Coronal Magnetic Field Evolution Research Articles

Simulating the Formation and Eruption of Flux Rope by Magneto-friction Model Driven by Time-dependent Electric Fields

Aiming to capture the formation and eruption of flux ropes (FRs) in the source active regions (ARs), we simulate the coronal magnetic field evolution of the AR 11429 employing the time-dependent magneto-friction model (TMF). The initial field is driven by electric fields that are derived from time-sequence photospheric vector magnetic field observations by invoking ad hoc assumptions. The simulated magnetic structure evolves from potential to twisted fields over the course of two days, followed by rise motion in the later evolution, depicting the formation of an FR and its slow eruption later. The magnetic configuration resembles an inverse S-sigmoidal structure, composed of the potential field enveloping the inverse J-shaped fields that are sheared past one another and a low-lying twisted field along the major polarity inversion line. To compare with observations, proxy emission maps based on averaged current density along the field lines are generated from the simulated field. These emission maps exhibit a remarkable one-to-one correspondence with the spatial characteristics in coronal extreme ultraviolet images, especially the filament trace supported by the twisted magnetic field in the southwest subregion. Further, the topological analysis of the simulated field reveals the cospatial flare ribbons with the quasi-separatrix layers, which is consistent with the standard flare models; therefore, the extent of the twist and orientation of the erupting FR is indicated to be the real scenario in this case. The TMF model simulates the coronal field evolution, correctly capturing the formation of the FR in the observed timescale and the twisted field generated from these simulations serves as the initial condition for the full MHD simulations.

Data-driven Simulations of Magnetic Field Evolution in Active Region 11429: Magneto-frictional Method Using PENCIL CODE

Coronal magnetic fields evolve quasi-statically over long timescales and dynamically over short timescales. As of now there exist no regular measurements of coronal magnetic fields, and therefore generating the coronal magnetic field evolution using observations of the magnetic field at the photosphere is a fundamental requirement to understanding the origin of transient phenomena from solar active regions (ARs). Using the magneto-friction (MF) approach, we aim to simulate the coronal field evolution in the solar AR 11429. The MF method is implemented in the open source Pencil Code along with a driver module to drive the initial field with different boundary conditions prescribed from observed vector magnetic fields at the photosphere. In order to work with vector potential and the observations, we prescribe three types of bottom boundary drivers with varying free-magnetic energy. The MF simulation reproduces the magnetic structure, which better matches the sigmoidal morphology exhibited by Atmospheric Imaging Assembly (AIA) images at the pre-eruptive time. We found that the already sheared field further driven by the sheared magnetic field will maintain and further build the highly sheared coronal magnetic configuration, as seen in AR 11429. Data-driven MF simulation is a viable tool to generate the coronal magnetic field evolution, capturing the formation of the twisted flux rope and its eruption.

A comparative study of data-driven MHD simulations of solar coronal evolution with photospheric flows derived from two different approaches

Data-driven simulation proves to be a powerful tool in revealing the dynamic process of the solar corona, but it remains challenging to implement the driving boundary conditions in a self-consistent way and match the observables at the photosphere. Here, we test two different photospheric velocity-driven MHD simulations in studying the quasi-static evolution of solar active region NOAA 11158. The two simulations were identically initialized with an MHD equilibrium as relaxed from a non-linear force-free field extrapolation from a vector magnetogram. Then, we energized the MHD system by applying the time series of photospheric velocity at the bottom boundary as derived by two different codes, the DAVE4VM and PDFI, from the observed vector magnetograms. To mimic the small-scale flux cancellation on the photosphere, the magnetic diffusion at the bottom boundary was set to be inversely proportional to the local scale length of the magnetic field. The result shows the evolution curves of the total magnetic energy and unsigned magnetic flux generated by the PDFI velocity match the corresponding curves from the observations much better than those by the DAVE4VM one. The structure of the current layer and synthetic image in PDFI simulation also has a more reasonable consistency with SDO/AIA 131 Å observation. The only shortage of the PDFI velocity is its capability in reproducing the morphology of sunspots, as characterized by a slightly lower correlation coefficient for the bottom magnetic field in simulations and magnetograms. Overall, this study suggests the superiority of each method in the models driven by the bottom velocity, which represents a further step toward the goal of reproducing more realistically the evolution of coronal magnetic fields using data-driven modeling.

