2 What is a Solar-Like Star?

The present Sun is a G2 V star with a surface effective temperature of approximately 5780 K. Stellar evolution theory indicates, however, that the Sun has shifted in spectral type by several subclasses, becoming hotter by a few hundred degrees and becoming more luminous (the bolometric luminosity of the Sun in its zero-age main-sequence [ZAMS] phase amounted to only about 70% of the present-day output; Siess et al. 2000Jump To The Next Citation Point). In understanding the solar past, we must therefore also consider stars of mid-to-late spectral class G. On the other hand, alternative evolutionary scenarios have suggested continuous mass loss from the young Sun at a high rate that would require a somewhat earlier spectral classification of the young Sun (Sackmann and Boothroyd, 2003Jump To The Next Citation Point). In any case, magnetic activity in the outer stellar atmospheres is predominantly controlled by the depth of the stellar convection zone and stellar rotation, both of which also evolve during stellar evolution. For our understanding of magnetic activity, the precise spectral subclass is rather likely to play a minor role. When discussing “solar analogs”, I will therefore concentrate on stars mostly of early-to-mid-G spectral types but will occasionally also consider general information from outer atmospheres of somewhat lower-mass stars if available.

The situation is more complex for stars in their PMS stage. The Sun spent much of its PMS life as a mid-K (K5 IV) star when it moved down the Hayashi track. But again, the precise spectral subtype matters even less for magnetic activity in this stage, the more important key parameters being the age of the star (controlling its total luminosity, its radius, and the development and therefore the depth of the convection zone), the presence and dispersal of a circumstellar disk (controlling mass accretion and, via magnetic fields, the spin of the star), and the presence and strength of outflows (controlling, together with accretion, the final evolution of the stellar mass). A somewhat more generous definition of “pre-main sequence solar analogs” is clearly in order, given that the Sun’s history of rotation, accretion, the circumsolar disk, and the solar mass loss cannot be precisely assessed. Quite generally, I will take solar-like stars in the PMS phase to be, from the perspective of “magnetic activity”, stars with masses of roughly 0.5 – 1.5 solar masses, covering spectral classes from early G to late K/early M.

The expression “solar twin” (Cayrel de Strobel and Bentolila, 1989) is occasionally used. This term should be used solely in the context of a solar analog with an age close to the Sun’s, i.e., of order 4 – 6 Gyr, an age range in which the internal structure and the rotation period of a 1 M ⊙ (and therefore, its activity level) evolve only insignificantly. Efforts toward identifying real solar twins have been important in the context of putting our Sun into a wider stellar context; nearby solar analogs that are essentially indistinguishable from the Sun with regard to spectral type, effective temperature, gravity, luminosity, age, rotation, and magnetic activity (Porto de Mello and da Silva, 1997Jump To The Next Citation Point) prove that the Sun can be robustly used as an anchor to calibrate evolutionary trends – the Sun is not an exception but is representative of its age and mass, a conclusion also reached by Gustafsson (1998) from a rather general comparison of the Sun with sun-like stars.1

Table 1 gives a list of terms, symbols, and acronyms used throughout the text.

Table 1: Symbols and units used throughout the text.
Symbol, acronym Explanation
c Speed of light [≈ 3 × 1010 cm s–1]
k Boltzmann’s constant [≈ 1.38 × 10–16 erg K–1]
G Gravitational constant [≈ 6.67 × 10–8 dyn cm2 g–2]
R∗ Stellar radius [cm]
R⊙ Solar radius [7 × 1010 cm]
M Stellar or planetary mass [g]
M ⊙ Solar mass [2 × 1033 g]
M˙w Mass loss rate (by wind) [M ⊙ yr–1]
P Rotation period [d]
Ω Angular rotation frequency
vrot Equatorial rotation velocity [km s–1]
T Temperature, also coronal electron temperature [K]
Tav Average coronal temperature [K]
Teff Effective temperature [K]
Texo Exospheric (planetary) temperature [K]
B Magnetic field strength [G]
f Surface filling factor
L Coronal magnetic loop semi-length [cm]
LX X-ray luminosity [erg s–1]
Lbol Stellar bolometric luminosity [erg s–1]
F Flux (line- or band-integrated) [erg cm–2 s–1]
Ro Rossby number
t, t6, t9 Stellar age, in Myr, in Gyr
ωcycl Activity cycle frequency
ISM Interstellar Medium
EM Emission Measure
(ZA)MS (Zero-Age) Main Sequence
PMS Pre-Main Sequence
(C/W)TTS (Classical/Weak-line) T Tauri Star
UV Ultraviolet radiation
FUV Far-Ultraviolet radiation
EUV Extreme Ultraviolet radiation
XUV Ultraviolet-to-X-ray radiation
IUE International Ultraviolet Explorer (NASA, ESA, U.K.)
EUVE Extreme Ultraviolet Explorer (NASA)
ROSAT Röntgensatellit (German/U.K./NASA X-ray satellite)
VLA Very Large Array radio telescope (U.S.A.)
MRI Magneto-Rotational Instability
CAI Calcium-Aluminum-rich Inclusion
(I)FIP (Inverse) First Ionization Potential Effect

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