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NASA NTRS1994

Carbon isotopic fractionation in lipids from methanotrophic bacteria: relevance for interpretation of the geochemical record of biomarkers

Experiments with cultured aerobic methane oxidising bacteria confirm that their biomarker lipids will be significantly depleted in 13C compared to the substrate. The methanotrophic bacteria Methylococcus capsulatus and Methylomonas methanica, grown on methane and using the RuMP cycle for carbon assimilation, show maximum 13C fractionation of approximately 30% in the resultant biomass. In M. capsulatus, the maximum fractionation is observed in the earliest part of the exponential growth stage and decreases to approximately 16% as cells approach stationary phase. This change may be associated with a shift from the particulate form to the soluble form of the methane monooxygenase enzyme. Less than maximum fractionation is observed when cells are grown with reduced methane availability. Biomass of M. capsulatus grown on methanol was depleted by 9% compared to the substrate. Additional strong 13C fractionation takes place during polyisoprenoid biosynthesis in methanotrophs. The delta 13C values of individual hopanoid and steroid biomarkers produced by these organisms were as much as l0% more negative than total biomass. In individual cultures, squalene was 13C-enriched by as much as 14% compared to the triterpane skeleton of bacteriohopaneaminopentol. Much of the isotopic dispersion in lipid metabolites could be attributed to shifts in their relative abundances, combined with an overall reduction in fractionation during the growth cycle. In cells grown on methanol, where there was no apparent effect of growth stage on overall fractionation there were still significant isotopic differences between closely related lipids including a 5.3% difference between the hopane and 3 beta-methylhopane skeletons. Hopane and sterane polyisoprenoids were also 13C-depleted compared to fatty acids. These observations have significant implications for the interpretation of specific compound isotopic signatures now being measured for hydrocarbons and other lipids present in sediments and petroleum. In particular, biomarker lipids produced by a single organism do not necessarily have the same carbon isotopic composition.

NASA Center ARC↗

NASA NTRS2018

Chain Formation as a Mechanism for Mass-Independent Fractionation of Sulfur Isotopes in the Archean Atmosphere

The anomalous abundances of sulfur isotopes in ancient sediments provide the strongest evidence for an anoxic atmosphere prior to ∼2.45 Ga, but the mechanism for producing this 'mass-independent' fractionation pattern remains in question. The prevailing hypothesis has been that it is created by differences in the UV photolysis rates of different SO2 isotopologues. We investigate here a recently proposed additional source of fractionation during gas-phase formation of elemental sulfur (S4 and S8). Because two minor S isotopes rarely occur in the same chain, the longer S4 and S8 chains should be strongly, and roughly equally, depleted in all minor isotopes. This gives rise to negative ∆(sup 33) S values and positive ∆(sub 36) S values in elemental sulfur-just the opposite of (and much larger than) what is predicted from SO2 photolysis itself. Back-reactions during chain formation, specifically photolysis of S2 and S3, pass sulfur having the opposite fractionation back to atomic S, and thence to other sulfur species, causing H2S, SO2, sulfate, and short-chain elemental sulfur to have positive ∆(sup 33) S and negative ∆(sup 36) S. Positive ∆(sup 33) S values in elemental sulfur produced in laboratory SO2 photolysis experiments could be caused by the initial fractionation during photolysis, combined with rapid condensation of short-chain sulfur species on the walls of the reaction chamber, along with a scarcity of back-reactions. The simulated fractionations produced by the chain formation mechanism do not directly match fractionations from the rock record. The mismatch might be explained if the isotopic signals leaving the atmosphere were significantly modulated by life, by uncertainties in the rates of reactions of both major and minor isotopic sulfur species, or by the relatively large potential range of atmospheric parameters. Further work is needed to better constrain these uncertainties, but this novel mechanism suggests new avenues to explore in our search for a explanation for the S-MIF record.

