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Results for “OPTICAL EMISSION SPECTROSCOPY”

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NASA NTRS1997

The Nature of the Optical "Jets" in the Spiral Galaxy NGC 1097

We present new observations of the jet features in the barred spiral galaxy NGC 1097, including optical spectroscopy of the brightest jet features, two-color optical imagery, new VLA mapping at 327 MHz, and archival 1.4 GHz VLA data reprocessed for improved sensitivity. No optical emission lines appear to an equivalent width limit of 15-30 A (depending on the line wavelength). The jets are uniformly blue, with B - V = 0.45 for the two well-observed jets R1 and R2. No radio emission from the jets is detected at either frequency; the 327-MHz data set particularly stringent limits on "fossil" emission from aging synchrotron electrons. The morphology of the jets is shown to be inconsistent with any conical distribution of emission enhanced by edge-brightening; their combination of transverse profile and relative narrowness cannot be reproduced with cone models. The optical colors, lack of radio emission, and morphology of the features lead us to conclude that they are tidal manifestations, perhaps produced by multiple encounters of the small elliptical companion NGC 1097A with the disk of NGC 1097. We present photometric and morphological comparisons to the tail of NGC 465 1, which is similar in scale and morphology to the northeast "dogleg" feature R1 in NGC 1097.

Wehrle, Ann E.↗

NASA NTRS2024

The Mega-MUSCLES Treasury Survey: X-Ray to Infrared Spectral Energy Distributions of a Representative Sample of M Dwarfs

We present 5–1 × 107 Å spectral energy distributions (SEDs) for 12 M dwarf stars covering spectral types M0–M8. Our SEDs are provided for community use as a sequel to the Measurements of the Ultraviolet Spectral Characteristics of Low-mass Exoplanetary Systems (MUSCLES) survey. The 12 stars include eight known exoplanet hosts and four stars chosen to fill out key parameter space in spectral type and rotation period. The SEDs are constructed from Hubble Space Telescope ultraviolet spectroscopy and XMM Newton, Chandra, and/or Swift X-ray observations, and completed with various model data, including Lyα reconstructions, PHOENIX optical models, APEC coronal models, and differential emission measure models in the currently-unobservable extreme ultraviolet. We provide a complete overview of the Mega-MUSCLES program, including a description of the observations, models, and SED construction. The SEDs are available as MAST high-level science products and we describe the various data products here. We also present ensemble measurements from our sample that are of particular relevance to exoplanet science, including the high-energy fluxes in the habitable zone and the farultraviolet to near-ultraviolet ratio. Combined with MUSCLES, Mega-MUSCLES provides SEDs covering a wide range of M dwarf spectral types and ages such that suitable proxies for any M dwarf planet host of interest may be found in our sample. However, we find that ultraviolet and X-ray fluxes can vary even between stars with similar parameters, such that observations of each exoplanet host star will remain the gold standard for interpreting exoplanet atmosphere observations.

David J. Wilson↗

DOE OSTI2026

Highly Anisotropic Quasi‐Direct Organic Metal Halide Hybrids: A Platform for Polarization‐Sensitive Optoelectronics

Low-dimensional organic–inorganic metal halide hybrids (OMHHs) exhibit remarkable optical properties and enhanced environmental stability. We investigate a 1D OMHH with formula C 4 N 2 H 14 PbBr 4 , consisting of Pb–Br chains separated by organic cations, which shows a large Stokes shift (0.83 eV) and broadband emission. Through first-principles calculations and polarized Raman spectroscopy, we characterize the material's vibrational properties and identify the specific phonon modes that drive exciton self-trapping. Our novel GW/Bethe-Salpeter equation force formalism reveals that low-frequency phonons (∼ 100 cm −1 , primarily involving Pb–Br motions) couple strongly with excitons, with a remarkably high Huang-Rhys factor of 137 ± 4, and gives a pathway for ultrafast structural analysis during the absorption process. This phonon-exciton coupling mechanism explains the material's broadband emission and provides a pathway for controlling optical properties through vibrations and for tuning vibrations through optical excitations. The material also exhibits highly anisotropic optical properties and electronic transport, with bands that are dispersive along the Pb–Br chains but nearly flat in perpendicular directions, resulting in direction-dependent electrical conductivity that is calculated to be an order of magnitude higher along the chain direction and consistent with measurements. These combined properties make this system an excellent platform for polarization-sensitive optoelectronic devices.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Fundamental optical transitions in hexagonal boron nitride epilayers

