Mechanical Energy Flux Research Articles

On the relation between coronal heating, flux tube divergence, and the solar wind proton flux and flow speed

A one-fluid solar wind model is used to investigate some relations between coronal heating, the flux tube divergence near the Sun, and the solar wind proton flux and flow speed. The effects of energy addition to the supersonic region of the flow are also studied. We allow for a mechanical energy flux that heats the corona, and an Alfven wave energy flux that adds energy, mainly to the supersonic flow, both as momentum and as heat. We find that the mechanical energy flux determines the solar wind mass flux, and in order to keep an almost constant proton flux at the orbit of Earth with changing flow geometry, that the mechanical energy flux must vary linearly with the magnetic field in the inner corona. This thermally driven wind generally has a low asymptotic flow speed. When Alfven waves are added to the thermally driven flow, the asymptotic flow speed is increased and is determined by the ratio of the Alfven wave and the mechanical energy fluxes at the coronal base. Flow speeds characteristic of recurrent high-speed solar wind streams can be obtained only when the Alfven wave energy flux, deposited in the supersonic flow, is larger than the mechanical energy flux heating the corona.

On radiating baroclinic instability of zonally varying flow

The baroclinic instability characteristics of zonally varying flow are examined in a quasigeostrophic, two-layer, beta-plane model. The most unstable eigenmode is determined numerically by solving a one-dimensional initial value problem. Emphasis is placed on determining how the basic state vertically averaged wind, U B , local maximum in vertical wind shear, Δ U T , and length of the locally unstable region, λ L , combine to yield local instabilities whose energy fluxes radiate deep into the locally neutral far field. The existence of such zonally radiating instabilities (RIs), which represent a transition between trapped and global instabilities, requires that λ L not exceed some critical value and that Δ U T / U B lie within a certain range. In sharp contrast to the trapped and global instabilities, the RIs have horizontal wavelengths that increase dramatically with distance from the locally unstable region. If λ L and Δ U T / U B are both sufficiently small, the local instability that emerges is characterized by a vertical asymmetry in its horizontal spatial structure; the disturbance in the upper layer has a longer zonal wavelength than its counterpart in the lower layer. For slowly varying basic states, analysis of the local disturbance energetics reveals that the baroclinic energy conversion predominates within the locally unstable region. For basic states that vary rapidly in the downstream direction, the barotropic energy conversion associated with the horizontal deformation field may predominate over the baroclinic conversion depending on the relative importance of Δ U T and U B . For RIs, the energy budget outside the locally unstable region is primarily due to the advection of total energy and the convergence of mechanical energy flux. Calculations of the basic state tendencies show that the net effect of the local (trapped or radiating) instabilities is to redistribute energy from the baroclinic to the barotropic component of the basic state flow. The fluxes produced by the trapped modes reduce the vertical shear downstream of the jet center, while the fluxes produced by the radiating modes reduce the vertical shear both downstream and near the jet center. DOI: 10.1034/j.1600-0870.1993.00005.x

Macroscopic properties of a two-phase potential dispersion composed of identical unit cells

The potential flow solution for flow of fluid past dispersed objects in a “unit cell” is used to derive several macroscopic properties, including the mean pressures in the phases and on the walls, the momentum and kinetic energy density, the force function and mechanical energy flux. These properties are derived from the “resistivity” of the unit cell, which has a tensorial character in general. Various macroscopic forms of Bernoulli's equation relate the properties. Equations of motion for uniform arrays of cells are derived. Various other features, such as minimization of kinetic energy density and forces at concentration jumps, are analyzed.

