Open Access. Powered by Scholars. Published by Universities.®
- Publication Year
- Publication
- Publication Type
Articles 1 - 30 of 49
Full-Text Articles in Entire DC Network
Libstatmech And Applications To Astrophysics, Tianhong Yu
Libstatmech And Applications To Astrophysics, Tianhong Yu
All Theses
In this work an introduction to Libstatmech is presented and applications especially to astrophysics are discussed. Libstatmech is a C toolkit for computing the statistical mechanics of fermions and bosons, written on top of libxml and gsl (GNU Scientific Library). Calculations of Thomas-Fermi Screening model and Bose-Einstein Condensate based on libstatmech demonstrate the expected results. For astrophysics application, a simple Type Ia Supernovae model is established to run the network calculation with weak reactions, in which libstatmech contributes to compute the electron chemical potential and allows the weak reverse rates to be calculated from detailed balance. Starting with pure 12C …
Branchings And Time Evolution Of Reaction Networks, Changyuan Wang
Branchings And Time Evolution Of Reaction Networks, Changyuan Wang
All Dissertations
In this thesis I analyze flows in reaction networks in terms of branchings
in a digraph. If the coupled differential equations governing the rate
of change of probabilities X of a state or species are finite-differenced in time, a matrix equation (I + Adt)X(t+dt) = X(t) results, where X(t) is a vector giving the probabilities at time t and X(t+dt) is a vector giving the probabilities at time t + dt. I demonstrate that the matrix (I + Adt) may be written as the product of an incidence matrix and a weight matrix for a directed graph (digraph) representing the …
Neutrino-Nucleus Reaction Cross Sections For Light Element Systhesis In Supernova Explosions, Takashi Yoshida, Toshio Suzuki, Satoshi Chiba, Toshitaka Kajino, Hidekazu Yokomakura, Keiichi Kimura, Akira Takamura, Dieter H. Hartmann
Neutrino-Nucleus Reaction Cross Sections For Light Element Systhesis In Supernova Explosions, Takashi Yoshida, Toshio Suzuki, Satoshi Chiba, Toshitaka Kajino, Hidekazu Yokomakura, Keiichi Kimura, Akira Takamura, Dieter H. Hartmann
Publications
The neutrino-nucleus reaction cross sections of 4He and 12C are evaluated using new shell model Hamiltoni-ans. Branching ratios of various decay channels are calculated to evaluate the yields of Li, Be, and B producedthrough the ν -process in supernova explosions. The new cross sections enhance the yields of7Li and11B pro-duced during the supernova explosion of a 16.2 M⊙star model compared to the case using the conventionalcross sections by about 10%. On the other hand, the yield of10B decreases by a factor of two. The yieldsof6Li,9Be, and the radioactive nucleus10 Be are found at a level of ∼ 10−11M⊙. The temperature …
Neutrino Oscillation Effects On Supernova Light Element Synthesis, Takashi Yoshida, Toshitaka Kajino, Hidekazu Yokomakura, Keichi Kimura, Akira Takamura, Dieter H. Hartmann
Neutrino Oscillation Effects On Supernova Light Element Synthesis, Takashi Yoshida, Toshitaka Kajino, Hidekazu Yokomakura, Keichi Kimura, Akira Takamura, Dieter H. Hartmann
Publications
Neutrion oscillations affect light-element synthesis through the v-process in supernova explosions. The 7Li and 11B yields produced in a supernova explosion of a 16.2 M ⊙ star model increase by factors of 1.9 and 1.3 in the case of the large mixing angle solution with a normal mass hierarchy of sin^2 2θ13 >~ 2x10^-3 compared with those without the oscillations. In the case of an inerted mass hierarchy or a nonadiabatic 1-3 mixing resonance, the increment of their yields is much smaller. Neutrino oscillations raise the reaction rates of charged-current v-process reactions in the region outside oxygen-rich layers. The number …
Line Shape Diagnositics Of Galactic 26al, K. Kretschmer, R. Diehl, Dieter H. Hartmann
Line Shape Diagnositics Of Galactic 26al, K. Kretschmer, R. Diehl, Dieter H. Hartmann
Publications
The shape of the gamma-ray line from radioactive 26Al, at 1808.7 keV energy in the frame of the decaying isotope,is determined by its kinematics when it decays, typically 106y after its ejection into the interstellar medium from its nucleosyn-thesis source. Three measurements of the line width exist: HEAO-C’s 1982 value of (0 + 3) keV FWHM, the GRIS 1996 valueof (5. 4 ± 1. 3) keV FWHM, and the recent RHESSI value of (2. 0 ± 0. 8) keV FWHM, suggesting either “cold”, “hot”, or “warm”26Al in the ISM. We model the line width as expected from Galactic rotation, expanding …
