An attempt to interpret the temperature profile of the KTB pilot drillhole (Germany) by paleoclimatic considerations

The temperature profile of the KTB pilot drillhole, T(z)_KTB-PH,is distinctly nonlinear: a temperature deficit ΔT (relative to a linear temperature-depth profile) is especially pronounced in the depth range 500–3500 m. The depth dependence of the deficit, Δ(z) is compared to be anticipated effect of surface paleoclimatic variations, ΔT_pc(z), at the drillsite on the temperature profile. The latter can be calculated from available paleo-climatic models. If ΔT_pc(z) is added to T(z)_KTB-PH, a nearly linear temperature-depth curve results with an average geothermal gradient of 27.9°C/km. This, together with an average vertical thermal conductivity of 3.0 W/mK, estimated from KTB drillcore data, implies a heat flow density at the KTB site of 84 mW/m². This modelled value is in good agreement with heat flow determinations in the adjacent Eger graben structure (Western Bohemian massif).     

Thermal bremsstrahlung hard X-rays and primary energy release in flares

Various methods are explored for obtaining regularized solutions of the severely ill-posed Laplace inversion problem involved in deriving plasma temperature (T) structure (differential emission measure(T)) from bremsstrahlung spectra. Inversions of simulated data show that zero-order regularisation (Tikhonov regularisation inL ² space) is very unsatisfactory even with weighting, while first-order regularisation (Tikhonov regularisation in Sobolev space) yields reasonable results.The method is applied to a high-resolution hard X-ray flare spectrum observed by Lin and Schwartz (1987) and yields a positive solution for(T) showing that a purely thermal interpretation is possible for that event. The form of(T) found has two broad features: one peaking at around 10⁷ K and falling off steeply toward 2 × 10⁸ K; a second spread around a peak near 4.5 × 10⁸ K. The interpretation of such(T) in terms of plasma heating and conductive flux is discussed in terms of plasma heat fluxes and heating rates. For 1-D geometry, the distribution of the plasma heating rateH(T) per unit volume is inferred from(T) in the limits of classical diffusive conduction and of saturated heat flux, the former being relevant atT below around 5 × 10⁷ K and the latter at much higherT. We find there exists a maximum inH(T) around 2 × 10⁸ K, a fact which may be important for energy release theories.     

The brightness temperatures of solar type III bursts

There is a characteristic maximum brightness temperature T _B 10¹⁵K for type III solar radio bursts in the solar wind. The suggestion is explored that the maximum observed values of T _Bmay be attributed to saturation of the processes involved in the plasma emission. The processes leading to fundamental and second harmonic emission saturate when T _Bis approximately equal to the effective temperature T _Lof the Langmuir waves. The expected maximum value of T _Bis estimated for this saturation model in two ways: from the growth rate for the beam instability, and from the maximum amplitude of the observed Langmuir turbulence. The agreement with the observed values is satisfactory in view of the uncertainties in the estimates (a) of the intrinsic brightness temperature from the observed brightness temperature, (b) of the actual growth rate of the beam instability, which must be driven by local, transient features (that are unobservable using available instruments) in the electron distribution, and (c) in the k-space volume filled by the Langmuir waves, and this is consistent with the observational data on two well-studied events at the orbit of the Earth and with statistical data for events over a range of radial distances from the Sun.     

On the temperature of the helium emission regions in the solar atmosphere

An analysis of the spectral distribution of intensity of the Hei recombination continuum is probably the only direct method for determination of the electron temperature of helium emission regions on the Sun. On the basis of data on the Hei Lyman continuum, obtained by Dupree and Reeves from OSO-4, the electron temperature of undisturbed helium regions is determined: T _e = = 12500 K. Such a low T _e value is a serious argument in favour of the predominant role of UV coronal radiation in the helium ionization on the Sun. Comparison of the Hei Lyman continuum data with results of observations of the 10830 line showed that the visible helium lines and Hei Lyman continuum are produced within the same regions of the undisturbed solar atmosphere at T _e = 12500 K.     

