The Galactic 511 keV Line as a Positron Budget: The Required Annihilation Rate and What Each Candidate Source Can Pay

The spectrometer SPI on INTEGRAL measures a 511 keV annihilation line from the Galactic bulge with a flux of (0.96 ± 0.07) × 10⁻³ photons cm⁻² s⁻¹, a disk component of (1.66 ± 0.35) × 10⁻³ photons cm⁻² s⁻¹, and a total Galactic line intensity of (2.74 ± 0.25) × 10⁻³ photons cm⁻² s⁻¹ (Siegert et al. 2016). Converting these fluxes with the measured positronium fraction f_Ps ≈ 0.97, which gives 0.545 line photons per annihilated positron, the bulge alone requires a steady positron annihilation rate of 1.52 × 10⁴³ e⁺ s⁻¹, and a distance-based conversion of the total flux gives 4.35 × 10⁴³ e⁺ s⁻¹ for the Galaxy as a whole. This paper assembles the payment side of the budget from the published yields and rates of each candidate source. Radioactive ²⁶Al, measured directly through its 1.809 MeV line, supplies 3.24 × 10⁴² e⁺ s⁻¹. Positrons from ⁵⁶Co in Type Ia supernovae supply 3.09 × 10⁴², 9.27 × 10⁴², or 1.54 × 10⁴³ e⁺ s⁻¹ for positron escape fractions of 1%, 3%, and 5% respectively. ⁴⁴Ti supplies at most 1.55 × 10⁴² e⁺ s⁻¹, and novae at most 2 × 10⁴¹ e⁺ s⁻¹. The summed conventional budget, with Type Ia supernovae at a 3% escape fraction, is 1.43 × 10⁴³ e⁺ s⁻¹, a factor of 3.0 below the required Galactic total. The deficit is far worse where the emission is brightest: only about 2.42 × 10⁴² e⁺ s⁻¹ of the conventional budget is delivered to the bulge, a factor of 6.3 below the bulge requirement of 1.52 × 10⁴³ e⁺ s⁻¹, because ²⁶Al and ⁴⁴Ti follow massive stars in the disk and contribute essentially nothing to the bulge, while Type Ia supernovae deliver only about a quarter of their positrons there. Low-mass X-ray binaries and microquasars could in principle pay up to about 10⁴³ e⁺ s⁻¹ if their jets are dominated by electron–positron pairs, but the pair content of the jets is unmeasured. A light dark-matter particle annihilating directly to e⁺e⁻ pairs would need a velocity-averaged cross section of about 5 × 10⁻³¹ (m_χ/MeV)² cm³ s⁻¹ to supply the bulge, a requirement that sits above the strongest current INTEGRAL-based profile limits at MeV masses. The budget therefore does not close with conventional sources at their measured rates, and the morphology mismatch — 35% of the annihilation flux arising in the bulge, against a bulge share of essentially 0% for the ²⁶Al distribution and about 25% for the Type Ia distribution — is the sharpest statement of the problem.