Titanium-44 (44Ti^{44}\mathrm{Ti}), with a half-life of about 60 years, is synthesized in the innermost ejecta of core-collapse supernovae, and its gamma-ray decay lines should expose every young Galactic supernova remnant bright enough to detect. Yet all surveys to date have firmly detected only Cassiopeia A. Dufour & Kaspi (2013) showed by population synthesis that a single detection is statistically compatible with plausible ranges of per-event 44Ti^{44}\mathrm{Ti} yields, the Galactic supernova rate and type ratios, and progenitor spatial-distribution models, and predicted 5–14 detections at a line-flux limit of 10−610^{-6} and 8–21 at 10−710^{-7} photons cm−2^{-2} s−1^{-1}. The unresolved scientific problem is the joint determination of those inputs: the progenitor-mass dependence of Type II 44Ti^{44}\mathrm{Ti} yields and the true spread for Types Ibc and Ia; the contribution of rare high-yield classes such as calcium-rich gap transients to the steady-state Galactic 44Ti^{44}\mathrm{Ti} budget; the type-resolved Galactic core-collapse rate; the massive-star spatial distribution; the poorly measured fluxes of individual candidate remnants (G1.9+0.3; the disputed Vela Jr claim); and the possible modification of the effective 44Ti^{44}\mathrm{Ti} decay lifetime by ionization in young ejecta. Later surveys (INTEGRAL/IBIS 2016) and individual-source measurements through 2025 have added no new firm Galactic detections and left even the SN 1987A yield in factor-of-two tension, so the joint population problem remains open.

Background

A supernova remnant (SNR) is the expanding stellar-ejecta structure left after a supernova. The isotope 44Ti^{44}\mathrm{Ti} is produced mainly in the deepest, silicon-burning layers ejected by core-collapse supernovae (the explosions of massive stars), and to a lesser extent in some thermonuclear (Type Ia) events. It is radioactive with a half-life of about 60 years, decaying by electron capture through 44Sc^{44}\mathrm{Sc} to stable 44Ca^{44}\mathrm{Ca} and emitting characteristic gamma-ray lines at 68, 78, and 1157 keV. Because the isotope dies away on a few-century timescale, any SNR detectable in these lines must be young — the isotope is a radioactive 'clock' that also measures, through its inferred ejecta mass, how deeply the explosion excavated the star's interior.

Observationally, the gamma-ray line sky at MeV energies has been mapped by the COMPTEL instrument on the Compton Gamma Ray Observatory and by the IBIS and SPI instruments on INTEGRAL. The only firmly detected Galactic 44Ti^{44}\mathrm{Ti} source is Cassiopeia A (Cas A), the youngest known Galactic core-collapse remnant (age roughly 330–350 years), with a decay-line flux of about 2.5×10−52.5\times10^{-5} photons cm−2^{-2} s−1^{-1}. Two further candidate signals shaped the debate: the COMPTEL report of 44Ti^{44}\mathrm{Ti} lines from the Vela Jr remnant (RX J0852.0−4622), whose reality was disputed from the outset, and a weak 44Sc fluorescence signal from G1.9+0.3, the youngest known Galactic remnant, whose flux is poorly measured. In the Large Magellanic Cloud, SN 1987A was later confirmed as a 44Ti^{44}\mathrm{Ti} source by INTEGRAL.

The puzzle is that simple expectations predicted more detections. The steady-state Galactic 44Ti^{44}\mathrm{Ti} production rate inferred from the interstellar abundance of its decay product 44Ca^{44}\mathrm{Ca} is between 5.5×10−55.5\times10^{-5} and 6.0×10−4 M⊙6.0\times10^{-4}\,M_\odot per century (The et al. 2006), and The et al. argued that 'several' 44Ti^{44}\mathrm{Ti}-bright remnants should therefore have been seen, making the lone Cas A detection improbable (about 1.2% in their estimate). Dufour & Kaspi (2013) re-examined this with a population-synthesis calculation — a Monte Carlo scheme that draws supernova events from assumed spatial-distribution models, assigns each a 44Ti^{44}\mathrm{Ti} yield by type, decays the isotope, and computes the resulting flux distribution, with priors on all inputs sampled by Markov-chain Monte Carlo (MCMC, a standard Bayesian parameter-sampling method). They found the single detection of Cas A to be statistically acceptable (probability 2.7−2.4+10.0%2.7^{+10.0}_{-2.4}\% of exactly one detection above a flux limit of 10−510^{-5} photons cm−2^{-2} s−1^{-1}, with 2–9 expected detections), showed that Cas A's surprisingly high Galactic longitude is unremarkable if it is the brightest source, and predicted 5–14 detections at a 10−610^{-6} flux limit and 8–21 at 10−710^{-7} for future, more sensitive missions.

