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GregroxMun

Star Tutorial Draft

GregroxMun
Mar 1st, 2019
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  1.  
  2.  
  3. B U I L D I N G A S T A R
  4.  
  5. a tutorial by GregroxMun
  6.  
  7.  
  8. --------------------------------------------------
  9.  
  10. SECTION 1: Introduction.
  11.  
  12. When designing a solar system for any worldbuilding project, including KSP planet modding, it is important to know the properties and characteristics of your system's star. If you leave designing the star to a time late in your design process, you may end up with a system that is inconsistent, unplayable, or even worse: UNREALISTIC.
  13.  
  14. A star is the heart of a solar system, and will have vast implications on the types and locations of planets, their orbits, and the habitable zone!
  15.  
  16. For most of this tutorial we'll be working in sun-relative units. So instead of 69,000 km, we'll say 1 solar radius, for example.
  17.  
  18. --------------------------------------------------
  19.  
  20. SECTION 2: Determining your star's spectral type.
  21.  
  22. There are many types of stars in our great universe. Astronomers have historically used many different methods to categorize stars, but modern astronomy generally uses the Morgan-Keenan system. This system uses usually three characters to describe a star. A letter, a number, and a roman numeral.
  23.  
  24. For example, the Sun is type G2V.
  25.  
  26. The letter is the spectral class. There are seven main spectral types.
  27.  
  28. *sung to the tune of Twinkle Twinkle Little Star*
  29.  
  30. O B A F G K M
  31. That's star types, how we classify them
  32. O is hot, M is cold
  33. later types can get so old
  34. color-temperature a major theme
  35. Oh be a fine Greg* kiss me.
  36.  
  37. *substitute your preferred gendered "G" noun as necessary.
  38.  
  39. O B A F G K M is in decreasing temperature order and generally speaking for main sequence stars (those which are fusing hydrogen in their cores) they are in decreasing mass order. For example, K type stars are less massive and cooler than F type stars.
  40.  
  41. The number is the temperature sub-class. Higher numbers are cooler, lower numbers are hotter. For example, a G9 star is cooler than a G2 star, but a K9 star is hotter than an M2 star. The letters go from 0 to 9. A cooler star is considered to be "late" and a hotter star is considered to be "early." For example, K2 might be considered early-K, while K8 would be considered late-K.
  42.  
  43. The roman numeral is the luminosity class.
  44.  
  45. 0: Hypergiants.
  46. Ia: Very-Supergiants.
  47. Ib: Supergiants.
  48. II: Bright Giants.
  49. III: Giants
  50. IV: Subgiants.
  51. V: Dwarfs/Main Sequence.
  52. VI or prefix sd: Subdwarfs.
  53. VII or prefix D: Degenerate dwarfs. (white dwarfs)
  54.  
  55. We can plot stars in the universe out on a Hertzsprung-Russell (HR) Diagram. This maps decreasing temperature on the X axis and increasing luminosity on the Y axis.
  56.  
  57. Here is an example of an HR Diagram: https://upload.wikimedia.org/wikipedia/commons/6/6b/HRDiagram.png
  58.  
  59. You'll notice that the Dwarfs / Main Sequence has the vast majority of stars. This is why it is called the main sequence. This diagram is made from a plot of stars from the Hipparcos catalogue and the Gliese catalogue. There is an important observation bias to consider: more luminous stars are much easier to detect. That's why the majority of main sequence stars in this diagram seem to be towards the higher end of the main sequence.
  60.  
  61. In reality, the main sequence is dominated overwhelmingly by M-type red dwarfs, with a general negative correlation between temperature and population. O-type stars are exceedingly rare, but incredibly bright and so can be seen from afar. M-dwarfs are exceedingly common but even the closest of them (Proxima Centauri) are not visible without telescopes.
  62.  
  63. This tutorial will only discuss the construction of Main Sequence Stars. Giants are more difficult to construct and make up a tiny portion of real stars. Bright- and Super-Giants are incredibly rare and short-lived.
  64.  
  65. White dwarfs, while being quite common, are also outside the scope of this tutorial.
  66.  
  67. Here is a list of the spectral classes of main sequence stars and their characteristics. (Taken from Wikipedia here: https://en.wikipedia.org/wiki/Stellar_classification#Harvard_spectral_classification)
  68.  
  69.  
  70.  