Great Oxidation Event↗

DOE OSTI2025

Upconversion of non-recycled MSW paper fractions into biochar via slow pyrolysis and life cycle analysis: Pathways to net negative GHG emission

This study presents an integrated and sustainable approach to valorizing non-recycled municipal solid waste (MSW), a heterogeneous and underutilized waste stream destined for landfilling, by converting it into valuable biochar resources. Specifically, we investigated the upcycling of nonrecycled paper waste based on compositional analysis into four major fractions: high cellulose, high lignin, high contamination, and high ash content papers. These fractions were then homogenized and subjected to slow pyrolysis. The high cellulose fraction (36.1 %) was the most abundant, and contained 66.7 % cellulose, while the high lignin fraction showed the highest lignin (12.1 %) and carbon content (44 %), resulting in highest energy value of 17.4 MJ kg −1 . Biochar yields ranged from 25.6 % to 35.6 %, with the high ash fraction producing the highest yield and alkalinity (pH ≈ 11.2) due to its higher mineral content. Elemental analysis revealed enhanced carbon content up to 76.9 % and reduced oxygen and hydrogen, confirming effective carbonization. The high lignin-derived biochar showed the highest aromatic carbon content (82.8 %) and greater structural stability, while contaminated and ash-rich fractions exhibited dense, low-porosity surfaces due to the presence of contaminants and minerals. Spectroscopic analysis revealed degradation of carbohydrates, disappearance of cellulose peaks and formation of aromatic and mineral derived phases. The scaled life cycle process yielded a global warming potential (GWP) of 119.3 kg CO 2 -eq per ton of dry paper waste, offset by soil carbon sequestration of − 556.41 kg CO 2 -eq, resulting in a net impact of − 427.36 kg CO 2 -eq. This represents a net carbon removal exceeding by ~186 % the emissions associated with landfilling paper waste with electricity generation.

09 BIOMASS FUELS↗

DOE OSTI2026

A fractional calculus framework for open quantum dynamics: From Liouville to Lindblad to memory kernels

Open quantum systems exhibit dynamics ranging from unitary evolution to irreversible dissipation. While the Gorini–Kossakowski–Sudarshan–Lindblad equation uniquely characterizes Markovian completely positive and trace-preserving (CPTP) evolution, many physical platforms display non-Markovian features such as algebraic relaxation and coherence backflow. Fractional calculus provides a natural way to model such long-memory behavior through power-law temporal kernels introduced by fractional time derivatives. Here, we develop a unified framework that embeds fractional master equations within the broader hierarchy of open-system formalisms. The fractional equation forms a structured subclass of memory-kernel models, reduces to the Lindblad form at unit order, and, through Bochner–Phillips subordination, admits a CPTP representation as an average over Lindblad semigroups. Its resolvent structure further connects fractional dynamics to established non-Markovian approaches, including Nakajima–Zwanzig kernels and hierarchical equations of motion, providing a compact surrogate for long-memory effects. This formulation positions fractional calculus as a rigorous and practical language for modeling non-Markovian quantum dynamics in chemical physics and physical chemistry, providing a CPTP-preserving, computationally efficient surrogate for structured condensed-phase environments where long-time memory and dissipation play a central role.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Mass dependence of halo baryon fractions from the kinetic Sunyaev–Zeldovich effect

ABSTRACT We detect the kinetic Sunyaev–Zeldovich imprint of peculiar motions of galaxy groups and clusters, using the photometric Dark Energy Spectroscopic Instrument Legacy Surveys together with cosmic microwave background (CMB) maps from the Atacama Cosmology Telescope (ACT). We develop a comprehensive forward model based on the AbacusSummit cosmological simulations: Mock galaxy group catalogues and synthetic kinetic Sunyaev–Zeldovich (kSZ) maps are generated, together with a reconstructed peculiar velocity field that allows for photo-z errors, redshift-space distortions, and survey masks. We investigate possible contamination from the cosmic infrared background (CIB), finding that CIB effects are subdominant to the kSZ signal in the relevant ACT frequency channel. We then predict the kSZ signal expected when stacking CMB temperature maps around groups, taking account of their estimated radial velocities. Comparing the model with observations, we are able to constrain the total baryon fraction within haloes, as well as their internal gas profiles. We find evidence for mass dependence of the halo baryon fraction within the virial radius. The gas fraction in massive groups is consistent with the universal baryon fraction, but low-mass groups ($10^{12.5} \lesssim M\, /\, h^{-1}\, \mathrm{M}_\odot \lesssim 10^{14}$) are depleted to $0.38 \pm 0.11$ times the universal baryon fraction. We find this low virial baryon fraction to be consistent with an extended gas profile, for which the total baryon content reaches the universal value well beyond the virial radius. This conclusion is consistent with previous analyses using X-ray, kSZ, and weak lensing, and plausibly reflects energetic feedback processes from the galaxies in these haloes.

