Pulsations in MESA

How many ways to do pulsations in MESA?

As you have seen today, there are many different codes packaged with MESA designed for analyzing stellar pulsations/oscillations. Which particular code is best, will depend on the type of star/pulsations you plan to study. We’ve compiled a list here, with some references to help you choose.

A reminder of some of the terminology:

Linear: pulsations remain “small”, code calculates frequencies and eigenfunctions but cannot provide information about amplitude
Adiabatic: heating term in the perturbed energy equation can be neglected, code cannot provide information about the growth rates/stability of pulsation
Frozen convection approximation: an approximation that can be made to simplify nonadiabatic mode calculations, where the perturbations to the convective flux are neglected

Code	Linearity	Adibaticity	Notes	References
Adipls	linear	adiabatic	Similar to GYRE, perhaps less user friendly	ADIPLS
GYRE	linear	adiabatic & nonadiabatic	When doing nonadiabatic calculations GYRE uses the frozen convection approximation, can also calculate tidally force oscillations	GYRE intro, GYRE nonadiabatic method 1, GYRE nonadiabatic method 2, GYRE Tides
RSP-LNA	linear	nonadiabatic	Only does radial modes, restricted to homogeneous partially convective envelope, static model builder has limited range of convergence	RSP Method, Implementation in MESA
RSP Full	nonlinear	nonadiabatic	Only does radial modes, restricted to homogeneous partially convective envelope, static model builder has limited range of convergence	RSP Method, Implementation in MESA
TDC Pulsations (see lab 3)	nonlinear	nonadiabatic	Works for any envelope (or full stellar model) with additional evolutionary physics, significantly increased computation time	TDC Pulsations

RSP and TDC convection controls

RSP and MESA-star TDC use the same one-equation turbulent convection model. In this model, the turbulent kinetic energy $e_{t}$ evolves as

\frac{D e _{t}}{D t} + α_{p_{t}} P_{t} \frac{D ρ ^{- 1}}{D t} = ϵ_{q} + C - \frac{\partial L _{t}}{\partial m} .

The source/sink term and convective luminosity are

C = α e_{t}^{1/2} \frac{TPQ}{h 6} Y - α_{D} (\frac{8}{3} \frac{2}{3}) \frac{e _{t}^{3/2}}{α h} - \frac{48 σ γ _{r}}{α ^{2}} (\frac{T ^{3}}{ρ ^{2} c _{P} κ h ^{2}}) e_{t},

and

L_{conv} w = 4 π r^{2} α ρ c_{P} T \frac{w}{6} Y, = e_{t}^{1/2} .

RSP can also include a nonlocal turbulent-flux term,

L_{t} A = - A α α_{t} ρ h e_{t}^{1/2} \frac{\partial e _{t}}{\partial r}, = 4 π r^{2} .

The Lab 3 MESA-star TDC setup uses the same convection model in the local limit, without this nonlocal overshooting term.

Physical role	RSP control	MESA-star TDC control	Lab value
MESA label “mixing length”; $α$ in the convection terms	`RSP_alfa`	`mixing_length_alpha`	`1.77d0`
MESA label “convective flux”; scales $L_{conv}$	`RSP_alfac`	`TDC_alpha_C`	`1d0`
MESA label “turbulent source”; source term inside $C$	`RSP_alfas`	`TDC_alpha_S`	`1d0`
MESA label “turbulent dissipation”; cascade sink inside $C$	`RSP_alfad`	`TDC_alpha_D`	`1d0`
MESA label “turbulent pressure”; pressure-work term	`RSP_alfap`	`TDC_alpha_Pt`	`0d0`
MESA label “turbulent flux”; nonlocal overshoot term $L_{t}$	`RSP_alfat`	not used by local-limit MESA-star TDC	`0d0`
MESA label “eddy viscosity”; eddy viscous damping	`RSP_alfam`	`TDC_alpha_M`	`0.25d0`
MESA label “radiative losses”; radiative sink inside $C$	`RSP_gammar`	`TDC_alpha_R`	`0d0`

In the Lab 2 RSP-LNA setup, RSP_max_num_periods = 0 means RSP is only used for the linear analysis. In Lab 3, MESA-star TDC then follows the nonlinear finite amplitude pulsation with the corresponding TDC controls.

Outline Physics Concepts