Solar radio emissions J.-P. Raulin * , A.A. Pacini 1 Centro de Radioastronomia e Astrofisica Mackenzie, Universidade Presbiteriana Mackenzie, Rua da Consolac ¸a ˜ o 896, Sa ˜ o Paulo, 01302-907 SP, Brazil Received 3 June 2004; received in revised form 1 March 2005; accepted 1 March 2005 Abstract In this paper, we present a tutorial review which was presented at the first Advanced School on Space Environment (ASSE 2004). We first describe the basics of radioastronomy definitions, and discuss radiation processes relevant to solar radio emissions like plasma emission, free–free bremsstra ¨hlung and gyromagnetic emissions. We illustrate these fundamentals by describing recent solar radio observations and the constraints they bring on different solar physical parameters. We focus on solar radio emissions from the quiet sun, active regions and during explosive events known as solar flares, and how the latter can bring quantitative informations on the particles responsible for the emission. Finally, particular attention is paid to new radio diagnostics obtained at very high fre- quencies in the millimeter/submillimeter range, as well as to radio emissions relevant to Space Weather studies. Ó 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Solar radio astronomy; Radiation mechanisms; Solar flares; Submillimeter waves 1. Introduction 1.1. Why do we study the Sun at radio wavelengths? Although the Sun is an average (size, temperature and brightness) middle-aged star, its proximity to Earth of about 150,000,000 km (1 AU) makes it an extraordi- nary laboratory for astrophysics. This proximity results in a very strong signal in almost all the electromagnetic spectrum, which allows to study the Sun with high sen- sitivity, time and spectral resolution. The SunÕs large angular size of 32 0 as seen from the Earth also permits to describe in great details the solar surface and atmo- spheric features. As a consequence, a wealth of phenom- ena has been found to occur through the SunÕs atmosphere. For example, the well-known solar flares are sudden releases of a great amount of energy within high magnetic field regions called solar active regions. During flares, energy stored in magnetic fields within ac- tive centers is rapidly converted into thermal, kinetic and mechanical energies. As a consequence, the local plasma is heated to several or several tens of millions de- grees, while other ambient particles are accelerated up to high energies. During large flares as much as few 10 38 electrons per second are accelerated, as deduced from non-thermal bremsstra ¨hlung hard X-rays, which pro- vide a direct diagnostic of the electrons which collide in the dense low solar atmosphere. Since a flare may last few minutes, and assuming a typical coronal magnetic structure filled with 10 37 thermal particles, we see that the accelerated electron production rate is very high. It is also difficult to know on the relative positions of the acceleration regions (where the particles are accelerated) and the radiation sites (where they emit). This raises the question about the effects of the transport of these par- ticles, on the observed time flare history, on the energy spectrum of the particles, if, for example acceleration and radiation sites are different. Solar flare radio obser- vations give valuable informations in order to answer these questions. As it gives also access to the highest energy particles accelerated during flares, since high 0273-1177/$30 Ó 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2005.03.138 * Corresponding author. E-mail address: [email protected](J.-P. Raulin). 1 Present address: Instituto Nacional de Pesquisas Espaciais, Sa ˜o Jose ´ dos Campos, Brazil. www.elsevier.com/locate/asr Advances in Space Research 35 (2005) 739–754
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www.elsevier.com/locate/asr
Advances in Space Research 35 (2005) 739–754
Solar radio emissions
J.-P. Raulin *, A.A. Pacini 1
Centro de Radioastronomia e Astrofisica Mackenzie, Universidade Presbiteriana Mackenzie, Rua da Consolacao 896, Sao Paulo, 01302-907 SP, Brazil
Received 3 June 2004; received in revised form 1 March 2005; accepted 1 March 2005
Abstract
In this paper, we present a tutorial review which was presented at the first Advanced School on Space Environment (ASSE 2004).
We first describe the basics of radioastronomy definitions, and discuss radiation processes relevant to solar radio emissions like
plasma emission, free–free bremsstrahlung and gyromagnetic emissions. We illustrate these fundamentals by describing recent solar
radio observations and the constraints they bring on different solar physical parameters. We focus on solar radio emissions from the
quiet sun, active regions and during explosive events known as solar flares, and how the latter can bring quantitative informations
on the particles responsible for the emission. Finally, particular attention is paid to new radio diagnostics obtained at very high fre-
quencies in the millimeter/submillimeter range, as well as to radio emissions relevant to Space Weather studies.
� 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Solar radio astronomy; Radiation mechanisms; Solar flares; Submillimeter waves
1. Introduction
1.1. Why do we study the Sun at radio wavelengths?
Although the Sun is an average (size, temperature
and brightness) middle-aged star, its proximity to Earthof about 150,000,000 km (1 AU) makes it an extraordi-
nary laboratory for astrophysics. This proximity results
in a very strong signal in almost all the electromagnetic
spectrum, which allows to study the Sun with high sen-
sitivity, time and spectral resolution. The Sun�s large
angular size of �32 0 as seen from the Earth also permits
to describe in great details the solar surface and atmo-
spheric features. As a consequence, a wealth of phenom-ena has been found to occur through the Sun�satmosphere. For example, the well-known solar flares
are sudden releases of a great amount of energy within
high magnetic field regions called solar active regions.
