Radiative Loss Function Research Articles

Damping and Dispersion of Non-Adiabatic Acoustic Waves in a High-Temperature Plasma: A Radiative-Loss Function

The behavior of acoustic waves in a rarefied high-temperature plasma is studied; as an example, the plasma of the solar corona is considered. Effects of thermal conductivity and a heating/radiative loss are taken into account; data on a temperature distribution of a radiation intensity obtained from the CHIANTI 10 code are used. The classical Spitzer expression for a full-ionized plasma is used for the thermal conductivity. Based on the found values of the radiation-loss function, the cubic spline method is used to construct an approximate analytical expression necessary for studying linear waves. A dispersion relation is obtained, and a frequency, a phase speed, and a damping coefficient are found. Dispersion and damping properties are considered for a temperature of about 106 K and a particle density of about 1015m−3, which are typical for the coronal plasma. In sum, superiority in the dispersion and damping of the thermal conduction is shown; the heating and radiation loss manifest themselves at large wavelengths. In accordance with general results by Field, a condition was found under which the acoustic oscillations become unstable. It is shown that at certain values of the temperature and density, the wave damping is dominated by the heating/radiative loss misbalance. Thus, the earlier results on mechanisms of damping of observed acoustic waves in the solar corona are refined here.

The Effect of the Chromospheric Temperature on Coronal Heating

Recent observational and numerical studies show a variety of thermal structures in the solar chromosphere. Given that the thermal interplay across the transition region is a key to coronal heating, it is worth investigating how different thermal structures of the chromosphere yield different coronal properties. In this work, by MHD simulations of Alfvén-wave heating of coronal loops, we study how the coronal properties are affected by the chromospheric temperature. To this end, instead of solving the radiative transfer equation, we employ a simple radiative loss function so that the chromospheric temperature is easily tuned. When the chromosphere is hotter, because the chromosphere extends to a larger height, the coronal part of the magnetic loop becomes shorter, which enhances the conductive cooling. A larger loop length is therefore required to maintain the high-temperature corona against the thermal conduction. From our numerical simulations we derive a condition for the coronal formation with respect to the half loop length l loop in a simple form: , where is the minimum temperature in the atmosphere, and parameters a and l th have negative dependencies on the coronal field strength. Our conclusion is that the chromospheric temperature has a nonnegligible impact on coronal heating for loops with small lengths and weak coronal fields. In particular, the enhanced chromospheric heating could prevent the formation of the corona.

QUASI-PERIODIC FLUCTUATIONS AND CHROMOSPHERIC EVAPORATION IN A SOLAR FLARE RIBBON OBSERVED BY HINODE/EIS, IRIS, AND RHESSI

ABSTRACT The Hinode/Extreme-ultraviolet Imaging Spectrometer (EIS) obtained rapid cadence (11.2 s) EUV stare spectra of an M7.3 flare ribbon in AR 12036 on 2014 April 18. Quasi-periodic (P ≈ 75.6 ± 9.2 s) intensity fluctuations occurred in emission lines of O iv, Mg vi, Mg vii, Si vii, Fe xiv, and Fe xvi during the flare's impulsive rise, and ended when the maximum intensity in Fe xxiii was reached. The profiles of the O iv–Fe xvi lines reveal that they were all redshifted during most of the interval of quasi-periodic intensity fluctuations, while the Fe xxiii profile revealed multiple components including one or two highly blueshifted ones. This indicates that the flare underwent explosive chromospheric evaporation during its impulsive rise. Fluctuations in the relative Doppler velocities were seen, but their amplitudes were too subtle to extract significant quasi-periodicities. RHESSI detected 25–100 keV hard-X-ray sources in the ribbon near the EIS slit's pointing position during the peaks in the EIS intensity fluctuations. The observations are consistent with a series of energy injections into the chromosphere by nonthermal particle beams. Electron densities derived with Fe xiv (4.6 × 1010 cm−3) and Mg vii (7.8 × 109 cm−3) average line intensity ratios during the interval of quasi-periodic intensity fluctuations, combined with the radiative loss function of an optically thin plasma, yield radiative cooling times of 32 s at 2.0 × 106 K, and 46 s at 6.3 × 105 K (about half the quasi-period); assuming Fe xiv's density for Fe xxiii yields a radiative cooling time of 103 s (13 times the quasi-period) at 1.4 × 107 K.

