Skip to main content
SpringerLink
Log in

Time Series Analysis of Photospheric Magnetic Parameters of Flare-Quiet Versus Flaring Active Regions: Scaling Properties of Fluctuations

  • Published:
Solar Physics Aims and scope Submit manuscript

Abstract

Time series of photospheric magnetic parameters of solar active regions (ARs) are used to answer the question whether scaling properties of fluctuations embedded in such time series help to distinguish between flare-quiet and flaring ARs. We examine a total of 118 flare-quiet and 118 flaring AR patches, Helioseismic and Magnetic Imager Active Region Patches (called HARPs), which were observed from 2010 to 2016 by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). Specifically, the scaling exponent of fluctuations is derived applying the Detrended Fluctuation Analysis (DFA) method to a dataset of 8-day time series of 18 photospheric magnetic parameters at 12-min cadence for all HARPs under investigation. We first find a statistically significant difference in the distribution of the scaling exponent between the flare-quiet and flaring HARPs, in particular for some space-averaged, signed parameters associated with magnetic field line twist, electric current density, and current helicity. The flaring HARPs tend to show higher values of the scaling exponent compared to those of the flare-quiet ones, even though there is considerable overlap between their distributions. In addition, for both the flare-quiet and the flaring HARPs the DFA analysis indicates that i) time series of most of various magnetic parameters under consideration are non-stationary, and ii) time series of the total unsigned magnetic flux and the mean photospheric magnetic free energy density in general present a non-stationary, persistent property, while the total unsigned flux near magnetic polarity inversion lines and parameters related to current density show a non-stationary, anti-persistent trend in their time series.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

Similar content being viewed by others

References

  • Abry, P., Sellan, F.: 1996, The wavelet-based synthesis for fractional Brownian motion proposed by F. Sellan and Y. Meyer: Remarks and fast implementation. Appl. Comput. Harmon. Anal. 3(4), 377. DOI.

    Article  MathSciNet  MATH  Google Scholar 

  • Bardet, J.-M., Lang, G., Oppenheim, G., Philippe, A., Taqqu, M.S.: 2003, Generators of long-range dependent processes: A survey. In: Theory and Applications of Long-Range Dependence. https://hal.archives-ouvertes.fr/hal-00127929.

    MATH  Google Scholar 

  • Bobra, M.G., Couvidat, S.: 2015, Solar flare prediction using SDO/HMI vector magnetic field data with a machine-learning algorithm. Astrophys. J. 798(2), 135. DOI. ADS.

    Article  ADS  Google Scholar 

  • Bobra, M.G., Sun, X., Hoeksema, J.T., Turmon, M., Liu, Y., Hayashi, K., Barnes, G., Leka, K.D.: 2014, The Helioseismic and Magnetic Imager (HMI) vector magnetic field pipeline: SHARPs - space-weather HMI active region patches. Solar Phys. 289(9), 3549. DOI. ADS.

    Article  ADS  Google Scholar 

  • Couvidat, S., Schou, J., Hoeksema, J.T., Bogart, R.S., Bush, R.I., Duvall, T.L., Liu, Y., Norton, A.A., Scherrer, P.H.: 2016, Observables processing for the helioseismic and magnetic imager instrument on the solar dynamics observatory. Solar Phys. 291(7), 1887. DOI. ADS.

    Article  ADS  Google Scholar 

  • Deng, Y., Wang, J., Yan, Y., Zhang, J.: 2001, Evolution of magnetic nonpotentiality in NOAA AR 9077. Solar Phys. 204, 11. DOI. ADS.

    Article  ADS  Google Scholar 

  • Eke, A., Hermán, P., Bassingthwaighte, J., Raymond, G., Percival, D., Cannon, M., Balla, I., Ikrényi, C.: 2000, Physiological time series: Distinguishing fractal noises from motions. Pflügers Arch. 439(4), 403. DOI.

    Article  Google Scholar 

  • Falconer, D., Barghouty, A.F., Khazanov, I., Moore, R.: 2011, A tool for empirical forecasting of major flares, coronal mass ejections, and solar particle events from a proxy of active-region free magnetic energy. Space Weather 9(4), S04003. DOI. ADS.

    Article  ADS  Google Scholar 

  • Georgoulis, M.K.: 2012, Are solar active regions with major flares more fractal, multifractal, or turbulent than others? Solar Phys. 276(1–2), 161. DOI. ADS.

