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SU-F-T-258: Efficacy of Exit Fluence-Based Dose Calculation for Prostate Radiation Therapy

Purpose: To investigate the efficacy of exit-fluence-based dose computation for prostate radiotherapy by determining if it estimates true dose more accurately than the original planning dose. Methods: Virtual exit-fluencebased dose computation was performed for 19 patients, each with 9–12 repeat CT images. For each patient, a 78 Gy treatment plan was created utilizing 5 mm CTV-to-PTV and OAR-to-PRV margins. A Monte Carlo framework was used to compute dose and exit-fluence images for the planning image and for each repeat CT image based on boney-anatomyaligned and prostate-centroid-aligned CTs. Identical source particles were used for the MC dose-computations on the planning and repeat CTs to maximize correlation. The exit-fluence-based dose and image were computed by multiplying source particle weights by FC(x,y)=FP(x,y)/FT(x,y), where (x,y) are the source particle coordinates projected to the exit-fluence plane and we denote the dose/fluence from the plan by (DP,FP), from the repeat-CT as (DT,FT), and the exit-fluence computation by (DFC,FFC). DFC mimics exit-fluence backprojection through the planning image as FT=FFC. Dose estimates were intercompared to judge the efficacy of exit-fluence-based dose computation. Results: Boney- and prostate-centroid aligned results are combined as there is no statistical difference between them, yielding 420 dose comparisons per dose-volume metric. DFC is more accurate than DP for 46%, 33%, and 44% of cases in estimating CTV D98, D50, and D2 respectively. DFC improved rectum D50 and D2 estimates 54% and 49% respectively and bladder D50 and D2 47 and 49% respectively. While averaged over all patients and images DFC and DP were within 3.1% of DT, they differed from DT by as much as 22% for GTV D98, 71% for the Bladder D50, 17% for Bladder D2, 19% for Rectum D2. Conclusion: Exit-fluence based dose computations infrequently improve CTV or OAR dose estimates and should be used with caution. Research supported in part by Varian Medical Systems.

60 APPLIED LIFE SCIENCES↗

Axial-vector form factors of the nucleon from lattice QCD

In this paper, we present results for the form factors of the isovector axial vector current in the nucleon state using large scale simulations of lattice QCD. The calculations were done using eight ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2 + 1 + 1 dynamical flavors. These ensembles span three lattice spacings a ≈ 0.06 , 0.09, and 0.12 fm and light-quark masses corresponding to the pion masses M π ≈ 135, 225, and 310 MeV. High-statistics estimates allow us to quantify systematic uncertainties in the extraction of G A (Q 2 ) and the induced pseudoscalar form factor G P (Q 2 ) . We perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses of the axial charge radius r A data to obtain physical estimates. Using the dipole ansatz to fit the Q 2 behavior we obtain r A | dipole = 0.49(3) fm , which corresponds to M A = 1.39(9) GeV , and is consistent with M A = 1.35(17) GeV obtained by the miniBooNE collaboration. The estimate obtained using the z -expansion is r A | z - expansion = 0.46(6) fm, and the combined result is r A | combined = 0.48(4) fm. Analysis of the induced pseudoscalar form factor G P (Q 2 ) yields low estimates for g* P and g π NN compared to their phenomenological values. To understand these, we analyze the partially conserved axial current (PCAC) relation by also calculating the pseudoscalar form factor. Lastly, we find that these low values are due to large deviations in the PCAC relation between the three form factors, and in the pion-pole dominance hypothesis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Techno-economic evaluation of industrial heat pump applications in US pulp and paper, textile, and automotive industries

