Understanding the origin of the positron annihilation line and the physics of supernova explosions

Nuclear astrophysics, and particularly nuclear emission line diagnostics from a variety of cosmic sites, has remained one of the least developed fields in experimental astronomy, despite its central role in addressing a number of outstanding questions in modern astrophysics. Radioactive isotopes are co-produced with stable isotopes in the fusion reactions of nucleosynthesis in supernova explosions and other violent events, such as neutron star mergers. The origin of the 511 keV positron annihilation line observed in the direction of the Galactic Center is a 50-year-long mystery. In fact, we still do not understand whether its diffuse large-scale emission is entirely due to a population of discrete sources, which are unresolved with current poor angular resolution instruments at these energies, or whether dark matter annihilation could contribute to it. From the results obtained in the pioneering decades of this experimentally-challenging window, it has become clear that some of the most pressing issues in high-energy astrophysics and astro-particle physics would greatly benefit from significant progress in the observational capabilities in the keV-to-MeV energy band. Current instrumentation is in fact not sensitive enough to detect radioactive and annihilation lines from a wide variety of phenomena in our and nearby galaxies, let alone study the spatial distribution of their emission. In this White Paper (WP), we discuss how unprecedented studies in this field will become possible with a new low-energy gamma-ray space experiment, called ASTENA (Advanced Surveyor of Transient Events and Nuclear Astrophysics), which combines new imaging, spectroscopic and polarization capabilities. In a separate WP (Guidorzi et al. 39), we discuss how the same mission concept will enable new groundbreaking studies of the physics of Gamma–Ray Bursts and other high-energy transient phenomena over the next decades.


Introduction
Nuclear science is key to understanding the energy that makes stars and supernovae shine, as well as the synthesis of the variety of chemical elements that evolved from the H-He mix left behind after the big bang. Despite its central role however, nuclear astrophysics has mostly remained a theoretical field, rather than an experimentallyconfirmed science. It is in fact one of the most challenging and least developed fields of astronomy. The limited sensitivity and imaging capabilities of the gamma-ray instrumentation flown thus far has limited nuclear astrophysics studies only to the brightest nearby sources. This suggests that a large discovery space could be opened in this field by expanding the experimental frontier. Among the most relevant open issues of astro-particle physics today is certainly the origin of the 511 keV positron annihilation line from the Galactic bulge region and whether the seemingly diffuse emission is made up of a population of discrete unresolved sources. Another longoutstanding issue is a detailed understanding of the physical processes that shape the explosion of Type-Ia and core-collapse supernovae, which has been hindered because of the poorly-developed state of nuclear astrophysics. Specifically, Type-Ia SN are the most important distance indicators on cosmological scales, thanks to an empirical relation (the Phillips law, [61]), that links their luminosity at maximum with the post-peak decline rate, thus making SN-Ia good standard candles. A landmark experimental advance in this field would make nuclear line diagnostics an essential tool to develop self-consistent physical models of SN-Ia light curves, which will lead to understand the nature of the current observed scatter and their behaviour as standard candles. More generally the exponential fading exhibited by SN light curves is an indirect evidence of elements being made [23]. Nuclear gamma-ray astronomy carried out with the proposed mission concept ASTENA would provide a direct experimental confirmation of explosive nucleosynthesis theory, both in the continuum and in the lines emitted following the decay of 56 Co, 56 Ni, 44 Ti and 56 Fe.

The 511 keV positron annihilation line from the Galactic Center region
A recollection of the discovery and early observations of the 511 keV line can be found in the historical review on hard X-/soft gamma-ray astronomy by [17]. For

