Usage Guide#

Overview#

SAJAX computes light curves that include stellar contamination from active regions (spots and faculae). It takes stellar spectra, active region properties, and rotation parameters to produce wavelength-dependent light curves.

Basic Workflow#

Define spectra — provide quiet star and active region flux as functions of wavelength
Set stellar parameters — inclination, rotation velocity, limb-darkening
Define active regions — spot/faculae positions, sizes, and temperatures
Compute light curve — SAJAX returns flux as a function of rotational phase

Key Inputs#

Parameter	Description	Example
`wavelength`	Wavelength grid [μm]	`np.linspace(0.3, 5.0, 200)`
`flux_quiet`	Quiet star spectrum	Model atmosphere or measured spectrum
`flux_active`	Active region spectrum	Cooler (dimmer) or hotter (brighter) than quiet star
`ar_lat`, `ar_long`	Active region latitude/longitude [deg]	`[20.0]`, `[0.0]`
`ar_size`	Angular radius of active region [deg]	`[10.0]`
`phases_rot`	Rotation phases [deg]	`np.linspace(0, 360, 50)`
`inc_star`	Stellar inclination [deg]	`90.0` (equator-on)
`ldc_mode`	Limb-darkening law or intensity Profile	`"quadratic"`, `"nonlinear4"`, etc. or `"intensity_profile"`

Key Outputs#

Output	Shape	Description
`lc`	`(n_phases,)`	Broadband light curve (integrated over wavelength)
`epsilon`	`(n_phases, n_wavelengths)`	Contamination factor ε — how much active region contaminates each phase/wavelength
`star_maps`	`(n_phases, n_px, n_px)`	2D intensity maps of the star at each phase

What is Contamination?#

The contamination factor ε quantifies the flux deficit due to active regions:

\[\text{observed flux} = \text{true flux} \times (1 - \varepsilon)\]

Key insights:

ε = 0 → no contamination (quiet star)
ε > 0 → dimmer observed flux (active regions crossing disk)
ε wavelength-dependent → different limb-darkening at different wavelengths
ε phase-dependent → changes as star rotates

Limb-Darkening Modes#

SAJAX supports multiple limb-darkening laws:

linear — 1 coefficient
quadratic — 2 coefficients (most common)
power2, kipping3 — alternative parameterizations
nonlinear4 — 4-coefficient law
intensity_profile — full I(μ) profile

Common Use Cases#

Case 1: Single active region#

import numpy as np
from sajax import compute_light_curve

# Wavelength grid (e.g. in microns)
wavelength  = np.linspace(0.3, 5.0, 200)

# Flat spectra as a minimal example — replace with model atmospheres
flux_quiet    = np.ones_like(wavelength)
flux_active   = np.ones_like(wavelength) * 0.7   # active region is 30% dimmer

params = dict(
    u1          = 0.3,      # quadratic LD coefficient
    u2          = 0.1,
    inc_star    = 90.0,     # stellar inclination [deg]  (equator-on)
)

result = compute_light_curve(
    wavelength         = wavelength,
    flux_quiet         = flux_quiet,
    flux_active        = flux_active,
    params             = params,
    ar_lat             = [20.0],           # one active region at 20° latitude
    ar_long            = [0.0],
    ar_size            = [10.0],           # angular radius [deg]
    phases_rot         = np.linspace(0, 360, 50, endpoint=False),
    stellar_grid_size  = 100,             # stellar radius in pixels
    ve                 = 2.0,              # equatorial velocity [km/s]
    ldc_mode           = "Quadratic",      #treatment of limb darkening
    plot_map_wavelength= 1.0,
)

print(result["lc"])          # (50,)      broadband light curve
print(result["epsilon"])     # (50, 200)  contamination factor per phase/wavelength
print(result["star_maps"])   # (50, n, n) stellar flux maps

Case 2: Multiple active regions#

Replace

    ar_lat             = [20.0],           # one active region at 20° latitude
    ar_long            = [0.0],
    ar_size            = [10.0],           # angular radius [deg]

in the previous code, with

    ar_lat             = [20.0, -45.0],          # two active regions at 20° and -45° latitude
    ar_long            = [0.0, 15.0],
    ar_size            = [10.0, 5.0],           # angular radius [deg]

Next Steps#

📓 View the Interactive Tutorial — See a full working example with plots and live outputs
💾 Explore Examples Directory — Check out additional use cases and advanced examples in the GitHub repository
📚 Read the API Reference — Learn about all available functions, classes, and parameters

Usage Guide

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