Modelling low-lying, cool solar loops with optically thick radiative losses

We investigate the increase of the DEM (differential emission measure) towards the chromosphere due to small and cool magnetic loops (height $\lesssim8$~Mm, $T\lesssim10^5$~K). In a previous paper we analysed the conditions of existence and stability of these loops through hydrodynamic simulations, focusing on their dependence on the details of the optically thin radiative loss function used. In this paper, we extend those hydrodynamic simulations to verify if this class of loops exists and it is stable when using an optically thick radiative loss function. We study two cases: constant background heating and a heating depending on the density. The contribution to the transition region EUV output of these loops is also calculated and presented. We find that stable, quasi-static cool loops can be obtained by using an optically thick radiative loss function and a background heating depending on the density. The DEMs of these loops, however, fail to reproduce the observed DEM for temperatures between $4.6<\log T<4.8$. We also show the transient phase of a dynamic loop obtained by considering constant heating rate and find that its average DEM, interpreted as a set of evolving dynamic loops, reproduces quite well the observed DEM.

Stability of thermal modes in cool prominence plasmas

Context: Magnetohydrodynamic thermal modes may play an important role in the formation, plasma condensation, and evolution of solar prominences. Unstable thermal modes due to unbalance between radiative losses and heating can lead to rapid plasma cooling and condensation. An accurate description of the radiative loss function is therefore crucial for this process. Aims: We study the stability of thermal modes in unbounded and uniform plasmas with properties akin to those in solar prominences. Effects due to partial ionization are taken into account. Three different parametrizations of the radiative loss function are used. Methods: By means of a normal mode analysis, we investigate linear nonadiabatic perturbations superimposed on the equilibrium state. We find an approximate instability criterion for thermal modes, while the exact linear growth rate is obtained by numerically solving the general dispersion relation. The stability of thermal disturbances is compared for the three different loss functions considered. Results: Using up-to-date computations of radiative losses derived from the CHIANTI atomic database, we find that thermal modes may be unstable in prominences for lower temperatures than those predicted with previously existing loss functions. Thermal instability can take place for temperatures as low as 15,000 K, approximately. The obtained linear growth rates indicate that this instability might have an important impact on the dynamics and evolution of cool prominence condensations.

The bound-bound and free-free radiative losses for the nonthermal distributions in solar and stellar coronae

Context. The radiative-loss function is an important ingredient in the physics of the solar corona, transition region, and flares.Aims. We investigate the radiative losses due to the bound-bound transitions and bremsstrahlung for nonthermal κ - and n -distributions.Methods. The bound-bound radiative losses are computed by integrating synthetic spectra. An analytical expression is derived for nonthermal bremsstrahlung. The bremsstrahlung is computed numerically using accurate values of the free-free Gaunt factor.Results. We find that the changes in radiative-loss functions due to nonthermal distributions are several times greater than the errors due to the missing contribution of the free-bound continuum or errors in atomic data. For κ -distributions, the radiative-loss functions are in general weaker than for Maxwellian distribution, with a few exceptions caused by the behavior of Fe. The peaks of the radiative-loss functions are in general flatter. The situation is opposite for n -distributions, for which the radiative-loss functions have higher and narrower peaks. Local minima and maxima of the radiative-loss functions may also be shifted. The contribution from bremsstrahlung only changes by a few percent except in the extreme nonthermal case of κ = 2. Stability analysis reveals that the X-ray loops are stable against the radiatively-driven thermal instability.

