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NASA NTRS2004

Oceanic Tidal Mixing As a Contributor to Milankovitch-scale Climate Change

We propose that changes in the magnitude of oceanic tidal mixing on long time scales is an important, but previously unrecognized, contributor to global climate change. it is well known that Earth's orbital and rotational state changes significantly on 10(exp 4)-10(exp 5) year time scales, and that this influences the spatial and temporal pattern of incident radiation. It is widely supposed that climatic variations on these same time scales are, in large part, a response of the ocean-atmosphere-cryosphere system to this radiative forcing. Our proposal is that variations in the luni-solar tidal potential, induced by these same orbital and rotational variations, influences oceanic mixing and thus modulates meridional heat transport, by amounts which are competitive with the radiative forcing. There are some obvious differences between tidal potential and insolation. First is that the Sun and Moon both contribute to tides, whereas the radiation is entirely of solar origin. Second is that the Earth is transparent to gravity but opaque to radiation. Clipping associated with this opacity makes the radiation pattern temporal spectrum rather more complex than the tidal spectrum. A third point is that solar radiation directly delivers energy to Earth's surface whereas tidal mixing will only expedite lateral transport of heat in association with oceanic thermohaline circulation. The diurnal average insolation pattern is best parameterized via a Fourier series in time of year and Legendre polynomials in sine of latitude. Our present focus will be on the annual average terms. The Legendre degree n=0 term describes the global average insolation, and is nearly constant. The degree n=l term describes differences between northern and southern hemispheres, and the annual mean is zero. The degree n=2 term is the main contributor to the equator to pole variations, and varies with obliquity and orbital eccentricity, with the obliquity variation dominating. The lowest order decomposition of the tidal potential recognizes 3 constituents: semi-diurnal, diurnal, and long period, with solar and lunar contributions to each. Our present focus will be on long term variations in the mean square amplitude of the semi-diurnal constituent, with averaging over all the short period variations. For the solar tide that includes the day and year. For the lunar tide it includes the day, month, year, and the apsidal (8.85 year) and nodal (18.6 year) periods. We present calculations of the variations in radiative and tidal forcing for the past 3 million years. The two signals are quite similar. Both vary by approximately 1% of their respective mean values, are dominated by obliquity variations, and exhibit only secondary influence from orbital eccentricity.

Munk, Walter↗
NASA NTRS1995

Modeling of shallow and inefficient convection in the outer layers of the Sun using realistic physics

In an attempt to understand the properties of convective energy transport in the solar convective zone, a numerical model has been constructed for turbulent flows in a compressible, radiation-coupled, nonmagnetic, gravitationally stratified medium using a realistic equation of state and realistic opacities. The time-dependent, three-dimensional hydrodynamic equations are solved with minimal simplifications. The statistical information obtained from the present simulation provides an improved undserstanding of solar photospheric convection. The characteristics of solar convection in shallow regions is parameterized and compared with the results of Chan & Sofia's (1989) simulations of deep and efficient convection. We assess the importance of the zones of partial ionization in the simulation and confirm that the radiative energy transfer is negliglble throughout the region except in the uppermost scale heights of the convection zone, a region of very high superadiabaticity. When the effects of partial ionization are included, the dynamics of flows are altered significantly. However, we confirm the Chan & Sofia result that kinetic energy flux is nonnegligible and can have a negative value in the convection zone.

Kim, Yong-Cheol↗
NASA NTRS1980

Granulation in a main-sequence F-type star

The modal approach developed by Nelson and Musman (1977) is used to investigate convection in an F-type main-sequence star (effective temperature of 7300 K, g = 10,000 cm per sec per sec). The convective velocities and intensity contrasts are found to be larger than in the sun. Even though the convective flux is less than 1% of the total flux at a mean optical depth of unity, the spectral-energy distribution is strongly reddened as a result of the fluctuating opacity. This has important implications in the conversion scale from observed colors to effective temperature. The scale of the surface granulation is expected to be in the range 1000-5000 km. Calculations of the combined H-He I and He II convection zones support the prediction of Toomre et al. (1976) that the stable region between the zones is well mixed

Nelson, G. D.↗
NASA NTRS1990

The wavelength dependence of broadband linear polarization in cool stars

A model is developed to investigate the effect of wavelength dependence of magnetically generated broadband linear polarization (BLP) in late-type stars as a function of line blanketing, observation filters, and other variables. Linear polarization is assumed to be a single 'average' line and the line opacity, magnetic area filling factor, and continuum intensity are incorporated to establish an equation for disk-generated BLP. The method is investigated by computing special models for the flare star BY Dra and the sun which are compared to previous calculations. The model is shown to agree with the calculations of BLP, and the magnetic BLP dependent on wavelengths varies significantly from the simple power law dependences on wavelength. The model sets lower limits to the area occupied by magnetic regions, and an upper limit to the expected BLP also results from the formulation.

