Author: Ding Yuan and Robert W. Walsh at the University of Central Lancashire ; Jiangtao Su at the National Astronomical Observatories of China ; Fangran Jiao at the Shandong University at Weihai .

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### Introduction

Quasi-periodic propagating disturbances are observed in active region loops and polar plumes; the periodicity leads to the natural thought that they have to be driven by a periodic signal. Therefore, the propagating disturbances are dominantly interpreted as slow magnetoacoustic waves [1]. However, due to the observation of excess blue shift (up-flows) at the footpoints of active region loops, repetitive flows are proposed to explain the observation [2]. But periodic flow rarely happens by itself in nature. Recent simulations demonstrate that, after a flow becomes detached from its sources, it evolves as a slow wave [3]. In this study, we demonstrate that random bursty impulses contain intermittent intrinsic periodicities (a conjunction of randomness and finite lifetime), and their evolution along the magnetic field lines could indeed be described by the MHD wave theory [4].

### Mathematical model for random transients

Random finite-lifetime transients are modelled as a series of Gaussian functions with random amplitudes, widths, and peak times (see details in [4]). The random amplitude follows a uniform distribution; the width, related to the finite lifetime of a transient, is assumed to follow a normal distribution with a certain mean value and a spread; the occurrence interval between transients is also assumed to follow a normal distribution. Figure 1 plots an example of a series of transients with an mean life time of 100 s and occurrence interval of 300 s, quasi-periodicities are intrinsic part of it.

### Evolution in sunspot umbra and active region loops

We simulate the evolution of random finite-lifetime transients along an empirical sunspot umbra model, which considers the chromosphere, the transition region and the corona [4]. Figure 2 illustrates the evolution of the density (a) and velocity profiles (b). Time series are extracted at the height of z=1.8 Mm ((c), chromosphere) and 10 Mm ((d), corona), respectively. It is seen that at chromospheric height, both the long- and short-period oscillations are detected. The long period oscillations are the quasi-periodicity of the random finite-lifetime transients; while the short-period oscillations at about 3-7 minutes are the resonance period of the acoustic resonator [5]. At the coronal height, only the resonance period leaked out.

### Evolution in polar plumes

In this numerical experiment, we exclude the acoustic resonator to simulate the case of polar plumes, it is seen that the long period oscillations successfully leak out to coronal heights (Figure 3). This is probably why in polar plumes, one detects long period oscillations, and a connectivity with the spicular activities is found [6].

### Conclusions

We propose a mathematic model for random finite-lifetime transients and found that quasi-periodicy is an intrinsic part of it. Numerical experiments show that the random transient perturbations cannot penetrate throughout the acoustic resonator in sunspot umbra, so in active region loops, one can only observe the resonance period, rather than the perturbation of the driver in sunspots. However, at polar plumes such long-period oscillations could propagate to the upper atmosphere. Our work shows that an observed oscillatory signal in the corona does not automatically imply a periodic driver.

### References

- [1] Verwichte, E. et al. (2010), ApJ, 724, 194
- [2] De Pontieu, B. McIntosh, S. (2010), ApJ, 722, 1013
- [3] Fang, X. et al. (2015), ApJ, 813, 33
- [4] Yuan, D., Su, J.T., Jiao, F. Walsh R.W., (2016), ApJS (in press)
- [5] Botha, G., et al. (2011) ApJ, 728, 84
- [6] Jiao, F. et al. (2015), ApJ, 809, 17