Analytical model of static coronal loops

By solving the energy-equilibrium equation in the stationary case, we derive analytical formulae in the form of scaling laws for non-uniformly heated and gravitationally stratified coronal loops. The heating is assumed to be localized in the chromosphere and to exponentially decrease with increasing distance along the loop strand. This exponential behavior of the heating and pressure profiles implies that we need to use the mean-value theorem, and in turn fit the mean-value parameters of the scaling laws to the results of the numerical simulations. The radiative-loss function is approximated by a power-law function of the temperature, and its effect on the resulting scaling laws for coronal loops is studied. We find that this effect is more important than the effect of varying loop geometry. We also find that the difference in lengths of the different loop strands in a loop with expanding cross-section does not produce differences in the EUV emission of these strands significant enough to explain the observed narrowness of the coronal loops.

The Origin of High‐Speed Motions and Threads in Prominences

Prominences are among the most spectacular manifestations of both quiescent and eruptive solar activity, yet the origins of their magnetic-field and plasma structures remain poorly understood. We have made steady progress toward a comprehensive model of prominence formation and evolution with our sheared three-dimensional arcade model for the magnetic field and our thermal nonequilibrium model for the cool, dense material suspended in the corona. According to the thermal nonequilibrium model, condensations form readily along long, low-lying magnetic field lines when the heating is localized near the chromosphere. In most cases this process yields a dynamic cycle in which condensations repetitively form, stream along the field, and ultimately disappear by falling onto the nearest footpoint. Two key observed features were not adequately explained by our earlier simulations of thermal nonequilibrium, however: the threadlike (i.e., elongated) horizontal structure and high-speed motions of many condensations. In this paper we discuss how simple modifications to the radiative loss function, the heating scale, and the geometry of our model largely eliminate these discrepancies. In particular, condensations in nearly horizontal flux tubes are most likely to develop both transient high-speed motions and elongated threads. These results strengthen the case for thermal nonequilibrium as the origin of prominence condensations and support low-twist models of prominence magnetic structure.

Prominence Formation by Thermal Nonequilibrium in the Sheared‐Arcade Model

The existence of solar prominences—cool, dense, filamented plasma suspended in the corona above magnetic neutral lines—has long been an outstanding problem in solar physics. In earlier numerical studies we identified a mechanism, thermal nonequilibrium, by which cool condensations can form in long coronal flux tubes heated locally above their footpoints. To understand the physics of this process, we began by modeling idealized symmetric flux tubes with uniform cross-sectional area and a simplified radiative-loss function. The present work demonstrates that condensations also form under more realistic conditions, in a typical flux tube taken from our three-dimensional MHD simulation of prominence magnetic structure produced by the sheared arcade mechanism. We compare these results with simulations of an otherwise identical flux tube with uniform cross-sectional area, to determine the influence of the overall three-dimensional magnetic configuration on the condensation process. We also show that updating the optically thin radiative loss function yields more rapidly varying, dynamic behavior in better agreement with the latest prominence observations than our earlier studies. These developments bring us substantially closer to a fully self-consistent, three-dimensional model of both magnetic field and plasma in prominences.

Study of the detachment phases in the Wendelstein 7-AS stellarator

An experimental overview of the detachment process in the W7-AS stellarator with island divertors is given. Results of different spectroscopic methods are combined with those of Langmuir probes and neutral pressure measurements. Two phases of the detachment process are identified: the detachment transition due to the unstable range of the radiative loss function of carbon and a volume recombination phase for densities well above those needed for the onset of detachment. The first phase is characterized by a sudden drop in the temperature at the plasma edge and in the divertor. As a consequence, the particle fluxes at the divertor targets on top and at the bottom are reduced to a different degree, depending on the region. In the second phase, the plasma between the strike lines in the upper divertor is strongly recombining. Simultaneously, a strong carbon radiation belt is observed in the inboard scrape-off layer. The physical mechanisms of both phases are discussed.