Candidate sources -Detecting sources in flagranti
Due to the seemingly asymmetric disc reported by [81], an attempt was made to correlate the emission with the population of Low Mass X-ray Binaries (LMXRBs), dominating at 10 keV, as the distribution of the 71 known LMXRBs appeared tantalizingly similarly asymmetric (45 at negative longitudes, 26 at positive longitudes). While the asymmetry was not confirmed (see Fig. 1, from [81] and [13]), LMXRBs may still have a large contribution to the positron content of the Milky Way. As a result of annihilation of positrons produced in e + -e − pair-dominated jets [18] of black-hole systems or of γ -γ interactions in the inner regions of hightemperature/high-density accretion discs of XRB systems, the population of XRBs can potentially account for all the positrons seen to annihilate. This microquasar-511 keV conjecture is supported by detections of thermal pair plasma emission from three sources in outburst: 1E 1740.7-2942, also known as "the Great Annihilator" [12], Nova Musca [34], and V404 Cygni [68] -all of which have been debated though. Also, given the thousands of Chandra sources revealed within only 17 × 17 arcmin around Sgr A * [40], the possibility that the 511 keV line is due to a superposition of discrete sources remains an attractive solution.
Sgr A * itself is also a prominent candidate source in this context, either by a pairdominated jet, 'calming down' from past AGN activity, or triggering a starburst event several million years ago [3,62]. The possibility of a point-like source in the GC [69,73] requires confirmation, and still opens intriguing possibilities concerning the positron puzzle. Given the low angular resolution (2.7 • ) of SPI [76] and other experiments, [6] recall that "from the data it is unclear whether the emission is truly diffuse, or if it originates either from a single discrete source (e.g. SgrA * or 1E 1740.7-2942 [...]) or from a small number of discrete but unresolved sources.". Within 2.7 • at a distance of 8.1 kpc, a region as large as 400 pc fits into only one PSF of SPI. This size is reminiscent of the Central Molecular Zone, harbouring not only XRBs, but also molecular gas in which positrons may prefer to annihilate, as well as a dense cluster of stars -the nuclear stellar cluster. The population of flaring M-to G-type stars may in fact provide a complete solution as well: [8] estimated that the ∼ 10 11 stars in the Milky Way show a quasi-persistent 511 keV flux from intermittent stellar flares, Fig. 1 Sky map of the 511 keV positron annihilation line found with the INTEGRAL SPI telescope by [81] (left panel) and by [13] (right panel). According to [81], the integrated fluxes in the negative (−50 < l < 0) and positive (0 < l < 50) longitude bands, within 10 deg of the Galactic plane, are (4.3 ± 0.5) × 10 −3 photons cm −2 s −1 and (2.4 ± 0.5) × 10 −3 photons cm −2 s −1 , respectively. The integrated flux found by [13] was consistent with that reported by [81], but no asymmetry was found producing pions and β + -unstable nuclei. The sheer number of stars may appear as a diffuse flux of the order of 10 −3 photons cm −2 s −1 at 511 keV and would readily explain the bulge emission. The nuclear stellar cluster as well as a large number of the Milky Way's globular clusters would stand out of the otherwise diffuse glow and provide direct evidence for these types of scenarios. With arcmin resolution, it would furthermore be possible to distinguish among mildly relativistic, quiescent XRB outflows [7] or stellar flares as the latter would directly follow the globular cluster's radial profile.
A possible explanation for the positron puzzle is the β + -decay from radioactive ejecta of massive stars and their core-collapse supernovae (CCSNe), as well as of white dwarf systems in classical novae (CNe) or thermonuclear type Ia supernovae (SNe Ia). Here, the most important nuclei are 26 Al (T 1/2 ≈ 717 kyr; 1809 keV line; massive star winds, CCSNe, CNe), 44 Ti (T 1/2 ≈ 60 yr; 68, 78, 1157 keV lines; CCSNe, SNe Ia, e.g. [72]), 22 Na (T 1/2 ≈ 2.75 yr; 1275 keV line; CNe), and 56 Co (T 1/2 ≈ 0.2 yr; 847, 1238 keV lines, 2 CCSNe, SNe Ia, e.g. [22]). While the latter is the main energy producer for the light curves of SNe Ia and consequently the lineof-sight escape from the main sources is very uncertain (e.g. [59]), all the decay positrons have in common that they first have to slow down to explain the measured signal: β + -decay typically emits MeV positrons, but the line shape suggests positrons at eV energies (e.g. [20,44,69,71]). This slowing down is connected to the propagation of cosmic-ray positrons, and the interplay of the environmental conditions near the initial source and the properties of the interstellar medium between source and region of annihilation. This becomes even more important when pairproduced positrons from interactions of high-energy photons in the strong magnetic fields of pulsars are considered (e.g. [25]). In addition to these away-from-the-source scenarios, CNe systems are expected to show a short ∼ 1 hr flash or 511 keV radiation from the decay of short-lived 13 N and 18 F, which however has never been detected. In order to distinguish between either of these scenarios, or to establish whether more sources are required to explain the total signal, superb line sensitivity as well as unprecedented angular resolution is required. The focusing telescope part of the ASTENA mission concept we are proposing here will have a 511 keV sensitivity of ∼ 7 × 10 −6 in 1 Ms (see Fig. 17), with which it will be possible: 1) to detect 511 keV emission from SNe Ia up to a distance of ∼ 10 Mpc to directly measure the escape fraction of positrons, 2) to see CNe flashes up to 5 kpc and detect the decay positrons from 22 Na up to 1 kpc, 3) to unravel the annihilation regions in the vicinity of massive stars (e.g. Cygnus OB associations), 4) to discover the late light curve heating of CCSNe by measuring positron annihilation from 44 Ti in Cassiopeia A, and 5) to possibly detect extragalactic emission regions of 511 keV in the LMC and M31.
Ultimately, with our proposed instrumentation one will be able to discriminate between the diffuse vs. discrete origin of the 511 keV line, by performing a scan of selected regions near the GC, with a telescope with a much higher sensitivity and angular resolution than any current or planned instrumentation.

