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NASA NTRS1984

Numerical experiments on galaxy clustering in open universes

Numerical studies were performed on the dynamical effects on the evolution of clumps, filaments, voids, and galaxy clusters by various final Omega values. The final Omega values examined ranged from 0.03-1, and attention was given to defining observations of superclusters which would aid in determining an actual value for Omega. The numerical trials consisted of n-body integration programs governed by the total expansion and final Omega value and included comparisons between results for open and closed universes. All runs started from the same initial conditions. The dispersion trajectories of particles and the final galactic cluster forms were found to be equivalent, regardless of the final Omega value. The possibility of deriving a value for Omega from velocity data on galaxies which have not yet joined clusters is discussed.

Miller, R. H.↗
NASA NTRS2009

Evidence for an Intermediate Mass Black Hole in NGC 5408 X-1

We report the discovery with XMM-Newton of correlated spectral and timing behavior in the ultraluminous X-ray source (ULX) NGC 5408 X-1. An approx. 100 ksec pointing with XMM/Newton obtained in January, 2008 reveals a strong 10 mHz QPO in the > 1 keV flux, as well as flat-topped, band limited noise breaking to a power law. The energy spectrum is again dominated by two components, a 0.16 keV thermal disk and a power-law with an index of approx. 2.5. These new measurements, combined with results from our previous January 2006 pointing in which we first detected QPOs, show for the first time in a ULX a pattern of spectral and temporal correlations strongly analogous to that seen in Galactic black hole sources, but at much higher X-ray luminosity and longer characteristic time-scales. We find that the QPO frequency is proportional to the inferred disk flux, while the QPO and broad-band noise amplitude (root mean squared, rms) are inversely proportional to the disk flux. Assuming that QPO frequency scales inversely with black hole mass at a given power-law spectral index we derive mass estimates using the observed QPO frequency - spectral index relations from five stellar-mass black hole systems with dynamical mass constraints. The results from all sources are consistent with a mass range for NGC 5408 X-1 from 1000 - 9000 Stellar mass. We argue that these are conservative limits, and a more likely range is from 2000 - 5000 Stellar mass. Moreover, the recent relation from Gierlinski et al. that relates black hole mass to the strength of variability at high frequencies (above the break in the power spectrum), and the variability plane results of McHardy et al. and Koerding et al., are also suggestive of such a. high mass for NGC 5408 X-1. Importantly, none of the above estimates appears consistent with a black hole mass less than approx. 1000 Stellar mass for NGC 5408 X-1. We argue that these new findings strongly support the conclusion that NGC 5408 X-1 harbors an intermediate mass black hole.

Strohmayer, Tod E.↗
NASA NTRS2022

Line Emission Mapper Probing Physics of Cosmic Ecosystems

The Line Emission Mapper (LEM) is an X-ray Probe for the 2030s that will answer the outstanding questions of the Universe’s structure formation. It will also provide transformative new observing capabilities for every area of astrophysics, and to heliophysics and planetary physics as well. LEM’s main goal is a comprehensive look at the physics of galaxy formation, including stellar and black-hole feedback and flows of baryonic matter into and out of galaxies. These processes are best studied in X-rays; as emphasized by the 2020 Decadal Survey, emission-line mapping is the pressing need in this area. LEM will use a large microcalorimeter array/IFU (that builds on Athena XIFU technology developments), covering a 30 × 300 field with 1000 angular resolution, to map the soft Xray line emission from objects that constitute galactic ecosystems. These include supernova remnants, star-forming regions, superbubbles, galactic outflows (such as the Fermi/eROSITA bubbles in the Milky Way and their analogs in other galaxies), the Circumgalactic Medium in the Milky Way and other galaxies, and the Intergalactic Medium at the outskirts and beyond the confines of galaxies and clusters. LEM’s 1–2 eV spectral resolution in the 0.2–2 keV band will make it possible to disentangle the faintest emission lines in those objects from the bright Milky Way foreground, providing groundbreaking measurements of the physics of these plasmas, from temperatures, densities, chemical composition to gas dynamics. While the mission is optimized to provide critical observations that will push our understanding of galaxy formation, LEM will provide transformative capability for all classes of astrophysical objects, from the Earth’s magnetosphere, planets and comets to the interstellar medium and X-ray binaries in nearby galaxies, AGN, and cooling gas in galaxy clusters. In addition to pointed observations, LEM will perform a shallow all-sky survey that will dramatically expand the discovery space.

Ralph Kraft↗
DOE OSTI2026

Astrometric microlensing probes of the isolated neutron star population with Roman

Notoriously hard to detect and study, isolated neutron stars (NSs) might provide valuable answers to fundamental questions about stellar evolution and explosion physics. With the upcoming Roman Space Telescope, scheduled for launch in 2026, a new and powerful channel for their detection will become available: astrometric microlensing. We set out to create a realistic sample of simulated gravitational microlensing events as observed by Roman with the Galactic Bulge Time Domain Survey. We focus in particular on the population of NS lenses, which has until now been largely understudied. We used dedicated Galactic models tailored for application to microlensing by compact objects. In addition to populations of stars, white dwarfs, and black holes, we simulated four different NS populations with Maxwellian natal kick distributions: v = (150, 250, 350, 450) km/s. For each simulation, we applied projected Roman precision, cadence, and detectability criteria. We found that the parameter space log10 t E –log 10 θ E , which will be accessible to Roman observations, is efficient for the classification of stellar remnants. We found a feature in this space that is characteristic of NSs; using this feature, optimal samples of NS candidates can be constructed from Roman -like datasets. We describe the dependence of the observable parameter distributions on the assumed mean kick velocities. As the effects of natal kicks are very complex and mutually counteracting, we suggest that more detailed studies focused on the dynamics of NSs are needed in anticipation of Roman and future surveys. We estimate that Roman will observe approximately 11 000 microlensing events, including ~100 with NS lenses, whose photometric and astrometric signals are detectable; the event yield decreases by 38% when gap-filling low-cadence observations are not included. We make all simulated microlensing event datasets publicly available in preparation for Roman data.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1991

Radiative-hydrodynamical simulations of accretion disk coronae

An algorithm has been developed that will carry out detailed, two-dimensional, fully self-consistent radiative-hydrodynamical simulations of accretion disk coronae in X-ray-luminous compact sources. The calculation reported here, for an accreting neutron star radiating at 0.5 times the Eddington luminosity, reveals several striking features. (1) The corona is comprised of two main regions - an inner highly dynamic portion whose vertical structure varies cyclically on a dynamical time scale, and an outer, more stable zone in which the evaporated plasma rises to form a 'sheath' that gradually merges into a wind at large radii. (2) The coronal structure shows a density inversion that contrasts sharply with the Gaussian profiles of earlier hydrostatic models. (3) Interestingly, flow velocities as high as a few billion cm/s are not uncommon in portions of the corona. The relevance of this point to the large measured width of the emission features seen in low-mass X-ray binaries and the Galactic black hole candidates is discussed.

Melia, Fulvio↗
NASA NTRSDate not supplied

Presentation Summary: State of the AGN: Progress Toward Understanding Black Hole Accretion Processes

Accretion of plasma onto black holes power some of the most powerfulsystems in the cosmos. Supermassive black holes at the centers ofgalaxies represent the high-mass limit of these objects and so accountfor the most luminous accretors. As a result, their influence spansvast spatial and temporal scales of cosmic phenomena: intraclusterheating, intergalactic media, galactic feedback and star formation,kiloparsec-scale jets/outflows, variability over time scales of minutesto centuries, and luminous multi-wavelength electromagnetic emissionextending all the way down to its event horizon. Their intrigue isheightened by the fact that they lie at the intersection of variousphysical laws---e.g., general relativistic gravity,magnetohydrodynamics, radiation, high-energy particle physics,thermodynamics, and photo-ionization---which all must be reconciled toarrive at a fundamental understanding and probe for new physics, liketests of general relativity. These physics ingredients must beincorporated into simulations performed somehow on dynamical scalesranging from that of the event horizon to parsec-scales. Fortunately,new computational and theoretical techniques---such as GPU computing,radiation transport, and and novel gridding techniques---are enablingprogress to larger scales, more degrees of freedom, and even to binarysystems. Some of the topics we will survey include recent progress onsimulating the relationship between the disk-jet interaction, howtilted black holes behave, radiation-dominated flow, and how binaryAGN affect the standard picture of black hole accretion. Along theway, we will highlight how new technologies have enabled thesescientific rewards. Future directions and open questions will beprovided to inspire discussion and interaction during the session.