    Article  ADS  Google Scholar 

  • Georgoulis, M.K., Rust, D.M.: 2007, Quantitative forecasting of major solar flares. Astrophys. J. Lett. 661(1), L109. DOI. ADS.

    Article  ADS  Google Scholar 

  • Guo, X., Zhang, H., Yuan, T., Zhao, J., Xue, Z.: 2015, Detecting the temporal scaling behavior of the normalized difference vegetation index time series in China using a detrended fluctuation analysis. Remote Sens. 7(10), 12942. DOI. ADS.

    Article  ADS  Google Scholar 

  • Hardstone, R., Poil, S.-S., Schiavone, G., Jansen, R., Nikulin, V., Mansvelder, H., Linkenkaer-Hansen, K.: 2012, Detrended fluctuation analysis: A scale-free view on neuronal oscillations. Front. Physiol. 3, 450. DOI.

    Article  Google Scholar 

  • Hoeksema, J.T., Liu, Y., Hayashi, K., Sun, X., Schou, J., Couvidat, S., Norton, A., Bobra, M., Centeno, R., Leka, K.D., Barnes, G., Turmon, M.: 2014, The Helioseismic and Magnetic Imager (HMI) vector magnetic field pipeline: Overview and performance. Solar Phys. 289(9), 3483. DOI. ADS.

    Article  ADS  Google Scholar 

  • Holloway, P.M., Angelova, M., Lombardo, S., St Clair Gibson, A., Lee, D., Ellis, J.: 2014, Complexity analysis of sleep and alterations with insomnia based on non-invasive techniques. J. Roy. Soc. Interface 11(93), 20131112. DOI.

    Article  Google Scholar 

  • Kantelhardt, J.W., Ashkenazy, Y., Ivanov, P.C., Bunde, A., Havlin, S., Penzel, T., Peter, J.-H., Stanley, H.E.: 2002, Characterization of sleep stages by correlations in the magnitude and sign of heartbeat increments. Phys. Rev. E 65(5), 051908. DOI. ADS.

    Article  ADS  Google Scholar 

  • Király, A., Jánosi, I.M.: 2005, Detrended fluctuation analysis of daily temperature records: Geographic dependence over Australia. Meteorol. Atmos. Phys. 88(3–4), 119. DOI. ADS.

    Article  ADS  Google Scholar 

  • Kontogiannis, I., Georgoulis, M.K., Park, S.-H., Guerra, J.A.: 2017, Non-neutralized electric currents in solar active regions and flare productivity. Solar Phys. 292(11), 159. DOI. ADS.

    Article  ADS  Google Scholar 

  • Kontogiannis, I., Georgoulis, M.K., Park, S.-H., Guerra, J.A.: 2018, Testing and improving a set of morphological predictors of flaring activity. Solar Phys. 293(6), 96. DOI. ADS.

    Article  ADS  Google Scholar 

  • Kontogiannis, I., Georgoulis, M.K., Guerra, J.A., Park, S.-H., Bloomfield, D.S.: 2019, Which photospheric characteristics are most relevant to active-region coronal mass ejections? Solar Phys. 294(9), 130. DOI. ADS.

    Article  ADS  Google Scholar 

  • Lam, W.-S., Ray, W., Guzdar, P.N., Roy, R.: 2005, Measurement of Hurst exponents for semiconductor laser phase dynamics. Phys. Rev. Lett. 94(1), 010602. DOI. ADS.

    Article  ADS  Google Scholar 

  • Lee, E.-J., Park, S.-H., Moon, Y.-J.: 2018, Flare productivity of major flaring solar active regions: A time-series study of photospheric magnetic properties. Solar Phys. 293(12), 159. DOI. ADS.

    Article  ADS  Google Scholar 

  • Leka, K.D., Barnes, G.: 2003, Photospheric magnetic field properties of flaring versus flare-quiet active regions. II. Discriminant analysis. Astrophys. J. 595(2), 1296. DOI. ADS.

    Article  ADS  Google Scholar 

  • Leka, K.D., Barnes, G.: 2007, Photospheric magnetic field properties of flaring versus flare-quiet active regions. IV. A statistically significant sample. Astrophys. J. 656(2), 1173. DOI. ADS.