Chaos in the solar system

We have accumulated thousands of orbits of test particles in the Solar System from the asteroid belt to beyond the orbit of Neptune. We find that the time for an orbit to make a close encounter with a perturbing planet, T _c ,is a function of the Lyapunov time, T _ty .The relation is log (T _c /T _o )= a + b log (T _ly T _o )where T _o is a fiducial period which we have taken as the period of the principal perturber or the period of the asteroid. There are exceptions to this rule interior to the 2/3 resonance with Jupiter. There, at least in the restricted problem, for sufficiently small Jupiter mass, orbits may have a positive Lyapunov exponent and still be blocked from having a close approach to Jupiter by a zero velocity curve. Of more serious concern is whether the relation holds for purely secular resonances, and if it does, how to choose T _o .This is the case of interest for the planets in the solar system.     

Density and temperature diagnostics of solar emission lines from NeV/MgV and SiVII/MgVII Ions

We present NeV/MgV and SiVII/MgVII theoretical line intensity ratios as a function of electron densityN _e and temperatureT _e . These are shown in the form of ratio-ratio diagrams, which should in principle allow bothN _e andT _e to be deduced for the emitting region of the solar plasma. We apply these diagnostics in the solar atmosphere, and discuss the available observations made from space. In most cases, however, we deduceN _e andT _e from the computed absolute line intensities in a spherically symmetric model atmosphere of the Sun. Possible future applications of this investigation to spectral data from the Coronal Diagnostic Spectrometer (CDS) on the Solar and Heliospheric Observatory (SOHO) are briefly discussed.     

Subsurface temperature—depth profiles, anomalies due to climatic ground surface temperature changes or groundwater flow effects

Climatic temperature changes at the ground surface propagate downward to the subsurface creating transient disturbances to the temperature—depth (T(z)) profile. Due to the poor thermal diffusivity of rocks the disturbances are preserved long times in the bedrock, and in a conductive regime it is possible to reveal the ground surface temperature (GST) history from borehole temperature data with inversion techniques. Geothermal temperature measurements thus provide a source of palaeoclimatic information which so far has not been utilized extensively. Inversion of GST history is, however, not straightforward and any disturbing effects should be excluded before the data can be utilized in inversion. Groundwater flow is of special importance in this respect because it is a common phenomenon in bedrock and convection often produces temperature—depth profiles resembling those affected by palaeoclimatic GST changes. In interpreting temperature—depth (T(z)) logs it is therefore not always clear whether the recorded vertical gradient variations should be attributed to the effects of palaeoclimatic ground surface temperature (GST) changes or to groundwater circulation. Using several synthetic T(z) profiles and applying general least squares inversion techniques we simulate a situation of “misinterpreting” the curvature of the T(z) profile in terms of palaeoclimatic GST changes, although it is actually produced by convective heat transfer due to groundwater flow. For comparison the opposite case is also studied, namely, genuine palaeoclimatic effects are misinterpreted as being due to disturbances caused by groundwater flow. A homogeneous half-space model is used to model T(z) profiles disturbed conductively by GST changes during the time interval 10–10000 yr B.P. and a one-dimensional porous layer model is applied for convective heat transfer calculations. The results indicate that a given T(z) profile can be attributed to either of these effects with reasonable parameter values. In addition to the synthetic T(z) profiles, a case history from a 958 m deep drill hole at Lavia, southwestern Finland, is presented. Special care is needed in analyzing T(z) data. A knowledge of geothermal data, such as temperature, thermal conductivity and diffusivity is not necessarily adequate for determining which of the phenomena (or whether a combination of them) provides the most probable interpretation of a T(z) profile. Additional information on the hydrogeological properties of the drilled strata is essential.     

Do EUV Nanoflares Account for Coronal Heating?

Recent observations with EUV imaging instruments such as SOHO/EIT and TRACE have shown evidence for flare-like processes at the bottom end of the energy scale, in the range of E _th≈10²⁴–10²⁷ erg. Here we compare these EUV nanoflares with soft X-ray microflares and hard X-ray flares across the entire energy range. From the observations we establish empirical scaling laws for the flare loop length, L(T)∼T, the electron density, n _e(T)∼T ², from which we derive scaling laws for the loop pressure, p(T)∼T ³, and the thermal energy, E _th∼T ⁶. Extrapolating these scaling laws into the picoflare regime we find that the pressure conditions in the chromosphere constrain a height level for flare loop footpoints, which scales with h _eq(T)∼T ^−0.5. Based on this chromospheric pressure limit we predict a lower cutoff of flare loop sizes at L _∖min≲5 Mm and flare energies E _∖min≲10²⁴ erg. We show evidence for such a rollover in the flare energy size distribution from recent TRACE EUV data. Based on this energy cutoff imposed by the chromospheric boundary condition we find that the energy content of the heated plasma observed in EUV, SXR, and HXR flares is insufficient (by 2–3 orders of magnitude) to account for coronal heating.     

