5.6 Putting it all together: The XUV Sun in time

The above subsections provide the input for a comprehensive model of the spectral evolution of the “Sun in Time” in the wavelength band that is relevant for ionization of and chemical reactions in planetary atmospheres and circumstellar disks, namely the 1 – 1700 Å (≈ 0.007 – 10 keV) FUV/EUV/X-ray (“XUV”) range. The results are summarized in Tables 4 and 5 compiled using data from Ribas et al. (2005Jump To The Next Citation Point) (for the UV-EUV range) and Telleschi et al. (2005Jump To The Next Citation Point) (for the X-ray range). The table also contains data referring to the classical T Tauri star TW Hya, to be discussed in Section 6, and solar data (see Ribas et al. 2005Jump To The Next Citation Point for references).2 The line fluxes given in Table 4 are normalized to a distance of 1 AU and have also been normalized to the radius our Sun had at the age of the respective star. Note that the Lyα line fluxes were corrected for interstellar H i and D i absorption, i.e., they represent the pure stellar contribution.

Ribas et al. (2005Jump To The Next Citation Point) constructed band-integrated irradiances for the spectral ranges 1 – 20 Å (X-rays), 20 – 100 Å (soft X-rays and EUV), 100 – 360 Å (EUV), and 920 – 1180 Å (FUV). For the wavelength range of 1180 – 1700 Å, only line fluxes are provided because of increasing contributions from the photospheric continuum.

All integrated irradiances correlate tightly with the stellar rotation period or age, suggesting a rapid decay of activity at all atmospheric levels in concert. The relations are excellently represented by power laws, as illustrated in Figure 19View Imagea. The power-law fits to the fluxes of the form

F = αtβ9 (17 )

(α and β being constants) are given in Table 5. Note that the inaccessible spectral range of 360 – 920 Å (strongly absorbed by interstellar gas) has been interpolated between adjacent spectral ranges, assuming a decay law with β = –1.


