Although coronae radiate across the electromagnetic spectrum, the dominant losses occur in the soft-X-ray range; the radio regime provides complementary diagnostics on non-thermal processes. I concentrate on these two aspects (see Section 5.7 for details on radio emission).
The total X-ray output of a stellar corona depends on the available magnetic energy and is therefore a consequence of the dynamo operation. Younger and more rapidly rotating stars are more X-ray luminous; as is the case for UV and FUV radiation, the X-ray output decreases as the star ages and its rotation period increases. For solar analogs, the decay law is,
(where is the stellar age in Gyr) as derived from small but well-characterized samples (Maggio et al., 1987; Güdel et al., 1997b). This decay law holds for MS stars back in time as long as
The second condition is fulfilled only for ages higher than (at least) 100 Myr (Soderblom et al. 1993, see Section 5.2). Consequently, the X-ray luminosity of a solar analog is nearly only a function of rotation period for stars older than 100 – 200 Myr, and this dependence is given by
as derived from a sample of nearby solar analogs (Güdel et al. 1997b; see Figure 14; a very similar decay law is found from measurements conducted with broadband spectrometers on board XMM-Newton: LX 4.04 × 1030 [erg s–1], see Telleschi et al. 2005). The rotation-activity law (Equation 13) is confirmed by broader studies, also with regard to Rossby number Ro that is defined as the ratio between the two time scales of rotation and convection driving the dynamo (, where is the convective turnover time; Noyes et al. 1984; Mangeney and Praderie 1984). All studies find roughly LX / Lbol P–2 for late-type stars (e.g., Randich 2000). Also, other activity indicators such as the surface X-ray flux follow an equivalent law.
Alternatively, the X-ray output roughly scales with the square of the equatorial velocity,
(Pallavicini et al., 1981; Ayres and Linsky, 1980; Maggio et al., 1987; Wood et al., 1994). The X-ray output is an excellent indicator of dynamo activity. The coronal output is strongly determined by parameters that control the magnetic dynamo.
For the most active stars, LX is somewhat suppressed, for reasons that are not well understood. The stars are in a “super-saturated” regime (Randich et al. 1996, see discussion in Güdel 2004).
The overall rotation and activity history of a solar analog star from ZAMS to the terminal stages of its MS life thus proceeds roughly as follows:
The non-flaring corona of the contemporary Sun shows temperatures of a few MK. Active regions tend to be hotter than the quiet corona, and consequently, the average coronal temperature during the Sun’s activity maximum is higher than at minimum. Peres et al. (2000) have studied the full-disk solar coronal emission measure distribution to find peak temperatures of 1 MK and 2 MK during minimum and maximum, respectively. The corresponding X-ray luminosities amount to LX 3 × 1026 erg s–1 and LX 5 × 1027 erg s–1, respectively. These solar observations suggest that regions of higher magnetic activity, but also episodes of higher overall magnetic activity, not only produce higher-luminosity plasma but also higher temperatures. Does this reflect in coronae of stars with widely varying activity levels?
The spectral evolution of the X-ray and EUV (coronal) Sun in time is illustrated in Figures 15, 16, and 17. These figures of course support the trend of decreasing flux with increasing age as described in Section 5.5.1, but they reveal other important features:
These spectral features clearly suggest higher temperatures in more active, younger solar analogs.
From full spectral interpretation, a tight correlation has indeed been found between the characteristic coronal temperature and the normalized coronal luminosity LX / Lbol: Stars at higher activity levels support hotter coronae (Vaiana, 1983; Schrijver et al., 1984; Stern et al., 1986; Schmitt et al., 1990; Dempsey et al., 1993; Maggio et al., 1994; Gagne et al., 1995a; Schmitt et al., 1995; Hünsch et al., 1996; Güdel et al., 1997b; Preibisch, 1997; Schmitt, 1997; Singh et al., 1999).
Figure 18 shows the correlation between average (emission-measure weighted) coronal temperature and the total X-ray luminosity for solar analogs, including solar maximum and minimum values (the latter from Peres et al., 2000). Numerically, the correlation for the stellar sample reads
where Tav is in MK, and LX has been determined in the 0.1 – 10 keV band (Telleschi et al. 2005, and similar results in Güdel et al. 1997b for the ROSAT energy band). Such relations continue to hold into the PMS domain where exceedingly hot coronae with temperatures up to 100 MK are found (Imanishi et al., 2001).
The trend seen in coronal X-ray emission is similar to the trends described previously for the UV, FUV, and X-ray bands (Sections 5.3, 5.4, and 5.5.1): The emission from stars at higher activity levels is harder, implying that harder emission decays more rapidly in the course of stellar evolution.
Three classes of models have been proposed to explain this correlation:
which fits to a sample of observations with T taken from single-T fits to stellar coronal spectra. Equation (16) holds because coronal heating directly relates to the production rate of magnetic fields, and the magnetic pressure is assumed to scale with the thermal coronal pressure.
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