0273-1177/$30 � 2005 COSPAR. Published by Elsevier Ltd. All rights reser
doi:10.1016/j.asr.2005.03.138
* Corresponding author.
E-mail address: [email protected] (J.-P. Raulin).1 Present address: Instituto Nacional de Pesquisas Espaciais, Sao
Jose dos Campos, Brazil.
During flares, energy stored in magnetic fields within ac-
tive centers is rapidly converted into thermal, kinetic
and mechanical energies. As a consequence, the local
plasma is heated to several or several tens of millions de-
grees, while other ambient particles are accelerated up to
high energies. During large flares as much as few 1038
electrons per second are accelerated, as deduced from
non-thermal bremsstrahlung hard X-rays, which pro-
vide a direct diagnostic of the electrons which collide
in the dense low solar atmosphere. Since a flare may last
few minutes, and assuming a typical coronal magnetic
structure filled with 1037 thermal particles, we see that
the accelerated electron production rate is very high. It
is also difficult to know on the relative positions of theacceleration regions (where the particles are accelerated)
and the radiation sites (where they emit). This raises the
question about the effects of the transport of these par-
ticles, on the observed time flare history, on the energy
spectrum of the particles, if, for example acceleration
and radiation sites are different. Solar flare radio obser-
vations give valuable informations in order to answer
these questions. As it gives also access to the highestenergy particles accelerated during flares, since high
742 J.-P. Raulin, A.A. Pacini / Advances in Space Research 35 (2005) 739–754
speed of light. Another quantity largely used in radioas-
tronomy is the brightness temperature Tb, which is the
equivalent temperature a black-body should have to
radiate an intensity Im given by Eq. (3). We thus have
a relation between Tb and Sm given by
Sm ¼2kBm2
c2
ZT b dX; ð4Þ
where X is the angle subtended by the emitting source.
Although the brightness temperature has been defined
for thermal emission of a black-body we can also use
it for non-thermal emitting sources. Non-thermal emis-
sion may be due to accelerated particles with energy E,
and in this case, we shall consider Tb as an effective tem-
perature Teff given by the kinetic temperature E/kB. In
the case of thermal emission, one should have Tb 6 T.We shall now distinguish between incoherent and
coherent emission mechanism. An incoherent radiation
mechanism is a process where particles behave indepen-
dently of each other. There is no phase relation between
the emitted photons, that is no coherence. In this case,
the resulting brightness temperature cannot exceed the
effective temperature Teff, that is the source temperature
for a thermal process, or the kinetic temperature for anon-thermal process. Thus for an incoherent non-
thermal emission, due to say MeV electrons as it is often
observed during solar flares, Tb is limited by the mean
particle energy, such that Tb 6 E/kB � 1010 K. During
a coherent process emitting particles can behave as a
whole, emitting photons between whose exists a phase
relation. Thus, a coherent emission is not the result of
individual particle emission, but rather a collective pro-cess for example triggered by waves when certain insta-
bilities develop in magnetized plasmas. The brightness
temperature resulting from a coherent emission mecha-
nism can thus largely exceed the mean particle energy,
and can reach few 1015 K as for some decimetric solar
radio bursts.
Due to the presence of a magnetic field an electro-
magnetic wave will propagate in two different modes:the extraordinary mode (X) and the ordinary (O) mode.
The above defined quantities will depend on the mode of
propagation. The detected radiation is said to be polar-
ized when the emission in one of the two modes domi-
nates that in the other (Kraus, 1966; Christiansen and
Hogbom, 1985; McLean and Labrum, 1985). In this
case, the degree of polarization is a measure of the inten-
sity received in one of the two modes, relative to the to-tal intensity. Since the Faraday rotation of the plane of
polarization is strong when radio waves propagate
through the solar corona, it suppresses any linear polar-
ization present at the emitting source, and thus only the
degree of circular polarization can be measured. How-
ever, see McLean and Labrum (1985) for examples of at-
tempts in detecting linearly polarized solar radio
emission.
3. Coherent radiation processes
As said earlier coherent processes may occur at the
time a magnetized plasma becomes unstable. Before
entering coherent mechanisms in more details, it is
important to remind some important parameters ofany given plasma. We will here describe few of them
and give simple expressions. For a general table of
plasma parameters relevant to solar processes, the reader
is referred to McLean and Labrum (1985, chapter 5).
