We study a class of metric-variation $f(R)$ models that accelerates the expansion without a cosmological constant and satisfies both cosmological and solar-system tests in the small-field limit of the parameter space. Solar-system tests alone place only weak bounds on these models, since the additional scalar degree of freedom is locked to the high-curvature general-relativistic prediction across more than 25 orders of magnitude in density, out through the solar corona. This agreement requires that the galactic halo be of sufficient extent to maintain the galaxy at high curvature in the presence of the low-curvature cosmological background. If the galactic halo and local environment in $f(R)$ models do not have substantially deeper potentials than expected in $\ensuremath{\Lambda}\mathrm{CDM}$, then cosmological field amplitudes $|{f}_{R}|\ensuremath{\gtrsim}{10}^{\ensuremath{-}6}$ will cause the galactic interior to evolve to low curvature during the acceleration epoch. Viability of large-deviation models therefore rests on the structure and evolution of the galactic halo, requiring cosmological simulations of $f(R)$ models, and not directly on solar-system tests. Even small deviations that conservatively satisfy both galactic and solar-system constraints can still be tested by future, percent-level measurements of the linear power spectrum, while they remain undetectable to cosmological-distance measures. Although we illustrate these effects in a specific class of models, the requirements on $f(R)$ are phrased in a nearly model-independent manner.

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Models of f(R) Cosmic Acceleration that Evade Solar-System Tests

The question of what heats the solar corona remains one of the most important problems in astrophysics. Finding a definitive solution involves a number of challenging steps, beginning with an identification of the energy source and ending with a prediction of observable quantities that can be compared directly with actual observations. Critical intermediate steps include realistic modeling of both the energy release process (the conversion of magnetic stress energy or wave energy into heat) and the response of the plasma to the heating. A variety of difficult issues must be addressed: highly disparate spatial scales, physical connections between the corona and lower atmosphere, complex microphysics, and variability and dynamics. Nearly all of the coronal heating mechanisms that have been proposed produce heating that is impulsive from the perspective of elemental magnetic flux strands. It is this perspective that must be adopted to understand how the plasma responds and radiates. In our opinion, the most promising explanation offered so far is Parker's idea of nanoflares occurring in magnetic fields that become tangled by turbulent convection. Exciting new developments include the identification of the “secondary instability” as the likely mechanism of energy release and the demonstration that impulsive heating in sub-resolution strands can explain certain observed properties of coronal loops that are otherwise very difficult to understand. Whatever the detailed mechanism of energy release, it is clear that some form of magnetic reconnection must be occurring at significant altitudes in the corona (above the magnetic carpet), so that the tangling does not increase indefinitely. This article outlines the key elements of a comprehensive strategy for solving the coronal heating problem and warns of obstacles that must be overcome along the way.

On Solving the Coronal Heating Problem

We present an overview of solar flares and associated phenomena, drawing upon a wide range of observational data primarily from the RHESSI era Following an introductory discussion and overview of the status of observational capabilities, the article is split into topical sections which deal with different areas of flare phenomena (footpoints and ribbons, coronal sources, relationship to coronal mass ejections) and their interconnections We also discuss flare soft X-ray spectroscopy and the energetics of the process The emphasis is to describe the observations from multiple points of view, while bearing in mind the models that link them to each other and to theory The present theoretical and observational understanding of solar flares is far from complete, so we conclude with a brief discussion of models, and a list of missing but important observations

An Observational Overview of Solar Flares

I have used my newly calculated iron group line list together with my earlier atomic and molecular line data, 58,000,000 lines total, to compute new opacities for the temperature range 2000K to 200000K. Calculations have been completed at the San Diego Supercomputer Center for 56 temperatures, for 21 pressures, for microturbulent velocities 0, 1, 2, 4, and 8 km/s, for 3,500,000 wavelength points divided into 1221 intervals from 10 to 10000 nm, for scaled solar abundances [+1.0], [+0.5], [+0.3], [+0.2], [+0.1], [+0.0], [−0.1], [−0.2], [−0.3], [−0.5], [−1.0], [−1.5], [−2.0], [−2.5], [−3.0], [−3.5], [−4.0], [−4.5], and [−5.0]. I have rewritten my model atmosphere program to use the new line opacities, additional continuous opacities, and an approximate treatment of convective overshooting. The opacity calculation was checked by computing a new theoretical solar model that matches the observed irradiance. Thus far I have completed a grid of 7000 model atmospheres at 2 km/s for all the abundances, for the temperature range 3500K to 50000K, and for log g from 0.0 to 5.0. This grid will allow a consistent theoretical treatment of photometry from K stars to B stars. Fluxes are tabulated from .09 to 160 micrometers. Preliminary results are reported for many photometric systems. Work is underway on grids for other microturbulent velocities. Microturbulent velocity strongly affects the interpretation of Cepheid and RR Lyrae photometry. The models, fluxes, and colors are available on magnetic tape and will also be distributed on CD-ROMs.

Model Atmospheres for Population Synthesis

▪ Abstract The information on the chemical compositions of stars encoded in their spectra plays a central role in contemporary astrophysics. Stellar element abundances are, however, not observed: to decipher the spectral fingerprints in terms of abundances requires realistic models for the stellar atmospheres and the line-formation processes. Still today, the vast majority of abundance analyses of late-type stars rely on one-dimensional (1D), hydrostatic model atmospheres and the assumption of local thermodynamic equilibrium (LTE). In this review possible systematic errors in studies of F-, G- and K-type stars introduced by these questionable approximations are discussed. Departures from LTE are commonplace and often quite severe, in particular for low surface gravities or metallicities, with minority species and low-excitation transitions being the most vulnerable. Recently, time-dependent, 3D, hydrodynamical model atmospheres have started to be employed for stellar abundance purposes, with large differe...

New light on stellar abundance analyses: Departures from LTE and homogeneity.

The described investigation is concerned with the solution of the non-LTE optically thick transfer equations for hydrogen, carbon, and other constituents to determine semiempirical models for six components of the quiet solar chromosphere. For a given temperature-height distribution, the solution is obtained of the equations of statistical equilibrium, radiative transfer for lines and continua, and hydrostatic equilibrium to find the ionization and excitation conditions for each atomic constituent. The emergent spectrum is calculated, and a trial and error approach is used to adjust the temperature distribution so that the emergent spectrum is in best agreement with the observed one. The relationship between semiempirical models determined in this way and theoretical models based on radiative equilibrium is discussed by Avrett (1977). Harvard Skylab EUV observations are used to determine models for a number of quiet-sun regions.

Structure of the solar chromosphere. III. Models of the EUV brightness components of the quiet sun

In our previous papers we described the mathematical formalism and the computed results for energy-balance hydrostatic models of the solar transition region. In this paper we discuss in some detail the limitations of the hydrostatic and one-dimensional assumptions used. Then we analyze the determination of helium emission when diffusion is included. We use transport coefficients estimated from kinetic theory to determine the helium departures from local ionization balance. We calculate the helium spectra for each of our models and evaluate the role of helium in the energy transport. Also, we investigate the effects of coronal illumination on the structure of the transition region and upper chromosphere, and show how coronal illumination affects various EUV lines and the He I 10830 A line. Comparing with both absolute intensities and detailed line profiles, we show that our models are consistent not only with the observed hydrogen spectra but also with the available helium spectra.

Energy balance in the solar transition region. III - Helium emission in hydrostatic, constant-abundance models with diffusion

Semiempirical model atmospheres are presented for the darkest parts of large sunspot umbrae, regions have called umbral cores. The approach is based on general-purpose computational procedures that are applicable to different types of stellar atmospheres. It is shown that recent umbral intensity measurements of the spectral energy distribution may be accounted for by an umbral core atmospheric model that varies with time during the solar cycle; the observed center-limb variation can be accounted for by the properties of the model. Three umbral core models are presented, corresponding to the early, middle, and late phases of the solar cycle. These three models also may be regarded as having the properties of dark, average, and bright umbral cores respectively. The effects of atomic, opacity, and abundance data uncertainties on the model calculations are briefly discussed. For comparison, a new reference model for the average quiet solar photosphere is given.

A new sunspot umbral model and its variation with the solar cycle

A procedure is demonstrated that is used to compute a one-component model of the solar atmosphere, including in that model the photosphere, chromosphere, and chromosphere-corona transition zone. In particular, the equations are described that are solved in order to determine this theoretical model.

Structure of the Solar Chromosphere. Basic Computations and Summary of the Results

The energy balance in the lower transition region is analyzed by constructing theoretical models which satisfy the energy balance constraint. The energy balance is achieved by balancing the radiative losses and the energy flowing downward from the corona. This energy flow is mainly in two forms: conductive heat flow and hydrogen ionization energy flow due to ambipolar diffusion. Hydrostatic equilibrium is assumed, and, in a first calculation, local mechanical heating and Joule heating are ignored. In a second model, some mechanical heating compatible with chromospheric energy-balance calculations is introduced. The models are computed for a partial non-LTE approach in which radiation departs strongly from LTE but particles depart from Maxwellian distributions only to first order. The results, which apply to cases where the magnetic field is either absent, or uniform and vertical, are compared with the observed Lyman lines and continuum from the average quiet sun. The approximate agreement suggests that this type of model can roughly explain the observed intensities in a physically meaningful way, assuming only a few free parameters specified as chromospheric boundary conditions.

R. Loeser

Papers

Structure of the solar chromosphere. III. Models of the EUV brightness components of the quiet sun

Energy balance in the solar transition region. III - Helium emission in hydrostatic, constant-abundance models with diffusion

A new sunspot umbral model and its variation with the solar cycle

Structure of the Solar Chromosphere. Basic Computations and Summary of the Results

Energy balance in the solar transition region. I - Hydrostatic thermal models with ambipolar diffusion