arXiv subjects

Roland Diehl

Publications and source records attributed to Roland Diehl.

At least 19 recordsLinked to original sources

arXiv2026

Relativistic $^{56}\text{Ni}$ Decay Lines in GRB 221009A

Long Gamma Ray Bursts are thought to originate from the core collapse of massive stars that give rise to energetic broad-lined Type Ic supernovae. The brightest burst ever recorded, GRB 221009A, has been linked to a broad-lined Type Ic supernova through late-time observations by the James Webb Space Telescope. An emission line evolving from $\sim$37 to $\sim$6~MeV is detected during the prompt phase. We propose that this time-evolving line is consistent with Doppler-boosted radioactive decay of nickel synthesized in the associated supernova and entrained in the relativistic jet, corresponding to the boosted 158~keV decay branch. We also report evidence for an additional higher-energy excess near $\sim$24~MeV at 290--300~s, detected at moderate statistical significance and consistent with the boosted 270~keV decay branch. The observed kinematics and flux evolution are compatible with expectations from radioactive decay, providing direct spectroscopic evidence linking prompt emission to supernova nucleosynthesis.

astro-ph.HE↗

arXiv2026

Nuclear astrophysics

Reactions between atomic nuclei are measured in great detail in terrestrial laboratory experiments; transferring and extrapolating this knowledge to how the same reactions act within cosmic environments presents major challenges. Cross-disciplinary efforts are needed in view of the many nuclear reactions that govern the chemical evolution of the universe, and occur in a broad range of stellar plasma conditions that require astrophysical exploration. Since the early identification of 'processes' of nucleosynthesis, new insights have been obtained on the complexity of nuclear reaction mechanisms. We use 12C induced capture and fusion processes to illustrate the challenge of low-energy measurements and of using theoretical methods to extrapolate measurements towards energy regimes within cosmic sources. Particle beam experiments at accelerator facilities above and deep underground simulate stellar reactions, new experimental facilities and methods complement these, and this is further complemented by improved theoretical tools to calculate the quantum effects of nuclear reactions at the various cosmic conditions. Astronomical signatures of cosmic nuclear reactions are deduced from light curves characterizing cosmic explosions through gamma-ray lines and presolar grains to the detection of rare neutrino particles from our Sun to distant cosmic events. High resolution spectroscopy of stars has been expanded to objects measured in the X-ray and the gamma energy range of the electromagnetic spectrum. Astro-seismology and isotopic analysis of meteoritic inclusions provide new tools. Chemical-evolution models describe the complex dynamics during the evolution of galaxies. This article summarizes the experimental and theoretical work, and the broad range of observational tools that test the experimental data and the theoretical interpretation of nuclear processes in the cosmos.

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arXiv2024

Origin of $^{60}$Fe nuclei in cosmic rays: the contribution of local OB associations

The presence of live $^{60}$Fe nuclei (lifetime of 3.8~Myr) in cosmic rays detected by the ACE/CRIS instrument suggests a nearby nucleosynthesis source. $^{60}$Fe is primarily produced in core-collapse supernovae, and we aim to clarify whether the detected $^{60}$Fe nuclei can be associated with a particular local supernova. We consider 25 OB associations and sub-groups located within 1 kpc of the solar system based on recent $Gaia$ census. A model is developed that combines stellar population synthesis within these OB associations, cosmic-ray acceleration within associated superbubbles, and cosmic-ray transport to the solar system. The most critical model parameter impacting $^{60}$Fe cosmic-ray production is the explodability criterion, which determines if a massive star ends its life as a supernova. Our study points to the Sco-Cen OB association as the most probable origin of the observed $^{60}$Fe nuclei, particularly suggesting they were accelerated in the Sco-Cen superbubble by a young supernova aged $\leq500$ kyr with a progenitor mass of approximately $13-20~M_\odot$. A less likely source is the supernova at the origin of the Geminga pulsar 342 kyr ago, if the progenitor originated in the Orion OB1 association. The contribution of local OB associations to the cosmic-ray density of stable $^{56}$Fe is estimated to be around 20\%, with some sensitivity to cosmic ray acceleration efficiency and diffusion coefficient. These findings shed light on the origins of cosmic-ray nuclei, connecting them to nucleosynthesis events within our local cosmic neighborhood.

