The Sun in Time: Activity and Environment

4.1.1 Doppler imaging of young solar analogs

The most advanced (indirect) imaging technique to map magnetic structure in stellar photospheres is Doppler imaging that uses deformations in spectral-line profiles to map starspots (Vogt and Penrod, 1983).

Surface imaging using Doppler reconstruction methods or spot modeling has been performed for several young, active solar analogs. Figure 1 shows views of the three examples discussed below. The colors code for temperature (from http://www.aip.de/groups/activity/DI/maps/).

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The photosphere of EK Dra has been extensively mapped using spot modeling (Järvinen et al., 2005) and Doppler imaging techniques (Strassmeier and Rice, 1998). Doppler images show spots both close to the visible pole but also near the equator, the dominant feature being located at latitudes of 70–80 deg (Strassmeier and Rice, 1998). This is supported by radial-velocity variations (König et al., 2005). The polar region of EK Dra is, however, less pronounced than in more active (binary) stars, perhaps indicating a trend toward lower-latitude spots for less active stars, as predicted by the Schüssler et al. (1996) theory of Coriolis-force driven magnetic flux tubes that converge to the pole for very rapid rotators (see below).

The Pleiades G dwarf HII 314 (P = 1.47 d) has been Doppler-imaged by Rice and Strassmeier (2001). Again, high-latitude and polar spots are visible. The still younger, “infant Sun” HD 171488 = V889 Her (P = 1.34 d, age = 30 Myr), a star in its last stage of evolution toward the ZAMS, shows very prominent polar spots and various high-latitude dark features (Strassmeier et al., 2003). Further Doppler maps have been presented for the early G-type ultra-fast rotators He 520 (P = 0.49 d) and He 699 (P = 0.61 d). Again, apart from the prominent polar spots, there is a definitive band of low-latitude (l ≲ 30–40 deg) spots on these stars as well (Barnes et al., 1998).

Although these surface spot distributions vary significantly between young solar analogs, there is agreement with regard to high-latitude magnetic activity on all of them (Rice and Strassmeier, 2001; Strassmeier et al., 2003).

The most recent Doppler technique uses spectropolarimetric observations of lines to apply Zeeman-Doppler Imaging (ZDI), which results in maps of radial, azimuthal, and meridional magnetic fields. Successful application to solar analog stars have been presented by Marsden et al. (2006) and Catala et al. (2007); excellent ZDI maps have also been derived for the somewhat cooler, young early-K star AB Dor (Donati et al., 2003b), and put into context with coronal X-rays (Jardine et al., 2002c; McIvor et al., 2003; Hussain et al., 2007). ZDI images (Figure 2) have shown non-solar magnetic features such as high-latitude “rings” of azimuthal (toroidal) field (Donati et al., 2003b; Marsden et al., 2006; Catala et al., 2007), possibly suggesting that the responsible magnetic dynamo is located close to the surface (a “distributed dynamo”) rather than (only) near the tachocline where azimuthal fields are expected for αΩ-type dynamos. The field distribution and orientation also serves as an important diagnostic to study and explain spot lifetimes based on numerical studies (Işik et al., 2007).

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4.1.2 Polar spots

Why are there polar spots in magnetically active stars? Schüssler and Solanki (1992) and Schüssler et al. (1996) suggested that strong Coriolis forces act on magnetic flux bundles that rise from the dynamo region at the boundary between the radiative core and the convective envelope of the star. This force would deflect rising flux to higher altitudes although, given the size of the radiative core, the maximum latitude would probably be no more than about 60 degrees. A parameter study confirms these findings systematically, with flux emergence latitudes increasing with i) rotation rate, ii) decreasing stellar mass (i.e., smaller radiative core radii), and iii) decreasing age; a fraction of the flux tubes will, however, also erupt in near-equatorial regions (Granzer et al., 2000). To produce truly polar spot regions, additional latitudinal transport of flux tubes is still required. A possibility is an additional pole-ward slip of a segment of a flux ring in the stellar interior after the eruption of flux at mid-latitudes in another segment of the same ring (Schüssler et al., 1996).

Alternatively, Schrijver and Title (2001) explored migration of surface magnetic fields toward the poles in a model developed by Schrijver (2001). Here, magnetic bipoles are injected randomly. These flux concentrations migrate pole-ward in a meridional flow and are subject to differential rotation. The bipoles can interact, i.e., fragment, merge, or cancel. The magnetic cycle is simulated by periodically varying the injection latitudes. Schrijver and Title (2001) simulated a star with a bipole injection rate 30 times higher than the present-day Sun, corresponding to a solar analog with a rotation period of 6 d, i.e., an age of a few 100 Myr. The differential rotation profile was assumed to be identical to the present-day Sun’s, and so was the length of the activity cycle (11 yr). In the present-day Sun, the pole-ward migration of the trailing flux in a bipole cancels with existing high-latitude flux of opposite polarity relatively rapidly. In the simulations of the active star, however, the magnetic concentrations contain more flux, resulting in slower diffusion and a longer lifetime before cancellation. The result of these simulations is that, first, there are strong magnetic features accumulating in the polar regions, and second, nested magnetic rings of opposite polarity form around the pole (Figure 3). These are suggestive sites of chromospheric and coronal interactions, perhaps leading to strong coronal heating and flares in these polar regions. As described above, ZDI images indeed provide evidence for high-latitude “rings” of azimuthal (toroidal) field (e.g., Marsden et al. 2006, Figure 2).

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Observationally, the picture is more complicated. In contrast to these simulations and also in contrast to the solar picture, Doppler images of very active, young stars (Figure 1) show intermingling of opposite polarities in longitude also at high latitudes (Mackay et al., 2004). Such features can indeed be reproduced if the latitudes of flux emergence are shifted poleward, to 50–70 degrees, and the meridional flow be made faster (Mackay et al., 2004; Holzwarth et al., 2006). The first modification is of course suggested from the Schüssler et al. (1996) theory.

The structure of polar spots (unipolar, multiple bi-polar regions, or nested rings of different polarity) is indeed also very important for the large-scale coronal field; unipolar magnetic spots suggest the presence of more polar open-field lines, therefore concentrating strong coronal X-ray emission to more equatorial regions, but also reducing the efficiency of angular momentum removal by the magnetized wind due to the smaller lever arm compared to equatorial winds (McIvor et al., 2003).

4.2.1 Magnetic loop models and active regions

This relation can only hold if L is smaller than the pressure scale height. Based on this expression, the luminous, hot plasma component in magnetically active stars seems to invariably require either very large, moderate-pressure loops with a large filling factor, or solar-sized high-pressure compact loops with a very small (< 1%) filling factor (Giampapa et al., 1985; Stern et al., 1986; Schrijver et al., 1989; Giampapa et al., 1996; Güdel et al., 1997b; Preibisch, 1997; Sciortino et al., 1999).

Schrijver et al. (1984) modeled T and the emission measure, EM (= n_en_HV, where n_e and n_H are the electron and hydrogen number densities, and V is the volume) of a sample of coronal sources based on RTV loop models and found several trends: i) inactive MS stars such as the Sun are covered to a large fraction by large-scale, cool (2 MK) loops of modest size (0.1 R_*); ii) moderately active dwarfs are dominated by very compact, high-density, hot (≈ 20 MK) loops that require high heating rates (up to 20 times more than for solar compact active region loops); iii) the most active stars may additionally form rather extended loops with heights similar to R_*.

Similar studies of loop models varied in their results, although for magnetically active stars, most authors reported results that require hot, compact, high-pressure loops (up to several 100 dyn cm⁻²), somewhat reminiscent of flaring loops (Stern et al., 1986; Giampapa et al., 1996; Maggio and Peres, 1997; Ventura et al., 1998; Sciortino et al., 1999). The hypothesis that the hottest plasma in magnetically active stellar coronae does not form in static loops but in flaring active regions will be encountered again — see Section 5.8.

If the Sun were entirely covered with active regions, the X-ray luminosity would amount to only ≈ (2–3) × 10²⁹ erg s⁻¹ (Vaiana and Rosner, 1978; Wood et al., 1994), short of L_X of the most active solar analogs by one order of magnitude. But the X-ray emission measure distributions of such active stars show excessive amounts of plasma around 10–20 MK (Güdel et al., 1997b), which incidentally is the typical range of solar flare temperatures. This again led to the suggestion that the high-T emission measure is in fact due to the superposition of a multitude of temporally unresolved flares (see Section 5.8).

4.2.2 Inferences from coronal density measurements

Comprehensive surveys of stellar coronal electron density (n_e) measurements based on X-ray spectroscopic line-flux ratios were presented by Ness et al. (2004) and Testa et al. (2004), including a sample of active solar analogs. These studies concluded that the surface filling factor (derived from the emission measure, the measured n_e, and a realistic coronal scale height) of magnetic loops containing cool X-ray emitting material increases from inactive to moderately active stars but then “saturates” at levels of about ten percent. In the most active stars, hot coronal loops are added, with a sharply increasing filling factor, thus probably filling the volume left between the cooler coronal magnetic loops. Observations of rotational modulation in very active solar analogs suggests, however, that the coronal volume filling remains significantly below 100% (see Section 4.2.3 below).

4.2.3 Inferences from rotational modulation

Inhomogeneous coronae may reveal signatures in light curves as the star rotates, although success of this method has been moderate given that coronal features evolve on time scales shorter than one rotation (e.g., owing to flares). Two young, near-ZAMS solar analogs have shown clear signatures of X-ray rotational modulation (EK Dra, Güdel et al. 1995c, and 47 Cas B, Güdel et al. 1995a), pointing to a filling factor below unity. This is unexpected because such stars are in the empirical X-ray saturation regime that has often been suggested to be due to complete filling of the surface with X-ray bright coronal magnetic loops (see Section 5.5 below). EK Dra also showed evidence for radio rotational modulation. The depth and length of the modulation (Figure 4a) constrains the X-ray coronal height, and also the electron densities to n_e > 4 × 10¹⁰ cm⁻³, in agreement with spectroscopic measurements (Ness et al., 2004). This leads to the conclusion that much of the emitting material is concentrated in large “active regions”.

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Because the X-ray luminosity in very rapidly rotating, “supersaturated” stars (Section 5.5.1) is below the empirical maximum, rotational modulation would give important structural information on the state of such coronae. A deep modulation in the young solar analog VXR45 (Figure 4b) suggests that extreme activity in these stars is again not due to complete coverage of the surface with active regions (Marino et al. 2003a).

4.2.4 Inferences from eclipses

Most binary systems that produce coronal eclipses are close binaries and the components are therefore in no ways similar to the young Sun. A remarkable exception is the relatively wide binary α CrB. Its X-ray active, young (age of few 100 Myr) solar analog of spectral type G5 V is totally eclipsed once every 17 days by the optical primary, an A0 V star that is perfectly X-ray dark. Other parameters are ideal as well, such as the non-central eclipse, the eclipse time-scale of a few hours, and the relatively slow rotation period of the secondary. Eclipse observations obtained by ROSAT (Schmitt and Kürster, 1993) and by XMM-Newton (Güdel et al., 2003a) were used to reconstruct projected 2-D images of the X-ray structure. They consistently reveal patches of active regions across the face of the G star; not much material is found significantly beyond its limb (Figure 5). The structures tend to be of modest size (≈ 5 × 10⁹ cm), with large, X-ray faint areas in between, although the star’s luminosity exceeds that of the active Sun by a factor of ≈ 30. These observations imply moderately high densities in the emitting active regions, and both studies mentioned above yielded average electron densities in the brightest active regions of a few 10¹⁰ cm⁻³. The picture of active coronae consisting of features similar to solar active regions thus seems to hold also for intermediately active, young solar analogs.

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4.2.5 Photospheric-field extrapolation to the corona

Information on coronal structure can also be derived indirectly from surface Zeeman-Doppler images as developed for and applied to the stellar case by Jardine et al. (2002a), Jardine et al. (2002b), Hussain et al. (2002), and Hussain et al. (2007) and further references therein. Jardine et al. (2002a) and Jardine et al. (2002b) explored potential field extrapolation, while Hussain et al. (2002) extended the models to include some form of currents in force-free fields.