The 511 keV line and the quest for dark matter
As summarised above, the pure astrophysical explanation of the 511 keV diffuse emission extending over ∼ 10 deg 2 around the GC is far from being clear, and it remains a challenge to explain the spectrum, intensity and morphology of the INTE-GRAL signal with candidate sources (see [62] for a review). Therefore, since the first detailed map of the GC by INTEGRAL SPI was released ( Fig. 1), many studies have tried to establish whether annihilation or decay of dark matter (DM) particles can possibly contribute to the 511 keV line production (e.g. [10,29], see also [9]). Even though the central slope of the dark matter density profile of our galaxy is still not well known, the number density of annihilating positrons depends on the square of the DM number density, which necessarily peaks near the GC. These first and more recent studies (e.g. [19]) have constrained the possible annihilation channels, annihilation cross sections, and dark matter mass range, finding that specific models with MeV-to-GeV masses can reproduce the 511 keV signal, and at the same time being consistent with the relic density of DM from cosmological observations. Other studies have instead found MeV annihilating relic dark matter inconsistent with cosmological data ( [83]). It is clear that the lack of knowledge of the physics of DM, makes these predictions quite speculative, especially when the contribution of discrete, currently unresolved sources to the 511 keV extended signal, is still not known. By disentangling the point source contribution from the 511 keV emission Fig. 3 Expected gamma-ray spectrum of a SN Ia at 20 days from the explosion for a range of models where the explosion energy, total mass, nickel mass and its distribution are varied across the range of current explosion models [42] with highly sensitive, sub-arcminute resolution maps, one will obtain a firm measurement of a possible excess of positrons in the galactic bulge. This will in turn significantly narrow down the range of DM physical parameters consistent with such excess, or lack thereof.