Iron Implantation In Presolar Supernova Grains, Donald D. Clayton, Bradley S. Meyer, Lih-Sin The, Mounib F. El Eid
Iron Implantation In Presolar Supernova Grains, Donald D. Clayton, Bradley S. Meyer, Lih-Sin The, Mounib F. El Eid
Publications
We consider the potential of measured iron isotopic ratios within presolar grains from supernovae (as discovered in meteorites) for identifying the gas from which the grains condensed. We show that although iron isotopic ratios vary dramatically with radial coordinate in the initial supernova, it seems likely that the concentration of iron that thermally condenses in SiC grains within the supernova interior may be smaller than the concentration that will later be implanted by high-speed grain-gas collisions following the penetration of the reverse shock into the supernova flow. In that case, the Fe isotopic composition is much altered. We propose that …
Nuclear Reactions Governing The Nucleosynthesis Of 44ti, L.-S. The, Donald D. Clayton, L Jin, Bradley S. Meyer
Nuclear Reactions Governing The Nucleosynthesis Of 44ti, L.-S. The, Donald D. Clayton, L Jin, Bradley S. Meyer
Publications
Large excesses of 44Ca in certain presolar graphite and silicon carbide grains give strong evidence for 44Ti production in supernovae. Furthermore, recent detection of the 44Ti c line from the Cas A super-nova remnant by the Compton Gamma Ray Observatory Compton Telescope shows that radioactive 44Ti is produced in supernovae. These make the 44Ti abundance an observable diagnostic of supernovae. Through use of a nuclear reaction network, we have systematically varied reaction rates and groups of reaction rates to experimentally identify those that govern 44Ti abundance in core-collapse supernova nucleosynthesis. We survey the nuclear-rate dependence by repeated calculations of the …
Theory Of Quasi-Equilibrium Nucelosynthesis And Applications To Matter Expanding From High Temperature And Density, Bradley S. Meyer, Tracy D. Krishnan, Donald D. Clayton
Theory Of Quasi-Equilibrium Nucelosynthesis And Applications To Matter Expanding From High Temperature And Density, Bradley S. Meyer, Tracy D. Krishnan, Donald D. Clayton
Publications
Our first purpose is construction of a formal theory of quasi-equilibrium. We define quasi-equilibrium, in its simplest form, as statistical equilibrium in the face of an extra constraint on the nuclear populations. We show that the extra constraint introduces a uniform translation of the chemical potentials for the heavy nuclei and derive the abundances in terms of it. We then generalize this theory to accommodate any number of constraints. For nucleosynthesis, the most important constraint occurs when the total number of heavy nuclei Yh within a system of nuclei differs from the number that would exist in nuclear statistical equilibrium …
The Evolution Of Galactic Boron And The Production Site Of The Light Elements, D K. Duncan, F Primas, L M. Rebull, A M. Boesgaard, Constantine P. Deliyannis, L M. Hobbs, Jeremy R. King, S G. Ryan
The Evolution Of Galactic Boron And The Production Site Of The Light Elements, D K. Duncan, F Primas, L M. Rebull, A M. Boesgaard, Constantine P. Deliyannis, L M. Hobbs, Jeremy R. King, S G. Ryan
Publications
The Goddard High Resolution Spectrograph (GHRS) of the Hubble Space Telescope (HST) has been used to obtain spectra of the 2500 Å region in eight stars with metallicities ranging from [Fe/H] = -0.4 to -3.0, including the most metal-poor star ever observed for boron. Spectrum synthesis utilizing latest Kurucz model atmospheres has been used to determine the B abundance for each star, with particular attention paid to the errors of each point, to permit judgment of the quality of the fit of models of Galactic chemical evolution. Previous observations were combined with new ones, bringing the number of stars analyzed …
Type X Silicon Carbide Presolar Grains: Type Ia Supernova Condensates?, Donald D. Clayton, David Arnett, Jave Kane, Bradley S. Meyer
Type X Silicon Carbide Presolar Grains: Type Ia Supernova Condensates?, Donald D. Clayton, David Arnett, Jave Kane, Bradley S. Meyer
