Freelance Traveller

BY Draconis-type Variable Stars

by Ken Pick

This article originally appeared in the March/April 2018 issue.

Some stars are “variable stars” whose brightness varies on a regular or irregular cycle. Mark McCabe’s article “Variable Stars and Dwarves: An Overview for Non-Astronomers” (Freelance Traveller #67, July 2015) listed and explored the various types of variable stars for Traveller use – regularly-pulsing Cepheids, irregular Mira-type dying stars casting off their outer layers, and “flare stars” intermittently wracked by mega-flares like miniature nova eruptions.

That article omits one type of variable – a type most likely to host habitable (or at least settleable) worlds: BY Draconis-type variables.

The BY Draconis Type Variable Star

BY Draconis-type variable stars are main-sequence orange/red dwarves (spectral class K or M, luminosity class V) afflicted with mega-starspots. The starspots are distributed irregularly, the star’s rotation bringing them in or out of view; the more (or larger) sunspots visible, the dimmer the star. Otherwise, they are normal main-sequence stars, the K-class orange dwarves having the best chance to host habitable or superhabitable life-bearing worlds, even more so than G-class yellow dwarves like Sol.

Sunspots

Sunspots are caused by interactions in a star’s magnetic field. A star’s rotation tends to “kink” its magnetic field, causing localized magnetic buildup and “reconnection” of the lines of force through pairs of sunspots. This is the same mechanism that causes solar flares; a flare is just a major explosive reconnection ejecting thermal and radioactive energy and (in the big ones) coronal matter.

These stellar dynamo effects are a “spectrum disorder”; on one end of the spectrum are “normal” stars like Sol (which varies about 4% on a 22-year sunspot cycle); at the other extreme are flare stars whose solar flares approach miniature nova explosions on an irregular cycle. BY Draconis-type variables are midway between these extremes, with heavy sunspot activity and frequent flares, but not the massive explosions of flare stars.

This is probably a continuous spectrum with much overlap; “normal” stars shade into BY Draconis-types which shade into flare stars. Age and size are a factor; younger stars tend to rotate faster which probably leads to stronger and “kinkier” magnetic fields. The younger/faster-spinning and less massive the star (like K-class orange dwarves and M-class red dwarves), the more it goes up the spectrum into BY Draconis-type/flare star territory. BY Draconis-type variables are almost all “cooler” K/V or M/V orange/red dwarves and flare stars almost entirely M/Ve red dwarves with unusual emission lines in their spectra.

Effects

BY Draconis-type stars have so much sunspot activity their sheer number/size cuts into the star’s brightness. These could be extremely large sunspots, clusters of a lot of smaller sunspots, or a combination of both.

Since sunspots are cooler and dimmer than the rest of the star’s photosphere, the star effectively dims as the spots cover more and more of its surface. Since sunspots are irregularly-distributed across the surface, a BY Draconis-type star is “rotationally-variable” as its rotation brings the spots in and out of visibility. And since sunspots are always changing – appearing, disappearing, growing, shrinking, moving around – the amount of dimming is randomly different when that side of the star once more rotates into view, making a BY Draconis-type an “irregular rotational-variable”, i.e., a semi-regular variable with a regular period component determined by rotation.

This variability has the effect of short-term climate and seasonal changes, stacking with other seasonal effects caused by the usual suspects: axial tilt and orbital eccentricity. The difference is the seasonal effects caused by solar variability are much shorter-term and more irregular than the predictable effects of axial tilt and orbital eccentricity.

Note that a BY Draconis-type star, on average, is slightly dimmer than a “normal” star of the same spectral and luminosity type.

Adaptation to Traveller

To adapt a BY Draconis-type star to a Traveller system, some initial questions must be answered:

What is the rotational period of the star?

From Kepler observational data, K-class orange dwarves have rotational periods between 3 and 30 days; M-class red dwarves between 10 and 30.