Spectroscopic study of the radiation in divertor I of ASDEX Upgrade at high density

Radiation losses in divertor I of ASDEX Upgrade have been studied at high density when the divertor is detached. Spectroscopic measurements in the visible and VUV spectral range allow a characterization of both the impurity source and radiation. Despite very low target temperatures of 1 eV, carbon is released from the target with high rates by chemical sputtering. Power losses are estimated from the resonance lines of deuterium and the carbon ions. A comparison with bolometry shows that 80% of the emission can be ascribed to carbon and deuterium. The composition of the carbon emission is compared with results obtained on JT-60 and DIII-D. Using the Braams-Eirene model of the detached divertor the influence of transport on the power losses is investigated. By means of a realistic radiative loss function we find that the enhancement of maximum power input into the divertor by non-coronal effects is not more than a factor of two.

Cooling of solar flares plasmas. 1: Theoretical considerations

view Abstract Citations (174) References (33) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Cooling of Solar Flare Plasmas. I. Theoretical Considerations Cargill, Peter J. ; Mariska, John T. ; Antiochos, Spiro K. Abstract Theoretical models of the cooling of flare plasma are reexamined. By assuming that the cooling occurs in two separate phase where conduction and radiation, respectively, dominate, a simple analytic formula for the cooling time of a flare plasma is derived. Unlike earlier order-of-magnitude scalings, this result accounts for the effect of the evolution of the loop plasma parameters on the cooling time. When the conductive cooling leads to an 'evaporation' of chromospheric material, the cooling time scales L5/6/p1/6, where the coronal phase (defined as the time maximum temperature). When the conductive cooling is static, the cooling time scales as L3/4n1/4. In deriving these results, use was made of an important scaling law (T proportional to n2) during the radiative cooling phase that was forst noted in one-dimensional hydrodynamic numerical simulations (Serio et al. 1991; Jakimiec et al. 1992). Our own simulations show that this result is restricted to approximately the radiative loss function of Rosner, Tucker, & Vaiana (1978). for different radiative loss functions, other scaling result, with T and n scaling almost linearly when the radiative loss falls off as T-2. It is shown that these scaling laws are part of a class of analytic solutions developed by Antiocos (1980). Publication: The Astrophysical Journal Pub Date: February 1995 DOI: 10.1086/175240 Bibcode: 1995ApJ...439.1034C Keywords: Cooling; Coronal Loops; Magnetohydrodynamics; Numerical Analysis; Plasmas (Physics); Solar Flares; Conductive Heat Transfer; Mathematical Models; Radiative Heat Transfer; Scaling Laws; Temperature Distribution; Solar Physics; MAGNETOHYDRODYNAMICS: MHD; PLASMAS; SUN: CORONA; SUN: FLARES full text sources ADS |

Instabilities in colliding winds

The significance of radiative cooling for the stability properties of colliding astrophysical flows is shown. In the cases of WR ring nebula NGC 6888 and WR binary V444 Cyg it is found that thermal instabilities in the radiative loss function A(T) Tβ, β = β(T) not only have an influence on the dynamics of the collision zone, but also that they lead to a quasi-periodic increase of the radiated energy.

