Harmonic Oscillations

From RHESSI Wiki

Revision as of 16:46, 6 July 2010

Introduction

Solar flare activity is often accompanied by quasi-periodic pulsations (QPP) in the flare emission, over a wide range of electromagnetic wavelengths. QPP carry important information about the processes occurring in flare regions and therefore are subjected to intensive scrutiny (see the [1] QPP events catalog]).

Covering a wide range of X-ray energy, the RHESSI satellite has great potential in this branch of solar physics. Two excellent examples of RHESSI usage on the QPP problem in solar flares were presented in the previous Nuggets 7 and 102.

However, one of the first rules of oscillation studies is that you should always be on the lookout for potential instrumental effects – we must always consider the possibility that oscillations in our data are artificial rather than real. In this Nugget we report on a striking instrumental effect leading to artificial oscillations of the RHESSI detector count rates during a powerful flare.

A striking example: the solar flare of 6 November 2004

Analysing the decay phase of the M9.3 class solar flare on November 6, 2004, extremely high-quality harmonic oscillations of RHESSI Corrected Count Rates in the 6-12 and 12-25 keV energy channels were surprisingly found. These oscillations have a characteristic period of 75 s and are clearly visible in the count-rate time profiles shown in Figure 1.

Figure 1: Count-rate time profiles of X-ray emission from the November 6, 2004 flare, observed by RHESSI (black, green, red, turquoise lines) and GOES-10 (blue and orange lines).

Such pure harmonic oscillations of X-ray emission of such duration and quality are not typical for solar flares. Moreover, X-ray detectors on board GOES-10 satellite, working in the same energy range, did not detect such periodicity. This leads us to consider two possibilities: 1) a rare solar flare phenomenon is discovered by RHESSI due to its sensitive detectors, or 2) an unexpected artifact of the RHESSI data is manifested.

Fortunately, RHESSI telemetry contains necessary information to resolve this dilemma.

RHESSI as a gyroscope

RHESSI rotates around its spin axis, pointed at the Sun, with time period of about 4 sec. As a result of this rotation, the imaging axis of the telescope, which is offset from the spin axis, describes circles on the Sun also with period of about 4 sec (see Nugget 57).

RHESSI's nine detectors with mounted collimators use this rotation to time-modulate the incident photon flux from the X-ray sources and reconstruct their images. However, because RHESSI is not infinitely far away from the Sun and the planets, it experiences the effects of small but significant external forces.

In this sense RHESSI can behave like a gyroscope, experiencing precession and nutation. Time periods of the RHESSI precession and nutation are of the order of several minutes and several tens of seconds, respectively. The precession and nutation, like the basic rotational motion, produce motions of the telescope axis with respect to the X-ray source position. This, in turn, modulates the photon flux reaching the RHESSI detectors through the collimator grids resulting in the modulation of the detectors count rates.

Not all of RHESSI's detector grids have the same field of view (FOV). This results in differing modulation depths of the count rates for individual detectors - the larger the FOV, the less the modulation depth. Detectors 1-6 are expected to be most prone to such effects, since their grids have the least FOV of 1.0 deg, while detectors 7, 8, and 9 have FOV of 4.4, 7.5, and 2.8 deg, respectively.

Let's return to the flare of 6 November 2004. In Figure 2(a) we plot time profile of the 4-second averaged angular distance (Delta) between the RHESSI imaging axis and the flare position on the Sun, jointly with the 20-second smoothed, detrended, and normalized corrected count rate (Normalized Amplitude) of the RHESSI detectors No 5 in the 6-12 keV energy channel during the time interval of the "pronounced" oscillations (see Figure 1).

Figure 2: 4-second averaged time profile of the angular distance [Delta; black] between the RHESSI imaging axis and the 2004 November 6 solar flare position and 20-second averaged normalized detrended light curves of the RHESSI detector No 5 [(a): red] and No 8 [(b): blue] in the 6-12 keV energy channel during the time interval of the pronounced oscillations marked by two vertical dashed lines in Figure 1.

It is clearly seen that Delta anti-correlates with the Normalized Amplitude, also oscillating with a period of about 75 sec (note, that Delta also reveals 4-second oscillations due to spacecraft rotation). This means that than greater the distance between the imaging axis and the flare position, than detected X-ray flux is smaller. Despite the fact that the nominal FOV of the RHESSI detector No 5 (1.0 deg) is significantly larger than Delta, modulation of the count rates is still presented. This is intuitively clear. Given FOV should not be regarded as absolute, but rather nominal values, because when dealing with X-rays, we inevitably fall under the influence of statistics.

Figure 2 also illustrates the fact, that the modulation depth of the oscillations of the RHESSI detectors count rate decreases with increase of the FOV of the detectors grids, leading to dissapearance of the oscillations.

These arguments demonstrate that the observed oscillations are a consequence of the RHESSI nutation.

Antithesis of the 6 November flare: the "standard" flare of November 4

For comparison, we present analogous time series data of the M5.4 class flare from November 4, 2004, the decay phase of which behaved in the "standard" way without showing any obvious oscillations of the RHESSI count rates (Figure 3). This flare occurred in the same NOAA Active Region 10696 as the flare of November 6.

Figure 3: Time profiles of X-ray emission from the November 4, 2004 flare, observed by RHESSI (black, green, red, turquoise lines) and GOES-10 (blue and orange lines).

By comparing Figure 2 and Figure 4, it becomes evident that the modulation depth of the oscillations of the RHESSI detectors count rates is inversely proportional to the modulation depth of Delta oscillations. Relatively small modulation depth of Delta in the case of the 4 November flare does not lead to obvious oscillations of the RHESSI count rates.

Figure 4: 4-second averaged time profile of the angular distance (Delta; black) between the RHESSI imaging axis and the 2004 November 4 solar flare position and 20-second averaged normalized detrended corrected count rate integrated over the RHESSI detectors No 1,3,4,5,6,9 in the 6-12 keV energy channel (red) during the time interval marked by two vertical dashed lines in Figure 3. Note, that the slope of Delta represents drift of the RHESSI's spin axis (see Nugget 57).

Analysing several other solar flares, we came to the conclusion that the modulation depth of the Delta oscillations (due to nutation) is not the only factor affecting the appearance of the oscillations of the RHESSI count rates and their character. But this problem requires further careful study and is beyond the scope of this Nugget.

Conclusion

Undoubtedly, RHESSI is an effective tool to study QPP of X-ray emission in solar flares, but its data should be used with care to avoid erroneous interpretations. If you find periodicities of a few tens of seconds in RHESSI count rates, do the following steps to ensure that it is not the artefact described above:

1) Compare the oscillation period of the RHESSI count rates with that of the RHESSI imaging axis oscillations due to nutation. This information is contained in the RHESSI aspect solution database. If there is a correlation, then be wary.

2) Make light curves for individual RHESSI detectors, say, No 5 (nominal FOW is 1.0 deg) and No 8 (nominal FOW is 7.5 deg). If the modulation depth of the oscillations in detector 8 is smaller than in detector 5, then the oscillations can be considered suspect.

3) Try to confirm the oscillations by analysis of relevant data from other independent instruments. This is the most effective way of ensuring oscillations are of solar origin!