4.1.16. Ebv: Galactic interstellar extinction model

This model can be used to correct fluxes of optical/UV data for interstellar reddening in our Galaxy. The reddening is caused by dust absorption and scattering (extinction) in the interstellar medium.

There are two different models used, indicated by the parameter mode

For mode=1 or 2, the model uses the extinction curve of Cardelli et al. (1989). including the update for near-UV given by O’Donnell et al. (1994).

For mode=3, the model uses the SMC extinction curve of Gordon et al. (2003).

The extinction law can be expressed as:

({A_\lambda }/{A_V}) = {a_\lambda } + ({b_\lambda }/{R_V})

where, A_\lambda and A_V are the total extinctions (measured in magnitude) at wavelength \lambda and the V-band, respectively. The wavelength- dependent parameters a_\lambda and b_\lambda are provided by the aforementioned papers. The scalar R_V is defined as the ratio of total extinction A_V to selective extinction {A_{B} - A_{V}}, where A_B is the total extinction at the B-band. So the selective extinction {A_{B} - A_{V}} represents a colour excess, which is commonly denoted as {E(B-V)}. For the Milky Way, the typical value for R_V is reported to be 3.1. Thus, by specifying E(B-V) and R_V, the extinction A_\lambda can be derived, which in turn gives us the unreddened flux (F_\lambda) from the observed reddened flux (F_{\lambda}^*) using F_\lambda = (10^{\,0.4 A_\lambda})\, F_{\lambda}^*. Note that at energies above the Lyman limit, the transmission of the model is set to 1 in SPEX, thus it can be used alongside the Galactic interstellar X-ray absorption models in SPEX.

These parameterisations are in particular derived for the optical-UV band. The model can formally be used also at longer wavelengths; we have secured that the transmission does not rise above 1 at long wavelengths, which for some parameter settings may occur. Note however that for an accurate IR extinction model (inclusive silicate features etc.) other models are needed which are not (yet) included in SPEX.

The extinction model of Cardelli et al. is currently the best model for the Milky Way. However, the extinction curve of the Milky Way has a famous broad bump at 2175 \mathrm{\AA}. The origin of this bump is still not fully understood. Interestingly, this feature (due to dust) is seen in the Milky Way and not in other galaxies like in AGN. If one would use the ebv model to correct for extinction in the host galaxy of an AGN, it is best to remove this bump from the model as it can have an effect on the fit to the data. The bump can be removed by setting the model parameter to 2; alternatively, the Gordon et al. SMC model can be used.

The parameters of the model are:

ebv:

The colour excess E(B-V). The value is set by the user.

rv:

The scalar R_{V}. Default (recommended) value: 3.1

icov:

Type of the covering fraction. Default value: 2 (constant,set by fcov). If icov=1, full covering is applied. If icov=3, covering fraction follows a tangent function that increases with energy. If icov=4, covering fraction follows an inverse tangent function that decreases with energy. See description in pion.

fcov:

The covering factor of the absorber if icov=2. Default value: 1 (full covering). If icov=3 or 4, it sets the covering factor at the high energy end.

lcov:

The covering factor of the absorber at the low energy end. Default value: 1. lcov is applied only when icov=3 or 4. See description in pion.

ecov:

The energy when the covering factor changes from lcov to fcov. Only applied if icov=3 or 4.

acov:

The width of the transit on covering factor. Only applied if icov=3 or 4.

mode:

1: Cardelli et al. model with bump (default); 2: Cardelli et al. model without bump; 3: Gordon et al. SMC model. It is suggested to use R_V = 4 for this last case.

Recommended citation: Cardelli et al. (1989) and O’Donnell et al. (1994) for mode=1 and 2, and <https://ui.adsabs.harvard.edu/abs/2003ApJ…594..279G/abstract>`_ for mode=3