Black Holes↗
DOE OSTI2022

Cosmological analysis of three-dimensional BOSS galaxy clustering and Planck CMB lensing cross correlations via Lagrangian perturbation theory

In this work, we present a formalism for jointly fitting pre- and post-reconstruction redshift-space clustering (RSD) and baryon acoustic oscillations (BAO) plus gravitational lensing (of the CMB) that works directly with the observed 2-point statistics. The formalism is based upon (effective) Lagrangian perturbation theory and a Lagrangian bias expansion, which models RSD, BAO and galaxy-lensing cross correlations within a consistent dynamical framework. As an example we present an analysis of clustering measured by the Baryon Oscillation Spectroscopic Survey in combination with CMB lensing measured by Planck. The post-reconstruction BAO strongly constrains the distance-redshift relation, the full-shape redshift-space clustering constrains the matter density and growth rate, and CMB lensing constrains the clustering amplitude. Using only the redshift space data we obtain Ω m = 0.303 ± 0.008, $H_0$ = 69.21 ± 0.78 and $σ_8$ = 0.743 ± 0.043. The addition of lensing information, even when restricted to the Northern Galactic Cap, improves constraints to Ω m = 0.303 ± 0.008, $H_0$ = 69.21 ± 0.77 and $σ_8$ = 0.707 ± 0.035, in tension with CMB and cosmic shear constraints. The combination of Ω m and $H_0$ are consistent with Planck, though their constraints derive mostly from redshift-space clustering. The low $σ_8$ value are driven by cross correlations with CMB lensing in the low redshift bin ($\textit{z}$ ≃ 0.38) and at large angular scales, which show a 20% deficit compared to expectations from galaxy clustering alone. We conduct several systematics tests on the data and find none that could fully explain these tensions.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2004

Masses and Luminosities of X-Ray Binaries

Using SIM, we will perform narrow-angle observations of several X-ray binaries to determine their orbits, and we will observe about 50 X-ray binary systems in wide-angle mode to measure their distances and proper motions. Sources with mass estimates for the compact component of greater than 3 solar masses are generally called black hole candidates since this mass is above the theoretical neutron star limit. Narrow-angle observations of these sources provide a direct test of the dynamical mass estimates on which the black hole evidence is based. Better measurements of the black hole masses will provide constraints on possible evolutionary paths that lead to black hole formation. When combined with X-ray data, mass measurements may provide additional constraints on the black hole spin. Precise mass determinations of neutron star systems can address the question of whether neutron stars can be significantly more massive than 1.4 solar masses, which would eliminate soft models of the neutron star equations of state. The wide-angle observations will probe the Galactic distribution of X-ray binaries through parallaxes and proper motions. They will also eliminate the uncertainties in the luminosities of individual sources, which is currently up to a full order of magnitude. This will enable more detailed comparisons of X-ray observations to physical models such as advection-dominated accretion flows (ADAFs). We intend to carry out the following measurements: 1) Determine the orbits of two black hole candidates to measure the black hole masses; 2) Obtain precise mass measurements for two neutron star systems to constrain neutron star equations of state; 3) Determine the distances and thus luminosities of selected representatives of various classes of X-ray binaries (black hole candidates, neutron stars, jet sources); 4) In the process of distance determination, proper motions will also be measured, from which the age of the population can be estimated.

Quirrenbach, Andreas↗
NASA NTRS1995

Multiple rings around Wolf-Rayet evolution

We present optical narrow-band imaging of multiple rings existing around galactic Wolf-Rayet (WR) stars. The existence of multiple rings of material around Wolf-Rayet stars clearly illustrates the various phases of evolution that massive stars go through. The objects presented here show evidence of a three stage evolution. O stars produce an outer ring with the cavity being partially filled by ejecta from a red supergiant of luminous blue variable phase. A wind from the Wolf-Rayet star then passes into the ejecta materials. A simple model is presented for this three stage evolution. Using observations of the size and dynamics of the rings allows estimates of time scales for each stage of the massive star evolution. These are consistent with recent theoretical evolutionary models. Mass estimates for the ejecta, from the model presented, are consistent with previous ring nebula mass estimates from IRAS data, showing a number of ring nebulae to have large masses, most of which must in be in the form of neutral material. Finally, we illustrate how further observations will allow the determination of many of the parameters of the evolution of massive stars such as total mass loss, average mass loss rates, stellar abundances, and total time spent in each evolutionary phase.