Rotating Stellar Interiors (Review Paper)

AbstractRotation has two main qualitative effects on the structure of a star: it distorts the shape and it reduces the total luminosity. The luminosity depends only on the total angular momentum but the shape, and so the observable properties, depends on the internal distribution of angular momentum. The expected distribution, even for main-sequence stars, is an unsolved problem. Redistribution of angular momentum can occur as a result of large-scale circulation currents, instabilities and magnetic stresses and there may be no steady state. If shear instabilities are dominant, then stars may rotate nearly uniformly. Studies of non-radial oscillations might perhaps eventually lead to a direct probing of the internal angular momentum distribution by the methods now being used to study the internal rotation of the Sun. Differential rotation near the surface would probably give rise to turbulent motions, which could generate the mechanical energy flux which seems to be a necessary input to the winds in hot stars.

On the existence of hot coronae around cool stars

A star cannot have a solar-like corona if the available mechanical energy flux in the chromosphere is either too large or decreases outward more rapidly than the pressure. This result might be relevant for hybrid stars and cool giants.

On the extended chromosphere of Alpha Orionis

A detailed examination of the extended chromosphere of Alpha Orionis was performed in an attempt to characterize the matter-emitting processes of red giants and supergiants. The problem was approached using an Alfven wave driven stellar wind model to compute the density, temperature, and velocity structure of the wind. It is shown that the mechanical energy fluxes necessary to maintain the observed chromospheric temperatures are commensurate with the momentum deposition necessary to extend the chromosphere. The chromospheric model constructed is, however, inconsistent with the kinematics of the observed symmetric profiles, which could correspond to a fountain-type model that described infalling, rather than escaping, ejected material such as He.

Stellar Winds and Spindown — Observations

Stars with masses ≲ 1 M⊙are observed to rotate more slowly as they age. The angular momentum loss is undoubtedly caused by the coupling of the stellar magnetic field to the escaping wind (Schatzman 1962). Chromospheric and coronal radiative losses depend upon rotation (Wilson 1966a, b; Kraft 1967; Skumanich 1972; Hall 1976; Bopp 1980; Walter and Bowyer 1981; Walter 1981; Vaiana et al. 1981). It is therefore likely that both magnetic fields (Skumanich 1972) and the mechanical energy fluxes required to drive mass loss also depend upon rotation as well. This complicated feedback between magnetic fields, winds, and rotation must control the variation of solar-type activity over much of the HR diagram, and may have very important effects on pre-main sequence evolution.

Photoelectric observations of propagating sunspot oscillations

Repeated intensity and velocity images of a large, isolated sunspot in both the chromospheric Ca II 8542 A and photospheric Fe I 5576 line were performed. It is shown by means of a movie of the digital data for the chromospheric line that a relationship exists between the propagating umbral disturbances and the running penumbral waves. Power spectra of the oscillations show a sharp peak at a period of about 170 sec in both the velocity and intensity signals, and the oscillations at any point in the sunspot are found to be very regular. The phase relationship between the velocity and the intensity of the chromospheric oscillations contrasts with that for the quiet sun. The mechanical energy flux carried by the observed umbral disturbances does not appear to be a significant contributor to the overall energy budget of the sunspot or the surrounding active region.

Mechanical wave-energy fluxin magnetoatmospheres: Discrete and continuous spectra

This paper deals with a rather general class of magnetoatmospheres — media for which the restoring forces of buoyancy, compressibility and magnetic tension/pressure are important in sustaining wave motion. The magnetic field has the general form (B0(z), 0,0) and there is also an aligned shear flow (U0(z), 0, 0) present. After discussion of the equilibrium and stability of such systems, and certain mathematical properties of a particular system (an isothermal atmosphere with uniform magnetic field, of interest in solar physics), theory is developed which enables expressions to be written down for the mechanical wave energy flux associated with wave motion due to a transient source. These analytic expressions are very general and contain contributions from the continuous and discrete frequency spectra, corresponding respectively to freely propagating and trapped (or surface) waves. These fluxes are evaluated for various ranges of magnetic field, horizontal wavenumber, characteristic source times and frequency, for a simple constant-parameter atmosphere. The source is taken to be a transient fluctuation of the lower boundary, (modelling convective overshoot) which is taken to be located at the level τ5000=0.08 in the solar atmosphere. The relative distribution of wave energy flux in the various modes is discussed in the context of solar physics parameters. The possible significance of ‘leaky’ modes arising from supergranular or other flow, for the local flux balance in the solar chromosphere is outlined.