Fundamental optical transitions in hexagonal boron nitride (h-BN) epilayers grown on sapphire by metal–organic chemical vapor deposition (MOCVD) using triethylboron as the boron precursor have been probed by photoluminescence (PL) emission spectroscopy. The low temperature (10 K) PL spectrum exhibits two groups of emission lines. The first group includes the direct observation of the free exciton and impurity bound exciton (BX) transitions and phonon replicas of the BX transition, whereas the second group is attributed to the direct observation of the band-to-band transition and its associated phonon replicas. The observations of zero-phonon lines of the band-to-band and exciton transitions, which are supposedly forbidden or “dark” in perfect h-BN crystals, result from a relaxed requirement of momentum conservation due to symmetry-breaking in the presence of high concentrations of impurities/defects and strain, which in turn provided more deterministic values of the energy bandgap (E g ), exciton binding energy (E x ), and binding energy of impurity bound excitons (E BX ) in h-BN epilayers. Excitonic parameters of h-BN epilayers grown by MOCVD, carbon-free chemical vapor deposition, and high purity h-BN bulk materials are compared and discussed. The present results, together with available information in the literature, represent a significant improvement in the understanding of the fundamental optical properties and excitonic parameters of h-BN ultrawide bandgap semiconductors.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Models and Measurements Quantify Photon Recycling, Charge-Carrier Diffusion and Photon Scattering Contributions to Photoluminescence in InP Nanowire Arrays

Nanowire arrays present many unique advantages for solar-to-chemical energy conversion. One possible advantage is that photon recycling between neighboring nanowires has the potential to increase solar energy conversion efficiencies. Here, in this work, we explore three underlying mechanisms of optical and electronic coupling between neighboring nanowires─incident photon scattering, photon recycling, and charge-carrier transport from the photoexcited nanowire to the neighboring nanowire via the underlying substrate─using single nanowire-level microscopy and spectroscopy measurements. We present a comprehensive analysis of light absorption and emission of a single nanowire at open circuit, and subsequent re-absorption and re-emission by a neighboring nanowire. We developed a novel correlated single nanowire microspectroscopy and widefield imaging methodology to spatially resolve photon communication pathways between neighboring nanowires and selectively image re-emitted and reflected photons. We developed unique multiphysics models to couple wave optics and semiconductor photophysics to especially isolate contributions from photon recycling and electronic transport to photon emission from neighboring nanowires. By systematically varying the morphologies of the nanowires modeled, we identified pathways to maximize photon recycling between neighboring nanowires. We concluded that the measured photoluminescence is more strongly influenced by the diffusion of charge carriers as compared to photon recycling in materials with moderate-to-large charge-carrier mobilities (>10 cm 2 V –1 s –1 ), and that photon recycling dictates photoluminescence intensity only when the charge-carrier mobility is low (<1 cm 2 V –1 s –1 ). The experimental and simulation platforms developed herein for photon management strategies can be leveraged by the semiconductor photocatalysis community to enhance solar-to-chemical conversion efficiencies in semiconductor nanowire arrays.

25 ENERGY STORAGE↗

DOE OSTI2024

Optical Properties of Low‐Defect Large‐Area Hexagonal Boron Nitride for Quantum Applications

Intrinsic defects and their concentrations in hexagonal boron nitride (h-BN) play a key role in single-photon emission. In this study, the optical properties of large-area multilayer h-BN-on-sapphire grown by metal-organic chemical vapor deposition are explored. Based on the detailed spectroscopic characterization using both cathodoluminescence (CL) and photoluminescence (PL) measurements, the material is devoid of random single-point defects instead of a few clustered complex defects. The emission spectra of the measurements confirm a record-low-defect concentration of ≈10 4 cm −2 . Post-annealing, no significant changes are observed in the measured spectra and the defect concentrations remain unaltered. Through CL and PL spectroscopy, an optically active boron vacancy spin defect is identified and a novel complex defect combination arising from carbon impurities is revealed. This complex defect, previously unreported, signifies a unique aspect of the material. In these findings, the understanding of defect-induced optical properties in h-BN films is contributed, providing insights for potential applications in quantum information science.