Saar, Steven H.↗
NASA NTRS1994

Equilibrium structure of solar magnetic flux tubes: Energy transport with multistream radiative transfer

We examine the equilibrium structure of vertical intense magnetic flux tubes on the Sun. Assuming cylindrical geometry, we solve the magnetohydrostatic equations in the thin flux-tube approximation, allowing for energy transport by radiation and convection. The radiative transfer equation is solved in the six-stream approximation, assuming gray opacity and local thermodynamic equilibrium. This constitutes a significant improvement over a previous study, in which the transfer was solved using the multidimensional generalization of the Eddington approximation. Convection in the flux tube is treated using mixing-length theory, with an additional parameter alpha, characterizing the suppression of convective energy transport in the tube by the strong magnetic field. The equations are solved using the method of partial linearization. We present results for tubes with different values of the magnetic field strength and radius at a fixed depth in the atmosphere. In general, we find that, at equal geometric heights, the temperature on the tube axis, compared to the ambient medium, is higher in the photosphere and lower in the convection zone, with the difference becoming larger for thicker tubes. At equal optical depths the tubes are generally hotter than their surroundings. The results are comparatively insensitive to alpha but depend upon whether radiative and convective energy transport operate simultaneously or in separate layers. A comparison of our results with semiempirical models shows that the temperature and intensity contrast are in broad agreement. However, the field strengths of the flux-tube models are somewhat lower than the values inferred from observations.

Hasan, S. S.↗
NASA NTRS1973

Numerical models of the primitive solar nebula.

The equations giving force balance in the radial and vertical directions in the primitive solar nebula are developed. The techniques used to compute the gravitational potential and to compute the opacity of the gas for energy transport in the vertical direction are described, as well as the properties of the primitive solar nebula models thus constructed. The rate at which gaseous dissipation should occur within the solar nebula, producing the sun by inward flow of matter, is discussed.

Cameron, A. G. W.↗
NASA NTRS1986

Synthetic spectra of cool stars for the wavelength range 2550-3200 A

In order to interpret the ultraviolet spectra of cool stars obtained with IUE and to determine the physical conditions in their outer atmospheres, synthetic IUE spectra of stars cooler than the Sun, mainly the Sun and the metal-deficient, carbon-rich CH stars were calculated. Results are encouraging. Synthetic spectra for the Sun over the range 2550 to 3300 A give roughly the observed level of overall emission and relative strengths or various absorption features (Fe II, Mg II, Mg I, and Fe I) although they still require extra sources of continuous opacity longward of 2650 A. Spectra of the CH stars have roughly the correct shape in the ultraviolet continuum for the expected effective temperature, although these models are problematic in that the electron density, hence H(-) opacity, is directly proportional to the Mg-Si-Fe density and the ratio of line to continuum opacity is only slightly affected by changing metallicity.