Nonlinear boussinesq convective model for large scale solar circulations

We present extensive numerical calculations for a model of thermal convection of a Boussinesq fluid in an equatorial annulus of a rotating spherical shell. The convection induces and maintains differential rotation and meridian circulation. The model is solved for an effective Prandtl number P = 1, with effective Taylor number T in the range 10² <T <10⁶, and effective Rayleigh number R between the critical value for onset of convection, and a few times that value. With = 2.6 × 10^–6 s^–1, d = 1.4 × 10¹⁰ cm (roughly the depth of the solar convection zone) the range of Taylor number is equivalent to kinematic viscosities between 10¹⁴ and 10¹² cm² s^–1, which encompasses eddy viscosities estimated from mixing length theory applied to the Sun.The convection does generally make equatorial regions rotate faster, the more so as T is increased, but local equatorial deceleration near the surface is also produced at intermediate T for large enough R above critical. The differential rotation is maintained primarily through momentum transport in the cells up the gradient, rather than by meridian circulation. Differential rotation energy increases relative to cell energy with increasing T, surpassing it near T = 3 × 10⁴. The differential rotation tends to stretch out the convective cells, analogously to what is thought to happen to solar magnetic regions. Differential rotation and meridian circulation energies are nearly equal for T = 10³, but the meridian circulation energy falls off relative to differential rotation like T ^–1 for larger T. The meridian circulation is always toward the poles near the surface, contrary to models of Kippenhahn, Cocke, Köhler, and Durney and Roxburgh. The radial shear produced in the differential rotation is almost always positive, as in the Köhler model, but contrary to the assumptions made by Leighton for his random walk solar cycle model.Solutions in the neighborhood of T = 3 × 10⁴ seem to compare best with various solar observations including differential rotation amplitude, cell wavelength, tilted structure, horizontal momentum transport, and weak meridian circulation. The local equatorial deceleration (equatorward of 10–15°) has not been observed, although the techniques of data analysis may not have been sensitive to it. The most important deficiency of the model is that all the solutions with T 10³ show the vertical heat transport a rather strong function of latitude, with a maximum at the equator, no evidence of which is seen at the solar surface.The National Center for Atmospheric Research is sponsored by The National Science Foundation.     

Flare Plasma Cooling from 30 MK down to 1 MK modeled from Yohkoh,GOES, and TRACE observations during the Bastille Day Event (14 July 2000)

We present an analysis of the evolution of the thermal flare plasma during the 14 July 2000, 10 UT, Bastille Day flare event, using spacecraft data from Yohkoh/HXT, Yohkoh/SXT, GOES, and TRACE. The spatial structure of this double-ribbon flare consists of a curved arcade with some 100 post-flare loops which brighten up in a sequential manner from highly-sheared low-lying to less-sheared higher-lying bipolar loops. We reconstruct an instrument-combined, average differential emission measure distribution dEM(T)/dT that ranges from T=1 MK to 40 MK and peaks at T ₀=10.9 MK. We find that the time profiles of the different instrument fluxes peak sequentially over 7 minutes with decreasing temperatures from T≈30 MK to 1 MK, indicating the systematic cooling of the flare plasma. From these temperature-dependent relative peak times t _peak(T) we reconstruct the average plasma cooling function T(t) for loops observed near the flare peak time, and find that their temperature decrease is initially controlled by conductive cooling during the first 188 s, T(t)∼[1+(t/τ_cond)]^−2/7, and then by radiative cooling during the next 592 s, T(t)∼[1−(t/τ_rad)]^3/5. From the radiative cooling phase we infer an average electron density of n _e=4.2×10¹¹ cm⁻³, which implies a filling factor near 100% for the brightest observed 23 loops with diameters of ∼1.8 Mm that appear simultaneously over the flare peak time and are fully resolved with TRACE. We reproduce the time delays and fluxes of the observed time profiles near the flare peak self-consistently with a forward-fitting method of a fully analytical model. The total integrated thermal energy of this flare amounts to E _thermal=2.6×10³¹ erg. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1014257826116     

