The Alfven Speed above a Sunspot, and Gamma-rays

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Number: 148
1st Author: H. Hudson
2nd Author: L. Fletcher
Published: 12 April 2011
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It is common for powerful flares to occur actually within sunspots, with their H-alpha ribbons blithely crossing over these regions of very strong magnetic field. What does this association mean for flare theory, and what does it mean for the interesting differences RHESSI has discovered between flares with and without gamma-rays? We discuss these issues in the context of the X-class flare of February 15, 2011. This was only the second X-class flare of this solar maximum; it was not a gamma-ray event but it was the source of a clear sunquake.

Observations from Hinode and RHESSI

The flare was well-observed by the SOT white-light imager on Hinode, with 20-second cadence in three broad-band optical filters. This data set is quite remarkable because of the excellent resolution and brilliant image contrast achieved by the SOT telescope, the largest solar telescope ever put in space. Figure 1 shows an overlay of the patches of white-light emission extracted from the several images taken during the impulsive phase of the flare, which is when we ordinarily observe hard X-rays and gamma-rays.

Figure 1: The bright patches of the white-light flare emission, shown in different colors for the several different images at enhanced contrast. The background image is an unaltered view of the active region, which has well-developed spots. The white-light flare patches extend well into the umbrae of the spots.

At the same time as these white-light emissions, what was RHESSI seeing? Figure 2 offers a simplified view of the RHESSI counting rates, mainly to illustrate the distinct lack of a gamma-ray signature. RHESSI has shown that gamma-ray flares are quite different from ordinary flares, i.e. that the "big flare syndrome" (where everything scales together) does not apply in this case - here we see a big flare, with a sunquake as well, and yet no gamma rays. For this flare, Figure 2 shows that there was negligible 2.2 MeV gamma-ray emission line, RHESSI's most sensitive tool for this purpose, and that the hard X-ray spectrum was weak above 50 keV.

Figure 2: Time series of counts at 100 keV (blue), 200 keV (gold) and at 2200-2250 keV (red), the latter a crude indication of the presence or absence of gamma-rays. In this case, despite the X classification of the flare, there were no detectable gamma rays and only a weak hard X-ray signature with a relatively steep spectrum.


As the image in Figure 1 shows, in this flare - as with many of the most powerful events - we are essentially looking deep into the core of the active region. In these cases the many signatures of non-thermal effects in the lower solar atmosphere (hard X-rays, H-alpha, EUV, and intense white light) all implicate the strong magnetic fields to be found in the umbra and penumbra regions of major sunspots.

In this Nugget we remind readers that the coronal volume just above a sunspot is a particularly interesting and ill-understood place. Many research workers will express surprise at the strength of the coronal magnetic field above a big spot, about the Alfvén speed, and about the plasma beta as well - all are extreme, according to the best observational estimates. The Alfvén speed, if computed naively, exceeds the speed of light below a few Mm above a big spot! Figure 3 details some of these parameters for a conservatively chosen set of model conditions above a very large sunspot. One of the problems of the corona above a spot umbra is so dark and non-emissive that ordinary astronomical techniques do not work very well, and so in fact there are major observational uncertainties. The theory behind the extrapolations in Figure 3 is very simple and safe, though. For a spot like this we estimate an Alfvén speed, using the usual relationship, to exceed the speed of light. Of course this is non-physical, but it is strikingly different from the usual assumption about the Alfvén speed. This is just what reasonable estimates of B and n lead to, and the result suggests that plasma processes in the coronal regions of a sunspot must be treated relativistically.

Figure 3: Three panels showing, as a function of height above the center of a major sunspot, the magnetic field, the Alfvén speed as estimated by the standard formula, and the plasma beta. The assumed parameters for the sunspot are a central field of 3500 G and an umbral radius of 10,000 km. The dashed line shows the speed of light. Note added 30-December 2015: our thanks to Serge Koutchmy for noticing that the original version of this figure was grossly erroneous.

Is this estimation, which is based on Allen's Astrophysical Quantities, at all relevant to the particular flare we are discussing? Perhaps not directly, since the Hinode magnetographic observations suggest field intensities about a factor of three smaller, and the spatial scales smaller as well. That means that the coronal field (intensity and scale) and Alfvén speed will be correspondingly smaller in this particular event. A survey of a number of representative events will clearly be warranted, and we hope that Cycle 24 will bring us events ten times as powerful.

Speculation and Conclusion

This Nugget suggests that we begin to combine observations of the manifestations of major flares within sunspots, with new thinking about the theory of the processes in the corona just above them. A relativistic Alfvén speed means that the Poynting flux can rival the motions of accelerated particles, for example, in terms of the speed of energy transport. Although the theory of these phenomena is still at its bare beginnings, it also seems likely that such extreme values of Alfvén speed and plasma beta will also help to accelerate the particles that RHESSI detects through hard X-rays and gamma rays. But why, in the case of the flare we have illustrated here, were there no gamma rays to speak of? And yet, there was a sunquake; there have been suggestions that high-energy ions (the sources of flare gamma rays) might be implicated in sunquake activity. Does the ion acceleration require a still stronger magnetic field? In any case we now have marvelous tools to study these questions observationally, and so we may expect some progress via studies of this and other flares with these tools; this Nugget and the sunquakes Nugget on the same event have only described parts of the rich data available now.

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