Design of a mission to measure the shape and substructure of the 511 keV gamma-ray line from the center of the Milky Way
The 511 keV electron-positron annihilation feature near the galactic center has been detected for more than half a century, yet its origin remains a mystery. In this paper, we describe a concept for a balloon-borne 511 keV $\gamma$-ray mission called the 511-Spectrometer Mission. The mission will use Transition-Edge Sensor (TES) arrays with thick metal absorbers that are thermally coupled to the TES. The strength of the approach is a projected energy resolution of 200 eV Full Width Half Maximum (FWHM) at 511 keV, enabling detailed studies of the shape and substructure of the 511 keV emission from the galactic center region. A first mission equipped with 8,192 $\gamma$-ray detectors and a fully active shield and collimator could detect the galactic center with ~35 $\sigma$ statistical significance. We present the mission concept as well as first results obtained with a prototype detector equipped with $1.35\times1.35\times2$ mm$^{3}$ Bi absorbers. The detector has a quantum efficiency of 15% for 511 keV photons in photoelectric effect interactions. In tests with a $^{137}$Cs source, these prototype detectors show an energy resolution of 525 eV FWHM at 662 keV. We end with a discussion of follow-up missions that use coded mask imaging, or use concentrating or focusing optics to scrutinize the sources of 511 keV $\gamma$-rays on smaller angular scales.