Solar-Terrestrial Physics/1970: Proceedings of the International Symposium on Solar-Terrestrial Physics Held in Leningrad, U.S.S.R. 12–19 May 1970

185 Pages·1972·5.164 MB·English

by  C. De Jager (auth.), C. de Jager, E. R. Dyer (eds.)

THE SUN
THE SUN
PART I
OF
SOLAR-TERRESTRIAL PHYSICS/1970
COMPRISING THE PROCEEDINGS OF THE
INTERNATIONAL SYMPOSIUM ON SOLAR-TERRESTRIAL PHYSICS
HELD IN LENINGRAD, U.S.S.R.
12-19 MAY 1970
Sponsored by COSPAR, IAU, IUGG-IAGA, and URSI
C. DEJAGER
Editor
E.R.DYER
General Editor of the Proceedings
D. REIDEL PUBLISHING COMPANY
DORDRECHT-HOLLAND
ISBN 978-90-277-0210-4 ISBN 978-94-010-3126-4 (eBook)
DOI 10.1007/978-94-010-3126-4
TABLE OF CONTENTS
C. DE JAGER / Solar Energy Sources 1
M. KUPERUS / Structure and Dynamics of the Solar Corona 9
v. BUMBA / Large-Scale Magnetic Fields and Activity Patterns on the Sun 21
A. B. SEVERNY / Local Magnetic Fields on the Sun 38
A. BRUZEK / Properties of Solar Active Regions 49
M. PICK / Permanent Sources of Particle Emission from the Sun 61
z. SVESTKA / Solar Discrete Particle Events 72
A. BOISCHOT / Solar Radiobursts 87
T. A. CHUBB / Evidence that Solar X-Ray Emission is of Purely Thermal Origin
(Also Observation of Far UV Flash During 28 August 1966 Proton Flare) 99
S. I. SYROVA TSKY / Particle Acceleration and Plasma Ejection from the Sun 119
H. ELLIOT / Particle Diffusion in the Solar Corona 134
H. W. DODSON and E. R. HEDEMAN / Time Variations in Solar Activity 151
A. B. SEVERNY and N. v. STESHENKO / Methods for the Forecasting of Solar
Flares 173
SOLAR ENERGY SOURCES
C.DE JAGER
The Astronomical Institute, Utrecht, The Netherlands
Abstract. The energy content of the sun is considered, and mechanisms for the dissipation and emis
sion of the various kinds of energy are examined. The most important energy flux is the radiant
flux originating from nuclear reactions in the solar interior. In the outermost 105 km of the solar
body this flux is transported convectively. On top of the convective layer, a region of about 600 km
thick constituting the photosphere and low chromosphere is in near-radiative equilibrium. The
structure of the chromosphere and corona is mainly due to a mechanical energy flux emanating
from the outer convective region. The various transient solar phenomena, which for a part involve
high energy processes in magnetic regions, demand thermodynamic upgrading of energy, which,
in general terms, can only occur in a motion field with locally a non-zero curl, i.e. solar differential
rotation or convection. It is shown that the secular decrease of solar rotational energy can be due
to the emission of transformed rotational energy by flares. It is suggested that this happens through
the intermediary of differential rotation, which in turns originates by coupling of the solar rotation
with convection (see Figure 1).
1. The Basic Problem of Solar-Terrestrial Physics
The basic problem of solar-terrestrial physics is to understand the interaction between
two celestial bodies, through the emission of particles, magnetic fields and electro
magnetic radiation from one to the other.
(a) The first body is a cloud of gas, mass 2 x 1033 gram, composition by mass
60% H, 40% He, and less than 1 % heavier particles, with a given age (5 x 109 years),
angular momentum, and magnetic moment.
(b) The other body, at a distance of 1.5 x 108 km, is diamagnetic but has a known
nearly poloidal magnetic field, has an atmosphere, with a given mass and compo
sition.
The above boundary values of the problem would suffice to establish the complete
picture of solar-terrestrial interactions. If we would fully understand it all, the data
would allow one to predict why a certain flare would originate at a certain moment
with its particular emissions, and one should be able to understand what is happening
in the solar atmosphere, interplanetary space, in the magnetosphere and ionosphere.
