Fourier models or any other simple model incl. piece-wise anything are meant to model the shape of the light curve of pulsating variable stars only. Sometimes used to generate time-of-maximum for O-C curve generation to monitor for stellar evolution through the H-R diagram instability region. Logical to use Fourier if nothing else as RR Lyr stars are pulsators of a type of harmonic, periodic non-linear oscillation.
If you want to model real physical processes doing a search using basic Google AI 
gives:
To generate an RR Lyrae light curve from real physical processes rather than empirical mathematical curves, astrophysicists use Non-linear Radiative Hydrodynamic (RHD) Stellar Pulsation Models.
Instead of treating the star as a collection of arbitrary sine waves, these models treat the star as a 3D or 1D physical sphere of gas governed by the fundamental laws of thermodynamics, gravity, and fluid dynamics.
1. The Core Physical Processes Simulated
To generate a true physical light curve, a computer program must model three main coupled physical mechanisms acting simultaneously on the star’s layers:
[ Gravity pulling inward ] <===> [ Gas & Radiation Pressure pushing outward ]
▲
│ (Regulated by)
[ Kappa Mechanism ]
- The Thermodynamic Driving Engine (The $\kappa$-Mechanism): This is the physical “valve” that powers the pulsation. In the ionization zones of Helium (He II to He III), compressing the gas makes it more opaque ($\kappa$ increases) rather than hotter and more transparent. This traps radiation from the core, building up immense pressure.
- Non-linear Hydrodynamics: Once the pressure builds up, the layer explodes outward. As it expands, it cools, becomes transparent, releases the trapped radiation (causing the steep rise in the light curve), and gravity pulls the layer back down to compress and restart the loop.
- Time-Dependent Convection: Energy doesn’t just radiate; it moves via boiling gas currents (convection). Modern physical models must simulate how turbulent convection interacts with the expanding and contracting shockwaves.
2. The Governing Equations of a Real Physical Model
A physical code solves a system of partial differential equations for dozens of concentric spherical shells (“zones”) across the star. For a shell at radius $r$ with mass coordinate $M_r$, density $\rho$, pressure $P$, velocity $v$, and luminosity $L$, the core equations are:
$$\text{Conservation of Mass (Continuity):} \quad \frac{\partial r}{\partial M_r} = \frac{1}{4\pi r^2 \rho}$$
$$\text{Conservation of Momentum (Equation of Motion):} \quad \frac{\partial v}{\partial t} = -4\pi r^2 \frac{\partial (P + Q)}{\partial M_r} - \frac{GM_r}{r^2}$$
$$\text{Conservation of Energy:} \quad \frac{\partial E}{\partial t} + P \frac{\partial (1/\rho)}{\partial t} = -\frac{\partial L}{\partial M_r}$$
- (Note: $Q$ is the artificial viscosity used to handle physical shockwaves traveling through the stellar atmosphere, and $E$ is internal energy).
3. Industry-Standard Physical Software Packages
Astronomers do not use Fourier series to create these; they run heavy structural software packages to let the physical equations evolve over time. The most widely used codes include:
- MESA (Modules for Experiments in Stellar Astrophysics): The modern global open-source standard. MESA includes a dedicated RSP (Radial Stellar Pulsation) module. You input basic physical parameters—Mass ($M$), Luminosity ($L$), Effective Temperature ($T_{\rm eff}$), and Metallicity ($Z$)—and MESA physically simulates the pulsations over time, naturally outputting a raw, physical light curve.
- The Warsaw Nonlinear Pulsation Code: Developed by Smolec and Moskalik, this hydrodynamical code is specifically optimized for classical pulsators like Cepheids and RR Lyrae to study non-linear behaviors, mode selections, and period changes.
- The Florida-Budapest Hydro Code: A foundational code used extensively to model the highly non-linear shock waves that propagate through RR Lyrae atmospheres during their rapid expansion phase.
Comparison: Physical Model vs. Fourier Model
| Metric / Attribute |
Real Physical Model (e.g., MESA RSP) |
Fourier Model |
| Inputs |
Mass ($M$), Radius ($R$), Temperature ($T$), Composition ($X,Y,Z$) |
Amplitude ($A_k$), Phase ($\phi_k$), Period ($P$) |
| Underlying Math |
Partial Differential Equations (Hydrodynamics) |
Trigonometric Polynomials |
| Predictive Power |
High. Explains why the star pulsates and changes. |
Low. It only describes what the light curve looks like. |
| Computational Cost |
High (Minutes to hours of CPU time per star) |
Extremely Low (Milliseconds of CPU time) |
If you want to explore running or understanding these models, let me know:
- Would you like to walk through how to configure the physical inputs (Mass, Temperature, Metallicity) in a simulation code like MESA RSP?
