📙 Reddening Coefficients
After obtaining E(B−V), one can correct the observed color index for reddening ((B−V)0 = (B−V)obs − E(B−V)) to recover the star’s intrinsic color. However, E(B−V) only provides the color excess relative to B−V. To perform corrections in other photometric bands (such as G, J, V) and color indices (such as BP−RP, V−K), it is necessary to know the ratio between the extinction in that band and E(B−V) — this ratio is known as the reddening coefficient.
Heads-up
Corrections on magnitudes are usually called extinction corrections; corrections on colors are reddening corrections.
Formulas:
\[ m_{\lambda,0} = m_{\lambda,\mathrm{obs}} - A_\lambda = m_{\lambda,\mathrm{obs}} - R_\lambda\,E(B-V) \]
\[ (a-b)_0 = (a-b)_{\mathrm{obs}} - E(a-b) = (a-b)_{\mathrm{obs}} - R_{(a-b)}\,E(B-V) \]
where \(R_\lambda\) / \(R_{(a-b)}\) is the reddening coefficient for the band or color.
📙 Recommended sources: Zhang et al. (2024) [broadly applicable] / Zhang et al. (2023) [narrower range, higher precision]
Zhang et al. (2024)
Using Gaia DR3 XP spectra and LAMOST DR7 for about five million cross-matched sources, a direct measurement of the Milky Way extinction curve was made via stellar pair technique; about 370k high-quality spectra were used to construct a median Galactic extinction curve.
You can use the median curve from Zhang et al. (2024) here to quickly estimate either a band extinction or a color reddening:
- Select Extinction correction or Reddening correction.
- Pick the band(s) or color.
- Enter E(B−V) and \(T_{\rm eff}\).
The system returns [\(R_\lambda\) and \(A_\lambda\)] or [\(R(a-b)\) and \(E(a-b)\)] based on the 2024 median extinction curve.
Quick coefficient estimate
If you only need a reasonable average coefficient for preliminary work, use typical values:
- E(B−V) = 0.3 mag (median for stars with Gaia XP spectra)
- Teff = 5500 K (solar-type)
For high-precision work, compute per-source with the actual \(E(B-V)\) and \(T_{\rm eff}\).
For broader band coverage (the 2024 paper supports arbitrary filter curves via uploads) or batch calculations, see Zhang et al. (2024), ApJ, 972, 207 and the accompanying XP_Extinction_Toolkit.
Zhang et al. (2023)
The estimates in Zhang et al. (2024) combine BOSZ spectral library, filter throughput, and measured extinction curves; pure empirical results may differ slightly. When computing extinction/reddening in GALEX, PS1, SDSS, Gaia, 2MASS, and WISE, and when E(B−V) ∈ [0, 0.5] mag and Teff ∈ [4000, 10000] K, we recommend the empirical package from Zhang et al. (2023): extinction_coefficient.
Zhang et al. (2023), ApJS, 264, 14 does not support custom throughput curves. If your system is supported and the target \(E(B-V)\) and \(T_{\rm eff}\) fall within 0–0.5 mag and 4000–10000 K, this empirical set is recommended for quick corrections.
Important note
The 2023 coefficients are tied to the SFD map. If your E(B−V) comes from this 3D dust map, multiply by 1/0.834 before feeding it into the extinction_coefficient package to correct the systematic difference with SFD (see Wang et al. 2025, Fig. 17).