Momentum and energy deposition in late-type stellar atmospheres and winds

The present study calculates the response of the outer atmospheres of cool low-gravity stars to the passage of the mechanical energy fluxes of solar magnitude in the form of acoustic waves and Alfven waves. It is shown that Alfven waves are efficient in generating outflow, and can account for the order of magnitude of observed mass loss in late-type luminous stars. However, unless these magnetic waves undergo some dissipation within several stellar radii of the surface, the predicted terminal velocities of the resulting stellar winds are far too high. Alfven wave dissipation should give rise to extended warm chromospheres in low-gravity late-type stars, a prediction which can be observationally tested.

Stellar Mass Flux and Coronal Heating by Shock Waves

The heating of the solar corona and the solar wind phenomenon are basically related, however, the two parts are generally modelised independently: the models of the transition zone and corona are restricted to levels lower than the temperature maximum and the solar wind models begin above it. Here we study a self-consistent oversimplified model which maintains the global balance of energy sources and sinks from the chromospheric level to the interplanetary medium. The heating mechanism chosen is the shock wave dissipation; it was shown by Gonczi et al (1977) that overlapping shock waves could carry a significant mechanical energy flux towards a static corona; here we apply the same mechanism to an expanding corona. The model includes self-consistently the different coupling between convective energy flux, conductive flux, radiative losses in optically thin atmosphere, shock wave pressure and dissipation terms. The input parameters are the base pressure, the base temperature and the mechanical flux introduced at chromospheric level in form of shock waves. If these three parameters allow a solar wind expansion, the output results are the radial variations of the density, of the temperature, of the solar wind velocity and of the mechanical flux. Due to the presence of a boundary layer associated to the steep temperature gradient in the transition zone, the three input parameters cannot be arbitrarily fixed, in fact when we impose two of them, the third one cannot vary within a large interval (i.e. within a factor of two or less), this point has been qualitatively discussed in a previous paper : Couturier et al. (1979)

Performance Energétique des Echangeurs de Matière et de Chaleur: Interprétation Energétique des Analogies de Reynolds et de Colburn

The conventional analogy between heat, mass and momentum transfer is presented here under its energy form: the fluxes of transfer for thermal energy and diffusional energy, as well as the flux of degradation for mechanical energy, are put in parallel. The Reynolds analogy is then given by ▪ in which the NTU are the classical ‘Number of Transfer Units’ and NEU is the ‘Number of Energy degradation Units’. The generalised Colburn analogy is given by ▪ The Lf numbers are only equal to unity in the particular case when the Colburn analogy is strictly observed. In general, they are used to represent the deviation from such an analogy. Numerical expressions of the Lf number are given as a function of the Reynolds number, for various types of exchangers: fixed or fluidised porous beds, particles in free sedimentation, etc. We define the energetic performance of a heat- or mass-exchanger as the ratio of the transferred enthalpy flux to the degraded mechanical energy flux. A general expression of the performance is established as a function of the Number of Transfer Units, and of the properties of a special exchanger taken as a reference unit and called the ‘double-unit-exchanger’. Such an exchanger is defined as that equivalent to one equilibrium theoretical stage in which one unit of energy is degraded.

Relationship between Envelope Structure and Energy Source of Non-Thermal Motions

AbstractThe ionization zone in the envelope of the late type stars is reasonably considered as a heat engine to transform some of the radiative energy into mechanical energy. This idea is suggestive for explaining Linsky and Haisch’s (1979) observation, which shows the sharp division into solar-type and non-solar type stars in the outer atmosphere. Also non-thermal velocity fields in “microturbulence” and in Wilson-Bappu effect are proposed to be formed essentially from this engine. Therefore, their envelope structure dependence observationally obtained is possibly explained by the envelope parameters (g, Te) dependence of the generated mechanical energy flux in this layer. If “microturbulence” is not contaminated by the other surface activities, it is expected to show a clear relation with envelope parameters (g, Te) similar to Wilson-Bappu effect.

