Here’s the first section of the world-design system laid out in the Architect of Worlds project.

As a preview: the design sequence begins by walking the user through the parameters of a star system, one or more stars in a gravitationally-bound group that move together through the Galaxy. We begin by determining the mass of the primary star, which we define here as either the only star in the group, or the one that begins its life with the greatest mass. In later steps we will determine whether there are any additional stars in the system, the mass of any companion stars, the age and metallicity of the overall system, the current status of each star, and finally the orbital parameters of the system.

In later sections of the design sequence, the user will be able to place planetary systems around a given star, and design the physical parameters of individual worlds.

Readers may be a little confused as to why we’re beginning by generating the primary star’s mass. Most design sequences like this one (including at least one previous version of Architect of Worlds) start by determining how many stars are in a given system, and then move on to generate the details of each one. It turns out that a star system’s multiplicity is strongly dependent on the primary star’s mass; more massive stars are significantly more likely to appear in pairs or larger groups. That dependence is complex enough to require we take things in this order if we want plausible results.

One more thing I’d like to point out (the final book will be explicit about this): what we’re generating here is the initial mass of a given star. It’s entirely possible that the object will end up with different mass than what we have here, specifically if we find that it has aged past its red-giant phase and is now a stellar remnant. That detail will be addressed in a later step of the sequence.

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Step One: Primary Star Mass

This step determines the initial mass of the primary star in the star system being generated. We will measure the mass of stars in solar masses.

The lowest-mass objects to be generated here are brown dwarfs, substellar objects massive enough to have planetary systems of their own, but not massive enough to sustain hydrogen fusion. Brown dwarfs are not stars, but they are sometimes referred to as such, and for the purposes of setting design they can be treated that way. Brown dwarfs have masses between about 4,000 and 25,000 times that of Earth, or between about 0.15 and 0.08 solar masses.

At 0.08 solar masses and above, objects can sustain hydrogen fusion and are considered stars. Most stars, by far, form with between 0.08 and 2.0 solar masses.

Stars can be extremely massive, up to a theoretical maximum mass of about 150 solar masses, but such gigantic stars are quite rare. Very massive stars also tend to burn through their hydrogen fuel and die very quickly, which means that they rarely get the chance to move far from the open clusters or OB associations where they were formed. Most local neighborhoods of the galaxy will have no such massive stars.

Procedure

Select a mass for the primary star of the star system being generated. To determine a mass at random, begin by rolling d% on the Primary Star Category Table.

Primary Star Category Table
Roll (d%)	Category
01-03	Brown Dwarf
04-82	Low-Mass Star
83-95	Intermediate-Mass Star
96-00	High-Mass Star

Depending on the category the primary star falls into, roll d% on the pertinent columns of the Stellar Mass Table on the next page. The result will be in solar mass units.

Feel free to select a mass for the star that is somewhere between two specific entries on the table. For example, if the result on the table indicates an intermediate-mass star of 0.92 solar masses, it would be appropriate to select an actual value greater than 0.92 but less than 0.94 solar masses. Such a selection will require you to do interpolation of several table entries in later steps.

Selecting for an Earthlike world: Instead of determining the primary star’s mass completely at random, assume it is an intermediate-mass star, and go directly to those columns on the table to determine its mass. Stars in this range are bright enough that they can have Earthlike worlds at a distance sufficient to avoid tide-locking, but are also long-lived enough that complex life is likely to have time to evolve.

Stellar Mass Table
Brown Dwarfs		Low-Mass Stars		Intermediate-Mass Stars		High-Mass Stars
Roll (d%)	Mass	Roll (d%)	Mass	Roll (d%)	Mass	Roll (d%)	Mass
01-10	0.015	01-13	0.08	01-07	0.70	01-06	1.28
11-29	0.02	14-23	0.10	08-13	0.72	07-12	1.31
30-45	0.03	24-34	0.12	14-19	0.74	13-18	1.34
46-60	0.04	35-43	0.15	20-24	0.76	19-23	1.37
61-74	0.05	44-52	0.18	25-29	0.78	24-30	1.40
75-87	0.06	53-59	0.22	30-34	0.80	31-36	1.44
88-00	0.07	60-65	0.26	35-39	0.82	37-43	1.48
		66-70	0.30	40-43	0.84	44-50	1.53
		71-74	0.34	44-47	0.86	51-58	1.58
		75-77	0.38	48-51	0.88	59-65	1.64
		78-80	0.42	52-55	0.90	66-71	1.70
		81-83	0.46	56-59	0.92	72-77	1.76
		84-86	0.50	60-62	0.94	78-84	1.82
		87-89	0.53	63-65	0.96	85-93	1.90
		90-92	0.56	66-68	0.98	94-00	2.00
		93-95	0.59	69-71	1.00
		96-97	0.62	72-74	1.02
		98-99	0.65	75-78	1.04
		00	0.68	79-82	1.07
				83-85	1.10
				85-89	1.13
				90-92	1.16
				93-95	1.19
				96-97	1.22
				98-00	1.25

Examples

Alice is aiming for a star system in which an Earthlike planet will appear, so she ignores the Primary Star Category Table and assumes the primary star will of intermediate mass. She rolls d% for a result of 36 and consults the appropriate columns on the Stellar Mass Table. The primary star’s mass is 0.82 solar masses.

Bob has no preconceived ideas about the nature of the Beta Nine system, and indeed he is designing a setting in which even small red dwarf or brown dwarf stars might be significant. He therefore rolls on the Primary Star Category Table and gets a result of 10 on the d%. The Beta Nine primary is a low-mass star. He rolls on the Stellar Mass Table, consulting the columns for low-mass stars, and gets a result of 48 on the d%. The primary star’s mass is 0.18 solar masses.

Modeling Notes

Astronomers have developed several different empirical rules for the distribution of stellar mass, each of which follows one or more power laws. In other words, the frequency of stars of a given mass seems to be proportional to that mass raised to a given power. The specific distribution we observe is called the initial mass function, and it appears to be consistent no matter where in the Galaxy we take a census of stars.

The Primary Star Category Table and Stellar Mass Table here are derived from an estimate for the initial mass function developed by the astronomer Pavel Kroupa. Citation:

Kroupa, P. (2001). On the variation of the initial mass function. Monthly Notices of the Royal Astronomical Society, volume 322, pp. 231–246.