[mesa-users] Cepheid variability with MESA's hydrodynamic mode?

[Warrick Ball]

Hi everyone,

I won't bore you with how, but at some point I came to wonder whether 
MESA, given its hydrodynamic abilities, would be able to follow the 
pulsations of large-amplitude classical oscillators like Cepheids.  After 
all, Paper III already showed that it's possible to get red supergiant 
pulsations.  So, a few weeks ago, I finally got around to trying to land a 
model in the classical instability strip, then taking that model and 
running it with the velocity variable turned on and nuclear reactions 
turned off (which probably doesn't matter), just to see if it would start 
to oscillate.  I had already read in Yoon & Cantiello (2010) and 
references therein that the timestep would have to be small (much shorter 
than the pulsation period) for the implicit time integration not to 
squelch the pulsations.

Luckily, I seemed to land a suitable model more or less from the get go, 
which I ran with something like the attached inlist.  It took a long time 
for the pulsations to build up (that run has now been going for many 
days), so I've also attached a model from somewhere during the "evolution" 
so you can reproduce this result.  Finally, I've also attached a plot of 
the luminosity as a function of age using this inlist and model, for the 
first 5000 steps (or about 2 periods) so you can see that the star does 
indeed pulsate.  It's quite messy, though the radius as a function of age 
is much smoother.  Also, though it takes a long time to appear, there are 
plenty of long term modulations, even after the apparent limiting 
amplitude (about 0.8 dex) is reached.  (If anyone is interested in the 
much longer "time series" I've computed, I have a 1.2GB history file to 
offer...)

Once I found the model pulsating, I tried to consult some literature to 
see if I could work out what was going on, since I know nearly nothing 
about modelling this kind of thing but I think I'd need much more time to 
really understand what's going on.  My experiment is probably the most 
naive possible way of approaching the problem.  I'm aware, for example, 
that by using MLT the model lacks any interaction between pulsation and 
convection.  I also haven't used (or don't think I've used?) any of the 
artificial viscosity terms available in MESA, though I'm under the 
impression that Cepheid/RR Lyrae hydro models use a different kind of 
artificial viscosity from what's described in MESA III.  I also simply 
allowed the numerical noise to slowly grow into the large amplitude 
pulsations now present in the model.  So I didn't initiate the pulsation 
using eigenfunctions from a linear analysis, nor am I in any way filtering 
out other modes (as seemed to be the case in Stobie 1969). I also honestly 
haven't had time to try to work out the details of what's going on inside 
the model.  All I've really glanced at so far are the surface properties.

My question, then, is: what would it take to make MESA capable of 
modelling Cepheid light curves, even to some basic level?  Is it 
interesting, worthwhile, or even possible?  I'd love to hear from anyone 
who has some experience in this area!

Cheers,
Warrick

PS:  One of the more useful starting points I found for my literature 
search was Rados\B3aw Smolec's PhD thesis:

http://users.camk.edu.pl/smolec/phd_smolec.pdf


------------
Warrick Ball
Postdoc, School of Physics and Astronomy
University of Birmingham, Edgbaston, Birmingham B15 2TT
wball at bison.ph.bham.ac.uk
+44 (0)121 414 4552
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&star_job
  ! save a model at the end of the run
    load_saved_model = .true.
    saved_model_name = 'start.mod'

    change_v_flag = .true.
    change_initial_v_flag = .true.
    new_v_flag = .true.

  ! for convenience
    set_initial_age = .true.
    initial_age = 0
    set_initial_model_number = .true.
    initial_model_number = 0
  
/ !end of star_job namelist


&controls
 !  following Baraffe et al. (1998)
    initial_z = 0.004
    initial_y = 0.25

  ! starting specifications
    initial_mass = 5 ! in Msun units
    
    photo_interval = 10000 ! 50
    profile_interval = 10000
    write_model_with_profile = .true. ! .false.

    dxdt_nuc_factor = 0 ! 1 ! should stop chemical evolution...
    max_timestep = 120 ! 0
/ ! end of controls namelist
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