3.1. Natural plasma parameters
The first parameter is the plasma frequency fpa ofplasma specie a. More often, we find in the literature,
the angular frequency xpa related to fpa by the relation
xpa = 2pfpa. The plasma frequency for electrons can be
simply written in terms of the ambient electronic plasma
density, Ne, the charge and mass of the electron
fpe ¼1
2pN ee
2
mee0
� �1=2
¼ 9� 10�3ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiN e ½cm�3�
pMHz. ð5Þ
To understand the meaning of fpe let us assume a plasma
composed of electrons and ions on which acts an exter-
nal electric field ~E. Due to ~E there will be a charge sep-
aration which will be responsible for the creation of arestoring electric field to compensate the effect of ~E. Ifwe suddenly shut down ~E and study the motion of the
electrons, neglecting collisions between particles as well
as ions motions, we find that electrons will oscillate
around an equilibrium position with the frequency fpe.
These undamped oscillations are called plasma oscilla-
tions. In the cold plasma wave theory, these oscillations
are called Langmuir waves at the frequency x = xpe,and taking into account the electron temperature Te
(or the pressure gradient term in the equation of the
electron motion), Langmuir waves can propagate and
have a dispersion relation given by
x2 ¼ x2pe þ 3
2k2v2e ; ð6Þ
where k is the wave number and ve the mean electron
thermal velocity. It is important to note that the Lang-
muir waves are electrostatic waves, that do not transportany electromagnetic energy.
In the presence of a magnetic field another natural
plasma frequency is the gyrofrequency, fbe (for elec-
trons), defined by the frequency with which an electron
gyrate around magnetic field lines due to the Lorentz
force. fbe, often referred to Xe in the literature
(Xe = 2pfbe), can be expressed using
Xe ¼eBme
¼ 2p � 2.8� 106B½G� Hz; ð7Þ
where B is the magnetic field strength. Thus, taking into
account the magnetic field and the presence of ions, the
Fig. 5. Velocity distribution function of a thermal background plus a
fast beam, showing the velocity region where turbulence can develop.
J.-P. Raulin, A.A. Pacini / Advances in Space Research 35 (2005) 739–754 743
electron plasma frequency given by Eq. (5) will be
slightly modified and will fall in the range given by the
upper hybrid frequency, xUH, and the lower hybrid fre-
quency, xLH, given by
xUH ¼ ðx2pe þ X2
eÞ1=2
;
xLH ¼ 1
x2pi þ X2
i
þ 1
XeXi
!�1=2
� ðXeXiÞ1=2.ð8Þ
In the solar corona, we generally have the relation
xUH P xpe > Xe � xLH > xpi � Xi.
The Debye length, kD is a useful parameter to study
collisions in a plasma. It defines the distance over which
a test electron from the plasma will not feel anymore the
electrostatic field from an ion. kD is the ratio of the ther-mal speed to the plasma frequency, and thus depends on
the ambient electron density Ne and the plasma temper-
ature T, through the following equation:
kD ¼ 6.9
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiT e ½K�
N e ½cm�3�
scm ð9Þ
being then much lower in the cool and low altitude
dense solar atmosphere compared to its value in the di-
lute and hot corona.
The plasma parameter b is a measure of the gas-to-
magnetic pressure ratio. For b � 1 like close to the solar
surface, the particles dominate the plasma dynamics and
they drag along magnetic field lines. In the outer solaratmosphere, i.e., the solar corona, we have everywhere
b � 1 implying that the plasma is confined by the mag-
netic field.
3.2. Coherent emission mechanism
The most known coherent process to produce radio
emission is the plasma emission, which is a multi-stepprocess. It first involves some kind of Langmuir turbu-
lence, generally attributed to a streaming instability.
The next step is to convert the energy available in the
plasma turbulence into fundamental electromagnetic
transverse radiation at or close to the local plasma fre-
quency (x = xpe) which can escape from the medium
and be detected. This is because Langmuir turbulence
does not propagate and can only be detected in situ.Other steps requiring the production of secondary Lang-
muir waves and the conversion into transverse electro-
magnetic emission will not be discussed here. Extended
references on these steps which involve scattering of
plasma waves on ions or on coronal density gradients,
and wave–wave interactions, can be found in Benz
(1993) and McLean and Labrum (1985).
Although the study of the system composed of abackground thermal plasma where a beam of particles
propagate is a very simplified situation, it gives already
some important details on the production of plasma tur-
bulence. The hydromagnetic treatment, that is a back-
ground plasma composed of cold particles (electrons
and ions) and a beam of cold or monoenergetic particles
(electrons with velocity Ve0), can be done graphically
(Sturrock, 1994; Kivelson and Russell, 1995). The solu-
tion of the dispersion relation given by
1 ¼x2
pi
x2þ
x2pe
ðx� kV e0Þ2
!ð10Þ
may lead to a complex solution for x of the formx = xr ± ixi. Such that any perturbation in the plasma
will varies in time as e�ixt = e�ixrtect where c = xi.
