The radio Sun in time

5.7 The radio Sun in time

Magnetically active stars are sources of vigorous radio emission, which is mostly due to gyroemission from accelerated electrons that are trapped in coronal magnetic fields. Radio emission thus provides diagnostics for coronal magnetic fields and at the same time for high-energy electron populations.

5.7.1 Overview

Solar radio emission is a mixture of various kinds of radiation, some of which are thermal while others are of non-thermal origin. The total solar radio emission is strongly variable and is dominated by different radiation types at different times.

Thermal radiation dominates as long as no strong flares are occurring. Three principal types of thermal radiation are observed (e.g., Gary and Hurford, 1994 ):

Thermal bremsstrahlung from chromospheric layers is seen across the solar disk. The emission is dominated by contributions from the optically thick layer. The brightness temperature is of order 10⁴ K, depending somewhat on wavelength.
Above active regions with strong magnetic fields, gyroresonance (cyclotron) emission at low harmonics of the gyrofrequency is often observed. The dominant contributions come from the highest harmonic that is optically thick. This radiation is patchy and covers only a small fraction of the solar disk. Gyroresonance emission may also be accompanied by bremsstrahlung that originates from optically thick layers with coronal temperatures.
Some faint, optically thin coronal bremsstrahlung can also be seen from coronal loops that are filled with hot plasma.

The third contribution is usually rather weak; the non-flaring solar radio emission is dominated by the first and second contributions. Although variable, the average radio luminosity at 3.6 cm wavelength from these contributions is log L_R $≈$ 10.80–11.15 [erg s^–1 Hz^–1] (Drake et al., 1993 ). The picture changes entirely during solar flares, when two new contributions dominate the solar radio output:

Various forms of non-thermal emission from coherent radiation processes such as electron cyclotron masers or plasma radiation mechanisms are signatures of unstable, non-thermal electron populations. The emission is often (but not exclusively) narrow-band and occurs in short bursts (from milliseconds to a few seconds). More persistent coherent emission is occasionally seen.
Gyrosynchrotron radiation originates from non-thermal electron populations that are trapped in magnetic fields. This emission shows a broad spectrum with optically thick and thin components, with a turnover from the former to the latter in the 1–10 GHz range. Gyrosynchrotron emission is a direct tracer of accelerated particle populations.

5.7.2 Observational results

The discovery of solar analogs in radio waves (Güdel et al., 1994 ) was motivated by a correlation between radio and X-ray luminosities that holds for M-type MS stars, but also extends to RS CVn-type binaries and seems to hold similarly for solar flares (Güdel and Benz, 1993 ; Benz and Güdel, 1994 ). The following systematics apply:

The radio emission of detected solar analogs follows the same radio vs. X-ray luminosity relation as found for active M dwarfs.
Only stars with “hard” X-ray spectra, i.e., X-ray emission from very hot coronal plasma (10 MK and more), are non-thermal radio sources.
The detected solar analogs that are not components of spun-up binaries are therefore young ( $∼<$ a few 100 Myr), magnetically active stars.

Figure 23 shows a summary of normalized radio luminosities of solar analogs with different rotation periods. Like X-ray emission, the radio output decays with increasing rotation period (i.e., decreasing magnetic activity), although the decay is much steeper. The radio decay is reminiscent of the very steep decay of the harder portion of soft X-ray emission which is also an excellent tracer of magnetic activity. The steep decline of non-thermal radio emission therefore extends the trend observed above (Section 5.6): Radio emission originates from the most energetic electrons in the stellar atmosphere.

Figure 24 shows the radio luminosity as a function of the average coronal temperature of solar analogs; only radio upper limits are available for the intermediately active coronae with temperatures T_av $≈$ 3–5 MK; a regression fit to the points including the upper limits therefore provides a lower limit to the slope:

(based on the APEC emission line code; Telleschi et al. 2005 ). This empirical relation shows again, and explicitly, that strong non-thermal radio emission develops only in very active stars with hot coronae. Because non-thermal electrons need to be replenished on short time scales, presumably in flare-like processes, a model in which the very hot plasma component is formed by the same flares is suggestive. Alternatively, non-thermal electron distributions may be accelerated continuously out of a Maxwellian distribution into a runaway tail by electric fields (Holman, 1986 ), a concept also proposed to operate in solar flares (Holman and Benka, 1992 ). Such mechanisms of course work best if very hot plasmas are present.

Figure 23:

Relation between L_R/L_bol and the stellar rotation period. Note upper limits for slow rotators. The dotted line illustrates the slope of the X-ray decay law as a function of P (Equation 13

), while the solid line shows the slope of the most rapidly decaying, “hot” X-ray lines (slopes from Table 5 and using Equation 7

; adapted from Güdel and Gaidos 2001 ).

Figure 24:

Relation between non-thermal radio emission and average coronal temperature (from Telleschi et al., 2005

, reproduced by permission of AAS). Open and filled circles refer to different atomic emission line codes used for the temperature determination.

Other types of radio emission are too faint to be detected from solar analogs. Signatures for thermal gyroresonance emission have been found in an M dwarf (Güdel and Benz, 1989 ), and Drake et al. (1993 ) reported evidence for non-flaring radio emission probably related to chromospheric bremsstrahlung and some active-region gyroresonance emission in the nearby F-type subgiant Procyon; more systematic observations of solar analogs during all phases of their MS life will require more sensitive radio telescopes than hitherto available.