The next section of the star-system design sequence follows. Here, we determine whether the star system is a single or multiple star, and in the case of a multiple star we determine how many stellar components are present.

---

Step Two: Stellar Multiplicity

This step determines how many stars exist in the star system being generated.

Our own sun is a single star, traveling through the galaxy with no other stars as gravitationally bound companions. Many stars do have such companions. Double stars, gravitationally bound pairs, are very common. Multiple stars, groups of three or more stars traveling together, are much less common but do occur. Most multiple stars are trinary stars, sets of three. Sets of four or more are possible – in fact, star systems with up to seven stellar components are known – but they are quite rare.

Multiple stars are almost always found arranged in a hierarchy of pairs. That is, the stars in a system can usually be divided into pairs of closely bound partners. Each pair circles around its own center of mass, and the pairs themselves follow (usually much wider) orbital paths around the center of mass of the entire system. Any odd star is usually bound with one of the pairs. This kind of arrangement is very stable over long periods of time.

Very young multiple star systems can form trapezia, in which three or more stars follow chaotic, closely spaced paths around the system’s center of mass. This arrangement is highly unstable, and is unlikely to last very long after the stars’ original formation. Some members of a trapezium will normally be ejected, to travel as singletons. The remaining stars soon settle down into a more stable hierarchy-of-pairs arrangement.

Procedure

To begin, select whether the system being generated is a multiple star. To determine this at random, roll 3d6 and refer to the Multiplicity Threshold Table.

Multiplicity Threshold Table
Primary star’s mass (in solar masses) is . . .	Then the star is multiple on a 3d6 roll of . . .
Less than 0.08	14 or higher
At least 0.08, less than 0.70	13 or higher
At least 0.70, less than 1.00	12 or higher
At least 1.00, less than 1.30	11 or higher
At least 1.30	10 or higher

If the star system is multiple, roll d% on the Stellar Multiplicity Table. Star systems with five or more components are possible, but so rare that they should not be selected at random.

Stellar Multiplicity Table
Roll (d%)	Number of Stars
01-75	2
76-95	3
96-00	4

Selecting for an Earthlike world: Earthlike planets can appear in single or multiple star systems, although the arrangement of components in a multiple star system (determined in the next step) will affect the presence of such worlds.

Examples

Arcadia: Alice determines the multiplicity of the Arcadia star system. She knows that multiple stars might still have Earthlike worlds, but decides not to take any chances. She determines that Arcadia’s primary star will be a singleton, and does not roll on the Stellar Multiplicity Table.

Beta Nine: Bob continues to work at random while generating the Beta Nine system. He rolls 3d6 to determine whether the Beta Nine system is multiple, and gets a result of 15. Even with the primary’s star’s low mass of 0.18 solar masses, this suggests that the system will, in fact, be a multiple star system. Bob rolls d% and refers to the Stellar Multiplicity Table. His result of 46 indicates that the Beta Nine system will be a double star system.

Modeling Notes

There has been considerable recent work on the frequency of multiple star systems, leading to the (rather surprising) discovery that most stars, especially low-mass stars, are not multiple. Two of the most useful sources for this are:

Lada, C. (2006). Stellar Multiplicity and the Interstellar Mass Function: Most Stars are Single. The Astrophysical Journal Letters, volume 640, pp. 63-66.

Duchêne, G. and A. Kraus (2013). Stellar multiplicity. Annual Review of Astronomy and Astrophysics, volume 51, pp. 269-310.

Step Three: Arrange Stellar Components

This step determines how the components of a multiple star system are arranged into a hierarchy of pairs, and the initial mass of each companion star in the system. This step may be skipped if the star system is not multiple (i.e., the primary star is the only star in the system).

Astronomers normally tag the various stellar components in a multiple star system with capital letters in the Latin alphabet: A, B, C, and so on. So, for example, the famous trinary star Alpha Centauri has three components: the bright yellow-white star Alpha Centauri A, its relatively close orange companion Alpha Centauri B, and a distant red dwarf companion Alpha Centauri C (also called Proxima Centauri, since it is noticeably closer to Sol than the A-B pair).

Unfortunately, astronomers are not always consistent about which component is given which alphabetic tag. In this book, we will always tag the primary star, the most star with the highest initial mass in the system, as the A-component. The other components will be tagged in order of their distance from the primary star.

 

Procedure

The procedure for arranging stars in a system varies, depending on the multiplicity of the system.

Stars other than the primary in a multiple star system are sometimes called companion stars. These stars can have any mass, from tiny brown dwarfs up to stars almost as massive as the primary, although there is a clear tendency toward the latter.

Binary Star Systems

There is only one possible arrangement for the two stars of a binary system. There are two components, A and B, and the primary star or A-component is in a gravitationally bound pair with the B-component.

Select the mass for the companion star. To generate its mass at random, roll d% on the Companion Star Mass Table to determine a mass ratio for the companion.