    Article  ADS  Google Scholar 

  • Lim, D., Moon, Y.-J., Park, J., Park, E., Lee, K., Lee, J.-Y., Jang, S.: 2019, Forecast of daily major flare probability using relationships between vector magnetic properties and flaring rates. J. Korean Astron. Soc. 52(4), 133. DOI. ADS.

    Article  ADS  Google Scholar 

  • Ma, Q.D.Y., Bartsch, R.P., Bernaola-Galván, P., Yoneyama, M., Ivanov, P.C.: 2010, Effect of extreme data loss on long-range correlated and anticorrelated signals quantified by detrended fluctuation analysis. Phys. Rev. E 81(3), 031101. DOI. ADS.

    Article  ADS  Google Scholar 

  • MacLachlan, G.A., Shenoy, A., Sonbas, E., Coyne, R., Dhuga, K.S., Eskandarian, A., Maximon, L.C., Parke, W.C.: 2013, The Hurst exponent of Fermi gamma-ray bursts. Mon. Not. Roy. Astron. Soc. 436(4), 2907. DOI. ADS.

    Article  ADS  Google Scholar 

  • Mandelbrot, B.B., van Ness, J.W.: 1968, Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10(4), 422. DOI. ADS.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Mason, J.P., Hoeksema, J.T.: 2010, Testing automated solar flare forecasting with 13 years of Michelson Doppler imager magnetograms. Astrophys. J. 723(1), 634. DOI. ADS.

    Article  ADS  Google Scholar 

  • Park, S-h., Chae, J., Wang, H.: 2010, Productivity of solar flares and magnetic helicity injection in active regions. Astrophys. J. 718(1), 43. DOI. ADS.

    Article  ADS  Google Scholar 

  • Park, S.-H., Lee, J., Choe, G.S., Chae, J., Jeong, H., Yang, G., Jing, J., Wang, H.: 2008, The variation of relative magnetic helicity around major flares. Astrophys. J. 686(2), 1397. DOI. ADS.

    Article  ADS  Google Scholar 

  • Peng, C.-K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E., Goldberger, A.L.: 1994, Mosaic organization of DNA nucleotides. Phys. Rev. E 49(2), 1685. DOI. ADS.

    Article  ADS  Google Scholar 

  • Peng, C.-K., Havlin, S., Stanley, H.E., Goldberger, A.L.: 1995, Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos 5(1), 82. DOI. ADS.

    Article  ADS  Google Scholar 

  • Pesnell, W.D., Thompson, B.J., Chamberlin, P.C.: 2012, The Solar Dynamics Observatory (SDO). Solar Phys. 275(1–2), 3. DOI. ADS.

    Article  ADS  Google Scholar 

  • Ravindra, B., Venkatakrishnan, P., Tiwari, S.K., Bhattacharyya, R.: 2011, Evolution of currents of opposite signs in the flare-productive solar active region NOAA 10930. Astrophys. J. 740(1), 19. DOI. ADS.

    Article  ADS  Google Scholar 

  • Romano, P., Zuccarello, F.: 2007, Photospheric magnetic evolution of super active regions. Astron. Astrophys. 474(2), 633. DOI. ADS.

    Article  ADS  Google Scholar 

  • Scherrer, P.H., Schou, J., Bush, R.I., Kosovichev, A.G., Bogart, R.S., Hoeksema, J.T., Liu, Y., Duvall, T.L., Zhao, J., Title, A.M., Schrijver, C.J., Tarbell, T.D., Tomczyk, S.: 2012, The Helioseismic and Magnetic Imager (HMI) investigation for the Solar Dynamics Observatory (SDO). Solar Phys. 275(1–2), 207. DOI. ADS.

    Article  ADS  Google Scholar 

  • Schrijver, C.J.: 2016, The nonpotentiality of coronae of solar active regions, the dynamics of the surface magnetic field, and the potential for large flares. Astrophys. J. 820(2), 103. DOI. ADS.

    Article  ADS  Google Scholar 

  • Song, Q., Zhang, J., Yang, S.-H., Liu, Y.: 2013, Flares and magnetic non-potentiality of NOAA AR 11158. Res. Astron. Astrophys. 13(2), 226. DOI. ADS.

    Article  ADS  Google Scholar 

  • Sun, X., Hoeksema, J.T., Liu, Y., Wiegelmann, T., Hayashi, K., Chen, Q., Thalmann, J.: 2012, Evolution of magnetic field and energy in a major eruptive active region based on SDO/HMI observation. Astrophys. J. 748(2), 77. DOI. ADS.

