Here’s the next section, a little more math-intensive, but the models are still fairly simple and straightforward. In these steps of the design sequence, the user will generate the age of the star system under development, as well as its metallicity. This last is a measure of the prevalence of heavy elements in the star system’s formation, where “heavy elements” is defined the way astronomers do, as “anything past helium on the periodic table.”

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Step Four: Star System Age

This step determines the age of the star system being generated. All the stars in the star system will be the same age, as measured from the moment that the primary star began to fuse hydrogen in its core.

The universe is currently estimated to be 13.8 billion years old. A few stars in our Milky Way Galaxy have been determined to be about the same age, and must have formed very soon after the beginning of the universe. The Galaxy itself is not much younger than that, growing through the accretion of gas and the assimilation of smaller galaxies across billions of years.

The oldest globular clusters appear to have formed about 12.6 billion years ago, and the galactic halo must date to about the same time. Since old halo stars often have orbital paths that carry them through the galactic plane, a few of them are always likely to be found in any given neighborhood of the galactic disk. The disk itself, and the first spiral arms, appear to have formed about 8.8 billion years ago. Most stars in any given neighborhood of the disk will be younger than that.

Procedure

Select an age for the star system being generated, no greater than 13.5 billion years.

To determine an age at random, begin by rolling d% on the Stellar Age Table. Take the unmodified d% roll when generating a region of space like that of our own neighborhood (close to the plane of the Galaxy and within one of the spiral arms, but not in an active star-formation region or inside an open cluster).

Stellar Age Table
Roll (d%)	Population	Base Age	Age Range
01-05	Extreme Population I	0.0	0.5
06-31	Young Population I	0.5	2.5
32-82	Intermediate Population I	3.0	5.0
83-97	Disk Population	8.0	1.5
98-99	Intermediate Population II	9.5	2.5
00 or more	Extreme Population II	12.0	1.5

 

Population I stars are relatively young stars which make up most of the galactic disk and the spiral arms. Population II stars are old, metal-poor stars that are normally found in the galactic bulge, the galactic halo, and the globular clusters.

To determine the star system’s exact age, roll d% again, treat the result as a number between 0 and 1, multiply that number by the Age Range, and add the result to the Base Age. The result will be the age in billions of years. You may wish to round the age to two significant figures.

Selecting for an Earthlike world: Instead of determining the age completely at random, assume the star system is in the Intermediate Population I. Stars in this range of ages are most likely to be metal-rich enough to have life-bearing planets, but are also old enough for complex life to have developed there.

Examples

Arcadia: Alice wishes to determine the age of the Arcadia star system. Since she wishes the system to have at least one Earthlike world, she does not roll on the Stellar Age Table, but assumes that the star system will be Intermediate Population I. She takes a Base Age of 2.5 billion years, an Age Range of 5.0 billion years, and rolls d% for a result of 62. The age of the Arcadia system is:

Alice accepts this value for the age of the Arcadia system. The Arcadia system is apparently about a billion years older than Sol.

Beta Nine: Bob continues to work completely at random while generating the Beta Nine system. He rolls on the Stellar Age Table, getting a result of 20 on the d% roll. The Beta Nine system is in the Young Population I. He rolls another d% for a result of 82. The age of the Beta Nine system is:

Bob rounds this off to two significant figures. The Beta Nine system is 2.1 billion years old, a relatively young star system, possibly not old enough to have developed complex life.

Modeling Notes

Most surveys of the solar neighborhood suggest that there are only a few Population II stars in our vicinity. For the model in this book, we assume that this proportion is about 3% of all stars in any given region of the galactic disk. As for the younger stellar populations, astronomers tend to assume that the star-formation rate in the Galaxy has been constant for the past 8-9 billion years, which suggests a “flat” distribution of stellar ages.

Step Five: Star System Metallicity

This step determines the metallicity of the star system being generated.

Most of the matter in the universe is composed of hydrogen and helium, both of which were created in the “Big Bang” at the beginning of time. Heavier chemical elements were almost entirely created by the processes of nuclear fusion in the heart of stars. As it happens, terrestrial planets like Earth, and living beings like us, are largely made up of these heavier elements.

Early in the universe’s history, the supply of such elements was very limited, so very old stars are unlikely to have terrestrial planets capable of supporting life. However, as billions of years passed, stars “baked” the heavier elements and then scattered them back into the interstellar medium. Stars like the Sun formed in interstellar clouds of gas and dust that had been already been enriched in these heavier elements. The presence and relative abundance of these elements is what is measured by metallicity.

We will simplify by assuming that all stars in a star system have the same metallicity. This is not always observed to be the case in multiple star systems, although it is rare for members of the same multiple system to have very different metallicities.

Very old stars can have metallicity as low as zero, composed almost entirely of hydrogen and helium with only tiny traces of heavier elements. A few young stars have been located with metallicity is high as 2.5 or 3.0, with several times as great an abundance of heavy elements as the Sun. The Sun itself seems to be rather metal-rich when compared to other stars of a similar age. In general, metallicity seems to be only weakly correlated with a star’s age – even old stars can turn out to be metal-rich.

Procedure

Select a value for the star system’s metallicity. To determine metallicity at random, apply the following formula, using a roll of 3d6:

Here, M is the metallicity value, and A is the age of the star system in billions of years. Modify the result with the following two cases.

• If the star system is a member of Population II (and is therefore at least 9.5 billion years old), subtract 0.2 from the metallicity, with a minimum metallicity of 0.
• To account for the occasional unusually metal-rich star, roll 1d6. On a 1, roll 3d6 again, multiply the result by 0.1, and add it to the metallicity value, to a maximum metallicity of 3.0. This step can be applied even to very old stars.

You may wish to round metallicity to two significant figures.

Selecting for an Earthlike world: A star likely to have terrestrial planets like Earth should have a metallicity of at least 0.3. If the star’s age was selected with an Earthlike world in mind in Step Four, it is very likely to have sufficient metallicity.

Examples

Arcadia: Alice wishes to determine the metallicity of the Arcadia star system. Since she has already selected the star system’s age to try to yield at least one Earthlike world, she decides to select the metallicity value at random and see what she gets. She rolls 3d6 for a result of 8, and computes:

Rolling 1d6, she gets a value of 3, and leaves the metallicity value where it is. The Arcadia star system is rather metal-poor in comparison to our own, but it should have enough heavy elements to form terrestrial planets.

Beta Nine: Bob continues to work completely at random while generating the Beta Nine system. He rolls 3d6 for a result of 13, and computes:

Bob rounds this result off to 1.4. He then rolls 1d6 and gets a 1, indicating that the Beta Nine system formed in an unusually metal-rich region of space. He rolls 3d6 for a result of 11, and adds 1.1 to the result, for a total metallicity of 2.5. He decides that the Beta Nine system might be a good location for a mining or industrial colony.

Modeling Notes

For this book, we assume that the average metallicity of newly formed stars has been rising at a constant rate since the formation of the Galaxy. Most studies have shown that metallicity can vary widely even for stars of similar age, indicating that the distribution of heavy elements in the Galaxy is often very uneven. Data from the following paper was used to produce a rough estimate for the age-metallicity relation for stars in the solar neighborhood:

Edvardsson, B. et al. (1993). The Chemical Evolution of the Galactic Disk – Part One – Analysis and Results. Astronomy and Astrophysics, volume 275, pp. 101-152.