Thoughts about stars and stellar evolution in US2

[Matyasz]

Dear developers and players!
(Edited)

I would like to take a moment of your time sharing with you my thoughts about US2 and particularly stellar evolution within it. I apologize for a very lengthy post! I am leaving for a vacation for two weeks now, so I cannot reply until I am back, but I wanted to post this to open discussions on the topic for you.

I am just a humble hobby-enthusiast of astrophysics, recently majorly focusing on stars. I have really enjoyed the simulator since the moment I bought it and I feel the developers have reached great milestones in developing it. The stellar bit was particularly interesting and it eventually gave me the push to create an MS Excel file that would eventually provide most stellar calculations. I'm particularly proud of its HR-diagram! Anyway, US2 serves very well as a source of experimental data and playground for the file, so have spent hundreds of hours churning various types of stars manually but without ever touching any of the values. However, the experiments showed several apparent simplifications and minor inconsistencies in US2. Most of the problems seem to revolve around stellar evolution, yet again, that field is unknown waters for modern science in many of its aspects.

Massive stars seem to be problematic. Supernova explosion has been hard-coded to 11.6 Msun. I can't think of anything else connected to that mass but the mass of Betelgeuse! Recently the limit can be avoided in certain circumstances, like I managed to produce 200+ Msun stars by colliding smaller radii stars so that part of it is inside the larger star, thus avoiding supernova. It's also worth noting that almost anything ends to a supernova, and the remnant is, if not a black hole, a "partial" white dwarf, i.e. its mass is typically within Chandrasekhar limit but radius, luminosity, density and chemical composition (perhaps everything else, too?) remain unchanged. However, I have yet to experiment possible results in other remnant types.

However, the 11.6 Msun limit shows still in luminosity. That very same 220 Msun star had the luminosity of <1 Lsun. It appears so that currently it is tied to main-sequence mass-luminosity relation (or something similar) instead of more accurate Boltzmann's law (relating Radius-Temperature-Luminosity). The law would have given the star a luminosity beyond 1E+7!

Density tends to deviate greatly from reality as well. I tend to create stars manually by colliding gas giants, usually in static or orbital mode, until I get desired values. Density tends to follow somewhat until the point when the object transforms into a star (currently at ~77 Mjupiter). The maximum tends to lay around 10 g/cm³. After that point, density becomes static and won't reflect any related changes until the star becomes massive enough to suddenly lose most of its density (I need to check out what that point was, sorry!). The fall may be very dramatic, going from 10K down to 50 kg/m³.

Stellar evolution is still under experimentation for me as it takes time, understanding of astrophysics, and effort, all of which I'm lacking lately. However, it does seem to work to various extents. Around Msun it seems to be quite accurate (I suppose most of us want to know what happens to our star!).

One of the most significant problems for stellar modeling in US2 seems to be something probably unnoticed by many players: the composition. Stars burn chemical elements roughly in order of their atomic mass up to Fe (iron) or less. The shifts ("flash") between the element being fused generally border the many evolutionary stages. US2 has H (hydrogen), Si (silicon), H₂O (water) and Fe (iron)... of which water cannot exist in stars (immediate evaporation due to heat) and most of iron exists only during the very last moments of very massive stars and as a tiny fractions in other stars and ev. stages. US2 ignores entirely the most important pair to hydrogen: Helium... and C (carbon), N (nitrogen), O (oxygen) as well as D (deuterium), Li (lithium) if sub-stars count and of course several others up to iron. Mg, Ne, Zr and a few other elements are notable in some spectral classes. There are, in fact, special stars and evolutionary stages that are rich of these elements, thus identified by that abundance. The amount of the elements beyond H+He, so called metallicity, factors to luminosity, radius and several other values.

I could imagine one solution to model stars and their evolution more accurately would be adding more accuracy to chemical composition and accuracy / consistency in other parameters. If modeling actual fusion is too demanding, the stars could imitate it somehow, for example by an (arbitrary) H>He conversion rate, perhaps also including C, N & O as those concern the Sun as well. Sub-stars burn deuterium, methane and lithium among other things. If these chemical elements obey their physical rules, these could greatly affect the accuracy. In addition, US2 could then properly reflect the existence of carbon stars, Wolf-Rayet stars, white dwarf sub-types and so on... perhaps even modeling theoretical types that are likely to exist in the future, such as iron stars and black dwarfs.

Finally, I mentioned inconsistencies in values and their units. Although fairly insignificant, you may have noticed that radius is shown to precision of meters until 1E+10 (then switches to scientific), mass, composition and luminosity to kg and W in scientific notation up to 2 decimals. The composition bit is particularly awkward since sometimes small fractions are completely ignored. However, I do see that the point is merely to show the ratios to players. Most formulas used in astrophysics relate kg/m/s/W/etc and g/cm/s/W/etc respectively and exactly so inconsistencies affect the results although it's true that very precise values are incredibly hard to obtain for real stars and small differences are often negligible. It is also annoying that the simulator forgets easily preferred units, switching back and forth between units if the info is closed.

