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The Sun in Time: Activity and Environment 35
5.5 The extreme-ultraviolet and X-ray Sun in time
The present-day Sun’s corona can be characterized by its total radiative output (mostly in the soft-
X-ray regime) of a few times 10 26 erg s −1 at minimum activity level to a few times 10 27 erg s −1
at maximum activity level outside very strong flares; its electron temperature of about 1 – 5 MK,
depending on the magnetic coronal structure under consideration; and its filling factor. The latter
is difficult to define as a large variety of (partly expanding) structures confined by closed or open
magnetic fields define the magnetic corona. Suffice it to say that the strongest magnetic active
regions are confined the volumes closely attached to photospheric sunspot complexes, and the latter
cover less than 1% of the solar surface even at activity maximum. Clearly, the solar corona is far
from being filled by luminous active regions.
5.5.1 The solar X-ray corona in time
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,
LX ≈ (3 ± 1) × 10 28 t −1.5±0.3
9 [erg s −1 ] , (12)
(where t9 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
• Equation 12 predicts a luminosity at or below saturation for a solar analog, i.e., LX/Lbol ∼ < 10 −3 ,
or LX ∼ < 4 × 10 30 erg s −1 ;
• the rotation period is a function of age for a star of given mass.
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
LX = 10 31.05±0.12 P −2.64±0.12 [erg s −1 ] (13)
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 × 10 30 P −2.03±0.35 [erg s −1 ], see Telleschi et al. 2005). The rotationactivity
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 (Ro = P/τc, where τc 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,
LX ≈ 10 27 (v sin i) 2
[erg s −1 ] (14)
(Pallavicini et al., 1981; Ayres and Linsky, 1980; Maggio et al., 1987; Wood et al., 1994). The Xray
output is an excellent indicator of dynamo activity. The coronal output is strongly determined
by parameters that control the magnetic dynamo.
Living Reviews in Solar Physics
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