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All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Scattering in the atmosphere of Venus. I - Line profiles and curves of growth for isotropic scattering

Line profiles and curves of growth were computed for both reflected and transmitted radiation for typical lines in CO2 bands (in the photographic infrared) which occur in the spectrum of Venus. In the model, the pressure variation with altitude was considered, and the base of the cloud deck was set at the 2 bar level. The temperature was held constant at 250 K, and a Voigt profile was used for the line shape. It was also assumed that the scale height of the cloud particles was equal to the scale height of the gas. The calculations were made for four values of the scattering optical thickness (0.1, 1.0, and 100) using a continuum single-scattering albedo of 0.9975 (which gives a Bond albedo of 0.896 for a scattering optical thickness of 100, the value observed for Venus at these wavelengths). Curves of growth are also presented for reflected radiation which has been averaged over the visible disk for three values of the Venus phase angle (0, 86, and 166 deg).

Young, L. D. G.↗
NASA NTRS1980

A probabilistic approach to radiative energy loss calculations for optically thick atmospheres - Hydrogen lines and continua

An approximate probabilistic radiative transfer equation and the statistical equilibrium equations are simultaneously solved for a model hydrogen atom consisting of three bound levels and ionization continuum. The transfer equation for L-alpha, L-beta, H-alpha, and the Lyman continuum is explicitly solved assuming complete redistribution. The accuracy of this approach is tested by comparing source functions and radiative loss rates to values obtained with a method that solves the exact transfer equation. Two recent model solar-flare chromospheres are used for this test. It is shown that for the test atmospheres the probabilistic method gives values of the radiative loss rate that are characteristically good to a factor of 2. The advantage of this probabilistic approach is that it retains a description of the dominant physical processes of radiative transfer in the complete redistribution case, yet it achieves a major reduction in computational requirements.

Canfield, R. C.↗
NASA NTRS2000

Solar UV Radiation and the Origin of Life on Earth

We have started a comprehensive, interdisciplinary study of the influence of solar ultraviolet radiation on the atmosphere of of the early Earth. We plan to model the chemistry of the Earth atmosphere during its evolution, using observed UV flux distributions of early solar analogs as boundary conditions in photochemical models of the Earth's atmosphere. The study has four distinct but interlinked parts: (1) Establishing the radiation of the early Sun; (2) Determining the photochemistry of the early Earth's atmosphere; (3) Estimating the rates of H2 loss from the atmosphere; and (4) Ascertaining how sensitive is the photochemistry to the metallicity of the Sun. We are currently using STIS and EUVE to obtain high-quality far-UV and extreme-UV observations of three early-solar analogs. We will perform a detailed non-LTE study of each stars, and construct theoretical model photosphere, and an empirical model chromospheres, which can be used to extrapolate the continuum to the Lyman continuum region. Given a realistic flux distribution of the early Sun, we will perform photochemical modeling of weakly reducing primitive atmospheres to determine the lifetime and photochemistry of CH4. In particular, we will make estimates of the amount of CH4 present in the prebiotic atmosphere, and estimate the atmospheric CH4 concentration during the Late Archean (2.5-3.0 b.y. ago) and determine whether it would have been sufficiently abundant to help offset reduced solar luminosity at that time. Having obtained a photochemical model, we will solve for the concentrations of greenhouse gasses and important pre-biotic molecules, and perform a detailed radiative transfer calculations to compute the UV flux reaching the surface.

Heap, Sara R.↗
NASA NTRS2009

A Finite Element Theory for Predicting the Attenuation of Extended-Reacting Liners

A non-modal finite element theory for predicting the attenuation of an extended-reacting liner containing a porous facesheet and located in a no-flow duct is presented. The mathematical approach is to solve separate wave equations in the liner and duct airway and to couple these two solutions by invoking kinematic constraints at the facesheet that are consistent with a continuum theory of fluid motion. Given the liner intrinsic properties, a weak Galerkin finite element formulation with cubic polynomial basis functions is used as the basis for generating a discrete system of acoustic equations that are solved to obtain the coupled acoustic field. A state-of-the-art, asymmetric, parallel, sparse equation solver is implemented that allows tens of thousands of grid points to be analyzed. A grid refinement study is presented to show that the predicted attenuation converges. Excellent comparison of the numerically predicted attenuation to that of a mode theory (using a Haynes 25 metal foam liner) is used to validate the computational approach. Simulations are also presented for fifteen porous plate, extended-reacting liners. The construction of some of the porous plate liners suggest that they should behave as resonant liners while the construction of others suggest that they should behave as broadband attenuators. In each case the finite element theory is observed to predict the proper attenuation trend.