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arXiv2024

Tracing the ejecta from cosmic nucleosynthesis

Long-lived radioactive by-products of nucleosynthesis provide an opportunity to trace the flow of ejecta away from its sources for times beyond where ejecta can be seen otherwise. Gamma rays from such radioactive decay in interstellar space can be measured with space-borne telescopes. A prominent useful example is 26Al with a radioactive decay time of one My. Such observations have revealed that typical surroundings of massive stars are composed of large cavities, extending to kpc sizes. Implications are that material recycling into new stars is twofold: rather direct as parental clouds are hosts to new star formation triggered by feedback, and more indirect as these large cavities merge with ambient interstellar gas after some delay. Kinematic measurements of hot interstellar gas carrying such ejecta promises important measurements complementing stellar and dense gas kinematics.

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arXiv2023

Cosmic Radioactivity and Galactic Chemical Evolution

The description of the tempo-spatial evolution of the composition of cosmic gas on galactic scales is called 'modelling galactic chemical evolution'. It aims to use knowledge about sources of nucleosynthesis and how they change the composition of interstellar gas, following the formation of stars and the ejection of products from nuclear fusion during their evolution and terminating explosions. Sources of nucleosynthesis are diverse: Stars with hydrostatic nuclear burning eject some of the products, and core-collapse supernovae add ejecta. Binary interactions lead to sources such as thermonuclear supernovae and kilonovae. Tracing ejecta from sources, with their different frequencies and environments, through the interstellar medium and successive star formation cycles is the goal of model descriptions. A variety of formalisms exist, from analytical through semi-analytical, numerical or stochastic approaches, gradually making descriptions of compositional evolution of cosmic matter more realistic, teaching us about the astrophysical processes involved in this complex aspect of our universe. Radioactive isotopes add important ingredients to such modelling: The intrinsic clock of the radioactive decay process adds a new aspect to the modelling algorithms that leads to different constraints on the important unknowns of star formation activity and interstellar transports. Several prominent examples illustrate how modelling the abundances of radioactive isotopes and their evolution have resulted in new lessons; among these are the galaxy-wide distribution of 26Al and 60Fe, the radioactive components of cosmic rays, the interpretations of terrestrial deposits of 60Fe and 244Pu, and the radioactive-decay daughter isotopes that were found in meteorites and characterise the birth environment of our solar system.

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arXiv2023

Galactic Population Synthesis of Radioactive Nucleosynthesis Ejecta

Diffuse gamma-ray line emission traces freshly produced radioisotopes in the interstellar gas, providing a unique perspective on the entire Galactic cycle of matter from nucleosynthesis in massive stars to their ejection and mixing in the interstellar medium. We aim at constructing a model of nucleosynthesis ejecta on galactic scale which is specifically tailored to complement the physically most important and empirically accessible features of gamma-ray measurements in the MeV range, in particular for decay gamma-rays such as $^{26}$Al, $^{60}$Fe or $^{44}$Ti. Based on properties of massive star groups, we developed a Population Synthesis Code which can instantiate galaxy models quickly and based on many different parameter configurations, such as the star formation rate, density profiles, or stellar evolution models. As a result, we obtain model maps of nucleosynthesis ejecta in the Galaxy which incorporate the population synthesis calculations of individual massive star groups. Based on a variety of stellar evolution models, supernova explodabilities, and density distributions, we find that the measured $^{26}$Al distribution from INTEGRAL/SPI can be explained by a Galaxy-wide population synthesis model with a star formation rate of $4$-$8\,\mathrm{M_{\odot}\,yr^{-1}}$ and a spiral-arm dominated density profile with a scale height of at least 700 pc. Our model requires that most massive stars indeed undergo a supernova explosion. This corresponds to a supernova rate in the Milky Way of $1.8$-$2.8$ per century, with quasi-persistent $^{26}$Al and $^{60}$Fe masses of $1.2$-$2.4\,\mathrm{M_{\odot}}$ and $1$-$6\,\mathrm{M_{\odot}}$, respectively. Comparing the simulated morphologies to SPI data suggests that a frequent merging of superbubbles may take place in the Galaxy, and that an unknown but strong foreground emission at 1.8 MeV could be present.