Models of coronal hole flows

Models of plasma flow in a coronal hole fall naturally into four classes. These are: (i) radial flow on a streamline along which the divergence is assumed to vary differently than as the square of the radial distance from the Sun; (ii) global flow along streamlines determined in some independent manner; (iii) empirical models originating in, or based strongly on observation; (iv) dynamic models using magnetic and plasma boundary conditions low in the corona to find both the geometry of streamlines and the flow field. To date, models both of ideal coronal holes and of specific observed coronal holes indicate that flow velocities above 100 km s+1, and temperatures of perhaps 2 × 106K are possible at 2R ⊙ heliocentric distance, where densities of 2 × 105 cm+3 have been reported. These velocities are at, or just above the sound speed, although still sub-Alfvenic. There is also general agreement among models of large polar holes that conversion of mechanical wave energy flux into solar wind kinetic energy is occurring in the 2R ⊙ to 5R ⊙ range, perhaps occurs even further outwards, and that the magnitude and extent of this energy deposition depends on the size and on the geometrical divergence of the hole. However, each model exhibits distinct weaknesses counteracted only by the complimentary nature of the various types of models. Models in class (i) are simply not global representations, but are tractable when dealing with complex forms of the energy equation or with several ion species. Class (ii) models lack any geometrical information beyond the ad hoc assumption of known streamline geometry, but have the same advantages as those in class (i). Class (iii) models cannot determine streamline geometry within a hole and do not extend further from the Sun than the available data — although they place important constraints on models in the other classes. Class (iv) models are limited to simple forms of the energy equation and/or to quasi-radial flow, but are the only models producing self-consistent streamline geometries through inclusion of transverse magnetic stresses in the momentum equation. Most limitations in coronal hole flow models can be eliminated by using known numerical techniques to combine models in classes (i), (ii), and (iv). This would allow detailed models of coronal holes and corresponding interplanetary conditions to be developed for specific time periods, at the cost of flexibility and possibly also general conceptual understanding. Nevertheless, the concept of a coronal hole is now reasonably well established, and acceptable modelling approaches are rapidly filling the literature. It can be anticipated that the evolution of these models, together with present and future observations, will bring us much nearer to understanding coronal energetics and dynamics.

Dynamics of the solar transition zone

Time-resolved profiles of the 1548-A C IV line arising from the solar transition region are analyzed in order to determine whether the 300-sec oscillations characteristic of the photosphere and chromosphere penetrate into the transition zone and to measure the rms amplitude of transition-zone disturbances as well as their dependence on solar activity. The rms velocity amplitude is used to set limits on the mechanical energy flux available for solar heating. A power-spectrum analysis indicates that acoustic waves appear to have been detected in the transition zone, that at least one case of a strong 200- to 300-sec oscillation was observed, but that strong periodicities are not found on the average in either the intensity or the velocity field. It is suggested that the rms velocity that may be attributed to directly observable wave motion is between 3 and 7 km/s, depending on whether the individual emission elements seen in rocket spectra are coherent or independent in phase.

Hydrodynamic instability of convectively unstable atmospheres in shear flow

Results are presented concerning the interaction between regions of convectively unstable fluid, bounded above and below by stable fluid, with a basic horizontal flow field, sheared in a vertical direction. The analysis is conveniently based on the definition of the mechanical energy flux associated with wave motion in a stratified compressible fluid, and enables bounds to be placed on the real and complex phase velocities of overstable modes, in addition to some general results on the net upward wave energy flux. It is shown that purely exponentially growing modes (with horizontal wavevectors spanwise to the shear) do not exist. A known sufficient condition for the stability of stable atmospheres is reproduced here with an interesting modification, and details of energy-flux discontinuities at certain singular points of the equations are given. The work is relevant to any astrophysical and geophysical situations in which convectively unstable regions and shear flows are likely to be together present, but the special motivation here is that of describing some aspects of the interaction between supergranular flow and granular convection.