Therefore we see that c > 0 will imply an exponentially
growing perturbation. Although this simple situation
shows that under some circumstances Langmuir turbu-
lence can grow at a rate c within a plasma, it does not
tell us from where comes the energy provided to the tur-
bulence nor when the amplification will stop. To solvethis problem, it is necessary to adopt a more detailed
treatment taking into account the temperatures of the
background plasma and the beam particles, that is ki-
netic effects. In Fig. 5, we show a more realistic situation
for the velocity distribution of a background plasma
where a fast particle beam propagates. It can be shown
(Benz, 1993) that c / xrof0ovz
where xr is the real part of
the frequency given by Eq. (6). Fig. 5 shows that inthe region where of0
ovxis positive plasma turbulence with
phase velocity x/k, may suffer strong amplification.
For such a turbulence, with a phase velocity V/, we basi-
cally have more particles with velocity greater than V/
than we have particles with velocity lower than V/. So
the net effect is the growth of the turbulence, at the ex-
pense of a reduction of the beam velocity. Then, as a
function of time, the beam velocity distribution will bedestroyed, and become rather a ‘‘plateau’’. It is then a
wave–particle interaction effect, where energy is trans-
ferred from the particle beam to the waves present in
the plasma, which can explain the growth of the plasma
turbulence in a region where it exists a resonant condi-
tion between the particles and the waves. This instability
is the so-called bump-on-tail instability, which is impor-
tant to explain some kind of metric radio bursts likeType IIIs.
744 J.-P. Raulin, A.A. Pacini / Advances in Space Research 35 (2005) 739–754
Instability can develop also due to the presence of an
anisotropic velocity distribution. This occurs when par-
ticles are trapped in magnetic bottles, that is a region
bounded by two sites of high magnetic field strength
Bmax. Conservation (of energy and magnetic moment)
laws show that as a particle moves toward high magneticfield regions its velocity component parallel to ~B, vi de-creases. When arriving at the point where B = Bmax,
the particle can escape the bottle if vi > 0. Otherwise
the particle will be confined in the magnetic bottle.
The mirror ratio between Bmax and the minimum field
strength within the magnetic configuration defines an
angle (pitch-angle) am such that any particle with initial
pitch-angle a ¼ ðd~v;~BÞ < am will escape from the bottle
and those particle with a ¼ ðd~v;~BÞ > am will remaintrapped. This situation is illustrated in Fig. 6 where
the pitch-angle region shown by the gray filled area is
empty of charged particles. In plasmas where Xe P xpe
the above anisotropic configuration will transfer energy
into directly escaping electromagnetic radiation,
through an instability called electron cyclotron maser
(ECM). The ECM emission (Wu and Lee, 1979) is
responsible for planetary radio emissions and some verybright solar radio spikes.
4. Incoherent radiation processes
The basis for incoherent radio emission in low density
medium like the solar corona is the emission from free
accelerated particles. A charge in rectilinear uniformmotion creates in space an electromagnetic field which
energy is static and constant in time, i.e., does not prop-
agate. When the charge is accelerated we have an addi-
tional electromagnetic field component, which is time
dependent because of the time dependent velocity. Con-
trary to the static case, the electromagnetic energy now
propagates and we say that the charge is radiating. This
is what happens for example in the emission of radiowaves when electrons oscillate in an antenna.
Fig. 6. Loss-cone velocity distribution.
The Larmor formula (Rybicki and Lightman, 1979)
expresses the power radiated by a single accelerated
charge (q, mass m, velocity v) in the direction h relative
to the acceleration vector within the solid angle dX
dPdX
¼ q2 _v2
4pc2sin2ðhÞ; ð11Þ
where _v ¼ dv=dt, and which gives after integration on X
P ¼ 2q2 _v2
3c2. ð12Þ
Note on the radiation pattern, P, that: (i) the total
power is proportional to the charge; (ii) no power is
emitted in the direction of the acceleration; (iii) maxi-
mum power is emitted in a direction perpendicular
to the acceleration; (iv) since _v is �1/m, the power is
�1/m2 and the radiation from protons will be negligiable
compared to that emitted by electrons.
4.1. Free–free bremsstrahlung
This emission is due to Coulomb collisions between
charged particles in a plasma. In Fig. 7, we show an
example of a binary collision between an electron of
velocity v and an ion of charge Zi. The effect of the col-
lision is to deflect the incoming electron by an amountwhich depends on the impact parameter b. However in
the solar coronal plasma the situation is quite different.
This is due to the very high number of particles present
in the Debye sphere (see Eq. (9)). The ratio of small-to-
large angle encounters can be approximated by kD/rcwhere rc is the impact parameter b which produces a
90� deflection. As a consequence small-angle collisions
dominate and the trajectory of an incoming electron israther determined by a multitude of small deviations.