Yet the actual situation is different, and our insufficient knowledge of the application
of basic physics to astrophysical problems, let it be our lack of imagination, forces
us to build up the picture, as we actually do, from the observational side. The observa
tions are apparently the stepping stones that allow us to cross the river of our ignorance,
and to build up an as yet incoherent picture of solar-terrestrial relations.
2. Solar Energies
The sun has the following energy contents:
Gravitational energy being the energy acquired during the contraction of solar
Dyer (ed.), Solar Terrestrial Physics 11970: Part I, 1-8. All Rights Reser¥ed.
Copyright © 1972 by D. Reidel Publishing Company, Dordrecht-Holland.
2 C.DEIAGER
matter from infinity: EG=bGM2/R, where G is the gravitation constant, M the solar
mass=2 x 1033 g and R its radius=7 x 1010 cm; b is a factor of the order unity,
dependent on the internal mass distribution. With a reasonable assumption about b,
based on model computations, one finds EG = 8 X 1048 erg.
Thermal or translation energy ET = INkTd V, where N is the particle number density,
and d V a volume element. ET = 3 X 1048 erg.
The excitation and ionization energies
f
f
EEl = N L Vi {.~ xi} (Xli + XiieXiie)} d V,
J= 1 e= 1
where Vi is the fractional number of particles of species i, xii the degree of ionization
(j) of the particles i, and Xij the ionization energy; Xije is the excitation energy of
particles i in the state of ionization j and of excitation e. Generally one defines
ET+EEI=Ei, the internal energy. Further Ei+EG is the total supranuclear energy.
Hf'
Hydrogenic nuclear energy EH=Lk2 X dm where LI is the mass defect of alpha
particles with respect to four times the number of protons, per gram of protons
(LI =0.0072 gig); X the solar mass fraction of hydrogen, dm a mass element, and Ml
the mass of that part of the solar interior where nuclear reactions can occur; roughly
Ml~O.l M. With X=0.5, EH=6x 1051 erg.
Rotational energy ER = Iff r2ro2 dm = 2 x 1042 erg, where r is the distance between
the mass element dm and the axis of rotation, ro is the angular velocity.
The energy of differential rotation EDR = Iff r2(ro-w)2 dm, needs some evaluation,
since it depends on the way angular rotation is distributed through the solar body.
On the basis of various recent models of the solar inner rotation EDR ~ 2 x 1040 erg
may appear to be a good average value.
The magnetic energy EM = (l/4n) I B2 d V can not yet be estimated with any reasonable
certainty.
The subnuclear energy M c2 = 2 X 1054 erg is not important in the present context.
3. Energy Fluxes
If the above described energies would remain constant, the sun would be invisible
to any observer with any observational technique.
The way the sun interacts with the surrounding celestial bodies like the earth, is
by dissipation of any of the above given energies. This dissipation yields energy fluxes
F=dE/dt, that will next be estimated. The most important flux is the radiant flux FR,
due to thermonuclear H-+He reactions in the solar interior. Observationally:
FR = 3.8 x 1033(± 2%) erg sec-1,
which corresponds to a flux per cm2: fR = 6 X 1010 erg cm -2 sec -1. If the sun would
contract, its gravitational energy EG would decrease and Ei and ET would change
SOLAR ENERGY SOURCES 3
correspondingly. By a simple thermodynamic reasoning it can be shown that
3y -4
dET = dE; + dEG = 3( y-l) dEG,
1'=4-
where l' is the ratio of specific heats of matter. With (mono-atomic gases),
one obtains dET=!dE so that half of the lost gravitational energy would be emitted
G,
as radiation. However, in its actual phase of evolution the sun would slightly expand
rather than contract, but only so slowly that the corresponding fluxes are wholly
unimportant for the solar energy balance. So we may neglect the changes of the
gravitation, thermal, excitation and ionization energy contents of the sun as sources
of emitted energy.
Rotational energy can decrease by viscous losses due to non-uniform rotation of
the solar body, or through its transformation into magnetic energy and subsequent
annihilation or emission of magnetic fields. These losses of rotational and magnetic
energy (by neutralization or by dragging out of magnetic fields by expelled gases)
will be discussed in Section 5.