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arXiv2023

Gamma-ray spectroscopy of galactic nucleosynthesis

Diffuse gamma-ray emission from the decay of radioactive $^{26}$Al is a messenger from the nucleosynthesis activity in our current-day galaxy. Because this material is attributed to ejections from massive stars and their supernovae, the gamma-ray signal includes information about nucleosynthesis in massive star interiors as it varies with evolutionary stages, and about their feedback on the surrounding interstellar medium. Our method of population synthesis of massive-star groups has been refined as a diagnostic tool for this purpose. It allows to build a bottom-up prediction of the diffuse gamma-ray sky when known massive star group distributions and theoretical models of stellar evolution and core-collapse supernova explosions are employed. We find general consistency of an origin in such massive-star groups, in particular we also find support for the clumpy distribution of such source regions across the Galaxy, and characteristics of large cavities around these. A discrepancy in the integrated $^{26}$Al gamma-ray flux is interpreted as an indication for excess $^{26}$Al emission from nearby, distributed in cavities that extend over major regions of the sky.

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arXiv2022

$^{26}$Al gamma rays from the Galaxy with INTEGRAL/SPI

The presence of radioactive $^{26}$Al at 1.8 MeV reflects ongoing nucleosynthesis in the Milky Way. Diffuse emission from its decay can be measured with gamma-ray telescopes in space. The intensity, line shape, and spatial distribution of the $^{26}$Al emission allow a study of these nucleosynthesis sources. The line parameters trace massive-star feedback in the interstellar medium due to its 1~My lifetime. We aim to deepen previous studies of the $^{26}$Al emission in the Milky Way, using all gamma-ray data including single and double events as collected with SPI on INTEGRAL from 2003 until 2020. We apply improved spectral response and background as evaluated from tracing spectral details over the entire mission. The exposure for Galactic $^{26}$Al emission is enhanced using all event types measured within SPI. We re-determine the intensity of Galactic $^{26}$Al emission across the entire sky, through maximum likelihood fits of simulated and model-built sky distributions to SPI spectra for single and for double detector hits. We find an all-sky flux of (1.84$\pm$0.03$)\times$10$^{-3}$~ph~cm$^{-2}$s$^{-1}$ in the 1.809~MeV line from $^{26}$Al, determined as fitted to sky distributions from previous observations with COMPTEL. Significant emission from higher latitudes indicate an origin from nearby massive-star groups and superbubbles, also supported by a bottom-up population synthesis model. The line centroid is found at (1809.83$\pm$0.04~keV, and line broadening from source kinematics integrated over the sky is (0.62$\pm0.3$)~keV (FWHM).

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arXiv2022

Cosmic nucleosynthesis: a multi-messenger challenge

The origins of the elements and isotopes of cosmic material is a critical aspect of understanding the evolution of the universe. Nucleosynthesis typically requires physical conditions of high temperatures and densities. These are found in the Big Bang, in the interiors of stars, and in explosions with their compressional shocks and high neutrino and neutron fluxes. Many different tools are available to disentangle the composition of cosmic matter, in material of extraterrestrial origins such as cosmic rays, meteorites, stardust grains, lunar and terrestrial sediments, and through astronomical observations across the electromagnetic spectrum. Understanding cosmic abundances and their evolution requires combining such measurements with approaches of astrophysical, nuclear theories and laboratory experiments, and exploiting additional cosmic messengers, such as neutrinos and gravitational waves. Recent years have seen significant progress in almost all these fields; they are presented in this review. Models are required to explore nuclear fusion of heavier elements. These have been confirmed by observations of nucleosynthesis products in the ejecta of stars and supernovae, as captured by stardust grains and by characteristic lines in spectra seen from these objects, and also by ejecta material captured by Earth over millions of years in sediments. All these help to piece together how cosmic materials are transported in interstellar space and re-cycled into and between generations of stars. Our description of cosmic compositional evolution needs observational support, as it rests on several assumptions that appear challenged. This overview presents the flow of cosmic matter and the various sites of nucleosynthesis, as understood from combining many techniques and observations, towards the current knowledge of how the universe is enriched with elements.