Roper, Finn A [Institute for Astronomy, University↗

DOE OSTI2026

Measurement of 𝐵 meson production fraction ratios in proton-proton collisions at √𝑠 = 13 TeV using open-charm and charmonium decays

Production fraction ratios of 𝐵 + , 𝐵 0 , and 𝐵$^{0}_{𝑠}$ mesons are measured in proton-proton collisions at √𝑠 = 13 TeV using a special dataset recorded in 2018 with high-rate triggers designed to collect an unbiased sample of 1⁢010 𝑏 hadrons with the CMS experiment at the LHC. These data allow the study of the open-charm decays of 𝐵 mesons (𝐵 (𝑠) → 𝜋⁢𝐷 (𝑠) ) where the 𝐷 meson decays into fully hadronic final states. By utilizing known branching fractions and precise theoretical calculations, production fraction ratios as functions of 𝐵 meson transverse momentum (𝑝 T ) and rapidity (𝑦) are measured using open-charm decays in the kinematic range of 8 < 𝑝 T < 60 GeV and |𝑦| <2.25. In addition, the same dataset is used to measure the relative production fraction ratios with the charmonium decay channels [𝐵 (𝑠) →𝑋⁢𝐽/𝜓 with 𝑋 indicating a 𝐾 + , 𝐾*(892) 0 , or 𝜙⁡(1020) meson] where the 𝐽/𝜓 meson decays into a pair of muons. The open-charm results are used to normalize the relative production fraction ratios obtained from the charmonium samples. Measurements of the ratios of branching fractions of 𝐵 meson decays to charmonium and open-charm final states are also reported, which will improve the world-average values of these ratios. Finally, we test isospin invariance in 𝐵 meson production in proton-proton collisions and observe that it holds within the experimental precision.

Bottom mesons↗

DOE OSTI2025

Fractional Quantum Anomalous Hall Effect

The realization of the fractional quantum anomalous Hall effect (FQAHE) in a zero-field fractional Chern insulator is a new advancement in condensed matter physics, resulting from the interplay among strong correlations, topology, and spontaneous time-reversal symmetry breaking in lattice systems. In this review, we highlight the experimental and theoretical progress toward achieving FQAHE in two material platforms: twisted bilayer MoTe 2 and rhombohedral-stacked multilayer graphene. These systems host narrow topological bands with nontrivial Chern numbers, enabling interaction-driven fractionalized states analogous to the fractional quantum Hall effect, but without external magnetic fields. We discuss how spontaneous ferromagnetism, moiré lattice reconstruction, and band topological effects underpin the emergence of FQAHE in twisted MoTe 2 . We describe experimental discoveries of zero-field fractional Chern insulators in both transport and optical experiments, as well as signatures of composite Fermi liquids and higher-energy Chern band, which may shed light on engineering nonabelian states. In rhombohedral graphene/hexagonal boron nitride moiré superlattices, we review the recent observations of fractionally quantized Hall resistance, connections between FQAHE and extended quantum anomalous Hall phases, and the coexistence of superconductivity and FQAHE. Furthermore, these discoveries not only deepen our understanding of strongly correlated topological matter but also open new frontiers for exploring nonabelian anyons, fault-tolerant quantum computation, and topological opto-spintronics free of magnetic fields.

bilayer↗

NASA NTRS1976

Geochemistry of grain-size fractions of soils from the Taurus-Littrow valley floor

Results are presented for a study in which high-precision instrumental neutron activation analysis was applied to determine the abundances of seven rare-earth and nine other elements in two grain-size fractions (90 to 150 microns and less than 20 microns) of eight soils from the Taurus-Littrow Valley floor and one Apollo 11 bulk-soil fraction with grain sizes of less than 1 mm. Compositional differences between the two size fractions of two valley-floor soils are examined, and mixing of soil components is investigated. It is found that a five-component mixing model describes very adequately the chemical composition of bulk soils with grain sizes of less than 1 mm as mixtures of local Apollo 17 rock types (basalt, anorthositic gabbro, noritic breccia), orange glass, and meteorites, but does not describe well the chemical compositions of the other two size fractions. A ten-component model is used to show that the compositions of those two size fractions can be well represented as mixtures of the five components if the mineralogy and chemical composition of the basalt component are allowed to vary in the size fractions.

