If we assume a solar neighborhood like distribution of stars, an interstellar empire spanning
a somewhat modest, 250,000 ly^3 will contain about 1000 stars.
Which is a number large enough to be awe inspiring but small enough to be dealt with in a single
video tutorial – albeit a rather lengthy one.
Strap yourself in! Today we're gonna learn how to build 1000 stars!
So, on average, 1000 Milky Way stars contain: 900 main sequence stars, 96 white dwarfs and
4 giant stars. Which is very cool!
Cooler still, is that the main sequence is comprised of many different types of stars:
O,B,A,F,G,K and M stars statistically broken down like so. This is known as the MK classification
system which orders stars by spectral type – high mass to low mass.
Remembered by the mnemonic: Oh, be a fine Gungan; kiss me.
Now, if we apply these percentages to our 900 main sequence stars - and round to one
sig fig – the stellar ingredients of our little demo empire will be:
1 O star 1 B star
5 A stars 30 F stars
70 G stars 100 K stars
700 M stars 100 White dwarfs
and 4 Giant stars.
And although not represented in our little sample size, I'll chuck in a neutron star
and a black hole - just for good measure!
Let's build!
MAIN SEQUENCE:
Main sequence stars are sun-like stars, happily undergoing hydrogen burning in their cores.
They are inherently very stable so we'll be able to say a lots about them.
MASS:
First step when building any star is to set the mass. This is crucial! Main sequence stars
have masses between 0.08 and 50 solar masses - consider these hard limits. Within these
limits we have smaller mass ranges based on stellar type – consider these softer limits.
Decide what class of star you're gonna build and choose an appropriate mass.
Now, only stars between about 0.5 and 1.4 solar masses are considered “habitable”
– that is, habitable in the sense that carbon based, humanoid lifeforms could naturally
evolve on planets orbiting these stars.
Everything else isn't “uninhabitable” per say – their planets could be locations
for colonies, mining expeditions, and/or exile locations for little green lads with terrible
syntax.
RADIUS:
If you've chosen a mass less than our sun, your stars radius will be given by: R = M^0.8
If you star is more massive than our sun, use
the formula: R = M^0.5
With the mass and radius defined you can go ahead and calculate the circumference, surface
area, volume and density of your star.
Pro tip: Worldbuilders HATE constants: π...uck! Get rid of 'em. Worldbuilders deal in proportionality
- it's much easier. A star twice as large of our sun will have
twice the circumference, 4 times the surface area and 8 times the volume etc. Simple!
LUMINOSITY:
The luminosity, or intrinsic brightness of your star, will be given by the mass-luminosity
relationship: L = M^3.5
It's quiet a good fit for the main sequence but it's not perfect; we could be more accurate.
For example, we could make order of magnitude estimations, like so, but frankly, for our
purposes, it's kinda overkill. Stick with this formula!
LIFETIME:
The amount of time your star will spend on the main sequence will be given by T_ms = M
/ L
Multiplying by a solar lifetime, 10 billion years, gives you your stars lifetime in earth
years.
Interesting side note: the least massive stars will stay on the main sequence for about 6
trillion years which is a long time.
In fact up to 400 times longer than time itself!!
TEMPERATURE:
The effective temperature, i.e., the surface temperature, of your star will be given by:
T = (L/R^2)^1/4
Multiplying by the temperature of the sun, 5778 K, give you your stars temperature in
kelvin.
Then use this chart to gauge the color of your star from blue to a light orangey red.
To be clear, when seen by humanoid lifeforms from the surface of a planet, ALL stars, regardless
of spectral type, appear white! The colors on the chart are an attempt at defining “true”
colors. Links in the dooblydoo for further reading and clarification and, yes, photoshop
users those are hex values!
HABITABLE ZONE:
If you intend to have life supporting planets orbiting your stars, make sure those planets
orbit in the habitable zone.
The inner boundary of the habitable zone, in AU, is given by: sqrt(L/1.1) and the outer
boundary, in AU, is given by sqrt(L/0.53)
Massive caveat! I'm defining habitability in terms of earth-like lifeforms. Silicon
based lifeforms may require a totally different habitable zone, as would life using methane
as a solvent for example. But exo-biology is topic for another day.
