux growth rate, \(R_{\mathrm{N}}\), was defined under the assumption that the saturated total unsigned flux, \(F_{\mathrm{MAX}}\), equals unity. Out of 42 ARs in our initial list, 36 events were successfully fitted, and they form two subsets (with a small overlap of eight events): the ARs with a short (\(<13\) hours) interval \(\Delta t_{2}\) and a high (\(>0.024~\mbox{hour}^{-1}\)) normalized flux emergence rate, \(R_{\mathrm{N}}\), form the “rapid” emergence event subset. The second subset consists of “gradual” emergence events, and it is characterized by a long (\(>13\) hours) interval \(\Delta t_{2}\) and a low \(R_{\mathrm{N}}\) (\(<0.024~\mbox{hour}^{-1}\)). In diagrams of \(R_{\mathrm{MAX}}\) plotted versus \(F_{\mathrm{MAX}}\), the events from different subsets do not overlap, and each subset displays an individual power law. The power-law index derived from the entire ensemble of 36 events is \(0.69 \pm 0.10\). The rapid emergence is consistent with a two-step emergence process of a single twisted flux tube. The gradual emergence is possibly related to a consecutive rising of several flux tubes emerging at nearly the same location in the photosphere.


Active regions, magnetic fields Magnetic fields, photosphere 



SDO is a mission for NASA’s Living With a Star (LWS) program. The SDO/HMI data were provided by the Joint Science Operation Center (JSOC). The reported study was supported by the RFBR research projects 16-02-00221 A and 16-42-910493 and the Presidium of the Russian Academy of Science Program 7. VYu acknowledges support from AFOSR FA9550-15-1-0322 and NSF AGS-1250818 grants and Korea Astronomy and Space Science Institute. We thank the International Space Science Institute for enabling interesting discussions. We are grateful to the anonymous referee for critical comments and suggestions that helped us very much to improve the article.

Supplementary material

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • V. I. Abramenko
    • 1
    • 2
  • A. S. Kutsenko
    • 1
  • O. I. Tikhonova
    • 1
  • V. B. Yurchyshyn
    • 3
    • 4
  1. 1.Crimean Astrophysical ObservatoryRussian Academy of ScienceBakhchisarayRussia
  2. 2.Central (Pulkovo) Astronomical ObservatoryRussian Academy of Science (GAO RAN)Saint-PetersburgRussia
  3. 3.Big Bear Solar ObservatoryNew Jersey Institute of TechnologyBig Bear CityUSA
  4. 4.Korea Astronomy and Space Science InstituteDaejeonSouth Korea

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