Watson, W. R.↗
NASA NTRS1973

Calculation of total electron excitation cross-sections and partial electron ionization cross-sections for the elements

Computer programs were used to calculate the total electron excitation cross-section for atoms and the partial ionization cross-section. The approximations to the scattering amplitude used are as follows: (1) Born, Bethe, and Modified Bethe for non-exchange excitation; (2) Ochkur for exchange excitation; and (3) Coulomb-Born of non-exchange ionization. The amplitudes are related to the differential cross-sections which are integrated to give the total excitation (or partial ionization) cross-section for the collision. The atomic wave functions used are Hartree-Fock-Slater functions for bound states and the coulomb wave function for the continuum. The programs are presented and the results are examined.

Green, T. J.↗
NASA NTRS2014

Hypersonic Separated Flows About "Tick" Configurations With Sensitivity to Model Design

This paper presents computational results obtained by applying the direct simulation Monte Carlo (DSMC) method for hypersonic nonequilibrium flow about "tick-shaped" model configurations. These test models produces a complex flow where the nonequilibrium and rarefied aspects of the flow are initially enhanced as the flow passes over an expansion surface, and then the flow encounters a compression surface that can induce flow separation. The resulting flow is such that meaningful numerical simulations must have the capability to account for a significant range of rarefaction effects; hence the application of the DSMC method in the current study as the flow spans several flow regimes, including transitional, slip, and continuum. The current focus is to examine the sensitivity of both the model surface response (heating, friction and pressure) and flowfield structure to assumptions regarding surface boundary conditions and more extensively the impact of model design as influenced by leading edge configuration as well as the geometrical features of the expansion and compression surfaces. Numerical results indicate a strong sensitivity to both the extent of the leading edge sharpness and the magnitude of the leading edge bevel angle. Also, the length of the expansion surface for a fixed compression surface has a significant impact on the extent of separated flow.

Moss, J. N.↗
NASA NTRS2015

Computational Modeling and Experimental Characterization of Martensitic Transformations in Nicoal for Self-Sensing Materials

Fundamental changes to aero-vehicle management require the utilization of automated health monitoring of vehicle structural components. A novel method is the use of self-sensing materials, which contain embedded sensory particles (SP). SPs are micron-sized pieces of shape-memory alloy that undergo transformation when the local strain reaches a prescribed threshold. The transformation is a result of a spontaneous rearrangement of the atoms in the crystal lattice under intensified stress near damaged locations, generating acoustic waves of a specific spectrum that can be detected by a suitably placed sensor. The sensitivity of the method depends on the strength of the emitted signal and its propagation through the material. To study the transition behavior of the sensory particle inside a metal matrix under load, a simulation approach based on a coupled atomistic-continuum model is used. The simulation results indicate a strong dependence of the particle's pseudoelastic response on its crystallographic orientation with respect to the loading direction and suggest possible ways of optimizing particle sensitivity. The technology of embedded sensory particles will serve as the key element in an autonomous structural health monitoring system that will constantly monitor for damage initiation in service, which will enable quick detection of unforeseen damage initiation in real-time and during onground inspections.

Wallace, T. A.↗
NASA NTRS1991

Eigenvalue sensitivity analysis of planar frames with variable joint and support locations

Two sensitivity equations are derived in this study based upon the continuum approach for eigenvalue sensitivity analysis of planar frame structures with variable joint and support locations. A variational form of an eigenvalue equation is first derived in which all of the quantities are expressed in the local coordinate system attached to each member. Material derivative of this variational equation is then sought to account for changes in member's length and orientation resulting form the perturbation of joint and support locations. Finally, eigenvalue sensitivity equations are formulated in either domain quantities (by the domain method) or boundary quantities (by the boundary method). It is concluded that the sensitivity equation derived by the boundary method is more efficient in computation but less accurate than that of the domain method. Nevertheless, both of them in terms of computational efficiency are superior to the conventional direct differentiation method and the finite difference method.

