Advances in Space Research 35 (2005) 739–754 www.elsevier.com/locate/asr

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 (ASSE 2004). We first describe the basics of radioastronomy definitions, and discuss processes relevant to radio emissions like 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 on solar radio emissions from the quiet , 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 studies. 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Solar radio ; Radiation mechanisms; Solar flares; Submillimeter waves

1. Introduction During flares, stored in magnetic fields within ac- tive centers is rapidly converted into , kinetic 1.1. Why do we study the Sun at radio wavelengths? and mechanical . As a consequence, the local plasma is heated to several or several tens of millions de- Although the Sun is an average (size, grees, while other ambient particles are accelerated up to and brightness) middle-aged , its proximity to high energies. During large flares as much as few 1038 of about 150,000,000 km (1 AU) makes it an extraordi- per second are accelerated, as deduced from nary laboratory for . This proximity results non-thermal bremsstra¨hlung hard X-rays, which pro- in a very strong signal in almost all the electromagnetic vide a direct diagnostic of the electrons which collide spectrum, which allows to study the Sun with high sen- in the dense low solar . Since a flare may last sitivity, and spectral resolution. The SunÕs large few minutes, and assuming a typical coronal magnetic angular size of 320 as seen from the Earth also permits structure filled with 1037 thermal particles, we see that to describe in great details the solar and atmo- the accelerated production rate is very high. It spheric features. As a consequence, a wealth of phenom- is also difficult to know on the relative positions of the ena has been found to occur through the SunÕs acceleration regions (where the particles are accelerated) atmosphere. For example, the well-known solar flares and the radiation sites (where they emit). This raises the are sudden releases of a great amount of energy within question about the effects of the transport of these par- high magnetic field regions called solar active regions. 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- * Corresponding author. E-mail address: [email protected] (J.-P. Raulin). vations give valuable informations in order to answer 1 Present address: Instituto Nacional de Pesquisas Espaciais, Sa˜o these questions. As it gives also access to the highest Jose´ dos Campos, Brazil. energy particles accelerated during flares, since high

0273-1177/$30 2005 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2005.03.138 740 J.-P. Raulin, A.A. Pacini / Advances in Space Research 35 (2005) 739–754 frequency radio diagnostics are more sensitive to these ative transfer of radio waves are discussed in Section 5, particles than are hard X-rays produced by non-thermal and in Section 6 we present selected solar radio observa- bremsstra¨hlung. Clues on the above mentioned ques- tions to illustrate the content of the previous sections. tions: particle number, energy and spectrum, transport Section 7 reviews and discuss some very high radio fre- of particles, are important to ultimately confront with quency solar observations, and in Section 8 we present the existing acceleration models (see Miller et al., 1997, radio observations relevant to studies. for a review on models and how they are constrained In Section 9 we present our conclusions. by observations). During solar flares, large scale magnetic field struc- 1.2. How do we observe solar radio waves? tures can be destabilized, and be propelled into the , along with the large it developed during the last fifty contains, to form the so-called coronal ejections , that is relatively early compared to X-ray, ultravi- (CMEs). It is now recognized that CMEs are the prin- olet and techniques. The reason lies in the fact cipal drivers of the Space Weather and the near-Earth that most radio radiation penetrates down to the ground conditions. All these phenomena will emit at radio level. In Fig. 1, we show how the Earth atmosphere af- wavelengths in a frequency range covering over seven fects the incoming radiation from space as a function of orders of from few tens of kHz up to few its wavelength. We see that the atmosphere is completely tens or hundreds of GHz. Although many of the above transparent for waves between few centimeters and phenomena are well documented by the available 10 m. Below 0.5 mm the radiation is almost totally ab- observations, they raise questions that are still unre- sorbed. In the range 0.05–3 cm, there are some absorp- solved. For example, it is not clear at all what trigger tion regions mainly due to the presence of and the initiation of large CMEs. Plasma flows produced vapour (Ulich, 1980), separated by windows of by filaments disruptions have been proposed (Wu variable transparency. At the other end of the radio et al., 2000), although they might not be a general spectrum, radiation with wavelengths greater than cause for all CMEs (Simnett, 2000). The relationship about 20 m are totally blocked by the EarthÕs between flares and CMEs is still a subject of discussion . since many CMEs are detected without any flare man- To collect radio photons and concentrate them, ifestation. Although CMEs occurrence follows approx- radiotelescopes are used. These instruments can be imately the solar activity cycle, no clear associations single-dish antenna, as for example the 100 m diame- with the number have been found so far (How- ter Effelsberg radiotelescope shown in Fig. 2 and lo- ard et al., 1985; Webb, 2000). cated in Germany. The main limitation of such In the remaining part of this section, we briefly de- single-dish instruments are their poor capability of scribe how solar radio waves are observed. In the fol- resolving two distinct point sources on the , which lowing section, are presented basic definitions and is given by the angular separation a (in radians) relations useful in radio astronomy. Sections 3 and 4 are relative to radio emissions due to coherent and inco- k a ¼ 1.22 ; ð1Þ herent processes, respectively. Some aspects of the radi- D

Fig. 1. of the Earth atmosphere as a function of wavelength (from NASA/IPAC). J.-P. Raulin, A.A. Pacini / Advances in Space Research 35 (2005) 739–754 741