  71. +=======+=================+===================+================+================+===================+========================+
  72. | Class | Temperature | Color | Mass | Radius | luminosity | Percent of m.s. stars. |
  73. +=======+=================+===================+================+================+===================+========================+
  74. | O | >30,000 K | Blue | >16 suns | >6.6 suns | >30,000 suns | 0.00003% |
  75. +-------+-----------------+-------------------+----------------+----------------+-------------------+------------------------+
  76. | B | 10,000-30,000 K | Pale-Blue | 2.1-16 suns | 1.8-6.6 suns | 25-30,000 suns | 0.13% |
  77. +-------+-----------------+-------------------+----------------+----------------+-------------------+------------------------+
  78. | A | 7,500-10,000 K | Bluish-White | 1.4-2.1 suns | 1.4-1.8 suns | 5-25 suns | 0.6% |
  79. +-------+-----------------+-------------------+----------------+----------------+-------------------+------------------------+
  80. | F | 6,000-7,500 K | White | 1.04-1.4 suns | 1.15-1.4 suns | 1.5-5 suns | 3% |
  81. +-------+-----------------+-------------------+----------------+----------------+-------------------+------------------------+
  82. | G | 5,200-6,000 K | Very-Pale-Yellow | 0.8-1.04 suns | 0.96-1.15 suns | 0.6-1.5 suns | 7.6% |
  83. +-------+-----------------+-------------------+----------------+----------------+-------------------+------------------------+
  84. | K | 3,700-5,200 K | Pale-Orange | 0.45-0.8 suns | 0.7-0.96 suns | 0.08-0.96 | 12.1% |
  85. +-------+-----------------+-------------------+----------------+----------------+-------------------+------------------------+
  86. | M | 2,000-3,700 K | Orange | 0.08-0.45 suns | 0.1-0.7 suns | <0.0005-0.08 suns | 76.45% |
  87. +-------+-----------------+-------------------+----------------+----------------+-------------------+------------------------+
  88.  
  89.  
  90. This isn't 100% rigid. Since the spectral types are based upon the strength of hydrogen emission lines, and not temperature, some stars near the boundaries might have the spectral characteristics of one type but be a little too cool or too hot for that type. Or their mass may be a little lower or higher than other stars of the same luminosity and color. Note that O-type stars are in excess of 30,000 solar luminosities. That's in part because O-type stars are where the main sequence and the supergiants meet up on the HR diagram.
  91.  
  92. Star lifetimes are also an important consideration. There is a strong negative correlation between stellar mass and main-sequence lifetime. This can be approximated as the Lt = M^-2.5 where Lt is the lifetime in units of 10 billion years, and M is the mass of the star in solar masses. O type stars may live for less than 3 million years, sun-like stars will live 10 billion years, and M-type red dwarfs may live for hundreds of trillions of years.
  93.  
  94. How to choose which type of star to use? Well, it depends upon what your goal is. If you just want to make a star system with planets, then your design goal will be different than if you want to make a habitable system.
  95.  
  96. If your system will have planets, then O and B type stars are not good candidates. They are too young to have mature planetary systems. They will also output so much Ultraviolet radiation that they would fry any habitable planets.
  97.  
  98. A-type stars can have planetary systems, but nothing old enough for complex life to develop, and even if they did, they too would be fried by ultraviolet radiation.
  99.  
  100. F-type stars are perfectly fine candidates for planetary systems in general, but habitable planets will find the problem of their star dying before they can really get complex life going.
  101.  
  102. G-type stars like our sun are great candidates for planetary systems. They will have plenty of time to mature, their planets will have plenty of time to develop complex life, and despite the presence of ultraviolet radiation, planetary atmospheres can block out the bulk of it and life can adapt. These stars aren't the most ideal for habitable planets due to their ultraviolet and their relatively short lifetimes of only 10 billion years or so.
  103.  
  104. K-type stars are great candidates for planetary systems and probably the best systems for life. They have little to no ultraviolet radiation, but still produce plenty of energetic visible-light wavelengths. They will also last for hundreds of billions of years.
  105.  
  106. M-type stars are great candidates for planetary systems. They're not great for life, however. Red dwarfs tend to flare up during their youth (and given how long M-stars live, their youth lasts a LONG time). Most red dwarfs are flare stars, glowing bright and releasing huge amounts of ultraviolet for any planets that orbit them, for hours at a time, at random. These could occur as rarely as once every decade or so, or as commonly as once every few days. Or they may not flare up at all. Flare stars are bad candidates for life obviously, but even calm red dwarfs don't produce energetic enough light to drive photosynthesis, so complex life is unlikely around these stars.
