Context: Tracing unstable isotopes produced in supernova nucleosynthesis provides a direct diagnostic of supernova explosion physics. Theoretical models predict an extensive variety of scenarios, which can be constrained through observations of the abundant isotopes $^{56}$Ni and $^{44}$Ti. Direct evidence of the latter was previously found only in two core-collapse supernova events, and appears to be absent in thermonuclear supernovae.Aims: We aim to to constrain the supernova progenitor types of Cas A, SN 1987A, Vela Jr., G1.9+0.3, SN1572, and SN1604 through their $^{44}$Ti ejecta masses and explosion kinematics. Methods: We analyzed INTEGRAL/SPI observations of the candidate sources utilizing an empirically motivated high-precision background model. We analyzed the three dominant spectroscopically resolved de-excitation lines at 68, 78, and 1157,keV emitted in the decay chain of $^{44}$Ti. The fluxes allow the determination of the production yields of $^{44}$Ti. Remnant kinematics were obtained from the Doppler characteristics of the lines. Results: We find a significant signal for Cas A in all three lines with a combined significance of 5.4$sigma$. The fluxes are $(3.3 pm 0.9) times 10^{-5}$ ph cm$^{-2}$ s$^{-1}$, and $(4.2 pm 1.0) times 10^{-5}$ ph cm$^{-2}$ s$^{-1}$ for the $^{44}$Ti and $^{44}$Sc decay, respectively. We obtain higher fluxes for $^{44}$Ti with our analysis of Cas A than were obtained in previous analyses. We discuss potential differences. Conclusions: We obtain a high $^{44}$Ti ejecta mass for Cas A that is in disagreement with ejecta yields from symmetric 2D models. Upper limits for the other core-collapse supernovae are in agreement with model predictions and previous studies. The upper limits we find for the three thermonuclear supernovae consistently exclude the double detonation and pure helium deflagration models as progenitors.
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