Variable Stars Simulations

Overview

This module simulates multiband variable-star light curves in g/r/i by sampling empirical templates, phase-folding the input observation times, and interpolating the template in each band. A single magnitude offset is applied to all bands so that the simulated light curves preserve the template’s intrinsic colors while matching a desired mean magnitude in a chosen reference band.

The RR Lyrae template set used here is from BaezaVillagra et al 2025.

Quick start

The main function is simulate_rrlyae(). It returns a dict mapping each band to simulated magnitudes evaluated at the provided observation times.

import numpy as np
import matplotlib.pyplot as plt
from MicroLIA_Sim.variable_stars import simulate_rrlyae

rng = np.random.default_rng(1909)

# Example observation times (days; e.g., MJD)
t_g = 7000.0 + np.sort(rng.uniform(0, 365, size=500))
t_r = 7000.0 + np.sort(rng.uniform(0, 365, size=500))
t_i = 7000.0 + np.sort(rng.uniform(0, 365, size=500))

times = {"g": t_g, "r": t_r, "i": t_i}

mags = simulate_rrlyae(
    times=times,
    bailey=1, # 1=RRab, 2=RRc, 3=Cepheid-like
    period=None, # days; if set, bailey is ignored
    reference_band="i",
    reference_mean_mag=18.0,
    rng=rng, # controls random phase zero-point (T0) and template
)

plt.plot(t_g, mags["g"], "go", label="g")
plt.plot(t_r, mags["r"], "r*", label="r")
plt.plot(t_i, mags["i"], "k.", label="i")
plt.gca().invert_yaxis()
plt.legend()
plt.show()

Bailey-type priors

If period is not provided:

bailey == 1 (RRab): $P \sim \mathcal{N}(0.6, 0.15)$ days
bailey == 2 (RRc): $P \sim \mathcal{N}(0.33, 0.10)$ days
bailey == 3 (Cepheid-like): $P = 10^{X}$ , where $X \sim \mathrm{LogNormal}(0.0, 0.2)$

Note

In the current implementation, bailey == 3 uses the RRc templates and is thus intended as an approximation.

Reproducibility

There are two random elements, the template selection and the phase zero-point. Passing a seeded rng makes these reproducible.