42 ENGINEERING↗

DOE OSTI2021

Li Isotope Signatures using Optical Spectroscopies

The primary goal of this work is to investigate the detection capabilities of laser ablation molecular isotopic spectrometry (LAMIS) and Raman spectroscopy for lithium isotopic determination as related to Li enrichment activities. LAMIS is an emerging spectroscopic technique that takes advantage of the fact that molecules exhibit much larger isotopic wavelength shifts in molecular emission spectra than their atomic counterparts. Raman spectroscopy has been shown to exhibit isotopic shifts if a given molecular vibration involves the isotope of interest. Both techniques are comprised of the same basic hardware: a spectrometer, a laser system (pulsed for LAMIS, pulsed or CW for Raman), and an intensified charge-coupled device (ICCD). Shifts in Raman spectra due to lithium isotopes in Li 2 C0 3 and LiOH*H 2 0 were observed. LAMIS measurements of the same compounds have not been successful yet, as no lithium containing molecular emissions have been identified to this point. However, an isotopic shift of the self-reversal of an atomic lithium emission was observed, which is another optical technique used to measure isotopes.

07 ISOTOPE AND RADIATION SOURCES↗

NASA NTRS2005

Optical and X-ray studies of chromospherically active stars: FR Cancri, HD 95559 and LO Pegasi

We present a multiwavelength study of three chromospherically active stars, namely FR Cnc (= BD +16 degrees 1753), HD 95559 and LO Peg (=BD +22 degrees 4409), including newly obtained optical photometry, (for FR Cnc) low-resolution optical spectroscopy, as well as archival IR and X-ray observations. The BVR photometry carried out during the years 2001 - 2004 has found significant photometric variability to be present in all three stars. For FR Cnc, a photometric period 0.826685 +/- 0.000034 d has been established. The strong variation in the phase and amplitude of the FR Cnc light curves when folded on this period implies the presence of evolving and migrating spots or spot groups on its surface. Two independent spots with migration periods of 0.97 and 0.93 years respectively are inferred. The photometry of HD 95559 suggests the formation of a spot (group) during the interval of our observations. We infer the existence of two independent spots or groups in the photosphere of LO Peg, one of which has a migration period of 1.12 years. The optical spectroscopy of FR Cnc carried out during 2002-2003, reveals the presence of strong and variable Ca I1 H and K, H(sub beta) and H(sub alpha) emission features indicative of high level of chromospheric activity. The value of 5.3 for the ratio of the excess emission in H(sub alpha) to H(sub beta), EH(sub alpha)/EH(sub beta), suggests that the chromospheric emission may arise from an extended off-limb region. We have searched for the presence of color excesses in the near-IR JHK bands of these stars using 2MASS data, but none of them appear to have any significant color excess. We have also analyzed archival X-ray observations of HD 95559 and LO Peg carried out by with the ROSAT observatory. The best fit models to their X-ray spectra imply the presence of two coronal plasma components of differing temperatures and with sub-solar metal abundances. The inferred emission measures and temperatures of these systems are similar to those found for other active dwarf stars. The kinematics of FR Cnc suggest that it is a very young (35 - 55 Myrs) main-sequence star and a possible member of the IC 2391 supercluster. LO Peg also has young disk-type kinematics and has been previously suggested to be a member of the 100 Mys old Local Association (Pleiades Moving Group). The kinematics of HD 95559 indicate it is a possible member of the 600 Myrs old Hyades supercluster.

Pandey, J. C.↗

DOE OSTI2023

Giant room-temperature nonlinearities in a monolayer Janus topological semiconductor

Abstract Nonlinear optical materials possess wide applications, ranging from terahertz and mid-infrared detection to energy harvesting. Recently, the correlations between nonlinear optical responses and certain topological properties, such as the Berry curvature and the quantum metric tensor, have attracted considerable interest. Here, we report giant room-temperature nonlinearities in non-centrosymmetric two-dimensional topological materials—the Janus transition metal dichalcogenides in the 1 T’ phase, synthesized by an advanced atomic-layer substitution method. High harmonic generation, terahertz emission spectroscopy, and second harmonic generation measurements consistently show orders-of-the-magnitude enhancement in terahertz-frequency nonlinearities in 1 T’ MoSSe (e.g., > 50 times higher than 2 H MoS 2 for 18 th order harmonic generation; > 20 times higher than 2 H MoS 2 for terahertz emission). We link this giant nonlinear optical response to topological band mixing and strong inversion symmetry breaking due to the Janus structure. Our work defines general protocols for designing materials with large nonlinearities and heralds the applications of topological materials in optoelectronics down to the monolayer limit.