astro-ph.HE↗

arXiv2022

Radioactive Decay

Radioactive decay of unstable atomic nuclei leads to liberation of nuclear binding energy in the forms of gamma-ray photons and secondary particles (electrons, positrons); their energy then energises surrounding matter. Unstable nuclei are formed in nuclear reactions, which can occur either in hot and dense extremes of stellar interiors or explosions, or from cosmic-ray collisions. In high-energy astronomy, direct observations of characteristic gamma-ray lines from the decay of radioactive isotopes are important tools to study the process of cosmic nucleosynthesis and its sources, as well as tracing the flows of ejecta from such sources of nucleosynthesis. These observations provide a valuable complement to indirect observations of radioactive energy deposits, such as the measurement of supernova light in the optical. Here we present basics of radioactive decay in astrophysical context, and how gamma-ray lines reveal details about stellar interiors, about explosions on stellar surfaces or of entire stars, and about the interstellar-medium processes that direct the flow and cooling of nucleosynthesis ashes once having left their sources. We address radioisotopes such as $^{56}$Ni, $^{44}$Ti, $^{26}$Al, $^{60}$Fe, $^{22}$Na, $^{7}$Be, and also how characteristic gamma-ray emission from the annihilation of positrons is connected to these.

astro-ph.HE↗

arXiv2021

Radioactive isotopes in the interstellar medium

Radioactive components of the interstellar medium provide an entirely-different and new aspect to the studies of the interstellar medium. Injected from sources of nucleosynthesis, unstable nuclei decay along their trajectories. Measurements can occur through characteristic gamma rays that are emitted with the decay, or in cosmic material samples through abundances of parent and daughter isotopes as they change with decay. The dynamics and material flows within interstellar medium are thus accessible to measurement, making use of the intrinsic clock that radioactive decay provides. We describe how measurements of radioactive decay have obtained a break-through in studies of the interstellar medium, after first summarizing the characteristics of radioactivity and the sources of unstable nuclei.

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arXiv2021

The Radioactive Nuclei $^{\textbf{26}}$Al and $^{\textbf{60}}$Fe in the Cosmos and in the Solar System

The cosmic evolution of the chemical elements from the Big Bang to the present time is driven by nuclear fusion reactions inside stars and stellar explosions. A cycle of matter recurrently re-processes metal-enriched stellar ejecta into the next generation of stars. The study of cosmic nucleosynthesis and of this matter cycle requires the understanding of the physics of nuclear reactions, of the conditions at which the nuclear reactions are activated inside the stars and stellar explosions, of the stellar ejection mechanisms through winds and explosions, and of the transport of the ejecta towards the next cycle, from hot plasma to cold, star-forming gas. Due to the long timescales of stellar evolution, and because of the infrequent occurrence of stellar explosions, observational studies are challenging. Due to their radioactive lifetime of million years, the 26Al and 60Fe isotopes are suitable to characterise simultaneously the processes of nuclear fusion reactions and of interstellar transport. We describe and discuss the nuclear reactions involved in the production and destruction of 26Al and 60Fe, the key characteristics of the stellar sites of their nucleosynthesis and their interstellar journey after ejection from the nucleosynthesis sites. We connect the theoretical astrophysical aspects to the variety of astronomical messengers, from stardust and cosmic-ray composition measurements, through observation of gamma rays produced by radioactivity, to material deposited in deep-sea ocean crusts and to the inferred composition of the first solids that have formed in the Solar System. We show that considering measurements of the isotopic ratio of 26Al to 60Fe eliminate some of the unknowns when interpreting astronomical results, and discuss the lessons learned from these two isotopes on cosmic chemical evolution.