However, in the cool and very dense low solar atmo-
sphere, the effect of large angle encounters is enhanced
since there the Debye sphere is much smaller. Then high
energy electrons can undergo large deflection and lose
most of their energy emitting high energy hard X-ray
photons. In the tenuous solar corona, the emitted pho-
tons may fall in the radio wavelength range, and thisis what we are interested in the following. In this case,
the bremsstrahlung emission from one incoming
Fig. 7. Binary Coulomb collision showing the impact parameter and
the deflection angle.
J.-P. Raulin, A.A. Pacini / Advances in Space Research 35 (2005) 739–754 745
electron is calculated using the small-angle approxima-
tion (Rybicki and Lightman, 1979)
dW ðbÞdx
¼ 8
3pZ2i e
6
m2ec
3
� �1
ðbvÞ2e�2xb=v
� 8
3pZ2i e
6
m2ec3
� �1
ðbvÞ2ð13Þ
for b � v/x. Taking into account the total incoming
electron flux, 2pbdbnev, where ne is the electron density,
colliding in a plasma with an ion density ni, and integrat-
ing Eq. (13) between impact parameters bmin = 4Zie2/
pmev2 corresponding to a 90� deflection and bmax = v/x
above which the emitted power is negligiable, we get
the bremsstrahlung emission per unit time, volume and
frequency
dW ðbÞdxdV dt
¼ 16e6
3c3m2evneniZ2
i Lnbmax
bmin
� �¼ 16pe6
33=2c3m2evneniZ2
i gffðv;xÞ; ð14Þ
where gff(v,x) is the Gaunt factor (Karzas and Latter,1961) which is slightly dependent on the frequency m.For a totally ionized electron–proton plasma like the so-
lar corona (ne = ni and Zi = 1), composed of thermal
particles, we get the thermal bremsstrahlung emissivity
gm at the frequency m (x = 2pm) by integrating Eq. (14)
over v using a Maxwellian distribution function
gm ¼25pe6
3mec32p
3mekB
� �1=2
n2eT�1=2gffðv;xÞ. ð15Þ
We thus conclude that the radio emissivity from a free–
free bremsstrahlung emitting plasma is proportional to
the ambient density and inversely proportional to the
plasma temperature. We also note that as long as radia-
tive transfer of the radiation is not taken into account,
there is almost no dependence of the emission as a func-tion of the frequency.
4.2. Magnetobremsstrahlung emission
In the presence of an external magnetic field ~B, a
charged particle will spiral around field lines due to
the Lorentz force, and thus suffer continuous velocity
direction changes that will produce electromagneticradiation. In the absence of an electric field the acceler-
ation term is perpendicular to ~B, a^ = Xv^, where X is
the gyrofrequency given by Eq. (7). Using the Larmor
formula (Eq. (12)), we get the power emitted by an accel-
erated electron
P ¼ c22e2
3c3v2?e
2B2
m2ec
2; ð16Þ
where c is the Lorentz factor. In the electron reference
frame the power emitted is dipolar, and seen from a rest
frame it is beamed along the direction of ~v, also called
the forward beam. The time T, it takes for the emission
cone to pass in front the observer is 2/Xe. Because of
Doppler shift, this time s will be shorter for an observer
at rest by a factor 1 � v/c. For energetic electrons, we
have s = 2p/(c2Xe). Thus, as a function of time, thepower P(t) emitted by an electron is a succession of
pulses of width s separated by 2pc/Xe, i.e., occurring
with the frequency Xe/2pc. In the spectral domain, the
electron emission is then different depending on the Lor-
entz factor. For monoenergetic cold electrons, the emis-
sion occurs at the frequency Xe and is also called
cyclotron emission. For higher energy thermal electrons
(few eV to tens of eV) the time profile is modified andharmonics of Xe appear in the spectral domain. The
emission called gyroresonance then occurs at low har-
monics number (s = 1,2,3, . . .) of the Larmor frequency.
For mildly relativistic electrons (few tens of keV to few
hundreds of keV), P(t) presents much thinner and sepa-
rated peaks, resulting in a broadband frequency range
emission from harmonics of Xe in the range s = 10–
100. This emission is called gyrosynchrotron emission.For highly relativistic electrons, the angular pattern of
emission is beamed along the particle velocity. The emis-
sion called synchrotron emission will mainly occur along
the particle velocity at very high harmonics s � c3 of theLarmor frequency.
The treatment of magnetobremsstrahlung emission
from a collection of electrons is complex since it needs
the knowledge of the velocity and pitch-angle distribu-tions of the particles (Pacholczyk, 1979). Moreover,
the effects of the ambient medium and of an inhomoge-
neous magnetic field structure in the emitting region
should be taken into account. Complete calculations
of the emissivity for an isotropic velocity distribution
of electrons in an homogeneous magnetic field have been
performed (Ramaty, 1969; Ramaty et al., 1994). Semi-
empirical useful formulae for gm obtained within thesame conditions and valid in a restricted range of har-
monic numbers s have been estimated (Dulk and Marsh,
1982; Dulk, 1985). Inhomogeneous magnetic field mod-
els and absorption of the radiation by the ambient med-
ium have been studied (Klein and Trottet, 1984; Klein,
1987), as well as the effects of anisotropic electron
pitch-angle distribution (Lee and Gary, 2000).
