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 1026 erg s–1 at minimum activity level to a few times 1027 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) × 1028t−91.5±0.3 [erg s−1] , (12 )

(where t9 is the stellar age in Gyr) as derived from small but well-characterized samples (Maggio et al., 1987Jump To The Next Citation PointGüdel et al., 1997bJump To The Next Citation Point). 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

LX = 1031.05±0.12P− 2.64±0.12 [erg s−1] (13 )

as derived from a sample of nearby solar analogs (Güdel et al. 1997bJump To The Next Citation Point; see Figure 14View Image; a very similar decay law is found from measurements conducted with broadband spectrometers on board XMM-Newton: LX ∝ 4.04 × 1030 P− 2.03±0.35 [erg s–1], see Telleschi et al. 2005Jump To The Next Citation Point). The rotation-activity law (Equation 13View Equation) 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. 1984Mangeney 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.

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Figure 14: Left: X-ray luminosity of solar analogs (from the “Sun in Time” sample), and power-law fit (slope = –2.6). The three objects marked with open squares are close binaries consisting of two early-G solar analogs that rotate synchronously with their orbit motion. These latter stars are in the saturation regime (“RS” and “MEKAL” refer to two different atomic line codes used for the spectral interpretation; from Güdel et al. 1997bJump To The Next Citation Point, reproduced by permission of AAS). Right: Normalized X-ray and C iv luminosities as a function of rotational velocity for solar analogs. Luminosities of the fastest rotators do not follow the regression laws because of saturation (from Ayres, 1997Jump To The Next Citation Point, reprinted with permission).

Alternatively, the X-ray output roughly scales with the square of the equatorial velocity,

LX ≈ 1027(v sin i)2 [erg s−1] (14 )

(Pallavicini et al., 1981Ayres and Linsky, 1980Maggio et al., 1987Wood 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 2004Jump To The Next Citation Point).

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:

5.5.2 The coronal temperature in time

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. (2000Jump To The Next Citation Point) 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 15View Image, 16View Image, and 17View Image. 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.

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Figure 15: Extracts of the EUV spectra of solar analogs with different ages. All spectral fluxes have been transformed to irradiances at 1 AU from the star. The spectra have been shifted along the ordinate, by multiples of 10 erg cm–2 s–1 Å–1 (from Ribas et al., 2005Jump To The Next Citation Point, reproduced by permission of AAS).
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Figure 16: Fluxed high-resolution X-ray spectra of solar analogs with different ages, obtained with the RGS instruments on board XMM-Newton. The topmost two spectra are from K-type T Tauri stars (BP Tau is a classical T Tauri star, V410 Tau a weak-line T Tauri star), while the other spectra are from MS solar analogs. Fluxes are given at a distance of 1 AU from the star, in erg cm–2 s–1 per bin, where the bin width is given in parentheses after the star’s name in each panel (usually 0.05 Å except for β Com where a bin width of 0.0875 Å has been used). Note the anomalously strong O vii (and also Ne ix) lines in the CTTS BP Tau, indicating an excessive amount of cool plasma (the “soft excess”; adapted from Telleschi et al. 2005Jump To The Next Citation Point and Telleschi et al. 2007bJump To The Next Citation Point).
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Figure 17: Low-resolution CCD X-ray spectra of solar analogs with different ages, obtained with the EPIC MOS instrument on board XMM-Newton. The topmost two spectra are from K-type T Tauri stars (BP Tau is a CTTS, V410 Tau a WTTS), while the other spectra are from MS solar analogs. The sequence of the spectra from top to bottom is reflected in the lower left panel, and also by the colors of the spectra used for the stellar names. Count rate spectra have been normalized to the distance of 47 Cas (33.56 pc); the spectrum of BP Tau has been shifted upward by an additional factor of 30 for clarity (adapted from Telleschi et al. 2005Jump To The Next Citation Point and Telleschi et al. 2007bJump To The Next Citation Point).

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, 1983Schrijver et al., 1984Jump To The Next Citation PointStern et al., 1986Schmitt et al., 1990Dempsey et al., 1993Maggio et al., 1994Jump To The Next Citation PointGagne et al., 1995aSchmitt et al., 1995Hünsch et al., 1996Güdel et al., 1997bJump To The Next Citation PointPreibisch, 1997Jump To The Next Citation PointSchmitt, 1997Singh et al., 1999Jump To The Next Citation Point).

Figure 18View Image 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., 2000Jump To The Next Citation Point). Numerically, the correlation for the stellar sample reads

26 4.05±0.25 −1 LX = 1.61 × 10 Tav [erg s ] , (15 )

where Tav is in MK, and LX has been determined in the 0.1 – 10 keV band (Telleschi et al. 2005Jump To The Next Citation Point, and similar results in Güdel et al. 1997bJump To The Next Citation Point 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., 2001Jump To The Next Citation Point).

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:

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Figure 18: Mean coronal temperature of solar analogs as a function of the X-ray luminosity. The dashed and solid lines are the regression fits to results based on different atomic data. The triangles mark the range of the solar corona between activity minimum and maximum (figure from Telleschi et al., 2005Jump To The Next Citation Point, reproduced by permission of AAS).

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