Historical Type Ia supernovae are a leading candidate for the source of positrons observed through their diffuse annihilation emission in the Galaxy . However , search for annihilation emission from individual Type Ia supernovae has not been possible before the improved sensitivity of INTEGRAL . The total 511 keV annihilation flux from individual SNe Ia , as well as their contribution to the overall diffuse emission , depends critically on the escape fraction of positrons produced in ^ { 56 } Co decays . Late optical light curves suggest that this fraction may be as high as 5 % . We searched for positron annihilation radiation from the historical Type Ia supernova SN 1006 using the SPI instrument on INTEGRAL . We did not detect significant 511 keV line emission , with a 3 \sigma flux upper limit of 0.59 \times 10 ^ { -4 } photons cm ^ { -2 } s ^ { -1 } for \sim 1 Msec exposure time , assuming a FWHM of 2.5 keV . This upper limit corresponds to a 7.5 % escape fraction , 50 % higher than the expected 5 % escape scenario , and rules out the possibility that Type Ia supernovae produce all of the positrons in the Galaxy ( \sim 12 % escape fraction ) , if the mean positron lifetime is less than 10 ^ { 5 } years . Future observations with INTEGRAL will provide stronger limits on the escape fraction of positrons , the mean positron lifetime , and the contribution of Type Ia supernovae to the overall positron content of the Galaxy .