techniques, the reader is referred to Kraus (1966), Chris- tiansen and Hogbom (1985), McLean and Labrum (1985). Since the solar spectrum varies in time, and since the spectrum of the radio emission can inform us about the emission mechanism, it is common to record the solar emission as a function of both frequency and time. Such way of representing the intensity of the radio emission is called a dynamic spectrum, shown for example in Fig. 4. Fig. 2. The 100 m diameter single-dish antenna radio at Effelsberg (Germany). After aries.phys.yorku.ca/bartel/SNmovie/ Effelsberg.jp. 2. Radio astronomy: basic relations where k is the radio wavelength of observation and D is The radio emission received by a is the diameter of the antenna. Thus, even observing the measured in terms of its intensity Im, which is the power Sun at a wavelength of 3 cm, the radiotelescope shown received per square meter, per frequency unit Hz, and in Fig. 2 will not be able to resolve solar features with per unit (Kraus, 1966). Integrating Im over 0 angular separation smaller than 1 , i.e., a projected size the solid angle subtended by the emitting source we on the solar surface of 42,000 km. Eq. (1) informs us get a quantity, Sm called the spectral flux that higher spatial resolution can be obtained by using Z larger dishes, but clearly implying construction difficul- Sm ¼ Im dX. ð2Þ ties as well as high costs. To overcome this problem techniques have been developed based on the interfer- The unit of 1 W m2 Hz1 is quite large for most of the ometry theory. The idea is to combine the signals from radio emitting astrophysical objects, and a new flux den- many radiotelescopes arranged as to form a linear array sity unit has been defined and called (Jy), with for example. The angular resolution of such an array is 1Jy=1026 Wm2 Hz1. In solar radioastronomy, given by an equation similar as Eq. (1), where D is not and since the radio signal from the Sun is quite strong anymore the diameter of a single antenna, but the (few orders of magnitude stronger than the brightest greater distance between two individual antennae. The non-solar radio sources in microwaves), we commonly obtained array (or arrays) of antennae is called a radio use solar flux units (SFU) define as 1 SFU = 104 Jy = 22 2 1 interferometer as shown for example in Fig. 3. This ar- 10 Wm Hz . The expression of Im radiated by a ray named the (VLA) is located near black-body at temperature T, at the frequency m, is given Socorro (New , USA), and is composed of 27 by the PlanckÕs law antennae of 25 m diameter. Although the VLA is shown 2hm3 1 2m2k T in Fig. 3 in a compact configuration, the highest distance I B ; m ¼ 2 hm=k T 2 ð3Þ between two individual antennas can reach 40 km. c e B 1 c Thus, at a frequency of 5 GHz (k = 6 cm), the VLA where we have used the Raleigh–Jeans approximation can resolve solar features with angular size less than for radio photons, i.e., hm kBT, where h is the PlanckÕs 00 1 , i.e., a projected size on the solar surface lower than constant, kB is the and c is the 700 km. This kind of instrument will, thus, be able to produce radio images of the Sun with enough angular resolution to show details of the intensity distribution on the solar disk. For further details on interferometric

Fig. 3. The very large array (Socorro, NM, USA) in its more compact Fig. 4. Example of dynamic spectrum showing fast and slow frequency configuration Photo courtesy AUI/NRAO after http://sky- drifting bursts. Time (in minutes) is shown on the horizontal axis, and server.sdss.org/dr1/en/proj/advanced/quasars/images/vla.gif. the observed frequency (MHz) on the vertical axis. 742 J.-P. Raulin, A.A. Pacini / Advances in Space Research 35 (2005) 739–754 of . Another quantity largely used in radioas- 3. Coherent radiation processes tronomy is the brightness temperature Tb, which is the equivalent temperature a black-body should have to As said earlier coherent processes may occur at the radiate an intensity Im given by Eq. (3). We thus have time a magnetized plasma becomes unstable. Before a relation between Tb and Sm given by entering coherent mechanisms in more details, it is Z important to remind some important parameters of 2k m2 S ¼ B T dX; ð4Þ any given plasma. We will here describe few of them m c2 b and give simple expressions. For a general table of where X is the angle subtended by the emitting source. relevant to solar processes, the reader Although the brightness temperature has been defined is referred to McLean and Labrum (1985, chapter 5). for thermal emission of a black-body we can also use it for non-thermal emitting sources. Non-thermal emis- 3.1. Natural plasma parameters sion may be due to accelerated particles with energy E, and in this case, we shall consider Tb as an effective tem- The first parameter is the plasma frequency fpa of perature Teff given by the kinetic temperature E/kB.In plasma specie a. More often, we find in the literature, the case of thermal emission, one should have Tb 6 T. the angular frequency xpa related to fpa by the relation We shall now distinguish between incoherent and xpa =2pfpa. The plasma frequency for electrons can be coherent emission mechanism. An incoherent radiation simply written in terms of the ambient electronic plasma mechanism is a process where particles behave indepen- density, Ne, the charge and mass of the electron dently of each other. There is no phase relation between 1 N e2 1=2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the emitted photons, that is no coherence. In this case, e 3 3 fpe ¼ ¼ 9 10 N e ½cm MHz. ð5Þ the resulting brightness temperature cannot exceed the 2p mee0 effective temperature Teff, that is the source temperature for a thermal process, or the kinetic temperature for a To understand the meaning of fpe let us assume a plasma non-thermal process. Thus for an incoherent non- composed of electrons and on which acts an exter- ~ ~ thermal emission, due to say MeV electrons as it is often nal electric field E. Due to E there will be a charge sep- observed during solar flares, T is limited by the mean aration which will be responsible for the creation of a b ~ particle energy, such that T 6 E/k 1010 K. During restoring electric field to compensate the effect of E.If b B ~ a coherent process emitting particles can behave as a we suddenly shut down E and study the of the whole, emitting photons between whose exists a phase electrons, neglecting collisions between particles as well relation. Thus, a coherent emission is not the result of as ions , we find that electrons will oscillate individual particle emission, but rather a collective pro- around an equilibrium position with the frequency fpe. cess for example triggered by waves when certain insta- These undamped oscillations are called plasma oscilla- bilities develop in magnetized plasmas. The brightness tions. In the cold plasma wave theory, these oscillations temperature resulting from a coherent emission mecha- are called Langmuir waves at the frequency x = xpe, nism can thus largely exceed the mean particle energy, and taking into account the electron temperature Te and can reach few 1015 K as for some