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5.1 Inferring the mass loss history of the Sun

UpdateJump To The Next Update Information In addition to stellar mass loss rates, Table 1 lists coronal X-ray luminosities from the ROSAT PSPC instrument (see Hünsch et al., 1999Schmitt and Liefke, 2004). Solar-like winds have their origins in stellar coronae (see Section 2.1), so one might expect the winds to be correlated with coronal properties such as X-ray emission. Thus, in Figure 14View Image the mass loss rates
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Figure 14: Measured mass loss rates (per unit surface area) plotted versus X-ray surface flux (Wood et al., 2005aJump To The Next Citation Point). The filled and open circles are main sequence and evolved stars, respectively. For the main sequence stars with logF < 8 × 105 ergscm −2s− 1 X, mass loss appears to increase with coronal activity, so a power law has been fitted to these stars, and the shaded region is the estimated uncertainty in the fit. The saturation line represents the maximum FX value observed from solar-like stars.
measured from the astrospheric Lyα absorption (per unit surface area) are plotted versus X-ray surface fluxes (Wood et al., 2005aJump To The Next Citation Point). For the main sequence stars mass loss increases with coronal activity. A power law is fitted to these GK stars in Figure 14View Image. Quantitatively, this relation is
M˙ ∝ FX1.34±0.18. (1 )
The saturation line in Figure 14View Image indicates the maximum X-ray flux observed from solar-like stars (Güdel et al., 1997).

It is interesting to note that during the solar cycle, the Sun’s wind strength is actually anticorrelated with its X-ray flux. The solar wind is weaker at solar maximum than at solar minimum despite coronal X-ray fluxes being much higher (Lazarus and McNutt Jr, 1990). This is presumably due to the fact that winds are more associated with the large scale dipole component of the solar magnetic field instead of the small scale active regions responsible for most of the Sun’s X-ray emission. The dipole field actually weakens at solar maximum along with the wind. However, the interior magnetic dynamo is ultimately responsible for both the small scale and large scale fields, so as a whole both field components should increase with increasing dynamo activity, consistent with the mass loss/activity correlation in Figure 14View Image (Schrijver et al., 2003).

The evolved stars are clearly inconsistent with the main sequence stars in Figure 14View Image. The very active coronae of λ And and DK UMa produce surprisingly weak winds, though it should be noted that both of these astrospheric detections are flagged as being questionable in Table 1. There are three main sequence stars with 5 − 2 −1 log FX > 8 × 10 ergs cm s, which have low mass loss measurements that are not consistent with the wind-activity correlation that seems to exist for the low activity main sequence stars. Two of these stars (Proxima Cen and EV Lac) are tiny M dwarf stars. If these were the only discrepant data points one could perhaps argue that the discrepancy is due to these M dwarfs being significantly less solar-like than the G and K dwarfs that make up the rest of the main sequence sample of stars. However, this interpretation is invalidated by the third discrepant measurement, that of ξ Boo. Being a binary with two rather solar-like stars (G8 V+K4 V), there is no easy way to dismiss the ξ Boo measurement, which implies that the power law relation does not extend to high activity levels for any type of star. More mass loss measurements of active stars would clearly be helpful to better define the characteristics of solar-like winds at high coronal activity levels.

Based on the available data, the mass-loss/activity relation appears to change its character at 5 −2 −1 log FX ≈ 8 × 10 ergscm s. One possible explanation for this concerns the existence of polar spots for very active stars. Low activity stars presumably have starspot patterns like that of the Sun, where spots are confined to low latitudes. However, for very active stars not only are spots detected at high latitudes, but a majority of these stars show evidence for large polar spots (Strassmeier, 2002). The existence of high latitude and polar spots represents a fundamental change in the stellar magnetic geometry (Schrijver and Title, 2001), and it is possible that this dramatic change in magnetic field structure could affect the winds emanating from these stars. Perhaps stars with polar spots might have a magnetic field with a strong dipolar component that could envelope the entire star and inhibit stellar outflows, thereby explaining why active stars have weaker winds than the mass-loss/activity relation of less active main sequence stars would predict. For ξ Boo A, high latitude spots of some sort have been detected (Toner and Gray, 1988). Petit et al. (2005) have detected a strong global dipole field component for ξ Boo A, consistent with the picture presented above. They also detected a large-scale toroidal field component, which would have no solar analog whatsoever, consistent with the idea that very active solar-like stars have significantly different magnetic field structures from those of the Sun and other low-activity stars.

Figure 14View Image illustrates how mass loss varies with coronal activity. But what about age? There is a known connection between activity and age, for the following reasons. The gravitational contraction of interstellar clouds that results in star formation leads to rapid rotation for young, newly born stars. This rapid rotation leads to vigorous dynamo activity and therefore high surface magnetic activity and high coronal X-ray emission. However, the magnetic fields of these young, rapidly rotating stars drag against their winds, and this magnetic braking gradually slows the stellar rotation. This in turn leads to lower activity levels and X-ray fluxes. An enormous amount of effort has been expended in the past few decades to observationally establish exactly how rotation relates to stellar age (see Skumanich, 1972Soderblom et al., 1993) and how rotation relates to stellar activity, which is most easily measured through X-ray emission (see Pallavicini et al., 1981Walter, 19821983Caillault and Helfand, 1985Micela et al., 1985Fleming et al., 1989Stauffer et al., 1994). For solar-like stars, Ayres (1997) finds

Vrot ∝ t− 0.6±0.1 (2 )
for the rotation/age relation, while X-ray flux and rotation are related by
FX ∝ V 2.9±0.3. (3 ) rot

Equations (1View Equation), (2View Equation), and (3View Equation) can be combined to obtain the following relation between mass loss and age for solar-like stars:

M˙ ∝ t−2.33±0.55. (4 )
This is the first empirically determined mass loss evolution law for solar-like stars, and Figure 15View Image shows what this relation implies for the mass loss history of the Sun in particular (Wood et al., 2005aJump To The Next Citation Point).
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Figure 15: The mass loss history of the Sun suggested by the power law relation from Figure 14View Image (Wood et al., 2005a). The low mass-loss rate measurement for ξ Boo implies that the wind weakens at t ≈ 0.7Gyr as one goes back in time.

The truncation of the power law relation in Figure 14View Image leads to the truncation of the mass-loss/age relation in Figure 15View Image at about t = 0.7 Gyr. The location of ξ Boo is shown in order to infer what the solar wind might have been like at earlier times. Despite the high activity cutoff, the mass loss measurements obtained so far clearly suggest that winds are generally stronger for young solar-like stars, and as a consequence the solar wind was presumably much stronger early in the Sun’s lifetime. This has many important implications, some of which are discussed in Sections 5.2, 5.3, and 5.4.

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