Marston, A. P.↗
NASA NTRS1991

A post-core-collapse model for the nucleus of M33

A model for the post-collapse core of M33 is proposed. By analogy with globular clusters, the formation of tight binary systems powers the reexpansion of the core, and it is expected that low-mass X-ray binaries form at a rate about equal to that of all galactic globular clusters combined. About a dozen such binaries should be present, and their combined emission may explain the large and enigmatic unresolved X-ray emission from the nucleus of M33. In addition, tidal formation of cataclysmic binaries may lead to a nova rate of more than about one per century. Numerous blue stragglers have probably formed through mergers caused by stellar collisions, but their density is probably too low to explain the blue color of the nucleus. Young stars are the likely cause for the color, and their presence may complicate the simple dynamical picture presented here.

Hernquist, Lars↗
NASA NTRS1992

Spectral-luminosity evolution of active galactic nuclei and the cosmic X- and gamma ray background

Coherent electromagnetic dynamo acceleration processes, which act on charge particles within the context of black hole accretion disk scenarios, are generally regarded as the underlying central power source for active galactic nuclei (AGN). If the precursor active galaxies (PAG) for such AGN are formed at high redshift and contain initial seed black holes with mass approximately equal to 10(exp 4) solar masses, then the Eddington limited X-ray radiation emitted during their lifetime will undergo the phenomenon of 'spectral-luminosity evolution'. When accretion disks are first formed at the onset of galaxy formation the accretion rate occurs at very high values of luminosity/size compactness parameter L/R greater than 10(exp 30) erg/cm-sec. In the absence of extended structure, such high values of L/R generate dynamic constraints which suppress coherent, black hole/accretion disk dynamo particle acceleration processes. This inhibits nonthermal radiation processes and causes the spectrum of X-radiation emitted by PAG to be predominantly thermal. A superposition of PAG sources at z is greater than or equal to 6 can account for the residual cosmic X-ray background (CXB) obtained from the total CXB after subtraction of foreground AGN sources associated with present epoch Seyfert galaxies. The manner in which the PAG undergo spectral-luminosity evolution into Seyfert galaxies is investigated.

Leiter, Darryl↗
NASA NTRS2002

Planetary System Physics

Contents include a summary of publications followed by their abstracts titeled: 1. On microlensing rates and optical depth toward the Galactic center. 2. Newly discovered brown dwarfs not seen in microlensing timescale frequency distribution? 3. Origin and evolution of the natural satellites. 4. Probing the structure of the galaxy with microlensing. 5. Tides, Encyclopedia of Astronomy and Astrophysics. 6. The Puzzle of the Titan-Hyperion 4:3 Orbital Resonance. 7. On the Validity of the Coagulation Equation and the Nature of Runaway Growth. 8. Making Hyperion. 9. The MESSENGER mission to Mercury: Scientific objectives and implementation. 10. A Survey of Numerical Solutions to the Coagulation. 11. Probability of detecting a planetary companion during a microlensing event. 12. Dynamics and origin of the 2:l orbital resonances of the GJ876 planets. 13. Planetary Interior Structure Revealed by Spin Dynamics. 14. A primordial origin of the Laplace relation among the Galilean Satellites. 15. A procedure for determining the nature of Mercury's core. 16. Secular evolution of hierarchical planetary systems. 17. Tidally induced volcanism. 18. Extrasolar planets and mean motion resonances. 19. Comparison of a ground-based microlensing search for planets with a search from space.