Type Ia SNe
SN Ia are the outcome of the thermonuclear explosion of either a single Carbon/Oxygen white dwarf with a mass near the Chandrasekhar limit in a close binary system or a pair of merging white dwarfs. The burning of the Carbon/Oxygen mixture provides the required kinetic energy, while the decay of 56 Ni −→ 56 Co with a half-life of 6.1 days and that of 56 Co −→ 56 Fe, with a half-life of 77.7 days, power the optical light curve, as shown by the SN2014J observations with INTEGRAL, 50 and 100 days after the explosion [21,27], in agreement with theoretical expectations, e.g., by [49]. Using the SPI and the IBIS/ISGRI telescopes aboard INTEGRAL, [21] reported the detection of the 56 Co lines at energies of 847 keV and 1238 keV and a γ -ray continuum in the 200-400 keV band. Detection of the 56 Co gamma rays establishes directly that 0.6 ± 0.1 solar masses of radioactive 56 Ni were synthesized Reprinted from [28] during the explosion [21,27]. On the other side, about three weeks after the explosion of this same SN, from data obtained with the SPI telescope, [28] reported the detection of both the 158 and 812 keV lines from the 56 Ni decay, with intensities of (1.10 ± 0.42) × 10 −4 photons cm −2 s −1 and (1.90 ± 0.66) × 10 −4 photons cm −2 s −1 , respectively. This evidence of radioactive 56 Ni near the surface, later confirmed by [43], points to explosion asymmetries, if not an initial, triggering, surface explosion (see discussion in [28]).
Understanding the physical processes leading to explosions of type Ia SNe is very important, given that SN Ia are used as distance indicators at cosmological scale, extrapolating the empirical Phillips correlation far beyond the established nearby redshift regime. The Phillips relation between maximum luminosity and post-peak decline rate allows one to standardize the absolute luminosity and correct for individual SN Ia properties, as shown by reducing the light peak dispersion of the observed SNe from 1.5 mag to 0.1-0.2 mag. A robust physical modeling of the Phillips law could further improve the accuracy in the distance measurement, as, e.g., effects of different metallicity on the explosion would be included in a truly-physical model. Given the primary role of 56 Ni and its products in powering the light curve, the measurement of SNe Ia gamma-ray lines and continuum spectrum is a crucial diagnostic tool to understand the physics of the explosion and its evolution [35].
At early times from the explosion (see Fig. 2), the spectrum is dominated by the 56 Ni main lines (158 keV and 812 keV) and from the 847 keV and 1238 keV lines due to the radioactive 56 Co. The strongest lines are the 158 keV line and the 812 and 847 keV lines. However, given the limited energy resolution of gamma-ray detectors, it is difficult to separate the last two lines. Thus, for the study of the early evolution of the SNe Ia, the study of the 158 keV offers the best approach.
The strength of the gamma-ray spectra depends on the mass and velocities of the ejecta, nickel mass, and distribution. Figure 3 shows the dependence of gamma-ray lines on these explosion properties. A direct access to the total flux and line features will provide a novel powerful tool to measure these physical properties, thus probing the nature of the thermonuclear engine behind these supernovae.
In Fig. 4, we show the 158 keV line detected with INTEGRAL from SN2014J, with an exposure time of 150 ks [28]. The estimated line intensity of (1.1±0.4)×10 −4 photons cm −2 s −1 corresponds to a detection confidence level of 2.5σ . For comparison, the ASTENA Narrow Field Telescope (NFT) will reach a 3σ sensitivity at the same energy (see Fig. 17) of approximately 10 −6 photons cm −2 s −1 in 100 ksec observations.
As a result, ASTENA NFT will be capable of detecting lines from SNe that synthesize lower masses of 56 Ni than those found near the surface of SN2014J (0.06 M , [28], D = 3.3 Mpc), or to detect lines from SN Ia at greater distances. Given the significantly higher sensitivity and angular resolution of ASTENA, we also expect to be able to study the spatial distribution and the evolution of both line and continuum in the case of Galactic SNe. From theoretical estimates (Figs. 2 and 3) as well as observational evidence (SN2014J), we expect to significantly increase the number of SNe Ia that could be investigated in gamma rays. ASTENA's superior line sensitivity around 158 keV as well as the more than two orders of magnitude better continuum sensitivity around 200-400 keV would allow to follow-up between 50 and 200 SNe Ia per year, up to a distance of 120 Mpc (z 0.03). Consequently, ASTENA would tremendously contribute to understanding the diversity of SNe Ia, their different explosion mechanisms (progenitor problem), as well as shed light on supernova cosmology.