Publications
In terms of nucleosynthesis issues alone, we demonstrate that the type X silicon carbide particles have chemical and isotopic compositions resembling those from explosive helium burning in 14N-rich matter. These particles are extracted chemically from meteorites and were once interstellar particles. They have already been identifed by their discoverers as supernova particles on the basis of their isotopic composi-tions, but we argue that they are from supernovae of Type Ia that explode with a cap of helium atop their CO structure. The relative abundances of the isotopes of C and Si and trace N, Mg, and Ca match those in …
Placing The Sun In Galactic Chemical Evolution: Mainstream Sic Particles, Donald D. Clayton, F X. Timmes
Placing The Sun In Galactic Chemical Evolution: Mainstream Sic Particles, Donald D. Clayton, F X. Timmes
Publications
We examine the consequences and implications of the possibilities that the best-fit m = 4/3 line of the silicon isotopic ratios measured in mainstream SiC grains is identical or parallel to the mean ISM evolution line of the silicon isotopes. Even though the mean ISM evolution proceeds along a line of unity slope when deviations are expressed in terms of the native representation (the mean ISM), the evolution line can become a slope 4/3 line in the solar representation, provided that the solar composition is displaced from the mean ISM evolution. During the course of this analysis, we introduce new …
Constraints From 26al Measurements On The Galaxy's Recent Global Star Formation Rate And Core-Collapse Supernovae Rate, F. X. Timmes, R. Diehl, Dieter H. Hartmann
Constraints From 26al Measurements On The Galaxy's Recent Global Star Formation Rate And Core-Collapse Supernovae Rate, F. X. Timmes, R. Diehl, Dieter H. Hartmann
Publications
Gamma rays from the decay of 26Al o†er a stringent constraint on the GalaxyÏs global star formation rate over the past million years, supplementing other methods for quantifying the recent Galactic star formation rate, such as equivalent widths of Ha emission. Advantages and disadvantages of using 26Al gamma-ray measurements as a tracer of the massive star formation rate are analyzed. Estimates of the Galactic 26Al mass derived from COMPTEL measurements are coupled with a simple, analytical model of the 26Al injection rate from massive stars and restrict the GalaxyÏs recent star formation rate to 5^4 yr~1. In addition, we show …
Galactic Evolution Of Silicon Isotopes: Applications To Presolar Sic Grains From Meteorites, F X. Timmes, Donald D. Clayton
Galactic Evolution Of Silicon Isotopes: Applications To Presolar Sic Grains From Meteorites, F X. Timmes, Donald D. Clayton
Publications
We calculate and discuss the chemical evolution of the isotopic silicon abundances in the interstellar medium (ISM) at distances and times appropriate to the birth of the solar system. This has several objectives, some of which are related to anomalous silicon isotope ratios within presolar grains extracted from meteorites; namely: (1) What is the relative importance for silicon isotopic compositions in the bulk ISM of Type II supernovae, Type Ia supernovae, and AGB stars? (2) Are 29Si and 30Si primary or secondary nucleosynthesis products? (3) In what isotopic direction in a three-isotope plot do core-collapse supernovae of different mass move …
Implications Of The Broad 26a1 1809 Kev Line Observed By Gris, Wan Chen, Roland Diehl, Neil Gehrel, Dieter H. Hartmann, Mark Leising, Juan E. Naya, Nikos Prantzos, Jack Tueller, Peter Von Ballmoos
Implications Of The Broad 26a1 1809 Kev Line Observed By Gris, Wan Chen, Roland Diehl, Neil Gehrel, Dieter H. Hartmann, Mark Leising, Juan E. Naya, Nikos Prantzos, Jack Tueller, Peter Von Ballmoos
Publications
The surprisingly large width of the 1809 ke V gamma-ray line from decay old radioactive Al, recently observed by GRIS (Naya et al. 1996), has profound astrophysical implications. While there may be no apparent, single mechanism that can explain the oberved broadening, wen identify high speed dust grains, extremely hot superbubbles, and a large, low density, gaseous halo in the Galactic center region as the possible origins and iscuss their intriguing revelation of the hot gas content in the ISM.