Such models also require specification of the base thermal pressure of the plasma with respect to the local magnetic pressure, and some cutoff of the corona at locations where the thermal pressure might open up the coronal field lines. They can successfully recover, at least qualitatively, the total X-ray emission measure, the average electron density, and the low level of rotational modulation observed on very active, young stars such as AB Dor. The X-ray rotational modulation is to a large extent suppressed by the highly complex coronal structure, involving both very large magnetic features and more compact loops anchored predominantly at polar latitudes.

Schrijver and Aschwanden (2002) used the model of surface magnetic-field development devised by Schrijver (2001) and Schrijver and Title (2001) (Section 4.1 above) to extrapolate surface magnetic fields into the corona, assuming a potential-field approach. The resulting magnetic structure is illustrated in Figure 6 for a solar-activity star, and two examples with a 10fold and a 30fold magnetic injection rate (the latter corresponding to a solar analog with an age of a few 100 Myr). Near cycle minimum, the coronae of the active stars are dominated by a large-scale dipolar field although the low-activity example also shows compact active regions, more so than the active stars. At activity maximum, the active stars show magnetic-field arcades between the polar rings of opposite polarity, weakening the contribution from the global dipole components. Not all of these loops will be X-ray bright, however; the loop brightness depends on its heating rate, which in turn depends on the mode of coronal heating of a given magnetic loop (see Schrijver and Aschwanden 2002 for further details).

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4.2.6 Summary on coronal structure

Despite numerous, complementary approaches to the study of coronal structure, the results appear to be inconclusive. Compact active regions are inferred from (and required by) the presence of rotational modulation, and field extrapolation and numerical models suggest compact regions as well. Extended, global fields are more difficult to infer, and this is the consequence of two observational biases rather than implying the absence of such structures. First, most observational methods (e.g., X-ray eclipse and rotational modulation) are insensitive to large structures. Second, the pressure scale height of typical coronal plasma is less than one stellar radius for solar analogs. The n_e2 dependence of X-ray emission will therefore bias X-ray loop detection toward low heights. There is, nevertheless, evidence for large-scale magnetic fields on young, active stars, from two directions: surface field extrapolation based on observed spot features or based on numerical models of flux transport (Section 4.2.5) imply the presence of structures resembling global dipole components; and spatially resolved radio observations of active stars indeed do show very extended magnetic structures (predominantly above the polar regions; Benz et al. 1998; Mutel et al. 1998), although such evidence has not yet been demonstrated for young solar analogs. In summary, then, observational evidence and model simulations point to the presence of both compact active regions and extended magnetic structures in the young Sun. The relative proportions are likely to relate to the distribution of magnetic field on the stellar surface, as in the models presented by Schrijver and Aschwanden (2002).

There is clear evidence that the surface magnetic filling factor increases with increasing activity (and decreasing rotation period), both from observations (e.g., Montesinos and Jordan, 1993) and theoretical and modeling studies (Montesinos and Jordan, 1993; Fawzy et al., 2002); in contrast, the photospheric magnetic field strength is thought to be primarily restricted by pressure equilibrium with respect to the ambient gas pressure, i.e., the field strength is primarily dependent on spectral type, although a weak activity dependence is also present (e.g., Montesinos and Jordan, 1993). The higher filling factors lead to less expansion of photospheric/chromospheric flux tubes because the tubes merge with adjacent tubes (Cuntz et al., 1999). Therefore, toward more active stars, coronal magnetic fields interact progressively more frequently due to their denser packing. A higher rate of large flares is a consequence. Since flares enhance the electron density along with the temperature, stars with a higher activity level should reveal a predominance of hotter structures (Güdel et al., 1997b). Such a trend is observationally well supported; as further described in Section 5.5.2 below, coronae at higher activity levels are systematically hotter.

4.3.1 Starspot cycles of solar analogs

Messina and Guinan (2002) specifically studied starspot cycles of stars from the “Sun in Time” program. Activity cycles are found in all of them, with periods ranging from 2.1 yr to 13.1 yr. A comparison with the more comprehensive survey and the theoretical interpretations presented by Saar and Brandenburg (1999) confirms the presence of two or three branches: i) inactive solar analogs show cycles about 100 times longer than the rotation period, P; ii) active stars reveal cycles 200–600 times longer than P; iii) and “super-active” stars show cycles about 4 order of magnitude longer than P (Figure 7a). Among G-type stars, only EK Dra appears to be compatible with the third class (Messina and Guinan 2002).

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The brightness amplitude increases with increasing inverse Rossby number (i.e., increasing rotation rate for constant turnover time), indicating that spots produce progressively more modulation toward higher activity levels (Figure 7b). A plateau is suggested for the most active stars, indicating a saturation effect when spots cover a large fraction of the stellar surface (Messina and Guinan, 2002).

The standard near-ZAMS solar analog, EK Dra, has been an important target for cycle studies. Dorren and Guinan (1994a and Dorren and Guinan (1994b) showed that its long-term photometric variations by ≈ 0.07 mag are consistent with a period of about 12 yr. Variations compatible with this time scale are also found in Ca ii HK, Mg ii h and k, and the ultraviolet C iv, C ii, and He ii fluxes (Dorren and Guinan, 1994a), and in X-rays (see Section 4.3.2 below). The spot periodicity has been confirmed by Messina and Guinan (2002) although their best estimate for the period is 9.2 ± 0.4 yr (Figure 8). The star is optically faintest when chromospheric and transition-region activity is highest. On top of this cyclic behavior, there is a long-term trend in the optical light, namely a decline of the blue light by 0.0017 ± 0.0004 mag yr⁻¹ for an investigated time span of 35 yr (Fröhlich et al. 2002; see also Messina and Guinan 2003 and Järvinen et al. 2005). Further, two active longitudes shift in phase in concert with the activity cycles (Järvinen et al., 2005). The dominant spot concentration switches between the two preferred longitudes with a “flip-flop” cycle of about 4–4.5 yr. These features suggest the coexistence of axisymmetric and non-axisymmetric dynamo modes (Berdyugina et al., 2002).

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Messina and Guinan (2003) have studied photometric periods from spot modulations, arguing that — as in the solar case — the varying dominant latitudes of the spots should induce a periodic variation of the rotation period in phase with the activity cycle, because of differential rotation. These correlated period variations are indeed present in solar analogs (Messina and Guinan, 2003), although two patterns are seen: either, the period decreases as the cycle proceeds (solar behavior), or it increases (anti-solar behavior). The former effect is due to spot migration toward the equator where the surface rotation is faster. The second effect could be due to pole-ward acceleration of rotation at higher latitudes where active stars predominantly show spots, while the individual spots may still migrate toward the equator. Messina and Guinan (2003), however, suggest that high-latitude spots migrate toward the (slower-rotating) pole, which induces an anti-solar behavior in particular for stars with small inclination angles. This model is preferred because correlations involving the fractional variation in the rotation period show the same behavior for the two subclasses. Support for the model comes from simulations of magnetic-field migration toward the poles in very active stars, as performed by Schrijver and Title (2001) (Section 4.1.2). Specifically, Messina and Guinan (2003) have found a power-law relation between the rotation-period variation, ΔP, and the average rotation period, P, of the form (see Figure 9a)

$$\Delta P \propto {P^{1.42 \pm 0.5}}.$$

(2)

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Differential rotation has also been measured on other very active stars (e.g., Donati et al. 2003a), among them a solar-like post-T Tauri star (Donati et al., 2000), in particular based on Doppler imaging techniques (Section 4.1.1). Differential rotation was found to be solar-like in these examples, although time-variable, which may hint at dynamo processes that periodically convert magnetic into kinetic energy and vice versa (Donati et al., 2003a).

4.3.2 X-ray cycles of solar analogs

Given the much stronger variability in the outer, coronal layers of a stellar atmosphere, an activity cycle may be more easily identified in the X-ray or radio domains. However, such cycles have eluded detection until recently because no appropriate program had been carried out for sufficiently long periods. A few notable examples have now been reported from X-ray monitoring.

First tentative evidence for an X-ray cycle came from the young solar analog EK Dra that was monitored between 1990 and 2000 using ROSAT, ASCA, and XMM-Newton. Initial results were presented in Dorren et al. (1995), a more complete time series has been published by Güdel (2004). There is a suggestive anti-correlation between X-ray flux and photospheric brightness (the star is optically brightest at its activity minimum), although the total X-ray luminosity varies by no more than a factor of ≈ 2–3.

Other reports refer to inactive solar analogs and K-type stars. Hempelmann et al. (2003) and Hempelmann et al. (2006) have reported a correlation between X-ray luminosity and the Ca H & K S index for the two K-type stars 61 Cyg A and B. Both show chromospheric modulations on time scales of about 10 years, one being regular and the other irregular. A gradual X-ray modulation was also seen during a time span 2.5 years in the G2 V star HD 81809, although there seems to be a phase shift by about 1 year with respect to the Ca cycle (Favata et al., 2004).

Additional information on potential coronal activity cycles has been collected from multiple observations of young open clusters and star-forming regions. Generally, such samples indicate that magnetically active, solar-like stars mostly lack well-expressed X-ray cycles unless their cycle-induced variability is no more than a factor of ≈ 2 (Gagné and Caillault, 1994; Gagné et al., 1995a, b; Stern et al., 1994, 1995; Micela et al., 1996; Sciortino et al., 1998; Grosso et al., 2000; Marino et al., 2002, 2003b).

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 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

$${L_{\rm{X}}} = {10^{31.05 \pm 0.12}}\;{P^{- 2.64 \pm 0.12}}\;\;[{\rm{erg}}\;{{\rm{s}}^{- 1}}]$$

(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: L_X ∝ 4.04 × 10³⁰ P^{−2 03}±^0.35 [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 (Ro = P/τ _C , where τ _C is the convective turnover time; Noyes et al. 1984; Mangeney and Praderie 1984). All studies find roughly L_X/L_bol ≈ 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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(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, L_X 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).

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. (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 L_X ≈ 3 × 10²⁶ erg s⁻¹ and L_X ≈ 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:

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From full spectral interpretation, a tight correlation has indeed been found between the characteristic coronal temperature and the normalized coronal luminosity L_X/L_bol: 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; Gagné 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

$${L_{\rm{X}}} = 1.61 \times {10^{26}}T_{{\rm{av}}}^{4.05 \pm 0.25}\;\;[{\rm{erg}}\;{{\rm{s}}^{- 1}}],$$

(15)

where T_av is in MK, and L_X 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).

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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.

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.

5.7.2 Observational results

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.

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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:

$${L_{\rm{R}}} \approx 1.69 \times {10^9}T_{{\rm{av}}}^{5.29 \pm 0.74}\quad [{\rm{erg}}\;{{\rm{s}}^{- 1}}\;{\rm{H}}{{\rm{z}}^{- 1}}]$$

(19)

(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.

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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.

5.8.1 Flare energy distributions and coronal heating

5.8.2 Phenomenological evidence

There is abundant evidence that flare-like processes are important in magnetically active stars:

• A linear correlation between the time-averaged power from optical flares and the low-level, “quiescent” X-ray luminosity suggests that flares are important contributors to the overall stellar coronal heating (Doyle and Butler, 1985; Skumanich, 1985; Whitehouse, 1985).

• Over the entire solar magnetic cycle, the monthly average soft X-ray luminosity scales in detail and linearly with the rate of detected Hα flares (Pearce et al., 1992).

• In analogy, the stellar “quiescent” X-ray luminosity correlates approximately linearly with the rate of X-ray flares (above a given lower energy threshold; Audard et al. 2000).

• The “quiescent” X-ray luminosity of magnetically active stars correlates linearly with the contemporaneous (non-flaring) radio gyrosynchrotron emission. The latter requires accelerated electrons, for which flares are an obvious source (Güdel and Benz, 1993)

• This latter correlation holds similarly for many solar and stellar flares (Benz and Güdel, 1994).

• The ratio between energy losses in coronal X-rays and in the chromospheric Mg ii lines is the same in flares and in quiescence (Haisch et al., 1990).

• The ratio between energy losses in coronal X-rays and in the chromospheric UV emission measured in broad filter bands is the same in flares and in quiescence (Mitra-Kraev et al., 2005).

• A tight correlation exists between L_X and H _γ luminosity that it the same for flares and for quiescence (Mathioudakis and Doyle, 1990).