Companion Star Mass Table
Roll (d%)	Mass Ratio
04 or less	0.05
05-08	0.10
09-12	0.15
13-16	0.20
17-20	0.25
21-24	0.30
25-28	0.35
31-32	0.40
35-36	0.45
37-40	0.50
41-45	0.55
46-50	0.60
51-55	0.65
56-60	0.70
61-65	0.75
66-71	0.80
72-78	0.85
79-87	0.90
88 or more	0.95

In each case, feel free to select a mass ratio that is just above the result of the table, increasing the ratio by less than 0.05. For example, if the result on the table indicates a mass ratio of 0.60, it would be appropriate to select an actual ratio greater than 0.60 but less than 0.65. The mass ratio cannot be lower than 0.05 or higher than 1.00.

In a binary star system, the companion star’s mass will be equal to the mass of the primary star, multiplied by the companion’s mass ratio. Round the companion’s mass off to the nearest hundredth of a solar mass unit. You may wish to round the companion’s mass off further, to match one of the entries in the Stellar Mass Table (see Step One). In no case will the mass of a companion star be less than 0.015 solar masses; round any such result up to that number.

Trinary Star Systems

There are two possible configurations for the three stars (components A, B, and C) of a trinary system.

One possibility is that the primary star (the A-component) has no close companion, but the B and C components move some distance away as a gravitationally bound pair of close companions (A and B-C).

The other is that the primary star and the B-component move as a bound pair of close companions, with the C-component moving alone at a greater distance (A-B and C).

Both arrangements appear to be about equally common. When designing a trinary star system, select either one. To select one at random, flip a coin.

In a trinary star system which is composed of a single A-component and a close B-C pair, the mass of the B component is computed using the Companion Star Mass Table, based on the mass of the primary star. The mass of the C-component is computed based on the mass of the B-component. When rolling on the Companion Star Mass Table, add 30 to the roll for the C component.

In a trinary star system which is composed of an A-B close pair and a C distant companion, the mass of each of the B and C components is computed using the Companion Star Mass Table, based on the mass of the primary star. When rolling on the table, add 30 to the roll for the B component.

Quaternary Star Systems

There are many possible arrangements for the four stars (components A, B, C, and D) of a quaternary system. However, by far the most common arrangement, and the most stable over long periods of time, is one in which two binary pairs (A-B and C-D) orbit one another at a wide separation.

In a quaternary star system, the mass of each of the B and C components is computed using the Companion Star Mass Table, based on the mass of the primary star. The mass of the D-component is computed based on the mass of the C-component. When rolling on the Companion Star Mass Table, add 30 to the roll for both the B component and the D component.

Examples

Arcadia: Alice skips this step for the Arcadia star system, since she already knows that the primary star is a singleton.

Beta Nine: Bob continues to work at random while generating the Beta Nine system. Since he has already established that the system is binary, he knows that there will be an A component (the primary star) and a B component (its companion). To determine the mass of the companion star, he rolls on the Companion Star Mass Table, and gets a result of 27 on the d%, for a mass ratio of 0.35. The mass of the companion star will be:

In this case, rounding the companion star’s mass off to the nearest hundredth of a solar mass unit means that it will exactly match one of the entries for brown dwarfs on the Stellar Mass Table. Bob decides to accept this result as is. The companion “star” in the Beta Nine system will be a brown dwarf.

Modeling Notes

Studies have found that the ratio of mass between the components of a binary star appears to be evenly distributed, although there seems to be a statistically significant peak for ratios of 0.95 or higher in the data.

Mass ratios seem to be somewhat dependent on the orbital period. In particular, binary pairs which orbit one another at a short distance seem more likely to be close matches in mass. For simplicity’s sake, the model set out in this book largely ignores this effect, although in trinary and higher-multiplicity star systems we do assume that the close pairs are more likely to be matched. The paper by Duchêne and Kraus (cited under Step Two) discusses these statistical phenomena in some detail.

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.

---

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.

One of my ongoing projects is a book, with the working title of Architect of Worlds. The goal of this book will be to provide science-fiction fans with the tools they need to design plausible worlds and planetary systems, using any preferred combination of random chance and deliberate selection.

From the draft Introduction for the book:

As a child in the late 1960s and early 1970s, I was fascinated by astronomy. I haunted the local library and read every book they had on the subject. I pestered my parents to plan trips to the planetarium, or to the local college when the astronomy department gave talks for the public. When I was twelve, my father purchased a high-powered telescope for me. That Celestron 8 machine saw a great deal of use over the next decade. Forty years later it is still in my possession, although (alas) I now live in a part of the country where city lights make star-gazing impractical.

I can’t be sure whether my life-long love for science fiction is a cause or an effect of that fascination with the universe around us. I grew up on stories by Asimov, Clarke, and Heinlein, and watched Star Trek re-runs at every opportunity. I was enthralled by stories of men and women going to the places I read about in my astronomy texts, discovering new worlds and meeting the strange people who lived there. I was particularly struck by authors who “showed their work” with respect to the physical environment. Authors like Poul Anderson, Hal Clement, or Larry Niven could make the settings of their stories both plausible and compelling.

