The solar wind in time

5.1 The solar wind in time

Stellar magnetic winds are a crucial consequence of “stellar activity” but their detection in solar analogs is very difficult. Although the wind formation and acceleration mechanisms are still not conclusively understood in the Sun, it is clear that magnetic fields play a major role, be it for acceleration of the wind, for its heating, or for guiding the wind at least out to the Alfvén radius. A close relation between wind and magnetic corona is obvious (Parker, 1958 ), the former being related to open magnetic field lines and the latter predominantly to closed magnetic structures.

The best – albeit indirect – proof of the presence of magnetized winds is the spin-down of convective stars on the main sequence as such a wind carries away angular momentum from the star. I will discuss this in Section 5.2.

Direct measurement of ionized winds from solar-like stars has not yet succeeded; potential detection methods include the measurement of thermal radio emission from the winds (Lim and White, 1996 ; Gaidos et al., 2000 ), and signatures of charge exchange in X-ray spectra (Wargelin and Drake, 2001 ). Lim and White (1996 ) and van den Oord and Doyle (1997 ) gave upper limits to the mass-loss rates of $˙ −12 −1 Mw ≈ 10 M ⊙ yr$ for “solar-like” winds with T $≈$ 1 MK emanating from M-type dwarfs. Gaidos et al. (2000 ) derived upper limits to $M˙$ for three young solar analogs ( $π1$ UMa, $κ1$ Cet, and $β$ Com), finding $M˙w ∼< (4 − 5) × 10 −11M ⊙ yr− 1$ .

The most promising approach to date is an indirect method making use of Ly $α$ absorption in so-called “astrospheres”; the latter are suggested to be a consequence of interactions between stellar winds and the interstellar medium (ISM). This subject has been extensively reviewed in the Living Reviews in Solar Physics article by Wood (2004 ); I will therefore only briefly summarize the essential results.

Solar/stellar winds collide with the interstellar medium, forming, with increasing distance from the star, a termination shock (where the wind is shocked to subsonic speeds), a heliospause (separating the plasma flows from the star and the ISM), and the bow shock (where the ISM is shocked to subsonic speeds). The heliosphere is permeated by interstellar H i with T $≈$ (2–4) $×$ 10⁴ K (Wood et al., 2002 ). Much of this gas is piled up between the heliospause and the bow shock, forming the so-called “hydrogen wall” that can be detected as an absorption signature in the Ly $α$ line. The excess absorption from the Sun’s own hydrogen wall is, due to the deceleration of the ISM relative to the star, redshifted, while that of other astrospheres is blueshifted.

The measurable absorption depths are compared with results from hydrodynamic model calculations (Wood et al., 2002 , 2005 ). The important point is that the amount of astrospheric absorption should scale with the wind ram pressure, $Pw ∝ M˙wVw$ , where $Vw$ is the (unknown) wind velocity (Wood and Linsky, 1998 ). The latter is usually assumed to be the same as the solar wind speed. From this, $M˙w$ is derived.

The Sun’s hydrogen wall was detected in ultraviolet spectra by Linsky and Wood (1996 ), and an equivalent astrosphere around $α$ Cen A and B was interpreted by Gayley et al. (1997 ). Further important wind mass loss measurements based on this method have been presented by Wood et al. (2002 ) (and references therein) and Wood et al. (2005 ). A systematic study of all derived mass-loss rates shows that $˙ ℳw$ per unit stellar surface correlates with the stellar X-ray surface flux,

(an equivalent relation therefore holds between $M˙w$ and L_X); using the activity-age relation (Section 5.5.1), one finds

(Wood et al., 2005 ). These two laws indicate that stellar-wind mass loss is – in principle – a genuine activity indicator, the mass-loss being higher in young, magnetically active stars. Extrapolating the above law up to the X-ray saturation limit (F_X $≈$ 2 $×$ 10⁷ erg cm^–2 s^–1) would suggest $ℳw˙$ (or $M˙w$ ) of the youngest solar analogs to be about a thousand times higher than the present-day solar mass loss ( $M˙⊙ ≈ 2 × 10 −14M ⊙ yr− 1$ ; e.g., Feldman et al. 1977 ). However, this power-law relation breaks down for the most active stars with F_X $> ∼$ 8 $×$ 10⁵ erg cm^–2 s^–1 (Wood et al. 2005 , Figure 10 ). Stars at this limit show $˙ Mw$ about 100 times the present solar value, while $M˙w$ drops toward higher activity levels to about 10 times the solar value. The reason for this breakdown between X-ray activity and wind-mass loss may be related to the appearance of high-latitude active regions (spots) in the most active stars (Section 4.1.2); if the magnetic field becomes more akin to a global dipole, then wind escape may be inhibited in such stars (Wood et al., 2005 ).

Figure 10:

Left (a): Mass-loss rates per unit surface area vs. stellar X-ray surface fluxes. MS stars are shown by filled circles. The trend for inactive stars (shaded area) is not followed by more active stars. – Right (b): Inferred mass-loss history of the Sun. Again, the trend shown for inactive stars (shaded area) breaks down for the most active stars (from Wood et al., 2005

, reprinted with permission of AAS).