🌠🔭 Assessing the Predictability of 𝛿 Scuti Variable Stars for Spacecraft Navigation

We assess the predictability of a large dataset of δ Scuti variable stars in detail. Few methods currently exist that can reliably determine the stability or predict the luminosity behavior of δ Scuti variable stars. To address this, we develop a computational framework to identify δ Scuti variable stars whose luminosity behavior can be accurately modeled as superpositions of sinusoidal functions. These predictive models provide a foundation for identifying δ Scuti variable stars suitable for use in practical applications such as autonomous deep-space navigation systems for spacecraft, which rely on such stars as navigational aid. This project provides the computational framework for modeling the light curves of δ Scuti variable stars outlined in the study.

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📂 Contents

• final_code_base.py

  This is the main script that contains all the methods used to model, assess and analyze the light curves of δ Scuti variable stars. It includes:

  • Algorithms to model light curves as superpositions of sinusodial functions
  • R²_LSP and epsilon time error analysis
  • Detrending of TESS light curves and model accuracy assessment
  • Plotting and interactive tools for light curves, target pixel files and periodograms

• Master_Data_Sets_FULL

  This directory contains the entire data set of analyzed δ Scuti variable stars, including:

  • Cleaned light curve datasets
  • Star metadata (e.g., KIC IDs, TIC IDs, pulsation modes, magnitudes in Kepler photometric band, etc.)
  • Outputs (e.g., fitted parameters, NRMSE, epsilon, etc.)

• Legacy_supporting_files

  Contains legacy and non-essential scripts, including:

  • Initial versions of the modeling code
  • Alternate modeling approaches
  • Additional plotting and visualization tools

  ⚠️ Files within Legacy_supporting_files may not be stable

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📧 Points of Contact

• Corresponding Author: Ahmed Khan ahmedk2@illinois.edu
• Institution: Department of Aerospace Engineering, University of Illinois at Urbana-Champaign
• Collaborators: Tiger Hou linyhi2@illinois.edu, Siegfried Eggl eggl@illinois.edu

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💻 Usage

• ✅ Actively Maintained – The package is current and stable for general use.
• 🚫 Not a Standalone Package – To run the scripts, clone the repository and run them directly within Python. We recommend using an Anaconda environment.
• ⚠️ Requires Manual Data Handling – Inputs will need to be directly inputed by the user.

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🚀 Quickstart

🔧 Prerequisites

Make sure the following are installed:

pip install numpy pandas matplotlib scipy lightkurve scipy astropy unpopular scienceplots astroquery 

▶️ Running the Code

From the root directory:

Run:

python final_code_base.py

🌌 Sample Usage

Here is an example of using the framework within final_code_base.py to model a δ Scuti variable star:

import re
import numpy as np
import matplotlib.pyplot as pt 
import lightkurve as lk 
from scipy.optimize import curve_fit
from scipy.signal import find_peaks, lfilter
from scipy.interpolate import interp1d
from scipy.spatial.distance import cdist
import pandas as pd
from scipy.optimize import minimize
from scipy.interpolate import interp1d
from astroquery.mast import Tesscut
from astroquery.mast.utils import parse_input_location
import unpopular
import scienceplots

# Corresponds to KIC 3429637
name_star = '3429637'

# Generate the predictive model
predictive_model_array, light_curve, predictive_model_string = getCompositeSine2_deep(name_star) 

# Plot the composite function, residuals and light curve
plotsidebyside_deep(name_star)

# Extract epsilon values
epsilon_array, standard_deviation, slope_fit, P_MAX = get_epsilon_value(name_star, predictive_model_string)

# Produce the R^2_LSP and spectral residual value between the light curve and the predictive model

spectral_residuals, R2_LSP = SpectralResiduals(name_star, predictive_model_string)

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📜 Background Documentation & Links

• [Gerald Handler; Delta Scuti Variables. AIP Conf. Proc. 16 September 2009; 1170 (1): 403–409.] (https://doi.org/10.1063/1.3246528)
• [Hou, L., Bansal, I., Davis, C., & Eggl, S. (2025). Position and Time Determination without Prior State Knowledge via Onboard Optical Observations of Delta Scuti Variable Stars. arXiv] (https://doi.org/10.48550/arXiv.2406.17609)

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📁 Summary of Files:

Files	Purpose
final_code_base.py	Core Modeling Framework
Master_Data_Sets_FULL/	Complete Datasets
Legacy_supporting_files/	Non-Essential, Legacy Scripts