Industrial process heat decarbonization through electrification could contribute significantly to climate change mitigation efforts. In the US industry, thermal processes accounted for more than two-thirds of the total final energy demand in 2021. Cross-cutting electrification technologies like industrial heat pumps are suitable for the process heat supply to several industrial unit operations in a sustainable way while also improving overall energy efficiency. This study employs a bottom-up approach to investigate the techno-enviro-economic potentials of deploying high-temperature and steam-generating heat pumps in US textile, pulp and paper, and automotive sectors in different timeframes. The results show that the annual technical potential energy and CO 2 savings by electrifying heat supply are 310 PJ (or 36% of the projected energy demand) and 28 MtCO 2 (or 71% of the projected CO 2 emissions) in 2050 respectively, however, these incur additional costs in each sector (ranging between 5 and 18 $\$$/GJ). The required heating capacity of industrial heat pumps is estimated at 15 GW, which translates roughly into a market of over 6000 heat pump units and an investment volume of $\$$7 billion in the studied processes. Although there may be individual cost-effective opportunities for electrifying heat supply in specific industrial sites, the overall costs are estimated to be high in the three industrial sectors due to the large disparity between electricity and natural gas prices and low heat source temperatures. To overcome the identified techno-economic barriers, comprehensive action plans for different stakeholders are also given. This study provides novel insights that should inform policymakers’ and executives’ decisions about the electrification of the current and future US industrial heat supply in relevant industrial sectors.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Evaluation of the economic implications of varied pressure drawdown strategies generated using a real-time, rapid predictive, multi-fidelity model for unconventional oil and gas wells

Experience has suggested that pressure maintenance in hydraulically fractured reservoirs via lower, more sustained production drawdowns may offer improved cumulative recovery and overall resource extraction efficiency compared to more rapid drawdown approaches aimed at generating high initial production. However, given the inherent variability of oil and natural gas markets, operators pursue production strategies that maximize profitability over resource extraction efficiency. This study focuses on evaluating the implications of contrasting pressure drawdown strategies on the long-term production and resulting economics for a real, producing unconventional gas well in the Marcellus Shale of the Appalachian Basin using a techno-economic analysis approach. Our research combines elements of well-specific horizontal well design, production forecasting, equipment sizing and capital cost estimation, operating cost estimation, and revenue and tax calculations. Gas production forecast outlook scenarios were generated under varying pressure drawdowns using two approaches: 1) a novel physics-informed machine learning workflow and 2) traditional reservoir simulation. A discounted cash flow model was used to evaluate the resulting economic implications for each drawdown scenario—generating output for exploring the coupled effect of factors like the timing and volume of gas production, prevailing economic and market conditions for natural gas, and overall estimated ultimate recovery on profitability metrics such as internal rate of return and net present value. Results show that there is potential to maximize the cumulative gas produced in the specific case study well by employing a lower pressure drawdown. Conversely, the greatest profitability is achieved using rapid drawdown as signified by a small, specific subset of our outlook scenarios. On an averaging basis, we find that the combinations of highest cumulative producing and most profitable scenarios occur under lower drawdowns with long (>40 years) producing timeframes, but require higher relative gas price and lower discounting considerations. Further, the machine learning predictive outlooking capability proved effective for enabling rapid generation of a multitude of scenario forecasts. As a result, a variety of prominent example cases could be generated to strike the balance of greater productivity and economic return given their associated producing features and economic conditions when compared to similar producing scenarios—critical insight that offers improved decision support for unconventional oil and gas operations.

42 ENGINEERING↗

Pulmonary Edema and Plasma Volume Changes in Dysbarism

Two groups of anesthetized, fasted pigs were utilized. One group of 13 animals (8.5 to 16.6 kilograms) was exposed to a high-pressure environment, and the other group of eight animals (6.9 to 20.0 kilograms) constituted the control group. The experimental group was subjected to an atmosphere of 90 percent nitrogen and 10 percent oxygen at a pressure of 50 psig for 30 minutes and then decompressed at a rate 10 psi/min. Plasma volumes, using both iodine-125-tagged-albumin and chromium-51-tagged-cell dilution techniques, were measured before, immediately after, and at 30 and 60 minutes after decompression. Aortic and right-ventricular systolic pressures were also recorded. At 60 minutes after decompression, blood samples were taken, the animals were sacrificed, and the water content of the lungs, kidneys, livers, and spleens was estimated by measuring tissue wet weight and dry weight. Protein extravasation and tissue blood volumes were determined by measuring the iodine-125-tagged-albumin and chromium-51-tagged-cell spaces in homo-genates of the organs under investigation.

Joki, J. A.↗

A study of IMRT planning parameters on planning efficiency, delivery efficiency, and plan quality

Purpose: To improve planning and delivery efficiency of head and neck IMRT without compromising planning quality through the evaluation of inverse planning parameters.Methods: Eleven head and neck patients with pre-existing IMRT treatment plans were selected for this retrospective study. The Pinnacle treatment planning system (TPS) was used to compute new treatment plans for each patient by varying the individual or the combined parameters of dose/fluence grid resolution, minimum MU per segment, and minimum segment area. Forty-five plans per patient were generated with the following variations: 4 dose/fluence grid resolution plans, 12 minimum segment area plans, 9 minimum MU plans, and 20 combined minimum segment area/minimum MU plans. Each plan was evaluated and compared to others based on dose volume histograms (DVHs) (i.e., plan quality), planning time, and delivery time. To evaluate delivery efficiency, a model was developed that estimated the delivery time of a treatment plan, and validated through measurements on an Elekta Synergy linear accelerator. Results: The uncertainty (i.e., variation) of the dose-volume index due to dose calculation grid variation was as high as 8.2% (5.5 Gy in absolute dose) for planning target volumes (PTVs) and 13.3% (2.1 Gy in absolute dose) for planning at risk volumes (PRVs). Comparison results of dose distributions indicated that smaller volumes were more susceptible to uncertainties. The grid resolution of a 4 mm dose grid with a 2 mm fluence grid was recommended, since it can reduce the final dose calculation time by 63% compared to the accepted standard (2 mm dose grid with a 2 mm fluence grid resolution) while maintaining a similar level of dose-volume index variation. Threshold values that maintained adequate plan quality (DVH results of the PTVs and PRVs remained satisfied for their dose objectives) were 5 cm{sup 2} for minimum segment area and 5 MU for minimum MU. As the minimum MU parameter was increased, the number of segments and delivery time were decreased. Increasing the minimum segment area parameter decreased the plan MU, but had less of an effect on the number of segments and delivery time. Our delivery time model predicted delivery time to within 1.8%. Conclusions: Increasing the dose grid while maintaining a small fluence grid allows for improved planning efficiency without compromising plan quality. Delivery efficiency can be improved by increasing the minimum MU, but not the minimum segment area. However, increasing the respective minimum MU and/or the minimum segment area to any value greater than 5 MU and 5 cm{sup 2} is not recommended because it degrades plan quality.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

U.S. Industrial and Commercial Motor System Market Assessment Report. Volume 3: Energy Saving Opportunity

This report seeks to inform the potential for motor systems to support decarbonization by estimating their potential energy, electricity cost, and CO 2 emissions reduction potential from adoption of proven energy efficiency actions and advanced technologies. This is the third and final report in a series of reports disseminating the findings of the U.S. Department of Energy’s (DOE’s) Motor System Market Assessment (MSMA). The MSMA and this report focus on polyphase motor systems greater than or equal to 1 horsepower (hp) in the industrial and commercial sectors. In the U.S. Industrial and Commercial Motor System Market Assessment Report Volume 1: Characteristics of the Installed Base (Volume 1 report), it was determined that these motor systems consume more than 1,000 terawatt-hours (TWh) annually. This equates to 29% of the U.S. electric grid load and results in 765 million metric tons (MMT) of CO 2 emissions and $166 billion in electricity costs. This report finds that substantial reductions to these energy, cost, and emissions impacts are possible, with three areas of significant opportunity being (1) improved load matching, (2) replacing older inefficient motors with more efficient motors, and (3) improving the condition of fluid (e.g., air, water, compressed air) distribution systems. A summary of the savings potential from these three opportunities placed within the context of the overall consumption for motor systems is illustrated in Figure ES 1 (industrial) and Figure ES 2 (commercial).

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Estimating the health benefits of planned public transit investments in Montreal

Highlights: • An integrated burden of transportation in association with planned modifications of the public transit infrastructure. • Based on our results planned public transit projects in Montreal will not reduce significantly the burden of transportation. • Future work needs to address land use and public transit projects needed to further reduce the burden of transportation. Since public transit infrastructure affects road traffic volumes and influences transportation mode choice, which in turn impacts health, it is important to estimate the alteration of the health burden linked with transit policies.