Table 4: Integrated fluxes (in units of erg cm–2 s–1) of strong emission features normalized to a distance of 1 AU and the radius of a one solar mass star. UV and EUV fluxes of π1 UMa and 1 χ Ori have been averaged. Data for solar analogs are from Telleschi et al. (2005Jump To The Next Citation Point) and Ribas et al. (2005Jump To The Next Citation Point), and for TW Hya from Herczeg et al. (2002Jump To The Next Citation Point), Herczeg et al. (2004Jump To The Next Citation Point), Kastner et al. (2002Jump To The Next Citation Point), and Stelzer and Schmitt (2004Jump To The Next Citation Point); the radius of TW Hya is 1R⊙ and its distance is 56 pc, see Herczeg et al. (2004Jump To The Next Citation Point). Fluxes of TW Hya have not been corrected for (small) photoabsorption and extinction.
λ Ion log Tmax 0.01 Gyr
________ 0.1 Gyr ____________
_______ 0.3 Gyr ___________
0.65 Gyr 1.6 Gyr 4.56 Gyr 6.7 Gyr
(Å)     TW Hya 47 Cas EK Dra 1 π UMa 1 χ Ori 1 κ Cet β Com Sun β Hyi
1.85 Fe xxv 7.84 2.57 ± 0.63 1.29 ± 0.45
4.72 xvi 7.41 1.87 ± 0.29
10.62 Fe xxiv 7.27 <1.4 2.52 ± 2.10 1.70 ± 1.06
6.18 Si xiv 7.21 1.2 ± 0.8 4.62 ± 0.87 2.00 ± 0.38
5.04 xv 7.18 3.72 ± 0.67 1.08 ± 0.20
11.74 Fe xxiii 7.18 <1.7 5.50 ± 0.72 3.48 ± 0.45
12.29 Fe xxi 7.04 6.72 ± 1.43 4.20 ± 0.94 0.39 ± 0.12 0.21 ± 0.07 0.33 ± 0.05
6.65 Si xiii 7.01 2.3 ± 1.1 7.33 ± 2.65 3.32 ± 0.44 0.21 ± 0.04 0.14 ± 0.02 0.19 ± 0.03 0.02 ± 0.00
8.42 Mg xii 7.01 0.9 ± 0.6 8.70 ± 0.48 3.46 ± 0.51 0.11 ± 0.03 0.07 ± 0.02 0.19 ± 0.03 0.01 ± 0.01
12.83 Fe xx 6.98 <5.1 8.73 ± 0.03 4.59 ± 0.96 0.27 ± 0.06 0.14 ± 0.06 0.24 ± 0.05
13.52 Fe xix 6.92 8.32 ± 1.41 3.64 ± 1.08 0.46 ± 0.07 0.18 ± 0.09 0.22 ± 0.07 0.02 ± 0.02
14.20 Fe xviii 6.84 1.6 ± 1.3 10.52 ± 0.67 6.57 ± 0.50 0.65 ± 0.09 0.54 ± 0.04 0.57 ± 0.04 0.04 ± 0.02
9.17 Mg xi 6.81 11.30 ± 0.40 5.32 ± 0.43 0.41 ± 0.04 0.30 ± 0.02 0.45 ± 0.03 0.04 ± 0.01
12.13 Ne x 6.76 16.1 ± 1.7 17.69 ± 1.25 5.30 ± 0.69
15.01 Fe xvii 6.72 <31.6 16.89 ± 0.69 12.02 ± 0.52 1.96 ± 0.09 1.62 ± 0.05 1.50 ± 0.06 0.21 ± 0.02
16.78 Fe xvii 6.71 2.4 ± 1.6 7.86 ± 0.66 4.78 ± 0.48 0.99 ± 0.09 0.78 ± 0.06 0.86 ± 0.05 0.12 ± 0.02
13.45 Ne ix 6.59 24.1 ± 2.3 10.08 ± 1.51 2.78 ± 1.15 0.25 ± 0.13 0.32 ± 0.08 0.36 ± 0.10
13.70 Ne ix 6.59 6.8 ± 1.7 0.16 ± 0.06 0.19 ± 0.04 0.24 ± 0.04
18.97 viii 6.48 42.4 ± 3.9 23.03 ± 0.63 9.25 ± 0.36 1.05 ± 0.05 0.89 ± 0.03 1.02 ± 0.29 0.15 ± 0.01 0.029
335 Fe xvi 6.35 36.6
9.7
2.6
361 Fe xvi 6.35 15.7
6.6
1.6 0.016
21.60 vii 6.33 21.3 ± 2.6 3.53 ± 0.74 1.44 ± 0.42 0.38 ± 0.05 0.28 ± 0.04 0.37 ± 0.05 0.07 ± 0.02 0.063
22.10 vii 6.32 0.5 ± 0.7 1.55 ± 0.37 1.25 ± 0.37 0.27 ± 0.05 0.20 ± 0.04 0.22 ± 0.04 0.08 ± 0.02 0.041
24.77 vii 6.32 12.6 ± 2.4 2.45 ± 0.33 1.03 ± 0.17 0.07 ± 0.03 0.05 ± 0.01 0.09 ± 0.02 0.01 ± 0.01 0.009
284 Fe xv 6.30 22.0
5.0
2.4 0.025
284 Fe xv 6.30 22.0
5.0
2.4 0.025
33.73 vi 6.13 6.1 ± 1.1 2.01 ± 0.27 0.96 ± 0.16 0.08 ± 0.03 0.09 ± 0.02 0.12 ± 0.02 0.03 ± 0.01 0.016
610&625 Mg x 6.08
0.028
1032 vi 5.42 41.3 3.1
0.75
0.43 0.16 0.050 0.048
1038 vi 5.42 20.0 1.5
0.38
0.21 0.074 0.025 0.022
630 v 5.26
0.037
789 iv 5.05
0.017
1550 iv 5.00 378.0 9.1
2.21
1.02 0.40 0.146 0.082
834 ii 4.80
0.015
304 He ii 4.75 44.3
8.3
2.3 0.260
1640 He ii 4.75 180.0 6.0
0.99
0.56 0.040
1400 Si iv 4.75 14.6 4.3
1.59
0.77 0.28 0.083 0.097
977 iii 4.68 58.6 5.0
1.22
0.59 0.30 0.150 0.124
1176 iii 4.68 55.9 3.4
0.73
0.37 0.15 0.053 0.046
1206 Si iii 4.40
1.12
0.75 0.095
584 He i 4.25
0.032
1335 ii 4.25 45.2 4.7
1.52
0.95 0.36 0.188 0.155
1304 i 3.85 126.4 4.3
1.18
0.60 0.45 0.143 0.163
1657 i 3.85 29.2 4.1
0.97
0.78 0.47 0.202 0.210
1026 i 3.84
3.1
0.80 0.098
1216 i 3.84 ≈16,000
42.2
29.3 6.19


Table 5: Parameters of the power-law fits to the measured integrated fluxes and individual line fluxes from MS solar analogsa (data from Telleschi et al. 2005Jump To The Next Citation Point and Ribas et al. 2005Jump To The Next Citation Point). The parameters α and β are defined in Equation 17View Equation.
λ (interval) (Å)
α β
[1 – 20]
2.40 –1.92
[20 – 100]
4.45 –1.27
[100 – 360]
13.5 –1.20
[360 – 920]
4.56 (–1.0)
[920 – 1180]
2.53 –0.85
[1 – 360]+[920 – 1180]
24.8 –1.27
[1 – 1180]
29.7 –1.23
λ (Å) Ion Tmax   β
12.29 Fe xxi 7.04   –1.77
6.65 Si xiii 7.01   –1.91
8.42 Mg xii 7.01   –2.14
12.83 Fe xx 6.98   –2.09
13.52 Fe xix 6.92   –1.94
14.20 Fe xviii 6.84   –1.80
9.17 Mg xi 6.81   –1.80
15.01 Fe xvii 6.72   –1.44
16.78 Fe xvii 6.71   –1.33
13.45 Ne ix 6.59   –1.73
18.97 O viii 6.48   –1.58
361 Fe xvi 6.35   –1.86
21.60 O vii 6.33   –1.18
22.10 O vii 6.32   –1.01
24.77 N vii 6.32   –1.74
284 Fe xv 6.30   –1.79
33.73 C vi 6.13   –1.35
1032 O vi 5.42   –1.00
1038 O vi 5.42   –1.02
1550 C iv 5.00   –1.08
304 He ii 4.75   –1.34
1640 He ii 4.75   –1.28
1400 Si iv 4.75   –0.97
977 C iii 4.68   –0.85
1176 C iii 4.68   –1.02
1206 Si iii 4.40   –0.94
1335 C ii 4.25   –0.78
1304 O i 3.85   –0.78
1657 C i 3.85   –0.68
1026 H i 3.84   –1.24
1216 H i 3.84   –0.72
a Relationship of the form: Flux = αtβ 9.

View Image

Figure 19: Left (a): Power-law decays in time for various spectral ranges, normalized to the present-day solar flux. Note that the hardest emission decays fastest (from Ribas et al., 2005Jump To The Next Citation Point, reproduced by permission of AAS). Right (b): Flux decay slope (given as its absolute value) as a function of formation temperature of the respective line; each cross marks one emission line reported in Table 5.

The power laws steepen monotonically with decreasing wavelength, i.e., with increasing temperature (or roughly, height) of the atmospheric layer. The steepest decay is seen in the luminosity of the hot corona, with F ∝ t−91.92, while for the ultraviolet transition-region spectrum, F ∝ t−90.85. These power-laws are compared in Figure 19View Imagea after normalization to the present-day solar fluxes. For individual lines, the steepness of the decay, β in Equation 17View Equation, is compared in Figure 19View Imageb for a wide range of line formation temperatures. A fit to β as a function of formation temperature gives

− β = − 0.46 + 0.32log T . (18 ) max

Although the photospheric bolometric luminosity of the Sun has steadily increased during its MS life, starting at a level approximately 30% lower than today, the magnetically induced radiation from the outer atmosphere has steeply decayed during the same time, by factor of ≈ 1500 – 2000 for coronal X-ray emission and a factor of ≈ 25 for the FUV spectral region. The total XUV emission decayed by a factor of ≈ 100. A summary of the enhancement factors at various stages of the solar past compared to the contemporaneous Sun is given in Table 6. Given the ionizing power of some of this radiation and the importance of UV radiation for line excitation, this emission must have had profound consequences for the environment of the young Sun, most notably circumstellar disks and planetary atmospheres. This will be discussed in Section 6.5 and 7.2. As an example, (see Ribas et al., 2005Jump To The Next Citation Point), for EK Dra, the luminosity of the C iii λ 977 line alone exceeds the entire integrated luminosity of the present-day Sun below 1200 λ.


Table 6: Enhancement factors of X-ray/EUV/XUV/FUV fluxes in solar historya.
Solar age Time before
___________________ Enhancement in ______________________________
(Gyr) present (Gyr) X-Rays (1 – 20 Å) Soft-X (20 – 100 Å) FUV (920 – 1180 Å)
      EUV (100 – 360 Å)  
      XUV (1 – 1180 Å)  
0.1 4.5 1600b 100 25
0.2 4.4 400 50 14
0.7 3.9 40 10 5
1.1 3.5 15 6 3
1.9 2.7 5 3 2
2.6 2.0 3 2 1.6
3.2 1.4 2 1.5 1.4
4.6 0 1 1 1

a normalized to ZAMS age of 4.6 Gyr before present

b large scatter possible due to unknown initial rotation period of Sun


This “softening” of the spectral irradiance in time is illustrated in Figure 20View Image where the entire spectral irradiance from 1 – 3500 Å (except the strongly absorbed EUV range) is shown for various solar analogs. While the UV flux varies moderately and mostly due to emission lines (Figure 21View Image), the EUV and X-ray level drops dramatically along the MS evolution.

An alternative illustration is provided by the luminosity-luminosity diagram in Figure 22View Image in which the relation between normalized coronal X-ray and transition-region UV emission is shown for solar-like stars. The two emissions follow a power-law with a slope of 1.9, indicating that toward higher activity levels, X-rays increase more rapidly than UV fluxes (Ayres, 1997Jump To The Next Citation Point).

View Image

Figure 20: Top: Spectral irradiance of EK Dra for a distance of 1 AU. The various instruments used for the reconstruction are marked. Bottom: Irradiances at 1 AU from solar analogs with different ages (from Guinan and Ribas, 2002Jump To The Next Citation Point, reprinted with permission of ASP).
View Image

Figure 21: UV irradiances of EK Dra (upper spectrum) and the very old solar analog, β Hyi (lower spectrum). Note progressively higher flux levels in EK Dra toward shorter wavelengths (from Guinan and Ribas, 2002, reprinted with permission of ASP).
View Image

Figure 22: Correlation between normalized coronal X-ray and transition-region (C iv) UV emission for solar-like field and cluster stars (from the ROSAT/IUE All Sky Survey [RIASS], see Ayres 1997Jump To The Next Citation Point, reprinted with permission).

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