4. The Radiation Flux; Structure of the Outer Solar Convection Zone and Photosphere
The solar radiation flux FR may propagate outward in two modes: convectively
and radiatively. The mode that actually occurs in a certain part of the solar
body depends on which of the two absolute values of the temperature gradient is the
smaller:
the radiative gradient: (ddT)
16uT 4nr2'
r fad
or
(1 _! )!:
the convective gradient: (dT) = dP,
dr cony l' P dr
where is the absorption coefficient of solar matter, and (] the mass density; u is
I(;
Stefan-Boltzmann's constant; l' is the ratio of specific heats of matter. The importance
of convection is that it produces a system of up and downward motions, hence a
motion field with locally a non-zero curl. Therefore a convective region is a source
of waves, that can give rise to non-thermal effects like the heating of the solar corona,
and that may also lead to other suprathermal effects of wave-gas interaction.
There seems to be a small convective region in the very solar centre, but this may
have no direct influence on the sun's outer parts.
The travel time of a sound wave from the solar centre to its surface t.= J~ dr/v.
is of the order of a few hours, but it would be completely damped on its way out.
A radiative disturbance would take a time of
fR
t, = I(;7:P dr
o
where is the mean free path of a photon, the average lifetime of an excited state
I(; -1 7:
4 C.DEJAGER
and /3 a multiplication term describing the effect of the brownian motions of photons
propagating through the solar interior. With reasonable assumptions (K= 10-3 cm -1,
,= 10-8 sec; /3> 10) one obtains tr > 7 X 106 sec, i.e. more than 100 days. Solar core
flashes, should they ever exist, would be fully smeared out in time. Henceforth in
this paper we shall disregard the central convective region and its possible influence
on the outer layers.
The outer convective region is of far greater importance. It extends from a depth
of about 105 km up to very close to the surface and is manifest in the well-known solar
granulation pattern. Actually photospheric observations show the convective motions
to extend up to a level, about 200 km below the limb surface (monochromatic optical
depth at 5000 A: '5 = J~ K5 dr~O.I). In the uppermost 100 km of the convection zone
the observed average up- and downward velocities are about 2 km/sec in fair agree
ment with theoretical predictions; they decrease rapidly in the denser deeper regions.
Notwithstanding these large convective velocities the uppermost 100 or 200 km of
the convection zone are in near radiative equilibrium i.e. energy is transported
radiatively there, which is due to the large mean free paths of the photons in this
already very transparent part of the sun.
The radiative domain extends upward to '5 ~ 10-4, i.e. a level about 200 km above
the limb level. Hence the zone that is nearly completely in radiative equilibrium
occurs between monochromatic optical depths of approximately = 10 - and 2,
'5 4
and has a total thickness of about 600 km.
In this whole range of depths the temperature distribution is defined by the laws
of radiative equilibrium, but deviations occur at the two extremities. Near '5 = 10-5
a temperature inversion occurs and higher upward the temperature increases steeply.
This is due to dissipation of mechanical energy; waves emerging from the convection
zone and visible as large-scale vibrations of the upper photosphere and chromosphere,
propagate upward into the more and more tenuous outer solar layers. They carry
a mechanical energy fluxfm= 8(!v2vs, where v is the velocity amplitude of the waves,
Vs the velocity of sound, and 8 a quantity of the order unity. Since the mechanical flux
in the lowest chromospheric levels is constant with height the velocity amplitude
initially increases with decreasing (!. By the effect of second order terms in the wave
equation the waves, when propagating upward, lose their sinusoidal character and
change into shockwaves which dissipate energy. Otherwise stated: higher harmonics
with larger frequencies are generated: these are more efficient in dissipating energy.
The temperature in the region above '5 = 10-4 is nearly completely defined by the
dissipation of the mechanical energy flux by viscous losses in shock waves whereas
the main radiative flux passes without being absorbed. Hence we may call this upper
region the mechanical domain in contrast to the radiative and convective regions
below it. The mechanical flux as deduced from a comparison of the observed and
theoretically predicted temperature distributions near log '5 = - 4 is about 2 x 106 erg
cm-2 sec-1 hence 3 x 10-5 times the radiative flux.
We compare this flux with the total wave energy of a column with 1 cm2 cross
section of the solar convective zone.
SOLAR ENERGY SOURCES 5
'1 '1
'1 '2
Here and are the lower and upper limits of the convection zone, and v is the
velocity amplitude; g is the acceleration of gravity. A comparison of Ec withfm shows
that the dissipation efficiency of this energy is approximately 2 x 10-7 sec -1 • Yet this
relatively small amount of energy is sufficient for yielding the whole chromosphere,
corona and solar wind.
