Types of Star Systems
- Single-star systems
- Binary star systems, which have two sub-types; and,
- Multiple-star systems, which have a wide variety of possible configurations.
Let's look at them in more detail:
1. Single-star systems are like our own Solar System, with one star comprising the dominant mass component;
2. Binary-star systems comprise two stars in gravitational interaction. There are two main varieties* of binary systems: close- and wide-binary systems.
These may be:
2a. Observationally identified, gravitationally bound pairs;
2b. Visual doubles, which are stars that have not been observationally identified to be gravitational binaries, but have been deduced to be binaries, through:
2b1. Spectroscopic analysis;
2b2. Changes in brightness due to syzygial activity; or,
2b3. Anomalies in proper motion—these last are usually of the close-binary variety.
2c. In close-binary star systems, the two stars orbit quite close to one another (astronomically speaking), together comprising the primary mass component of the system, and all other bodies in the system orbit them as a unit, in what are called P-type orbits (more on this later);
Thus, wide-binary star systems can be thought of as two stellar planetary systems that are in orbit about one another. Planetary orbits, etc., for each member of a wide-binary system are calculated exactly as for single-star systems, with a few critical exceptions (outlined later). When such gravitationally bound binary pairs are resolvable as separate units in the field of a telescope, these are called visual binaries.
3. Multiple-star systems have three or more stars in gravitational interaction. Some possible configurations include:
3a. A half-dozen or more newly ignited stars milling about amongst one another; stars in this configuration most probably follow Lissajous or halo orbits in a highly complex pattern.
3b. A close-binary pair with a single-wide binary companion, such as the Alpha Centauri system;
3c. A close-binary pair with a second close-binary pair in wide-binary relationship to them;
3d. A very massive single star with two much smaller mass companions in a close-binary configuration in a wide-binary relationship with it....
Fundamental Orbital Limits
Innermost Stable Orbit
The first of these orbital distances is the Innermost Stable Orbit. This is the closest a body can orbit the star in a stable orbit, and there are two ways of determining this orbit, dependent upon the mass and/or luminosity of the star.
Why the jog in the IS(L) graph line? Recall from this blog that the formula for calculating the luminosity of a star based on its mass is one function for stars <0.43 solar masses and another function for stars from 0.43 ≤ M < 2.0 solar masses.
Between the smallest possible stellar mass (0.08 Solar masses) and 1.0 Solar mass, the largest difference produced by the two methods is a hundred times greater, but still a modest 0.025 AU (3.74 million kilometers, or about 9.73 times the distance between Earth and Moon).
Of course, at 1.0 Solar mass (and, therefore, 1.0 Solar luminosity), both equations produce the same result. Beyond that point, the luminosity-based method produces consistently larger values, and the gap between the results becomes ever greater.
At the maximum Sun-like stellar mass (1.4 Solar masses), the difference in calculated orbits is ~0.056 AU (8.38 million kilometers, or 21.79 times the Earth-Moon distance.
The nucleal distance is calculated to assume the most absolutely Earth-like conditions; that is, the orbit at which the star would have the same apparent brightness as the Sun does when seen from Earth.
Note, the nucleal distance is not the average or median orbit between the inner and outer limits; even Earth is located within the first 10% of the conservative calculation of the Sun’s habitable zone.
The following equations allow the determination of the inner, nucleal, and outer habitable zone distances based on the luminosity of the star.
The nucleal habitable orbit is straightforward to calculate:
AB = the apparent brightness of the star (expressed in solar units);
L = the luminosity of the star (expressed in solar units);
D = the semi-major axis of the orbit (expressed in astronomical units)
Deriving this equation to solve for D:
Below are the equations for determining these orbital limits:
The Optimistic Habitable Zone covers 1.02 AU; its outer limit is 2.36 times farther from the star than its inner limit.
The Conservative Habitable Zone covers 0.42 AU; its outer limit is 1.442 times farther from the star than its inner limit.
The Conservative Habitable Zone is about 41.2% of the wider Optimistic Habitable Zone.
Below is an illustration of the theory of habitable zones, using figures for the Sun:
Note that the span of the conservative habitable zone is always 41.18% of the span of the optimistic habitable zone, regardless of the luminosity of the star: ((1.77 - 0.75) ÷ (1.37 - 0.95)) ⨉ 100 = 41.18%
Note that the nucleal distance (1.0 AU for the Sun), is not at the midpoint of the range, but is closer to 33% of the total span of the habitable zone for the optimistic range and about 13.5% for the conservative range.
The Frost Line (or Ice Line)
The Frost Line distance is calculated by:
The zone closer to the star than the innermost habitable limit is what I call the calorozone, from the Latin word for “hot” (whence comes our word "calorie"). The region between the habitable zone outer limit (conservative or optimistic) and the Frost Line I call the friozone, from the Latin for “chilly”. And orbits beyond the Frost Line lie in what I've termed the cryozone, obviously named for the Latin word for "cold" or "frozen"*.
Below is a graphical representation of these thermal zones: