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Validating Drag and Heating Coefficients for Hollow Reentry Objects in Continuum Flow Using a Mach 7 Ludwieg Tube

Drag and heating coefficient databases and models are crucial to destructive reentry simulation. The NASA Orbital Debris Program Office (ODPO) develops, maintains, and performs analysis with the Object Reentry Survival Analysis Tool (ORSAT), which comprises drag and heating models for free molecular, transitional, and continuum flow regimes. These models have, in the past, only included solid, convex, blunt shapes (such as boxes, spheres, and cylinders). Previous work led by ODPO includes the extension of these models to hollow cylinders and square boxes in free molecular and transitional flow using the Direct Simulation Monte Carlo (DSMC) method. Since 2019, the ODPO has continued its program of DSMC simulations and extended the project to include analyses with the NASA Data Parallel Line Relaxation (DPLR) program on hollow cylinders and boxes (with varying wall thickness-diameter ratio). In fall 2022, the ODPO began a collaboration with the University of Texas San Antonio (UTSA) to use the Mach 7 Ludwieg Tube facility to validate the model built using numerical simulations. This facility can replicate (at a scale of approximately 100:1) the conditions seen by reentering objects near typical demise altitudes. We present here the drag and heating coefficients derived from the continued DSMC simulations, the new DPLR simulations, and the 26-test series at UTSA.

Chris Ostrom↗

Validating Drag and Heating Coefficients for Hollow Reentry Objects in Continuum Flow Using a Mach 7 Ludwieg Tube

Drag and heating coefficient databases and models are crucial to destructive reentry simulation. The NASA Orbital Debris Program Office (ODPO) develops, maintains, and performs analysis with the Object Reentry Survival Analysis Tool (ORSAT), which comprises drag and heating models for free molecular, transitional, and continuum flow regimes. These models have, in the past, only included solid, convex, blunt shapes (such as boxes, spheres, and cylinders). Previous work led by ODPO includes the extension of these models to hollow cylinders and square boxes in free molecular and transitional flow using the Direct Simulation Monte Carlo (DSMC) method. Since 2019, the ODPO has continued its program of DSMC simulations and extended the project to include analyses with the NASA Data Parallel Line Relaxation (DPLR) program on hollow cylinders and boxes (with varying wall thickness-diameter ratio). In fall 2022, the ODPO began a collaboration with the University of Texas San Antonio (UTSA) to use the Mach 7 Ludwieg Tube facility to validate the model built using numerical simulations. This facility can replicate (at a scale of approximately 100:1) the conditions seen by reentering objects near typical demise altitudes. We present here the drag and heating coefficients derived from the continued DSMC simulations, the new DPLR simulations, and the 26-test series at UTSA.

Chris Ostrom↗

Empirical models for spacecraft damage from orbital debris penetration and effects on spacecraft survivability

Semi-empirical models of hole diameter and tip-to-tip crack length for different multi-wall shielding systems currently under development for the International Space Station are presented. These equations were developed using light gas gun test data at impact velocities of 6.5 km/s and inhibited shaped charge test data for an impact velocity of 11.3 km/s. These models are incorporated into a survivability analysis using the manned spacecraft crew survivability computer code to determine whether or not module unzipping or crew incapacitation would occur under a specific set of impact conditions.

Williamsen, Joel↗

Survival after aortic valve replacement for severe aortic stenosis with low transvalvular gradients and severe left ventricular dysfunction

OBJECTIVE: We sought to assess whether aortic valve replacement (AVR) among patients with severe aortic stenosis (AS), severe left ventricular (LV) dysfunction and a low transvalvular gradient (TVG) is associated with improved survival. BACKGROUND: The optimal management of patients with severe AS with severe LV dysfunction and a low TVG remains controversial. METHODS: Between 1990 and 1998, we evaluated 68 patients who underwent AVR at our institution (AVR group) and 89 patients who did not undergo AVR (control group), with an aortic valve area < or = 0.75 cm(2), LV ejection fraction < or = 35% and mean gradient < or = 30 mm Hg. Using propensity analysis, survival was compared between a cohort of 39 patients in the AVR group and 56 patients in the control group. RESULTS: Despite well-matched baseline characteristics among propensity-matched patients, the one- and four-year survival rates were markedly improved in patients in the AVR group (82% and 78%), as compared with patients in the control group (41% and 15%; p < 0.0001). By multivariable analysis, the main predictor of improved survival was AVR (adjusted risk ratio 0.19, 95% confidence interval 0.09 to 0.39; p < 0.0001). The only other predictors of mortality were age and the serum creatinine level. CONCLUSIONS: Among select patients with severe AS, severe LV dysfunction and a low TVG, AVR was associated with significantly improved survival.

NASA Discipline Cardiopulmonary↗

Bioprocessing in space

Attachment to a substrate and survival of human embryonic kidney cells (HEK) was tested in an incubator installed in the flight-deck of the space shuttle Challenger. The HEK cells produce the enzyme urokinase and are candidates for electrophoretic separation. Attachment of the cells to a substrate is mandatory for survival. Analysis of the samples shows that cells adhere, spread and survive in 0 g conditions as well as the ground controls at 1 g.

Tschopp, A.↗

Improvements to NASA's Debris Assessment Software

NASA's Debris Assessment Software (DAS) has been substantially revised and expanded. DAS is designed to assist NASA programs in performing orbital debris assessments, as described in NASA s Guidelines and Assessment Procedures for Limiting Orbital Debris. The extensive upgrade of DAS was undertaken to reflect changes in the debris mitigation guidelines, to incorporate recommendations from DAS users, and to take advantage of recent software capabilities for greater user utility. DAS 2.0 includes an updated environment model and enhanced orbital propagators and reentry-survivability models. The ORDEM96 debris environment model has been replaced by ORDEM2000 in DAS 2.0, which is also designed to accept anticipated revisions to the environment definition. Numerous upgrades have also been applied to the assessment of human casualty potential due to reentering debris. Routines derived from the Object Reentry Survival Analysis Tool, Version 6 (ORSAT 6), determine which objects are assessed to survive reentry, and the resulting risk of human casualty is calculated directly based upon the orbital inclination and a future world population database. When evaluating reentry risks, the user may enter up to 200 unique hardware components for each launched object, in up to four nested levels. This last feature allows the software to more accurately model components that are exposed below the initial breakup altitude. The new DAS 2.0 provides an updated set of tools for users to assess their mission s compliance with the NASA Safety Standard and does so with a clear and easy-to-understand interface. The new native Microsoft Windows graphical user interface (GUI) is a vast improvement over the previous DOS-based interface. In the new version, functions are more-clearly laid out, and the GUI includes the standard Windows-style Help functions. The underlying routines within the DAS code are also improved.

Opiela, J.↗

Spacecraft Orbital Debris Reentry: Aerothermal Analysis

In the past 40 years, thousands of objects have been placed in Earth orbit and are being tracked. Space hardware reentry survivability must be evaluated to assess risks to human life and property on the ground. The objective of this paper is to present results of a study to determine altitude of demise (burn-up) or survivability of reentering objects. Two NASA/JSC computer codes - Object Reentry Survival Analysis Tool (ORSAT) and Miniature ORSAT (MORSAT) were used to determine trajectories, aerodynamic aerothermal environment, and thermal response of selected spacecraft components. The methodology of the two codes is presented, along with results of a parametric study of reentering objects modeled as spheres and cylinders. Parameters varied included mass, diameter, wall thickness, ballistic coefficient, length, type of material, and mode of tumbling/spinning. Two fragments of a spent Delta second stage undergoing orbital decay, stainless steel cylindrical propellant tank and titanium pressurization sphere, were evaluated with ORSAT and found to survive entry, as did the actual objects. Also, orbital decay reentry predictions of the Japanese Advanced Earth Observing Satellite (ADEOS) aluminum and nickel box-type components and the Russian COSMOS 954 satellite beryllium cylinders were made with MORSAT. These objects were also shown to survive reentry.

Rochelle, Wm. C.↗

Comparison of ORSAT and SCARAB Reentry Analysis Tools for a Generic Satellite Test Case

Reentry analysis is essential to understanding the consequences of the full life cycle of a spacecraft. Since reentry is a key factor in spacecraft development, NASA and ESA have separately developed tools to assess the survivability of objects during reentry. Criteria such as debris casualty area and impact energy are particularly important to understanding the risks posed to people on Earth. Therefore, NASA and ESA have undertaken a series of comparison studies of their respective reentry codes for verification and improvements in accuracy. The NASA Object Reentry Survival Analysis Tool (ORSAT) and the ESA Spacecraft Atmospheric Reentry and Aerothermal Breakup (SCARAB) reentry analysis tools serve as standard codes for reentry survivability assessment of satellites. These programs predict whether an object will demise during reentry and calculate the debris casualty area of objects determined to survive, establishing the reentry risk posed to the Earth's population by surviving debris. A series of test cases have been studied for comparison and the most recent uses "Testsat," a conceptual satellite composed of generic parts, defined to use numerous simple shapes and various materials for a better comparison of the predictions of these two codes. This study is an improvement on the others in this series because of increased consistency in modeling techniques and variables. The overall comparison demonstrated that the two codes arrive at similar results. Either most objects modeled resulted in close agreement between the two codes, or if the difference was significant, the variance could be explained as a case of semantics in the model definitions. This paper presents the main results of ORSAT and SCARAB for the Testsat case and discusses the sources of any discovered differences. Discussion of the results of previous comparisons is made for a summary of differences between the codes and lessons learned from this series of tests.

Kelley, Robert L.↗

Statistical analysis of astronomical data containing upper bounds - General methods and examples drawn from X-ray astronomy

Statistical procedures taken from the field of survival analysis have been adapted to astronomical usage and have been applied to a sample of stars in the B-V color range between 0.1 and 0.5 with measured soft X-ray luminosities and projected equatorial velocities. The two-sample problem and linear regression problem with arbitrarily censored data were studied. A new method for determining the linear regression between two random variables in the presence of arbitrary censoring has been developed which can also be used for a likelihood-ratio test for the independence of two random variables and for principal-component analysis in the presence of arbitrary censoring. The required numerical computations can be carried out straightforwardly and rapidly.

Schmitt, J. H. M. M.↗

Centrifugation of Cultured Osteoblasts And Macrophages as a Model To Study How Gravity Regulates The Function of Skeletal Cells

Mechanical loading helps define the architecture of weight-bearing bone via the tightly regulated process of skeletal turnover. Turnover occurs by the concerted activity of osteoblasts, responsible for bone formation. and osteoclasts, responsible for bone resorption. Osteoclasts are specialized megakaryon macrophages, which differentiate from monocytes in response to resorption stimuli, such as reduced weight-bearing. Habitation in space dramatically alters musculoskeletal loading, which modulates both cell function and bone structure. Our long-term objective is to define the molecular and cellular mechanisms that mediate skeletal adaptations to altered gravity environments. Our experimental approach is to apply hypergravity loads by centrifugation to rodents and cultured cells. As a first step, we examined the influence of centrifugation on the structure of cancellous bone in rats to test the ability of hypergravity to change skeletal architecture. Since cancellous bone undergoes rapid turnover we expected the most dramatic structural changes to occur in the shape of trabeculae of weight-bearing, cancellous bone. To define the cellular responses to hypergravity loads, we exposed cultured osteoblasts and macrophages to centrifugation. The intraosseous and intramedullary pressures within long bones in vivo reportedly range from 12-40 mm Hg, which would correspond to 18-59 gravity (g) in our cultures. We assumed that hydrostatic pressure from the medium above the cell layer is at least one major component of the mechanical load generated by centrifuging cultured cells. and therefore we exposed the cells to 10-50g. In osteoblasts, we examined the structure of their actin and microtubule networks, production of prostaglandin E2 (PGE2), and cell survival. Analysis of the shape of the cytoskeletal networks provides evidence for the ability of centrifugation to affect cell structure, while the production of PGE2 serves as a convenient marker for mechanical stimulation. We examined cell survival, reasoning that osteoblasts might mold skeletal structure in a hypergravity environment in part by regulating apoptosis and thus the duration of osteoblast productivity. Finally, we tested the influence of centrifugation on microbial activation of a macrophage cell line (RAW264.7). In response to the appropriate hormonal stimulation, this cell line is reportedly capable of undergoing differentiation to express osteoclast markers. In addition, a component of the cell wall of gram-negative bacteria, lipopolysaccaride (LPS), stimulates the formation of osteoclasts in vivo. Thus we tested the influence on centrifugation on RAW264.7 cells stimulated with LPS to provide an index of the function of osteoclast precursors.

Globus, Ruth K.↗

T wave alternans as a predictor of recurrent ventricular tachyarrhythmias in ICD recipients: prospective comparison with conventional risk markers

INTRODUCTION: The current standard for arrhythmic risk stratification is electrophysiologic (EP) testing, which, due to its invasive nature, is limited to patients already known to be at high risk. A number of noninvasive tests, such as determination of left ventricular ejection fraction (LVEF) or heart rate variability, have been evaluated as additional risk stratifiers. Microvolt T wave alternans (TWA) is a promising new risk marker. Prospective evaluation of noninvasive risk markers in low- or moderate-risk populations requires studies involving very large numbers of patients, and in such studies, documentation of the occurrence of ventricular tachyarrhythmias is difficult. In the present study, we identified a high-risk population, recipients of an implantable cardioverter defibrillator (ICD), and prospectively compared microvolt TWA with invasive EP testing and other risk markers with respect to their ability to predict recurrence of ventricular tachyarrhythmias as documented by ICD electrograms. METHODS AND RESULTS: Ninety-five patients with a history of ventricular tachyarrhythmias undergoing implantation of an ICD underwent EP testing, assessment of TWA, as well as determination of LVEF, baroreflex sensitivity, signal-averaged ECG, analysis of 24-hour Holter monitoring, and QT dispersion from the 12-lead surface ECG. The endpoint of the study was first appropriate ICD therapy for electrogram-documented ventricular fibrillation or tachycardia during follow-up. Kaplan-Meier survival analysis revealed that TWA (P < 0.006) and LVEF (P < 0.04) were the only significant univariate risk stratifiers. EP testing was not statistically significant (P < 0.2). Multivariate Cox regression analysis revealed that TWA was the only statistically significant independent risk factor. CONCLUSIONS: Measurement of microvolt TWA compared favorably with both invasive EP testing and other currently used noninvasive risk assessment methods in predicting recurrence of ventricular tachyarrhythmias in ICD recipients. This study suggests that TWA might also be a powerful tool for risk stratification in low- or moderate-risk patients, and needs to be prospectively evaluated in such populations.

Non-NASA Center↗

Assessing the Effect of Spaceflight on the Propensity for Astronauts to Develop Disk Herniation

BACKGROUND: A previous study [1] reported that the instantaneous risk of developing a Herniated Nucleus Pulposus (HNP) was higher in astronauts who had flown at least one mission, as compared with those in the corps who had not yet flown. However, the study only analyzed time to HNP after the first mission (if any) and did not account for the possible effects of multiple missions. While many HNP's occurred well into astronauts' careers or in some cases years after retirement, the higher incidence of HNPs relatively soon after completion of space missions appears to indicate that spaceflight may lead to an increased risk of HNP. The purpose of this study was to support the Human System Risk Board assessment of back pain, evaluate the risk of injury due to dynamic loads, and update the previous dataset which contained events up to December 31, 2006. METHODS: Data was queried from the electronic medical record and provided by the Lifetime Surveillance of Astronaut Health. The data included all 330 United States astronauts from 1959 through February 2014. Cases were confirmed by Magnetic Resonance Imaging, Computerized Tomography, Myelography, operative findings, or through clinical confirmation with a neurologist or neurosurgeon. In this analysis, astronauts who had an HNP at selection into the corps or had an HNP diagnosis prior to their first flight were excluded. The statistical challenges in using the available data to separate effects of spaceflight from those associated with general astronaut training and lifestyle on propensity to develop HNPs are many. The primary outcome is reported date of first HNP (if any), which at best is only an approximation to the actual time of occurrence. To properly analyze this data with a survival analysis model, one must also know the "exposure" time - i.e. how long each astronaut has been at risk for developing an HNP. If an HNP is reported soon after a mission, is it mission caused or general? If the former, exposure time should be counted from the time of landing (assuming the risk of HNP occurring during a mission is zero). If the latter, exposure time should be counted from the time of selection; however we can't directly know which one to use. In our analysis we take both of these possibilities into account with a competing risks model, wherein two distinct stochastic processes are going on: TG = time to HNP (general) and TS = time to HNP (spaceflight). Under this type of model, whichever of these occurs first is what we observe; in other words we don't observe TG or TS, only min(TG, TS). Here, we parameterized the model in terms of separate Weibull hazard functions for each process and estimated all parameters using maximum likelihood. In addition, we allowed for a "cured fraction" - i.e. the possibility that some astronauts may never develop an HNP. RESULTS: Results will include a depiction of the competing hazard functions as well as a probability curve for the relative likelihood that an HNP reported at a given time after a mission is actually mission caused. Other factors, such as dwell time in microgravity and vehicle landing environment will be explored. An overall assessment as to whether spaceflight truly exacerbates HNP risk will be made.

Feiveson, A. H.↗

Analysis of the Einstein sample of early-type galaxies

The EINSTEIN galaxy catalog contains x-ray data for 148 early-type (E and SO) galaxies. A detailed analysis of the global properties of this sample are studied. By comparing the x-ray properties with other tracers of the ISM, as well as with observables related to the stellar dynamics and populations of the sample, we expect to determine more clearly the physical relationships that determine the evolution of early-type galaxies. Previous studies with smaller samples have explored the relationships between x-ray luminosity (L(sub x)) and luminosities in other bands. Using our larger sample and the statistical techniques of survival analysis, a number of these earlier analyses were repeated. For our full sample, a strong statistical correlation is found between L(sub X) and L(sub B) (the probability that the null hypothesis is upheld is P less than 10(exp -4) from a variety of rank correlation tests. Regressions with several algorithms yield consistent results.

Eskridge, Paul B.↗

Advanced statistical methods for improved data analysis of NASA astrophysics missions

The investigators under this grant studied ways to improve the statistical analysis of astronomical data. They looked at existing techniques, the development of new techniques, and the production and distribution of specialized software to the astronomical community. Abstracts of nine papers that were produced are included, as well as brief descriptions of four software packages. The articles that are abstracted discuss analytical and Monte Carlo comparisons of six different linear least squares fits, a (second) paper on linear regression in astronomy, two reviews of public domain software for the astronomer, subsample and half-sample methods for estimating sampling distributions, a nonparametric estimation of survival functions under dependent competing risks, censoring in astronomical data due to nondetections, an astronomy survival analysis computer package called ASURV, and improving the statistical methodology of astronomical data analysis.

Feigelson, Eric D.↗

Gateway Program Safety and Mission Assurance Integration - the Future of Safe Deep Space Human Exploration

As a foundational element of the National Aeronautics and Space Administration (NASA) Artemis Campaign, the Gateway is an incrementally built cislunar spacecraft that will serve as a platform for deep space human exploration, science, and technology demonstration. The Gateway will be a unifying catalyst for international partners around the world to establish sustained deep space scientific investigations, lunar surface access, and missions to Mars. As human exploration moves farther away from Earth, spacecraft designs must prioritize and optimize mass and volume allocations, while minimizing human and spacecraft risk. To accomplish this objective, the Gateway Program Safety and Mission Assurance functions develop, implement, and ensure compliance with requirements, in concert with the accurate characterization and transparent communication of residual hazard risks, for integrated safety, reliability and maintainability and quality assurance. Safety and Mission Assurance was a key contributor during Gateway program pre-formulation and formulation activities where safety and reliability analysis was embedded in the Gateway Systems Engineering and Integration team. During these early program stages, a preliminary Gateway Integrated Hazard Analysis and Preliminary Gateway Probabilistic Risk Assessment assisted in Gateway architectural and operational definition as part of a risk-informed design process. As the deep space architecture has matured, the integrated Safety and Mission Assurance analyses have matured, new safety review processes have been developed, and requirements have been refined to ensure compliance with integrated safety and mission assurance objectives. The Gateway Program is currently concluding the preliminary design review informed milestone, where the primary objectives included: - Ensured completeness and consistency of the preliminary design, including the meeting of all requirements within appropriate margins and acceptable risk posture. - Identification of any major issues moving forward to the Critical Design phase. At this milestone, Safety and Mission Assurance provided numerous products, including Gateway Top Risks and Risk Mitigation Plans, updated integrated hazard analyses, updated probabilistic risk assessment, Crew Survival Analysis Report, and updated Safety and Mission Assurance Requirements and Plans. These products provide a many-faceted perspective on the inherent risk and available mitigations involved in flying the current proposed vehicle design and anticipated stack configurations. In addition, Safety and Mission Assurance identified top technical, process and workforce concerns to be addressed as the program progresses toward the critical design phase. This paper will detail the evolution of the Gateway Program Safety and Mission Assurance integration functions, provide its current status and lessons learned for future human spaceflight programs. Throughout this paper the key tenets of the Gateway Program Safety and Mission Assurance will be discussed: - Application of a risk-informed approach to identify and mitigate areas of highest risk. - Leverage of valuable processes and lessons learned from earlier spaceflight programs. - Development of Safety and Mission Assurance products to inform design risk trades. - Utilization of common Safety and Mission Assurance practices to identify safety risks for multiple perspectives: top-down, bottom-up, and across lines of integration. - Approval of safety hazards at the appropriate level of authority, keeping most deliberation closest to design expertise and elevating risks of greatest concern for program-level consideration. - Championing of Safety and Mission Assurance processes and forums to foster a pervasive safety culture that is transparent, inclusive, and collaborative between all partners. These tenets have allowed the Gateway Safety and Mission Assurance function to play a key role in optimized vehicle design evolution, and early identification and mitigation of Gateway program and Artemis mission risk.