MHD Modeling of Solar Coronal Magnetic Evolution Driven by Photospheric Flow

It is well-known that magnetic fields dominate the dynamics in the solar corona, and new generation of numerical modeling of the evolution of coronal magnetic fields, as featured with boundary conditions driven directly by observation data, are being developed. This paper describes a new approach of data-driven magnetohydrodynamic (MHD) simulation of solar active region (AR) magnetic field evolution, which is for the first time that a data-driven full-MHD model utilizes directly the photospheric velocity field from DAVE4VM. We constructed a well-established MHD equilibrium based on a single vector magnetogram by employing an MHD-relaxation approach with sufficiently small kinetic viscosity, and used this MHD equilibrium as the initial conditions for subsequent data-driven evolution. Then we derived the photospheric surface flows from a time series of observed magentograms based on the DAVE4VM method. The surface flows are finally inputted in time sequence to the bottom boundary of the MHD model to self-consistently update the magnetic field at every time step by solving directly the magnetic induction equation at the bottom boundary. We applied this data-driven model to study the magnetic field evolution of AR 12158 with SDO/HMI vector magnetograms. Our model reproduced a quasi-static stress of the field lines through mainly the rotational flow of the AR's leading sunspot, which makes the core field lines to form a coherent S shape consistent with the sigmoid structure as seen in the SDO/AIA images. The total magnetic energy obtained in the simulation matches closely the accumulated magnetic energy as calculated directly from the original vector magnetogram with the DAVE4VM derived flow field. Such a data-driven model will be used to study how the coronal field, as driven by the slow photospheric motions, reaches a unstable state and runs into eruptions.

Simulating the Coronal Evolution of Bipolar Active Regions to Investigate the Formation of Flux Ropes

The coronal magnetic field evolution of 20 bipolar active regions (ARs) is simulated from their emergence to decay using the time-dependent nonlinear force-free field method of Mackay, Green, and van Ballegooijen (Astrophys. J. 729, 97, 2011). A time sequence of cleaned photospheric line-of-sight magnetograms, which covers the entire evolution of each AR, is used to drive the simulation. A comparison of the simulated coronal magnetic field with the 171 and 193 Å observations obtained by the Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA), is made for each AR by manual inspection. The results show that it is possible to reproduce the evolution of the main coronal features such as small- and large-scale coronal loops, filaments and sheared structures for 80% of the ARs. Varying the boundary and initial conditions, along with the addition of physical effects such as Ohmic diffusion, hyperdiffusion and a horizontal magnetic field injection at the photosphere, improves the match between the observations and simulated coronal evolution by 20%. The simulations were able to reproduce the build-up to eruption for 50% of the observed eruptions associated with the ARs. The mean unsigned time difference between the eruptions occurring in the observations compared to the time of eruption onset in the simulations was found to be ≈5 hrs. The simulations were particularly successful in capturing the build-up to eruption for all four eruptions that originated from the internal polarity inversion line of the ARs. The technique was less successful in reproducing the onset of eruptions that originated from the periphery of ARs and large-scale coronal structures. For these cases global, rather than local, nonlinear force-free field models must be used. While the technique has shown some success, eruptions that occur in quick succession are difficult to reproduce by this method and future iterations of the model need to address this.

Data-driven MHD Simulation of the Formation and Initiation of a Large-scale Preflare Magnetic Flux Rope in AR 12371

Abstract Solar eruptions are the most powerful drivers of space weather. To understand their cause and nature, it is crucial to know how the coronal magnetic field evolves before eruption. Here we study the formation process of a relatively large-scale magnetic flux rope (MFR) in active region NOAA 12371 that erupts with a major flare and coronal mass ejection on 2015 June 21. A data-driven numerical magnetohydrodynamic model is employed to simulate three-dimensional coronal magnetic field evolution of 1 day duration before the eruption. Comparison between the observed features and our modeled magnetic field discloses how the pre-eruption MFR forms. Initially, the magnetic field lines were weakly twisted as being simple sheared arcades. Then a long MFR was formed along the polarity inversion line due to the complex photospheric motion, which is mainly shearing rather than twisting. The presence of the MFR is evidenced by a coherent set of magnetic field lines with twist number above unity. Below the MFR a current sheet is shown in the model, suggesting that tether-cutting reconnection plays a key role in the MFR formation. The MFR’s flux grows as more and more field lines are twisted due to continuous injection of magnetic helicity by the photospheric motions. Meanwhile, the height of the MFR’s axis increases monotonely from its formation. By an analysis of the decay index of its overlying field, we suggest that this is because the MFR runs into the torus instability regime and becomes unstable, which finally triggers the eruption.