Some implications of the nanoflare concept

view Abstract Citations (233) References (71) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Some Implications of the Nanoflare Concept Cargill, Peter J. Abstract The concept that the corona is heated by small flares (named 'nanoflares' by Parker) is examined. A model in which the closed, active region corona is comprised of many hundred of small elemental flux loops randomly heated by nanoflares is presentd. The cooling of these flux loops is examined using analytic techniques. It is assumed that the heated loops cool initially by conduction and at later times by radiation. Radiative cooling with and without downward mass flows are discussed, the experimental signature of such a coronal model are predicted. The distribution of temperatures in these loops peaks at around 2 x 106 K, while the distribution of densities peaks above 1010/cu cm. For 2 x 105 K less than T less than 106 K, radiative cooling with mass flows gives an emission measure that scales as T1.5, in agreement with existing observations. For T greater than 106 K, the emission measure increases more steeply, scaling as T4.5. These scalings are entirely due to the temperature dependence of the radiative loss function. It is shown that such a loop model has filling factors (defined as the ratio of the volume of hot plasma to the total volume) of order unity for subarcsecond energy release scales. A brief survey of the dependence of the results on the parameters of the system is presented. The temperature distribution function and emission measure are relatively insensitive to the loop length, coronal energy loss, number of elemental loops, and nanoflare energy, but the filling factor is dependent on these quantities. A simple scaling for this dependence is presented. Publication: The Astrophysical Journal Pub Date: February 1994 DOI: 10.1086/173733 Bibcode: 1994ApJ...422..381C Keywords: Coronal Loops; Solar Cooling; Solar Corona; Solar Flares; Solar Physics; Solar Temperature; Magnetohydrodynamics; Numerical Analysis; Stellar Models; Solar Physics; MAGNETOHYDRODYNAMICS: MHD; SUN: CORONA; SUN: FLARES full text sources ADS |

A one-dimensional model for radiative thermal equilibrium and stability of the tokamak edge plasma

The multifaceted asymmetric radiation from the edge (MARFE) instability observed in the peripheral radiative layer in the high-density tokamaks is considered for a spatially smooth profile of radiative-loss function in equilibrium. The instability which is driven by the impurity radiation and opposed by the finite thermal conductivity, was considered previously by Drake [J. F. Drake, Phys. Fluids 30, 2429 (1987)] as a surface wave on a sharp radiative layer (step-function-like) at the edge. A novel exponential model is presented for the radiative loss function and it is shown that the two crucial features of MARFE: (i) stability to poloidally symmetric perturbations and (ii) a threshold value of radiative loss for the growth of asymmetric perturbations, explained earlier by Drake’s theory, are contained in this model of radiative equilibrium, also. Since, from the earlier theory, these features appear to be equilibrium specific and related to the form of radiative-loss function, the present work broadens the class of radiation profiles which can explain the MARFE, by recovering all the old results by an entirely different mathematical treatment.

Stability, structure, and evolution of cool loops

The criteria for the existence and stability of cool loops are reexamined. It is found that the stability of the loops strongly depends on the form of the heating and radiative loss functions and that if the Ly-alpha peak which appears in most calculations of the radiative loss function is real, cool loops are almost certainly unstable. Removing the hydrogen contribution from the recent loss function Q(T) by Cook et al. (1989) does not produce the much-used result, Q proportional to T-cubed, which is so favorable to cool loop stability. Even using the probably unrealistically favorable loss function Q1 of Cook et al. with the hydrogen contribution removed, the maximum temperature attainable in stable cool loops is a factor of 2-3 too small to account for the excess emission observed in lower transition region lines. Dynamical simulations of cool loop instabilities reveal that the final state of such a model is the hot loop equilibrium.

The effects of nonequilibrium ionization on the radiative losses of the solar corona

The emissivity of the ions of carbon and oxygen has been recalculated for a set of solar coronal loop models with a steady state siphon flow. The ion densities were calculated from the plasma velocities, temperatures, and densities of the models, and large departures from equilibrium were found. For purposes of comparison, the emissivity was calculated with and without the approximation of ionization equilibrium. Considerable differences in the radiative loss function Lambda(T) curve between equilibrium and nonequilibrium conditions were found. The nonequilibrium Lambda(T) function was then used to solve again the steady state flow equations of the loop models. The differences in the structure of these models with respect to the models calculated adopting the Lambda(T) curve in equilibrium are discussed.