Chuang, Ching H.↗
NASA NTRSDate not supplied

Trajectory Engineering with Modular Patched Conics for Entry Systems and TPS (TEMPEST)

Brief Presenter Biography (35 word limit): Bohdan Wesely is an Aerospace Engineer in the Entry Systems and Technology Division at Ames. He has worked on a variety of projects for NASA including integrated TPS (thermal protection system) flight hardware deliveries and testing services for commercial partners. Introduction: TEMPEST is a new trajectory analysis framework that is designed to fill the gap between dedicated flight mechanics tools and aerothermal and TPS sizing tools. The project started as an SJSU master’s thesis and has since evolved into a general conceptual design tool capable of studying a wide variety of entry problems. Development is ongoing in the Entry Systems and Technology Division at NASA ARC. Why TEMPEST: Space missions involving entry into a planetary atmosphere involve a series of unique requirements across multiple disciplines. Whether it is traditional entry descent and landing (EDL), or aerocapture, the vehicle must navigate to its target landing location or orbit state, and the TPS must protect the payload during entry. The design process typically involves iterative handoffs between various flight mechanics, flow solver, and material response level tools. During the early conceptual phase, a wide variety of feasible trajectories are simulated in a Monte Carlo scenario which broadly satisfy the mission or landing requirements. Next, computational fluid dynamics (CFD), direct simulation Monte Carlo (DSMC), and other flow solver analyses are performed at various key trajectory points to generate an aero-database, heating and TPS design requirements also emerge at this stage. At this point, with updated aerodynamics from the various flow solvers, trajectories can be re-run, this in turn can change the required freestream conditions for the CFD tools, and as a project progresses, these analyses converge, and uncertainty is reduced. However, there is always a “hand-off” occurring between two inherently coupled phenomena. Analysis Description: One of the goals with TEMPEST is to use a variety of first principles estimation methods coupled with an atmosphere model to predict vehicle aerothermodynamics across the entire flight regime while propagating a 3 or 6 degree of freedom (DoF) trajectory. Aerodynamics methods include modified Newtonian, Maxwell and Cercignani- Lampis-Lord (CLL) for continuum, transitional, and free molecular flow regimes. Aerothermodynamics include boundary layer and reference enthalpy methods, and Mutation++ for non-equilibrium chemistry modeling. TEMPEST is also capable of stitching multiple trajectory segments together to study mission scenarios like multi-pass aerocapture and aero-gravity assists. Most of the program is implemented in MATLAB using modern system objects, it relies on several C++ shared libraries for supporting tools like Gmsh, the Global Reference Atmospheric Model (GRAM), and Mutation++. The various first principles aerothermal estimation methods are discretized across either a structured axisymmetric panel mesh or an unstructured tri-mesh generated from an open-source tool such as Gmsh, this allows solutions on the same mesh to be compared across tools such as CB-Aero. CFD Coupling. A physics-aware, gaussian process CFD anchoring scheme is proposed to adjust the various first principles methods as a CFD database is populated. One goal for this anchoring module is to inform the project where CFD should be run. Full knowledge of the entire trajectory, atmosphere, and aerothermodynamics allows for easier identification of high sensitivity areas and uncertainty quantification. While the first principles effects are well known and proven accurate in existing tools such as CB- Aero and Cart3D, a physics aware CFD anchoring scheme increases tool credibility across a project lifecycle. Material Response Modeling. Correct TPS sizing is critical for optimizing mass for science payloads and ensuring mission success. The process typically involves a thermal analysis along the trajectory with surface heating environments as a boundary condition. Several design constraints are maximum bondline temperature and maximum recession with various margining techniques. The material response tool FIAT, developed out of NASA Ames, is currently being integrated into the TEMPEST environment. TPS recession, shape change, mass loss, and mass property alteration are all factors that can perturb an entry trajectory. For missions like Mars 2020, recession was minimal and was safely handled separately as a post process. For missions such as Jupiter Galileo with a high TPS mass fraction or asteroid entries, recession plays a major role. The proposed fully coupled scheme is to use an epoch-based approach where the trajectory integration is halted after a recession threshold, the energy balance and FIAT are solved at each panel, the mesh, aerodynamics, and mass properties are updated, and the trajectory continues. Several computational tradeoffs have been made during the development of TEMPEST to limit the cost of a single trajectory and preserve its utility as a conceptual, rapid iteration tool. Conclusion: Development of TEMPEST is ongoing and the project is still in its infancy. This talk aims to showcase its unique capabilities to support future NASA entry systems missions.