decimetric solar (or the pressure gradient term in the equation of the radio bursts. electron motion), Langmuir waves can propagate and Due to the presence of a magnetic field an electro- have a given by magnetic wave will propagate in two different modes: x2 ¼ x2 þ 3k2v2; ð6Þ the extraordinary mode (X) and the ordinary (O) mode. pe 2 e The above defined quantities will depend on the mode of where k is the wave number and ve the mean electron propagation. The detected radiation is said to be polar- thermal . It is important to note that the Lang- ized when the emission in one of the two modes domi- muir waves are electrostatic waves, that do not transport nates that in the other (Kraus, 1966; Christiansen and any electromagnetic energy. Hogbom, 1985; McLean and Labrum, 1985). In this In the presence of a magnetic field another natural case, the of is a measure of the inten- plasma frequency is the gyrofrequency, fbe (for elec- sity received in one of the two modes, relative to the to- trons), defined by the frequency with which an electron tal intensity. Since the Faraday of the plane of gyrate around magnetic field lines due to the Lorentz polarization is strong when radio waves propagate force. fbe, often referred to Xe in the literature through the solar corona, it suppresses any linear polar- (Xe =2pfbe), can be expressed using ization present at the emitting source, and thus only the eB 6 degree of can be measured. How- Xe ¼ ¼ 2p 2.8 10 B½G Hz; ð7Þ ever, see McLean and Labrum (1985) for examples of at- me tempts in detecting linearly polarized solar radio where B is the magnetic field strength. Thus, taking into emission. account the magnetic field and the presence of ions, the J.-P. Raulin, A.A. Pacini / Advances in Space Research 35 (2005) 739–754 743 electron plasma frequency given by Eq. (5) will be bulence. The hydromagnetic treatment, that is a back- slightly modified and will fall in the range given by the ground plasma composed of cold particles (electrons upper hybrid frequency, xUH, and the lower hybrid fre- and ions) and a beam of cold or monoenergetic particles quency, xLH, given by (electrons with velocity Ve0), can be done graphically (Sturrock, 1994; Kivelson and Russell, 1995). The solu- 2 2 1=2 xUH ¼ðxpe þ Xe Þ ; tion of the dispersion relation given by ! 1=2 ! 1 1 ð8Þ x2 x2 x ¼ þ ðX X Þ1=2. pi pe LH 2 2 e i 1 ¼ 2 þ 2 ð10Þ xpi þ Xi XeXi x ðx kV e0Þ In the solar corona, we generally have the relation may lead to a complex solution for x of the form xUH P xpe > Xe xLH > xpi Xi. x = xr ±ixi. Such that any in the plasma ixt ixrt ct The , kD is a useful parameter to study will varies in time as e =e e where c = xi. collisions in a plasma. It defines the distance over which Therefore we see that c > 0 will imply an exponentially a test electron from the plasma will not feel anymore the growing perturbation. Although this simple situation electrostatic field from an . kD is the ratio of the ther- shows that under some circumstances Langmuir turbu- mal speed to the plasma frequency, and thus depends on lence can grow at a rate c within a plasma, it does not the ambient electron density Ne and the plasma temper- tell us from where comes the energy provided to the tur- ature T, through the following equation: bulence nor when the amplification will stop. To solve sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi this problem, it is necessary to adopt a more detailed T ½K k 6.9 e cm 9 treatment taking into account the of the D ¼ 3 ð Þ N e ½cm background plasma and the beam particles, that is ki- netic effects. In Fig. 5, we show a more realistic situation being then much lower in the cool and low altitude for the velocity distribution of a background plasma dense solar atmosphere compared to its value in the di- where a fast particle beam propagates. It can be shown lute and hot corona. of0 (Benz, 1993) that c / xr o where xr is the real part of The plasma parameter b is a measure of the gas-to- vz the frequency given by Eq. (6). Fig. 5 shows that in magnetic pressure ratio. For b 1 like close to the solar of0 the region where o is positive plasma turbulence with surface, the particles dominate the plasma dynamics and vx phase velocity x/k, may suffer strong amplification. they drag along magnetic field lines. In the outer solar For such a turbulence, with a phase velocity V , we basi- atmosphere, i.e., the solar corona, we have everywhere / cally have more particles with velocity greater than V b 1 implying that the plasma is confined by the mag- / than we have particles with velocity lower than V .So netic field. / the net effect is the growth of the turbulence, at the ex- pense of a reduction of the beam velocity. Then, as a 3.2. Coherent emission mechanism function of time, the beam velocity distribution will be destroyed, and become rather a ‘‘plateau’’. It is then a The most known coherent process to produce –particle interaction effect, where energy is trans- emission is the plasma emission, which is a multi-step ferred from the particle beam to the waves present in process. It first involves some kind of Langmuir turbu- the plasma, which can explain the growth of the plasma lence, generally attributed to a streaming instability. turbulence in a region where it exists a resonant condi- The next step is to convert the energy available in the tion between the particles and the waves. This instability plasma turbulence into fundamental electromagnetic is the so-called bump-on-tail instability, which is impor- transverse radiation at or close to the local plasma fre- tant to explain some kind of metric radio bursts like quency (x = x ) which can escape from the medium pe Type IIIs. and be detected. This is because Langmuir turbulence does not propagate and can only be detected . 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 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 a background thermal plasma where a beam of particles propagate is a very simplified situation, it gives already Fig. 5. Velocity distribution function of a thermal background plus a some important details on the production of plasma tur- fast beam, showing the velocity region where turbulence can develop. 