• Many observations have shown continuous low-level variability in the stellar X-ray output, with time scales reminiscent of coronal flares (Audard et al. 2003a; see Figure 25 for the X-ray light curve of EK Dra). In particular, a strong temporal correlation between H _γ flare flux and simultaneous low-level X-ray flux in dMe stars suggests that a large number of flare-like events are always present (Butler et al., 1986). Up to 50% of the X-ray output in PMS stars may be due to relatively strong flares (Montmerle et al., 1983), which has become particularly evident in recent observations of the Orion region (Feigelson et al., 2002b; Wolk et al., 2005).

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5.8.3 Stellar flare energy distributions

Motivated by the above phenomenology, several studies have addressed flare distributions in stellar coronae. Earlier work by Collura et al. (1988) and Pallavicini et al. (1990) indicated power laws with α < 2 although the sensitivities used in those observations were quite limited, and flares from different stars at different distances were lumped together. This also holds for a study by Osten and Brown (1999) for RS CVn-type binaries.

To avoid bias with regard to detection limits at lower energies, new methods have been devised by Audard et al. (1999), Audard et al. (2000), Kashyap et al. (2002), Güdel et al. (2003b), and Arzner and Güdel (2004), the latter three using Monte Carlo forward methods and analytical inversion. Work by Wolk et al. (2005), Arzner et al. (2007), and Stelzer et al. (2007) has extended flare statistics into the PMS domain.

Most of these recent studies converge to α ≈ 2.0–2.5 (Figure 26), indicating a potentially crucial role of flares in coronal heating if the power-law flare energy distribution extends by about 1–2 orders of magnitude below the actual detection limit in the light curves. The X-ray coronae of active stars would be an entirely hydrodynamic phenomenon rather than an ensemble of hydrostatic loops.

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5.8.4 Stochastic flares and coronal observations

This mechanism has been studied specifically for young solar analogs by Güdel et al. (1997b), Güdel (1997), Audard et al. (1999), and Telleschi et al. (2005), in particular with regard to synthetic light curves and emission measure distributions.

Güdel et al. (1997b) found that the time-averaged emission measure distribution of solar flares adds a characteristic, separate emission measure component at high temperatures (> 10 MK); numerical simulations support this picture (Güdel, 1997), and corresponding hot emission measure components are indeed also identified in active solar analogs from X-ray spectroscopic observations. If a full distribution of flares contributes, including small flares with lower temperature, then the entire observed X-ray emission measure could be formed by the continually heating and cooling plasma in flares. The predicted steep low-T slope (up to ≈ 4) of an emission measure distribution induced by stochastic flaring compares very favorably with observations of active stars (Güdel et al., 2003b). This holds true specifically for solar analogs for which α = 2.2–2.8 is implied from the emission measure slopes (Telleschi et al., 2005).

Audard et al. (1999) and Audard et al. (2000) derived the flare energy distribution of young solar analogs (Figure 26, where the cumulative distributions are plotted, with a power-law index that is shallower by one unit) and studied consequences for the thermal structure of the active coronae. They speculated that the higher temperatures in active coronae are due to a larger rate of (larger) flares, although they left undecidedwhether there is a larger rate of reheating events of the same coronal structures or whether a higher number of active regions produce the higher flare rate.

5.8.5 Summary: The importance of stochastic flares

5.9.1 Abundances in stellar coronae

Although detailed studies of coronal composition require high-resolution X-ray spectra, anomalies in the coronal composition of magnetically active stars have been recognized already in the early days of X-ray astronomy. Most notably, a significant deficiency of coronal Fe, by factors of a few when compared to the solar composition, has been noted (e.g., Swank et al. 1981; White et al. 1994). There are two caveats with regard to early abundance measurements: i) low-resolution X-ray spectroscopy does not isolate individual spectral lines of any element with the exception of Fe, which produces a line system at 6.7 keV that can be measured by low-resolution (e.g., CCDtype) detectors. This line, however, forms at very high temperatures (formation temperature ≈ 60–70 MK), and knowledge of the thermal structure at those high temperatures is required if the element abundances are to be trusted; ii) more severely, for most stars no reliable photospheric abundances are known (again, the exception is mostly Fe). Because the photospheric composition of stars may significantly differ from the solar photosphere, any coronal abundance anomaly in stars should really be defined with respect to the underlying photosphere. In any case, before the advent of spectroscopy with XMM-Newton and Chandra, a sufficient body of data clearly showed that the most active stars reveal strong depletion of most heavy elements, with little FIP-related systematics (Singh et al., 1999).

Early observations of the extremely active subgiant HR 1099 (Brinkman et al., 2001) and the MS K-type ZAMS star AB Dor (Güdel et al., 2001) with the XMM-Newton Reflection Grating Spectrometer uncovered a new, systematic FIP-related bias in magnetically active stars: In contrast to the solar case, low-FIP abundances are systematically depleted with respect to high-FIP elements, a trend now known as the “inverse FIP effect” (IFIP). The ratio between the abundances of Ne (highest FIP) and Fe (low FIP) is therefore unusually large, of order 10 in the most extreme cases (when compared to the solar photospheric mixture). This pattern has been confirmed for many further active stars (e.g., Drake et al. 2001; Huenemoerder et al. 2001, 2003 etc). Only highly active stars show the IFIP pattern. Toward intermediately active stars, the effect weakens, until eventually flat abundance distributions are recovered (Audard et al., 2003b).

5.9.2 The composition of the young solar corona

Solar analogs provide the best basis for a systematic study of abundance trends because they directly link to the solar case. Fortuitously, many well-studied solar analogs with different ages and activity levels are available for study in the solar vicinity. Again, the “Sun in Time” sample is outstanding in that the photospheric mix has been well documented, often for several elements apart from Fe. The principal result is that all of them show photospheric abundances close to solar (see summary table in Telleschi et al. 2005). The only independent parameter for this sample with regard to coronal abundance anomalies is therefore again the activity level or, equivalently, age.

The sample shows a clear systematic development from an inverse FIP effect in the youngest examples (with underabundances of Fe and Si) to a marked FIP effect in objects at ages of about 300 Myr and older (see Figure 27). As long as the IFIP pattern is present, all abundances appear to be sub-solar, but the Fe/H abundance ratio gradually rises with decreasing coronal activity. The abundance pattern reverts to a normal, solar-type FIP anomaly for stars at activity levels of log L_X/L_bol ≲ − 4 (Telleschi et al., 2005). Unexpectedly, this transition also seems to coincide with i) the transition from coronae with a prominent hot (T ≳ 10 MK) component to cooler coronae, and ii) with the transition from prominent non-thermal radio emission to the absence thereof (Telleschi et al., 2005).

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5.9.3 The Ne/O abundance ratio: Subject to evolution?

Figure 28 shows an anomaly for the O/Ne ratio which is found at values of 0.3–0.7 times the solar ratio, apparently regardless of the stellar activity level. Because both O and Ne are high-FIP elements, their abundance ratio could reflect the photospheric ratio. But then, the Sun’s composition would be anomalous.

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The tabulations of several solar element abundances have recently been revised (Asplund et al., 2005b), resulting in significant discrepancies between solar models and helioseismological results (see Antia and Basu, 2005, and references therein) unless further solar abundances were also different. A Ne abundance higher by a factor of at least 2.5 than hitherto assumed would be needed. Therefore, Telleschi et al. (2005) were the first to point out that the systematically nonsolar O/Ne abundance ratio (by a similar factor) calls for a revision of the solar Ne abundance tabulation which at the same time would solve the solar helioseismology problem. This was further elaborated by Drake and Testa (2005) who suggested a factor of 2.7 upward revision of the adopted solar Ne abundance.

Two directions should be taken to verify this suggestion. First, further coronal abundances of low-activity solar-analog stars should be derived. So far, agreement with solar values has in fact been reported for α Cen A (Raassen et al., 2003), Procyon (Raassen et al., 2002), and for β Com, the latter with large error bars, however (Telleschi et al., 2005). There seems to be a trend toward higher O/Ne ratios in Figure 28 indeed. New results for α Cen have been reported by Liefke and Schmitt (2006), placing the Ne/O abundance ratio significantly lower than values for active stars, albeit not as low as the presently accepted solar photospheric value. Second, verification of the solar Ne/O ratio is needed. Although Ne cannot be measured directly in the photosphere, the Ne/O ratio can be derived from coronal measurements the same way as done for stellar observations. Recent analysis of solar active region X-ray spectra and of EUV spectra from transition-region levels (Schmelz et al., 2005; Young, 2005) both report the standard Ne/O abundance ratios, rejecting an upward correction of Ne. The issue should therefore be considered to be open for the time being. A FIP-related, i.e., “evolutionary” enrichment of Ne in active corona remains a viable possibility (Asplund et al., 2005a).

6.2.1 Evolutionary stages: Overview

Modern theory of star formation together with results from comprehensive observing programs have converged to a picture in which a forming low-mass star evolves through various stages with progressive clearing of a contracting circumstellar envelope. In its “class 0” stage (according to the mm/infrared classification scheme), the majority of the future mass of the star still resides in the contracting molecular envelope. “Class I” protostars have essentially accreted their final mass while still being deeply embedded in a dust and gas envelope and surrounded by a thick circumstellar disk. Jets and outflows may be driven by these optically invisible “infrared stars”. Once the envelope is dispersed, the stars enter their “Classical T Tauri” stage (CTTS, usually belonging to infrared class II with an IR excess) with excess Hα line emission if they are still surrounded by a massive circumstellar disk; the latter results in an infrared excess. “Weak-line T Tauri” stars (also “naked T Tauri stars”, Walter 1986; usually with class III characteristics, i.e., essentially showing a photospheric spectrum) have lost most of their disk and are dominated by photospheric light (Walter et al., 1988).

6.2.2 New features: Accretion, disks, and jets

Moving back in time from the MS into the PMS era of solar evolution, we encounter changes in the Sun’s internal structure and in fundamental stellar parameters such as radius and T_eff. The typical “T Tauri” Sun at an age of 0.5–3 Myr was bolometrically 1–4 times more luminous and 1.7–3.6 times larger in radius, while its surface T_eff ≈ 4260 K, corresponding to a K5 star (after Siess et al., 2000). The interior of T Tauri stars evolving on the Hayashi track is entirely convective. The operation of an αΩ dynamo should not be possible, yet very high levels of magnetic activity are clearly observed on T Tauri stars. Alternative dynamos such as convective dynamos may be in operation. “Solar analogy” no longer holds collectively for all stellar parameters, except (roughly) for stellar mass. Also, there is a complex stellar environment, including an accretion disk, outflows and jets, and probably a large-scale stellar magnetosphere that interacts with these structures (Camenzind 1990; Königl 1991; Collier Cameron and Campbell 1993; Shu et al. 1994; Figure 29). Magnetic interactions between the star and its environment are important in the following contexts:

• Star-disk magnetic fields may form large magnetospheres that lead to star-disk locking and disk-controlled spin rates of the star. Generally, disk-surrounded CTTS rotate relatively slowly, probably due to disk locking, with P = 5–10 d, compared to only a few days for diskless, non-accreting WTTS (Bouvier et al., 1993); if a rotation-induced magnetic dynamo is at work in CTTS, then it may be dampened compared to dynamos in freely (and rapidly) rotating diskless WTTS.

• Non-synchronized rotation may be possible in particular in very young systems in spite of magnetic fields connecting the star with the inner border of the disk. The different rotation rates produce shear in the star-disk magnetic fields, eventually leading to field lines winding up around the star and reconnecting, releasing energy and plasmoids that stream out along large-scale magnetic fields (Hayashi et al., 1996; Montmerle et al., 2000). This may be a viable model for the production of protostellar jets.

• Star-disk magnetic fields are thought to define the basic route of material accreting from the disk to the star (Uchida and Shibata, 1984; Camenzind, 1990; Königl, 1991). This star-disk magnetospheric complex (Figure 29) is in the center of present-day studies of PMS magnetic “activity” as it links the accretion process to stellar magnetic fields and probably to outflows and jets. Although the details of the magnetic interface between the star and the circumstellar disk are far from being understood, the physics of mass-loading of the magnetic field lines is being addressed in detail based on theoretical (e.g., Shu et al., 1994; Ferreira and Zanni, 2007) and numerical investigations (e.g., Romanova et al., 2006). Magnetically funneled material forms “hot spots” on the stellar surface that can be observed as an ultraviolet excess (e.g., Calvet and Gullbring, 1998).

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6.2.3 New emission properties: Solar-like or not?