Continuous Null-point Magnetic Reconnection Builds Up a Torus Unstable Magnetic Flux Rope Triggering the X9.3 Flare in Solar AR 12673

Abstract Two X-class solar flares occurred on 2017 September 6 from active region NOAA 12673: the first one is a confined X2.2 flare, and it is followed only ∼3 hr later by the second one, which is the strongest flare in solar cycle 24, reaching X9.3 class and accompanied by a coronal mass ejection. Why did these two X-class flares occur in the same position with similar magnetic configurations, but one is eruptive while the other is not? Here we track the coronal magnetic field evolution via nonlinear force-free field extrapolations from a time sequence of vector magnetograms with high cadence. A detailed analysis of the magnetic field shows that a magnetic flux rope (MFR) forms and grows gradually before the first flare, and shortly afterward, the MFR’s growth is significantly enhanced with a much faster rise in height, from far below the threshold of torus instability to above it, while the magnetic twist only increases mildly. Combining EUV observations and the magnetic field extrapolation, we found that overlying the MFR is a null-point magnetic topology, where recurrent brightening is seen after the first flare. We thus suggest a scenario to interpret the occurrence of the two flares. The first flare occurred since the MFR reached a high enough height to activate the null point, and its continuous expansion forces the null-point reconnection recurrently. Such reconnection weakens the overlying field, allowing the MFR to rise faster, which eventually crosses the threshold of torus instability and triggers the second, eruptive flare.

Time-dependent Data-driven Modeling of Active Region Evolution Using Energy-optimized Photospheric Electric Fields

In this work, we present results of a time-dependent data-driven numerical simulation developed to study the dynamics of coronal active region magnetic fields. The evolving boundary condition driving the model, the photospheric electric field, is inverted using a time sequence of vector magnetograms as input. We invert three distinct electric field datasets for a single active region. All three electric fields reproduce the observed evolution of the normal component of the magnetic field. Two of the datasets are constructed so as to match the energy input into the corona to that provided by a reference estimate. Using the three inversions as input to a time-dependent magnetofrictional model, we study the response of the coronal magnetic field to the driving electric fields. The simulations reveal the magnetic field evolution to be sensitive to the input electric field despite the normal component of the magnetic field evolving identically and the total energy injection being largely similar. Thus, we demonstrate that the total energy injection is not sufficient to characterize the evolution of the coronal magnetic field: coronal evolution can be very different despite similar energy injections. We find the relative helicity to be an important additional metric that allows one to distinguish the simulations. In particular, the simulation with the highest relative helicity content produces a coronal flux rope that subsequently erupts, largely in agreement with extreme-ultraviolet imaging observations of the corresponding event. Our results suggest that time-dependent data-driven simulations that employ carefully constructed driving boundary conditions offer a valuable tool for modeling and characterizing the evolution of coronal magnetic fields.

Simulating the Coronal Evolution of AR 11437 Using SDO/HMI Magnetograms

Abstract The coronal magnetic field evolution of AR 11437 is simulated by applying the magnetofrictional relaxation technique of Mackay et al. A sequence of photospheric line-of-sight magnetograms produced by the Solar Dynamics Observatory (SDO)/Helioseismic Magnetic Imager (HMI) is used to drive the simulation and continuously evolve the coronal magnetic field of the active region through a series of nonlinear force-free equilibria. The simulation is started during the first stages of the active region emergence so that its full evolution from emergence to decay can be simulated. A comparison of the simulation results with SDO/Atmospheric Imaging Assembly (AIA) observations show that many aspects of the active region’s observed coronal evolution are reproduced. In particular, it shows the presence of a flux rope, which forms at the same location as sheared coronal loops in the observations. The observations show that eruptions occurred on 2012 March 17 at 05:09 UT and 10:45 UT and on 2012 March 20 at 14:31 UT. The simulation reproduces the first and third eruption, with the simulated flux rope erupting roughly 1 and 10 hr before the observed ejections, respectively. A parameter study is conducted where the boundary and initial conditions are varied along with the physical effects of Ohmic diffusion, hyperdiffusion, and an additional injection of helicity. When comparing the simulations, the evolution of the magnetic field, free magnetic energy, relative helicity and flux rope eruption timings do not change significantly. This indicates that the key element in reproducing the coronal evolution of AR 11437 is the use of line-of-sight magnetograms to drive the evolution of the coronal magnetic field.