Mainly two kind of particle distributions are usuallyused: Maxwellian and power-law. In the first case, the
dominant mechanism is the gyroresonance emission at
discrete and low harmonic number of Xe, which emissiv-
ity can be written as a function of the density ne, the
magnetic field strength B and its direction relative to
the observer. Thus, gyroresonance emission will be rele-
vant to study magnetic field structure above solar active
regions. In the case of a non-thermal power-law energydistribution of electrons AE�d, the gyrosynchrotron
emissivity has also a power-law spectrum which can
746 J.-P. Raulin, A.A. Pacini / Advances in Space Research 35 (2005) 739–754
then be used to estimate the injected particle distribution
parameters as well as the magnetic field strength B. This
will mostly be useful to study gyrosynchrotron from
flare accelerated particles.
5. Radiative transfer
After to have reviewed how emission can be obtained
from different processes, through the emissivity term gmin W m�3 St�1 Hz�1, we will now study how this radia-
tion is transported (Kraus, 1966). The change of inten-
sity Im at the frequency m (see Eq. (3)) along a ray path
s is given by dIm = gmds. The radiation is also absorbedalong the ray path by an amount dIm = �jmImds where
jm is an absorption coefficient per unit of length. Putting
together these two expressions leads to the equation of
radiative transfer
dI mds
¼ gm � kmI m. ð17Þ
The first term is a source term while the second term is
an absorption term. The latter is used to define the opti-
cal depth sm as the integrated absorption along the line
of sight, i.e., sm ¼R s0jmds. By integrating Eq. (17) with
jm = 0 (pure emitting medium), we see that the change
in intensity is the integrated emissivity along the lineof sight. Similarly, an integration with gm = 0 (pure
absorbing medium) shows that the intensity decreases
exponentially with sm. The solution of Eq. (17) can be
written as:
Im ¼ Imð0Þe�sm þ gmjm
ð1� e�smÞ. ð18Þ
This equation means that the outgoing radiation from
an absorbing medium will be the entering radiation
Im(0) absorbed through the medium plus the radiative
balance within the medium (integrated source emissionminus absorption). At the thermodynamical equilibrium
(Eq. (17) equals 0), when the source absorbs as much as
it emits, the ratio gm/jm is given by the Planck function
(see Eq. (3)). Moreover, when dividing the former equa-
tion by 2kBm2/c2 we get
T b ¼ T b0e�sm þ T effð1� e�smÞ. ð19Þ
As already discussed in Section 2 for a source in thermo-
dynamical equilibrium Teff is the source temperature,
and for non-thermal emitting particles, Teff is to be con-
sidered as given by E/kB where E is the mean energy of
the radiating particles.
Two important regimes are found from Eq. (19): (i)
when sm � 1 the source is said to be optically thick;
(ii) when sm � 1 the source is said to be optically thin.These two cases lead, respectively, to:
T b ¼ T eff ðsm � 1Þ;T b ¼ T b0ð1� smÞ þ smT eff ðsm � 1Þ. ð20Þ
These equations will allow to compute for different emis-
sion mechanisms the variations of Tb (or Sm using Eq.
(4)) as a function of the frequency, that is to get the
radio spectrum.
For a given emission mechanism, it is common to use
the corresponding optical depth or opacity, rather thanthe emissivity, although both can be related at the ther-
modynamical equilibrium. As an example for a fully
ionized e�–p plasma we can use Eq. (15) to get the
free–free bremsstrahlung opacity (Dulk, 1985):
sff ¼9.78� 10�3 N 2e‘
m2T 3=2ð18.2þ 1.5 ln T � ln mÞ
ðT < 2� 105 KÞ; ð21Þ
sff ¼9.78� 10�3 N 2e‘
m2T 3=2ð24.5þ ln T � ln mÞ
ðT > 2� 105 KÞ; ð22Þ
where the Gaunt factor has been evaluated for two tem-perature regimes, and where ‘ is the size of the emitting
medium along the line of sight. Thus, free–free brem-
sstrahlung emission is mainly a diagnostic of the plasma
temperature and density. Note also that the radio free–
free opacity is increasing for decreasing T, i.e., very sen-
sitive to cool and dense plasmas. Because of the small
dependence of the term in brackets, the radio spectrum
(Sm as a function of m) will increase as m2 in the opticallythick regime and will be roughly constant for an opti-
cally thin source.