Peale, S. J.↗
NASA NTRSDate not supplied

State of the AGN: Progress Toward Understanding Black Hole Accretion Processes

Accretion of plasma onto black holes power some of the most powerful systems in the cosmos. Supermassive black holes at the centers of galaxies represent the high-mass limit of these objects and so account for the most luminous accretors. As a result, their influence spans vast spatial and temporal scales of cosmic phenomena: intracluster heating, intergalactic media, galactic feedback and star formation, kiloparsec-scale jets/outflows, variability over time scales of minutes to centuries, and luminous multi-wavelength electromagnetic emission extending all the way down to its event horizon. Their intrigue is heightened by the fact that they lie at the intersection of various physical laws---e.g., general relativistic gravity, magnetohydrodynamics, radiation, high-energy particle physics, thermodynamics, and photo-ionization---which all must be reconciled to arrive at a fundamental understanding and probe for new physics, like tests of general relativity. These physics ingredients must be incorporated into simulations performed somehow on dynamical scales ranging from that of the event horizon to parsec-scales. Fortunately, new computational and theoretical techniques---such as GPU computing, radiation transport, and and novel gridding techniques---are enabling progress to larger scales, more degrees of freedom, and even to binary systems. Some of the topics we will survey include recent progress on simulating the relationship between the disk-jet interaction, how tilted black holes behave, radiation-dominated flow, and how binary AGN affect the standard picture of black hole accretion. Along the way, we will highlight how new technologies have enabled these scientific rewards. Future directions and open questions will be provided to inspire discussion and interaction during the session.

LISA↗
DOE OSTI2023

Simulations of Precessing Jets and the Formation of X-shaped Radio Galaxies

Abstract Jet precession is sometimes invoked to explain asymmetries in radio galaxy (RG) jets and “X/S/Z-shaped” RGs, caused by the presence of a binary black hole companion to the source active galactic nucleus or by accretion instabilities. We present a series of simulations of RG jet precession to examine how these sources would evolve over time, including a passive distribution of cosmic-ray electrons so we can model radio synchrotron emissions and create synthetic radio maps of the sources. We find that a single source viewed from different angles can result in differing RG morphological classifications, confusing physical implications of these classifications. Additionally, the jet trajectories can become unstable due to their own self-interactions and lead to “reorientation events” that may look like the effects of external dynamics such as shocks, winds, or cold fronts in the medium. Finally, something akin to an “Odd Radio Circle” may be observed in the case of viewing the radio remnant of such a precessing source from a line of sight near the precession axis.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2007

GRB070125: The First Long-Duration Gamma-Ray Burst in a Halo Environment

We present the discovery and high signal-to-noise spectroscopic observations of the optical afterglow of the long-duration gamma-ray burst GRB070125. Unlike all previously observed long-duration afterglows in the redshift range 0.5 < z < 2.0, we find no strong (rest-frame equivalent width W > 1.0 A) absorption features in the wavelength range 4000 - 10000 A. The sole significant feature is a weak doublet we identify as Mg 11 2796 (W = 0.18 +/- 0.02 A), 2803 (W = 0.08 +0I.-01 ) at z = 1.5477 +/- 0.0001. The low observed Mg II and inferred H I column densities are typically observed in galactic halos, far away from the bulk of massive star formation. Deep ground-based imaging reveals no host directly underneath the afterglow to a limit of R > 25.4 mag. Either of the two nearest blue galaxies could host GRB070125; the large offset (d >= 27 kpc) would naturally explain the low column density. To remain consistent with the large local (i.e. parsec scale) circum-burst density inferred from broadband afterglow observations, we speculate GRB070125 may have occurred far away from the disk of its host in a compact star-forming cluster. Such distant stellar clusters, typically formed by dynamical galaxy interactions, have been observed in the nearby universe, and should be more prevalent at z>l where galaxy mergers occur more frequently.

Bradley, Cenko S.↗
NASA NTRS2011

The Radio/Gamma-Ray Connection in Active Galactic Nuclei in the Era of the Fermi Large Area Telescope

We present a detailed statistical analysis of the correlation between radio and gamma-ray emission of the active galactic nuclei (AGNs) detected by Fermi during its first year of operation, with the largest data sets ever used for this purpose.We use both archival interferometric 8.4 GHz data (from the Very Large Array and ATCA, for the full sample of 599 sources) and concurrent single-dish 15 GHz measurements from the OwensValley RadioObservatory (OVRO, for a sub sample of 199 objects). Our unprecedentedly large sample permits us to assess with high accuracy the statistical significance of the correlation, using a surrogate data method designed to simultaneously account for common-distance bias and the effect of a limited dynamical range in the observed quantities. We find that the statistical significance of a positive correlation between the centimeter radio and the broadband (E > 100 MeV) gamma-ray energy flux is very high for the whole AGN sample, with a probability of <10(exp -7) for the correlation appearing by chance. Using the OVRO data, we find that concurrent data improve the significance of the correlation from 1.6 10(exp -6) to 9.0 10(exp -8). Our large sample size allows us to study the dependence of correlation strength and significance on specific source types and gamma-ray energy band. We find that the correlation is very significant (chance probability < 10(exp -7)) for both flat spectrum radio quasars and BL Lac objects separately; a dependence of the correlation strength on the considered gamma-ray energy band is also present, but additional data will be necessary to constrain its significance.