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 The Larmor formula (Rybicki and Lightman, 1979) anisotropic velocity distribution. This occurs when par- expresses the power radiated by a single accelerated ticles are trapped in magnetic bottles, that is a region charge (q, mass m, velocity v) in the direction h relative bounded by two sites of high magnetic field strength to the acceleration vector within the solid angle dX B . Conservation (of energy and magnetic moment) max dP q2v_2 laws show that as a particle moves toward high magnetic ¼ sin2ðhÞ; ð11Þ dX 4pc2 field regions its velocity component parallel to ~B, vi de- creases. When arriving at the point where B = Bmax, where v_ ¼ dv=dt, and which gives after integration on X the particle can escape the bottle if vi > 0. Otherwise 2q2v_ 2 the particle will be confined in the magnetic bottle. P ¼ . ð12Þ 3c2 The mirror ratio between Bmax and the minimum field strength within the magnetic configuration defines an Note on the radiation pattern, P, that: (i) the total power is proportional to the charge; (ii) no power is angle (pitch-angle) am such that any particle with initial d emitted in the direction of the acceleration; (iii) maxi- pitch-angle a ¼ð~v;~BÞ < a will escape from the bottle m d mum power is emitted in a direction perpendicular a ~v;~B > a and those particle with ¼ð Þ m will remain to the acceleration; (iv) since v_ is 1/m, the power is trapped. This situation is illustrated in Fig. 6 where 2 1/m and the radiation from will be negligiable the pitch-angle region shown by the gray filled area is compared to that emitted by electrons. empty of charged particles. In plasmas where Xe P xpe the above anisotropic configuration will transfer energy 4.1. Free–free bremsstra¨hlung into directly escaping electromagnetic radiation, through an instability called electron cyclotron This emission is due to Coulomb collisions between (ECM). The ECM emission (Wu and Lee, 1979)is charged particles in a plasma. In Fig. 7, we show an responsible for planetary radio emissions and some very example of a binary collision between an electron of bright solar radio spikes. velocity v and an ion of charge Zi. The effect of the col- lision is to deflect the incoming electron by an amount which depends on the impact parameter b. However in 4. Incoherent radiation processes the solar coronal plasma the situation is quite different. This is due to the very high number of particles present The basis for incoherent radio emission in low density in the Debye (see Eq. (9)). The ratio of small-to- medium like the solar corona is the emission from free large angle encounters can be approximated by kD/rc accelerated particles. A charge in rectilinear uniform where r is the impact parameter b which produces a motion creates in space an electromagnetic field which c 90 deflection. As a consequence small-angle collisions energy is static and constant in time, i.e., does not prop- dominate and the of an incoming electron is agate. When the charge is accelerated we have an addi- rather determined by a multitude of small deviations. tional electromagnetic field component, which is time However, in the cool and very dense low solar atmo- dependent because of the time dependent velocity. Con- sphere, the effect of large angle encounters is enhanced trary to the static case, the electromagnetic energy now since there the Debye sphere is much smaller. Then high propagates and we say that the charge is radiating. This energy electrons can undergo large deflection and lose is what happens for example in the emission of radio most of their energy emitting high energy hard X-ray waves when electrons oscillate in an antenna. photons. In the tenuous solar corona, the emitted pho- tons may fall in the radio wavelength range, and this is what we are interested in the following. In this case, the bremsstra¨hlung emission from one incoming

Fig. 7. Binary Coulomb collision showing the impact parameter and Fig. 6. Loss-cone velocity distribution. 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- frame it is beamed along the direction of ~v, also called tion (Rybicki and Lightman, 1979) the forward beam. The time T, it takes for the emission cone to pass in front the observer is 2/X . Because of dW ðbÞ 8 Z2e6 1 e ¼ i e2xb=v Doppler shift, this time s will be shorter for an observer dx 3p m2c3 ðbvÞ2 e at rest by a factor 1 v/c. For energetic electrons, we 2 2 6 have s =2p/(c Xe). Thus, as a function of time, the 8 Zi e 1 2 3 2 ð13Þ power P(t) emitted by an electron is a succession of 3p me c ðbvÞ pulses of width s separated by 2pc/Xe, i.e., occurring for b v/x. Taking into account the total incoming with the frequency Xe/2pc. In the spectral domain, the electron flux, 2pbdbnev, where ne is the electron density, electron emission is then different depending on the Lor- colliding in a plasma with an ion density ni, and integrat- entz factor. For monoenergetic cold electrons, the emis- 2 ing Eq. (13) between impact parameters bmin =4Zie / sion occurs at the frequency Xe and is also called 2 pmev corresponding to a 90 deflection and bmax = v/x cyclotron emission. For higher energy thermal electrons above which the emitted power is negligiable, we get (few eV to tens of eV) the time profile is modified and the bremsstra¨hlung emission per unit time, and harmonics of Xe appear in the spectral domain. The frequency emission called gyroresonance then occurs at low har- monics number (s = 1,2,3,...) of the Larmor frequency. dW ðbÞ 16e6 b ¼ n n Z2Ln max For mildly relativistic electrons (few tens of keV to few dxdV dt 3c3m2v e i i b e min hundreds of keV), P(t) presents much thinner and sepa- 6 16pe 2 rated peaks, resulting in a broadband frequency range ¼ 3=2 neniZi gff ðv; xÞ; ð14Þ 3 2 emission from harmonics of Xe in the range s = 10– 3 c me v 100. This emission is called gyrosynchrotron emission. where gff(v,x) is the Gaunt factor (Karzas and Latter, For highly relativistic electrons, the angular pattern of 1961) which is slightly dependent on the frequency m. emission is beamed along the particle velocity. The emis- For a totally ionized electron– plasma like the so- sion called synchrotron emission will mainly occur along lar corona (ne = ni and Zi = 1), composed of thermal the particle velocity at very high harmonics s c3 of the particles, we get the thermal bremsstra¨hlung emissivity Larmor frequency. gm at the frequency m (x =2pm) by integrating Eq. (14) The treatment of magnetobremsstra¨hlung emission over v using a Maxwellian distribution function from a collection of electrons is complex since it needs 25pe6 2p 1=2 the knowledge of the velocity and pitch-angle distribu- g ¼ n2T 1=2g ðv; xÞ. ð15Þ m 3m c3 3m k e ff tions of the particles (Pacholczyk, 1979). Moreover, e e B the effects of the ambient medium and of an inhomoge- We thus conclude that the radio emissivity from a free– neous magnetic field structure in the emitting region free bremsstra¨hlung emitting plasma is proportional to should be taken into account. Complete calculations the ambient density and inversely proportional to the of the emissivity for an isotropic velocity distribution plasma temperature. We also note that as long as radia- of electrons in an homogeneous magnetic field have been tive transfer of the radiation is not taken into account, performed (Ramaty, 1969; Ramaty et