Roll 2D and multiply by 3 for the rotational period; note that the 3x multiplier results in periods in even 3-day increments; this simplifies things later on.

Depending on the age of the star and whether it has large planets (gas giants) to brake its rotation, a DM of -1 to +3 could be applied to the 2D roll before 3x multiplication. The younger the star and less massive its planetary system, the faster it rotates and the smaller the DM.

What is the range of sunspot activity (minimum to maximum)?

This is an arbitrary decision, setting the maximum and minimum levels of sunspot intensity on a scale of 1-6. What are the seasonal equivalents of Intensity 1 (clear sun) and Intensity 6 (dark sun). How crazy do you want to go?

There are six levels of sunspot intensity; the more/larger sunspots, the dimmer the sun:
 

(NOTE: This example is a large range; a “normal” star’s Intensity 6 would only be Intensity 2 on this scale; 1-6 represents the entire spread for the star regardless of severity.)

To generate the sunspot intensity and its changes, divide the sun into three longitudinal sections and roll 1D for sunspot intensity for each. Each of these sections has a duration of 1/3 the sun’s rotational period (which is the reason for the 3x multiplier for rotational period above; each section will be 2D± any DMs long). Whenever a new section rotates into view, the sunspot intensity changes; go to the next section’s intensity number, roll 1D for any change in that number on the table below, and apply that seasonal variation until the next section rotates into view.
 

Alternately, a roll of 6 when already at “dark sun” maximum could indicate a major solar flare. This is most likely when:

• The star is young and fast-spinning (short rotation period).
• The star has a wide range of maximum-to-minimum brightness.
• The star has a large planet in a Close orbit causing tidal stress.

The more of these conditions, the more likely the star is to flare when going to Intensity 6/dark sun maximum. These are not the pseudo-nova megaflares of a true flare star, but are powerful enough to cause EMP effects on-world and radiation hazard effects off-world.

Even without triggering flares, light and dark sun causes random chaotic seasonal effects, from clear-sun summer to dark-sun winter. These effects usually take a couple days to surface, and grow in severity until the next section (with different intensity) rotates into view.

The longer the rotational period, the more time the effects have to grow in severity; if the star has a rotational period of less than a week (less than two days between change of intensity), the seasonal effects do not have time to set in and the brightness changes (except for the occasional major solar flare) will be mostly cosmetic.

If the rotational period is slow enough and the “bright sun” and “dark sun” are extreme, the result is chaotic seasons, from summer-winter whipsaw over a period of one to two weeks to (if all three segments are similar intensity) single seasons that could last from months to years.

NOTE: This effect stacks with seasonal effects from other causes (orbital eccentricity and/or axial tilt). Combined with other seasonal cycles, the change in solar intensity could stack for randomly-mild to extreme winters or summers, or cause random variations in the beginning or ending of seasons.

Examples

BY Draconis System

Exemplar of the type, BY Draconis itself is a young trinary system some 16 parsecs distant from Sol; on the Traveller master map, its position roughly corresponds to Ayling or Baytapik along the Imperium-Solomani border in Denebola Subsector, Alpha Crucis Sector.

The system consists of two orange dwarves, BY Drac A (K5V) and B (K7V) with a separation of .05 AU (Close) and an orbital period of only six days. BY Draconis A is the BY Draconis-type variable, with a rotation period of only three days. (Other sources list BY Drac A as a K6V orange dwarf and B as an M0V red dwarf flare star; if so, B’s flaring is probably caused by a more extreme BY Drac effect.)

The third component, BY Drac C (M5V) is a nondescript red dwarf in Orbit 11bis around AB. Though gravitationally-bound to AB as a trinary, at that distance it’s more like a separate red dwarf system flying in formation.

There are no known planets, at least none that have been detected from TL9bis Earth. Any stable orbits around AB would be a minimum of Orbit 1 or 2 and a maximum of Orbit 6 or 7. C has no such minimum-orbit restrictions, but there are probably no gas giants insystem and any planets are probably newly-formed primeval rockballs.

