Dust Extinction

JAX-bandflux includes support for Milky Way dust extinction models that can be applied to supernova spectra. Three standard extinction laws are implemented: CCM89, O’Donnell 1994, and Fitzpatrick 1999.

Available Dust Laws

The following dust extinction laws are available:

CCM89 (dust_type=0): Cardelli, Clayton & Mathis (1989) - Standard Galactic extinction law
OD94 (dust_type=1): O’Donnell (1994) - Improved UV extinction
F99 (dust_type=2): Fitzpatrick (1999) - More flexible parameterization

Basic Usage

To apply dust extinction to SALT3 model calculations, add dust parameters to your model parameters dictionary:

import jax.numpy as jnp
import jax_supernovae as js

# Load data for a supernova
times, fluxes, fluxerrs, zps, band_indices, unique_bands, bridges, fixed_z = js.data.load_and_process_data('19dwz')

# Define SALT3 parameters with dust extinction
params = {
    'z': fixed_z[0],
    't0': 58650.0,
    'x0': 1e-5,
    'x1': 0.0,
    'c': 0.0,
    # Dust parameters
    'dust_type': 0,  # CCM89 law
    'ebv': 0.1,      # E(B-V) reddening
    'r_v': 3.1       # Total-to-selective extinction ratio
}

# Calculate model fluxes with dust extinction applied
model_fluxes = js.salt3.optimized_salt3_multiband_flux(times, bridges, params, zps=zps, zpsys='ab')
model_fluxes = model_fluxes[jnp.arange(len(times)), band_indices]

Comparing Dust Laws

Different dust laws produce different extinction curves, particularly in the UV:

import jax.numpy as jnp
from jax_supernovae import dust
import matplotlib.pyplot as plt

# Define wavelength grid
wave = jnp.linspace(2000, 10000, 500)
ebv = 0.1
r_v = 3.1

# Calculate extinction for each law
ext_ccm89 = dust.ccm89_extinction(wave, ebv, r_v)
ext_od94 = dust.od94_extinction(wave, ebv, r_v)
ext_f99 = dust.f99_extinction(wave, ebv, r_v)

# Plot extinction curves
plt.figure(figsize=(10, 6))
plt.plot(wave, ext_ccm89, label='CCM89')
plt.plot(wave, ext_od94, label='OD94')
plt.plot(wave, ext_f99, label='F99')
plt.xlabel('Wavelength (Å)')
plt.ylabel('A(λ) (mag)')
plt.legend()
plt.title(f'Dust Extinction Laws (E(B-V)={ebv}, R_V={r_v})')
plt.show()

Effect on Light Curves

Dust extinction affects blue bands more than red bands, changing both the color and amplitude of light curves:

import jax.numpy as jnp
import jax_supernovae as js

# Parameters without dust
params_nodust = {'z': 0.1, 't0': 0.0, 'x0': 1e-5, 'x1': 0.0, 'c': 0.0}

# Parameters with moderate dust
params_dust = params_nodust.copy()
params_dust.update({'dust_type': 0, 'ebv': 0.2, 'r_v': 3.1})

# Calculate fluxes for comparison
phases = jnp.linspace(-20, 50, 100)

# Using a blue bandpass (more affected)
flux_nodust_blue = js.salt3.salt3_bandflux(phases, blue_bandpass, params_nodust)
flux_dust_blue = js.salt3.salt3_bandflux(phases, blue_bandpass, params_dust)

# Using a red bandpass (less affected)
flux_nodust_red = js.salt3.salt3_bandflux(phases, red_bandpass, params_nodust)
flux_dust_red = js.salt3.salt3_bandflux(phases, red_bandpass, params_dust)

# Dust reduces flux more in blue than red
blue_reduction = flux_dust_blue / flux_nodust_blue  # ~0.6 for E(B-V)=0.2
red_reduction = flux_dust_red / flux_nodust_red     # ~0.8 for E(B-V)=0.2

Parameter Reference

Dust Extinction Parameters
Parameter	Type/Range	Description
`dust_type`	int (0, 1, 2)	Dust law selection: 0=CCM89, 1=OD94, 2=F99
`ebv`	float (≥0)	E(B-V) color excess in magnitudes
`r_v`	float (typically 2-5)	Ratio of total to selective extinction (default: 3.1)

Notes

Dust extinction is applied to the rest-frame SED before redshifting
The implementation matches sncosmo extinction laws for consistency
All dust laws are JIT-compiled for performance
Gradients flow through dust parameters for optimization