al., 1994). Semi- there is almost no dependence of the emission as a func- empirical useful formulae for gm obtained within the tion of the frequency. same conditions and valid in a restricted range of har- monic numbers s have been estimated (Dulk and Marsh, 4.2. Magnetobremsstra¨hlung emission 1982; Dulk, 1985). Inhomogeneous magnetic field mod- els and absorption of the radiation by the ambient med- In the presence of an external magnetic field ~B,a ium have been studied (Klein and Trottet, 1984; Klein, charged particle will spiral around field lines due to 1987), as well as the effects of anisotropic electron the Lorentz force, and thus suffer continuous velocity pitch-angle distribution (Lee and Gary, 2000). direction changes that will produce electromagnetic Mainly two kind of particle distributions are usually radiation. In the absence of an electric field the acceler- used: Maxwellian and power-law. In the first case, the ~ ation term is perpendicular to B, a^ = Xv^, where X is dominant mechanism is the gyroresonance emission at the gyrofrequency given by Eq. (7). Using the Larmor discrete and low harmonic number of Xe, which emissiv- formula (Eq. (12)), we get the power emitted by an accel- ity can be written as a function of the density ne, the erated electron magnetic field strength B and its direction relative to 2e2 v2 e2B2 the observer. Thus, gyroresonance emission will be rele- P ¼ c2 ? ; ð16Þ vant to study magnetic field structure above solar active 3c3 m2c2 e regions. In the case of a non-thermal power-law energy where c is the Lorentz factor. In the electron reference distribution of electrons AEd, the gyrosynchrotron frame the power emitted is dipolar, and seen from a rest 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 These equations will allow to compute for different emis- parameters as well as the magnetic field strength B. This sion mechanisms the variations of Tb (or Sm using Eq. will mostly be useful to study gyrosynchrotron from (4)) as a function of the frequency, that is to get the flare accelerated particles. radio spectrum. For a given emission mechanism, it is common to use the corresponding optical depth or opacity, rather than 5. Radiative transfer the emissivity, although both can be related at the ther- modynamical equilibrium. As an example for a fully After to have reviewed how emission can be obtained ionized e–p plasma we can use Eq. (15) to get the from different processes, through the emissivity term gm free–free bremsstra¨hlung opacity (Dulk, 1985): in W m3 St1 Hz1, we will now study how this radia- 2 tion is transported (Kraus, 1966). The change of inten- 3 N e ‘ sff ¼9.78 10 ð18.2 þ 1.5 ln T ln mÞ 2 3=2 sity Im at the frequency m (see Eq. (3)) along a ray path m T 5 s is given by dIm = gmds. The radiation is also absorbed ðT < 2 10 KÞ; ð21Þ along the ray path by an amount dIm = jmImds where 2 3 N e ‘ j is an absorption coefficient per unit of length. Putting sff ¼9.78 10 ð24.5 þ ln T ln mÞ m m2T 3=2 together these two expressions leads to the equation of 5 radiative transfer ðT > 2 10 KÞ; ð22Þ dI where the Gaunt factor has been evaluated for two tem- m ¼ g k I . ð17Þ ds m m m perature regimes, and where ‘ is the size of the emitting medium along the line of sight. Thus, free–free brem- The first term is a source term while the second term is sstra¨hlung emission is mainly a diagnostic of the plasma an absorption term. The latter is used to define the opti- temperature and density. Note also that the radio free– cal depth s as the integrated absorption along the line m R free opacity is increasing for decreasing T, i.e., very sen- of sight, i.e., s ¼ s j ds. By integrating Eq. (17) with m 0 m sitive to cool and dense plasmas. Because of the small j = 0 (pure emitting medium), we see that the change m dependence of the term in brackets, the radio spectrum in intensity is the integrated emissivity along the line 2 (S as a function of m) will increase as m in the optically of sight. Similarly, an integration with g = 0 (pure m m thick regime and will be roughly constant for an opti- absorbing medium) shows that the intensity decreases cally thin source. exponentially with s . The solution of Eq. (17) can be m The opacity for the gyroresonance mechanism, s , written as: gr can be obtained similarly as done above for the free–free g sm m sm bremsstra¨hlung (Dulk, 1985; and Kundu, 1997). Im ¼ Imð0Þe þ ð1 e Þ. ð18Þ jm sgr is slightly dependent of the density and the tempera- This equation means that the outgoing radiation from ture of the plasma, but strongly depends on the mag- an absorbing medium will be the entering radiation netic field strength and on its direction with respect to the observer. Gyroresonance opacity is higher for the Im(0) absorbed through the medium plus the radiative balance within the medium (integrated source emission X mode compared to the 0 mode, such that the emission minus absorption). At the thermodynamical equilibrium will be highly polarized. In units of the magnetic scale (Eq. (17) equals 0), when the source absorbs as much as height, the thickness of the gyroresonance layer is about v/c, where v is the speed of the emitting thermal elec- it emits, the ratio gm/jm is given by the Planck function (see Eq. (3)). Moreover, when dividing the former equa- trons. Thus, the gyroresonance layer is a very thin por- 2 2 tion of the atmosphere with an almost constant tion by 2kBm /c we get magnetic field value. sm sm T b ¼ T b0e þ T eff ð1 e Þ. ð19Þ For higher energy electrons with a power-law distri- As already discussed in Section 2 for a source in thermo- bution in energy, the spectrum of the radio flux density dynamical equilibrium Teff is the source temperature, decreases with the observed frequency in the optically and for non-thermal emitting particles, Teff is to be con- thin part. The peak frequency mpeak is the frequency be- sidered as given by E/kB where E is the mean energy of low which the radio emission is self-absorbed in the opti- the radiating particles. cally thick part of the spectrum. The optically thin part Two important regimes are found from Eq. (19): (i) of the spectrum is important since its slope is directly re- when sm 1 the source is said to be optically thick; lated to the slope of the injected distribution of electrons (ii) when sm 1 the source is said to be optically thin. (Dulk, 1985). The higher the frequency the higher the These two cases lead, respectively, to: energy of the emitting electrons, and thus high fre- quency radio observations provide a diagnostic of the T ¼ T ðs 1Þ; b eff m highest energy electrons accelerated during solar flares. T b ¼ T b0ð1 smÞþsmT eff ðsm 1Þ. ð20Þ 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 emission is largely due to the MeV energy electrons.