42 ENGINEERING↗

DOE OSTI2021

Characterization of a boron-loaded deuterated liquid scintillator for fast and thermal neutron detection

The preparation and characterization of novel boron-loaded deuterated liquid scintillators (BLDLS) are presented for the first time to investigate the performance of a detector sensitive to both fast and thermal neutrons intended for future neutron spectroscopy measurements. Three deuterated toluene-based scintillation cocktails were produced, one without boron, one loaded with ortho-carborane (natural boron isotopic abundance), and one with 96 wt% 10B enriched ortho-carborane. General optical and material properties were analyzed to include the composition, density, index of refraction, photoluminescence emission spectra, and absorbance spectra in addition to the relative light yield, resolution, relative efficiency, and pulse-shape-discrimination performance for all three scintillators and a hydrogen-based EJ-309 scintillator to evaluate the effects of boron loading in comparison with a common commercially-available scintillator and feasibility for future neutron spectroscopy measurements. Finally, the detection of shielded neutron sources was explored to capitalize on the 10B thermal neutron capture reaction. The results showed loading the scintillators with boron deteriorated the PSD performance slightly compared to the unloaded deuterated scintillator and resulted in a relative light yield loss of 26% and 41% for the 10B enriched and natural boron BLDLS, respectively. Lastly, the BLDLS have a higher relative detection efficiency than the unloaded deuterated scintillator for shielded neutron sources, based on total count rate, a desirable characteristic for missions related to finding and characterizing illicitly-trafficked special nuclear material.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

NASA NTRS1992

Walls and windows in the molecular Milky Way

Estimates are presented of the distances to the nearest CO-emitting material along 31,500 lines of sight in the northern Milky Way on the basis of an analysis of the Massachusetts-Stony Brook survey of CO emission in the first Galactic quadrant. For Galactic latitudes between -1.0 and +1.0 deg and longitudes between 8 and 53 deg, significant CO emission (greater than 1.2 K) and associated optical obscuration (greater than 1.2 mag) is found within 2 kpc of the sun in 21,149 of the lines of sight. Much of this local emission is associated with the Aquila Rift system of dark clouds. Another 8,179 lines of sight are obscured at distances between 2 and 10 kpc. The remaining 2,172 lines of sight are completely free of significant CO emission. These cloud-free positions can be used as 'offs' for radio or IR spectroscopy of molecular sources in the Galactic plane, as 'ons' for studies of the diffuse intercloud medium itself, and as possible 'windows', through which distant disk and bulge stars might be optically observable.

Waller, William H.↗

DOE OSTI2020

Systematic Assessment of Retrieval Methods for Canopy Far-Red Solar-Induced Chlorophyll Fluorescence Using High-Frequency Automated Field Spectroscopy

Remote sensing of solar-induced chlorophyll fluorescence (SIF) offers potential to infer photosynthesis across scales and biomes. Many retrieval methods have been developed to estimate top-of-canopy SIF using ground-based spectroscopy. However, inconsistencies among methods may confound interpretation of SIF dynamics, eco-physiological/environmental drivers, and its relationship with photosynthesis. Using high temporal- and spectral resolution ground-based spectroscopy, we aimed to (1) evaluate performance of SIF retrieval methods under diverse sky conditions using continuous field measurements; (2) assess method sensitivity to fluctuating light, reflectance, and fluorescence emission spectra; and (3) inform users for optimal ground-based SIF retrieval. Analysis included field measurements from bi-hemispherical and hemispherical-conical systems and synthetic upwelling radiance constructed from measured downwelling radiance, simulated reflectance, and simulated fluorescence for benchmarking. Fraunhofer-based differential optical absorption spectroscopy (DOAS) and singular vector decomposition (SVD) retrievals exhibit convergent SIF-PAR relationships and diurnal consistency across different sky conditions, while O2A-based spectral fitting method (SFM), SVD, and modified Fraunhofer line discrimination (3FLD) exhibit divergent SIF-PAR relationships across sky conditions. We find that such behavior holds across system configurations, though hemispherical-conical systems diverge less across sky conditions. O 2 A retrieval accuracy, influenced by atmospheric distortion, improves with a narrower fitting window and when training SVD with temporally local spectra. This may impact SIF-photosynthesis relationships interpreted by previous studies using O 2 A-based retrievals with standard (759–767.76 nm) fitting windows. Fraunhofer-based retrievals resist atmospheric impacts but are noisier and more sensitive to assumed SIF spectral shape than O 2 A-based retrievals. We recommend SVD or SFM using reduced fitting window (759.5–761.5 nm) for robust far-red SIF retrievals across sky conditions.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1995