Korotev, R. L.↗

NASA NTRS1978

Methane-producing bacteria - Natural fractionations of the stable carbon isotopes

Procedures for determining the C-13/C-12 fractionation factors for methane-producing bacteria are described, and the fractionation factors (CO2/CH4) for the reduction of CO2 to CH4 by pure cultures are 1.045 for Methanosarcina barkeri at 40 C, 1.061 for Methanobacterium strain M.o.H. at 40 C, and 1.025 for Methanobacterium thermoautotrophicum at 65 C. The data are consistent with the field determinations if fractionation by acetate dissimilation approximates fractionations observed in natural environments. In other words, the acetic acid used by acetate dissimilating bacteria, if they play an important role in natural methane production, must have an intramolecular isotopic fractionation (CO2H/CH3) approximating the observed CO2/CH4 fractionation.

Games, L. M.↗

NASA NTRS1980

Possible isotopic fractionation effects in sputtered minerals

A model which makes definite predictions for the fractionation of isotopes in sputtered material is discussed. The fractionation patterns are nonlinear, and the pattern for a particular set of isotopes depends on the chemical matrix within which those isotopes are contained. Calculations are presented for all nonmonoisotopic elements contained in the minerals perovskite, anorthite, ackermanite, enstatite, and troilite. All isotopes are fractionated at the level of approximately 4-6 deg/o per atomic mass unit. Oxygen is always positively fractionated (heavier isotopes sputtered preferentially), and heavier elements are generally negatively fractioned (light isotopes sputtered preferentially). The value of Delta (O-18:O-16) is always less by about 1.8 deg/o than a linear extrapolation based upon the calculated delta (O-17:O-16) value would suggest. The phenomenon of both negative and positive fractionation patterns from a single target mineral are used to make an experimental test of the proposed model.

Haff, P. K.↗

NASA NTRS1982

On determination of fibre fraction in continuous fibre composite materials

It is pointed out that the fiber volume fraction is probably the most important parameter influencing the properties of fibrous composite materials. The present investigation is concerned with questions regarding the accurate determination of this parameter. It is found that an estimate of the fiber volume fraction based on determinations from several coupons taken from different regions of a laminate is not accurate. At present fiber volume fractions are not directly measured but rather are calculated from the fiber weight fraction and densities of the composite and fiber. Image analysis techniques can and should be applied to determine fiber volume fraction. However, several factors have to be considered in this connection. It is necessary to make many measurements of the local fiber area fractions, and the preparation of representative planar cross sections parallel to the fiber axis may be difficult.

Whittenberger, J. D.↗

NASA NTRS1990

Xenon fractionation in porous planetesimals

The distinctively fractionated Xe on Mars and earth may have its root in a common source from which both planets accreted. Beginning with Ozima and Nakazawa's (1980) hypothesis that terrestrial Xe fractionation was caused by gravitational separation of adsorbed solar nebular gases inside large porous planetesimals, it is pointed out that Xe would have been trapped as the planetesimal grew and pores were squeezed shut by lithostatic pressure. It is shown that enough fractionated Xe to supply the earth could have been trapped this way. The degree of fractionation is controlled by the lithostatic pressure at the pore-closing front and so would have been roughly the same for all large planetesimals. The predicted degree of fractionation agrees well with that preserved in terrestrial and Martian Xe. Relative to Xe, this source is strongly depleted in other noble gases. In contrast to the original Ozima and Nakazawa hypothesis, the present hypothesis predicts the observed fractionation, and it allows planetary accretion to occur after the dissipation of the solar nebula.

Zahnle, Kevin↗

NASA NTRS1992

The optimal fiber volume fraction and fiber-matrix property compatibility in fiber reinforced composites

Although the question of minimum or critical fiber volume fraction beyond which a composite can then be strengthened due to addition of fibers has been dealt with by several investigators for both continuous and short fiber composites, a study of maximum or optimal fiber volume fraction at which the composite reaches its highest strength has not been reported yet. The present analysis has investigated this issue for short fiber case based on the well-known shear lag (the elastic stress transfer) theory as the first step. Using the relationships obtained, the minimum spacing between fibers is determined upon which the maximum fiber volume fraction can be calculated, depending on the fiber packing forms within the composites. The effects on the value of this maximum fiber volume fraction due to such factors as fiber and matrix properties, fiber aspect ratio and fiber packing forms are discussed. Furthermore, combined with the previous analysis on the minimum fiber volume fraction, this maximum fiber volume fraction can be used to examine the property compatibility of fiber and matrix in forming a composite. This is deemed to be useful for composite design. Finally some examples are provided to illustrate the results.