The Production Of 44ti And 60co In Supernovae, F. X. Timmes, S. E. Woosley, Dieter H. Hartmann, R. D. Hoffman
The Production Of 44ti And 60co In Supernovae, F. X. Timmes, S. E. Woosley, Dieter H. Hartmann, R. D. Hoffman
Publications
The production of the radioactive isotopes 44Ti and 60Co in all types of supernovae is examined and compared to observational constraints inculding Galactic gamma-ray surveys, measurements of the diffuse 511 keV radiation, gamma-ray observations of Cas A, the late-time light curve of SN 1987A, and isotopic anomalies found in silicon carbide grains in meteorities. The (revished) line flux from 44Ti decay in the Cas A supernova remnant reported by COMPTEL on the Compton Gamma Ray Observatory is near the upper bound expected from our models. The necessary concurrent ejection of 56Ni would also imply that Cas A was a brighter …
48ca Production In Matter Expanding From High Temperature And Density, B S. Meyer, Tracy D. Krishnan, Donald D. Clayton
48ca Production In Matter Expanding From High Temperature And Density, B S. Meyer, Tracy D. Krishnan, Donald D. Clayton
Publications
We calculate with a large nuclear reaction network the nuclear dynamics associated with the expansions and cooling of initially hot and dense matter. We study matter with neutron excess near that of 48Ca, because one objective is to clarify the nucleosynthesis of that abundant neutron-rich nucleus, whose origin has been enigmatic. Expecting that supernovae provide the site of its origin, we take initial temperatures near T9 = 10 but survey a wide range of initial densities, corresponding to a wide range in initial entropies. The highest entropies are probably associated with winds from newborn neutron stars in Type II collapse …
Cgro/Osse Observations Of The Cassiopeia A Snr, L.-S. The, M. D. Leising, J. D. Kurfess, W. N. Johnson, Dieter H. Hartmann, N. Gehrels, J. E. Grove, W. R. Purcell
Cgro/Osse Observations Of The Cassiopeia A Snr, L.-S. The, M. D. Leising, J. D. Kurfess, W. N. Johnson, Dieter H. Hartmann, N. Gehrels, J. E. Grove, W. R. Purcell
Publications
We present all OSSE observation to date the Cas A supernova remnant. The objective are to detect the 44Ti lines, one of which has been reportedly detected by COMPTEL, and the hard X-ray continum above 40 keV, as indicated by HEAO-A2 measurements. Our best fit flux in each of three 44Ti lines is (+1.76±1.51/1.48) x 10^-5 gamma cm^-2 s^-1 with X2v = 1.01, d.o.f. = 1780. The implied 44Ti mass ~10^-4 M⊙ is compatible with explosive nucleosynthesis calculations. OSSE detected also a continuum below 200 keV at better than 4σ confidence level with a flux of ~9 x 10^-4 gamma …
A New Interpretation Of 26al In Meteoritic Inclusions, Donald D. Clayton, Liping Jin
A New Interpretation Of 26al In Meteoritic Inclusions, Donald D. Clayton, Liping Jin
Publications
We suggest that the large 26Al/27Al ϭ 5 ϫ 10Ϫ5 abundance ratio found in calcium-aluminum–rich inclusions (CAIs) in meteorites is produced by energetic particle irradiation in the early solar system but only in a thin (0.2 g cmϪ2) skin of the solar preplanetary disk that stops the energetic particles. Buildup of that 26Al concentration happens only during the quiescent, or passive, phase of the solar disk, after accretion and associated turbulence has ceased. We propose that CAIs also originate in the form of fine Al-rich dust within a coronal-type environment atop the disk. In this model only the CAIs among …
Gamma Rays, Cosmic Rays, And Extinct Radioactivity In Molecular Clouds, Liping Jin, Donald D. Clayton
Gamma Rays, Cosmic Rays, And Extinct Radioactivity In Molecular Clouds, Liping Jin, Donald D. Clayton
Publications
No abstract provided.