Near-infrared and optical spectroscopy of FSC 10214+4724

New infrared and optical spectroscopic observations, obtained with the W. M. Keck Telescope, are reported for the highly luminous infrared source FSC 10214+4724. The rest frame optical spectrum shows new emission lines of (Ne III), (Ne V), (O I), (O II), (S II), and He(+), while the rest frame ultraviolet spectrum shows new lines of O IV) + Si IV, N III, N IV), Si II, Ne IV, and possibly N II and (Ne III), as well as clearly showing that Ly-alpha is self-absorbed. The emission-line spectrum is most characteristic of a Seyfert 2 nucleus. The preponderance of spectroscopic evidence strengthens the case for a dust-enshrouded Active galactic nuclei (AGN) powering much or most of the observed luminosity. The various spectral lines lead to a wide range in the inferred reddening and ionization parameter for this system, suggesting that we are viewing several environments through differing extinctions.

Soifer, B. T.↗

DOE OSTI2022

Metal (hydr)oxide surface precipitates and their effects on potassium sorption

Surface precipitation has been shown to occur on rapid time scales in clay and metal oxide mineral systems. The formation of surface precipitates is hypothesized to present new potential sorption sites for potassium (K), where K can become incorporated into newly formed interlayer spaces (e.g., between tetrahedral–octahedral–tetrahedral stacked sheets). The objective of this study is to determine the effects of newly formed mineral surface precipitates on K sorption. Potassium adsorption experiments were conducted by utilizing Al 2 O 3 and SiO 2 sorbents in the presence of various cations (magnesium, zinc, and nickel) that helped to catalyze the formation of surface precipitates. Dissolved concentrations of elements were monitored via inductively coupled plasma optical emission spectrometry (ICP-OES). Solids were characterized via X-ray diffraction (XRD), and K surface complexation was analyzed via X-ray absorption near edge structure (XANES) spectroscopy. X-ray diffraction analysis indicated bayerite, layered double hydroxides (LDH), and silicated LDH were formed as reaction products, thus creating new surface sites for potential K adsorption. The presence of Si increased K adsorption perhaps due to its role in the formation of LDH surface precipitates. When the differences between observed and theoretical surface area normalized K sorption densities were averaged, a 31% increase in K adsorption was observed in the presence of Si. XANES analysis indicated that the binding mechanism of K to Si is different than that of K to Al, perhaps due to the presence of inner-sphere complexation of K to Al-oxide. Samples reacted for one month versus one week yielded more intense XANES post-edge peaks which indicated that the K sorption complex changes over time. Altogether, our findings provide novel insights into the mechanisms of K fixation in soil and has high implication in providing improved K fertilizer recommendation to growers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2008

Nova V2362 Cygni (Nova Cygni 2006): Spitzer, Swift, and Ground-Based Spectral Evolution

Nova V2362 Cygni has undergone a number of very unusual changes. Ground-based spectroscopy initially revealed a normal sequence of events: the object faded and its near-infrared emission lines gradually shifted to higher excitation conditions until about day 100 when the optical fading reversed and the object slowly brightened. This was accompanied by a rise in the Swift X-ray telescope flux and a sudden shift in excitation of the visible and IR spectrum back to low levels. The new lower excitation spectrum revealed broad line widths and many P-Cygni profiles, all indicative of the ejection of a second shell. Eventually, dust formed, the X-ray brightness -- apparently unaffected by dust formation -- peaked and then declined, and the object faded at all wavelengths. The Spitzer dust spectra revealed a number of solid-state emission features that, at this time, are not identified.