Eaton, Joel A.↗
NASA NTRS2002

Atomic Data and Spectral Line Intensities for Ne III

A number of satellites and rockets have been launched to observe radiation from the Sun and other astrophysical objects. Line radiation is emitted when the electron impact excited levels decay to the lower levels by photon emission. From this radiation, the physical parameters such as electron temperature and density of the astrophysical plasma, elemental abundance, and opacity can be inferred. Ne III lines have been observed in H II regions, Ne-rich filaments in supernovae, and planetary nebulae. The allowed line at 489.50 Angstroms due to the transition 2s(sup 2) 2p(sup 5) (sup 3) P2 (goes to) 2s(sup 2)2p(sup 4)(sup 3)P2 has been identified in the solar spectrum by Vernazza and Reeves using Skylab observations. Other Ne III lines in the solar EUV spectrum have been reported by Thomas and Neupert based on observations from the Solar EUV Rocket Telescope and Spectrograph (SERTS) instrument. Atomic data for Ne III have been calculated by using a set of programs developed at, University College, London. The Superstructure and Distorted Wave (DW) programs have been updated over the years. In the Superstructure program, configuration interaction can be taken into account and radial functions are calculated in a modified Thomas-Fermi-Amaldi potential. This is a statistical potential and depends on parameters lambda 1 which are determined by optimizing the weighted sum of term energies. They are found to be lambda(sub 0)=1.2467, lambda(sub 1)=1.1617, and lambda(sub 2)=1.0663. The relativistic corrections are included by using the Breit-Pauli Hamiltonian as a perturbation to the nonrelativistic Hamiltonian. The same potential is used to calculate reactance matrices in the DW approximation in LS coupling. Collision strengths in intermediate coupling are obtained by using term coupling coefficients obtained from the Superstructure program. In this calculation, the configurations used are 2s(sup 2)2p(sup 4), 2s2p(sup 5), 2s(sup 2)2p(sup 3)3s, 2s(sup 2)p(sup 3)3d giving rise to 57 fine-structure levels in intermediate coupling.

Bhatia, A. K.↗
NASA NTRS1991

The computation of standard solar models

Procedures for calculating standard solar models with the usual simplifying approximations of spherical symmetry, no mixing except in the surface convection zone, no mass loss or gain during the solar lifetime, and no separation of elements by diffusion are described. The standard network of nuclear reactions among the light elements is discussed including rates, energy production and abundance changes. Several of the equation of state and opacity formulations required for the basic equations of mass, momentum and energy conservation are presented. The usual mixing-length convection theory is used for these results. Numerical procedures for calculating the solar evolution, and current evolution and oscillation frequency results for the present sun by some recent authors are given.

Ulrich, Roger K.↗
NASA NTRS1992

Photovoltaic array for Martian surface power

Missions to Mars will require electric power. A leading candidate for providing power is solar power produced by photovoltaic arrays. To design such a power system, detailed information on solar-radiation availability on the Martian surface is necessary. The variation of the solar radiation on the Martian surface is governed by three factors: (1) variation in Mars-Sun distance; (2) variation in solar zenith angle due to Martian season and time of day; and (3) dust in the Martian atmosphere. A major concern is the dust storms, which occur on both local and global scales. However, there is still appreciable diffuse sunlight available even at high opacity, so that solar array operation is still possible. Typical results for tracking solar collectors are also shown and compared to the fixed collectors. During the Northern Hemisphere spring and summer the isolation is relatively high, 2-5 kW-hr/sq m-day, due to the low optical depth of the Martian atmosphere. These seasons, totalling a full terrestrial year, are the likely ones during which manned mission will be carried out.

Appelbaum, J.↗
NASA NTRS1992

Photovoltaic arrays for Martian surface power

Missions to Mars will require electric power. A leading candidate for providing power is solar power produced by photovoltaic arrays. To design such a power system, detailed information on solar-radiation availability on the Martian surface is necessary. The variation of the solar radiation on the Martian surface is governed by three factors: (1) variation in Mars-sun distance; (2) variation on solar zenith angle due to Martian season and time of day; and (3) dust in the Martian atmosphere. A major concern is the dust storms, which occur on both local and global scales. However, there is still appreciable diffuse sunlight available even at high opacity, so that solar array operation is still possible. Typical results for tracking solar collectors are also shown and compared to the fixed collectors. During the Northern Hemisphere spring and summer the isolation is relatively high, 2-5 kW-hr/sq m-day due to the low optical depth of the Martian atmosphere. These seasons, totalling a full terrestrial year, are the likely ones during which manned mission will be carried out.

Appelbaum, Joseph↗
NASA NTRS1994

Acoustic waves in M dwarfs: Maintaining a corona

We use a time-dependent hydrodynamics code to follow the propagation of acoustic waves into the corona of an M dwarf star. An important qualitative difference between M dwarfs and stars such as the Sun is that the acoustic spectrum in M dwarfs is expected to peak at periods close to the acoustic cutoff P(sub A): this allows more effective penetration of waves into the corona. In our code, radiative losses in the photosphere, chromosphere, and corona are computed using Rosseland mean opacities, Mg II kappa and Ly alpha emission, and optically thin emissivities respectively. We find that acoustic heating can maintain a corona with a temperature of order 0.7-1 x 10(exp 6) K and a surface X-ray flux as large as 10(exp 5)ergs/sq cm/s. In a recent survey of X-rays from M dwarfs, some (20%-30%) of the stars lie at or below this limiting X-ray flux: we suggest that such stars may be candidates for acoustically maintained coronae.