I think this is getting way too long now, so it's best for me to stop here! I really hope there was something here that picks your interest, sparks new opinions and ideas, anything else!

Thank you very much for your time. Have a wonderful day!

[SyzygyΣE]

Wow, really nice post. Though I know less than you about stellar science, you really took many words out of my mouth about these inaccuracies. Very interesting ideas for the devs to take note of. I absolutely agree with what you are saying, but I can also assure you that stars are being worked on. In the next update, a new stellar evolution model should be implemented. While I don't expect it to create perfectly accurate stars, it will be the first major step in getting there.

[Matyasz]

Thank you so much for your kind words!

While stars do obviously obey physical laws, simulating them accurately is incredibly difficult since in many cases we don't know much if anything at all about certain laws. For example, there are some extremely massive stars that, based on our understanding of stellar mechanism, shouldn't exist... yet they do. Also, recently many well-defined laws have been found out to be either incomplete or incorrect. Chandrasekhar limit is one of them, it's the maximum mass limit for a degenerate star to avoid collapsing. It was thought to be strictly 1.39 Msun but there are now some objects that clearly disobey that.

There are also numerous "rules" that are more or less entirely based on empirical data and approximated patterns that they (may) follow. Some of those, such as the well-known mass-luminosity relation for main-sequence stars are all over the media but almost all info is either greatly simplified (like L = M^3.5 which is only partially valid) or each source shows slightly different values... It's not like they are outright false but the values often depend on the data used to obtain it.

That's why US2 is so amazing! The more accurately it is programmed to follow what we know about stars, the better as a simulation it will be. Moreover, it could then even help to model various stellar scenarios more or less accurately and perhaps even widen our understanding. Computed models tend to be incredibly smart and accurate when they are fed with enough information! Of course planets and other objects should get their love as well. It's just that physically they are really simple to model since they are basically dead objects that only change according to their parents.

The downside is, however, that all this information would basically melt the PC of your regular player. That's probably why developers stuck with approximation rather than exact accuracy. Of course, if the code allows, I think US2 could be programmed to include specific settings allowing special accuracy models that could be disabled for lower end computers.

I'm sorry for writing such a lengthy reply, again... Shame on me!

[Matyasz]

By the way, here's the HR-Diagram I mentioned. It's still incomplete so it's rather crude visually.
A few notes about it:

• All plotted stars except the Sun are those created in US2. The Sun is there so that I can "calibrate" all the information together. You can see how it's in the cross-point for several lines.
• The green, more diagonal, lines show radius zones. Those are accurately calibrated to temperature-luminosity based on Boltzmann law.
• The oddly uneven orange-ish line shows mass-luminosity relation. It is partially erroneous at the moment for several reasons but partially because there is no well-understood way to relate mass-radius-temperature-luminosity correctly. This line was based on the Wikipedia's values (more or less correct), first calibrated by mass-radius relation and then converted to Temp-Luminosity with Boltzmann law. The most apparent error can be seen in almost vertical line. The slope's turning point is at around 39,000 K, which seems very odd to me (calculated as 3200*Mass for stars beyond 20Msun)...
• The blue horizontal lines show absolute (bolometric) magnitude. It's accurately calibrated to Sun's value of 4.74.
• The stars have Spectral and luminosity classes marked. Those are partially erroneous for numerous reasons.
• • First, I made W (Wolf-Rayet) to temporarily represent stars beyond 52,000 K (O-type generally stops at that point) and capped it to 220,000 which is the highest observed effective temperature.
    
  • White dwarfs are simplified to D without further specification until I figure out how to relate the differences numerically.
  • The number between spectral and luminosity type, temperature subdivision, is calculated by dividing spectral class temperatures evenly by 10. They contain fractions so I rounded them.
  • Luminosity class is a tricky one, thus incorrect! I solved it temporarily so that the mass-luminosity relation functions as the base and the various classes are distributed by the order of magnitude difference in luminosity. For example, V (main sequence) is coded to be within 0.1 and 10*mass-luminosity.
  • Those funny circles there and here represent a couple major star types. Obviously, most of them are still missing and placing is intentionally very approximate. I use those for rough calibrations.
  • The sun's value with all these calculations is G2V, which interestingly is perfectly correct! Among the worst errors is the red supergiant with K7V (just before its collapse)...

Have fun looking at that awful piece of work, knowing that I spent tens of hours on it to still have numerous errors all over!

Also, have a wonderful day!

[Plasmic Physics]

In addition to your concerns, I wouldlike to raise four further points of interest.

1. White dwarves and neutron stars, or other hyper-dense objects should exhibit gravitional lensing, not just black holes.
2. Stellar granulation should not be present in neutron stars, they should have a uniform appearance.
3. On the matter of black holes - Hawking radiation, ergo evaporation.
4. Due to to the energy-mass equivalence, the radiated energy should cause a star to lose mass, in addition to its solar wind.

I'm not sure on this, but it looks like to the size of granules are limited for increasing star radius. I've seen in other more realistic simlators, and I've heard the explanaition, which I can't recall, that some super low density stars are not even spherical, but appear like they are singular giant-granules, blob-like in appearance.