54 ENVIRONMENTAL SCIENCES↗

Comparative Study of Optical and Radio-Frequency Communication Systems for a Deep-Space Mission

We have performed a study on telecommunication systems for a hypothetical mission to Mars. The objective of the study was to evaluate and compare the benefits that microwave-X-band (8.4 GHz) and Ka-band (32 GHz) - and optical communications technologies a afford to future missions. The telecommunication systems were required to return data after launch and in orbit at 2.7 AU with daily data volumes of 0.1, 1.0, or 10.0 Gbits (Gb). Spacecraft terminals capable of delivering each of the three data volumes were proposed and characterized in terms of mass, power consumption, size, and cost. The estimated parameters for X-band, Ka-band, and optical frequencies are compared and presented here. For all cases, the optical light terminal exhibits about 60 percent of the mass of the corresponding radio frequency (RF) subsystem. Power consumption is comparable for all three technologies at a 0.1 Gb/day data volume, but the power required at either Ka-band or optical is less than half of the X-band requirement at 10 Gb/day. These benefits can be obtained only with a suitable investment in reception facilities for Ka-band or optical frequencies.

Hemmati, H.↗

A Bayesian statistical approach to inferring particle dynamics from in-situ pump POC and chloropigment data from the Mediterranean Sea

Concentrations of chloropigments and particulate organic carbon (POC) in large-volume in-situ pump samples from the Mediterranean Sea were used to estimate rate constants of processes that control the fate of particles, and specifically chloropigments, in the water column. In this paper we introduce a Bayesian statistical inversion method that combines the data with a new box model and has the capacity to infer rate constants for POC respiration/dissolution, chlorophyll and pheopigment degradation, and particle aggregation and disaggregation. We use first-order kinetics to model disaggregation, and use both first-order and second-order kinetics to model aggregation. Using these methods, the estimated small-particle (1–70 μm) POC respiration rate constant was 2.44 -1.00 +1.69 yr -1 (0.41 yr). The estimated disaggregation and second-order aggregation rate constants were 85.6 -36.4 +63.4 yr -1 (1.17×10 -2 yr) and 2.78 -1.17 +2.01 μM -1 yr -1 , respectively. Using the optimal rate constants and the corresponding particle concentrations, disaggregation is ~4.2 times faster than the small-size POC dissolution rate, which indicates that disaggregation is a dominant processes at the time of sampling. More importantly, by comparing our results with those of previous studies, we conclude that sampling methods have less influence than tracers themselves on inferring particle dynamic rate constants. We previously introduced a somewhat similar approach to modeling SV sediment trap data, but large volume pumps are a much more common sample collection method in oceanographic surveys than SV sediment traps, and thus our new model should have a wider applicability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Estimating Everglades Peat Reserves and Losses on a Landscape-Scale

The Florida Everglades formed from sawgrass and other aquatic plant remains that have accumulated over thousands of years and is a patterned peatland. The region was initially drained for agricultural and urban development in the late 1800s by the lowering of Lake Okeechobee water levels through canal drainage. Over the course of the past century, the Everglades has further been altered by the construction of canals and levees to provide control of Lake Okeechobee and Everglades water levels. The drainage has caused the loss of much of the peat of the Everglades by peat fires and microbial oxidation, much of it occurring between the 1880s and the 1950s. Plans for Everglades restoration are designed to provide additional water to flow through the remaining Everglades. Additional water into the Everglades would prevent further peat loss by reducing oxidation and encouraging the accretion of peat that has been lost. This potentially could result in the sequestration of significant quantities of atmospheric carbon. We used historic records to determine how much peat was there originally and how much has been lost. Over the past century and a half, approximately 50% of the original Everglades has been lost to agricultural and urban development. In addition, much of the peat in the remaining Everglades Protection Area has been lost. We used Geographic Information Systems technologies to determine the volume and mass of peat, the mass of carbon for each of the predrainage landscapes as well as the current Everglades regions. To do this, historical and current surveys within the Everglades were used to create elevation maps. With these maps, along with a bedrock contour map of south Florida, and soils data from the USEPA, we estimated Everglades peat characteristics. These calculations provide rough, quantitative estimates of the historical Everglades, its current condition, and the changes in the peat soil that have taken place since the 19th century. Given the uncertainties in the hindcasting of some of these data sets, this analysis provides rough estimates for the peat volumes and related constituents. Our calculations indicate that the current Everglades roughly contains less than 24% of theoriginal peat volume, 17% of its mass and 19% of its carbon. The work described was fully supported by the South Florida Water Management District, West Palm Beach, FL

Thomas Walter Dreschel↗

TH-E-17A-08: Estimation of Image Quality of 4-Dimensional Computed Tomography (4DCT) Via Fourier Analysis of Corresponding 1D Breathing Surrogate

