|MadSci Network: Astronomy|
Unfortunately I could not find a simple answer to your question. In order to have an habitable zone we need to consider first the possibility of forming a planet there and then the possibility of forming life. It is believed that stars form at the centers of rotating disks in a cloud of interstellar gas and dust. Friction in the disk (and gravity!) makes the dust and gas fall to the center to form the star. Planets are believed to form from the remains of the disk. It is possible that two disks form close enough to form a pair of stars that rotate around each other. This is called a binary star system or simply a binary.
It was thought that close binary stars could not have planetary systems because each star of the system would truncate the disk of the other and remove material that is needed in the formation of planets. However the team of Mexican, American and Spanish astronomers Rodriguez, D'Alessio, Wilner, Ho, Torrelles, Curiel, Gomez, Lizano, Peldar, Cant� and Raga (Nature, Vol. 395, p. 355, 1998) discovered that probably there is a binary in L1551 IRS5 with two well-separated disks with radii around 10 times the Earth-Sun distance and with masses between 0.03 and 0.06 of a solar mass. That's enough to form a solar system, comets and all included, according to some researchers like Weidenschilling (Astrophysics and Space Science, Vol. 51, p. 153, 1977) and Hayashi (Progress in Theoretical Physics, Supplement Vol. 70, p. 35, 1981), who have made theoretical calculations on how much material was needed to form the solar system out of a primordial nebula.
The condition to form a planetary system in a binary is that the stars are not too close and that one of the stars is massive enough to keep the planets in elliptical orbits that are not too elongated. If the components of the binary are too close and have similar masses, whatever planets are formed in the primordial nebula will wander around the stars in chaotic orbits or will have very elongated orbits and could even be expelled from the binary. If one of the stars is far enough or have much less mass than the other, planets will form around the more massive star, called the primary star, and will have nearly circular orbits. This is important to prevent the planet from becoming too hot or too cold at different times of the year.
The question of the formation of life in a binary is therefore equal to the formation of life around a single star. First, neither of the two stars must be too hot or too cold, so that molecules that could form life are not fried or frozen on the planet surface. Second, it is necessary that the right molecules fall on the right planet. The planet must be in the habitable zone of the star, that is, neither too close nor too far from the primary star. Since all life on Earth requires liquid water, there must be enough water in the material that forms at least one planet. It is believed that enough water was delivered to planets like Earth or Mars by bodies with highly elongated orbits during the formation of the Solar System. Those bodies formed throughout the Solar System, but their orbits were perturbed by Jupiter and turned into highly elongated orbits that took them far and close to the Sun. Collisions of these objects were more likely near the Sun, where their orbits come close to one another. Eventually the water-rich material left over by the collisions formed Earth and other planets in the inner solar system. This is the story told by computer simulations done by geophysicists and astronomers like Morbidelli, Chambers, Lunine, Petiti, Vasechhi, and Cyr (Meteoritics and Planetary Sciences, Vol. 35, P. 1309, 2000) and Raymond (Astrobiology, Vol. 7, p. 66, 2007).
In conclusion a Jupiter-like planet must form around a star in order to deliver water to the inner part of the protoplanetary system and from there we hope that life somehow will follow. A recent computer simulation by Haghighipour and Raymond (The Astrophysical Journal, Vol. 666, p. 436, 2007) shows that the presence of another star in the system can increase the elongation of orbits in a planetary system by gravitational attraction and increase the water delivery mechanism to the habitable zone of the star.
As far as the effect of life on those planets, if we assume that the primary star is similar to our Sun, then the other star of the binary will probably be less massive and hence cold enough not to perturb life seriously. Distances in planetary systems are usually given in terms of the Earth-Sun distance, which is called an Astronomical Unit (AU). The two disks discovered by Rodriguez's team in L1551 IRS5, are separated by about 45 AU. That's larger than the distance from Pluto to the Sun. At that distance the Sun looks like a bright star and its heat would be barely felt on a planet. People on a planet in that binary would see a brilliant star in the sky day and night and probably many more comets than we do. In our solar system most brilliant comets we see come from the outer parts of the system, and their orbits can be perturbed by nearby stars. Such perturbations make their orbits around the Sun highly elongated, and make the comets visit our neighborhood with some frequency. It is the increased likelihood of a comet collision with a planet that could doom life on it. But that's another story. I have included here Figure 1 of Rodriguez's team that shows the images of the two disks of L1551 IRS5 obtained with a radio telescope (reprinted by permission from Macmillan Publishers Ltd. with license number 1781130737177 of Nature Publishing Group for use in www.madsci.org only, Nature, 395, 355, copyright 1998 ).
The possibility of having habitable planets orbiting around both stars is very small because their orbits would have to be too far from the system in order to be stable. Therefore we must limit ourselves to consider planets around one of the stars. There is no easy formula to find habitable zones around a binary, but most stars must be of solar type in order to have a habitable zone. The calculations that I mentioned before were done with sophisticated computer simulations that take into account a large number of effects like the amount of material in the disk of the primary star, the possibility of having a Jupiter-like planet, the separation of the stars and the eccentricity of the orbits of the component stars of the binary. They are really probabilistic calculations in which protoplanetary bodies that form randomly in the disk are followed in their orbits through millions of years by a computer simulation until they form a stable planetary system.
Computer simulations by Quintana, Adamas, Lissauer and Chambers (The Astrophysical Journal, Vol. 660, p. 807, 2007) show that planets can form within 2 AU from the primary when the minimum separation of two stars is 10 AU. That's not enough to form a Jupiter that will herd water-carrying bodies to the inner planets, but at least most planets in this case will have nearly circular orbits. Planets farther out will have too eccentric orbits or their orbits will be perturbed by the other star and will probably be expelled. Out of 200 extrasolar planets or so discovered so far 33 are known to orbit components of binaries or triple stars, but the separations of the stars are larger than 100 AU. At those distances, a solar type star will have no influence on the temperature of a planet closer to the primary. Three planets have been discovered in binaries with separations less than 20 AU. This does not mean that closer binaries have no planets, but discovering them with available techniques is difficult. By the way, a recent investigation by Eggenberger, Udry, Mazeh, Segal and Mayor (Astronomy and Astrophyics, Vol. 466, p. 1179, 2007) failed to confirm the existence of a Jupiter-like planet around HD 188753 A.
Vladimir Escalante Ramirez
Try the links in the MadSci Library for more information on Astronomy.