102. Do p-modes power the corona of cool stars?

Author: Richard Morton Northumbria University.

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Magnetohydrodynamic (MHD) waves are thought to play some role in the heating of cool, solar-like stars’ atmospheres, and acceleration of their winds. The role of acoustic (or longitudinal MHD) modes in energising stellar coronae has long been discounted, both from theoretical and observational considerations. The acoustic modes are predominantly excited by the turbulent convection (and are known as p-modes). Moreover, they clearly play some role in the structuring and dynamics of the chromosphere [1], with their energy being deposited there as they shock due to the increasing temperature. However, relatively recent theoretical results have shown that, in principle, the p-modes may generate Poynting flux in the corona. Given favourable alignments between the magnetic field and gravity, the longitudinal mode converts first to a fast MHD mode at the equipartition layer, where gas pressure and magnetic pressure are equal, followed by a secondary conversion to an Alfvénic mode at the transition region [2,3];  with only a small fraction of the available p-mode energy needing to be converted to satisfy the coronal energy budget.

If this process was in action in the Sun’s atmosphere, we should expect the coronal Alfvénic waves to display some signature of this. Previous studies [4,5] have indicated the presence of enhanced power (or ‘bump’) in the velocity power spectra of Alfvénic fluctuations derived from the Coronal Multi-Channel Polarimeter (CoMP [6]). However, these were limited to a few coronal regions on a couple of dates. Given the global nature of the p-modes and the expectation that they leak into the atmosphere through magneto-acoustic portals [7] (largely located at the network boundaries), one would anticipate that the enhanced power should be present globally, and should be more or less insensitive to the large-scale changes in the solar magnetic field activity cycle. We thought it was time to have a look! (For full details see [8].)

Figure 1. The corona on the 10 May 2014 as seen with the Solar Dynamics Observatory. A plethora of fine-scale magnetic structure is visible around the limb and is observed to support Alfvénic waves, a significant fraction of which appear to be driven ultimately by p-modes.

The coronal ‘bump’

CoMP has collected a large amount of data over a 7 year period, performing spectroscopic measurements of the Iron XIII 10747 Å coronal emission line on a near daily basis (see a previous nugget). We decided that in order to provide a more convincing case for the role of p-modes, we needed to examine the power spectra both globally and also across the 11-year cycle. This required a systematic analysis of Doppler velocity power spectra taken from many different sections of the corona. The accessible CoMP archive currently only has data from 2010, on the rise to solar maximum in 2013/2014, until 2018. We chose 5 different days between 2012 and 2015 to cover the rise and fall of the sunspot cycle and also had access to a special data set taken back in 2005, close to the end of the previous activity cycle. While this does not provide even sampling over the entire 11 year period, the Sun undoubtedly experienced large-scale changes in the global magnetic field over the time-span of the data.

Figure 2. Measurements of the location and scale parameter associated with the enhanced power found in Alfvénic wave power spectra.

We spilt the corona into 5-degree bins in order to average the velocity power spectra and increase signal-to-noise. This is a coarse approach to the problem, neglecting the presence of different magnetic geometries in each bin (see for example the structures in Figure 1); different magnetic regions, e.g. active region, coronal hole, having power spectra with different properties [9]. Each average spectrum was then fit with two models, a power law and a power law with a localised enhancement of power (represented by a log-normal function), where the enhanced power represents the contribution of p-modes to the coronal Alfvénic wave power spectra. We compared the two models’ ability to describe the spectra through Information Criteria. The results found that in the large majority of cases (>95%), the power law with the enhanced power was found to be the better model. This was the same for each data set we examined. The signature of p-modes is everywhere in the corona, and always seems to be present

Figure 3. Globally averaged velocity power spectra. The presence of an enhancement (‘bump’) is evident across all years.

Moreover, the model parameters that described the enhanced power, namely the frequency associated with the location parameter and the frequencies associated with the scale parameter are remarkably similar across the corona and all dates (Figure 2). The location of the enhanced power is predominantly around 4 mHz, shifted towards higher frequencies than the characteristic p-mode frequency of 3.3 mHz, while the typical scale was just greater than 1 mHz.

The prominent nature of this enhanced velocity power signal in the Sun’s corona is apparent, as it is still visible even after averaging over all the coronal power spectra (Figure 3). This signal is clearly global and ever present, and our results indicate that it identifies a fundamental component of the corona – namely the p-mode ‘driven’ Alfvénic waves (the quotes around driven are meant to imply that it is not directly the p-modes that drive the waves).


What does it mean to have p-mode ‘driven’ Alfvenic waves in the corona? One major implication is that many models of coronal heating and wind acceleration by Alfvénic wave turbulence are ignoring a sizeable source of Poynting flux. In the current models, it is largely assumed that the horizontal buffeting of photospheric flux tubes is the sole source of Poynting flux, with the waves entering the corona from below having relatively high frequencies (< 4mHz). Hence, we are suggesting that these models are missing a key piece of physics! Moreover, in order to understand the heating/acceleration of solar plasma requires including the extra energy injected at the transition region via the mode conversion process. While the broader consequences of including this extra energy are unknown, it will certainly play a role in energising the corona.

On a more speculative note, our results may provide a way to observe Alfvénic waves on other cool, magnetised stars, namely ones that generate stellar oscillations (of which Kepler has found many [10]). Current instrumentation is still some way from providing detailed observations of other stars’ coronae, although velocity measurements have been made in Antares’ atmosphere [11]. However, the signal in the Sun’s corona is global and striking in averaged velocity power spectra. It may be that even relatively crude Doppler measurements of emission lines in stellar corona will have enough resolution to identify this ‘bump’ in velocity power spectra.