Purpose: Motion artifacts are common in patient 4DCT, leading to an illdefined tumor volume with variation up to 110% or setting up a poor foundation with low imaging fidelity for tumor motion study. We developed a method to estimate 4DCT image quality by establishing a correlation between the severity of motion artifacts in 4DCT images and the periodicity of corresponding 1D respiratory wave-function (1DRW) surrogate used for 4DCT reconstruction. Methods: Fast Fourier Transformation (FFT) was applied to analyze 1DRW periodicity, defined as the sum of the 5 largest Fourier coefficients, ranging in 0–1. Distortional motion artifacts of cine-scan 4DCT at the junctions of adjacent couchposition scans around the diaphragm were identified in 3 categories: incomplete, overlapping and duplicate. To quantify these artifacts, the discontinuity of the diaphragm at the junctions was measured in distance and averaged along 6 directions in 3 orthogonal views. Mean and sum artifacts per junction (APJ) across the entire diaphragm were calculated in each breathing phase. To make the APJ inter-patient comparable, patientspecific motion was removed from APJ by dividing patient-specific diaphragmatic velocity (displacement divided by the mean period, from FFT analysis of the 1DRW) and the normalized APJ was defined as motion artifact severity (MAS). Twenty-five patients with free-breathing 10-phase 4DCT and corresponding 1DRW surrogate datasets were studied. Results: A mild correlation of 0.56 was found between 1DRW periodicity and 4DCT artifact severity. Higher MAS tends to appear around mid inhalation and mid exhalation and the lowest MAS tends to be around full exhalation. The breathing periodicity of >0.8 possesses minimal motion artifacts. Conclusion: The 1D-4D correlation provides a fast means to estimate 4DCT image quality. Using 1DRW signal, we can retrospectively screen out high-quality 4DCT images for clinical research (periodicity>0.8) and prospectively identify poor breathers as candidates of breath coaching prior to 4DCT scan. This research is in part supported by NIH (U54CA137788/132378). MC would like to thank MSKCC summer medical student research program supported by National Cancer Institute and hosted by Department of Medical Physics at MSKCC.

60 APPLIED LIFE SCIENCES↗

Minimum Detectable Activity for Tomographic Gamma Scanning System

For any radiation measurement system, it is useful to explore and establish the detection limits and a minimum detectable activity (MDA) for the radionuclides of interest, even if the system is to be used at far higher values. The MDA serves as an important figure of merit, and often a system is optimized and configured so that it can meet the MDA requirements of a measurement campaign. The non-destructive assay (NDA) systems based on gamma ray analysis are no exception and well established conventions, such the Currie method, exist for estimating the detection limits and the MDA. However, the Tomographic Gamma Scanning (TGS) technique poses some challenges for the estimation of detection limits and MDAs. The TGS combines high resolution gamma ray spectrometry (HRGS) with low spatial resolution image reconstruction techniques. In non-imaging gamma ray based NDA techniques measured counts in a full energy peak can be used to estimate the activity of a radionuclide, independently of other counting trials. However, in the case of the TGS each “view” is a full spectral grab (each a counting trial), and each scan consists of 150 spectral grabs in the transmission and emission scans per vertical layer of the item. The set of views in a complete scan are then used to solve for the radionuclide activities on a voxel by voxel basis, over 16 layers of a 10x10 voxel grid. Thus, the raw count data are not independent trials any more, but rather constitute input to a matrix solution for the emission image values at the various locations inside the item volume used in the reconstruction. So, the validity of the methods used to estimate MDA for an imaging technique such as TGS warrant a close scrutiny, because the pair-counting concept of Currie is not directly applicable. One can also raise questions as to whether the TGS, along with other image reconstruction techniques which heavily intertwine data, is a suitable method if one expects to measure samples whose activities are at or just above MDA levels. The paper examines methods used to estimate MDAs for a TGS system, and explores possible solutions that can be rigorously defended.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Minimum detectable activity for tomographic gamma scanning system - 15648

