skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A Bayesian Approach to Period Searching in Solar Coronal Loops

Abstract

We have applied a Bayesian generalized Lomb–Scargle period searching algorithm to movies of coronal loop images obtained with the Hinode X-ray Telescope (XRT) to search for evidence of periodicities that would indicate resonant heating of the loops. The algorithm makes as its only assumption that there is a single sinusoidal signal within each light curve of the data. Both the amplitudes and noise are taken as free parameters. It is argued that this procedure should be used alongside Fourier and wavelet analyses to more accurately extract periodic intensity modulations in coronal loops. The data analyzed are from XRT Observation Program 129C: “MHD Wave Heating (Thin Filters),” which occurred during 2006 November 13 and focused on active region 10293, which included coronal loops. The first data set spans approximately 10 min with an average cadence of 2 s, 2″ per pixel resolution, and used the Al-mesh analysis filter. The second data set spans approximately 4 min with a 3 s average cadence, 1″ per pixel resolution, and used the Al-poly analysis filter. The final data set spans approximately 22 min at a 6 s average cadence, and used the Al-poly analysis filter. In total, 55 periods of sinusoidal coronal loop oscillationsmore » between 5.5 and 59.6 s are discussed, supporting proposals in the literature that resonant absorption of magnetic waves is a viable mechanism for depositing energy in the corona.« less

Authors:
;  [1]
  1. Montana State University, P.O. Box 173840 Bozeman, MT 59717-3840 (United States)
Publication Date:
OSTI Identifier:
22661333
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 837; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ABSORPTION; ALGORITHMS; AMPLITUDES; APPROXIMATIONS; DATA ANALYSIS; GAMMA RADIATION; MAGNETOHYDRODYNAMICS; MODULATION; OSCILLATIONS; PERIODICITY; RESOLUTION; SUN; TELESCOPES; VISIBLE RADIATION; X RADIATION