The various energies discussed in this paper are summarized in Table I.
TABLE I
Solar energies
Energy
---------------------------------
Gravitational EG = 8 X 1048 erg
Thermal ET =3 x 1048 erg
Rotational ER = 2 X 1042 erg
Differential rotation EDR = 2 X 1040 erg
Wave energy of convection Ee = 6 x 1035 erg
Energy of supergranulation ESG = 1034 erg
Nuclear (hydrogen) EH =6 x 1051 erg
Subnuclear Es = 2 X 1054 erg
5. The Origin of Solar Variability
First we have to determine the source of the energy of the solar transient phenomena.
Since the most important of these, like solar flares, involve particle energies ranging
from 1 to 109 eV, the mechanism seems to demand at least partial thermodynamical
upgrading of energy. It may therefore seem that the purely radiative flux, although
being the largest of all should be excluded, since the only way to upgrade energy
seems to be through rotational or magnetic phenomena, hence by the introduction of
waves or by magnetohydrodynamic processes. However, it will be shown that the
convection zone, where the main solar energy flux is transported convectively may
contribute to this upgrading process.
TABLE II
Emitted flare energies
Component Characteristic Average Total Emitted or
particle particle number of carried
energy E density particles total
(cm-3) involved energy
JNdV (erg)
Optical flare plasma 2 eV 3 x 1013 3 X 1036 1031
Interplanetary plasma front 0.5keV 1089 1030
High energy flare plasma 20 keY 1010 1038 1030
(Sub-)relativistic particle component 0.2GeV 2 x 1033 1030
6 C.DEJAGER
We wish to compare the energy contents listed in Table I with the energy dissipated
in solar flares. In Table II we give values derived by us for a medium-type flare, of
importance 2. The table makes clear that for an average flare an average energy
of 1031 erg is emitted or fed into plasmas of greatly varying average particle energy.
For weak or strong flares (importances 1 and 4 respectively) the numbers may be
smaller or larger, approximately by factors 10 to 102•
Assuming that the average energy emitted during one average solar cycle is a few
thousand times the total energy emitted by a type 2 flare, hence a few times 1034 erg,
one obtains an average rate of dissipation of flare energy of a few times 1034/3 x 108
~ 1026 erg sec -1. This and other energy fluxes are given in Table III.
TABLE III
Solar energy fluxes
Radiative flux Frad = 4 X 1033 erg sec-l
Mechanical flux at top of photosphere Fmech 1029 erg sec-l
Coronal X-ray flux Fx 1027 erg sec-l
Flux of thermal energy in the solar wind Fwlnd 1025 erg sec-l
Dissipation of rotational energy by the solar wind Frot, wind = 1024 erg sec-l
Secular decrease of solar rotational energy FR = 8 X 1025 erg sec-l
Average energy dissipation in flares Fflares 1026 erg sec-l
J
It may seem surprising that the value of E N d V derived from this table for the
optical flare plasma is 1025 erg, hence about 106 times smaller than the total emitted
energy (last column) but this simply shows that during the life time of the optical
flare there is a continuous re-excitation of the particles in the cool flare plasma (actu
ally 106 times per particle during the life time of the optical flare).
The most essential problem of solar flares is how individual particles can acquire
the high particle energies, given in the second column of Table II.
We also have to observe the time scale: a flare may recur in a series of homologous
events with time intervals of the order of a day (lOs sec). On the other hand it seems
after H. Dodson-Prince and R. Hedeman (in this volume, p. 151), that it may take
an active region a couple of years before sufficient energy is accumulated to produce
real high particle energy flares. Another important aspect of flares is that their origin
is always related to electric currents, of at least 1011 amperes. Data about particle
energies and total energy, time rate and electric currents are necessary to define the
kind of flare producing mechanisms.
We examine the hypothesis that the origin of solar active regions and flares is
due, in .one way or the other to solar rotation and its differential effects. In the non
magnetic case the dissipation mechanism would just be viscosity, but in the magnetic
case differential rotation of a magnetized plasma would produce a current system
c
j = -curlB,
4n
which would upgrade and dissipate energy by an instability leading to current inter-