Calculations of the evolution of the giant planets

Evolutionary calculations are presented for spherically symmetric protoplanetary configurations with a homogeneous solar composition and with masses of 10^?3, 1.5 × 10^?3, 2.85 × 10^?4, and 4.2 × 10^?4M_⊙. Recent improvements in equation-of-state and opacity calculations are incorporated. Sequences start as subcondensations in the solar nebula with densities of ～10^?10 to 10^?11 g cm^?3, evolve through a hydrostatic phase lasting 10⁵ to 10⁷ years, undergo dynamic collapse due to dissociation of molecular hydrogen, and regain hydrostatic equilibrium with densities ～1 g cm^?3. The nature of the objects at the onset of the final phase of cooling and contraction is discussed and compared with previous calculations.     

Displaced mass,depth, diameter,and effects of oblique trajectories for impact craters formed in dense crystalline rocks

Empirical formulae are presented for calculating the displaced mass, depth, diameter, and effects of oblique trajectories for impact craters formed in dense crystalline rocks. The formulae are applicable to craters with diameters from approximately 10^?3–10³ cm that require, respectively, impact kinetic energies of approximately 10 to 10¹⁶ ergs for their formation. The experimental results are in poor agreement with Öpik’s theoretical calculations and raise questions on the validity of his theoretical model.     

Helium emission from model flare layers

A theoretical study is made of the visible and UV line radiation of He i atoms and He ii ions from a plane-parallel model flare layer. Solutions are obtained of the statistically steady state equations for a 30 level He i-ii-iii model, with parametric representation of the line and continuum radiation fields. Optical depths and some line intensities are presented for a 1000 km thick layer. Results are given for electron temperatures 10⁴ to 5 × 10⁴ K and electron densities 10¹⁰ to 10¹⁴ cm^–3.Work sponsored by the NASA, Marshall Space Flight Center, Alabama under contract NAS8-27988.     

Are the magnetic fields of millisecond pulsars ∼108 G?

It is generally assumed that the magnetic fields of millisecond pulsars (MSPs) are ～10⁸ G. We argue that this may not be true and the fields may be appreciably greater. We present six evidences for this: (1) The ～10⁸G field estimate is based on magnetic dipole emission losses which is shown to be questionable; (2) The MSPs in low mass X-ray binaries (LMXBs) are claimed to have <10¹¹ G on the basis of a Rayleygh-Taylor instability accretion argument. We show that the accretion argument is questionable and the upper limit 10¹¹ G may be much higher; (3) Low magnetic field neutron stars have difficulty being produced in LMXBs; (4) MSPs may still be accreting indicating a much higher magnetic field; (5) The data that predict ～10⁸ G for MSPs also predict ages on the order of, and greater than, ten billion years, which is much greater than normal pulsars. If the predicted ages are wrong, most likely the predicted ～10⁸ G fields of MSPs are wrong; (6) When magnetic fields are measured directly with cyclotron lines in X-ray binaries, fields ?10⁸ G are indicated. Other scenarios should be investigated. One such scenario is the following. Over 85% of MSPs are confirmed members of a binary. It is possible that all MSPs are in large separation binaries having magnetic fields >10⁸ G with their magnetic dipole emission being balanced by low level accretion from their companions.     

Molecules in the early universe

The formation of first molecules, negative Hydrogen ions, and molecular ions in a model of the Universe with cosmological constant and cold dark matter is studied. The cosmological recombination is described in the framework of modified model of the effective 3-level atom, while the kinetics of chemical reactions is described in the framework of the minimal model for Hydrogen, Deuterium, and Helium. It is found that the uncertainties of molecular abundances caused by the inaccuracies of computation of cosmological recombination are approximately 2–3%. The uncertainties of values of cosmological parameters affect the abundances of molecules, negative Hydrogen ions, and molecular ions at the level of up to 2%. In the absence of cosmological reionization at redshift z = 10, the ratios of abundances to the Hydrogen one are 3.08 × 10^–13 for H^–, 2.37 × 10^–6 for H₂, 1.26 × 10^–13 for H₂⁺, 1.12 × 10^–9 for HD, and 8.54 × 10^–14 for HeH⁺.     