    Article  ADS  Google Scholar 

  • Suthar, Y., Venkatakrishnan, P., Ravindra, B., Jaaffrey, S.N.A.: 2014, The evolution of the net twist current and the net shear current in active region NOAA 10930. Solar Phys. 289(7), 2459. DOI. ADS.

    Article  ADS  Google Scholar 

  • Suyal, V., Prasad, A., Singh, H.P.: 2009, Nonlinear time series analysis of sunspot data. Solar Phys. 260(2), 441. DOI. ADS.

    Article  ADS  Google Scholar 

  • Tarnopolski, M.: 2016, On the relationship between the Hurst exponent, the ratio of the mean square successive difference to the variance, and the number of turning points. Physica A 461, 662. DOI. ADS.

    Article  MATH  ADS  Google Scholar 

  • Telesca, L., Lasaponara, R., Lanorte, A.: 2008, Intra-annual dynamical persistent mechanisms in Mediterranean ecosystems revealed spot-vegetation time series. Ecol. Complex. 5(2), 151. DOI. Current Food-Web Theory.

    Article  Google Scholar 

  • Toriumi, S., Wang, H.: 2019, Flare-productive active regions. Living Rev. Solar Phys. 16(1), 3. DOI. ADS.

    Article  ADS  Google Scholar 

  • Toriumi, S., Schrijver, C.J., Harra, L.K., Hudson, H., Nagashima, K.: 2017, Magnetic properties of solar active regions that govern large solar flares and eruptions. Astrophys. J. 834(1), 56. DOI. ADS.

    Article  ADS  Google Scholar 

  • Vandewalle, N., Ausloos, M.: 1997, Coherent and random sequences in financial fluctuations. Physica A 246(3), 454. DOI. ADS.

    Article  ADS  Google Scholar 

  • Vemareddy, P., Venkatakrishnan, P., Karthikreddy, S.: 2015, Flux emergence in the solar active region NOAA 11158: The evolution of net current. Res. Astron. Astrophys. 15(9), 1547. DOI. ADS.

    Article  ADS  Google Scholar 

  • Welsch, B.T., Li, Y., Schuck, P.W., Fisher, G.H.: 2009, What is the relationship between photospheric flow fields and solar flares? Astrophys. J. 705(1), 821. DOI. ADS.

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors would like to thank an anonymous referee for valuable comments and suggestions. This work was supported by the BK21 plus program through the National Research Foundation (NRF) funded by the Ministry of Education of Korea, the Basic Science Research Program through the NRF funded by the Ministry of Education (NRF-2019R1A2C1002634), the Korea Astronomy and Space Science Institute (KASI) under the R&D program “Study on the Determination of Coronal Physical Quantities using Solar Multi-wavelength Images” (project No. 2019-1-850-02) supervised by the Ministry of Science and ICT, and Institute for Information & communications Technology Promotion (IITP) grant funded by the Korea government (MSIP) (2018-0-01422, Study on analysis and prediction technique of solar flares). The data used in this work are courtesy of the NASA/SDO and HMI science team. This research has made use of NASA’s Astrophysics Data System (ADS). S.-H.P. acknowledges support from the Institute for Space-Earth Environmental Research (ISEE) of Nagoya University as well as MEXT/JSPS KAKENHI Grant Number JP15H05814, Project for Solar-Terrestrial Environment Prediction (PSTEP).

Author information

Authors and Affiliations

  1. School of Space Research, Kyung Hee University, Yongin, Republic of Korea

    Eo-Jin Lee & Yong-Jae Moon

  2. Institute for Space-Earth Environmental Research (ISEE), Nagoya University, Nagoya, Japan

    Sung-Hong Park

  3. Department of Astronomy and Space Science, Kyung Hee University, Yongin, Republic of Korea

    Yong-Jae Moon

Authors
  1. Eo-Jin Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sung-Hong Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yong-Jae Moon
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sung-Hong Park.

Ethics declarations

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lee, EJ., Park, SH. & Moon, YJ. Time Series Analysis of Photospheric Magnetic Parameters of Flare-Quiet Versus Flaring Active Regions: Scaling Properties of Fluctuations. Sol Phys 295, 123 (2020). https://doi.org/10.1007/s11207-020-01690-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11207-020-01690-4

Keywords

Search

Navigation