Lesson 4: Bypassing the helium flash

For this lesson you will need:

• A 1 solar mass modin file
• A 3 solar mass modin file
• An appropriate data file

Back in Lesson 1, we evolved a solar model to the tip of the red giant branch, shere it promptly crashed at the onset of the core helium flash. For those of us interested in asymptotic giant branch stars, this is not particularly satisfactory -- we would very much like to evolve this star further! In this lesson, we'll learn how to get round this problem. First of all, we need our solar model again so re-run the above 1 solar mass model using the given data file. Note that we have changed it slightly: NSAVE (highlighted) is now equal to 10 so that we save every 10th model. We will need one of these models later. Make sure you save the output from this run! You should end up with a run that converges around 900 models and ends with a final core mass of about 0.46 solar masses (column 7 in the plot file, or the first number in the 3rd line of the short summary in the out file).

The code has trouble igniting helium under degenerate conditions. Once the degeneracy is lifted, everything should be fine. We just need to get round that first little hiccup. To get round this, we are going to make a more massive model that ignites helium under (almost) non-degenerate conditions. We are then going to manipulate this model until it has the same characteristics as the model we want. Then we can set it going again. Be warned -- the procedure is somewhat convoluted (and should not be used at extremely low metallicities due to the occurrence of dual core flashes)!

The first step is to evolve ourselves a more massive model. We will start with a 3 solar mass model (at lower metallicities you may be able to use a less massive model). As we evolve the model, we don't want it to burn any of the helium, so we need to set the IY switch to 0, as shown in the datafile below.

Once we have this model, we need to take one of the saved models just after helium burning has started under non-degenerate conditions. You will need to look at the summary models in the out file to decide which one to choose. One with a central psi equal to a few and a central temperature of over log T=8.0 should be fine -- I have decided to use model number 1100. This has psi=1.293 and log T=8.0386 with a helium luminosity of about 4 solar luminosities.

This model is too massive compared to our 1 solar mass model and it also hasa hydrogen exhausted core mass that is too small. We shall now fix these problems. The mass loss is easiest: we simply switch on RMG to a value of 1.00E-5 (if this value is too high the model may not converge -- I find this value a good trade off between ease of convergence and the amount of time you have to wait). It is also useful to switch DT1 to 1.00. This stops the code reducing the timestep (unless it fails to converge) and minimises the time you have to wait. The data file I have used is shown below (changes to the previous file are circled in red):

Note that we have set IX=0 (highlighted) -- this stops the core from growing in mass as we are removing mass from it. You may also find it necessary to reduce the timestep of the model you decide to use -- if it is too high, the code will fail to converge as it tries to rip off too much mass in one go. When you have run this, choose a model which has a mass close to 1 solar mass. It doesn't have to be exact -- when you load this model into modin, you can edit the mass of the model (the first number on the first line -- I shouldn't need to tell you this by now!) to give you exactly what you want. I have taken model 1160 which has a mass of 1.086938 solar mass, which I now set to exactly 1.000000.

Now we need to grow the core out to the same mass as our 1 solar mass model (0.46957). To do this, we set IX back to 1 and undo our changes to DT1 (restore it to 0.8) and RMG (set it back to zero). This will then allow the core to grow outward until it reaches the appropriate mass. Hey presto! You have a post-helium flash 1 solar mass model which you can now evolve as normal (once you have set IY back to 1). You should end up with a track that looks something like this:

The more pedantic amongst you will note two things:

1. The model we have just made doesn't have the same composition as the 1 solar mass model we originally made (because first dredge-up isn't the same in 1 and 3 solar mass stars).
2. I told you to make sure you saved that 1 solar mass model we initially made for later and we haven't done anything with it.