Bohdan O Wesely↗
NASA NTRSDate not supplied

Sensitivity of Single-Scattering Properties to Precipitation Particle Meltwater Geometry for GPM Passive Microwave and Radar Remote Sensing Applications

The objective of the current work is to describe the microwave single-scattering properties of partially melted ice-phase precipitation particles using physically-based computational methods, taking into full account the varied geometries of the initially “dry” ice particles and the distributions of liquid water that develop during the melting process. Ultimately, the bulk properties of ensembles of these partially-melted particles will be included in “scattering tables” to support radar and combined radar-radiometer remote sensing of precipitation. A meshless Lagrangian melting procedure (snowMELT) based on smoothed-particle hydrodynamics is applied to both spherical and finely-structured ice particle models to describe the full evolution of the particles from dry ice particles to liquid drops. The melting of spherical ice particles using snowMELT is compared to an alternative continuum physics model to validate melt times and internal thermodynamics. The discrete dipole approximation is then utilized to calculate the single-scattering properties of different mixed-phase particles throughout the melting process. The sensitivities of particle single-scattering properties to thermodynamic and hydrodynamic assumptions in snowMELT are explored, and the implications for combined radar-radiometer precipitation remote sensing from GPM are discussed.

William S Olson↗
NASA NTRSDate not supplied

Biological Data for Deep Space Mission Support

Increased biomedical risks and challenges associated with deep space missions (cis-Lunar, Mars transit, Mars surface) require new knowledge discovery and development of novel ecosystem and biomedical support capabilities. This paradigm shift supporting distant and long-duration missions requires biological data to be findable, accessible, interoperable, reusable (FAIR), and maximally open-access (i.e., there is a data governance continuum from closed to mediated to embargoed to open). The NASA “Open Science Data Repositories” (OSDR) aims to meet scientific, technical, and operational spaceflight needs, and offers the ability to upload, download, search, share, analyze, and visualize data across physiological, behavioral, ‘omics, and environmental monitoring telemetry datasets. OSDR includes NASA GeneLab, NASA Ames Life Sciences Data Archive (ALSDA), and NASA Biological Institutional Scientific Collection (NBISC). In the past year, ALSDA has undergone a transformation in its data collection, curation, and architecture methods. Standardizing non-genomic (phenotypic) datasets was, and will continue to be, a challenge because of their diverse nature (e.g., molecular, cellular, tissue, whole organism behavior; micro-computed tomography, intraocular pressure, fluorescence microscopy, western blot, ultrasonography; tabular, images, video). This year ALSDA, alongside GeneLab, introduced the Biological Data Management Environment (BDME) with the purpose to accept submission of data from space relevant experiments including spaceflight, radiation, simulated gravity, gravitropism, isolation and confinement, hostile closed environments and/or distance from Earth. In addition to bringing together omics, phenotypic, physiological, bioimaging, and behavioral data into one repository. By integrating with GeneLab a multi-project submission portal aims to reduce the burden on PIs submitting data and enabling the discovery of both omics and phenotypic data. The purpose of ALSDA is to collect, curate, and make all non-human space-relevant biological data maximally findable, accessible, interoperable, and reusable (FAIR). These scope of ALSDA data collected and submitted by PIs include study design metadata, subject metadata, assay metadata (parameters), raw and processed assay data, assay imagery/video, and subject-experienced mission data telemetry (radiation, temperature, humidity, acoustics, vibrations, etc.). In 2021, a community of researchers rallied to form the ALSDA Analysis Working Group (AWG) and provided scientific consensus on dataset sample and assay metadata. The community and excitement around the ALSDA/OSDR system has already led to several data reuse studies, demonstrating value using machine learning (ML), knowledge graphs, and meta-analysis approaches.