The Chromospheric Energy Balance

The problem of the solar atmospheric heat and energy balances is here divided into three sections. (i)Basically the problem is an outward temperature gradient involving additional radiation losses whose estimate involves a model atmosphere. Proposed models described are based on optical and radio emissions together with various theoretical considerations such as thermal conductivity. The models are useful in providing estimates of the required flux of mechanical energy from below. However, they are limited by the use of averaging processes, and the failure to take full account of the many structural features which make up the chromosphere.(ii)It has long been accepted that the main energy input is by acoustic waves generated in the ‘small-bubble’ Vitense model convection zone. We review recent observations of chromospheric magnetic and velocity fields and their interpretation which strongly suggest that this model is not valid and that the acoustic theory of heating is without basis. At the same time the new data remove the objections of Osterbrock and others to a theory of heating based on Alfvén and/or slow-mode hydromagnetic waves.(iii)Observations of a variety of individual magnetic-plasma chromospheric structures, together with the adoption of heating by waves which follow the field lines, suggest a new approach to the whole problem of the heat balance. We discuss the heating problem in a number of these magnetic-plasma structures including the emission network, spicules and related disk features, arch filament systems and flares.

Temperature-Density Structure in Coronal Helmets: the Quiescent Prominence and Coronal Cavity

view Abstract Citations (39) References (11) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Temperature-Density Structure in Coronal Helmets: the Quiescent Prominence and Coronal Cavity Pneuman, G. W. Abstract Physical processes which are most important in determining temperature and density distributions in closed coronal loop systems are studied within the context of how this type of magnetic geometry influences the local balance of mechanical energy flux, conductive flux, and radiative losses. For regions above the temperature maximum, there can be no net conductive loss since closed field lines prevent outward beat conduction and the vanishing temperature gradient at the level of the temperature maximum prohibits downward heat conduction there. Hence, the mechanical energy input at the base must ultimately be radiated away. This requirement, in addition to a condition on the lateral distribution of gas pressure at the level of T , is used in a computation which yields the density and temperature distribution throughout the helmet as a function of the mechanical energy input and magnetic field geometry. It is demonstrated that the quiescent prominences normally observed at the base of coronal helmets as well as the low-density cavity surrounding these structures are the natural consequences of the adjustment of density and temperature structui e in the helmet required to satisfy energy and mass balance conditions as modulated by the magnetic field. Publication: The Astrophysical Journal Pub Date: November 1972 DOI: 10.1086/151756 Bibcode: 1972ApJ...177..793P full text sources ADS |

A model of the chromosphere and transition zone. Radio and UV emission of these layers

A model of the chromosphere and transition zone for quiet regions of the Sun is given. The height dependence of temperature and density are different for the borders of the supergranules and for their inner parts. The difference is caused by the enhanced mechanical energy flux at the places of strengthened magnetic field. The average dependence of density on height is given by eclipse data, the corresponding values for temperatures are obtained by a trial and error method using calculation of solar radio emission for different wavelengths and comparison with observations. The adopted model is consistent with observational data on the solar visual, radio and UV emission. This model also accounts for the brightness distribution on spectroheliograms taken in Hα wings, K232 Caii and in several UV spectral lines.

Predicted X-ray fluxes of stellar coronas

Models of convection zones and corresponding mechanical energy fluxes were computed for 90 stellar photospheres with effective temperatures ranging from 2500 K to 41 600 K and acceleration of gravity values between 1 and 105. The most intense X-ray fluxes may be expected from stars with T ≈ 7200 K and logg ≈ 4. Detectable X-ray fluxes could be expected from Procyon, α Cen and β Cas.