PHOTOSPHERIC ELECTRIC FIELDS AND ENERGY FLUXES IN THE ERUPTIVE ACTIVE REGION NOAA 11158

How much electromagnetic energy crosses the photosphere in evolving solar active regions? With the advent of high-cadence vector magnetic field observations, addressing this fundamental question has become tractable. In this paper, we apply the "PTD-Doppler-FLCT-Ideal" (PDFI) electric field inversion technique of Kazachenko et al. (2014) to a 6-day HMI/SDO vector magnetogram and Doppler velocity sequence, to find the electric field and Poynting flux evolution in active region NOAA 11158, which produced an X2.2 flare early on 2011 February 15. We find photospheric electric fields ranging up to $2$ V/cm. The Poynting fluxes range from $[-0.6$ to $2.3]\times10^{10}$ ergs$\cdot$cm$^{-2}$s$^{-1}$, mostly positive, with the largest contribution to the energy budget in the range of $[10^9$-$10^{10}]$ ergs$\cdot$cm$^{-2}$s$^{-1}$. Integrating the instantaneous energy flux over space and time, we find that the total magnetic energy accumulated above the photosphere from the initial emergence to the moment before the X2.2 flare to be $E=10.6\times10^{32}$ ergs, which is partitioned as $2.0$ and $8.6\times10^{32}$ ergs, respectively, between free and potential energies. Those estimates are consistent with estimates from preflare non-linear force-free field (NLFFF) extrapolations and the Minimum Current Corona estimates (MCC), in spite of our very different approach. This study of photospheric electric fields demonstrates the potential of the PDFI approach for estimating Poynting fluxes and opens the door to more quantitative studies of the solar photosphere and more realistic data-driven simulations of coronal magnetic field evolution.

Coronal heating in multiple magnetic threads

Context. Heating the solar corona to several million degrees requires the conversion of magnetic energy into thermal energy. In this paper, we investigate whether an unstable magnetic thread within a coronal loop can destabilise a neighbouring magnetic thread. Aims. By running a series of simulations, we aim to understand under what conditions the destabilisation of a single magnetic thread can also trigger a release of energy in a nearby thread. Methods. The 3D magnetohydrodynamics code, Lare3d, is used to simulate the temporal evolution of coronal magnetic fields during a kink instability and the subsequent relaxation process. We assume that a coronal magnetic loop consists of non-potential magnetic threads that are initially in an equilibrium state. Results. The non-linear kink instability in one magnetic thread forms a helical current sheet and initiates magnetic reconnection. The current sheet fragments, and magnetic energy is released throughout that thread. We find that, under certain conditions, this event can destabilise a nearby thread, which is a necessary requirement for starting an avalanche of energy release in magnetic threads. Conclusions. It is possible to initiate an energy release in a nearby, non-potential magnetic thread, because the energy released from one unstable magnetic thread can trigger energy release in nearby threads, provided that the nearby structures are close to marginal stability.

QUASI-STATIC THREE-DIMENSIONAL MAGNETIC FIELD EVOLUTION IN SOLAR ACTIVE REGION NOAA 11166 ASSOCIATED WITH AN X1.5 FLARE

We study the quasi-static evolution of coronal magnetic fields constructed from the Non Linear Force Free Field (NLFFF) approximation aiming to understand the relation between the magnetic field topology and ribbon emission during an X1.5 flare in active region (AR) NOAA 11166. The flare with a quasi-elliptical, and two remote ribbons occurred on March 9, 2011 at 23:13UT over a positive flux region surrounded by negative flux at the center of the bipolar AR. Our analysis of the coronal magnetic structure with potential and NLFFF solutions unveiled the existence of a single magnetic null point associated with a fan-spine topology and is co-spatial with the hard X-ray source. The footpoints of the fan separatrix surface agree with the inner edge of the quasi-elliptical ribbon and the outer spine is linked to one of the remote ribbons. During the evolution, the slow footpoint motions stressed the fieldlines along the polarity inversion line and caused electric current layers in the corona around the fan separatrix surface. These current layers trigger magnetic reconnection as a consequence of dissipating currents, which are visible as cusped shape structures at lower heights. The reconnection process reorganised the magnetic field topology whose signatures are observed at the separatrices/QSL structure both in the photosphere and corona during the pre-to-post flare evolution. In agreement with previous numerical studies, our results suggest that the line-tied footpoint motions perturb the fan-spine system and cause null point reconnection, which eventually causes the flare emission at the footpoints of the fieldlines.