Plasma emission due to isotropic fast electrons,and types I,II, and V solar radio bursts

The theory of plasma emission is developed under the assumption that the Langmuir waves are generated by an isotropic distribution of fast electrons. Emission from inverse power-law distributions tend to favor emission at the second harmonic with brightness temperatures up to about 10⁸ K at 100 MHz. The concept of a gap (in velocity space) distribution is developed. Very bright plasma emission can result from a gap distribution. For brightness temperatures between 10⁹ K and 10¹¹ K for the second harmonic the fundamental has a brightness temperature between 10⁸ K and 10⁹ K. For higher brightness temperatures the fundamental is amplified and can be very much brighter than the second harmonic. The maximum brightness temperatures for the fundamental and second harmonic at 100 MHz are about 10¹⁶ K and 10¹³ K respectively. Mechanisms by which a gap distribution might be formed are discussed and two effective mechanisms are identified. The theory is applied to the interpretation of radio bursts of types I, II, stationary IV and V. In each case the suggested mechanism appears to be favorable.     

Galilean satellite eclipse studies: III. Jovian methane abundance

The methane abundance in the lower Jovian stratosphere is measured using Galilean satellite eclipse light curves. Spectrally selective observations in and between absorption bands are compared. An average mixing ratio at the locations measured is [CH₄]/[H₂] ～ 1.3 × 10^?3, larger than the value 0.9 × 10^?3 expected for a solar abundance of carbon. Some zenographic variation of the mixing ratio may occur. Observationally compatible values are 1.3–2.0 × 10^?3 in the STZ, 1.3– 2.6 × 10^?3 on the GRS/STrZ edge, and 0.7–1.3 × 10^?3 in the GRS.     

Atmospheres of extreme metal-deficient stars

Atmospheric models have been constructed for effective temperatures 4000°, 4500° and 5000° and for hydrogen-to-metal ratios of 1, 10², 10³ and 10⁴ times the solar values, and for surface gravities of 2×10⁴ and 2×10². The effect of metal deficiency on the atmospheric structure of these stars are studied.National Academy of Sciences, National Research Council Postdoctoral Research Associate.     

Some weak interaction processes in highly evolved stars

Some weak interaction processes which are important in stars whose central temperatures and densities exceed 10^9°K and 10⁶ gm/cm³ are discussed. Simple analytic expressions for reaction rates which are convenient for computer studies of the late stages of stellar evolution are given.Of the National Bureau of Standards and University of Colorado.     

Light noble gases and cosmogenic radionuclides in Estherville,Budulan, and other mesosiderites: Implications for exposure histories and production rates

Abstract— We report measurements of ²⁶AI, ¹⁰Be, ⁴¹Ca, and ³⁶Cl in the silicate and metal phases of 11 mesosiderites, including several specimens each of Budulan and Estherville, of the brecciated meteorite Bencubbin, and of the iron meteorite Udei Station. Average production rate ratios (atom/atom) for metal phase samples from Estherville and Budulan are ²⁶Al/¹⁰Be = 0.77 ± 0.02; ³⁶Cl/¹⁰Be = 5.3 ± 0.2. For a larger set of meteorites that includes iron meteorites and other mesosiderites, we find ²⁶Al/¹⁰Be = 0.72 ± 0.01 and ³⁶Cl/¹⁰Be = 4.5 ± 0.2. The average ⁴¹Ca/³⁶Cl production rate ratio is 1.10 ± 0.04 for metal separates from Estherville and four small iron falls. The ⁴¹Ca activities in dpm/(kg Ca) of various silicate separates from Budulan and Estherville span nearly a factor of 4, from <400 to >1600, indicating preatmospheric radii of >30 cm. After allowance for composition, the activities of ²⁶Al and ¹⁰Be (dpm/kg silicate) are similar to values measured in most ordinary chondrites and appear to depend only weakly on bulk Fe content. Unless shielding effects are larger than suggested by the ³⁶Cl and ⁴¹Ca activities of the metal phases, matrix effects are unimportant for ¹⁰Be and minor for ²⁶Al. Noble gas concentrations and isotopic abundances are reported for samples of Barea, Emery, Mincy, Morristown, and Marjalahti. New estimates of ³⁶Cl/³⁶Ar exposure ages for the metal phases agree well with published values. Neon‐21 production rates for mesosiderite silicates calculated from these ages and from measured ²¹Ne contents are consistently higher than predicted for L chondrites despite the fact that the mesosiderite silicates have lower Mg contents than L chondrites. We suggest that the elevation of the ²¹Ne production rate in mesosiderite silicates reflects a “matrix effect,” that is, the influence of the higher Fe content of mesosiderites, which acts to enhance the flux of low‐energy secondary particles and hence the ²¹Ne production from Mg. As ¹⁰Be production is relatively insensitive to this matrix effect, ¹⁰Be/²¹Ne ages give erroneously low production rates and high exposure ages. By coincidence, standard ²²Ne/²¹Ne based “shielding” corrections give fairly reliable ²¹Ne production rates in the mesosiderite silicates.     