Lynch, David K.↗

NASA NTRS2020

Optical Spectroscopy and X-Ray Observations of the D-Type Symbiotic Star EF Aql

We performed high-resolution optical spectroscopy and X-ray observations of the recently identified Mira-type symbiotic star EF Aql. Based on high-resolution optical spectroscopy obtained with SALT, we determine the temperature (~55 000 K) and the luminosity (~5.3 L⨀) of the hot component in the system. The heliocentric radial velocities of the emission lines in the spectra reveal possible stratification of the chemical elements. We also estimate the mass-loss rate of the Mira donor star. Our Swift observation did not detect EF Aql in X-rays. The upper limit of the X-ray observations is 10(exp -12) erg cm(exp -2) s(exp -1), which means that EF Aql is consistent with the faintest X-ray systems detected so far. Otherwise, we detected it with the UVOT instrument with an average UVM2 magnitude of 14.05. During the exposure, EF Aql became approximately 0.2 UVM2 magnitudes fainter. The periodogram analysis of the V-band data reveals an improved period of 320.4±0.3 d caused by the pulsations of the Mira-type donor star. The spectra are available upon request from the authors.

Symbiotic binary stars↗

DOE OSTI2023

Amplified spontaneous emission from europium-based molecular complexes coupled to photonic crystal cavities

Rare-earth ion-based materials bear many remarkable optical properties that render them highly appealing for lighting and quantum-related applications. However, their small oscillator strength and weak emission often pose limitations. Here, in this work, we synthesize and couple Eu(III)-based molecular complexes to nanobeam photonic crystals supporting air modes. A reasonable spatial overlap between the molecular complexes and cavity modes leads to an average spontaneous emission coupling efficiency of 0.19. Our pump power-dependent photoluminescence measurements evidence amplified spontaneous emission from the molecular complexes with an amplification threshold as low as 4.4 W/cm 2 , likely benefiting from the efficient coupling. These findings suggest that integrating rare-earth ion-based molecular complexes with photonic structures could be a viable approach for regulating their emission characteristics for particular applications.

36 MATERIALS SCIENCE↗

NASA NTRS2020

Discovery of the Optical Afterglow and Host Galaxy of Short GRB 181123B at z = 1.754: Implications for Delay Time Distributions

We present the discovery of the optical afterglow and host galaxy of the Swift short-duration gamma-ray burst (SGRB) GRB 181123B. Observations with Gemini-North starting ≈9.1 hr after the burst reveal a faint optical afterglow with i ≈ 25.1 mag at an angular offset of 0 59 ± 0." 16 from its host galaxy. Using grizYJHK observations, we measure a photometric redshift of the host galaxy of z = 1.77+0.30-0.17. From a combination of Gemini and Keck spectroscopy of the host galaxy spanning 4500–18000 Å, we detect a single emission line at 13390 Å, inferred as Hβ at z = 1.754 ± 0.001 and corroborating the photometric redshift. The host galaxy properties of GRB 181123B are typical of those of other SGRB hosts, with an inferred stellar mass of ≈9.1 × 109Msun, a mass-weighted age of ≈0.9 Gyr, and an optical luminosity of ≈0.9L*. At z = 1.754, GRB 181123B is the most distant secure SGRB with an optical afterglow detection and one of only three at z > 1.5. Motivated by a growing number of high-z SGRBs, we explore the effects of a missing z > 1.5 SGRB population among the current Swift sample on delay time distribution (DTD) models. We find that lognormal models with mean delay times of ≈4–6 Gyr are consistent with the observed distribution but can be ruled out to 95% confidence, with an additional ≈one to five Swift SGRBs recovered at z > 1.5. In contrast, power-law models with ∝t−1 are consistent with the redshift distribution and can accommodate up to ≈30 SGRBs at these redshifts. Under this model, we predict that ≈1/3 of the current Swift population of SGRBs is at z > 1. The future discovery or recovery of existing high-z SGRBs will provide significant discriminating power on their DTDs and thus their formation channels.

K Paterson↗