At some point I discovered the world of conflict simulation games, sophisticated tabletop games that were designed to emulate various real-world political or military struggles. Most such games focused on historical conflicts, such as the American Civil War or the Second World War. A few, though, ventured into the realm of science fiction.

Almost by accident, my father brought home one such game for me, and it proved quite the revelation. This was the game Starforce, released by Simulations Publications, Incorporated in 1974.

Starforce was a simulation of human expansion into interstellar space, beginning in the twenty-fourth century. Redmond Simonsen, the game’s designer, meticulously worked out the technologies, the social and political conditions, and a complete “future history” for the game. In particular, he did careful research to build a map of space within about 20 light-years of Sol. His map included dozens of stars that could only be found in obscure astronomical catalogs, every one accurately placed.

Be it admitted, Star Trek has never worried very much about the real geography of the galaxy. Some of my favorite literary authors have done a much better job. But the fact that this game map existed – that we knew enough about our galactic neighborhood to make it possible – set my imagination alight. I spent years poring through what sources I could find, making lists of nearby stars, studying everything that was known about them, drawing maps and imagining what worlds might actually be out there.

One tool that came to my hand was another game. My father (again) came across the classic roleplaying game Traveller, and brought home a copy of the core rules for me. That game, published in 1977 by Game Designers’ Workshop, was the first to include a semi-random process for the design of star maps and worlds as settings for play. The world-building rules in the core game were very simplistic, but in the Scouts supplement (1983) a more sophisticated version appeared. This version took into account the properties of a world’s primary star, which made it possible for me to apply the system to the real stars I had been studying.

One result was the first original space-opera universe I ever designed – one which is never likely to be published, since it’s a little too obviously the result of an immature imagination. Another was a growing awareness that the Traveller rules were incomplete. To be sure, the designers produced a remarkable achievement, versions of which are still in use among Traveller players to this day. Still, they had oversimplified some details for ease of use, and the system included a few outright errors.

I set out to learn how to do better. In a sense, I’ve spent most of my adult life in that quest: a study of the universe around us, for the purpose of educating my creative imagination.

Years later, I spent about a decade writing and doing editorial work for the game publisher Steve Jackson Games. Ironically, this was at a time when they held a license to publish materials for the Traveller game and its fictional universe. That gave me the opportunity to design and publish three world-building systems of my own, which appeared in the books GURPS Traveller: First In (1999), GURPS Traveller: Interstellar Wars (2006), and GURPS Space, Fourth Edition (2006).

The last of these was the most comprehensive. It was published after the first discovery of exoplanets, worlds actually known to be circling other stars. It made an honest attempt to take into account some of the things we had already learned about the structure of planetary systems other than our own. Even so, in the years since its publication it has become dated with startling speed. In particular, the launch of the Kepler observatory in 2009 led to the discovery of hundreds of new exoplanets in just a few years. It’s become clear that the model of planetary formation I’ve used in the past was naïve at best, hopelessly wrong at worst.

Fortunately, as of this writing, the astronomical community seems to be converging on a new model, similar to the old but considerably refined. This model accounts for the great variety of exoplanets we’ve discovered, while still explaining most of the known features of our home planetary system. There is still a great deal of work to be done, and we’re likely to be surprised by what we learn in the years to come. Still, it seems possible to build a new set of world-building guidelines for the creative imagination, one which once again takes into account all that we’ve learned about the universe.

This book is intended as a resource for authors, game designers, game referees, readers, and fans of science fiction. It presents an overview of scientific concepts that might be applied to high-level design of a space-based fictional setting: the placement of stars, the arrangement of planetary systems, and the properties of individual worlds. It also presents a set of procedures for such design, allowing the reader to generate regions of space suitable for science fiction stories or games. The results should at least be plausible, given our present understanding of the universe.

More personally, this book is a collection of all the research I’ve done over the past forty years, ever since I was first inspired by those games I enjoyed as a teenager. Over the decades I’ve picked up many world-building tricks to apply in my own game writing and literary work, which I hope will be of use to others.

I’ve actually written two complete sections of Architect of Worlds, laying out how to design stars and their planetary systems. At the moment, I’m reviewing those sections and applying minor tweaks, and also ensuring that I’ve included citations to my research sources where that’s practical. I’m still working on research and development for the third major section, in which one can work out the physical details of a given world and determine what kind of environments it might support. I’m tentatively planning other sections, but those will come later.

Eventually this project is going to be compiled and sold as an e-book. One thing I plan to do with this blog is to publish an interim draft of the guidelines and systems in the book, so my readers can provide me with feedback. Entries in that series of blog entries will be posted with the architect of worlds and worldbuilding tags. Meanwhile, the book is going to be somewhat reminiscent of my work for the GURPS roleplaying game, even though it isn’t being written specifically for that game and I don’t have any reason to believe that Steve Jackson Games would be interested in publishing it. Still, I imagine GURPS fans may take a specific interest, so I’ll be posting those entries with a gurps tag as well.

Once I’ve finished posting a section of the draft here, I’ll also post a PDF of the complete section to the Sharrukin’s Archive static site. Those will eventually come down, as the book approaches readiness for publication, but that won’t be for a while.