Pan, Ning↗

NASA NTRS1993

A study of fiber volume fraction effects in notched unidirectional SCS-6/Ti-15V-3Cr-3Al-3Sn composite

Notched unidirectional SCS-6/Ti-15-3 composite of three different fiber volume fractions (vf = 0.15, 0.37, and 0.41) was investigated for various room temperature microstructural and material properties including: fatigue crack initiation, fatigue crack growth, and fracture toughness. While the matrix hardness is similar for all fiber volume fractions, the fiber/matrix interfacial shear strength and matrix residual stress increases with fiber volume fraction. The composite fatigue crack initiation stress is shown to be matrix controlled and occurs when the net maximum matrix stress approaches the endurance limit stress of the matrix. A model is presented which includes residual stresses and presents the composite initiation stress as a function of fiber volume fraction. This model predicts a maximum composite initiation stress at vf approximately 0.15 which agrees with the experimental data. The applied composite stress levels were increased as necessary for continued crack growth. The applied Delta(K) values at crack arrest increase with fiber volume fraction by an amount better approximated using an energy based formulation rather than when scaled linear with modulus. After crack arrest, the crack growth rate exponents for vf37 and vf41 were much lower and toughness much higher, when compared to the unreinforced matrix, because of the bridged region which parades with the propagating fatigue crack. However, the vf15 material exhibited a higher crack growth rate exponent and lower toughness than the unreinforced matrix because once the bridged fibers nearest the crack mouth broke, the stress redistribution broke all bridged fibers, leaving an unbridged crack. Degraded, unbridged behavior is modeled using the residual stress state in the matrix ahead of the crack tip. Plastic zone sizes were directly measured using a metallographic technique and allow prediction of an effective matrix stress intensity which agrees with the fiber pressure model if residual stresses are considered. The sophisticated macro/micro finite element models of the 0.15 and 0.37 fiber volume fractions presented show good agreement with experimental data and the fiber pressure model when an estimated effective fiber/matrix debond length is used.

Covey, Steven J.↗

NASA NTRS1994

Mars atmospheric loss and isotopic fractionation by solar-wind-induced sputtering and photochemical escape

We examine the effects of the loss of Mars atmospheric constituents by solar-wind-induced sputtering and by photochemical escape during the past 3.8 billion years. Sputtering is capable of efficiently removing species from the upper atmosphere, including the light noble gases; nitrogen and oxygen are removed by photochemical processes as well. Due to diffusive separation (by mass) above the homopause, removal from the top of the atmosphere will fractionate the isotopes of each species, with the lighter mass being preferentially lost. For carbon and oxygen, this allows us to determine the size of nonatmospheric reservoirs which mix with the atmosphere; these reservoirs can be CO2 adsorbed in the regolith and H2O in the polar ice caps. We have constructed both simple analytical models and time-dependent models of the loss of volatiles from and supply to the martian atmosphere. Both argon and neon require continued replenishment from outgassing over geologic time. For argon, sputtering loss explains the fractionation of (Ar-36)/(Ar-38) without requiring a distinct epoch of hydrodynamic escape (although fractionation of Xe isotopes still requires very early hydrodynamic loss). For neon, the current (Ne-22)/(Ne-20) ratio represents a balance between loss to space and continued resupply from the interior; the similarity of the ratio to the terrestrial value is coincidental. For nitrogen, the loss by both sputtering and photochemical escape would produce a fractionation of (N-15)/(N-14) larger than observed; an early, thicker carbon dioxide atmosphere could mitigate the nitrogen loss and produce the observed fractionation, as could continued outgassing of juvenile nitorgen. Based on the isotopic constraints, the total amount of carbon dioxide lost over geologic time is probably on the order of tens of millibars rather than a substantial fraction of a bar. The total loss from solar-wind-induced sputtering and photochemical escape, therefore, does not seem able to explain the loss of a putative thick, early atmosphere withput requiring formation of extensive surface carbonate deposits or other nonatmospheric reservoirs for CO2.