A model of impulsive loop flares revisited

A critical examination of the components of the recent impulsive loop flare model of Takakura is made. It is found that his analysis of the stability of the electron distribution resulting from anomalous heat conduction is in error and electron plasma waves would not be excited. Rather, in the regions where the electron/proton temperature ratioT _e/T _i 10, electrostatic ion-cyclotron waves would be excited and in the regions whereT _e 10, ion-acoustic waves would be excited. Ratios ofT _e/T _i 10 occur only in the late time development behind the conduction fronts. Since the anomalous resistivity due to electrostatic ion-cyclotron waves is fortuitously about 70% of the one used by Takakura, the general development will follow closely the one calculated by him. Because the anomalous resistivity due to ion-acoustic waves is about 95 times the one used by Takakura, the development in the parts of the loop whereT _e/T _i 10 for late times would be altered considerably.Also Guest Worker at NOAA Space Environment Laboratory, Boulder, Colorado, U.S.A.     

Relation between superheating and superacceleration of helium in the solar wind

Solar-wind data obtained by the OGO-5 and IMP-6-8 Earth satellites show a positive correlation between the ratio of helium to hydrogen temperatures, T /T _p, and the velocity difference between the two ions, v - v _p . Although this result disagrees with the Prognoz-1 results reported earlier in this journal, it is consistent with the expected control by Coulomb collisions when the solar-wind density is high.     

The peculiarities of diffusion of the galactic cosmic rays at low energies

I give an interpretation of a result of Simpsonet al. (1988) on the variation with kinetic energyT _i of the mean pathlengthX _m (T _i ) of the galactic cosmic rays (CGRs) in the range 0.1T _i 10.0 GeV nucl^–1. I argue that the data onX _m (T _i ) may be interpreted in terms of a model of GCR diffusion on the one-dimensional Alfvén-wave turbulence, having a cutoff in the spectrum at frequencies _h , where _h is the proton gyrofrequency. The cutoff results in changing of the character of variation of the GCR diffusion coefficientD(T _i )T ^a in the rangeT _i 1 GeV nucl^–1 towards some more complicated variation at 0.1T _i 1.0 GeV nucl^–1 due to the peculiarities of the pitch-angle scattering at 90⁰.     

An electron temperature distribution derived from optical and radio measurements of HII regions

Radio measurements of the electron temperature ofHii regions are obtained from the ratio of the brightness temperature of a hydrogen recombination line to that of the adjacent continuum, while optical measurements are obtained from the ratio of [Oiii] forbidden-line intensities. The radio and optical measurements made under the assumption of an isothermalHii region,T _R andT _opt respectively, are combined to derive a temperature distribution for an entire nebula. A sphericalHii region in local thermodynamic equilibrium with constant density which is optically thin in both the line and the continuum is used as a model. Assuming linear temperature gradients withT _R=6000K andT _opt=10000K, it is found thatT=12000K (1–0.74r/R), wherer is the distance from the center andR is the radius of the nebula.     

Non-thermal solar wind heating by supra-thermal ions

The effect of a new energy source due to energies transferred from supra-thermal secondary ions on the temperature profile of the solar wind has been considered. For this purpose a solution of a tri-fluid model of the solar wind including solar electrons, protons, and -particles, and starting with the boundary conditions of Hartle and Barnes at 0.5 AU is given. On the base of the assumption that suprathermal He⁺-ions which have four times the temperature of suprathermal protons are predominantly coupled to solar -particles by Alfvén waves, it is shown that the temperature T of solar -particles should be appreciably higher than those T _p of solar protons beyond the orbit of the Earth. For 1 AU a temperature excess T over T _p according to that which has been found in some solar wind ion spectrograms can only be explained for a small part of the orbit of the earth which is inside the cone of enhanced helium densities. Around 1 AU the temperatures T and T _p are found to decrease much slighter with solar distance than given in the two-fluid model of Hartle and Barnes. Beyond 1.7 and 2.2 AU the temperatures T and T _p even start increasing with solar distance and come up to about 10⁵ at about 10 AU. These predictions should lend some support to future temperature measurements with deep-space probes reaching Solar distances of some AU.Forschungsberichte des Astronomischen Institutes, Bonn, 72-10.     