- Are you interested in how physical shockwaves in the star’s atmosphere create the specific asymmetric features seen on the final light curve?
To generate an RR Lyrae light curve from real physical processes rather than empirical mathematical curves, astrophysicists use Non-linear Radiative Hydrodynamic (RHD) Stellar Pulsation Models.
Instead of treating the star as a collection of arbitrary sine waves, these models treat the star as a 3D or 1D physical sphere of gas governed by the fundamental laws of thermodynamics, gravity, and fluid dynamics.
1. The Core Physical Processes Simulated
To generate a true physical light curve, a computer program must model three main coupled physical mechanisms acting simultaneously on the star’s layers:
[ Gravity pulling inward ] <===> [ Gas & Radiation Pressure pushing outward ]
▲
│ (Regulated by)
[ Kappa Mechanism ]
- The Thermodynamic Driving Engine (The $\kappa$-Mechanism): This is the physical “valve” that powers the pulsation. In the ionization zones of Helium (He II to He III), compressing the gas makes it more opaque ($\kappa$ increases) rather than hotter and more transparent. This traps radiation from the core, building up immense pressure.
- Non-linear Hydrodynamics: Once the pressure builds up, the layer explodes outward. As it expands, it cools, becomes transparent, releases the trapped radiation (causing the steep rise in the light curve), and gravity pulls the layer back down to compress and restart the loop.
- Time-Dependent Convection: Energy doesn’t just radiate; it moves via boiling gas currents (convection). Modern physical models must simulate how turbulent convection interacts with the expanding and contracting shockwaves.
2. The Governing Equations of a Real Physical Model
A physical code solves a system of partial differential equations for dozens of concentric spherical shells (“zones”) across the star. For a shell at radius $r$ with mass coordinate $M_r$, density $\rho$, pressure $P$, velocity $v$, and luminosity $L$, the core equations are:
$$\text{Conservation of Mass (Continuity):} \quad \frac{\partial r}{\partial M_r} = \frac{1}{4\pi r^2 \rho}$$
$$\text{Conservation of Momentum (Equation of Motion):} \quad \frac{\partial v}{\partial t} = -4\pi r^2 \frac{\partial (P + Q)}{\partial M_r} - \frac{GM_r}{r^2}$$
$$\text{Conservation of Energy:} \quad \frac{\partial E}{\partial t} + P \frac{\partial (1/\rho)}{\partial t} = -\frac{\partial L}{\partial M_r}$$
- (Note: $Q$ is the artificial viscosity used to handle physical shockwaves traveling through the stellar atmosphere, and $E$ is internal energy).
3. Industry-Standard Physical Software Packages
Astronomers do not use Fourier series to create these; they run heavy structural software packages to let the physical equations evolve over time. The most widely used codes include:
- MESA (Modules for Experiments in Stellar Astrophysics): The modern global open-source standard. MESA includes a dedicated RSP (Radial Stellar Pulsation) module. You input basic physical parameters—Mass ($M$), Luminosity ($L$), Effective Temperature ($T_{\rm eff}$), and Metallicity ($Z$)—and MESA physically simulates the pulsations over time, naturally outputting a raw, physical light curve.
- The Warsaw Nonlinear Pulsation Code: Developed by Smolec and Moskalik, this hydrodynamical code is specifically optimized for classical pulsators like Cepheids and RR Lyrae to study non-linear behaviors, mode selections, and period changes.
- The Florida-Budapest Hydro Code: A foundational code used extensively to model the highly non-linear shock waves that propagate through RR Lyrae atmospheres during their rapid expansion phase.
Comparison: Physical Model vs. Fourier Model
| Metric / Attribute |
Real Physical Model (e.g., MESA RSP) |
Fourier Model |
| Inputs |
Mass ($M$), Radius ($R$), Temperature ($T$), Composition ($X,Y,Z$) |
Amplitude ($A_k$), Phase ($\phi_k$), Period ($P$) |
| Underlying Math |
Partial Differential Equations (Hydrodynamics) |
Trigonometric Polynomials |
| Predictive Power |
High. Explains why the star pulsates and changes. |
Low. It only describes what the light curve looks like. |
| Computational Cost |
High (Minutes to hours of CPU time per star) |
Extremely Low (Milliseconds of CPU time) |
If you want to explore running or understanding these models, let me know:
- Would you like to walk through how to configure the physical inputs (Mass, Temperature, Metallicity) in a simulation code like MESA RSP?
- Are you interested in how physical shockwaves in the star’s atmosphere create the specific asymmetric features seen on the final light curve?
I guess it depends on what you want to do. That AAVSO spectroscopy data being collected may be useful in providing some of the inputs for a physical model fit to an observed light curve. A paper in the future for someone to do and something to do in our spare time! 
gives: