How to Build a Star!

Learn how to create a scientifically plausible star.

Luminosity: L = M^3
Diameter: D = M^0.74
Surface Temperature: T = M^0.505
Lifetime: V = M^-2.5
Habitable zone (inner) : R = sqrt(L) x 0.95
Habitable zone (outer): R = sqrt(L) x 1.37

Credit: ESA/Hubble:

[zolikoff]

0:54 Screw lifetime, let's build an O-star just because!

[kieubasiarz]

Universe Sandbox 2 is a nice thingy for making all this stuff.

[wilfred]

it truly is wierd seeing a video of you this old; your quality has increased ten fold. keep growing and keep up the good work.

[thetyrus]

I can't thank you enough for making these videos. Now my world building addiction is truly infinite.

[PizzaChess]

I have a few issues with your exact values:

Luminosity: L ≈ M^4
Radius: R ≈ M^0.9
Temperature in K: T = 5778 K * (L/R^2)^0.25
Lifetime in years: T ≈ M/L * 10^10

But most importantly, the habitable zone:
Your estimates of 0.95 - 1.37 AU are the conservative estimates of James Fraser Kasting's incredibly important study from 1993 about habitability. The thing is, while he himself defined 0.95 - 1.37 AU as the (purely theoretical) conservative limits, he did acknowledge that the actual width of the habitable zone was probably a lot wider.

Personally, I have decided to calculate a more optimistic limit of the Sun's habitable zone. The method I'm using is based on the assumption that Mars and Venus both had liquid water on their surfaces a few Billion years ago, which today most scientists agree they did.

Beginning with the inner limit, we need to go ~1.5 - 2 Billion years back in time. The Sun's luminosity at that point was ~85 % of its current value. Venus at that time most likely still had liquid water on her surface. Due to the inverse square law, we can calculate (0.85 [L☉]/0.72^2 [AU]) ≈ 1.64 Seff, meaning that Venus back then received about 64 % more warmth and energy than Earth today receives from the Sun (that values has gone up to ~93 % today). To calculate the inner edge of today's habitable zone, we just need to calculate √(1 [L☉]/1.64 [Seff]) ≈ 0.78 AU.
That gives the Sun's current habitable zone an inner limit of 0.78 AU.

When it comes to the outer limit, we need to go ~4 Billion years back in time. The Sun's luminosity at that point was only ~75 % of its current value. Mars too back then most likely had liquid water on his surface. Due to the inverse square law, we can once more calculate (0.75 [L☉]/1.52^2 [AU]) ≈ 0.325 Seff, meaning that Mars back then received about 32.5 % of the warmth and energy that Earth today receives from the Sun (that values has gone up to ~43.3 % today). To calculate the outer edge of today's habitable zone, we just need to calculate √(1 [L☉]/0.325 [Seff]) ≈ 1.75 AU.
That gives the Sun's current habitable zone an outer limit of 1.75 AU.

The reason Mars is so dry and cold despite being within the Sun's habitable zone is that it's simply too small to hold on to any major atmosphere or even just a magnetic field, all of which just got stripped away by the solar wind within a few million years.

In summary, 0.78 - 1.75 AU is the most optimistic HZ limits that still make plausible sense. It's also the one that we have the most observational evidence. Again, these limits are very optimistic, and based on the assumption that Venus and Mars were both habitable in the past.

[WhirligigGirl]

The Mass/Luminosity, Mass/Radius, and Mass/Temperature equations are off. All of them individually may represent stars on the main sequence (but they may be very different compared to well known ones like Proxima Centauri and Sirius), but more importantly, they don't agree with each other. You should only find two of the above and plug them into the following equation to find the other:

This is the stefan-boltzmann law without all the constants.
L = R^2 * T^4.

For M = 2, M=L^3 yields 8 Lsol, while the physically correct law yields 11.3 Lsol.

Use these equations with caution! The best way to build a star is to consult HR diagrams and catalogs of real stars (or wikipedia articles of real stars) on the main sequence, and either copy them or modify your star based upon them. If instead you do choose to use this video's equations, make sure to find only two between L, R, and T, and solve for the other one.

Note that there is some leeway with the main sequence, the mass/radius, mass/luminosity, and mass/luminosity relationship isn't a strict law. But the relationship between Luminosity, Radius, and Temperature is a strict, physical law that should not be deviated from! Remember that Luminosity is probably the most important for worldbuilding as it directly determines the habitable zone of your star system.

Sirius gets 25 Lsol in real life with Mass of 2 Msol. These equations say it should have luminosity of 8 (L=M^3) or 11.3 (L=R^2 * T^4, where R and T use this video's equations). Proxima Centauri, M = 0.1221, has L = 0.0017, R = 0.1542, and T = 3042 Kelvins . The video's luminosity equation gives 0.0018, which is actually pretty close, but R = 0.211 and T = only 2005 Kelvin! That is so chilly that I'm not sure if there are M.S. stars that cool. L with the stefan-boltzmann law and this video's R and T is 0.00065. Now there are stars that are so dim, but they tend to be extremely tiny and very cool.