With these few parameters defined you can say, with confidence, that you've constructed
a main sequence star worthy of a it's own Wikipedia page! Now all that's left is to
run the process another 899ish times and move onto the post main sequence stars.
POST MAIN SEQUENCE:
Main sequence stars are like Shane from the Walking Dead and post-main sequence stars
are like...we'll...Shane from the Walking Dead - living stars hang out on the main sequence
and everything else is either dead or dying.
Dead or dying stars are, for the most part, extremely hard to describe using simple maths.
So let's take a break from the formulas for a bit and check out some nifty graphs!
GIANTS:
By definition, Giants have significantly larger radii and luminosities than main sequence
stars of the same temperature - they're bigger, they're brighter, but they ain't hotter!
Low to intermediate mass main sequence stars begin to evolve into Giants, when they start
to run out of hydrogen fuel, and leave the main sequence. Same goes for high mass main
sequence stars just they turn into Supergiants instead!
Supergiants are like regular Giants except on crack – they're even larger and even
more luminous than regular giants but, again, they're very cool. Tl;dr Giants are the mature
stage of stellar evolution.
Anyways, this is the Hertzsprung Russell diagram which plots the relationship between the luminosity
and temperature of stars.
Here's the main sequence and here's the giants. Simply pick something in the orange or blue
region and appropriate data for luminosity, temperature, radius and spectral type will
be generated for you.
Which is a relief! I mean look, this is a main a sequence star of 1.2 solar masses.
Watch what happens as it evolves off the main sequence. Simple formulas cannot account for
this level of insanity!
So use graphs to build your Giants. Links in the doobly-doo.
Let's talk habitability: We can calculate the habitable zone around a giant star just
like we did for our the main sequence stars.
However, as a star expands and grows in luminosity, close in planets will be swallowed up and
it's habitable zone will sweeps outwards. So unlike main sequence stars habitability
around giant stars would change drastically with time. For the most part, no planet will
remain in this migrant habitable zone long enough for life to arise naturally. But maybe
we don't need life to arise. Maybe all we need is for a suitable atmosphere to develop,
thus making the planet colonizable – this scenario though improbable is somewhat plausible.
Links in the doobly-doo
WHITE DWARFS, NEUTRON STARS AND BLACK HOLES:
The defining properties of compact objects are mass and radius. That is to say, white
dwarfs, neutron stars and black holes are all extremely tiny, and for their size, extremely
massive!
So let's focus on mass and radius.
White dwarfs have masses between 0.17 and 1.4 solar masses. Neutron stars lie between
1.4 and about 3 solar masses and at about 5 solar masses a compact object is likely
a stellar mass black hole.
Supermassive black holes, like those found in the centre of most galaxies, range from
hundreds of thousands to several tens of billions of solar masses.
So that's mass. What about radius?
Counterintuitively the more massive a white dwarf is the smaller it is.We can ballpark
the radius of a white dwarf using the formula: R = M^(-1/3)
So, a white dwarf of 1.4 solar masses will be about 90% the size of earth! Which looks
like this.
Neutron stars on the other hand will be confined to radii of about 10 – 13 km. Yes! You heard
right, KM! [Show scale]
Now, the size of black holes are determined by their event horizon or Schwarzschild radius
which is given, in km, by 2.95 * M.
So a 5 solar masses black hole will have an event horizon at about 15km.
1.5 times this distance gives us the photon sphere which, in effect is the lower bound
for any stable orbit.
In terms of habitability, none of these objects are particularly habitable: toxic levels of
radiation, inward migrating habitable zones, extreme tidal forces etc are all pretty life
hostile.
BUT ...I'll leave you with this really really speculative idea. Let's say an icy super-earth
was ejected into interstellar space. Let's say it passed by a stellar mass black hole
on a trajectory tangential to the black holes photon sphere and was captured.
Now, black holes emit almost no heat (Hawking radiation is negligible) but let's say our
planet slipped into an orbit such that the tidal forces it experienced were enough to
heat and thaw it's interior, but not enough to tear it apart. The planets interior would
melt and we'd be left with a sub surface liquid ocean. Life may evolve around thermal vents
deep within this ocean.
It's not probable. In fact its probably impossible but, hey, speculation courses through every
worldbuilder's veins!