astro-ph.HE↗

arXiv2021

Reticulum II: Particle Dark Matter and Primordial Black Holes Limits

Reticulum II (Ret II) is a satellite galaxy of the Milky Way and presents a prime target to investigate the nature of dark matter (DM) because of its high mass-to-light ratio. We evaluate a dedicated INTEGRAL observation campaign data set to obtain $γ$-ray fluxes from Ret II and compare those with expectations from DM. Ret II is not detected in the $γ$-ray band 25--8000 keV, and we derive a flux limit of $\lesssim 10^{-8}\,\mathrm{erg\,cm^{-2}\,s^{-1}}$. The previously reported 511 keV line is not seen, and we find a flux limit of $\lesssim 1.7 \times 10^{-4}\,\mathrm{ph\,cm^{-2}\,s^{-1}}$. We construct spectral models for primordial black hole (PBH) evaporation and annihilation/decay of particle DM, and subsequent annihilation of positrons produced in these processes. We exclude that the totality of DM in Ret II is made of a monochromatic distribution of PBHs of masses $\lesssim 8 \times 10^{15}\,\mathrm{g}$. Our limits on the velocity-averaged DM annihilation cross section into $e^+e^-$ are $\langle σv \rangle \lesssim 5 \times 10^{-28} \left(m_{\rm DM} / \mathrm{MeV} \right)^{2.5}\,\mathrm{cm^3\,s^{-1}}$. We conclude that analysing isolated targets in the MeV $γ$-ray band can set strong bounds on DM properties without multi-year data sets of the entire Milky Way, and encourage follow-up observations of Ret II and other dwarf galaxies.

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arXiv2021

INTEGRAL reloaded: spacecraft, instruments and ground system

ESA's INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL) was launched on 17 Oct 2002 at 06:41 CEST. Since then, it has been providing long, uninterrupted observations (up to about 47 hr, or 170 ksec, per satellite orbit of 2.7 days) with a large field-of-view (fully coded: 100 deg^2), msec time resolution, keV energy resolution, polarization measurements, as well as additional coverage in the optical. This is realized by two main instruments in the 15 keV to 10 MeV range, the spectrometer SPI (spectral resolution 3 keV at 1.8 MeV) and the imager IBIS (angular resolution 12 arcmin FWHM), complemented by X-ray (JEM-X; 3-35 keV) and optical (OMC; Johnson V-band) monitors. All instruments are co-aligned to simultaneously observe the target region. A particle radiation monitor (IREM) measures charged particle fluxes near the spacecraft. The Anti-coincidence subsystems of the main instruments are also efficient all-sky gamma-ray detectors, which provide omni-directional monitoring above ~75 keV. INTEGRAL can also rapidly (within a couple of hours) re-point and conduct Target of Opportunity observations. INTEGRAL has build an impressive legacy: e.g. discovery of >600 new high-energy sources; first-ever direct detection of 56Ni and 56Co radio-active decay lines from a Type Ia supernova; new insights on positron annihilation in the Galactic bulge and disk; pioneering gamma-ray polarization studies. INTEGRAL is also a successful in multi-messenger astronomy: INTEGRAL found the first prompt electromagnetic radiation in coincidence with a binary neutron star merger. More than 1750 papers based on INTEGRAL data have been published in refereed journals. Here we give a comprehensive update of the satellite status after more than 18 years of operations in a harsh space environment, and an account of the successful Ground Segment.

astro-ph.IM↗

arXiv2021

Exploration of Aspherical Ejecta Properties in Type Ia Supernova: Progenitor Dependence and Applications to Progenitor Classification