Cgro/Osse Observations Of The Cassiopeia A Supernova Remnant, Lih-Sin The, M D. Leising, Donald D. Clayton, W N. Johnson, R L. Kinzer, J D. Kurfess, M S. Strickman, G V. Jung, D A. Grabelsky, W R. Purcell
Cgro/Osse Observations Of The Cassiopeia A Supernova Remnant, Lih-Sin The, M D. Leising, Donald D. Clayton, W N. Johnson, R L. Kinzer, J D. Kurfess, M S. Strickman, G V. Jung, D A. Grabelsky, W R. Purcell
Publications
Cas A, the youngest known supernova remnant in the Galaxy and a strong radio and Xray source, was observed by OSSE July 16 - August 6, 1992. Its close distance (¸ 3 kpc) and its young age (¸ 300 yrs) make Cas A the best candidate among known supernova remnants for detecting 44 Ti fl-ray lines. We find no evidence of emission at 67.9 keV, 78.4 keV, or 1.157 MeV, the three strongest 44 Ti decay lines. From simultaneous fits to the three lines our 99% confidence upper limit to the flux in each line is 5.5Theta10 Gamma5 fl cm …
Search For Important Weak Interaction Nuclei In Presupernova Evolution, Maurice B. Aufderheide, Ikko Fushiki, Stanford E. Woosley, Dieter H. Hartmann
Search For Important Weak Interaction Nuclei In Presupernova Evolution, Maurice B. Aufderheide, Ikko Fushiki, Stanford E. Woosley, Dieter H. Hartmann
Publications
A search is made for the most important electron captures and beta-decays after core silicon buring in massive stars. A nuclear statistical equilibrium code is used to compute isotopic abundances. Electron capture and beta-decay rates are estimated for the 150 most abundant istopes in a simplifiec fashion which generally includes the strongest transitions. These estimates are made for nuclei in the fp-shell and use techniques similar to Fuller, Fowler, & Newman (1982a), and are compared to them. The general behaviour of Y is examined. These methods are then used to follow a typical stellar trajectory, seeking the most important weak …
The 57co Abundance In Sn 1987a, Donald D. Clayton, M D. Leising, Lih-Sin The, W N. Johnson, J D. Kurfess
The 57co Abundance In Sn 1987a, Donald D. Clayton, M D. Leising, Lih-Sin The, W N. Johnson, J D. Kurfess
Publications
We discuss several astrophysical consequences of the detection by OSSE (Kurfess et al. 1992) of 57Co gamma radiation from supernova 1987A. Models with low photoelectric absorption cannot account for both OSSE data and the bolometric luminosity. By burying the alpha-rich-freezeout portion at deeper gamma depths than in published models, we show that it remains barely possible that the bolometric luminosity during days 1200-1800 could derive from 57Co power without requiring 57/56 production ratios greater than twice solar. We illustrate this by slowing the expansion within the inner four solar masses of ejecta in model 10HMM.
Sic Particles From Asymptotic Giant Branch Stars: Mg Burning And The S-Process, Lawrence E. Brown, Donald D. Clayton
Sic Particles From Asymptotic Giant Branch Stars: Mg Burning And The S-Process, Lawrence E. Brown, Donald D. Clayton
Publications
The question of whether isotopically anomalous SiC particles found in meteorites originate in AGB stars is addressed. It is shown that if the peak helium shell flash temperatures of massive (6-9 solar masses) stars are about 10 percent larger than they are normally assumed to be, alpha particle reactions with the magnesium will become significant. Then the (Mg-29)(alpha, n)Si-29 reaction produces a large excess of Si-29. With a light element nuclear reaction network, the evolution of the silicon isotopic composition during AGB evolution is calculated. It is found that the experimentally determined correlation between excess Si-29 and excess Si-30 in …
Stochastic Evolution Of Refractory Interstellar Dust During The Chemical Evolution Of A Two-Phase Interstellar Medium, Kurt Liffman, Donald D. Clayton
Stochastic Evolution Of Refractory Interstellar Dust During The Chemical Evolution Of A Two-Phase Interstellar Medium, Kurt Liffman, Donald D. Clayton
Publications
The evolution course of refractory interstellar dust during the chemical evolution of a two-phase interstellar medium (ISM) is studied using a simple model of the chemical evolution of ISM. It is assumed that, in this medium, the stars are born in molecular clouds, but new nucleosynthesis products and stellar return are entered into a complementary diffuse medium; the well-mixed matter of each interstellar phase is repeatedly cycled stochastically through the complementary phase and back. The dust is studied on a particle-by-particle bases as it is sputtered by shock waves in the diffuse medium, accretes an amorphous mantle of gaseous refractory …
Origin Of Heavy Xenon In Meteoritic Diamonds, Donald D. Clayton
