Planet Formation in Binaries - Planetary Exploration and Science: Recent Results and Advances - page 324

Table 13.2 Samples of spectral weight factors

Narrow HZ Empirical HZ

Star Eff. temp Inner Outer Inner Outer

F0 7,300 0.850 0.815 0.902 0.806

F8V (HD 196885 A) 6,340 0.936 0.915 0.957 0.913

G0 5,940 0.981 0.974 0.987 0.973

G2V (Ǜ Cen A) 5,790 0.999 0.998 0.999 0.998

K1V (Ǜ Cen B) 5,214 1.065 1.100 1.046 1.103

K3 4,800 1.107 1.179 1.079 1.186

M1V (HD 196885 B) 3,700 1.177 1.383 1.154 1.419

M5 3,170 1.192 1.471 1.179 1.532

LM2 3,520 1.183 1.414 1.163 1.458

Fig. 13.12 Spectral weight factor W.f;T/ as a function of stellar effective temperature for the
narrow ( left ) and empirical ( right )HZs.The solid line corresponds to the inner and the dashed
line corresponds to the outer boundaries of HZ. We have normalised W.f;T/ to its solar value,
indicated on the graphs ( Sun )

13.7.4 Effect of Binary Eccentricity

To use Eq. ( 13.2 ) to calculate the boundaries of the HZ, we assume that the orbit of
the (fictitious) Earth-like planet around its host star is circular. In a close binary
system, the gravitational effect of the secondary may deviate the motion of the
planet from a circle and cause its orbit to become eccentric. In a binary with a
given semimajor axis and mass ratio, the eccentricity has to stay within a small to
moderate level to avoid strong interactions between the secondary star and the planet
and to allow the planet to maintain a long-term stable orbit (with a low eccentricity)
in the primary's HZ. The binary eccentricity itself is constrained by the fact that in
highly eccentric systems, periodic close approaches of the two stars truncate their
circumstellar discs depleting them from planet-forming material (Artymowicz and
Lubow 1994 ) and restricting the delivery of water-carrying objects to an accreting
terrestrial planet in the binary HZ (Haghighipour and Raymond 2007 ).