Ackermann, M.↗
DOE OSTI2022

Blanco DECam Bulge Survey (BDBS)

The Blanco DECam Bulge Survey (BDBS) has imaged more than 200 square degrees of the southern Galactic bulge, providing photometry in the ugrizy filters for ~250 million unique stars. The presence of a strong foreground disk population, along with complex reddening and extreme image crowding, has made it difficult to constrain the presence of young and intermediate age stars in the bulge population. We employed an accurate cross-match of BDBS with the latest data release (EDR3) from the Gaia mission, matching more than 140 million sources with BDBS photometry and Gaia EDR3 photometry and astrometry. We relied on Gaia EDR3 astrometry, without any photometric selection, to produce clean BDBS bulge colour-magnitude diagrams (CMDs). Gaia parallaxes were used to filter out bright foreground sources, and a Gaussian mixture model fit to Galactic proper motions could identify stars kinematically consistent with bulge membership. We applied this method to 127 different bulge fields of 1 deg 2 each, with |$\ell$| ≤ 9.5 ° and –9.5 ° ≤ b ≤ –2.5 °. The astrometric cleaning procedure removes the majority of blue stars in each field, especially near the Galactic plane, where the ratio of blue to red stars is .10%, increasing to values ~20% at higher Galactic latitudes. We rule out the presence of a widespread population of stars younger than 2 Gyr. The vast majority of blue stars brighter than the turnoff belong to the foreground population, according to their measured astrometry. We introduce the distance between the observed red giant branch bump and the red clump as a simple age proxy for the dominant population in the field, and we confirm the picture of a predominantly old bulge. Further work is needed to apply the method to estimate ages to fields at higher latitudes, and to model the complex morphology of the Galactic bulge. We also produce transverse kinematic maps, recovering expected patterns related to the presence of the bar and of the X-shaped nature of the bulge.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Direct Measurement of the Nickel Spectrum in Cosmic Rays in the Energy Range from 8.8 GeV/$\mathcal{n}$ to 240 GeV/$\mathcal{n}$ with CALET on the International Space Station

The relative abundance of cosmic ray nickel nuclei with respect to iron is by far larger than for all other transiron elements; therefore it provides a favorable opportunity for a low background measurement of its spectrum. Since nickel, as well as iron, is one of the most stable nuclei, the nickel energy spectrum and its relative abundance with respect to iron provide important information to estimate the abundances at the cosmic ray source and to model the Galactic propagation of heavy nuclei. However, only a few direct measurements of cosmic-ray nickel at energy larger than ~ 3 GeV/n are available at present in the literature, and they are affected by strong limitations in both energy reach and statistics. In this Letter, we present a measurement of the differential energy spectrum of nickel in the energy range from 8.8 to 240 GeV/n , carried out with unprecedented precision by the Calorimetric Electron Telescope (CALET) in operation on the International Space Station since 2015. The CALET instrument can identify individual nuclear species via a measurement of their electric charge with a dynamic range extending far beyond iron (up to atomic number Z = 40 ). The particle’s energy is measured by a homogeneous calorimeter (1.2 proton interaction lengths, 27 radiation lengths) preceded by a thin imaging section (3 radiation lengths) providing tracking and energy sampling. This Letter follows our previous measurement of the iron spectrum [O. Adriani et al. (CALET Collaboration), Phys. Rev. Lett. 126, 241101 (2021).], and it extends our investigation on the energy dependence of the spectral index of heavy elements. It reports the analysis of nickel data collected from November 2015 to May 2021 and a detailed assessment of the systematic uncertainties. In the region from 20 to 240 GeV/n our present data are compatible within the errors with a single power law with spectral index -2.51 ± 0.07 .

79 ASTRONOMY AND ASTROPHYSICS↗