The opacity for the gyroresonance mechanism, sgr,can be obtained similarly as done above for the free–free
bremsstrahlung (Dulk, 1985; White and Kundu, 1997).
sgr is slightly dependent of the density and the tempera-
ture of the plasma, but strongly depends on the mag-
netic field strength and on its direction with respect tothe observer. Gyroresonance opacity is higher for the
X mode compared to the 0 mode, such that the emission
will be highly polarized. In units of the magnetic scale
height, the thickness of the gyroresonance layer is about
v/c, where v is the speed of the emitting thermal elec-
trons. Thus, the gyroresonance layer is a very thin por-
tion of the atmosphere with an almost constant
magnetic field value.For higher energy electrons with a power-law distri-
bution in energy, the spectrum of the radio flux density
decreases with the observed frequency in the optically
thin part. The peak frequency mpeak is the frequency be-
low which the radio emission is self-absorbed in the opti-
cally thick part of the spectrum. The optically thin part
of the spectrum is important since its slope is directly re-
lated to the slope of the injected distribution of electrons(Dulk, 1985). The higher the frequency the higher the
energy of the emitting electrons, and thus high fre-
quency radio observations provide a diagnostic of the
highest energy electrons accelerated during solar flares.
This is demonstrated in Fig. 8 (Fig. 1 in White and
J.-P. Raulin, A.A. Pacini / Advances in Space Research 35 (2005) 739–754 747
Kundu, 1992) for different gyrosynchrotron spectra ob-
tained using different low-energy cutoff of the injected
electron distribution. One can see that millimeter emis-
sion is not affected until MeV electrons are removed,
showing that high frequency emission is largely due to
the MeV energy electrons.
Fig. 9. Variations with height of the plasma and gyromagnetic
frequencies. fs = 1 is the curve for which the free–free opacity is equal
unity (after Gary and Hurford, 2004).
6. Solar radio emissions
Before describing some selected solar radio observa-
tions, let us first have a rough idea of which process will
dominate at a given altitude in the solar atmosphere.
Fig. 9 (from Gary and Hurford, 2004) shows the varia-tions as a function of height of the plasma frequency mp,of the frequency for which sff = 1, as well as harmonics
of the gyrofrequency. At each altitude, the curve mp in-
forms us the cutoff frequency below which a wave does
not propagate. The solar plasma above the curve for
which sff = 1 is optically thin, thus, in the range 10–
200 MHz plasma emission mechanisms will dominate.
Although plasma radio emission above 200 MHz willbe partly absorbed by the ambient plasma through of
the effect of collisions, it may still be bright enough to
be detected. The reason is that plasma radio waves are
naturally extremely bright and can occur at harmonics
of the plasma frequency. The highest frequency at which
plasma radio emission may have been detected in the so-
lar corona is about 8 GHz. Thus, for frequencies be-
tween 200 MHz and �1 GHz, both mechanisms,plasma and bremsstrahlung can coexist. Between 1 and
3 GHz the hot and dense plasma from the active regions
is optically thick for free–free bremsstrahlung emission
which is then the dominant mechanism. Above about
3 GHz, the altitude for which the ambient plasma has
Fig. 8. A plot of non-thermal gyrosynchrotron flux spectra as a
function of frequency for different values of the low-energy cutoff. The
spectral index is 4, the magnetic field 300 G, the high-energy cutoff is
10 MeV and the angle between the line of sight and the magnetic field
is 45�. The curves are labelled according to the low-energy cutoff (after
White and Kundu, 1992).
a free–free opacity equals to 1 is lower than that corre-
sponding to low harmonics of the gyrofrequency. Con-
sequently, gyroresonance mechanism will prevail in
high magnetic field regions.
6.1. Non-flare radio emissions
The oldest observed solar radio emission at metricwavelengths is called a noise storm and has been re-
viewed by Elgaroy (1977). It is composed of short dura-
tion (61 s) metric radio enhancements called Type I
bursts, superimposed on a broad frequency band contin-
uum (McLean and Labrum, 1985). Noise storms are
spatially associated with active centers, but are not flare
related (Le Squeren, 1963), and they can last for several
consecutive days. Their importance lies on the fact thatthey are evidences for long lasting acceleration of elec-
trons up to suprathermal energies, which produce radio
emission through a collective process (Spicer et al., 1982;
Wentzel, 1986). Noise storms are triggered in a similar
way as flares (Raulin et al., 1991; Raulin and Klein,
1994), the emitted power being much less than that mea-
sured during flares, although the total energy budget is
comparable to that of a small flare. We finally note thatType I bursts may be the coronal signature of nanofl-
ares, and their peak flux density distribution suggests
that they may contribute to the heating of an active
coronal region (Mercier and Trottet, 1997). The slope
of the distribution, for small events, is much steeper than
that found at other wavelengths, indicating the possibil-
ity that Type I bursts participate to the heating of the so-
lar atmosphere.The quiet sun also emits at radio wavelengths
through the free–free bremsstrahlung mechanism. How-
ever the emission will greatly depend on the atmospheric
layer because of the dependence of the free–free opacity
sff (see Eqs. (21) and (22)), on the plasma density Ne, and
the local temperature T. Using a typical temperature of
Fig. 10. Optical (left) and radio (right) emissions above a sunspot.