Coronal Magnetic Field Evolution from 1996 to 2012: Continuous Non-potential Simulations

Coupled flux transport and magneto-frictional simulations are extended to simulate the continuous magnetic-field evolution in the global solar corona for over 15 years, from the start of Solar Cycle 23 in 1996. By simplifying the dynamics, our model follows the build-up and transport of electric currents and free magnetic energy in the corona, offering an insight into the magnetic structure and topology that extrapolation-based models cannot. To enable these extended simulations, we have implemented a more efficient numerical grid, and have carefully calibrated the surface flux-transport model to reproduce the observed large-scale photospheric radial magnetic field, using emerging active regions determined from observed line-of-sight magnetograms. This calibration is described in some detail. In agreement with previous authors, we find that the standard flux-transport model is insufficient to simultaneously reproduce the observed polar fields and butterfly diagram during Cycle 23, and that additional effects must be added. For the best-fit model, we use automated techniques to detect the latitude–time profile of flux ropes and their ejections over the full solar cycle. Overall, flux ropes are more prevalent outside of active latitudes but those at active latitudes are more frequently ejected. Future possibilities for space-weather prediction with this approach are briefly assessed.

A MAGNETOHYDRODYNAMIC MODEL OF THE 2006 DECEMBER 13 ERUPTIVE FLARE

We present a three-dimensional magnetohydrodynamic simulation that qualitatively models the coronal magnetic field evolution associated with the eruptive flare that occurred on 2006 December 13 in the emerging δ-sunspot region NOAA 10930 observed by the Hinode satellite. The simulation is set up to drive the emergence of an east–west-oriented magnetic flux rope at the lower boundary into a preexisting coronal field constructed from the Solar and Heliospheric Observatory/Michelson Doppler Imager full-disk magnetogram at 20:51:01 UT on 2006 December 12. The resulting coronal flux rope embedded in the ambient coronal magnetic field first settles into a stage of quasi-static rise and then undergoes a dynamic eruption, with the leading edge of the flux rope cavity accelerating to a steady speed of about 830 km s−1. The pre-eruption coronal magnetic field shows morphology that is in qualitative agreement with that seen in the Hinode soft X-ray observation in both the magnetic connectivity as well as the development of an inverse-S-shaped X-ray sigmoid. We examine the properties of the erupting flux rope and the morphology of the post-reconnection loops, and compare them with the observations.

MODELING THE DISPERSAL OF AN ACTIVE REGION: QUANTIFYING ENERGY INPUT INTO THE CORONA

In this paper a new technique for modeling non-linear force-free fields directly from line of sight magnetogram observations is presented. The technique uses sequences of magnetograms directly as lower boundary conditions to drive the evolution of coronal magnetic fields between successive force-free equilibria over long periods of time. It is illustrated by applying it to MDI observations of a decaying active region, NOAA AR 8005. The active region is modeled during a 4 day period around its central meridian passage. Over this time, the dispersal of the active region is dominated by random motions due to small scale convective cells. Through studying the build up of magnetic energy in the model, it is found that such small scale motions may inject anywhere from $2.5-3 \times 10^{25}$ erg s$^{-1}$ of free magnetic energy into the coronal field. Most of this energy is stored within the center of the active region in the low corona, below 30 Mm. After 4 days the build-up of free energy is 10% that of the corresponding potential field. This energy buildup, is sufficient to explain the radiative losses at coronal temperatures within the active region. Small scale convective motions therefore play an integral part in the energy balance of the corona. This new technique has wide ranging applications with the new high resolution, high cadence observations from the SDO:HMI and SDO:AIA instruments.