Mullan, D. J.↗
NASA NTRS1998

Ly(alpha) Photolysis in the Primitive Solar Nebula

This is the final report for the third year of work on this project. Our proposal was to quantitatively investigate the importance of photochemistry in the solar nebula. In the generally accepted theory for the chemical evolution of the primitive solar nebula, Prinn and Fegley argued that photochemistry is unimportant, and that thermochemistry controls the relative abundances of molecular species throughout the planet-forming region. They provided useful estimates of the chemical energy available to the solar nebula from a variety of sources, and established that even the small photolysis rate due to starlight is more important than the photolysis rate from direct sunlight (although small, the UV flux from starlight could have processed a non-negligible fraction of the solar nebula. The reason for this is that the opacity of the disk was so large that direct sunlight could only penetrate to 0.1 AU or so, despite the expectation that the protosun, if comparable to a T-Tauri star, would be emitting up to 10(exp 4) more H I Ly(alpha) photons than the current sun. We developed a Monte Carlo resonance fine radiative transfer code, capable of accurately calculating the radiation field of H I Ly(alpha), He I 584 A, and He II 304 A emissions throughout the nebula and the nearby interstellar medium in which it is embedded. We applied the code to two appropriate models of the primitive solar nebula. Our model provided the photolysis rates of various species over the entire surface layer of the nebula, and from this we evaluated the importance of UV photochemistry due to backscattered solar UV resonance line emissions on different parts of the nebula. The results discussed below were presented.

Gladstone, G. Randall↗
NASA NTRS1982

Cloud cover estimation: Use of GOES imagery in development of cloud cover data base for insolation assessment

The potential of using digital satellite data to establish a cloud cover data base for the United States, one that would provide detailed information on the temporal and spatial variability of cloud development are studied. Key elements include: (1) interfacing GOES data from the University of Wisconsin Meteorological Data Facility with the Jet Propulsion Laboratory's VICAR image processing system and IBIS geographic information system; (2) creation of a registered multitemporal GOES data base; (3) development of a simple normalization model to compensate for sun angle; (4) creation of a variable size georeference grid that provides detailed cloud information in selected areas and summarized information in other areas; and (5) development of a cloud/shadow model which details the percentage of each grid cell that is cloud and shadow covered, and the percentage of cloud or shadow opacity. In addition, comparison of model calculations of insolation with measured values at selected test sites was accomplished, as well as development of preliminary requirements for a large scale data base of cloud cover statistics.

Huning, J. R.↗
NASA NTRS1992

Evolutionary models and the p-mode oscillation spectrum of Alpha Centauri A and B

Spectroscopically observed abundances of Furenlid and Meylan (1990) and Los Alamos Opacity Library opacities specifically constructed for this mixture are used to construct the most detailed models to date for Alpha Cen A and B. Models including the effects of the diffusion of helium in Alpha Cen A's interior were constructed. Although the effect of helium diffusion is small in Alpha Cen A, it is slightly larger than in the sun because of the larger mass and therefore shallower convection zone of Alpha Cen A. Keeping the heavy-element mixture unchanged but varying Z within the uncertainties yields limits to the helium abundance of Y = 0.295 and 0.305, respectively. The derived age of Alpha Cen is 4.6 +/-0.4 Gyr, very similar to the solar age of 4.5 Gyr.

Edmonds, Peter↗
NASA NTRS1993

Contrast of faculae near the disk center and solar variability

We analyze simultaneous, or near-simultaneous, coregistered, digital, photometric images of solar photospheric intensity and line-of-sight magnetic field. Images were made with the Lockheed tunable filter instrument at the Swedish Solar Observatory, La Palma, with the video spectra-spectroheliograph system at the San Fernando Observatory and with the new NASA spectromagnetograph at the National Solar Observatory at Kitt Peak. We study the disk center contrasts of small magnetic elements. While active region faculae are dark at disk center quiet Sun network features are bright. The populations of magnetic field elements that make up these two kinds of features are quite different. Different contrast center-limb functions must be used when estimating their irradiance or luminosity contributions. The disk center contrasts of active region faculae are colar dependent and indicate a depth effect related to the H(-) opacity of the facular atmopshere. This results is important for calibration of monochromatic observations of faculae to bolometric irradiance fluctuations. We emphasize the value of cooperative observations among installations whose differing strengths are complementary.