Note the ‘‘horse-shoe’’ like structure of the radio source (Courtesy of
S.M. White, after http://www.astro.umd.edu/white/text/activeregio
nimages.html).
748 J.-P. Raulin, A.A. Pacini / Advances in Space Research 35 (2005) 739–754
106 K and density of 109 cm�3 we get sff � 1 in the
whole microwave range indicating that the quiet corona
will be optically thin at these frequencies. Through the
transition region to the chromosphere, Ne increases by
a factor of �100 and T decreases by about the same fac-
tor, implying a change of seven orders of magnitude insff resulting in an optically thick chromosphere. Zirin
et al. (1991) have effectively shown that the free–free
emission from the quiet sun center between 1.4 and
18 GHz was composed of the radiation of a thick upper
chromosphere at �11,000 K, observed through a thin
corona at 106 K and scale height of 5 · 109 cm. At meter
wavelengths the situation is somewhat different since the
corona will be optically thick at some height showingbrightness contrasts with extended regions called coro-
nal holes. These regions are cool and low density areas
in the corona, and their time variability is important
to characterize the high-speed solar wind. At much
higher frequencies (millimeter and submillimeter wave-
lengths), the radio emission is sensitive to the cool and
dense chromospheric material which provide enough
free–free opacity, while the corona remains totally opti-cally thin. Vernazza et al. (1981) tested successfully their
chromospheric atmosphere model deduced from EUV
observations, against 100 GHz radio measurements of
the quiet Sun which originate at layers where the tem-
perature was �6600 K. However, the same model atmo-
sphere seems to disagree with optically thick microwave
observations (Zirin et al., 1991; Bastian et al., 1996). On
the other hand, the latter radio observations are well ex-plained by chromospheric models based on CO line
measurements (Avrett, 1995), suggesting that a chromo-
spheric model which could explain, high frequency
radio, microwaves, EUV and line observations is still
missing.
Solar active regions are high density and high mag-
netic field regions located above sunspots. Radio emis-
sion will occur due to the two following mechanisms:gyroresonance and free–free bremsstrahlung. Which
mechanism will dominate depends on the density and
the magnetic field strength in the source, and the fre-
quency of observation. The former mechanism is
strongly dependent on the magnetic field strength, but
less on the plasma parameters, while free–free emission
mainly depends on the plasma temperature and density.
Fig. 9 has shown that below a frequency of a few GHzthe local plasma is optically thick to free–free emission.
Above few GHz and in the presence of strong magnetic
fields, low coronal regions of constant magnetic field
provide high gyroresonance opacity. As already men-
tioned sgr is only significant in thin coronal layers (Dulk,
1985; White and Kundu, 1997) where the observed fre-
quency is equals to low (s = 1, 2, 3, 4) harmonics of
the gyrofrequency. Therefore, providing an uniqueway of measuring magnetic field strength. The structure
of the gyroresonance emission source depends also
strongly of the angle h, between the magnetic field and
the line of sight, thus, explaining horse-shoe emission
shapes like the one shown in Fig. 10. Sunspots micro-
wave radio emission compared to model calculations
(Gopalswamy et al., 1996; Nindos et al., 1996) have con-
firmed that gyroresonance is the main mechanism atwork.
6.2. Solar flare radio emissions
Solar flares produce copious amount of coherent
radio waves, which have been classified for more than
40 years into different classes (see Kundu, 1965; McLean
and Labrum, 1985; Benz, 1993, for reviews). The mainobservational parameters for this classification are those
that can clearly be identified on dynamical spectra re-
cords (see Fig. 4), i.e., bandwidth, frequency drift rate
and duration of the emission. The different types of
coherent bursts in the decimetric/metric domains will
not be discussed here and the reader is referred to the
above reviews. Instead we rather describe some charac-
teristics of Type III solar bursts in the following para-graph, while properties of Type I solar bursts have
already been discussed in the previous section. We also
mention that there is no clearly accepted emission mech-
anism for any of the coherent solar radio bursts, and the
non-linear nature of the coherent process itself makes it
very difficult to conclude on quantitative estimations
like electron number and spectrum which represent cru-
cial informations to test particle acceleration models(Miller et al., 1997).
Type IIIs are among the more studied solar coherent
bursts, and generally occur at the beginning of the
impulsive phase of a solar flare. As seen in dynamic
spectra, Type IIIs are fast drifting bursts (see Fig. 4)
from high-to-low frequencies, i.e., from high critical
plasma frequency levels to low critical plasma fre-
quency levels. Reverse bursts are those which will showfast drifts from low-to-high frequencies. Type IIIs are