Context : The annihilation of cosmic positrons with electrons in the interstellar medium results in the strongest persistent \gamma -ray line signal in the sky .
For the past 50 years , this 511 keV emission - predominantly from the galactic bulge region and from a low surface-brightness disk - has puzzled observers and theoreticians .
A key issue for understanding positron astrophysics is found in cosmic-ray propagation , especially at low kinetic energies ( \lesssim 10 MeV ) .

Aims : We want to shed light on how positrons propagate and the resulting morphology of the annihilation emission .
We approach this ” positron puzzle ” by inferring kinematic information of the 511 keV line in the inner radian of the Galaxy .
This constrains propagation scenarios and positron source populations in the Milky Way .

Methods : By dissecting the positron annihilation emission as measured with INTEGRAL/SPI , we derive spectra for individual and independent regions in the sky .
The centroid energies of these spectra around the 511 keV line are converted into Doppler-shifts , representing the line-of-sight velocity along different galactic longitudes .
This results in a longitude-velocity diagram of positron annihilation .
From high-resolution spectra , we also determine Doppler-broadening from \gamma -ray line shape parameters to study annihilation conditions as they vary with galactic longitude .

Results : We find line-of-sight velocities in the 511 keV line that are consistent with zero , as well as with galactic rotation from CO measurements ( 2 – 3 ~ { } \mathrm { km~ { } s ^ { -1 } ~ { } deg ^ { -1 } } ) , and measurements of radioactive \mathrm { { } ^ { 26 } Al } ( 7.5 – 9.5 ~ { } \mathrm { km~ { } s ^ { -1 } ~ { } deg ^ { -1 } } ) .
The velocity gradient in the inner \pm 30 ^ { \circ } is determined to be 4 \pm 6 ~ { } \mathrm { km~ { } s ^ { -1 } ~ { } deg ^ { -1 } } .
The width of the 511 keV line is constant as a function of longitude at 2.43 \pm 0.14 keV , with possibly different values towards the disk .
The positronium fraction is found to be 1.0 along the galactic plane .

Conclusions : The weak signals in the disk leave open the question whether positron annihilation is associated with the high velocities seen in \mathrm { { } ^ { 26 } Al } or rather with ordinarily rotating components of the Milky Way ’ s interstellar medium .
We confirm previous results that positrons are slowed down to the 10 eV energy scale before annihilation , and constrain bulk Doppler-broadening contributions to \lesssim 1.25 keV in the inner radian .
Consequently , the true annihilation conditions remain unclear .