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, Fig. 9. Variations with height of the plasma and gyromagnetic frequencies. f is the curve for which the free–free opacity is equal of the frequency for which sff = 1, as well as harmonics s =1 unity (after Gary and Hurford, 2004). 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 a free–free opacity equals to 1 is lower than that corre- which sff = 1 is optically thin, thus, in the range 10– sponding to low harmonics of the gyrofrequency. Con- 200 MHz plasma emission mechanisms will dominate. sequently, gyroresonance mechanism will prevail in Although plasma radio emission above 200 MHz will high magnetic field regions. be partly absorbed by the ambient plasma through of the effect of collisions, it may still be bright enough to 6.1. Non-flare radio emissions be detected. The reason is that plasma radio waves are naturally extremely bright and can occur at harmonics The oldest observed at metric of the plasma frequency. The highest frequency at which wavelengths is called a storm and has been re- plasma radio emission may have been detected in the so- viewed by Elgaroy (1977). It is composed of short dura- lar corona is about 8 GHz. Thus, for frequencies be- tion (61 s) metric radio enhancements called Type I tween 200 MHz and 1 GHz, both mechanisms, bursts, superimposed on a broad frequency band contin- plasma and bremsstra¨hlung can coexist. Between 1 and uum (McLean and Labrum, 1985). Noise storms are 3 GHz the hot and dense plasma from the active regions spatially associated with active centers, but are not flare is optically thick for free–free bremsstra¨hlung emission related (Le Squeren, 1963), and they can last for several which is then the dominant mechanism. Above about consecutive days. Their importance lies on the fact that 3 GHz, the altitude for which the ambient plasma has they 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 that Type 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 Fig. 8. A plot of non-thermal gyrosynchrotron flux spectra as a through the free–free bremsstra¨hlung mechanism. How- function of frequency for different values of the low-energy cutoff. The ever the emission will greatly depend on the atmospheric 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 layer because of the dependence of the free–free opacity is 45. The curves are labelled according to the low-energy cutoff (after sff (see Eqs. (21) and (22)), on the plasma density Ne,and White and Kundu, 1992). the local temperature T. Using a typical temperature of 748 J.-P. Raulin, A.A. Pacini / Advances in Space Research 35 (2005) 739–754

6 9 3 10 K and density of 10 cm we get sff 1 in the strongly of the angle h, between the magnetic field and whole microwave range indicating that the quiet corona the line of sight, thus, explaining horse-shoe emission will be optically thin at these frequencies. Through the shapes like the one shown in Fig. 10. micro- transition region to the , Ne increases by wave radio emission compared to model calculations a factor of 100 and T decreases by about the same fac- (Gopalswamy et al., 1996; Nindos et al., 1996) have con- tor, implying a change of seven orders of magnitude in firmed that gyroresonance is the main mechanism at sff resulting in an optically thick chromosphere. Zirin work. et al. (1991) have effectively shown that the free–free emission from the quiet sun center between 1.4 and 6.2. Solar flare radio emissions 18 GHz was composed of the radiation of a thick upper chromosphere at 11,000 K, observed through a thin Solar flares produce copious amount of coherent corona at 106 K and scale height of 5 · 109 cm. At meter radio waves, which have been classified for more than wavelengths the situation is somewhat different since the 40 years into different classes (see Kundu, 1965; McLean corona will be optically thick at some height showing and Labrum, 1985; Benz, 1993, for reviews). The main brightness contrasts with extended regions called coro- observational parameters for this classification are those nal holes. These regions are cool and low density areas that can clearly be identified on dynamical spectra re- in the corona, and their time variability is important cords (see Fig. 4), i.e., bandwidth, frequency drift rate to characterize the high-speed solar . At much and duration of the emission. The different types of higher frequencies (millimeter and submillimeter wave- coherent bursts in the decimetric/metric domains will lengths), the radio emission is sensitive to the cool and not be discussed here and the reader is referred to the dense chromospheric material which provide enough above reviews. Instead we rather describe some charac- free–free opacity, while the corona remains totally opti- teristics of Type III solar bursts in the following para- cally thin. Vernazza et al. (1981) tested successfully their graph, while properties of Type I solar bursts have chromospheric atmosphere model deduced from EUV already been discussed in the previous section. We also observations, against 100 GHz radio measurements of mention that there is no clearly accepted emission mech- the quiet Sun which originate at layers where the tem- anism for any of the coherent solar radio bursts, and the perature was 6600 K. However, the same model atmo- non-linear of the coherent process itself makes it sphere seems to disagree with optically thick microwave very difficult to conclude on quantitative estimations observations (Zirin et al., 1991; Bastian et al., 1996). On like electron number and spectrum which represent cru- the other hand, the latter radio observations are well ex- cial informations to test particle acceleration models plained by chromospheric models based on CO line (Miller et al., 1997). measurements (Avrett, 1995), suggesting that a chromo- Type IIIs are among the more studied solar coherent spheric model which could explain, high frequency bursts, and generally occur at the beginning of the radio, microwaves, EUV and line observations is still impulsive phase of a solar flare. As seen in dynamic missing. spectra, Type IIIs are fast drifting bursts (see Fig. 4) Solar active regions are high density and high mag- from high-to-low frequencies, i.e., from high critical netic field regions located above sunspots. Radio emis- plasma frequency levels to low critical plasma fre- sion will occur due to the two following mechanisms: quency levels. Reverse bursts are those which will show gyroresonance and free–free bremsstra¨hlung. Which fast drifts from low-to-high frequencies. Type IIIs are 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 GHz the 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 Fig. 10. Optical (left) and radio (right) emissions above a sunspot. the gyrofrequency. Therefore, providing an unique Note the ‘‘horse-shoe’’ like structure of the radio source (Courtesy of way of measuring magnetic field strength. The structure S.M. White, after http://www.astro.umd.edu/white/text/activeregio of the gyroresonance emission source depends also nimages.html). J.