Given the similarity between WTTS and active, ZAMS stars, “activity” in WTTS as seen in spots, chromospheric and transition-region lines, and X-ray emission has conventionally been attributed to solar-like magnetic activity. Non-thermal gyrosynchrotron radio emission in WTTS suggests processes similar to those observed in active MS stars and subgiant binaries, processes that are thought to be related to electron acceleration in coronal flares (White et al., 1992a, b; Güdel, 2002). As for CTTS, strong optical and ultraviolet emission lines were initially assumed to give evidence for extremely active chromospheres and transition regions (Joy 1945; Herbig and Soderblom 1980, see review by Bertout 1989). Flares and “flashes” (e.g., Ambartsumian and Mirzoyan, 1982) also suggest analogy with magnetic flaring in more evolved stars and the Sun. Arguments in favor of solar-like magnetic coronal activity in all TTS include i) dominant, typical electron temperatures of order 10⁷ K that require magnetic confinement, and ii) the presence of flares (Feigelson and Decampli, 1981; Feigelson and Kriss, 1981, 1989; Walter and Kuhi, 1984; Walter et al., 1988).

However, the solar analogy seems to break down in the optical/UV range where strong flux excesses are recorded; these excesses are uncorrelated with X-rays (Bouvier, 1990) but seem to relate to the accretion process (Section 6.3.2). A similar excess recently discovered in soft X-rays may be related to both coronal magnetic fields and accretion (Güdel and Telleschi 2007, see Section 6.3.4). Also, thermal radio emission observed in CTTS, probably due to optically thick winds but also due to bipolar jets, reaches beyond the solar analogy (Cohen et al., 1982; Bieging et al., 1984). Clearly, emission across the electromagnetic spectrum needs to be understood in the context of the new features around accreting stars, and in particular the related magnetic fields, summarized in Section 6.2.2.

A summary of the present view of activity and other properties of PMS stars from the earliest stages to the arrival on the MS is given in Figure 30 (from Feigelson and Montmerle, 1999).

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6.3.1 The magnetic field of the T Tauri Sun

Surface magnetic fields have been successfully measured on “solar-analog” T Tauri stars, using Zeeman broadening (Johns-Krull et al., 1999; Valenti and Johns-Krull, 2004; Johns-Krull, 2007a). For example, BP Tau (a 0.65 M_⊙ CTTS) maintains a mean magnetic field strength (∑Bf) of 2.6±0.3 kG, i.e., the equivalent of sunspots for f = 1. Such field strengths exceed the equipartition value of T Tauri photospheres (≈ 1 kG, Johns-Krull et al. 1999; Johns-Krull 2007a), which may be a consequence of near-total surface filling (Solanki, 1994; Johns-Krull, 2007a). T Tauri photospheres are therefore dominated by magnetic pressure rather than thermal pressure, in contrast to MS stars and the Sun but similar to stellar coronae in general. The average surface magnetic fields of CTTS also exceed a prediction from X-rays, based on a correlation between X-ray luminosity and photospheric magnetic flux valid for MS stars and the Sun (Pevtsov et al., 2003). Upper limits of the net polarization of photospheric lines suggest that the photospheric magnetic fields form predominantly in small-scale structures, although a dipole may dominate at large distances (Johns-Krull et al., 1999; Valenti and Johns-Krull, 2004; Johns-Krull, 2007a). Large dipole components are also suggested from observations of spots concentrated at the poles of T Tauri stars, similar to active MS solar analogs (e.g., Joncour et al., 1994; Hatzes, 1995; Rice and Strassmeier, 1996). In any case, the observed fields should be strong enough to truncate circumstellar disks indeed (Johns-Krull et al., 1999; Johns-Krull, 2007a), even if rather complex (non-dipolar) surface magnetic field distributions are assumed (Gregory et al., 2006).

Zeeman-Doppler Imaging techniques have successfully been applied to extremely active solar analogs in the PMS phase. A particularly clear case was presented by Donati et al. (2000), finding solar-like differential rotation on a post-T Tauri star (see also Section 4.3.1). More recently, Donati et al. (2007) have reconstructed a rather complex, large-scale magnetic topology on the CTTS V2129 Oph; they found a relatively weak dipole but stronger octupolar fields that are tilted against the rotation axis, with strong near-polar spots. The accretion footpoints are also found to be located at high latitudes. An attempt was made at extrapolating the fields to the inner rim of the disk, showing that some field lines should successfully accrete toward the observed hot spots.

At coronal levels, X-ray rotational modulation provides information on the large-scale distribution of stellar magnetic fields. Rotational modulation is widespread among extremely active T Tauri stars (Flaccomio et al., 2005). Some 10% of the studied stars in the Orion X-ray sample show such evidence, suggesting that: i) the X-ray emitting active regions are not homogeneously distributed on the surface, i.e., despite the X-ray saturation level reached by these stars, the surface cannot be filled with X-ray-bright magnetic loops; ii) the X-ray emitting regions responsible for the rotational modulation are directly associated with the surface and cannot extend much beyond R_* (Flaccomio et al., 2005). A comparison of the modulation depth with the Sun’s modulation in fact shows that the longitudinal inhomogeneities are similar (Flaccomio et al., 2005).

6.3.2 The ultraviolet T Tauri Sun

A defining property of (accreting) classical T Tauri stars is their strong line emission of, e.g., Hα or Ca ii H & K. These strong lines were initially thought to be evidence of massive chromospheres similar to those seen on the Sun or in cool stars (see review by Bertout 1989), and the discovery of strong UV lines such as those of Si ii, Si iv, and C iv — equivalent to “transition region” lines in the Sun formed above 10⁴ K — supported this picture.

However, when compared with MS stars, including chromospherically very active examples, UV line and continuum emission is up to 10²–10⁴ times stronger in CTTS (see example of TW Hya in Table 4; Canuto et al. 1982, 1983; Bouvier 1990; Valenti et al. 2000), regardless of the photospheric effective temperature or the stellar rotation period but correlated with the mass accretion rates derived from optical continuum data (Bouvier 1990; Johns-Krull et al. 2000; Figure 32a below). Further, UV or Hα line surface fluxes of CTTS show, in contrast to more evolved stars, no correlation with coronal X-rays, the latter being in the range of RS CVn-type active binary systems or very active MS stars but the UV/Hα lines showing a wide range of excess flux (Bouvier, 1990).

Coronal and “chromospheric/transition region” fluxes are thus not correlated in CTTS, contrasting strongly with MS and subgiant stars for which a sharp correlation is taken as evidence for a common physical heating mechanism (operating in related magnetic fields; Section 5.6, Figure 22). An additional mechanism must be responsible for the optical/UV line flux excess. Apart from the line excess fluxes, there is also a strong blue continuum excess that leads to “veiling” in the optical spectrum, i.e., a filling-in of absorption lines by continuum emission; this emission is also not compatible with chromospheric radiation. The most obvious property common only to CTTS among the stars considered above is accretion; downfalling material could provide the energy to generate the optical/UV excess (Bertout et al., 1988; Basri and Bertout, 1989).

The present consensus, based on such concepts as well as line profile properties and correlations with the mass accretion rate, is that the UV excess emission originates from material heated in accretion shocks (e.g., Calvet and Gullbring, 1998; Gullbring et al., 1998). Some of the emission lines (e.g., Hα, Ca ii) may also form in the accretion funnels themselves, or in stellar winds (Ardila et al., 2002).

6.3.3 The X-ray T Tauri Sun in time

Feigelson et al. (2002b), Wolk et al. (2005), and Telleschi et al. (2007b) presented X-ray studies of near-solar-mass stars (stars in the ranges of 0.7 M_⊙ ≤ M ≤ 1.4 M_⊙ and 0.9 M_⊙ ≤ M ≤ 1.2 M_⊙, respectively, in the former two studies of the Orion Nebula cluster, and wider in the latter study of the Taurus star-forming region). The sample ages typically comprise the log t = 5.5–7 range and contain both disk-surrounded and disk-less T Tauri stars. The median X-ray luminosity in the Orion sample is found at log L_X = 30.25, i.e., three orders of magnitude above the average solar X-ray output, but there is evidence for a slow decay with age, log L_X ∝ t^−1.1 (Feigelson et al., 2002b; Wolk et al., 2005). A shallower decay was reported by Preibisch and Feigelson (2005) for the same stellar cluster, with an exponent between −0.2 and −0.5, but when considering normalized L_X/L_bol or average surface X-ray flux, then both Feigelson et al.’s and Preibisch & Feigelson’s studies indicate that the L_X decay law is roughly compatible with full saturation (i.e., L_X/L_bol ≈ 10⁻³) as the star descends the Hayashi track and its bolometric luminosity is decreasing (Feigelson et al., 2002b). Telleschi et al. (2007b) used the Taurus sample over a wider mass range but removed the strong L_X versus mass correlation in order to normalize the X-ray evolutionary behavior to a solar-mass star. The slope of the L_X vs. age correlation is fully compatible with the Orion results, with a power-law index of −0.36 ± 0.11 although the correlation is dominated by scatter from other sources, and its significance is marginal.

The evolutionary L_X decay is thus qualitatively different from that in MS stars: it is due to stellar contraction (and perhaps a change in the internal dynamo while the star transforms from a fully convective to a convective-radiative interior); in contrast, the decay of L_X in MS stars is due to stellar spin-down while the stellar structure and size remain nearly constant. Figure 31 shows the long-term evolution of the median X-ray output from PMS stages to the end of the MS evolution, for G-type stars with ages > 10 Myr and K-type stars with ages < 10 Myr (because the predecessors of MS G stars are PMS K stars; data from Güdel 2004). The slight trend toward decreasing L_X at ages < 10 Myr follows approximately L_X ≈ t^−0.3, in agreement with the individual trends for the Orion and the Taurus samples, albeit the scatter is large. No “onset ”of activity can be seen back to ages < 1 Myr.

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6.3.4 Coronal excesses and deficits induced by activity?

If the photoelectric absorption by the accreting gas is small, then the softest X-ray range may reveal the high-temperature tail of the shock emission measure thought to be responsible for the UV excesses (Section 6.3.2). Telleschi et al. (2007b) and Güdel et al. (2007b) identified an excess in the O VII/O VIII Lyα flux (or luminosity) ratio in CTTS when compared with WTTS or MS stars, the so-called X-ray soft excess of CTTS (Figure 32b). In the most extreme case of the CTTS T Tau, the excess O VII flux is such that this line triplet, formed at only ≈ 2 MK, is the strongest in the soft X-ray spectrum (see Figure 33; Güdel and Telleschi 2007).

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Interestingly, however, the X-ray soft excess in CTTS is comparatively moderate, the L(O VII r)/L(O VIII) line flux ratio being enhanced by factors of typically ≈ 3–4 times that of equivalent MS stars or WTTS (Figure 32). Furthermore, the excess X-ray line fluxes do not seem to be correlated with the UV line excesses but are correlated with the overall stellar coronal activity level traced, for example, by the O VIII Lyα line flux (Güdel and Telleschi, 2007). It appears that the X-ray soft excess depends on the level of magnetic (“coronal”) activity although it is, at the same time, related to the presence of accretion. The two dependencies may point to an interaction between accretion and magnetic activity at “coronal” heights.

The shock interpretation of the softest X-rays and the X-ray soft excess is appealing, but remains controversial until a larger sample of CTTS with various accretion properties has been interpreted. In particular, given the appreciable accretion rates, high shock densities of order 10¹²–10¹⁴ cm⁻³ are expected, as first indeed reported from density-sensitive line diagnostics of O vii and Ne ix in the CTTS TW Hya, forming at only a few MK (Kastner et al., 2002; Stelzer and Schmitt, 2004). However, some accreting PMS stars show much lower densities, such as AB Aur (Telleschi et al., 2007b) and T Tau (Güdel et al., 2007b); the same discrepancy between expected and observed densities has also been reported from ultraviolet density diagnostics (Johns-Krull et al., 2000).