Core collapse SNe
In Core Collapse supernova explosions (CCSN; also called SN Ib/c or SN II) that result from collapses of massive stars at the end of their stellar evolution, one of the most diagnostic synthesized elements is 44 [36]. Given the long decay time, these lines are visible at late times once the explosions are entirely transparent. Of the above lines, those so far clearly detected are the 67.9 keV, 78.4 keV, and 1157 keV lines from Cas A, a SN that exploded in 1671, with BeppoSAX [77], INTEGRAL [65,67] and NuSTAR [37], and from the Type II SN1987A [11,36]. The integrated line intensity from Cas A is about 2×10 −5 photons cm −2 s −1 . Thanks to the NuSTAR angular resolution (58 arcsec Half Power Diameter (HPD), [41]), it has been possible for the first time to study the spatial distribution of the line across the remnant [37,38]. For SN1987A, whose distance is about 50 kpc, an estimate of a synthesized mass of 44 Ti of (3.1 ± 0.8) × 10 −4 M was reported with INTEGRAL [36]; the NuSTAR measurement indicated that this intensity may have had a bias towards high values, the more-significant NuSTAR result is (1.5 ± 0.3) × 10 −4 M [11]. Obtaining the yields for key metals detected in supernova remnants through X-rays depends sensitively on the excitation of the atoms and out-of-equilibrium effects lead to large errors in the total abundances derived from X-ray observations. Photons from radioactive decay do not suffer from these systematics, providing a more-robust abundance measurement. Because 44 Ti is produced in the innermost supernova ejecta, it is an ideal probe of the explosion mechanism and potential asymmetries. The NuSTAR results [37,38] are considered to be the strongest evidence for an intrinsic explosion asymmetry and clumpiness, and the convective-engine paradigm behind core-collapse supernovae. 44 Ti production is extremely sensitive to the exact nature of the explosion (shock strengths and densities) and, by measuring the spatial distribution of the 44 Ti yields relative to iron, we can probe these diagnostic metal ratios.
The NFT telescope aboard ASTENA, thanks to its angular resolution (which is similar to that of NuSTAR), and its higher sensitivity, will be capable of performing more accurate spatial maps of the 67.9 keV and 78.4 keV lines across the remnant and extending this study to other remnants.
In addition, in the rare event of a nearby neutron star merger event or a Galactic supernova, a host of new isotopes may be detected [75]. For neutron star mergers within 10 Mpc, scientists can probe the mass and composition produced by heavy rprocess elements, firmly dictating the role that mergers play in r-process production and the robustness of their r-process composition [48,84]. For Galactic supernovae, over 10 isotopes will be detected, some probing the stellar burning layers, others probing the explosion energy and mixing. These unique probes of cosmic explosions will dramatically improve our understanding of the progenitors and engines behind them.

Classical nova systems
CNe systems are expected (see §2.2) on theoretical grounds to show a ∼ 1 hr flash of 511 keV radiation from the decay of short-lived 13 N and 18 F. Given a rate of ∼ 14±3 nova/yr for the galactic bulge [60] and the ASTENA sensitivity of ∼ 2 × 10 −5 at 511 keV in 100 ks, it will be possible to detect CNe flashes up to 3 kpc for a handful of Novae per year and to detect the decay positrons from 22 Na up to 1 kpc.

ASTENA mission concept
The ASTENA in-flight configuration is shown in Fig. 5, while its main properties are reported in Table 1

WFM-IS units
Essentially, each detection unit (see Fig. 7) of the WFM-IS is a Position Sensitive Detector (PSD) surmounted by a coded mask at 70 cm distance. The mask is supported by 4 Aluminum slabs with, inside, a Tungsten layer about 500 μm thick.

The position sensitive detector unit
The PSD unit consists of an array of 4×8 modules, each module consisting of 10 rows of hexagonal scintillator bars, with a distance between contiguous centres across hexagon flat sides of 5 mm (205 bars per module), read out, on the top (toward the     Fig. 8). The functioning principle of this detector is similar to that adopted for the X-Gamma-ray Imaging Spectrometer (XGIS) aboard the THESEUS mission [14]. It has the great advantage of a very broad passband (2 keV-20 MeV), a 3D position sensitivity to energy losses in the scintillator bars, and a very low intrinsic background, given its similarity to the phoswich system (see, e.g., [31]), in this case a "siswich" system as already demonstrated by [56,57]. In the case of the WFM-IS units, the top SDDs have 4 linear anodes for each scintillator bar (see Fig. 8). This configuration provides a 1D position sensitivity of 1.25 mm,  which is required to achieve, with a proper coded mask configuration (see below), a Point Source Localization Accuracy (PSLA) of 1 arcmin at low energies (<30 keV). The hexagonal cross section of the bars is crucial to obtain the instrument's unique polarimetric capabilities (see below). In the current design the scintillator material is CsI(Tl), but also other materials (like BGO and GAGG(Ce)) will be considered. Depending on the scintillator material, the length of the bars will be optimized also for exploiting the Compton interactions in different bars for the determination, under study, of the incident photon direction. Preliminary results, that will be part of a paper in preparation, have already been obtained for CsI(Tl) bars 50 mm long. The reported performance estimates are based on the assumption that the scintillation bars are made of CsI(Tl) 50 mm long (see Fig. 8).