Their conclusion, however, rested on inputs they themselves flagged as unresolved: per-event yields (the Type II progenitor-mass dependence and the spread for Types Ibc and Ia — for which 'calcium-rich gap transients', a class of faint, fast transients found in the remote outskirts of galaxies whose ejecta may be 5–50% 44Ti^{44}\mathrm{Ti}, are a potentially important wildcard); the Galactic core-collapse and type-resolved supernova rate; the spatial distribution of massive-star progenitors (radial profile, spiral arms, local overdensities); the poorly measured fluxes of G1.9+0.3 and the disputed Vela Jr claim; and a neglected physical effect — 44Ti^{44}\mathrm{Ti} decays by capturing an electron, so if the atoms are highly ionized in hot young ejecta the decay is suppressed and the effective lifetime changes (Mochizuki et al. 1999). These are not independent curiosities: they are the joint inputs of one population model whose output must match one observed record, which is why they constitute a single scientific problem rather than a list of separate measurements.

Problem Statement

Determine, as one joint inference problem, which combinations of (i) per-event 44Ti^{44}\mathrm{Ti} yields as a function of supernova type and progenitor — including the Type II progenitor-mass dependence, the true spread for Types Ibc and Ia, and whether rare high-yield events such as calcium-rich gap transients contribute appreciably to the steady-state Galactic 44Ti^{44}\mathrm{Ti} production of 5.5×10−55.5\times10^{-5} to 6.0×10−4 M⊙6.0\times10^{-4}\,M_\odot per century — (ii) the type-resolved Galactic supernova rate, (iii) the massive-star progenitor spatial distribution (radial profile, spiral-arm structure, local overdensities), and (iv) the effective 44Ti^{44}\mathrm{Ti} decay lifetime in young ejecta, including whether electron-capture decay is suppressed by ionization (Mochizuki et al. 1999), reproduce the full current record of 44Ti^{44}\mathrm{Ti} line survey detections and upper limits: Cassiopeia A as the only firm Galactic detection and the non-detections of the deepest surveys (COMPTEL, INTEGRAL/IBIS as compiled by Tsygankov et al. 2016, INTEGRAL/SPI as compiled by Weinberger et al. 2020), with the disputed COMPTEL Vela Jr claim and the poorly measured G1.9+0.3 flux entering that record under an explicitly stated statistical treatment — included, excluded, or marginalized over, case by case as in Dufour & Kaspi (2013) — rather than as detections required to be reproduced simultaneously with the later non-detections of the same objects. Throughout, 'reproduce' means consistency between the predicted and observed detections and upper limits at a stated credibility level under a stated likelihood, and every flux entering the record and the predictions below is a single-scalar 44Ti^{44}\mathrm{Ti} decay-line flux per remnant in the convention of Dufour & Kaspi (2013), a convention that fixes the flux representation only and not the effective decay-lifetime treatment of input (iv). The answer must then predict, with quantified uncertainties, the number and flux distribution of Galactic 44Ti^{44}\mathrm{Ti}-emitting young supernova remnants detectable at line-flux limits of 10−610^{-6} and 10−710^{-7} photons cm−2^{-2} s−1^{-1}, so that the Dufour–Kaspi forecasts of 5–14 and 8–21 detections at those limits can be tested or revised, and must state explicitly which combinations of yields, rates, spatial distributions, and effective decay-lifetime treatments the small-number statistics still permit.

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