For any radiation measurement system, it is useful to explore and establish the detection limits and a minimum detectable activity (MDA) for the radionuclides of interest, even if the system is to be used at far higher values. The MDA serves as an important figure of merit, and often a system is optimized and configured so that it can meet the MDA requirements of a measurement campaign. The non-destructive assay (NDA) systems based on gamma ray analysis are no exception and well established conventions, such the Currie method, exist for estimating the detection limits and the MDA. However, the Tomographic Gamma Scanning (TGS) technique poses some challenges for the estimation of detection limits and MDAs. The TGS combines high resolution gamma ray spectrometry (HRGS) with low spatial resolution image reconstruction techniques. In non-imaging gamma ray based NDA techniques measured counts in a full energy peak can be used to estimate the activity of a radionuclide, independently of other counting trials. However, in the case of the TGS each 'view' is a full spectral grab (each a counting trial), and each scan consists of 150 spectral grabs in the transmission and emission scans per vertical layer of the item. The set of views in a complete scan are then used to solve for the radionuclide activities on a voxel by voxel basis, over 16 layers of a 10x10 voxel grid. Thus, the raw count data are not independent trials any more, but rather constitute input to a matrix solution for the emission image values at the various locations inside the item volume used in the reconstruction. So, the validity of the methods used to estimate MDA for an imaging technique such as TGS warrant a close scrutiny, because the pair-counting concept of Currie is not directly applicable. One can also raise questions as to whether the TGS, along with other image reconstruction techniques which heavily intertwine data, is a suitable method if one expects to measure samples whose activities are at or just above MDA levels. The paper examines methods used to estimate MDAs for a TGS system, and explores possible solutions that can be rigorously defended. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Evaluations of secondary cancer risk in spine radiotherapy using 3DCRT, IMRT, and VMAT: A phantom study

This study evaluated the secondary cancer risk from volumetric-modulated arc therapy (VMAT) for spine radiotherapy compared with intensity-modulated radiotherapy (IMRT) and 3-dimensional conformal radiotherapy (3DCRT). Computed tomography images of an Radiological Physics Center spine anthropomorphic phantom were exported to a treatment planning system (Pinnacle{sup 3}, version 9.4). Radiation treatment plans for spine were prepared using VMAT (dual-arc), 7-field IMRT (beam angles: 110°, 130°, 150°, 180°, 210°, 230°, and 250°), and 4-field 3DCRT technique. The mean and maximum doses, dose-volume histograms, and volumes receiving more than 2 and 4 Gy to organs at risk (OARs) were calculated and compared. The lifetime risk for secondary cancers was estimated according to the National Cancer Registry Programme Report 116. VMAT delivered the lowest maximum dose to the esophagus (4.03 Gy), bone (8.11 Gy), heart (2.11 Gy), spinal cord (6.45 Gy), and whole lung (5.66 Gy) as compared with other techniques (IMRT and 3DCRT). The volumes of OAR (esophagus) receiving more than 4 Gy were 0% for VMAT, 27.06% for IMRT, and up to 32.35% for 3DCRT. The estimated risk for secondary cancer in the respective OAR is considerably lower in VMAT compared with other techniques. The results of maximum doses and volumes of OARs suggest that the risk of secondary cancer induction for the spine in VMAT is lower than IMRT and 3DCRT, whereas VMAT has the best target coverage compared with the other techniques.

61 RADIATION PROTECTION AND DOSIMETRY↗

X-ray selected quasars and Seyfert galaxies - Cosmological evolution, luminosity function, and contribution to the X-ray background

The cosmological evolution and the X-ray luminosity function of quasars and Seyfert galaxies (active galactic nuclei /AGNs/) are derived and discussed. The sample used consists of 56 objects extracted from the expanded Einstein Observatory Medium Sensitivity Survey, and it is exclusively defined by its X-ray properties. The distribution in space of X-ray selected AGNs is confirmed to be strongly nonuniform; the amount of cosmological evolution required by the data is in agreement with a previous determination based on a smaller sample of objects. The X-ray luminosity function (XLF) is derived. The high-luminosity part of the XLF is satisfactorily described by a power law of slope gamma approximately 3.6. A significant flattening is observed at low luminosities. The simultaneous determination of the cosmological evolution and of the X-ray luminosity function of AGNs is then used to estimate the contribution to the extragalactic diffuse X-ray background. Using the best fit values for the evolution of AGNs and for their volume density, it is found that they contribute approximately 80 percent of the 2 keV diffuse X-ray background. Uncertainties in this estimate are still rather large; however, it seems difficult to reconcile the data with a contribution much less than 50 percent.

Maccacaro, T.↗