Several explosions of thermonuclear supernovae (SNe Ia) have been found to exhibit deviations from spherical symmetry upon closer inspection. Examples are the gamma-ray lines from SN 2014J as measured by INTEGRAL/SPI, and morphology information from radioactive isotopes in older remnants such as Tycho. A systematic study on the effects of parameters such as ignition geometry and burning morphology in SNe Ia is still missing. We use a 2D hydrodynamics code with post-processing nucleosynthesis and simulate the double detonations in a sub-Chandrasekhar mass carbon-oxygen white dwarf starting from the nuclear runaway in the accumulated He envelope towards disruption of the white dwarf. We explore potential variety through four triggering scenarios that sample main asymmetry drivers. We further investigate their global effects on the aspherical structure of the ejecta based on individual elements. We apply the results to the well observed SN 2014J and other recently observed SN remnants in order to illustrate how these new observational data together with other observed quantities help to constrain the explosion and the progenitors of SNe Ia.

astro-ph.HE↗

arXiv2020

Galactic 26Al traces metal loss through hot chimneys

Radioactive 26Al is an excellent tracer for metal ejection in the Milky Way, and can provide a direct constraint on the modelling of supernova feedback in galaxy evolution. Gamma-ray observations of the 26Al decay line have found high velocities and hence require a significant fraction of the Galactic 26Al in the hot component. At the same time, meteoritic data combined with simulation results suggest that a significant amount of 26Al makes its way into stars before decay. We investigated the distribution into hot and cold channels with a simulation of a Milky-Way-like galaxy with massive-star feedback in superbubbles and with ejecta traced by 26Al. About 30-40 per cent of the ejecta remain hot, with typical cooling times of the order Gyr. 26Al traces the footpoints of a chimney-fed outflow that mixes metals turbulently into the halo of the model galaxy on a scale of at least 50 kpc. The rest diffuses into cold gas with temperatures less than about 10,000 K, and may therefore be quickly available for star formation. We discuss the robustness of the result by comparison to a simulation with a different global flow pattern. The branching ratio into hot and cold components is comparable to that of longer term average results from chemical evolution modelling of galaxies, clusters and the intracluster medium.

astro-ph.GA↗

arXiv2020

Steady-state nucleosynthesis throughout the Galaxy

Measurement and astrophysical interpretation of characteristic gamma-ray lines from nucleosynthesis was one of the prominent science goals of the INTEGRAL mission and in particular its spectrometer SPI. Emission from 26Al and from 60Fe decay lines originates from accumulated ejecta of nucleosynthesis sources, and appears diffuse in nature. 26Al and 60Fe are believed to originate mostly from massive star clusters. Gamma-ray observations open an interesting window to trace the fate and flow of nucleosynthesis ejecta, after they have left the immediate sources and their birth sites, and on their path to mix with ambient interstellar gas. The INTEGRAL 26Al emission image confirms earlier findings of clumpiness and an extent along the entire plane of the Galaxy, supporting its origin from massive-star groups. INTEGRAL spectroscopy resolved the line and found Doppler broadenings and systematic shifts from large-scale galactic rotation. But an excess velocity of ~200 km/s suggests that 26Al decays preferentially within large superbubbles that extend in forward directions between spiral arms. The detection of 26Al line emission from nearby Orion and the Eridanus superbubble supports this interpretation. Positrons from beta+ decays of 26Al and other nucleosynthesis ejecta have been found to not explain the morphology of positron annihilation gamma-rays at 511 keV that have been measured by INTEGRAL. The 60Fe signal measured by INTEGRAL is diffuse but too weak for an imaging interpretation, an origin from point-like/concentrated sources is excluded. The 60Fe/26Al ratio is constrained to a range 0.2-0.4. Beyond improving precision of these results, diffuse nucleosynthesis contributions from novae (through 22Na radioactivity) and from past neutron star mergers in our Galaxy (from r-process radioactivity) are exciting new prospects for the remaining mission extensions.

astro-ph.IM↗

arXiv2020

$^{44}\rm Ti$ ejecta in young supernova remnants

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$σ$. 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.

astro-ph.HE↗