Coded mask
Imaging capabilities of the WFM-IS are obtained by means of a double scale coded mask, one scale for the high energy photons (30-150 keV) that lose their energy in the scintillator bars, and another scale for the low energy photons (< 30 keV) that lose their energy in the SDD alone. The high energy mask is made of Tungsten 1 mm thick, while the low energy mask is made of stainless steel 0.5 mm thick. The high energy mask is a 43×41 element basic pattern of 10 x 10.1mm, with 79×79 of such elements for each detection unit, with 50% of open 2-dimension (2D) pixels, a Fully Coded Field of View (FCFOV) of 0.27 sr, and a Full Width at Zero Response (FWZR) of 2 sr. The expected Point Source Location Accuracy (PSLA) is approximately 5 arcmin for a 7 σ signal, and better for higher S/N signals.
Unlike the high energy mask, the low energy mask is 1-D (see left panel of Fig. 9), with a throughput of ∼ 65%, so as to allow the combined 2D/1D mask pattern (see right panel of Fig. 9) to have a throughput of 50% at high energies and about 33% at low energies. With these properties, by orienting the 1-D mask of each pair of detectors (see Fig. 5) perpendicularly to each other, we can achieve a PSLA of 1 arcmin, which is required to perform NFT follow-up observations of sources discovered with the WFM-IS.

WFM-IS polarimetric capabilities
Thanks to the hexagonal cross section of the scintillator bars and the 3D position sensitivity of the detector, each detection unit can be used as a Compton scattering polarimeter. In Fig. 10, we show the Minimum Detectable Polarization at 3σ level in the case of a GRB of 20 s duration and 2 different fluences. The assumed spectrum is a Band law with low-energy photon index α = 1.0, high energy photon index β = 2.3, and peak energy of the EF (E) spectrum equal to 300 keV.

WFM-IS continuum sensitivity
Considering the throughput of the coded mask, the geometric area of the WFM-IS through the mask is ∼ 5800 cm 2 below 30 keV and ∼ 6700 cm 2 in 30-150 keV. At higher energies the mask is transparent to the radiation therefore the on-axis area is about 1.4 m 2 . Assuming the background level expected for a nearly equatorial orbit, Fig. 11 shows the WFM-IS continuum sensitivity as a function of the exposure time for a source in the FOV of the NFT.

Narrow Field Telescope, NFT
As mentioned above, the NFT is based on a broad band (50-600 keV) Laue lens with ∼ 3 m diameter and 20 m focal length (see sketch in the left panel of Fig. 12), with a Position Sensitive Detector (PSD) in the focal plane. We separately discuss both, Laue lens and PSD.