-P. Raulin, A.A. Pacini / Advances in Space Research 35 (2005) 739–754 749 thought to be produced by plasma waves excited by particle energy, but only the gyrosynchrotron emission electron beams propagating at different levels of the so- is sensitive to the magnetic field, their comparison can lar atmosphere. Since electron beams propagate along bring clues on the transport and pitch-angle distribu- magnetic field lines, Type IIIs are used as tracers of tion of the emitting electrons, as well as on the mag- magnetic field structures. For example radio Type IIIs netic field strength. The transport of microwave are observed during the rearrangement of the magnetic emitting electrons has been studied by Lee and Gary field structure within active centers resulting in colli- (2000) and tested against spatially resolved radio and mated plasma outflows or ‘‘jets’’. In that case the elec- hard X-ray observations. As expected it is shown that tron beams, as imaged using multi-frequency radio the pitch-angle distribution of the injected electrons observations, nicely align with the jet material (Kundu precludes on the temporal evolution of the radio emis- et al., 1995; Raulin et al., 1996). The jet is observed in sion, and a rather beamed (a 6 30; see Section 3.1) soft X-rays, i.e., a diagnostic of the ambient electron injection distribution is needed. On the other hand, density which can be compared to that deduced from an example of efficient trapping is illustrated in Fig. the observed radio frequencies, thus, providing infor- 11 (Raulin et al., 1999), which shows that the impul- mations on the emission mechanism (Raulin et al., sive phase of a small flare is composed of a fast peak 1996). Similarly, different spacecrafts have been used seen in microwaves, millimeter-waves and hard X-ray, to reconstruct the trajectory of a Type III which es- and a few minutes duration emission intense in radio capes into the interplanetary medium (Reiner et al., wavelengths but with no counterpart in hard X-rays. 1998). The electron beam path is following a Parker The electron energy spectrum at the time of the first spiral (i.e., interplanetary magnetic field structure), rapid peak was harder at energies of 1 MeV (i.e., and the speed of the exciters electrons was measured microwave and mm-w emitting electrons), than at at about 100,000 km/s. 6 few 100 s keV (hard X-ray emitting electrons). This Bi-directional Type IIIs are identified on dynamic result has been observed during large flares (Trottet spectra as positive and negative (or reverse) fast fre- et al., 1998), and also during smaller events (e.g., quency drift bursts starting at a given frequency range. Kundu et al., 1994). However, in the absence of imag- Such analysis has been reported by Aschwanden et al. ing informations, it is not possible to conclude (1993), which allows to conclude that the acceleration whether the observed broken spectra are the result region was located at a plasma level of 300–500 MHz, of a single acceleration process, or if the low and high corresponding to an ambient density of 3 · 108– energy parts of the spectra are due to independent 3 · 109 cm3. More recently, other informations on the injections, for example localized at different places in acceleration and energy release sites were presented by the solar atmosphere. Paesold et al. (2001). In this work, double Type III sources were found to originate from the same metric spike source, suggesting that the fast spikes were closely related to the acceleration region. As mentioned earlier, part of the energy dissipated during solar flares is used to accelerate particles to high energies. As part of these, electrons propagate in the solar atmosphere emitting radio waves through the gyrosynchrotron mechanism when passing by high magnetic field strength regions, and eventually collide in the dense lower atmosphere where they are instan- taneously stopped and emit high energy hard X-ray photons through the non-thermal bremsstra¨hlung pro- cess. Both of these mechanism thus provide direct diagnostics of the energetic electrons. However, and when compared to non-thermal bremsstra¨hlung, the gyrosynchrotron process is quite sensitive to the pres- ence of even only a few numbers of energetic elec- trons, as long as they are spiralling in strong magnetic fields. This property allowed to detect gyro- synchrotron emission from very simple small flares (Kundu et al., 1994; Raulin et al., 1999), with flux density levels as low as 1.5 SFU, showing that flares Fig. 11. Time profile of a small flare at microwave (17 GHz; dashed), of all sizes are capable of accelerating electrons to hard X-rays (histogram) and at millimeter-waves (86 GHz, BIMA, MeV energies. Since both processes depend on the thick) (after Raulin et al., 1999). 750 J.-P. Raulin, A.A. Pacini / Advances in Space Research 35 (2005) 739–754

7. Solar radio emission at very high frequencies

The above 100 GHz has been mostly unexplored until the last years. Early micro- wave solar flare observations have shown radio flux spectra increasing with frequency, suggesting a spectral maximum above 30 GHz (Hachenberg and Wallis, 1961), which could represents the superposition of differ- ent synchrotron spectra or the emission from ultra- relativistic electrons. At higher frequencies, there are numerous examples of complex synchrotron spectra ob- tained during both large and small solar bursts showing flat or increasing fluxes with the observed frequency (see Fig. 2 of Kaufmann, 1996, for a summary). These exam- ples suggest a spectral peak located above the highest observed frequency of 100 GHz. Few solar observa- tions were made at even higher frequencies: at 250 GHz (Clark and Park, 1968) reported one minute Fig. 12. Radio spectrum at different peaks (P1 and P4) during the temporal fluctuations of the order of 100 K above ac- impulsive phase of the 2003, November 4 large solar event. Spectrum tive regions, and at 850 and 12,000 GHz 10–50 K varia- for fast submillimeter structures during P1 is also shown (after tions were detected by Hudson (1975). Kaufmann et al., 2004). A new solar submillimeter facility was conceived to fill the gap of observations above 100 GHz (Kaufmann, 212 and 405 GHz. Suggesting the detection of a new so- 1996). The solar dedicated Solar Sub-millimeter Tele- lar flare emission component radiating in the terahertz scope (SST) was installed in the argentinean andes in range only. These observations imply strong constraints 1999, May (Kaufmann et al., 2001a). The SST has four on the acceleration mechanisms, on the radiation pro- 212 GHz and two 405 GHz radiometers located at the cesses and the source parameters. In a non-thermal syn- plane of a 1.5 m diameter reflector, recording with chrotron interpretation, the high turnover frequencies 5 ms time resolution. The beam disposition allows to would imply ultra-relativistic emitting electrons, high estimate the position of the centroid emission for a small magnetic field values, and extreme conditions in the emit- source, using the multiple-beam technique (Gime´nez de ting region, like ultra compact sources and/or high ambi- Castro et al., 1999). The SST was operating during short ent , as to produce turnover frequencies in the solar observing campaigns till 2001, April when daily submillimeter wavelengths range or higher, as during observations began. The main results obtained for the the 2003, November, 4 solar event. A thermal interpreta- solar events analyzed so far are: (i) the existence of fast tion would require high density and cool plasma regions, subsecond pulses (Kaufmann et al., 2001b, 2002; Raulin like the chromosphere, to produce turnover frequencies et al., 2003; Makhmutov et al., 2003), superimposed on a at P400 GHz. But at the same time the high flux densi- slower bulk component emission which is the high- ties observed (e.g., during the 2003, November, 4 event) frequency tail of a microwave gyrosynchrotron spectrum need to be explained by a rather large emitting