Rapid neutron capture process in supernovae and chemical element formation

The rapid neutron capture process (r-process) is one of the major nucleosynthesis processes responsible for the synthesis of heavy nuclei beyond iron. Isotopes beyond Fe are most exclusively formed in neutron capture processes and more heavier ones are produced by the r-process. Approximately half of the heavy elements with mass number A > 70 and all of the actinides in the solar system are believed to have been produced in the r-process. We have studied the r-process in supernovae for the production of heavy elements beyond A = 40 with the newest mass values available. The supernova envelopes at a temperature >109 K and neutron density of 10²⁴ cm^?3 are considered to be one of the most potential sites for the r-process. The primary goal of the r-process calculations is to fit the global abundance curve for solar system r-process isotopes by varying time dependent parameters such as temperature and neutron density. This method aims at comparing the calculated abundances of the stable isotopes with observation. We have studied the r-process path corresponding to temperatures ranging from 1.0 × 10⁹ K to 3.0 × 10⁹ K and neutron density ranging from 10²⁰ cm^?3 to 10³⁰ cm^?3. With temperature and density conditions of 3.0 × 10⁹ K and 10²⁰ cm^?3 a nucleus of mass 273 was theoretically found corresponding to atomic number 115. The elements obtained along the r-process path are compared with the observed data at all the above temperature and density range.     

The URCA process at high temperatures and densities

The URCA neutrino loss rate from a hot stellar environment is investigated. The results indicate that the loss rates for URCA type processes from even mass number nuclei are comparable to the rates from odd mass number nuclei at temperatures above about 10⁹ K. Rates are calculated for some typical odd mass isobar pairs and for the even mass isobar fifty-six for temperatures between 5×10⁸ K to 5×10¹⁰ K.Supported in part by National Science Foundation Grant GP13959.     

The photodissociation lifetimes of the OH and OD radicals in comets

The rates of photodissociation of the OH and OD molecules from absorption of solar radiation in he X²Π-A²Σ⁺ electronic transition are calculated to lie between 3.5 and 6.7 × 10^?6 sec^?1 for OH for heliocentric velocities between -60 and +60 km sec^?1 and to be about 4.7 × 10^?7 sec^?1 for OD at 1 AU from the Sun. The corresponding lifetimes, which are upper bounds to the actual lifetimes, are generally consistent with the observational cometary data.     

Thermal equilibria of coronal magnetic loops

Equations of thermal equilibrium along coronal loops with footpoint temperatures of 2 × 10⁴ K are solved. Three fundamentally different categories of solution are found, namely hot loops with summit temperatures above about 4 × 10⁵ K, cool loops which are cooler than 8 × 10⁴ K along their whole length and hot-cool loops which have summit temperatures around 2 × 10⁴ K but much hotter parts at intermediate points between the summit and the footpoints. Hot loops correspond to the hot corona of the Sun. The cool loops are of relevance for fibrils, for the cool cores observed by Foukal and also for active-region prominences where the magnetic field is directed mainly along the prominence. Quiescent prominences consist of many cool threads inclined to the prominence axis, and each thread may be modelled as a hot-cool loop. In addition, it is possible for warm loops at intermediate summit temperatures (8 × 10⁴K to 4 × 10⁵ K) to exist, but the observed differential emission measure suggests that most of the plasma in the solar atmosphere is in either the hot phase or the cool phase. Thermal catastrophe may occur when the length or pressure of a loop is so small that the hot solution ceases to exist and there are only cool loop solutions. Many loops can be superimposed to form a coronal arcade which contains loops of several different types.     