Lawrence, J. K.↗
NASA NTRS2019

SI IV Resonance Line Emission during Solar Flares: Non-LTE, Non-equilibrium, Radiation Transfer Simulations

The Interface Region Imaging Spectrograph routinely observes the Si IV resonance lines. When analyzing quiescent observations of these lines, it has typically been assumed that they form under optically thin conditions. This is likely valid for the quiescent Sun, but this assumption has also been applied to the more extreme flaring scenario. We used 36 electron-beam-driven radiation hydrodynamic solar flare simulations, computed using the RADYN code, to probe the validity of this assumption. Using these simulated atmospheres, we solved the radiation transfer equations to obtain the non-LTE, nonequilibrium populations, line profiles, and opacities for a model silicon atom, including charge exchange processes. This was achieved using the "minority species" version of RADYN. The inclusion of charge exchange resulted in a substantial fraction of Si IV at cooler temperatures than those predicted by ionization equilibrium. All simulations with an injected energy flux F> 5 x 10(exp 10) erg cm(exp -2) s(exp -1) resulted in optical depth effects on the Si IV emission, with differences in both intensity and line shape compared to the optically thin calculation. Weaker flares (down to F ~ 10(exp 9) erg cm(exp -2) s(exp -1)) also resulted in Si IV emission forming under optically thick conditions, depending on the other beam parameters. When opacity was significant, the atmospheres generally had column masses in excess of 5 x 10-6 g cm-2 over the temperature range 40-100 kK, and the Si IV formation temperatures were between 30 and 60 kK. We urge caution when analyzing Si IV flare observations, or when computing synthetic emission without performing a full radiation transfer calculation.

Kerr, Graham S.↗
NASA NTRS2001

Our Sun IV: The Standard Model and Helioseismology: Consequences of Uncertainties in Input Physics and in Observed Solar Parameters

Helioseismic frequency observations provide an extremely accurate window into the solar interior; frequencies from the Michaelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft, enable the adiabatic sound speed and adiabatic index to be inferred with an accuracy of a few parts in 10(exp 4) and the density with an accuracy of a few parts in 10(exp 3). This has become a Serious challenge to theoretical models of the Sun. Therefore, we have undertaken a self-consistent, systematic study of the sources of uncertainties in the standard solar models. We found that the largest effect on the interior structure arises from the observational uncertainties in the photospheric abundances of the elements, which affect the sound speed profile at the level of 3 parts in 10(exp 3). The estimated 4% uncertainty in the OPAL opacities could lead to effects of 1 part in 10(exp 3); the approximately 5%, uncertainty in the basic pp nuclear reaction rate would have a similar effect, as would uncertainties of approximately 15% in the diffusion constants for the gravitational settling of helium. The approximately 50% uncertainties in diffusion constants for the heavier elements would have nearly as large an effect. Different observational methods for determining the solar radius yield results differing by as much as 7 parts in 10(exp 4); we found that this leads to uncertainties of a few parts in 10(exp 3) in the sound speed int the solar convective envelope, but has negligible effect on the interior. Our reference standard solar model yielded a convective envelope position of 0.7135 solar radius, in excellent agreement with the observed value of 0.713 +/- 0.001 solar radius and was significantly affected only by Z/X, the pp rate, and the uncertainties in helium diffusion constants. Our reference model also yielded envelope helium abundance of 0.2424, in good agreement with the approximate range of 0.24 to 0.25 inferred from helioseismic observations; only extreme Z/X values yielded envelope helium abundance outside this range. We found that other current uncertainties, namely, in the solar age and luminosity, in nuclear rates other than the pp reaction, in the low-temperature molecular opacities, and in the low-density equation of state, have no significant effect on the quantities that can be inferred from helioseismic observations. The predicted pre-main-sequence lithium depletion is uncertain by a factor of 2. The predicted neutrino capture rate is uncertain by approximately 30% for the Cl-27 experiment and by approximately 3% for Ga-71 experiments, while the B-8 neutrino flux is uncertain by approximately 30%.

Boothroyd, Arnold I.↗