I love your videos Artifexian, I have just found issue with these equations in particular. But your videos have helped me immensely, so please don't take this comment the wrong way!

[Haan_P]

Hey! This is a great video and I'm so glad you're doing the series, but if it's okay, I've got a small point of critique.
You see, the stats for the goldilock zone mentioned are from 1979(for .95AU) and 1993(for 1.37AU) and the estimations have since been updated several times, so they're no longer relevant. óMò; Currently, the goldilock zone is estimated to be roughly 0.5-1.7AU. With the current estimations, the atmosphere of the planet has become a much more important factor regarding its habitability than just its distance from the central star would be.
It probably can't be fixed in this video(except maybe with captions?), but eh, mayube it cna help some new watchers who also read comments?

[Smonserratm]

The letters give you the color and temperature of the star, not the mass. You can have massive stars undergoing their a giant phase in which they are usually redish (in the K-M range). The OBAFGKM usually comes with numbers from 0 to 9 to subdivide every letter (0 meaning hotest and 9 coolest) and a roman number to specify the type of star (From I being supergiants to VII being white dwarfs).
So this video is only true if your star is going to be in the main sequence, where it's just burning H into He.

Example:
Sun: G2 V, 1 solar mass
Beta Aquarii (Sadalsuud): G0 I, 6 solar masses

[allanjohnson]

Note that your description says diameter, but (after I tested the number a bit with a spreadsheet) it's actually the radius!

[ranuluscause]

When looking at your moons video you mentioned a frost line. I was talking it over with myself and others and I came to a Okie conclusion that the frost line is the end of the habitable zone at 137% so for alpha that's 1.97 au. Although some conformation would be nice. Thanks

[merkyuk]

for those finding the inner habitable-zone boundary less than the inner boundary especially with M class stars, perhaps try :

M < 0.43, use 0.23(M^2.3)
M > 0.43 and < 2, use (M^4)
M > 2 and < 55, use 1.4(M^3.5)
M>55 use 3200(M)

[dliessmgg]

I perfectly understand your other videos, but this one just confused me, with the units and such. If you ever decide to redo old videos better, make it this one.

[novvain]

What equation is for luminosity?
In the video it says M⁴, but in the description it says M³

[RRW]

I hear moons can increase a planet's magnetic field. Would it be possible to have a habitable planet close enough to a red dwarf to be tidally locked, but not have the star slowly pull the moon away?

[johnstewart]

I am not sure but I believe that there are a few possible errors:
first Luminosity is closer to 3.5 (Eddington, 1924)
second radius should be closer to 0.80 (Darling, 2004)
and because luminosity is proportional to R^2*T^4 (Boltzmann law)
temperature should be closer to 0.68
[I would recommend double checking this]
[note only for M<10]

[lasarith]

Updated, for Jan 4 2021 > (replacing old post)

Luminosity 1.2 x 1.2 x 1.2 x 1.2 = 2.07 (square ^4 M, K, G) (square ^5 F^)
Mass to radius seems to be 1.2 /100 x 95 = 1.14,
Habitable zone liquid water= √ (2.07) = 1.438((1.44 AU) (Planet -probably more like 85% -170%
Habitat zone (2)
1.44 /100 then x by (95 to 137) or (85 to 170) the second one is closer to the actual
Numbers, because the inner and outer habitat zones, -since the actual range for inner, outer, is disputed between these two numbers,

Temperature, 1.2 (square) 0.505 = 1.09644418662) (1.10)
Lifetime = 1.2/2.07x 10billion = 5.79 billion years (5, 797, 101, 449.28)
Lifetime 2= 1/1.2(square) 2.5 =0.63398914526 x 10 billion = 6, 339, 381, 452.61 (6.339 billion years)

[mesoth]

It is worth mentioning that the Goldilocks zone only works for Earth-like planets - a Venus-like planet, for example, would sustain liquid water if it was much, MUCH farther than the Goldilocks zone.

[autumnm.]

Who else saw the text on the calculator while he was doing calculations

[drifblim]

Technically speaking, habitable planets in binary systems are possible- as long as the stars orbit in such a way that they are far enough apart for a planet in the HZ to perhaps either have a sky like tatooine or have the two stars so far from eachother that one star looks like the sun and the other looks like, say, Jupiter or Venus viewed from Earth

[younscrafter]

as a star's mass decreases, its habitable zone will shrink faster tham its Diamater.
This Means that lighter stars will appear bigger to a being in their respective habitable zones,
a Star with a mass of 0.037 could sustain a Planet at the Inner Edge of its habitable zone whose inhabitants would see their star in about the same Size as the Minecraft sun