space biology↗
NASA NTRSDate not supplied

Biological Data for Deep Space Mission Support

Increased biomedical risks and challenges associated with deep space missions (cis-Lunar, Mars transit, Mars surface) require new knowledge discovery and development of novel ecosystem and biomedical support capabilities. This paradigm shift supporting distant and long-duration missions requires biological data to be findable, accessible, interoperable, reusable (FAIR), and maximally open-access (i.e., there is a data governance continuum from closed to mediated to embargoed to open). The NASA “Open Science Data Repositories” (OSDR) aims to meet scientific, technical, and operational spaceflight needs, and offers the ability to upload, download, search, share, analyze, and visualize data across physiological, behavioral, ‘omics, and environmental monitoring telemetry datasets. OSDR includes NASA GeneLab, NASA Ames Life Sciences Data Archive (ALSDA), and NASA Biological Institutional Scientific Collection (NBISC). In the past year, ALSDA has undergone a transformation in its data collection, curation, and architecture methods. Standardizing non-genomic (phenotypic) datasets was, and will continue to be, a challenge because of their diverse nature (e.g., molecular, cellular, tissue, whole organism, behavior; micro-computed tomography, intraocular pressure, fluorescence microscopy, western blot, ultrasonography; tabular, images, video). This year ALSDA, alongside GeneLab, introduced the Biological Data Management Environment (BDME) with the purpose to accept submission of data from space relevant experiments including spaceflight, radiation, simulated gravity, gravitropism, isolation and confinement, hostile closed environments and/or distance from Earth. In addition to bringing together omics, phenotypic, physiological, bioimaging, and behavioral data into one repository. By integrating with GeneLab a multi-project submission portal aims to reduce the burden on PIs submitting data and enabling the discovery of both omics and phenotypic data. The purpose of ALSDA is to collect, curate, and make all non-human space-relevant biological data maximally findable, accessible, interoperable, and reusable (FAIR). These scope of ALSDA data collected and submitted by PIs include study design metadata, subject metadata, assay metadata (parameters), raw and processed assay data, assay imagery/video, and subject-experienced mission data telemetry (radiation, temperature, humidity, acoustics, vibrations, etc.). In 2021, a community of researchers rallied to form the ALSDA Analysis Working Group (AWG) and provided scientific consensus on dataset sample and assay metadata. The community and excitement around the ALSDA/OSDR system has already led to several data reuse studies, demonstrating value using machine learning (ML), knowledge graphs, and meta-analysis approaches.

space biology↗
NASA NTRS2008

Uncertainty Analysis of Air Radiation for Lunar Return Shock Layers

By leveraging a new uncertainty markup technique, two risk analysis methods are used to compute the uncertainty of lunar-return shock layer radiation predicted by the High temperature Aerothermodynamic Radiation Algorithm (HARA). The effects of epistemic uncertainty, or uncertainty due to a lack of knowledge, is considered for the following modeling parameters: atomic line oscillator strengths, atomic line Stark broadening widths, atomic photoionization cross sections, negative ion photodetachment cross sections, molecular bands oscillator strengths, and electron impact excitation rates. First, a simplified shock layer problem consisting of two constant-property equilibrium layers is considered. The results of this simplified problem show that the atomic nitrogen oscillator strengths and Stark broadening widths in both the vacuum ultraviolet and infrared spectral regions, along with the negative ion continuum, are the dominant uncertainty contributors. Next, three variable property stagnation-line shock layer cases are analyzed: a typical lunar return case and two Fire II cases. For the near-equilibrium lunar return and Fire 1643-second cases, the resulting uncertainties are very similar to the simplified case. Conversely, the relatively nonequilibrium 1636-second case shows significantly larger influence from electron impact excitation rates of both atoms and molecules. For all cases, the total uncertainty in radiative heat flux to the wall due to epistemic uncertainty in modeling parameters is 30% as opposed to the erroneously-small uncertainty levels (plus or minus 6%) found when treating model parameter uncertainties as aleatory (due to chance) instead of epistemic (due to lack of knowledge).

Kleb, Bil↗
NASA NTRS1986

On the origin of the infrared and X-ray continua of active galactic nuclei

The continuum spectra of radio-quiet active galactic nuclei, which are steeper in the near-IR and flatter in the X-ray regime, can be produced in a synchrotron self-Compton model with a broken power law electron distribution that is flat at low, and steep at large, Lorentz factor values. While the steeper part generates the IR spectrum via synchrotron process, both parts together produce the flatter X-ray spectrum via Compton scattering. The intersection of the two spectra corresponds to equipartition between the magnetic field and synchrotron photon energy densities, giving approximately the same luminosities in the synchrotron and Compton components. The photon spectra are self-consistently computed here, taking the effects of cooling, e(+)e(-) pair production, and higher order Compton scattering into account.

