Acta Geod. Geoph. Hung., Vol. 36(3), pp. 257-259 (2001)

NOTE ON THE ESTIMATING THE SUN'S RADIATION OUTPUT DURING THE MAUNDER MINIMUM AND

THE PROBLEM OF SOLAR VARIABILITY

W SCHRODER1 and H-J TREDER2

[Manuscript received August 30, 1999]

The general problem of solar variability (including the solar constant and various minima) is discussed in detail. We have no theoretical arguments about the ampli­tudes of the solar cycle, today. A new point is the statement of White et al. (1992) on the temperature of solar-type non-cycling stars. The theorems of the creation and annihilation of vorticity and magnetical fields prove that these processes essentially have a thermodynamical component.

Keywords: Maunder minimum; solar constant

I

The fundamental measure of the total solar irradiance is the solar constant J which is determined by the mean Sun-Earth distance and by the energy budget in the interior of the Sun. The mean distance is the major semi-axis of the Earth orbit and therefore a constant of celestial mechanics. The energy production and transport in the interior of the Sun must be constant at least during a Helmholtz­Kelvin period. Actually, the heat budget of the sun is constant during some billion years.

These theoretical expectations are in good correspondence with the extraterres­trial measurements of the absolute constant J during the last 12 years (cf. Frohlich 1992). The observed variations of the total solar constant have relative magnitudes

6: of less than 0.001. These variations involve statistical fluctuations over time

scales of minutes and long terms with periods of the solar activity T = 11 years. The existence of these long-term-variations is caused by the periodical increase

and reduction of vorticity and magnetic energy in the atmosphere of the Sun. The dynamic and magnetic energies of these fields come from the energy of the heat current from the interior to the atmosphere of the Sun. The reduction of the solar activity implies an additional transfer of dynamic and magnetic energy to the energy of the heat radiation.

The building of the coupled magnetic and vorticity fields during the time of increasing solar activity is a negative source of heat energy and the breakdown of these fields during the times of decreasing solar activity is a positive source of

27rt heat energy. At the extremes of the periodical activity (let us say at T = 0 and

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258 W SCHRODER and H-J TREDER

27ft T = 7f) these transfer processes are not likely and the active value of J is its mean

value J = Jo .

A solar cycle starts with a minimum of activity at which all heat transported 27ft

from the interior to the Sun's atmosphere becomes radiation energy (phase T = 0,

with J = Jo ). For 0 < 2;t < 7f, a small part of the heat energy converts into the

magnetic and dynamic energy of the sunspots and the actual radiation energy is 27ft

less than the mean value (J < Jo ). At the activity maximum (T = 7f) this energy

conversion is stopped (J = Jo ). In the phase 7f < 2;t < 27f the magnetic and

dynamic energies of the activity centres convert into heat and the solar radiation becomes larger than the mean value (J > Jo ). An approximate formula is: J =

Jo - J sin (2;t). The mean (total) solar irradiation is a constant given by Jo and

independent of the solar activity. The dependence of the Earth's climate on solar activity may be a periodical

effect with a period of 11 years. In the case of longer activities we have larger amplitudes of the variation of the Earth's climate during the 11 year period and for all shorter activities we have smaller variations of the Earth's climate. However, the mean irradiance during longer times is constant.

II

The magneto-hydro dynamical dynamo models of the solar activity give a good and stringent explanation of the periods. But, today, the dynamo-models only work in a quasilinear approximation. This means, that the models cannot present assertions as to the absolute activities and amplitudes of the solar activity and its cycles. Estimations concerning historical minima (e.g. the so-called Sporer-, Maunder minimum) do not have a theoretical basis because such statements are only interpretations of historical records and contemporary fossile dates from den­drochnology, glaciology, geochemistry etc. The climatological dates may be very interesting. However, the climatological effects are very small and may only have periods of 11 years. Longer periods are connected with solar activity (cf. Pecker and Runcorn 1990, Schroder 1992, Schroder and Treder 1999).

With regard to the discussions of climatological records we have to note that we do not have objective and reproducible quantitative measurements of temperatures before D Fahrenheit (1686-1736), R Reaumur (1683-1757) and A Celsius (1701-1742). For earlier times only qualitative statements and speculations are available. Exact dates for these times are given by the fossile data only.

The empirical arguments for long-term variations of solar activity (with peri­ods of hundred and more years) are originally based on historical documents and sources. All these assertions are "argument a ex silentio", and such arguments are very questionable. The main point is that the historical dates are very often depen­dent on the attention given to sky phenomena by the observers (Schroder 1984).

Acta Geod. Geoph. Hung. 36, 2001

THE MAUNDER MINIMUM 259

The fossile dates with regard to the historical effect of modulations of the so­lar corpuscular radiation or solar component of cosmic rays in facies, sediments, glaciers, fossiles are likely more objective dates. However, the search for such frozen effects about the variation of solar variability pre-supposes the existence of such variations for which we have no theoretical basis.

Contrary, the long-term variations of irradiance which caused secular change of global climate of the Earth may be physically impossible. We note, the postulated theoretical periods for the hypothetical correspondence of modulation of the solar activity with the Earth's climate are quite different and apparently depending on the questions and methods of the researchers. An exact theory of solar activities has to incorporate non-linear magneto-hydro dynamics- and thermodynamics aspects.

However, the applications of magneto-hydrodynamics and thermodynamics to large cosmical objects are based on linearizing approximations of essentially non­linear equations and the deductions of the evolution of the magnetical fields in cosmically or geological relevant periods becomes very difficult and unsolved.

Reference

Frohlich C 1992: In: Proc. Worksh. Solar et Rad. Stud., R F DonaHy ed., Boulder Pecker J C, Runcorn S K 1990: The earth's climate and variability of the sun over recent

millennia: geophysical, astronomical and archaeological aspects. The Royal Society, London

Schroder W 1984: Auroral Borealis (Das Polarlicht). Darmstadt, Wiss. BuchgeseHschaft Schroder W 1992: J. Geomag. Geoelectr., 44, 119-128. Schroder W, Treder H-J 1999: Geofis. Intern., 38, 197-20l. White 0, Skumanich A, Lean J, Livingstone W C, Keil S I 1992: The sun in a non-cycling

state (preprint)

Acta Gead. Geaph. Hung. 36, 2001