Kapteyn’s Star (VZ Pictoris) System

Kapteyn’s Star (VZ Pictoris) is another BY Draconis-type variable only four parsecs from Sol; on the Traveller master map, its position corresponds to either Ililke or Markhashi in Dingir Subsector, Solomani Rim Sector.

The system consists of an M1V red dwarf about twice Sol’s age with two known planets:

Kapteyn b

5 T-mass @ 0.16 AU, period (year) 48 days. Travellerizes as…

Kapteyn I, a Size C (12) super-Venus in Orbit 0 (hab zone), tidally-locked with no moons. Though nominally in the hab zone, its size and dense atmo traps heat in a runaway greenhouse effect resulting in a Cytherean world.

Kapteyn c

7 T-mass @ 0.3 AU, period (year) 122 days. Travellerizes as…

Kapteyn II, a Gas Dwarf (7 T-mass) in Orbit 0bis or 1 (outer zone) with a few small moons (none above size 1 or 2). Any insystem activity/settlement will be on these airless moons. Because of its tidally-braked rotation, the planet’s cloud decks are arranged in “swirls” instead of the bands of a true gas giant. The gas dwarf’s atmosphere can be skimmed, but the resulting raw fuel is Contaminated (one step below Unrefined); normal fuel refining results in Unrefined fuel.

Kapteyn’s Star also has a real-life Traveller tie-in: The system is the setting of the 2012 SF novel Singularity, by William H Keith Jr (under the pen name of Ian Douglas).

Variant: RS Canis Venaticorum-type Variable

An RS Canis Venaticorum (RS CVn)-type variable is a close binary system (Traveller orbit Close) of two BY Draconis-type variables whose rotation has “synced up” in a tidal lock.

Note: BY Draconis itself is not an RS CVn-type variable; despite their six-day Close orbit, BY Drac A & B are too young to have tidal locked. BY Drac A has a definite rotation period between 3 and 4 days.

As such close binaries are tidal-locked, their rotation period is the same as their orbital period (usually 14 days or less). RS CVn components are also slightly larger and brighter than true BY Dracs; the brighter/hotter A component of the pair is usually an F or G-class yellow dwarf star and the dimmer B component a G or K yellow-to-orange dwarf.

BY Draconis-type sunspot variability in an RS CVn is probably proportional to tidal stress and inversely proportional to size, the smaller B component having more sunspots/variability. For Traveller purposes, this proportion could be approximated by the inverse of the relative component masses; if A is twice as massive as B, B would have twice the BY Drac sunspot activity and brightness spread as A.

As RS CVn stars are slightly larger and brighter than true BY Draconis-types and orbit each other in Close orbits, stable planetary orbits are possible starting around Orbit 2. As these Close orbits are short-period binaries, the BY Draconis-type rotational variability cycles too fast to have significant climate/weather changes on any planets; the main effect would be appearance (slight brightening/dimming of sunlight) and mild heat waves/cold snaps lasting a day or two. The closest of close binaries (period less than a few days) would not even have the latter effect, as the luminosity would vary too quickly.

Adaptation to Traveller

Since an RS CVn is two tidal-locked BY Draconis-types, just roll starspot intensity for both stars, sync up the rotations with the orbital period, and roll/apply the changes simultaneously to both stars. The combined sunspot intensity will be the average of the two; since sunspot changes are random, it’s possible to have a change on one offset or negate the change on the other.

Orbital and rotational periods are the same; roll 1Dx3 instead of 2Dx3 with no other DMs.

In such close binaries, the stellar hemispheres facing each other are usually brighter; sunspots will tend to be on the “dark” hemispheres; this damps out the more extreme effects, as the visible hemispheres will be “dark sun” for the nearer and “clear sun” for the farther as they orbit each other. (When rolling the initial sunspot intensity, start out with the lowest intensity on one and highest on the other.) The short orbital period also damps out the effects.