In stark contrast to the X-ray soft excess and the UV excess described above, it is now well established that CTTS show a moderate suppression of 0.1–10 keV soft X-ray emission, typically by a factor of ≈ 2 when compared with WTTS of similar properties (Strom and Strom, 1994; Damiani et al., 1995; Neuhäuser et al., 1995; Stelzer and Neuhäuser, 2001; Flaccomio et al., 2003; Preibisch et al., 2005; Telleschi et al., 2007a). Although selection/detection bias or different photoelectric absorption has been quoted to be responsible for these differences (see Güdel 2004 and references therein), the luminosity deficit in CTTS is now thought to be real; it appears that accretion suppresses coronal heating in a fraction of the coronal volume (Preibisch et al., 2005), or at least leads to larger amounts of cooler plasma, which is perhaps the same plasma inferred from the X-ray soft excess (Telleschi et al., 2007b; Güdel and Telleschi, 2007). Alternatively, the presence of a circumstellar disk could strip the outer parts of the stellar corona, thus reducing L_X (Jardine et al., 2006).

6.3.5 X-ray flaring of the T Tauri Sun

A high level of near-continuous flaring is found in PMS solar-mass stars. As much as half of the emitted X-ray energy, if not more, may be due to strong flares (Montmerle et al., 1983), and many TTS are nearly continuously variable probably also owing to flares (Mamajek et al., 2000; Feigelson et al., 2002a; Preibisch and Zinnecker, 2002; Skinner et al., 2003). Examples with extreme luminosities and temperatures up to 100 MK have been reported (e.g., Preibisch et al., 1995; Skinner et al., 1997; Tsuboi et al., 1998, 2000; Imanishi et al., 2002). The most extreme flares are found on CTTS and protostars, a possible hint at star-disk magnetic interactions during flares. Wolk et al. (2005) studied frequency and properties of flares in the Orion Nebula cluster, concluding that the median peak luminosity of their sample was log L_X = 30.97, with extremely hard spectra at peak time. The median electron temperature was found at 7 keV. An analogous study has been presented by Stelzer et al. (2007) for T Tauri stars in the Taurus Molecular Cloud. The extreme flaring recorded on these PMS stars may have an important bearing on coronal heating (see Section 5.8) and on the alteration of solids in the young stellar environment (see Section 6.6).

6.3.6 The radio T Tauri Sun in time

Early VLA surveys quickly reported strong radio emission from both CTTS and WTTS. Somewhat unexpectedly, however, radio emission comes in two principal flavors. The early, pioneering studies by Cohen et al. (1982), Bieging et al. (1984), Cohen and Bieging (1986), Schwartz et al. (1984), and Schwartz et al. (1986) recognized thermal wind-type emission with rising spectra and in cases large angular sizes for several CTTS. This radio emission can then be used to estimate mass loss rates; these are found to range up to ≲ 10⁻⁷ M_⊙ yr⁻¹ (André et al., 1987). The partly enormous kinetic wind energy derived under the assumption of a uniform spherical wind suggests anisotropic outflows while structural changes in the radio sources indicate variable outflows, probably along jet-like features; at shorter radio wavelength, dust emission from the disk becomes apparent as well (Cohen and Bieging, 1986; Rodríguez et al., 1992, 1994; Wilner et al., 1996). The thermal radio emission tells us nothing about the presence or absence of stellar magnetic fields. As described earlier, CTTS do show many signatures of magnetic activity, but whatever the possible accompanying radio emission, it seems to be absorbed by the circumstellar ionized wind.

The situation is different in WTTS in which the presence of huge flares (Feigelson and Montmerle, 1985; Stine et al., 1988; Stine and O’Neal, 1998), longer-term variability, and falling spectra clearly point to non-thermal gyrosynchrotron emission (Bieging et al., 1984; Kutner et al., 1986; Bieging and Cohen, 1989; White et al., 1992a; Felli et al., 1993; Phillips et al., 1996) analogous to radio emission observed in more evolved active stars. Conclusive radio evidence for the presence of solar-like magnetic fields in WTTS came with the detection of weak circular polarization during flares but also in quiescence (White et al., 1992b; André et al., 1992; Skinner, 1993). Extremely energetic particles radiating synchrotron emission may be involved, giving rise to linear polarization in flares on the WTT star HD 283447 (Phillips et al., 1996). VLBI observations showing large (∼ 10 R_*) magnetospheric structures with brightness temperatures up to T _b ≈ 10⁹ K fully support the non-thermal picture (Phillips et al., 1991).

As a WTT star ages, its radio emission drops rapidly on time scales of a few million years from luminosities as high as 10¹⁸ erg s⁻¹ Hz⁻¹ to values around or below 10¹⁵ erg s⁻¹ Hz⁻¹ at ages beyond 10 Myr. Young age of a star is thus favorable to strong radio emission (O’Neal et al., 1990; White et al., 1992a; Chiang et al., 1996), whereas toward the subsequent ZAMS stage it is only the very rapid rotators that keep producing radio emission at the 10¹⁵ erg s⁻¹ Hz⁻¹ level (Carkner et al., 1997; Magazzù et al., 1999; Mamajek et al., 1999).

6.3.7 The composition of the T Tauri Sun’s corona

Initial studies of a few accreting T Tau stars, in particular the old (≈ 10 Myr) TW Hya, have shown an abundance pattern in the X-ray source similar to the IFIP effect although the Ne/Fe abundance ratio is unusually high, of order 10 with respect to the solar photospheric ratio, and the N/O and N/Fe ratios are enhanced by a factor of ≈ 3.

These anomalous abundance ratios have been suggested (Stelzer and Schmitt, 2004; Drake and Testa, 2005) to reflect depletion of Fe and O in the accretion disk where almost all elements condense into grains except for N (Savage and Sembach, 1996; Charnley, 1997) and Ne (Frisch and Slavin, 2003) that remain in the gas phase which is accreted onto the star. If accretion occurs predominantly from the gas phase in the higher layers of the disk while the grains grow and/or settle at the disk midplane, then the observed abundance anomaly may be a consequence.

Larger systematics have made this picture less clear, however. Several CTTS and WTTS have revealed large Ne/Fe ratios (≈ 4 or higher), much larger than in MS active solar analogs (Kastner et al., 2004; Argiroffi et al., 2005, 2007; Telleschi et al., 2005, 2007b; Günther et al., 2006) but similar to RS CVn binaries (Audard et al., 2003b). In contrast, the CTTS SU Aur reveals a low Ne/Fe abundance ratio of order unity (Robrade and Schmitt, 2006; Telleschi et al., 2007b), similar to some other massive CTTS (Telleschi et al., 2007b).

Partial clarification of the systematics has been presented by Telleschi et al. (2007b) (see also Güdel et al., 2007b) who found that

• the abundance trends, and in particular the Ne/Fe abundance ratios, do not depend on the accretion status but seem to depend on spectral type or surface T_eff, the later-type stars showing a stronger IFIP effect (larger Ne/Fe abundance ratios); see Figure 34.

• the same trend is also seen in disk-less ZAMS stars.

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Anomalously high Ne/O abundance ratios remain, however, for TW Hya (Stelzer and Schmitt, 2004) and V4046 Sgr (Günther et al., 2006) when compared to the typical level seen in magnetically active stars, including PMS objects. The initial idea proposed by Drake et al. (2005) was that the selective removal of some elements from the accretion streams should occur only in old accretion disks such as that of TW Hya where cogulation of dust to larger bodies is ongoing, whereas younger T Tauri stars still accrete the entire gas and dust phase of the inner disk. However, the old CTTS MP Mus does not show any anomaly in the Ne/O abundance ratio (Argiroffi et al., 2007). Larger samples are needed for clarification.

6.4.1 Magnetic activity in the protostellar Sun

The protostellar Sun was deeply embedded in its molecular cloud envelope. Direct optical observation of protostars is preluded by high extinction; the best access to these objects is through infrared and X-ray observations, the former, however, picking up much of the emission from dust in the disk and the envelope. Recent efforts have succeeded in obtaining photospheric spectra of Class I protostars from light scattered off the bipolar cavities carved by the outflows (White and Hillenbrand, 2004). Somewhat perplexingly, the analysis of the Taurus sample of embedded objects reveals very little statistical diference between Class I and CTTS objects in Taurus, for example with respect to rotation rates, accretion rates, bolometric luminosities, spectral classes, and disk masses, providing evidence that this sample is co-eval with the CTTS sample; the embedded objects seem to be those with the longest envelope dispersal time, while they are all past their main accretion phase (White and Hillenbrand, 2004).

Magnetic field measurements are commensurately challenging. Johns-Krull (2007b) recently succeeded in obtaining near-infrared diagnostics to measure the photospheric magnetic field on a class I protostar. He reports a field strength of 3.6 kG, making this the highest mean surface field so far detected on any young stellar object.

Direct evidence for magnetic activity is seen in X-rays. Strong X-ray activity is found in considerable numbers of “Class I” protostars thanks to Chandra’s and XMM-Newton’s hard-band sensitivity (see, e.g., Imanishi et al., 2001; Preibisch and Zinnecker, 2001, 2002; Preibisch, 2003b; Getman et al., 2002; Güdel et al., 2007a). Their measured characteristic temperatures are very high, of order 20–40 MK (Tsujimoto et al., 2002; Imanishi et al., 2001). Some of these values may, however, be biased by strongly absorbed (“missing”) softer components in particular in spectra with limited signal-to-noise ratios. It is correspondingly difficult to characterize the L_X values in traditional soft X-ray bands for comparison with more evolved stars.

6.4.2 Magnetic flaring of the protostellar Sun

Strong X-ray flaring is a characteristic of protostellar solar analogs. Many of these events are extremely large, with total soft X-ray energies of up to ≈ 10³⁷ erg (Koyama et al., 1996; Kamata et al., 1997; Grosso et al., 1997; Ozawa et al., 1999; Imanishi et al., 2001; Preibisch, 2003a; Imanishi et al., 2003). Such flares realistically require large volumes, in fact to an extent that star-disk magnetic fields become a possibility for the flaring region (Grosso et al. 1997 for YLW 15 in p Oph), with important consequences for the irradiation of the stellar environment by high-energy photons and particles (see Section 6.5).

6.4.3 Radio emission from the protostellar Sun

At radio wavelengths, genuine, embedded class I protostars have most often been detected as thermal sources, and this emission is predominantly due to collimated thermal winds or jets. These jets are probably ionized by neutral winds that collide with the ambient medium at distances of around 10 AU and that are aligned with molecular outflows (e.g., Bieging and Cohen 1985; Snell et al. 1985; Brown 1987; Curiel et al. 1989; Rodríguez et al. 1989, 2003; Anglada 1995; Anglada et al. 1998). Ionized circumstellar material and winds easily become optically thick and therefore occult any non-thermal, magnetic emission from close to the star. However, the discovery of polarization in T Tau(S) (Phillips et al., 1993; Smith et al., 2003), in IRS 5 (Feigelson et al., 1998), in protostellar jet sources (Yusef-Zadeh et al., 1990) and the jet outflows themselves (Curiel et al., 1993; Hughes, 1997; Ray et al., 1997), as well as variability and negative spectral indices in T Tau(S) (Skinner and Brown, 1994) provided definitive evidence for magnetic fields and particle acceleration around these class I objects.

6.5.1 Circumstellar disk ionization

In terms of physical processes, ionization of the disk is important for the operation of the magneto-centrifugal instability (MRI; Balbus and Hawley 1991) thought to be the main driver of accretion in young stellar objects. Although cosmic rays have long been suspected to be an effective disk ionization source (Gammie, 1996), the high-level, hard coronal emission and frequent stellar flares may be more effective ionizing sources (Glassgold et al., 1997; Feigelson et al., 2002b). This is even more so as young solar analogs in the T Tau stage drive very strong winds that are very likely magnetized; such winds effectively shield the inner disk from cosmic rays, as does the present-day solar wind, at least for cosmic rays with energies < 100 MeV.

Glassgold et al. (1997) and Igea and Glassgold (1999) modeled ionization and heating of circum-stellar disks by stellar coronal X-ray sources. The incoming X-ray photons are subject to Compton scattering and photoelectric absorption as they propagate through the disk. X-ray photons may interact with molecules or atoms by ejecting a fast (primary) photoelectron. This photoelectron collisionally produces on average 27 secondary electrons and ions (for a photon energy of 1 keV). Harder photons on average penetrate deeper and thus ionize layers of the disk closer to the equatorial plane, while softer X-rays ionize closer to the disk surface. The disk ionization fraction is then determined when an equilibrium between ionization and recombination has been reached. Electron fractions of 10⁻¹⁵−10⁻¹⁰ are obtained at vertical disk column densities of N_H = 10²⁷−10²¹ cm⁻² (as measured from infinity) for distances of 0.1–10 AU from the central star. The precise results depend somewhat on the hardness of the X-ray spectrum (a modest L_X = 10²⁹ erg s⁻¹ has been assumed).

