[mesa-users] Rapidly Rotating A-Stars

[Matteo Cantiello]

Hi Jeremy,
MESA calculates the corrections to the stellar structure due to the presence of rotation following Endal & Sofia 1976. You can also find details in Paxton et al. 2013.
Basically the routines in star/private/hydro_rotation.f  calculate the rotational correction factors (fp_rot and ft_rot)
at each grid point (corresponding to the 'shellular coordinate', which is isobaric). The factor  fp_rot is used for pressure correction and ft_rot for temperature correction.
The pressure correction is used in the momentum equation, while both fp_rot and ft_rot are used for calculating the radiative temperature
gradient used by the MLT. So in MESA internal values of  R are 'effective' values on isobaric surfaces (shellular coordinate). 
Being 1D MESA has no formal knowledge of the '2D' structure of the star, which for a very rapid rotator would substantially depart from spherical symmetry in the very outer layers.
This said, polar and equatorial radius are calculated internally as one knows the distortion factors in the hydro_rotation.f, and these are output for user's convenience.
On the other hand no calculation of the temperature latitudinal profile is done internally, so you won't have values for T_eq and T_polar. Only 'averages' on isobars.

Note that in the 1D codes I've been using (including MESA) the correction factors (fp_rot and ft_rot) are usually limited to some value. Overall I think models calculated at omega/omega_crit close to 1 should be considered highly uncertain. While most of the star is still spherically symmetric  and one can argue that we can still say something important about what happens in the stellar interiors (lifetimes, mixing etc,) most of the deformation happens in the very outer layers, which are the layers you are interested in. Some of the interferometric observations seem to be in fairly good agreement with predictions of deformations and latitudinal dependence of temperature (Von Zeipel theorem), but still one has to use a grain of salt when comparing to 1D stellar evolution models.

So, to wrap up:

1) Mesa gives you r_eq and r_pol, as due to the rotational deformation.
2) Mesa do not gives you T_eq and T_pol. 
3) You wanna look into the limiting factors for fp_rot and ft_rot.
4) You need to be very careful when comparing 1D stellar evolution models to interferometric obs in this 'extreme' regime 

-Matteo


On Oct 4, 2013, at 1:25 PM, Jeremy Jones wrote:

> Hey mesa users,
> 
> I'm working on a project concerning interferometry of A-stars. Many of my targets are rapid rotators, and I'm looking into using mesa to determine their ages. I've played around with mesa a bit (I've included one of my inlists below). I have a question about how to compare my observables with the mesa outputs, in particular radius and temperature.
> 
> From the modeling I do of the inerferometric data, I get the full radius profile of the star (i.e. radius as a function of latitude). Likewise, I get the full temperature profile of the star.
> 
> My question is for a rapid rotator, which radius/temperature should I compare with the mesa outputs to get the age of the star? Polar radius/temperature, equatorial radius/temperature, something more involved?
> 
> Thanks for any insight!
> 
> ~Jeremy
> 
> The aforementioned inlist:
> ================
> &star_job
> 
>       mesa_dir = '../..'
> 
>       set_initial_age = .true.
>       initial_age = 0 ! in years
> 
>       set_initial_model_number = .true.
>       initial_model_number = 0
> 
>       create_pre_main_sequence_model = .true.
>       
>       new_omega_div_omega_crit = 0.5  
>       near_zams_relax_omega_div_omega_crit = .true.
> 
>       pgstar_flag = .true.
> 
> 
> / ! end of star_job namelist
> 
> 
> &controls
> 
>       min_timestep_limit = 1d-12 ! (seconds)
> 
>       ! check for retries and backups as part of test_suite
>       ! you can delete this for use outside of test_suite
>          max_number_backups = 400
>          max_number_retries = 900
>          max_model_number = 1500
> 
>          !max_allowed_nz = 20000 ! maximum number of grid points allowed
> 
>          initial_mass = 2
>          initial_z = 0.016
> 
>          photostep = 10
>          profile_interval = 10
>          history_interval = 1
>          terminal_interval = 2
>          write_header_frequency = 10
> 
> / ! end of controls namelist
> 
> 
> &pgstar
> 
> 	History_Track1_win_flag = .true.
> 	History_Track1_yname = 'log_R'
> 	History_Track1_yaxis_label = 'log(R/R_sun)'
> 	History_Track1_xname = 'log_Teff'
> 	History_Track1_xaxis_label = 'log(T/K)'
> 	History_Track1_title = 'Radius vs. Effective Temperature'
> 
> 	History_Track2_win_flag = .true.
> 	History_Track2_yname = 'surf_avg_v_rot'
> 	History_Track2_yaxis_label = 'Equatorial Velocity (km/s)'
> 	History_Track2_xname = 'star_age'
> 	History_Track2_xaxis_label = 'Age (yr)'
> 	History_Track2_title = 'Surface Velocity vs. Age'
> 
> / ! end of pgstar namelist
> ================
> 
> -- 
> Jeremy Jones
> Graduate Student Assistant
> Georgia State University
> Department of Physics & Astronomy
> jones at chara.gsu.edu
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Dr. Matteo Cantiello ------------------------
Kavli Institute for Theoretical Physics 
Room 2411 Kohn Hall CA 93106-4030
University of California, Santa Barbara
---------------- http://matteocantiello.com/

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