source, (Trottet et al., 2002); (ii) when both fast and bulk compo- and this was not the observed. nents are observed, the rapid pulsesÕ occurrences rate and Radio observations obtained in a large frequency amplitudes time profiles follow the time history of the range from 1 to 405 GHz has also been used to estimate main bulk emission at submillimeter-waves, and at hard the number of accelerated electrons and magnetic field X-rays and c-rays energies (Kaufmann et al., 2002; Rau- strength in the flaring region. Raulin et al. (2004) report lin et al., 2003); (iii) spectra of individual fast structures the study of the 2001, August 25 X5.6 solar flare which are increasing, or flat, between 212 and 405 GHz (Kauf- produced over 100,000 SFU at 89.4 GHz. The interpre- mann et al., 2001b; Raulin et al., 2003). More recently, tation of the radio spectra during the impulsive phase, Kaufmann et al. (2004) presented submillimeter, milli- as due to synchrotron emission from 20 MeV electrons, meter and microwave observations obtained during the requires that 5–6 · 1036 electrons with energies P20 keV large solar flare of 2003 November, 4. The properties are accelerated each second and radiate in a 1000– of the radio emission agree with the above mentioned 1100 G region. The self- of the 89.4 GHz properties (ii) and (iii). However, the main bulk emission emission during the most intense part of the event is com- at submillimeter-waves was clearly not the high fre- patible with a high density of non-thermal electrons quency part of the optically thin gyrosynchrotron micro- (1011 cm3 electrons above 20 keV). A suggestion is wave/millimeter spectrum, as shown in Fig. 12. Indeed that non-thermal electrons were accelerated in the low the bulk flux density has been found to increase between solar atmosphere, scenario which also agrees with the J.-P. Raulin, A.A. Pacini / Advances in Space Research 35 (2005) 739–754 751 fact that the most intense part of the event was triggered depression onto the solar disk and bright over the limb. along with the interaction of very compact low-lying Then the erupting material can be tracked in the corona magnetic loop systems. Such high non-thermal electron up to distances over 3 . More recently, Kun- numbers were also recently deduced using radio observa- du et al. (2004) have shown an example where a filament tions up to 80 GHz and hard X-ray data from the RHES- eruption starts far away (0.5 Rx) from the site of the SI detectors (White et al., 2003). In any case, the high associated flare, implying that if both phenomena are numbers deduced from these observations indicate that physically related, the destabilization of a large scale the acceleration mechanism should be very efficient. coronal magnetic field is required. Solar flare observations have also been performed at Secondary radio products of CMEs have also been 210, 230 and 345 GHz using the KOSMA radiotelescope observed in the form of Type II shocks, Type IV (see (Lu¨thi et al., 2004a,b), during two X class flares. The McLean and Labrum, 1985) and storm continua (see more relevant result of these studies is the finding of Pick, 1999, for a review). Bastian et al. (2001) report the source size at 212 GHz of about 1000 during the the imaging of a CME at decimeter-meter wavelengths impulsive phase of one of the events. During the gradual and in white-light using the Nanc¸ay Radioheliograph phase of few tens of minutes duration, the radio source (Kerdraon and Delouis, 1996) and the LASCO experi- size was as big as 10. ment (Brueckner et al., 1995), respectively. The authors show that the CME expanding arches are illuminated by 0.5–5 MeV electrons emitting in 8. Space weather related solar radio emissions a 0.1 G, and that these particles could have been pro- duced during the associated flare. Such observations During the last two decades it became clear that solar provide in principle independent diagnostics of the conditions greatly affects the Earth and its environment. CME magnetic field as well as of the ambient electron The solar influence acts through particles, radiation and density. The signatures of the interaction between two mass ejections, and their time variabilities define the CMEs can also be detected. Gopalswamy et al. (2001) space weather conditions. Extreme space weather condi- have studied the in the interplanetary space tions can in turn have practical consequences for on of subsequently ejected CMEs and noted that at about Earth and in space. Radio observations indices such as, the time the trajectory paths intersect each other, radio 245 MHz burst and noise storm fluxes, 10.7 cm flux, are enhancements are observed. The radio emission is inter- used in Space monitoring by the Space Environment preted as the result of the collision between the two Center (NOAA) to produce daily alerts. Occurrence of CMEs. The authors comment on the relevance of their Type II bursts (see McLean and Labrum, 1985, for a re- observations in the context of Space Weather and for view), which are characteristics of radio emissions asso- predicting the arrival of Earth directed perturbations. ciated with propagating disturbances in the corona and Recent observational suggestions have been reported interplanetary medium, are also used for this purpose. which might bring new informations on the processes at Coronal mass ejections (CMEs) in particular have a the origin of these energetic phenomena that are CMEs. great influence on the interplanetary medium, producing Kaufmann et al. (2003) presented a study on the associ- shocks and possible geomagnetic storms at the time of ation between the launch time of CMEs detected by their impact with the Earth magnetic field. Along with LASCO and the occurrence rate of fast submillimeter the destabilization of large scale magnetic structures that pulses observed at 212 and 405 GHz by the SST. Few form a CME, prominence eruptions are often detected of the CME examples presented were not associated (Gopalswamy et al., 2003) and sometimes well associ- with a flare on the solar disk. By extrapolating the ated with the bright core of the CME. The study of plas- CME positions back to the solar surface, the onset of ma ejections in radio waves allows to observe the the ejections were nearly coincident with a significant in- initiation of the ejection close to the solar surface, con- crease of the submillimeter pulsed activity. Although the trary to what can be done using coronographic observa- characteristics of the fast submillimeter bursts have al- tions. Also, white-light emission is only sensitive to the ready been reported (Makhmutov et al., 2003; Raulin density integrated along the line of sight, while radio et al., 2003), their origin is still unknown. They might emission can detect possible non-thermal particles asso- represent multiple small scale instabilities, and an early ciated with the ejection. signature of the launch and acceleration of large masses Prominence eruptions have been extensively studied of coronal plasma. at radio wavelengths, in particular at 17 GHz (see Gopalswamy et al., 2003 for a statistical study) by the Nobeyama Radioheliograph (Nishio et al., 1994). The 9. Conclusions emission mechanism is optically thick free–free brem- sstra¨hlung (see Eqs. (21) and (22)) from the cool and We have presented a tutorial review on solar radio dense prominence plasma, which generally appears in emissions where we have defined some radio astronomy 752 J.-P. Raulin, A.A. 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