The important points here are: 1) that the ionization fraction at the top of the disk is orders of magnitude higher than the ionization fraction that would result from standard cosmic-ray irradiation, and 2) that at vertical column densities of N_H = 10²⁴–10²⁵ cm⁻² and less, the disk is sufficiently ionized to become unstable against MRI. The disk surface will thus couple to the magnetic field and accrete to the star. In contrast, the deeper layers remain decoupled and therefore “quiescent”, at least within 5 AU (Figure 35, Igea and Glassgold 1999). These are the likely sites of planet formation (Glassgold et al., 1997). Modifications of these calculations by introducing trace heavy metals and diffusion have been discussed by Fromang et al. (2002) and Ilgner and Nelson (2006).

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Disk irradiation and photoionization by stellar UV photons is further responsible for photoevaporation of gaseous disks (Hollenbach et al., 1994; Clarke et al., 2001; Alexander et al., 2006a, b), and therefore the long-term accretion history of the star-disk system. Additional X-ray irradiation is, however, of secondary importance only (Alexander et al., 2004).

6.5.2 Circumstellar disk heating

Apart from disk ionization, X-ray irradiation also leads to disk heating (Igea and Glassgold, 1999; Glassgold et al., 2004). While dust disks are heated by the central star’s optical and UV light to a few 100 K at distances up to a few AU, the gas component may thermally decouple in particular in the upper layers where the density is small. A model calculation based on accretion viscosity heating combined with X-ray heating due to the central star shows that the upper layers of the gaseous disk (N_H ≲ 10²¹ cm⁻²) can be heated up to ≈ 5000 K (Figure 36). This holds even for low viscous heating efficiency where the X-ray heating contribution entirely dominates (Glassgold et al., 2004). At the same time, the strong temperature gradients in the temperature inversion region lead to the production of large amounts of “warm” CO. Similar calculations by Gorti and Hollenbach (2004) support the above picture of X-rays dominating gas heating at the disk surface.

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6.5.3 Observational evidence of disk irradiation

The elevated ultraviolet and X-ray activity level of young low-mass stars leads to significant irradiation of circumstellar accretion disks. Interactions between high-energy photons and disk matter is evident from X-ray photoabsorption in star-disk systems seen edge-on, but also from reprocessed starlight: Spatially unresolved FUV fluorescence lines of H₂ have been detected from several CTTS (Brown et al., 1981; Valenti et al., 2000; Ardila et al., 2002; Herczeg et al., 2002, 2006), but usually not from WTTS (Valenti et al., 2000); this emission is reprocessed stellar Lyα emission most intensely radiated from the accretion spots. At least in cases where the line radial velocities are coincident with stellar radial velocities, an origin of the fluorescence in a hydrogenic surface layer of the inner accretion disk at temperatures of 2000–3500 K is likely (Herczeg et al., 2002, 2004) although significantly blueshifted H₂ emission points to outflow-related fluorescence in some systems (Brown et al., 1981; Ardila et al., 2002; Walter et al., 2003; Saucedo et al., 2003; Herczeg et al., 2006). Fluorescent emission is also generated by reprocessing of X-ray photons; X-ray fluorescence is seen in particular in the 6.4 keV line of cold iron (Imanishi et al., 2001; Tsujimoto et al., 2005; Favata et al., 2005).

Simple energy considerations are revealing: Herczeg et al. (2004) estimate the rate of energy deposited in the environment of the CTTS TW Hya as a result of Lyα photoexcitation and subsequent far-ultraviolet fluorescence of H₂ to be 1.4 × 10²⁹ erg s⁻¹. The total soft X-ray luminosity of ≈ 1.4 × 10³⁰ erg s⁻¹ will at least partially heat the disk surface layer further (Igea and Glassgold, 1999).

Warm H₂ has also been detected through infrared 2.12 µm ro-vibrational emission from several T Tauri stars (Weintraub et al., 2000; Bary et al., 2003). This emission is thought to be excited by collisions between H₂ molecules and X-ray induced non-thermal electrons, or by an UV radiation field. High temperatures, of order 1000–2000 K, are required, but such temperatures are predicted from disk irradiation by X-rays out to several AU (Glassgold et al., 2004), or by UV radiation from the central star out to ≈ 10 AU if the star shows an UV excess (Nomura and Millar, 2005).

Glassgold et al. (2007) proposed forbidden [Ne II and Ne iii] infrared line emission at 12.81 µm and 15.55 µm, respectively, to be indicative of X-ray irradiation. The high first ionization potential of Ne (21.6 eV) indeed requires Ly continuum or X-ray photons for ionization (or cosmic rays, which are unlikely to be abundant in the inner disk region). The transitions are collisionally excited in warm gas, requiring temperatures of a few 1000 K, attained in disk surface layers out to about 20 AU for X-ray irradiated disks (Glassgold et al., 2004). The [Ne II] 12.81 µm transition has indeed been detected in several CTTS (Pascucci et al., 2007; Lahuis et al., 2007; Ratzka et al., 2007).

As a further consequence, specific chemical reactions may be induced. For example, Lyα itself can dissociate molecules like H₂ and H₂O and can ionize Si and C (Herczeg et al., 2004). Lyα radiation photodissociates HCN (but not CN), which leads to an enhancement of CN relative to HCN (Bergin et al., 2003).

7.1.1 The relevance of greenhouse gases

How the changes in the atmospheres came about is not entirely clear but may partly be related to the past solar activity (apart from, e.g., weathering, plate tectonics, volcanism, and biological activity). Although enhanced levels of solar EUV and X-ray emission will not directly alter the lower planetary atmospheres but only affect the higher thermosphere (where this radiation is absorbed) and the exosphere (see Section 7.2 below), the complex chemistry induced by photoionization, photodissociation, and heating through enhanced high-energy irradiation may be a key factor in determining what greenhouse gases were available in the young planetary atmospheres, as speculated by Ribas et al. (2005). For example, enhanced photodissociation may have influenced the abundances of ammonia and methane. Also, photochemistry and subsequent production of UV-shielding O₃ (Canuto et al., 1982, 1983) was important for the formation and evolution of life, and life itself eventually altered the composition of the young terrestrial atmosphere very significantly.

7.1.2 A bright young Sun?

A more radical remedy of the Faint Young Sun Paradox would be a Sun that was in fact not faint, i.e., did not follow the standard solar model calculations (see Sackmann and Boothroyd, 2003, for a discussion on controversies related to possible greenhouse effects, or their need, in the early atmospheres of Earth and Mars). Such would be possible if the ZAMS Sun had been more massive, having lost its mass in a wind at rates considerably higher than the present-day solar wind. The latter results in a mass loss of (2–3) × 10⁻¹⁴ i_⊙ yr⁻¹ (Wood, 2004, and references therein), and the radiative losses of energy transformed in thermonuclear reactions amount to about 3 times this rate. If the Sun had been subject to these present-day losses for its entire lifetime, its ZAMS mass would have been only 0.05% higher than the present-day value (Minton and Malhotra, 2007). This would change the young Sun’s bolometric luminosity negligibly (recall the mass-luminosity relation for MS stars, which requires approximately L_bol ∝ M³; based on Siess et al. 2000 ZAMS calculations for low-mass stars).

Higher wind mass-loss rates would be an interesting alternative (Graedel et al., 1991). Willson et al. (1987) hypothesized that intermediate-mass stars may lose appreciable amounts of mass during their MS life, in particular in the pulsation-instability strip; early G-type stars would then be descendants of A-type stars. Hobbs et al. (1989) concluded that a wind mass loss of 0.041 M_⊙ since the Sun’s arrival on the ZAMS would suffice to explain the low Li values observed in the present-day photosphere (because Li would be diluted when the wind-driving surface layer is progressively mixed with Li-free material entering from lower, hotter layers; see also Schramm et al. 1990; note, however, that there are other, and more important, processes that deplete Li, see Sackmann and Boothroyd 2003). A higher mass loss rate for the young Sun is in fact supported by meteoritic and lunar evidence, suggesting that 2.5–3.5 Gyr ago (solar age of 1–2 Gyr), the wind mass loss was on average 10 times higher than at present (Geiss and Bochsler, 1991). This would, however, result in a solar mass still only ≈ 0.1% higher at t = −3 Gyr than now (Sackmann and Boothroyd, 2003). To simultaneously fulfill the requirement of liquid water on young Mars, the initial solar mass would have to be ≳ 1.03 M_⊙ (Sackmann and Boothroyd, 2003).

Gaidos et al. (2000) used radio observations of three solar analogs at ages of a few 100 Myr to set upper limits to their present mass-loss rate. Because the spin rates of solar analogs reveal a power-law decay in time, Ω ∝ t^−0.6 (Equation 8, also Skumanich 1972 who gave an exponent of −0.5), Gaidos et al. (2000) argued for a power-law decay of the mass-loss rate as well (Equation 6), which, together with the radio upper limits, results in a maximum cumulative mass loss of 6% of the solar mass during the past 4 Gyr. This is close to the suggested mass losses to dilute Li (Hobbs et al. 1989, but note other Li depletion processes), is in agreement with the minimum loss of 3% required to explain liquid water on Mars (Sackmann and Boothroyd, 2003), and is also slightly lower than the upper limit of 7% of M_⊙ to avoid runaway greenhouse on Earth (Whitmire et al., 1995; Kasting, 1988) (the runaway greenhouse would evaporate the entire water ocean so that all water would be present in the atmosphere as steam; photodissociation and rapid loss of hydrogen by hydrodynamic escape [see Section 7.2.3 below] would lead to a dry planet — analogous to present-day Venus; see Ingersoll 1969).

Corresponding models have been computed by, among others, Boothroyd et al. (1991), Guzik and Cox (1995), and Sackmann and Boothroyd (2003). The upper limit for the ZAMS Sun allowed by the Li depletion purely due to wind-mass loss was found to be 1.1 M_⊙ (Boothroyd et al., 1991; Guzik and Cox, 1995). Helioseismology constraints are compatible with model calculations starting with ZAMS solar masses up to (1.07–1.10) M_⊙ (Boothroyd et al., 1991; Guzik and Cox, 1995) but the consequent enhanced mass loss should be confined to the earliest ≈ 200 Myr of the Sun’s life on the MS, implying loss rates as high as 5 × 10⁻¹⁰ M_⊙ yr⁻¹ (Guzik and Cox, 1995). Somewhat depending on the precise mass-loss law, the solar flux starts at values up to 7% higher than the present-day value (corresponding to mass-loss rates of ≈ 10⁻¹¹−10⁻¹⁰ M_⊙ yr⁻¹ at ZAMS age) to drop to a minimum no less than 80% after 1–2 Gyr, and to increase again in agreement with the evolution of the standard solar model (Figure 38). The highest acceptable initial solar mass is 1.07 M_⊙ to ensure that the young Earth would not lose its water via a greenhouse effect, photodissociation and subsequent loss of hydrogen into space (Sackmann and Boothroyd 2003; see also Section 7.2 below).

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However, the indirect inferences for the mass-loss rates of the young Sun derived by Wood et al. (2002) and Wood et al. (2005) (see Section 5.1) would again not support a significantly brighter ZAMS Sun. Using the power-law mass-loss decay relation of Wood et al. (2002) back to ZAMS, a total mass-loss of about 0.01 M_⊙ would result (Sackmann and Boothroyd, 2003), with an uncertainty of a factor of a few. Most of the mass loss would occur in the first few 100 Myr. The suppressed mass loss at early times, however (Wood et al., 2005), suggests that no more than 0.003 M_⊙ could be lost during the Sun’s MS life (Minton and Malhotra, 2007).

In summary, the main problem with the “bright young Sun” model remains the disagreement between climatic requirements for the young-Sun mass (i.e., a ZAMS solar mass of [1.03–1.07] M_⊙) and the indirectly measured mass-loss rates (Minton and Malhotra, 2007) that tend to be too small (Wood et al. 2005, i.e., resulting in a ZAMS mass of no more than 1.01 M_⊙), although radio upper limits (Gaidos et al., 2000) are still compatible with the required mass-loss rates.