Distribution and relations of 4- to 10-km-diameter craters to global geologic units of Mars

By correlating the 1:25,000,000 geologic map of Mars of Scott and Carr (1977) with 4- to 10-km-diameter crater density data from Mariner 9 images, the average crater density for 23 of the equatorial geologic-geomorphic units on Mars was computed. The correlation of these two data sets was accomplished by digitizing both the crater density data and geologic map at the same scale and by comparing them in a computer. This technique assigns the crater density value found in the corresponding location on the geologic data set to a discrete computer file assigned each of the 23 geologic units. By averaging the crater density values accumulated in each file, an “average” crater density for each geologic unit was obtained. Condit believes these average crater density values are accurate indicators of the relative age of the geologic units considered. The statistical validity of these average values is strongest for the geologic units of the largest areal extent. The relative ages as obtained from the average crater density values for the seven largest geologic units, from youngest to oldest, are: Tharsis volcanic material, 21 ± 4 craters/10⁶km²; smooth plains material, 57 ± 14 craters/10⁶km²; rolling plains material, 66 ± 16 craters/10⁶km²; plains materials, 80 ± 17 craters/10⁶km²; ridged plains material, 128 ± 25 craters/10⁶km²; hilly and cratered material, 137 ± 38 craters/10⁶km²; and cratered plateau material, 138 ± 27 craters/10⁶km².     

Mgix and Sixi line ratios in the sun

New theoretical emission line ratios for the Be-sequence ions Mgix and Sixi are presented. A comparison with observational data for two solar flares and an active region loop obtained with the Harvard EUV spectrometer and NRL XUV spectroheliograph aboard Skylab reveals that these plasmas are in ionization equilibrium at coronal temperatures. Unfortunately most of the density diagnostics are not particularly useful under solar plasma conditions, as they vary only slightly over the electron density range 10⁸–10¹³cm^–3. However the Sixi ratioI(³ P ^e ₂ -³ P ^o ₂)/I(³ P ^o ₁ –¹ S ^e ₀) is density sensitive in the range 10⁸ to 10¹⁰cm^–3, which is representative of electron densities found in solar active regions or small flares.     

Radiation effects on the MHD wave behavior in the solar corona

The effect of radiation losses on the dispersion and damping of magnetohydrodynamic waves in the solar corona is studied. The conditions are determined under which radiation losses are most appreciable. A damping of kink modes of coronal loops with plasma temperatures within 10⁶–10^6.3 K and 10^6.3–10⁷ K are compared. It is concluded that the radiation damping dominates in the temperature range 10⁶–10^6.3 K, which can cause the observed fast damping of kink oscillations of coronal loops. Radiation losses should be taken into account in full magnetohydrodynamic equations with radiative transfer.     

Dynamical effects of an extended cloud of dark matter on dwarf spheroidals

If the dwarf spheroidals are embedded in an extended cloud of dark matter then their density profiles can be reproduced by assuming a Maxwellian distribution of velocities for the constituent stars. The observed luminosity profiles of dwarf spheroidals imply densities for the dark matter in the range 10^-26 to 10^-25 g cm^-3, and mass-to-luminosity ratios which are typically an order of magnitude greater than those of globular clusters. Neutrinos of mass ∼ 10 eV and (v) ∼ 1000 km s^-1 can provide this requisite density for the background.     

Long term variations in solar flare activity

A statistical analysis of the contemporary (1954-1975) solar flare particle events has been made for the parametersF (integrated, proton fluence in cm^-2 in an event with kinetic energy above 10 MeV) andR ₀ (the characteristic rigidity). These data are compared with the long-term averaged values determined from stable- and radio-nuclide measurements of lunar samples. The analysis shows that the ancient solar flare proton spectrum was harder (higher R₀ values) compared to that observed in contemporary flares. A similar analysis can not be made for the mean long-term averaged flux (ˉJ, cm^-2 S^-1), since the contemporary averages suffer from an uncertainty due to the statistics of a single event. However, the average flux estimates for time durations 〈T〉 exceeding 10³ yr, are free from such uncertainties. The long-term averaged ˉJ values obtained over different time scales (10⁴ - 10⁶ yr) suggest a possible periodic variation in solar flare activity, with enhanced flux level during the last 10⁵ yr. The available data rule out the occurrence of giant flares, with proton fluence exceeding 10¹⁵ cm^-2 during the last million years.     

Disk models for cataclysmic variables

This paper presents disk models for cataclysmic variables in which convection in the central layers has been included. The calculation of the vertical structure at different points is presented. The models have a central mass of 1M _⊙ and matter fluxes of 10^?9, 10^?8, and 10^?7 M _⊙ yr^?1. The corresponding luminosities are 1.86, 1.86×10 and 1.86×10² L _⊙.