# What are the equations governing stellar evolution (Luminosity, Mass, Temperature, Radius)

I'm looking for ('simplified') equations governing stellar evolution. Especially how mass, luminosity, temperature and radius of a star change during it's lifetime. As well as equations which tell you how long a star stays in a certain stellar stage (PMS, MS, ...).

Extra clarification by example:

...

After that a star with a mass between x and y enters the main sequence for a duration of $\Delta T = formula$. During this phase it's mass changes according to $M = formula(t)$. after that it enters the xxx phase

...

For those who think this question is to broad, please give some suggestions, 'google terms', ... from which I can move forward.

• Question is too broad. You appear to be looking for universal relations that apply to these quantities, but there aren't any that apply to other than narrow mass ranges and narrow definitions of evolutionary phases. The equations that "govern stellar evolution" are the well known (differential) equations of stellar structure, that must be solved for cases of interest. – ProfRob Aug 2 '18 at 17:20
• what are those well known (differential) equations – Sam Coutteau Aug 2 '18 at 17:27
• Do these help course notes and lecture on equations of stellar structure help ? Note that there is a lot of work needed to turn the equations into a computer program that can solve them and get testable output from them... – astrosnapper Aug 2 '18 at 17:57
• I don't think we should be discouraging people from asking questions which unbeknownst to them have complicated answers. As such, I don't think this question is too broad. Having said that, from what I understand of stellar dynamics (which is comprised mainly of wikipedia articles), it is really complicated and star-specific. I'd go as far as to say that there are more types of star than there are planet, and the heavier the star, the more complicated the evolution. – Ingolifs Aug 3 '18 at 0:06
• en.wikipedia.org/wiki/… – ProfRob Aug 3 '18 at 3:26

## 1 Answer

What you want is hydrodynamic stellar evolution. The following starts with a brief review of hydrostatic case to give the fundamentals. The last paragraph discusses the hydrodynamic case.

For hydrostatic case, see this, or this. Simplified stellar evolution assumes hydrostatic equilibrium (i.e., time-independent fashion). The system of equations compose of i) mass conservation, ii) mass transportation (i.e., hydrostatic equilibrium), iii) energy conservation, and iv) energy transportation. The system also requires i) the equation of state, ii) opacity, and iii) nuclear energy generation for being solved in a close form. The close-form solution is typically in the form of polytrophs (i.e., Lane-Emden equation). More complicated model, which is still hydrostatic equilibrium, will include other factors such as composition, rotation, and binary interaction. Since it is static and equilibrium case, the time-dependent terms are zero.

For hydrodynamic case (i.e., time dependent) as you wanted, there is no close-form solution, therefore only hydrodynamic simulation is the method for the study. The simulation model uses the set of equations mentioned above without dropping the time-dependent terms. See, e.g., MESA.