Laue lens
For a review on the physics underlying the Laue lenses see [30]. Briefly, Laue lenses exploit the crystal diffraction in transmission configuration (Laue geometry). A Laue lens is made of a large number of crystal tiles in transmission configuration, that are disposed in such a way that they concentrate the incident radiation onto a common focal spot. A convenient way to visualize the geometry of a crystal lens is to consider it as a spherical cup covered with rings of crystal tiles having their diffracting planes perpendicular to the sphere and the focal spot is on the symmetry axis at a focal distance f = R/2 from the cup, with R being the curvature radius of the spherical cup. From the Bragg law and the geometry of the lens, it can be easily demonstrated that the reflected energy from a crystal at distance r from the lens symmetry axis is given by [30] where d hkl (inÅ) is the distance between the chosen lattice planes (hkl Miller indices) of the crystals, hc = 12.4 keV·Å and E is the energy of the gamma-ray photon (in keV). The approximated expression is valid for gamma-ray lenses, given the small diffraction angles involved. Thus the highest energies are diffracted from the nearest crystals and the lowest energies from the furthest crystals to the lens axis. At the University of Ferrara, with the project HAXTEL (Hard X-ray TELescope) we developed a technology for assembling Laue lenses with moderate focal length (< 10 m), using flat mosaic crystal tiles of Copper Cu(111) [32,78]. The disadvantage of flat crystals is that the minimum focal spot size is that of the crystal tiles. To overcome this limitation, bent crystals with the proper curvature are required. To this end, a technology for bending crystals and for assembling a Laue lens with long focal length (20 m) for astrophysical applications, was successfully developed as part of the LAUE project supported by the Italian Space Agency (ASI) (see, e.g, [80]). With the support of the European project AHEAD (integrated Activities in the High Energy Astrophysics Domain), the expected performance of a Laue lens prototype has also been simulated taking into account effects of possible crystal tile misalignments and radial distortions of the crystal curvature, as measured in laboratory experiments.
The lens under development is made of ∼19500 bent crystal tiles of Si(111) and Ge(111), with 40 m curvature radius (within 5% uncertainty). In the current design the crystal tiles have a 30×10 mm 2 cross section, and a 2 mm thickness. Bent crystals have been produced and a technology for an accurate alignment (the requirement is a misalignment < 10 arcsec) of the crystal tiles in the lens has been identified [79] with successful results (paper in preparation). The development of a lens prototype is the goal of a recently approved project TRILL (Technological Readiness level Increase for Laue Lenses) devoted to increase the Technology Readiness Level (TRL). The Laue lens we propose for ASTENA builds on this recent technological progress. The expected Point Spread Function of the entire lens, validated by measurements on several subsets of crystals, is shown in the right panel of Fig 12, with a Half Energy Width (HEW) of 30 arcsec.  Fig. 10 see Fig. 16 a Total geometric area through the mask or collimator Important features of the proposed lens are its energy passband, angular resolution, and Field of View (FOV). Thanks to the use of bent Si(111) and Ge(111) crystals tiles, an energy passband 50-600 keV is guaranteed; however we will explore the possibility to extend the energy band down to 30 keV, if the transparency of the passive materials in the lens under the crystals is still acceptable. Using simulations, validated by laboratory measurements on the performance of a large sample of bent crystals, we evaluated the angular resolution and FOV of the proposed lens. As shown in Fig. 13, an angular resolution of 0.5 arcmin can be achieved, with a useful FOV of approximately 4 arcmin.

Focal plane detector
The focal-plane detector is a solid state PSD made of 4 layers, with each layer made of 4 × 16 CdZnTe (CZT) elements. Each element is 2 cm thick with a cross section of 0.5×2 cm 2 , which exhibits a drift strip configuration for the anodes and orthogonally segmented cathodes in Parallel Transverse Field (PTF; see Fig. 14, [5,51]). The resulting PSD has a total cross section of 8 × 8 cm 2 and a total thickness of 8 cm. With this thickness, the PSD has a detection efficiency higher than 80% in the entire energy band of the NFT. The measured three-dimensional position resolution of a single element matches that required by the ASTENA NFT: 300 μm [50,51]. In this configuration, the PSD is also capable to work as a Compton polarimeter [16].