  107.  
  108. F, G, and K stars result in the most familiar star systems, but if you're building up a multi-star universe, remember to have more M-dwarfs than K, more K-dwarfs than G, etc.
  109.  
  110. The smaller a star is, the closer its planets orbit. Less luminous stars tend to be MUCH less luminous than they are less massive, so orbital velocities are higher around smaller stars for planets recieving the same illumination from their star. In addition, M-dwarfs and late-K dwarfs may tidally lock planets more easily than G stars. In general, you should expect that planets in the inner systems of red and orange dwarf stars should be tidally locked. Orange dwarf star's planets may only be tidally locked if they are very old. In addition, the size of the hill sphere (where moons can orbit) will be reduced around planets orbiting red and orange dwarfs. Terrestrial planets orbiting M-dwarfs will find it tough to hold on to moons unless they are in very low orbits.
  111.  
  112. Main Sequence Stars are usually "dwarfs". However, extremely metal-poor (see Section 3 for more details) stars will glow hotter for the same mass than metal-rich stars. These are sub-dwarfs, and have the same spectral class as main sequence stars, but have luminosity class VI or prefix "sd." These are bad candidates for planetary systems, since planetary formation is strongly dependant upon metallicity. Planets CAN form around these stars, but more rarely and they may be somewhat stunted. (This applies only to GKM "cool" subdwarfs, OB "hot" subdwarfs are formed by a completely different principle)
  113.  
  114. --------------------------------------------------
  115.  
  116. SECTION 2a: Gameplay Considerations.
  117.  
  118. Assuming you're building this star for a Kerbal Space Program planet mod, here's a few things to keep in mind about other stars.
  119.  
  120. Planets around M-dwarfs orbit much, much closer to their star than planets around G-dwarfs, due to the minuscule luminosity of red dwarfs compared to their gravity. As a result, planets orbiting M-dwarfs (and to a lesser extent, K-dwarfs) have very high orbital velocities compared to their counterparts in the solar system. Planets are spaced closer together around smaller stars, which reduces hohmann-transfer orbit delta-v. But they also orbit much faster, which increases hohmann-transfer delta-v. As a result, interplanetary orbital maneuvers around red dwarf stars require considerably more delta-v (and fuel). In fact, escape from the least massive red dwarfs from the habitable zone is near the very borderline of what can be accomplished with chemical rockets. Ironically enough, less massive stars can actually be HARDER to leave!
  121.  
  122. --------------------------------------------------
  123.  
  124. SECTION 3: On Mass, Age, and Metallicity
  125.  
  126. A star can be defined, at its most basic, through its mass, age, and metallicity.
  127.  
  128. Mass: How much stuff there is in the star. This is the most important characteristic of stars. Heavier stars are more luminous and they're hotter. Mass is most strongly related to luminosity, approximated with L = M^3.5.
  129.  
  130. Age: How long the star has been on the main sequence. Stars get gradually brighter as they age, by increasing their surface temperature and expanding slightly. The sun's luminosity when it first entered the main sequence was only 0.7 times what it is today. By the time it leaves the main sequence, it will be 1.4 times what it is today.
  131.  
  132. Metallicity: Percent of a star's mass that is not hydrogen or helium. In other words, "contaminant," or carbon, oxygen, neon, etc. That contaminant is what terrestrial planets are made out of, so this is very important to planetary formation. There are three populations of stars marked by major differences in stars. "Metal" comes from supernova fusion, and stars born out of supernova remanants have higher metallicity. There are three populations of stars. Population III are the hypermassive, ultra-hot first generation of stars with almost no metal, formed shortly after the Big Bang. Population II are the second generation of stars, with very low metallicity, and are the oldest stars that are currently around. Population I are the most recent and most populous stars in our galaxy, and includes our sun. They have higher metallicities. While they are generally organized into these populations, metallicity is a spectrum.
  133.  
  134. A lower metallicity means the star is more internally transparent, and as a result, will be smaller and have a higher surface temperature than other stars of the same mass. Higher metallicity stars are more internally opaque and will be more luminous and larger, but with lower surface temperatures. For the same surface temperature and spectral type, a low-metallicity subdwarf star may be as low as 0.8 times the mass of a moderate-metallicity star. Meanwhile, a very high metallicty star of a given spectral type may be up to 1.3 times as massive as a moderate-metallicity star. (0.8-1.3 are the extremes. In reality this will usually be a more subtle effect.)
  135.  
  136. There is a certain set of boundaries on earthlike-planet formation based upon metallicity. If the metallicity is too low, planets won't form except for somewhat small outer-system gas giants/superearths and an inner system of rocky debris. (Or no planets at all) If the metallicity is too high, gas giants will grow so fast that they migrate into the inner system and interrupt planetary formation. If it's a more reasonable metallicity, you can get nice terrestrial planets and super-earths in the inner system.
  137.  
  138. I have not provided any equations for these three characteristics aside from Mass because the actual equations behind them are rather intimidating and are not simple power laws. So instead, I've given you general rules of thumb for how these three defining characteristics shape a star. If your system will have gas giants in the habitable zone, or very massive planets, then perhaps your star is fairly metal-rich. If your system will have only a few sparse low-mass planets, then perhaps your star is fairly metal-poor. If your star is near the end of its lifetime, then it should be more luminous than average for its mass, and if it's zero-age-main-sequence then it should be somewhat dim for its mass.
  139.  
  140. --------------------------------------------------
  141.  
  142. SECTION 4: Actually Finding your Star's Info
  143.  
  144. By now you're probably getting a little tired of learning about stars and are wanting to get around to actually finding out what your star is like, in hard numerical values.
  145.  
  146. We're almost there.
  147.  
  148. By now you should have decided what spectral type you'd like your star to be, which gives you a rough mass estimate. From there you can determine its age and metallicity, and you should have a rough estimate by now of its luminosity.
  149.  
  150. The first and most important equation relates temperature and radius to luminosity. This equation is fundamental--there's no fudge factor allowed here.
  151.  
  152. L = T^4 * R^2
  153.  
  154. Where L = luminosity/sun, T = temperature Kelvins/5800 Kelvins, and R = radius/sun.
  155.  
  156. You should have temperature from your spectral class, and luminosity from mass, age, and metallicity. So you need to find the radius.
  157.  
  158. R = L^0.5 / T^2
  159.  
  160. So now you should have real numbers for Radius, Temperature, Mass, and Luminosity. (And age if you want)
  161.  
  162. For example, I'll build a late-K star.
  163.  
  164. Class: K8V
  165. Age: 5.3 Billion Years.
  166. Mass: 0.48 Suns.
  167. Temperature: 3820 K.
  168. Luminosity: 0.1 Suns.
  169. Radius: 0.48 Suns.
  170.  
  171. At this point it is usually a good idea to plot your star on an HR diagram with real stars shown (like the one linked in Section 2). If the star you've chosen is not on the main sequence or is far off the edge, then you may want to reevaluate your values. (Note that you can only plot Luminosity and Temperature on the diagram, if you want to check your mass you'll have to compare it against some real stars individually.) In my case, the star is just barely above and to the right of the nominal main sequence curve, but still well within the main sequence. The implication is that this represents a very standard star for the main sequence.
  172.  
  173. --What color should the star be?--
  174.  
  175. https://academo.org/demos/colour-temperature-relationship/
  176.  
  177. This calculator allows you to find the RGB and Hex color values for blackbody radiators, which stars are closely approximated by. Simply type in the temperature of your star (or use the slider) and the program will output the color. The calculator only goes up to 15,000 kelvins, but for hotter objects than this, the color pretty much doesn't change, the sky-blue color is as blue as stars get.
  178.  
  179. WolframAlpha will also give you a color, both rgb values and a color swatch, based upon a temperature, which is useful if you're making brown dwarfs which are cooler than the 1500 K minimum of the calculator. Example:
  180.  
  181. "color 1000 kelvins" https://www.wolframalpha.com/input/?i=color+1000+kelvins (brownish-red)
  182. "color 5800 kelvins" https://www.wolframalpha.com/input/?i=color+5800+kelvins (off-white)
  183. "color 80,000 kelvins" https://www.wolframalpha.com/input/?i=color+80,000+kelvins (pale blue)
  184.  
  185. --What about the habitable zone?--
  186.  
  187. The finding the habitable zone of your star is actually a very simple calculation, it's just Luminosity^0.5. This is specifically the "Earth insolation analogue," the distance at which the Earth would get the same amount of light as it does in its current solar orbit. To find the range of the habitable zone, multiply by your range of choice. Optimistic habitable zone goes from 0.9-1.4 au. More conservatively it might go from 0.97-1.2 au. So you'd multiply the Earth insolation analogue distance by 0.9 for the inner optimistic limit, and then multiply the Earth insolation analogue by 1.4 to get the outer optimistic limit.
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