Citation Formats

Scherrer, Bryan, and McKenzie, David. A Bayesian Approach to Period Searching in Solar Coronal Loops. United States: N. p., 2017. Web. doi:10.3847/1538-4357/AA5D59.
Scherrer, Bryan, & McKenzie, David. A Bayesian Approach to Period Searching in Solar Coronal Loops. United States. doi:10.3847/1538-4357/AA5D59.
Scherrer, Bryan, and McKenzie, David. Wed . "A Bayesian Approach to Period Searching in Solar Coronal Loops". United States. doi:10.3847/1538-4357/AA5D59.
@article{osti_22661333,
title = {A Bayesian Approach to Period Searching in Solar Coronal Loops},
author = {Scherrer, Bryan and McKenzie, David},
abstractNote = {We have applied a Bayesian generalized Lomb–Scargle period searching algorithm to movies of coronal loop images obtained with the Hinode X-ray Telescope (XRT) to search for evidence of periodicities that would indicate resonant heating of the loops. The algorithm makes as its only assumption that there is a single sinusoidal signal within each light curve of the data. Both the amplitudes and noise are taken as free parameters. It is argued that this procedure should be used alongside Fourier and wavelet analyses to more accurately extract periodic intensity modulations in coronal loops. The data analyzed are from XRT Observation Program 129C: “MHD Wave Heating (Thin Filters),” which occurred during 2006 November 13 and focused on active region 10293, which included coronal loops. The first data set spans approximately 10 min with an average cadence of 2 s, 2″ per pixel resolution, and used the Al-mesh analysis filter. The second data set spans approximately 4 min with a 3 s average cadence, 1″ per pixel resolution, and used the Al-poly analysis filter. The final data set spans approximately 22 min at a 6 s average cadence, and used the Al-poly analysis filter. In total, 55 periods of sinusoidal coronal loop oscillations between 5.5 and 59.6 s are discussed, supporting proposals in the literature that resonant absorption of magnetic waves is a viable mechanism for depositing energy in the corona.},
doi = {10.3847/1538-4357/AA5D59},
journal = {Astrophysical Journal},
number = 1,
volume = 837,
place = {United States},
year = {Wed Mar 01 00:00:00 EST 2017},
month = {Wed Mar 01 00:00:00 EST 2017}
}
  • We perform a Bayesian parameter inference in the context of resonantly damped transverse coronal loop oscillations. The forward problem is solved in terms of parametric results for kink waves in one-dimensional flux tubes in the thin tube and thin boundary approximations. For the inverse problem, we adopt a Bayesian approach to infer the most probable values of the relevant parameters, for given observed periods and damping times, and to extract their confidence levels. The posterior probability distribution functions are obtained by means of Markov Chain Monte Carlo simulations, incorporating observed uncertainties in a consistent manner. We find well-localized solutions inmore » the posterior probability distribution functions for two of the three parameters of interest, namely the Alfven travel time and the transverse inhomogeneity length scale. The obtained estimates for the Alfven travel time are consistent with previous inversion results, but the method enables us to additionally constrain the transverse inhomogeneity length scale and to estimate real error bars for each parameter. When observational estimates for the density contrast are used, the method enables us to fully constrain the three parameters of interest. These results can serve to improve our current estimates of unknown physical parameters in coronal loops and to test the assumed theoretical model.« less
  • A previous work of ours found the best agreement between EUV light curves observed in an active region core (with evidence of super-hot plasma) and those predicted from a model with a random combination of many pulse-heated strands with a power-law energy distribution. We extend that work by including spatially resolved strand modeling and by studying the evolution of emission along the loops in the EUV 94 Å and 335 Å channels of the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. Using the best parameters of the previous work as the input of the present one, we findmore » that the amplitude of the random fluctuations driven by the random heat pulses increases from the bottom to the top of the loop in the 94 Å channel and from the top to the bottom in the 335 Å channel. This prediction is confirmed by the observation of a set of aligned neighboring pixels along a bright arc of an active region core. Maps of pixel fluctuations may therefore provide easy diagnostics of nanoflaring regions.« less
  • Magnetic field extrapolation is an important tool to study the three-dimensional (3D) solar coronal magnetic field, which is difficult to directly measure. Various analytic models and numerical codes exist, but their results often drastically differ. Thus, a critical comparison of the modeled magnetic field lines with the observed coronal loops is strongly required to establish the credibility of the model. Here we compare two different non-potential extrapolation codes, a nonlinear force-free field code (CESE–MHD–NLFFF) and a non-force-free field (NFFF) code, in modeling a solar active region (AR) that has a sigmoidal configuration just before a major flare erupted from themore » region. A 2D coronal-loop tracing and fitting method is employed to study the 3D misalignment angles between the extrapolated magnetic field lines and the EUV loops as imaged by SDO /AIA. It is found that the CESE–MHD–NLFFF code with preprocessed magnetogram performs the best, outputting a field that matches the coronal loops in the AR core imaged in AIA 94 Å with a misalignment angle of ∼10°. This suggests that the CESE–MHD–NLFFF code, even without using the information of the coronal loops in constraining the magnetic field, performs as good as some coronal-loop forward-fitting models. For the loops as imaged by AIA 171 Å in the outskirts of the AR, all the codes including the potential field give comparable results of the mean misalignment angle (∼30°). Thus, further improvement of the codes is needed for a better reconstruction of the long loops enveloping the core region.« less
  • We report decaying quasi-periodic intensity oscillations in the X-ray (6–12 keV) and extreme-ultraviolet (EUV) channels (131, 94, 1600, 304 Å) observed by the Fermi Gamma-ray Burst Monitor and Solar Dynamics Observatory/Atmospheric Imaging Assembly (AIA), respectively, during a C-class flare. The estimated periods of oscillation and decay time in the X-ray channel (6–12 keV) were about 202 and 154 s, respectively. A similar oscillation period was detected at the footpoint of the arcade loops in the AIA 1600 and 304 Å channels. Simultaneously, AIA hot channels (94 and 131 Å) reveal propagating EUV disturbances bouncing back and forth between the footpointsmore » of the arcade loops. The period of the oscillation and decay time were about 409 and 1121 s, respectively. The characteristic phase speed of the wave is about 560 km s{sup −1} for about 115 Mm of loop length, which is roughly consistent with the sound speed at the temperature about 10–16 MK (480–608 km s{sup −1}). These EUV oscillations are consistent with the Solar and Heliospheric Observatory/Solar Ultraviolet Measurement of Emitted Radiation Doppler-shift oscillations interpreted as the global standing slow magnetoacoustic wave excited by a flare. The flare occurred at one of the footpoints of the arcade loops, where the magnetic topology was a 3D fan-spine with a null-point. Repetitive reconnection at this footpoint could have caused the periodic acceleration of non-thermal electrons that propagated to the opposite footpoint along the arcade and that are precipitating there, causing the observed 202 s periodicity. Other possible interpretations, e.g., the second harmonics of the slow mode, are also discussed.« less
  • In solar coronal loops, thermal non-equilibrium (TNE) is a phenomenon that can occur when the heating is both highly stratified and quasi-constant. Unambiguous observational identification of TNE would thus permit us to strongly constrain heating scenarios. While TNE is currently the standard interpretation of coronal rain, the long-term periodic evolution predicted by simulations has never been observed. However, the detection of long-period intensity pulsations (periods of several hours) has been recently reported with the Solar and Heliospheric Observatory /EIT, and this phenomenon appears to be very common in loops. Moreover, the three intensity-pulsation events that we recently studied with themore » Solar Dynamics Observatory /Atmospheric Imaging Assembly (AIA) show strong evidence for TNE in warm loops. In this paper, a realistic loop geometry from linear force-free field (LFFF) extrapolations is used as input to 1D hydrodynamic simulations. Our simulations show that, for the present loop geometry, the heating has to be asymmetrical to produce TNE. We analyze in detail one particular simulation that reproduces the average thermal behavior of one of the pulsating loop bundle observed with AIA. We compare the properties of this simulation with those deduced from the observations. The magnetic topology of the LFFF extrapolations points to the presence of sites of preferred reconnection at one footpoint, supporting the presence of asymmetric heating. In addition, we can reproduce the temporal large-scale intensity properties of the pulsating loops. This simulation further strengthens the interpretation of the observed pulsations as signatures of TNE. This consequently provides important information on the heating localization and timescale for these loops.« less