Annihilation of Positrons

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Number: 60
1st Author: Ron Murphy
2nd Author: Gerry Share
Published: 17 January 2007
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The solar atmosphere is relatively well understood. Temperatures increase slowly with altitude from a minimum of 4500 K close the photosphere and rise gradually through the complex region known as the chromosphere. Then there is a transition region where temperatures jump abruptly from tens of thousands of degrees Kelvin to the million-degree region characteristic of the solar corona. During solar flares the violent eruptions can drastically disturb these static conditions. Characterizing any layer of the solar atmosphere becomes difficult at these times because of the drastic changes related to the flare.

Protons and heavier ions accelerated in these flares can act as probes of the conditions in the chromosphere and even the photosphere. This is true because these ions can penetrate to depths where the overlying atmosphere can be in excess of 1 gram cm-2. These ions can interact with the ambient elements in the medium to produce new radioactive elements. One such element is 11C formed when a proton knocks out a neutron from the stable element 12C. Radioactive isotopes such as 11C decay with the emission of a positron into 11B, a stable isotope. Positrons are antimatter electrons which, when encountering an ordinary electron will mutually annihilate into gamma-rays (see an earlier Nugget for how RHESSI detects γ-rays). Depending on the temperature, density, and ionization state of the local medium, either two or three gamma-ray photons are emitted. The energies of the photons depend on the temperature through thermal Doppler shifts. Thus this radiation acts as a thermometer, barometer, and ionization meter in the depths of the solar atmosphere.

So how does a gamma-ray barometer work?

Actually the process is not as simple as one might envision from the above: a lonely positron wanders in search of an electron; they find one another and coalesce in the explosive emission of gamma-rays. But really only a few do. Most go through a more elaborate process that is key to their ability to characterize the flaring chromosphere and photosphere. The positrons from radioactive decay are typically emitted with energies of several hundred keV. The positrons first slow down in Coulomb collisions until they reach energies of less than 100 eV. From then on they can follow several paths: they can continue to slow down until they annihilate with an electron orbiting a proton (hydrogen atom), they can annihilate with a free electron, or they can form positronium, an atom made up of a positron and electron. Depending on the relative spins of the electron and positron they can form two states: "para-" and "ortho-positronium". The former decays very rapidly into two 511-keV gamma rays, while the latter takes more time to decay. If an orthopositronium atom collides with a hydrogen atom the spin of the positron or electron can flip and the atom can be converted into para-positronium and annihilate into two gamma-rays; if it avoids collision then it will decay into 3 photons, each below 511 keV, with a total energy of 1022 keV. After many annihilations the spectrum of the emitted radiation will contain a 511 keV line with a continuum below 511 keV falling with decreasing energy. The width of the annihilation line is determined by the temperature where the annihilation takes place.

Shown in Figure 1 are various line and continuum shapes that can occur in an active solar atmosphere depending on the temperature, density, and ionization. It takes an instrument such as RHESSI to resolve the annihilation line and to measure its width. RHESSI first measured this line in the 2002 July 23 solar flare. The width of the line was surprisingly large, suggesting that the positrons annihilated in an ambient medium with a temperature in excess of 100,000 K, a factor of more than twenty-times hotter than that observed from the static chromosphere.

Figure 1: Calculated line profiles for fully ionized medium at T = 104 and 106 K with nH = 1013 cm-3. The components contributing to the spectrum are indicated: radiative combination with free electrons (rc), direct annihilation with free electrons (daf) and the 3-photon positronium continuum (dotted curve). The 2003 October 28 flare offered more spectacular evidence for a highly dynamic atmosphere. Shown in the top panel of Figure 2 is the spectrum of the 511-keV line observed during the first ten minutes of the flare. The line was about 7 keV wide, again suggesting temperatures of a few hundred thousand K where the positrons annihilated. However, the width of the line narrowed within two minutes to a value expected for more traditional chromospheric conditions as shown in the bottom panel.

Figure 2: Observed count spectra and fits for the 2003 October 28 flare. The broad October 28 line is shown in the top panel with the Gaussian fit. The narrow October 28 line is shown in the lower panel with the Gaussian fit.

Complications and conclusions

There is evidence that this dynamic variability in the chromosphere was created by beams of ions and electrons that moved rapidly and heated different regions. Once these beams dissipated the local atmosphere was no longer heated and the positrons annihilated in a cooler less dynamic region.

There are several other RHESSI flares for which we have measurements of the annihilation line that are currently being analyzed. One of the complications that has required careful consideration in some of these flares is an instrumental background annihilation line formed in RHESSI itself when it is radiated by photons greater than about 16 MeV from the flare. This has required improvements in the RHESSI energy response matrix that are now being incorporated in the analysis. Stay tuned for new developments.

Biographical note: Ron Murphy and Gerry Share are RHESSI team members at the Naval Research Laboratory and the University of Maryland, College Park, respectively.

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