Helen Vaccaro↗

Demisability of GFRP and CFRP Components of Reentering Orbital Debris: Phase I Test Results

Observations of surviving reentry debris on the ground and research performed by Hyperschall Technologie Göttingen (HTG) [1] indicated that significantly more glass fiber-reinforced polymer (GFRP) and carbon fiber-reinforced polymer (CFRP) components survive reentry than current models predict. NASA’s Orbital Debris Program Office conducted a series of tests to evaluate the accuracy of material demise models for reentering orbital debris used in NASA’s Object Reentry Survival Analysis Tool (ORSAT) and Debris Assessment Software (DAS). Testing is planned in a multi-phase series to allow for quick quantification of results as well as refinement of methods resulting from lessons learned during early phases. The Phase 1 tests discussed here validated ORSAT models for homogeneous metals, provided an efficient quantification of composite material demisability properties like mass loss rate and overall time to demise, and identified potential failure modes, which are currently not well understood. Phase 2 tests will be used to further understand mass loss rates and modes of both thermal and mechanical failure in composite materials. The authors exposed 95 samples of aluminum, CFRP, Kevlar fiber-reinforced polymer, GFRP, and sheets of G10 fiberglass to conditions approximating the reentry environment using an inductively coupled plasma (ICP) torch facility. The cylindrical CFRP samples were exposed to the atmospheric pressure plasma, at both the end and the midpoint, to investigate the difference in demisability between parts with exposed edges, like panels, and parts with no edges, such as carbonoverwrapped pressure vessels (COPVs). In a non-oxidative environment, no composite materials demised within the 5-minute test time. In the oxidative, elevated heat flux environment, CFRP samples demised between 210 s and 270 s. For the first 100 s of insertion time, most of the mass loss was due to pyrolysis of resin, creating an approximately bi-linear mass-loss rate curve with time. In a non-oxidative environment, carbon filaments were observed to unravel from some of the CFRP end-burned samples; however, this effect did not seem to affect the overall time to demise for the samples significantly. These results indicate that both GFRP and CFRP components survive reentry with significantly more remaining mass than current models predict.

Greene, Benton R.↗

Continuum radiation from active galactic nuclei: A statistical study

The physics of the continuum spectrum of active galactic nuclei (AGNs) was examined using a large data set and rigorous statistical methods. A data base was constructed for 469 objects which include radio selected quasars, optically selected quasars, X-ray selected AGNs, BL Lac objects, and optically unidentified compact radio sources. Each object has measurements of its radio, optical, X-ray core continuum luminosity, though many of them are upper limits. Since many radio sources have extended components, the core component were carefully selected out from the total radio luminosity. With survival analysis statistical methods, which can treat upper limits correctly, these data can yield better statistical results than those previously obtained. A variety of statistical tests are performed, such as the comparison of the luminosity functions in different subsamples, and linear regressions of luminosities in different bands. Interpretation of the results leads to the following tentative conclusions: the main emission mechanism of optically selected quasars and X-ray selected AGNs is thermal, while that of BL Lac objects is synchrotron; radio selected quasars may have two different emission mechanisms in the X-ray band; BL Lac objects appear to be special cases of the radio selected quasars; some compact radio sources show the possibility of synchrotron self-Compton (SSC) in the optical band; and the spectral index between the optical and the X-ray bands depends on the optical luminosity.

Isobe, T.↗

Two component model for X-ray emission of radio selected QSO's

Using a large database of radio, optical, and x ray luminosities of AGNs with survival analysis, it was found that the x ray emission of the radio selected quasars has two components. One is related to the optical luminosity and the other is related to the radio luminosity.

Isobe, T.↗