7.1.3 Cosmic rays and a stronger solar wind

Shaviv (2003) suggested a link between the cosmic ray flux and average global temperatures on Earth. Although a physical basis and an accepted proof are still missing, there is suggestive evidence that elevated cosmic-ray fluxes have a cooling effect on the Earth’s atmosphere. In this picture, cosmic rays ionize tropospheric layers, and charged ion clusters lead to condensation nuclei that eventually form clouds. Low-lying clouds have a cooling effect (Shaviv, 2003).

Given that wind of the young Sun was stronger (Section 5.1), the cosmic-ray flux reaching the inner solar system was suppressed compared to present-day fluxes. Cloud formation would thus be suppressed, leading to a warmer climate. Model calculations (also including effects due to variable star-formation rate in the solar vicinity on the cosmic-ray generation, a more rapid rotation of the Earth, and a smaller land mass) suggest that about 2/3 of the temperature reduction associated with the fainter young Sun can be compensated.

7.2.1 Planetary atmospheric chemistry induced by high-energy radiation

The young Sun’s elevated ultraviolet flux had considerable impact on the photochemistry of planetary atmospheres. Ayres (1997) estimated the photoionization rates based on the evolution of ionizing flux of solar analogs. He concluded that photorates scale approximately as t−¹, implying rates that were nearly 100 times stronger at a solar age of 100 Myr than at present (Figure 40).

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UV radiation initiated the photochemical processes leading to the formation of O₂ and O₃ in the prebiotic terrestrial atmosphere (Canuto et al., 1982). Ozone absorbs strongly in the 200–300 nm band and therefore protects life from lethal doses of UV radiation.

(M stands for other molecules; there are also several reactions that destroy O₂ and O₃; see Canuto et al. 1982). Atmospheric chemical models subject to enhanced UV irradiation show that the surface mixing ratio of O₂ increases by a factor of 10⁴–10⁶ above the standard pre-biotic value of 10⁻¹⁵ due to enhanced levels of solar UV radiation (corresponding to 1–300 times the present-day Sun).

The UV irradiation of the young Earth was particularly strong during the Sun’s T Tauri phase, up to factors of 10³ above the present solar values. The potential influence on planet formation and the subsequent generation of planetary atmospheres should therefore have been very significant at those epochs — if any of the planetary atmospheres were indeed forming at such early times already. The UV irradiation could increase the total column of O₃ by 1–3 orders of magnitude (Canuto et al., 1983), thus shielding incoming solar UV radiation efficiently and protecting early forms of life.

7.2.2 High-energy radiation and the planetary biospheres in habitable zones

Ionizing radiation is of crucial importance also for the evolution of life. While high doses are lethal for life, modest doses are important drivers of genetic mutations and therefore biological evolution. Although at present most high-energy radiation is absorbed in the high atmosphere of the Earth, significant effects may be found in thinner atmospheres (e.g., Mars) or in the environment of the young Sun where the irradiation by XUV photons was hundreds of times stronger. Smith et al. (2004) have computed the propagation of ionizing radiation through model atmospheres of terrestrial-like planets.

The incident spectra are those of supernovae explosions, gamma-ray bursts and, relevant for us, coronal X-ray flares that occurred at a much higher rate and up to much higher total energies in the young Sun compared to the present (Telleschi et al., 2005; Audard et al., 2000). Monte Carlo methods were used to calculate the transfer of incident X-ray and gamma-ray photons via Compton scattering and photoabsorption. The incident high-energy photons ionize molecules, thereby creating primary electrons, which collide further to produce secondary photoelectrons. These excite molecules and create aurora-like emission. A single incident photon can cause ionization of tens of thousands of molecules. For a neutral gas, most of the secondary-electron energy, however, goes into molecule excitation rather than ionization (different from ionized gas; Smith et al. 2004).

Even planets with thick atmospheres that shield evolving life from direct ionizing radiation will shower their surfaces with UV radiation owing to stochastic flares occurring on the host star. The present-day Sun produces about one flare every 100 yr with a transmitted UV surface flux equal to or larger than the continuous solar UV flux in the 200–320 nm band (Smith et al., 2004). Whether the UV irradiation effect is of prime importance for a planet around a young solar-like star is not clear, but it appears to be important for planets orbiting lower-mass M dwarf flare stars (Smith et al., 2004).

7.2.3 Planetary atmospheric loss and high-energy radiation and particles

Various mechanisms induced by solar magnetic activity can lead to escape of planetary atmospheric species, both neutrals and ions. The principal losses strongly depend on the magnetic activity of the host star. Thermal escape processes relate to a Maxwellian particle distribution and are consequently determined by the temperature of the respective atmospheric layer, and therefore by its heating rate. Thermal escape is predominantly controlled by photon irradiation from the host star. Non-thermal escape is due to other processes in which energization and escape are related to microscopic non-thermal processes (e.g., particle acceleration; Lundin and Barabash 2004; Lundin et al. 2007). Key factors are high-energy particle streams from the central star, i.e., the solar/stellar winds, and the magnetic environment of the planet itself.

The heating of planetary upper atmospheres and the generation of ionospheres is primarily due to the solar XUV radiation. The thermosphere is the layer in which most of this radiation is absorbed and is transformed to heat, leading to a positive (upward) temperature gradient. In the exosphere, the mean free path of atmospheric species is large, so that collisions are negligible. The lighter species may escape from this layer into space if their thermal velocity exceeds the gravitational escape velocity. The base of the exosphere, the exobase, is located at the height where the mean free path is equal to the local scale height, H = kT_exo/mg, where k is the Boltzmann constant, T_exo is the exobase temperature, m is the mass of the main atmospheric species, and g is the gravitational acceleration (Kulikov et al., 2007).

Here, υ₀ = (2kT_exo/m)^1/2 is the most probable velocity of the particle (see, e.g., Chassefière and Leblanc, 2004; Kulikov et al., 2006).

If the mean thermal energy of the particles (3kT_exo/2) exceeds the gravitational energy, i.e., for X < 1.5 or analogously for temperatures T_exo > 2GMm/3kr or \(kT\gtrsim mv_{{\rm esc}}^{2}/2\), the exosphere becomes unstable and hydrostatic equilibrium does not apply. The top of the atmosphere “blows off”, i.e., moves radially away from the planet with a velocity near its thermal velocity. To produce sufficiently high temperatures, a high level of EUV irradiation is required. The incoming EUV energy is then no longer converted into thermal energy but directly into kinetic energy. “Hydrodynamic escape” calculations are required (Öpik, 1963; Hunten, 1973; Watson et al., 1981).

Models of XUV heating of the present-day Earth’s thermosphere predict an average exospheric temperature of ≈ 1000 K (Kulikov et al., 2007, and references therein), in agreement with measurements. For Venus, T_exo = 270 K (Kulikov et al., 2006, 2007) where the low value is due to efficient cooling by CO₂. And for Mars, T_exo = 220–240 K (Kulikov et al., 2007).

I now discuss results from applications to solar-system bodies and extrasolar planets.

7.2.4 Mercury: Erosion of atmosphere and mantle?

Mercury stands out among solar-system planets by showing the largest average density, and its core is large compared to other terrestrial planets (60% of its radius). It is possible that strong winds and enhanced XUV irradiation from the young Sun removed much of the early atmosphere and the outer mantle of Mercury (Tehrany et al., 2002; Ribas et al., 2005). It is thus possible that Mercury started as a planet similar in size to Earth but has lost its mantle as a consequence of interactions with the young, active Sun.

7.2.5 Venus: Where has the water gone?

The atmosphere of Venus is extremely dry when compared to the terrestrial atmosphere (a total water content of 2 × 10¹⁹ g or 0.0014% of the terrestrial ocean, vs. 1.39 × 10²⁴ g on Earth, Kasting and Pollack 1983). The similar masses of Venus and Earth and their formation at similar locations in the solar nebula would suggest that both started with similar water reservoirs (Kasting and Pollack, 1983). The Venus atmosphere also reveals a surprisingly high deuterium-to-hydrogen (D/H) abundance ratio of (1.6±0.2) × 10⁻² or 100 times the terrestrial value of 1.56 × 10⁻⁴ (Donahue et al., 1982; Kasting and Pollack, 1983). These observations have motivated a basic model in which water was abundantly available on the primitive Venus. Any water oceans would evaporate, inducing a “runaway greenhouse” in which water vapor would become the major constituent of the atmosphere (Ingersoll, 1969). This vapor was then photodissociated in the upper atmosphere by enhanced solar EUV irradiation (Kasting and Pollack, 1983), followed by the escape of hydrogen (but not deuterium) into space (Watson et al., 1981; Kasting and Pollack, 1983). Oxygen either (partly) followed the same route or (partly) reacted with reduced atmospheric gases or minerals in the crust (Kasting et al., 1984). Judged from the D/H abundance ratio, at least 0.3% of a terrestrial ocean should have been outgassed (Donahue et al., 1982). I summarize some of the results and problems discussed in the literature as far as they refer to solar activity and its much higher level in the early Sun.

Detailed atmospheric models have been calculated by, e.g., Watson et al. (1981), Kasting and Pollack (1983), Kasting et al. (1984), Kasting (1988), Chassefière (1996b), and Kulikov et al. (2006). These models solve the equations of continuity and difusion (e.g., constrained to the vertical direction in 1-D approaches) for a number of species, hydrostatic and heat balance equations, and equations of vibrational kinetics for radiating molecules. They include irradiation by solar XUV and UV and their long-term evolution (see Kulikov et al., 2007, for a review).

Kulikov et al. (2006) and Kulikov et al. (2007) presented results for Venus, assuming no atmospheric (in particular, hydrogenic) loss, i.e., the upper atmospheres are not hydrogen-rich and not humid (Figure 41). For present-day solar XUV irradiation, the calculated exospheric temperature is 270 K, in good agreement with measurements. However, increasing the XUV flux to levels of the young Sun, i.e., a 100fold EUV flux, thermospheric temperatures up to ≈ 8200 K are reached 4.5 Gyr ago, if the CO₂ content is the same as today (96%). Higher temperatures are obtained for lower CO₂ content.

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The blow-of limit in the exobase is reached at 4000 K, permitting hydrogenic blow-of during the first 250 Myr after the Sun’s arrival on the ZAMS. Detailed hydrodynamic computations by Chassefière (1996b) show high Jeans escape flux even for present-day solar XUV irradiation for a Venus-like planet with a hydrogen atmosphere.

The question on water on the young Venus then concentrates on the availability of water vapor in the young Venus upper atmosphere, that can photodissociate so that H escapes. The critical solar flux leading to complete evaporation of a water ocean (a “runaway greenhouse”, Ingersoll 1969) is ≈ 1.4 S_sun nearly independently of the amount of cooling CO₂ in the atmosphere (Kasting, 1988), where S_sun = 1360 Wm⁻² is the present-day solar constant. This critical flux is just about the flux expected from the young Sun at the orbit of Venus (and is about 70% of the present-day value at the same solar distance).

These model calculations suggest that the amount of water in the present terrestrial ocean could have escaped from Venus in only 50 Myr if the H₂O mass fraction (mass mixing ratio) was at least 0.46, and the XUV flux was 70–100 times the present values (Kulikov et al., 2007).

The remaining problem then is to explain the extremely low oxygen content in the present-day atmosphere of Venus (Chassefière, 1996a). In a strong hydrodynamic escape process on young Venus, heavier gases such as O may be dragged with H (Zahnle and Kasting, 1986; Zahnle et al., 1990) although Chassefière (1996a) concluded that such loss was modest. Ion pick-up by the solar wind and ionospheric erosion by Kelvin-Helmholtz instabilities may be the dominant O⁺ loss mechanism in the present atmosphere of Venus (Lammer et al., 2006; Chassefière, 1997). The denser, young solar wind (Wood et al., 2002) could in fact easily remove the expected amount of O⁺ from a massive water ocean (Chassefière, 1997; Kulikov et al., 2006). The equivalent of one terrestrial ocean could be removed in only 10 Myr if the solar wind had been 10³–10⁴ times stronger than today, i.e., the escape would be “instantaneous” compared with outgassing time scales (Chassefière, 1997) although it is doubtful whether the young solar wind was indeed as strong as required for such massive losses (Wood et al. 2005, see Section 5.1).