A comparison between bright points in a coronal hole and a quiet-sun region

A comparison is made of the morphological structure and temporal behavior of the emission from coronal bright points in a coronal hole and a quiet region, using data from the Harvard EUV experiment on Skylab. It is found that, in both regions, coronal bright points are located at network boundaries and cover a range of sizes from 10 to 40 in in linear extent. In a given bright pint, the peaks of emission in the six different lines, measured simultaneously through the same instrument slit, are not always cospatial, implying that bright points consist of a complex of small-scale loops at different temperatures. The intensity of bright points in both regions is also characterized by a significant temporal variability in all the wavelengths measured. This variability exhibits no regular periodicity. Yet the ratio of the varying (ac) to the constant (dc) components of the emission, in all the bright points studied, has a local maximum at 1-2 x 10 to the 5th k which coincides with the peak of the radiative loss function, and another local maximum at Mg x (1.4 x 10 to the 6th K). It is found that coronal bright points in a coronal hole or a quiet region are indistinguishable structures, and, therefore, conclude that they are independent of the overlying background corona.

Flare Loop Radiative Hydrodynamics - Part Two - Thermal Stability of Empirical Models

view Abstract Citations (54) References (18) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Flare Loop Radiative Hydrodynamics - Part Two - Thermal Stability of Empirical Models McClymont, A. N. ; Canfield, R. C. Abstract The importance of loop structures in the corona, both for flares and for the quiet Sun, has stimulated considerable attention to questions of their thermal stability. Previous studies have focused attention on the coronal part of the loop. In this paper we examine loop stability by treating the entire observable loop, from its photospheric footpoints to its coronal apex. This approach allows the chromosphere and corona to interact naturally, thus avoiding possibly artificial boundary conditions imposed at transition region footpoints. We develop a numerical eigenfunction method for the study of stability, which is based on the methods discussed in a previous paper. For exemplary purposes, we have applied these methods to several loop models based on semiempirical model chromospheres, under the assumption that the rate of ambient energy input per unit mass of plasma depends only on column depth. Our principal study is of a loop model based on the semiempirical model F of Vernazza, Avrett, and Loeser. We find that this loop model has one unstable eigenmode, with a growth time of 2 minutes. This mode appears in the transition region, centered on the peak of the optically thin radiative loss function at T ≍ 105 K. However, we provide evidence that suggests that this instability may not be a feature of real loops. More importantly, we find that (1) this atmosphere is stable to the hydrogen-induced radiative instability of optically thin gases at temperatures around 104.3 K; (2) were it not for radiative transfer effects, this atmosphere would be dramatically unstable, with growth times in the range 1 ≤ r ≤ 18 s; and (3) the stability when radiative transfer is taken into account can be understood primarily as a result of the reduction of the peak in the radiative loss rate at 104.3 K, due to hydrogen, that would exist if the chromosphere were optically thin. This reduction is due to the significant optical depth, and consequent low escape probability, of radiation of the dominant coolant, Lyα, at upper temperatures. Publication: The Astrophysical Journal Pub Date: February 1983 DOI: 10.1086/160693 Bibcode: 1983ApJ...265..497M full text sources ADS |

Theoretical chromospheric flare spectra

The equations of radiative transfer and statistical equilibrium are solved simultaneously for a model hydrogen atom including Lyman- alpha , Lyman- BETA , Balmer- alpha . and the Lyman, Balmer, and Paschen continua. The model atmospheres are the results of Nakagawa et al. (1973) for a kinematic model of the chromospheric solar flare. It is found that the models adequately predict the total intensity of B alpha , its wing broadening, the presence of a redshifted wing, the maximum electron density, the total line-ofsight second- level population, and the narrowness in height of the B alpha emitting region. The profile of B alpha is strongly self-reversed, however, and agrees with observations only in the presence of 40 to 70 km s/sup -1/ macroturbulent motion. It is found that Nakagawa et al. (1973) seriously overestimate the radiative loss function, which will have a large effect on their models. Proper radiative loss calculations must be included in any physically realistic model. (auth)