Expected NFT performance -Sensitivity to continuum emission
The expected NFT continuum sensitivity (3σ , 10 5 s, E = E/2) is shown in Fig. 15, compared with that of other missions or experiments. This unprecedented sensitivity (up to two orders of magnitude better than operating instruments in the same energy band) is obtained thanks mainly to the use of properly bent crystals and to the transmission geometry, that allows a projected geometric area of about 7 m 2 , with a very low mass of the lens (∼ 150 kg).
-Sensitivity to polarized radiation The unprecedented sensitivity, together with the focal plane characteristics (high segmentation, spatial resolution in 3D, and good energy resolution) will allow the NFT to enter a completely new territory in high-energy polarimetric measurements, making polarimetry a standard observation mode between 100 keV and 600/700 keV [15]. To measure the reliability of polarimetric measurements, we adopt the Minimum Detectable Polarization (MDP) parameter, which quantifies the confidence with which polarization is detected, i.e. that the source is not un-polarized. MDP should be significantly smaller than the degree of polarization to be measured. Following [82], the MDP at 99% confidence level can be expressed by where, in the case of a focusing instrument, A is the effective area of the focusing telescope, is the detection efficiency (i.e., the double events efficiency for a scattering polarimeter), S F is the source flux over the selected energy band (photons cm −2 s −1 ), B is the background count rate (counts/s) integrated inside the volume of the detector subtended by the lens PSF, and T is the observation time. The factor Q 100 is the polarimetric modulation factor of the detector (i.e., the measured modulation for a source 100% linearly polarized). The MDP achievable by the NFT can be estimated by evaluating the source count rate from the expected sensitivity reported in Fig. 15, in the energy band between 80 keV and 600 keV, and setting Q 100 = 0.6. The latter is a realistic value for the NFT required focal plane, as can be inferred from different experiments performed using CdTe spectro-imagers operated as scattering polarimeters [4,24]. Figure 16 shows this estimate as a function of both the observing time for a 10 mCrab source, and the source intensity integrated over 10 5 s. A Crab-like spectrum is assumed, with a background level given by [26] and later confirmed with the INTEGRAL SPI instrument, scaled to a low-Earth orbit. These results confirm unprecedented polarimetric performance of the NFT telescope with an achievable MDP of 5% for a 10 mCrab source for a 10 5 s observation time.
-Sensitivity to narrow emission lines In general, for a focusing telescope, the sensitivity to a narrow emission line expressed in photons cm −2 s −1 , superimposed onto a continuum source spectrum, at a confidence level of n σ , is given by: where E L is the line centroid, I c (E L ) is the source continuum intensity at the line centroid, E is the FWHM of the line profile that depends upon the energy resolution of the detector which has been assumed to be 2 keV (expected for our simulated detector; [46]). The other parameters, all calculated at the energy E L , are those defined above.
The sensitivity to an emission line for our Laue lens, at 3σ confidence level, is shown in Fig. 17 for an observation time of 10 5 s. Here we have adopted a typical scatter of the radial curvature of bent crystals (Gaussian deviation of 2.5% from the mean) and a tile misalignment within 10 arcsec; a continuum intensity given by our continuum sensitivity, a FWHM of the line of 2 keV and the fraction f = 0.5, corresponding to a half energy width of the PSF. This figure shows how the line sensitivity of the ASTENA/NFT in 10 5 s is approximately three orders of magnitude better than the SPI instrument aboard INTEGRAL at low energy, while it is about one order of magnitude better at 511 keV. 3 This sensitivity can be further improved with a suitable choice and configuration of the reflecting planes of bent crystals in the lens.
In the common pass-band, a comparison of these performances with the NASA Medium Probe design mission AMEGO [58] shows that ASTENA has a much higher sensitivity at low energies, while at 511 keV ASTENA's sensitivity is similar, but with an order of magnitude better angular resolution.

Conclusions
The ESA Science Programme "Voyage 2050" offers a formidable opportunity to address issues of primary importance for astrophysics and, more generally, for science. In this WP we have discussed two relevant open problems: 1) a detailed understanding of the physical processes that underpin the explosions of Type-Ia and core collapse supernovae; 2) the fifty-year long mystery of the origin of the 511 keV positron annihilation line from the Galactic bulge region. Their solution has been thus far hindered by the limited sensitivity and imaging capabilities of the gamma ray instrumentation flown and could be solved with the proposed satellite mission concept ASTENA. Thanks to its broad band (2 keV-20 MeV) WFM-IS and its focusing NFT with a 50-600 keV passband, ASTENA will provide hitherto unparalleled sensitivity to continuum and line emission, polarimetric capabilities, and unprecedented sub-arcmin angular resolution, that will make it a first-class investigation tool for high energy astrophysics, and will make a breakthrough possible in this field in general, and in the above poorly known areas in particular. Besides settling the problems we have discussed in this paper, ASTENA can tackle many other issues, like those concerning the transient sky (see WP by [39]), and several classes of Galactic (e.g., magnetars) and extragalactic (e.g., Blazars) sources, thus far scarcely explored at hard X/soft gamma rays (paper in preparation).