INITIATION OF CORONAL MASS EJECTIONS IN A GLOBAL EVOLUTION MODEL

Loss of equilibrium of magnetic flux ropes is a leading candidate for the origin of solar coronal mass ejections (CMEs). The aim of this paper is to explore to what extent this mechanism can account for the initiation of CMEs in the global context. A simplified MHD model for the global coronal magnetic field evolution in response to flux emergence and shearing by large-scale surface motions is described and motivated. Using automated algorithms for detecting flux ropes and ejections in the global magnetic model, the effects of key simulation parameters on the formation of flux ropes and the number of ejections are considered, over a 177-day period in 1999. These key parameters include the magnitude and sign of magnetic helicity emerging in active regions, and coronal diffusion. The number of flux ropes found in the simulation at any one time fluctuates between about 28 and 48, sustained by the emergence of new bipolar regions, but with no systematic dependence on the helicity of these regions. However, the emerging helicity does affect the rate of flux rope ejections, which doubles from 0.67 per day if the bipoles emerge untwisted to 1.28 per day in the run with greatest emerging twist. The number of ejections in the simulation is also increased by 20%-30% by choosing the majority sign of emerging bipole helicity in each hemisphere, or by halving the turbulent diffusivity in the corona. For reasonable parameter choices, the model produces approximately 50% of the observed CME rate. This indicates that the formation and loss of equilibrium of flux ropes may be a key element in explaining a significant fraction of observed CMEs.

Magnetic Reconnection Models of Prominence Formation

To investigate the hypothesis that prominences form by magnetic reconnection between initially distinct flux systems in the solar corona, we simulate coronal magnetic field evolution when two flux systems are driven together by boundary motions. In particular, we focus on configurations similar to those in the quiescent prominence formation model of Martens & Zwaan. We find that reconnection proceeds very weakly, if at all, in configurations driven with global shear flows (i.e., differential rotation); reconnection proceeds much more efficiently in similar configurations that are driven to collide directly, with converging motions along the neutral line that lead to flux cancellation; reconnected fields from this process can exhibit sheared, dipped field lines along the neutral line, consistent with prominence observations. Our field configurations do not possess the breakout topology, and eruptions are not observed, even though a substantial amount of flux is canceled in some runs.

The Frequency Agile Solar Radiotelescope

Abstract The Frequency Agile Solar Radiotelescope (FASR), a telescope concept currently under study, will be a ground based solar-dedicated radio telescope designed and optimized to produce high resolution, high-fidelity, and high-dynamic-range images over a broad frequency range (∼0.1–24 GHz). As such, FASR will address an extremely broad science program, including the nature and evolution of coronal magnetic fields, the physics of flares, drivers of space weather, and the quiet Sun. An important goal is to mainstream solar radio observations by providing a number of standard data products for use by the wider solar physics community. The instrument specifications and the key science elements that FASR will address are briefly discussed, as well as several operational issues.

The Frequency Agile Solar Radiotelescope

The Frequency Agile Solar Radiotelescope (FASR), a telescope concept currently under study, will be a ground based solar-dedicated radio telescope designed and optimized to produce high resolution, high-fidelity, and high-dynamic-range images over a broad frequency range (∼0.1–24 GHz). As such, FASR will address an extremely broad science program, including the nature and evolution of coronal magnetic fields, the physics of flares, drivers of space weather, and the quiet Sun. An important goal is to mainstream solar radio observations by providing a number of standard data products for use by the wider solar physics community. The instrument specifications and the key science elements that FASR will address are briefly discussed, as well as several operational issues.

Observational Determination of the Rate of Magnetic Helicity Transport through the Solar Surface via the Horizontal Motion of Field Line Footpoints

Magnetic helicity may be transported to the solar corona through the solar surface either via the passage of helical magnetic field lines from below or via the shuffling of footpoints of preexisting coronal field lines. In this Letter, we show how to observationally determine the rate of magnetic helicity transport via photospheric footpoint shuffling from a time series of line-of-sight magnetograms. Our approach is not confined to the previously known shear motions, such as differential rotation, but can be exploited to search for the possible existence of physically significant shear motions other than differential rotation. We have applied the method to a 40 hr run of high-resolution magnetograms of a small active region (NOAA Active Region 8011) taken by the Michelson Doppler Imager on board the Solar and Heliospheric Observatory. In this region, we find that the rate of magnetic helicity transport oscillates with periods of 1 to several hours. Our result suggests that the time-series analysis of the helicity transport rate might be a useful observational diagnostic for the role of photospheric flows in the evolution of coronal magnetic fields in solar active regions.