7.2.6 Earth: A CO₂ atmosphere and magnetic protection

There is evidence for early hydrodynamic escape from the Earth’s atmosphere. Compared to Venus, the lighter noble gases Ne and Ar are depleted in the Earth’s atmosphere with respect to the heavier Kr and Xe; the isotopic composition of the noble gases points in the same direction (Zahnle and Kasting, 1986; Zahnle et al., 1990; Chassefière and Leblanc, 2004, and references therein).

The Kulikov et al. () model of the terrestrial atmosphere shows that a ten-fold increase of the XUV flux, corresponding to the Sun > 3.8 Gyr ago, leads to exobase temperatures of > 10,000 K, which would imply escape rates not only for H but also for H₂, He, N, O, or C. The hydrogenic blow-of temperature is only about 5000 K. As a consequence of dissociation of H₂O, large amounts of water would thus have been lost unless there was a significantly higher CO₂ content in the early atmosphere, because CO₂ is efficiently cooling the upper atmosphere by radiation in the 15 band (Kulikov et al., 2007) Given the high early solar XUV flux, the atmospheric CO₂ content in the young Earth’s atmosphere may have been at similar levels as in the atmospheres of the present-day Venus and Mars (≈ 95%; Kulikov et al. 2007). Its reduction and consequently, the rise of T_exo, due to weathering onto the surface and the seafloor during the first 500 Myr was accompanied by a rapid decay of the solar EUV irradiation so that T_exo was kept below blow-of conditions.

An important factor of the young Earth’s atmosphere is the relatively strong (as compared to Venus or evolved Mars) terrestrial magnetosphere that protects the atmosphere from solar-wind pickup erosion. An early on-set of the dynamo was therefore essential to protect the atmosphere and the large water reservoir of the Earth (Kulikov et al., 2007; Lundin et al., 2007).

7.2.7 Mars: Once warmer and wetter?

There is substantial evidence for a warmer and wetter climate on ancient Mars (Carr, 1986). The presence of valley networks in the highlands as well as some crater morphology require the presence of liquid water (e.g., Craddock and Maxwell 1993). Using Mars Global Surveyor images and altimeter data, Carr and Head (2003) estimated the depth of a primitive Martian ocean at 150 m (over the whole planet). Judged from the near-absence of valleys in the younger northern areas, liquid water disappeared suddenly 3.5–4 Gyr ago (Chassefière and Leblanc, 2004). Temperatures above 0° C and a massive atmosphere were required at earlier epochs, with a substantial content of greenhouse gases (Chassefière and Leblanc, 2004).

Massive atmospheric loss is relatively easy to explain, given Mars’ low surface gravity and the absence of a global magnetic field protecting the atmosphere from the solar wind after about 700 Myr of the planet’s formation (Acuña et al., 1998). Intense erosion by direct interaction between solar wind and the extended atmosphere is thus possible although significant suppression of non-thermal escape by the magnetic field would be possible during the first 200–300 Myr (Hutchins et al., 1997; Kulikov et al., 2007). In present-day Mars, hydrogen is predominantly lost through thermal escape (five times more efficiently than by non-thermal escape), while loss of oxygen to space requires non-thermal processes (Lammer et al., 2003a).

Like for other planets, the thermal escape of the young atmosphere of Mars depended strongly on the solar EUV irradiation, and non-thermal escape processes would also have depended on the ancient solar wind strength. Blow-of conditions are reached for an exospheric temperature T_exo ≳ 1000 K (Lammer et al., 2003a). This requires an EUV flux ≈ 100 times the present solar value (Kulikov et al. 2007, see Figure 42), i.e., blow-off may apply to the the earliest times of the solar evolution, namely the first few 100 Myr after the Sun’s arrival on the ZAMS (when a strong solar wind would perhaps provide additional support, Chassefière 1996b, 1997; Chassefière and Leblanc 2004). For solar conditions 2.5 Gyr and 3.5 Gyr ago, Lammer et al. (2003a) concluded that the exospheric temperature was only T_exo = 350 K and 600 K, respectively (with a 3 times and 6 times higher solar EUV flux, respectively), insufficient for blow-off unless a significantly lower CO₂ mixing ratio applied (Kulikov et al., 2007), although Jeans escape and non-thermal escape of H remained operational.

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Calculations show that in contrast to the situation on Venus and Earth, a considerable fraction of O (from the dissociated H₂O molecules) may have been dragged of by the escaping H in the very young Mars (4–4.6 Gyr ago; Chassefière 1996a). Non-thermal escape processes (of O) alone may explain the loss of a 12–15 m Martian ocean during the past 3.5 Gyr (Lammer et al. 2003a; Chassefière and Leblanc 2004, and further references therein converging to similar numbers). Lammer et al. (2003a) and Chassefière and Leblanc (2004) summarized escape rates for three different epochs (present, 2.5 Gyr and 3.5 Gyr ago) to find that oxygen loss to space in the early epochs is predominantly due to sputtering (and also ion pick-up; see also Luhmann et al. 1992; Jakosky et al. 1994), in contrast to the present-day situation. During the last 2 Gyr, however, O escape was not sufficient to balance H escape from dissociated water, implying that oxygen must have reacted efficiently with surface material.

7.2.8 Venus, Earth, Mars: Similar start, different results?

Even if Venus, Earth, and Mars might all have started with dense, CO₂ rich atmospheres and a large reservoir of water, the outcome of atmospheric evolution shows three very different planets: a very arid Venus with its dense, greenhouse-effective hot CO₂ atmosphere; a water-rich Earth with a biologically transformed, intermediate-density atmosphere; and a cold Mars with frozen water reservoirs and a greenhouse-ineffective CO₂ atmosphere. Key factors that led to the variations between the present-day planets are, among others: the close distance of Venus to the Sun, potentially allowing for a runaway greenhouse leading to the complete escape of water into space; the Earth’s magnetic field that protected the atmosphere from erosion by the early and stronger solar wind, together with the biological activity unfolding on young Earth; and the low surface gravity of Mars coupled with the absence of a magnetic field that led, except during the initial few 100 Myr, to more efficient erosion of the early atmosphere. Further factors such as continents (allowing for a carbonate-silicate geochemical cycle and thus the removal of CO₂, see Section 7.1.1), plate tectonics (allowing for release of CO₂, see Kasting and Toon 1989), or volcanic activity may matter as well. Nevertheless, in all cases, the level of XUV emission and the strength of the solar wind in the early solar system were of prime importance. Figure 43 shows a sketch of the different evolutionary paths of the atmospheres of Venus, Earth, and Mars considering the long-term evolution of the Sun’s XUV radiation and the solar-wind strength (from Kulikov et al. 2007; see also Lundin et al. 2007).

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7.2.9 Titan: Early atmospheric blow-off?

The same atmospheric methodology as described for Venus and Mars can be applied to other solar-system atmospheres. There is a particularly interesting isotopic anomaly in the atmosphere of Titan, namely a ¹⁵N enrichment with respect to ¹⁴N by a factor of 3.9–4.5 (Penz et al., 2005, and references therein). Non-thermal escape processes alone cannot account for the enrichment unless an unrealistically strong solar wind is assumed for the first 500 Myr after the origin of the solar system (Lammer et al., 2000; Penz et al., 2005).

It is important to note that present-day Titan’s orbit resides entirely within Saturn’s magnetosphere, i.e., its atmosphere is protected from the solar wind. Because the latter has decayed during the Sun’s evolution (Section 5.1), Titan spent most of its time outside Saturn’s magnetosphere at ages of about 100 Myr, and still more than half of the time at an age of 1 Gyr; its atmosphere was therefore subject to direct solar-wind interactions. Nevertheless, sputtering and ion pick-up are not sufficient to explain the anomalous ¹⁵N/¹⁴N ratio (Penz et al., 2005).

Thermal escape is an alternative. The present exospheric temperature is in the range of T_exo ≈ 150–180 K, while for blow-off, T_exo > 8040 K is required (see Penz et al., 2005, and references therein). Scaling the present T_exo by using the XUV flux decay law derived for solar analogs (Section 5.6), one finds blow-off conditions for Titan during the first 200 Myr. Only 50 Myr would in fact suffice to remove 30 Titan atmospheres, needed to explain the anomalous ¹⁵N/¹⁴N isotopic ratio (Penz et al. 2005; see also Lunine et al. 1999).

7.2.10 Hot Jupiters: Mass evolution by evaporation?

The discovery of extrasolar, Jupiter-class planets very close to their parent stars (Mayor and Queloz, 1995) immediately brought up the question on the stability of such objects. Gaseous planets close to a solar-like star will efficiently evaporate. However, as discussed above, it is not the radiative effective temperature, T_eff, that is relevant for evaporation, but rather the exospheric temperature, T_exo, which is determined by the stellar XUV flux, and is therefore a consequence of stellar activity.

A “Hot Jupiter” orbiting a star like the present-day Sun at a distance of 0.04 AU is, with regard to solar XUV irradiation, an analog to a Jupiter-like planet in orbit around the ZAMS Sun at a distance of 1.3 AU. The analogy does not hold for the stellar wind, and there may also be a substantial effect due to synchronous (i.e., slow) rotation of hot Jupiters (Grießmeier et al., 2004).

Lammer et al. (2003b) derived the escape rate of a hydrogen atmosphere of a Jupiter-like exoplanet based on exospheric XUV absorption and heating. They used the time-dependent XUV fluxes from the “Sun in Time” program (Section 5.6). Although for Jupiter in its 5.2 AU orbit around the present-day Sun, XUV heating leads to T_exo ≈ 140 K only, a close-in hydrogen-rich Jupiter at distances < 0.3 AU may suffer blow-off temperatures T_exo > 2 × 10⁴ K. The XUV-absorbing atmospheric layer (the “exobase”) expands to several planetary radii, which has been directly confirmed by a planetary transit observation (Vidal-Madjar et al., 2003). The initial calculations by Lammer et al. (2003b led to very high mass-loss rates, initially criticized by Yelle (2004) who derived 20 times smaller escape rates by also including atmospheric chemistry in their calculations; in particular, they considered thermospheric cooling by H₃⁺ and the lowering of the solar energy deposition rate by ionization of H to H⁺, which either escapes, or recombines by emitting a photon, which escapes as well. In this case, the escape rate will not be large enough to substantially affect the planetary evolution. This was substantially confirmed by new calculations performed by the previous group (see Penz et al., 2007) who considered Roche-lobe effects to the hydrodynamic loss, and used realistic heating efficiencies (rather than an energy-limited, 100% efficiency assumption) and IR cooling terms for HD 209458b, a Jupiter-sized planet in orbit around an old, inactive solar analog. The temperatures at 1.5 R_planet then reach 6000–10,000 K (Figure 44) which, however, leads to blow-of thanks to gravitational effects by the Roche lobe. Loss rates of 7 × 10¹⁰ g s⁻¹ are obtained, in agreement with calculations by Yelle (2004) and Yelle (2006). Extrapolated to young MS ages of the host star (applying elevated XUV irradiation, i.e., a factor of 100 at an age of 0.1 Gyr, see Table 6), the loss rate may exceed 10¹² g s⁻¹, leading to an integrated mass loss of 1–3.4% of the present mass over the entire MS life time of the host star, a fraction that is not leading to substantial alterations in the planet. However, higher evaporation fractions are possible for planets orbiting closer to the host star.

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In summary, hot Jupiters around young solar analogs should be in a state of extensive atmospheric loss for four reasons. The first three, close distance, high XUV flux, and strong wind of the host star have been discussed above. The fourth is the lack of a strong planetary dynamo owing to the slow, synchronous rotation of the planet. This prevents the planet from building up an extensive magnetosphere that protects the upper atmospheric layers from erosion by the solar wind. In fact, during the first 500 Myr, the magnetosphere may not protect the atmospheres of hot Jupiters even if tidal locking were ignored (Grießmeier et al., 2004). The “hot Jupiter” would therefore interact with the solar/stellar wind in a similar way as present-day Venus. Such interactions are even further enhanced by collisions with coronal mass ejections (CMEs). Given that these were probably much more frequent in the young Sun, significant effects are expected for planets at larger distances. Khodachenko et al. (2007) found that in order to prevent atmospheric erosion down to the planetary core, a sufficiently strong planetary magnetic field must be present to deflect CME plasma at stand-off distances of at least 1.3 R_planet for hot Jupiters like HD 209458b. The very existence of numerous Jupiter-mass planets very close to their host stars may indicate that the planets are able to retain substantial magnetic moments (Khodachenko et al., 2007).