Thermalization of solar wind

Three kinetic equations describing the linear and non-linear wave-particle interaction for an anisotropic solar wind plasma have been developed. These equations have been solved numerically to find the variation inT /T with respect to time, whereT andT are the perpendicular and parallel temperatures with respect to the ambient magnetic field of the solar wind. For wave energy greater than a critical value (strong turbulence), non-linear wave-particle interactions are important but do not lead to thermalization. On the other hand, weak nonlinear interactions tend to increaseT /T , but make only a negligible contribution in the quantitative sense. Thus, only the linear wave-particle interaction remains as the significant contributer to the increase ofT /T .     

Singularitäten in der Allgemeinen Relativitätstheorie

“Regular solutions of EINSTEIN 's equations” mean very different things. In the case of the empty-space equations, R_ik = 0, such solutions must be metrics g_ik(x^l) without additionaly singular “field sources” (EINSTEIN 's “Particle problem”). – However the “phenomenological matter” is defined by the EINSTEIN equations R_ik – 1/2g_ikR =–xT_ik itselves. Therefore if 10 regular functions g_ik(x^l) are given (which the inequalities of LORENTZ -signature fulfil) then these g_ik define 10 functions T_ik(x^l) without singularities. But, the matter-tensor T_ik must fulfil the two inequalities T ≥ 0, T ≥ 1/2 T only and therefore the EINSTEIN -equations with “phenomenological matter” mean the two inequalities R ≥ 0, R ≤ 0 which are incompatible with a permanently regular metric with LORENTZ -signature, generally.     

The relationship between r.m.s. doppler velocities and temperature in the solar transition region

An attempt is made in this paper to determine the coefficient a in a power-law relationship of the form V ~T between the r.m.s. velocity fluctuation, V for raster images with 3 resolution and the temperature, T of line formation using SMM solar data. For T between 8000 and 10⁵ K, the data suggest a best fit with 3/4 < 1. It is argued, however, that unresolved fine structure tends to reduce the observed value of V and that higher resolution data may yield different values for . Skylab data have shown that the non-thermal line broadening velocity, , is proportional to T ^1/2. Also, for all temperatures less than 10⁵ K, V . This latter result, however, is again dependent on spatial resolution and may not be true in observations made with sufficient spatial resolution. The magnitudes of both V and indicate that bulk motions play important roles in the structure of the solar atmosphere as well as in its energy and momentum balance. It is important, therefore, to identify the true nature of such motions with better accuracy than is possible with currently available data.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Cosmochronology with the87Rb/87Sr isobaric pair

The long-lived cosmochronometer⁸⁷Rb (T _1/2=4.8×10¹⁰ yr) is studied. As its origin is partly due tos- and partly tor-process nucleosynthesis it can provide information about the time histories of these processes. The methods of using⁸⁷Rb quantitatively for a chronological analysis are described. Tentative calculations based on existing experimental data are also presented. The data indicate a larger-process age than thes-process age.     

Thermal properties of the solar wind plasma

In the solar wind, electrostatic ion cyclotron waves can be excited by electrons when the flow velocity becomes supersonic. The waves reduce the proton temperature anisotropy and heat the protons effectively. Temperature equations for T _e ,T _p and T _p are solved numerically in the region from 1 AU to the Sun, with the non-thermal proton heating rate included as a parameter. Distributions of T _e ,T _p , T _p and the proton heating rate are determined and found to be in good agreement with the proton heating rate expected from the linear growth rate of electrostatic ion cyclotron waves. The electron thermal conductivity is reduced approximately 2–3 times smaller than the usual collisional one due to the plasma wave instabilities. Effective energy exchange rates from proton-proton and electron-proton interactions are 1–10 and 10–100 times larger than the Coulomb collision rates v ppand v ep,respectively.