Jakosky, Bruce M.↗

NASA NTRS2002

The Fractional Step Method Applied to Simulations of Natural Convective Flows

This paper describes research done to apply the Fractional Step Method to finite-element simulations of natural convective flows in pure liquids, permeable media, and in a directionally solidified metal alloy casting. The Fractional Step Method has been applied commonly to high Reynold's number flow simulations, but is less common for low Reynold's number flows, such as natural convection in liquids and in permeable media. The Fractional Step Method offers increased speed and reduced memory requirements by allowing non-coupled solution of the pressure and the velocity components. The Fractional Step Method has particular benefits for predicting flows in a directionally solidified alloy, since other methods presently employed are not very efficient. Previously, the most suitable method for predicting flows in a directionally solidified binary alloy was the penalty method. The penalty method requires direct matrix solvers, due to the penalty term. The Fractional Step Method allows iterative solution of the finite element stiffness matrices, thereby allowing more efficient solution of the matrices. The Fractional Step Method also lends itself to parallel processing, since the velocity component stiffness matrices can be built and solved independently of each other. The finite-element simulations of a directionally solidified casting are used to predict macrosegregation in directionally solidified castings. In particular, the finite-element simulations predict the existence of 'channels' within the processing mushy zone and subsequently 'freckles' within the fully processed solid, which are known to result from macrosegregation, or what is often referred to as thermo-solutal convection. These freckles cause material property non-uniformities in directionally solidified castings; therefore many of these castings are scrapped. The phenomenon of natural convection in an alloy under-going directional solidification, or thermo-solutal convection, will be explained. The development of the momentum and continuity equations for natural convection in a fluid, a permeable medium, and in a binary alloy undergoing directional solidification will be presented. Finally, results for natural convection in a pure liquid, natural convection in a medium with a constant permeability, and for directional solidification will be presented.

Westra, Douglas G.↗

NASA NTRS2004

Evaporation and Accompanying Isotopic Fractionation of Sulfur from FE-S Melt During Shock Wave Heating

Chondrules probably formed by melting and subsequent cooling of solid precursors. Evaporation during chondrule melting may have resulted in depletion of volatile elements in chondrules. It is known that kinetic evaporation, especially evaporation from a melt, often leads to enrichment of heavy isotopes in an evaporation residue. However, no evidence for a large degree of heavy-isotope enrichment has been reported in chondrules for K, Mg, Si, and Fe (as FeO). The lack of isotopic fractionation has also been found for sulfur in troilites (FeS) within Bishunpur (LL3.1) and Semarkona (LL3.0) chondrules by an ion microprobe study. The largest fractionation, found in only one grain, was 2.7 +/- 1.4 %/amu, while all other troilite grains showed isotopic fractionations of <1 %/amu. The suppressed isotopic fractionation has been interpreted as results of (i) rapid heating of precursors at temperatures below the silicate solidus and (ii) diffusion-controlled evaporation through a surrounding silicate melt at temperatures above the silicate solidus. The kinetic evaporation model suggests that a rapid heating rate of >10(exp 4)-10(exp 6) K/h for a temperature range of 1000-1300 C is required to explain observed isotopic fractionations. Such a rapid heating rate seems to be difficult to be achieved in the X-wind model, but can be achieved in shock wave heating models. In this study, we have applied the sulfur evaporation model to the shock wave heating conditions of to evaluate evaporation of sulfur and accompanying isotopic fractionation during shock wave heating at temperatures below the silicate solidus.

Tachibana, S.↗

NASA NTRS2016

Normalizing a Relativistic Model of X-Ray Reflection Definition of the Reflection Fraction and Its Implementation in relxill

Aims. The only relativistic reflection model that implements a parameter relating the intensity incident on an accretion disk to the observed intensity is relxill. The parameter used in earlier versions of this model, referred to as the reflection strength, is unsatisfactory; it has been superseded by a parameter that provides insight into the accretion geometry, namely the reflection fraction. The reflection fraction is defined as the ratio of the coronal intensity illuminating the disk to the coronal intensity that reaches the observer. Methods. The relxill model combines a general relativistic ray-tracing code and a photoionization code to compute the component of radiation reflected from an accretion that is illuminated by an external source. The reflection fraction is a particularly important parameter for relativistic models with well-defined geometry, such as the lamp post model, which is a focus of this paper. Results. Relativistic spectra are compared for three inclinations and for four values of the key parameter of the lamp post model,namely the height above the black hole of the illuminating, on-axis point source. In all cases, the strongest reflection is produced for low source heights and high spin. A low-spin black hole is shown to be incapable of producing enhanced relativistic reflection. Results for the relxill model are compared to those obtained with other models and a Monte Carlo simulation. Conclusions. Fitting data by using the relxill model and the recently implemented reflection fraction, the geometry of a system can be constrained. The reflection-fraction is independent of system parameters such as inclination and black hole spin. The reflection-fraction parameter was implemented with the name reflec_frac all flavours of the relxill model, and the non-relativistic reflection model xillver, in v0.4a (18 January 2016).

accretion↗