Origin Of Heavy Xenon In Meteoritic Diamonds, Donald D. Clayton
Publications
The neutrino burst from the collapsed core in Type II supernovae liberates free neutrons by nu, nu-prime(n) reactions which drive isotopic abundances several mass steps heavier. The neutron fluence in the He shell, abetted by another burst 10 s later from alpha, n reactions, is about right for rendering Xe-136, the most abundant Xe isotope. The Xe isotopic composition is a good match to Xe-H, the unshielded neutron-rich Xe component abundant in carbonaceous meteorites. The He shell is implicated because it is the only C-rich shell in massive stars that can be expected to condense solid carbon thermally, a requirement …
Isotopic Anomalies: Chemical Memory Of Galactic Evolution, Donald D. Clayton
Isotopic Anomalies: Chemical Memory Of Galactic Evolution, Donald D. Clayton
Publications
New mechanisms for the chemical memory of isotopic anomalies are proposed which are based on the temporal change during the chemical evolution of the Galaxy of the isotopic composition of the mean ejecta from stars. Because of the differing temporal evolution of primary and secondary products of nucleosynthesis, the isotopic composition of the bulk interstellar medium changes approximately linearly with time, and thus any dust component having an age different from that of average dust will be isotopically anomalous. Special attention is given to C, O, Mg, Si, and isotopically heavy average-stellar condensates of SiC.
Positron Annihilation Gamma Rays From Novae, M D. Leising, Donald D. Clayton
Positron Annihilation Gamma Rays From Novae, M D. Leising, Donald D. Clayton
Publications
The potential for observing annihilation gamma rays from novae is investigated. These gamma rays, a unique signature of the thermonuclear runaway models of novae, would result from the annihilation of positrons emitted by beta(+)-unstable nuclei produced near the peak of the runaway and carried by rapid convection to the surface of the nova envelope. Simple models, which are extensions of detailed published models, of the expansion of the nova atmospheres are evolved. These models serve as input into investigations of the fate of nearby Galactic fast novae could yield detectable fluxes of electron-positron annihilation gamma rays produced by the decay …
Positron Annihilation Gamma Rays From Novae, Mark D. Leising, D D. Clayton
Positron Annihilation Gamma Rays From Novae, Mark D. Leising, D D. Clayton
Publications
The potential for observing annihilation gamma rays from novae is investigated. These gamma rays, a unique signature of the thermonuclear runaway models of novae, would result from the annihilation of positrons emitted by beta(+)-unstable nuclei produced near the peak of the runaway and carried by rapid convection to the surface of the nova envelope. Simple models, which are extensions of detailed published models, of the expansion of the nova atmospheres are evolved. These models serve as input into investigations of the fate of nearby Galactic fast novae could yield detectable fluxes of electron-positron annihilation gamma rays produced by the decay …
Galactic Chemical Evolution: Z Versus In(1/Mu) Relationship, Donald D. Clayton
Galactic Chemical Evolution: Z Versus In(1/Mu) Relationship, Donald D. Clayton
Publications
The ways in which a radial abundance gradient in a disk galaxy may be interpreted are reexamined, asking how metallicity Z depends upon gas mass fraction mu in analytic models characterized by a temporally varying history of metal-poor infall. Six different such models are studied, and it is shown that the metallicity versus gas fraction relationship is well approximated by an expression which is the analog of the Z = y ln(1/mu) relation for closed evolution. The approximation appears valid when the infall rate is nonneglible, but not so great that it dominates the gas budget.
Secondary Metallicity In Analytic Models Of Chemical Evolution Of Galaxies, Donald D. Clayton, Irani Pantelaki
Secondary Metallicity In Analytic Models Of Chemical Evolution Of Galaxies, Donald D. Clayton, Irani Pantelaki
Publications
Analytic models of the chemical evolution of galactic regions that grow in mass owing to the continuous infall of matter are characterized, emphasizing the solutions for secondary nuclei (defined as those nuclei whose stellar yields are proportional to the abundance of a primary seed nucleus) in the families of models described by Clayton (1984 and 1985). Wide variations in time dependence of both primary and secondary nuclei as well as in the ratio of secondary to primary are displayed by these model families, confirming again the usefulness of these families as interpretive guides if galaxies do in fact evolve with …