Zdziarski, A. A.↗
NASA NTRS1980

Application of finite-element-techniques to the interaction of conduction and radiation in an absorbing, scattering and emitting medium

In this paper, the authors demonstrate that a Galerkin finite element method of analysis, utilizing isoparametric elements, offers a viable means of solving continuum thermal radiation problems with conduction in a participating medium. The participating medium was considered to be a gray radiation medium exhibiting isotropic absorption, emission, and scattering characteristics and optical properties that are independent of temperature. The medium was considered to be bounded by infinite parallel opaque, gray surfaces with diffuse emission and reflection characteristics. In solving this problem, a finite element formulation was developed to describe a system in radiative equilibrium. Then the results of this first analysis were linked with a second finite element model which incorporated conduction into the analysis. The results of this study were found to be in good agreement with existing published data. The model offers the following advantageous features: geometric generality, a computational algorithm which is 'convenient' and 'computable', and a functional basis for extension of the radiation model to higher order approximation.

Wu, S. T.↗
NASA NTRS1997

A comparative modeling of supernova 1993J

The light curve of Supernova 1993J is calculated using two computational radiation transport approaches. The two approaches are represented by the computer codes STELLA and EDDINGTON. The emphasis is on the shock breakout and the photometry in the U, B and V bands during the first 120 days of the supernova. The STELLA model includes implicit hydrodynamics and is able to model early supernova evolution before the expansion is homologous. The STELLA model employs multi-group photonics and is able to follow the radiation as it decouples from the matter. The EDDINGTON code uses an algorithm for integrating the transport equation which assumes homologous expansion and uses a finer frequency resolution. The agreement between the two codes is considered to be satisfactory only in the case where compatible physical assumptions are made concerning the opacity. The assumptions are justified. The continuum spectrum for SN 1993J is predicted near the shock breakout to be superior to that predicted by standard single energy group hydrocodes. The uncertainties involved in current time dependent models of supernova light curves are discussed.

Blinnikov, Sergei↗
NASA NTRS2003

Kinematics and the implementation of an elephant's trunk manipulator and other continuum style robots

Traditionally, robot manipulators have been a simple arrangement of a small number of serially connected links and actuated joints. Though these manipulators prove to be very effective for many tasks, they are not without their limitations, due mainly to their lack of maneuverability or total degrees of freedom. Continuum style (i.e., continuous "back-bone") robots, on the other hand, exhibit a wide range of maneuverability, and can have a large number of degrees of freedom. The motion of continuum style robots is generated through the bending of the robot over a given section; unlike traditional robots where the motion occurs in discrete locations, i.e., joints. The motion of continuum manipulators is often compared to that of biological manipulators such as trunks and tentacles. These continuum style robots can achieve motions that could only be obtainable by a conventionally designed robot with many more degrees of freedom. In this paper we present a detailed formulation and explanation of a novel kinematic model for continuum style robots. The design, construction, and implementation of our continuum style robot called the elephant trunk manipulator is presented. Experimental results are then provided to verify the legitimacy of our model when applied to our physical manipulator. We also provide a set of obstacle avoidance experiments that help to exhibit the practical implementation of both our manipulator and our kinematic model. c2003 Wiley Periodicals, Inc.

Non-NASA Center↗
NASA NTRS1976

The Mg II h and k lines. II - Comparison with synthesized profiles and Ca II K

Measured high-dispersion center and limb profiles of the solar Mg II h and k resonance lines are compared with synthetic spectra computed with a partial-redistribution formalism and based on several upper-photosphere and lower-chromosphere temperature distributions. Profiles of the analogously formed Ca II K resonance line are also synthesized for the same atmospheric models. The spectrum-synthesis approach is outlined, and the collisional and fixed radiative rates appropriate to the adopted model atoms and solar atmosphere are discussed. It is found that the HSRA and VAL models predict systematically lower intensities in the h, k, and K inner wings than observed and that models with a somewhat higher minimum temperature (about 4450 K) can reproduce the measured inner wings and limb darkening. A 'Ca II' solar model with a minimum temperature of 4450 K is proposed as an alternative to the class of models based on continuum observations.

Ayres, T. R.↗