Clarify A(x)/A(V) units in docs

[icweaver]

Closes #43

[codecov]

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Project coverage is 99.62%. Comparing base (2dad230) to head (a3e7c72).
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[cgarling]

I think this is A(lambda) / A_V as currently implemented. I like returning A(lambda) / A_V for consistency with other models.

Above equation 2 in Calzetti 2000 we have k_full = A(lambda) / E(B-V).

The k we define on lines 57 and 59 is only the polynomial portion of the full k term. The full term would be k_full = 2.659 * k + R_v (see their equation 4). By the above, we have k_full = A(lambda) / E(B-V) = 2.659 * k + R_v. Therefore, what we return on line 61 is 1.0 + 2.659 * k / law.Rv == k_full / law.RV == A(lambda) / E(B-V) / law.RV == A(lambda) / A(V).

[cgarling]

I see you have it labeled as A(x)/A(V) in the plot above so this might be the only place it needs to be changed?

[icweaver]

Sweet! Not a dust guy, so thank you for walking me through that, it was bugging me. Updating now

Out of curiosity, are we using E(B-V) and E_s(B-V) interchangeably here? The reason I ask is because there seems to be some kind of conversion between them in Eq. 3 which k_full depends on

[cgarling]

I am using them interchangeably for simplicity but they are not in general the same. Part of the complexity is that the Calzetti 2000 law is technically an attenuation law rather than an extinction law (see here) although this distinction is not often discussed. Because C00 is measuring extragalactic attenuation, they employ different methods to constrain the observational E(B-V) values than studies looking at extinction in the MW. The nebular emission line tracers they use to measure E(B-V) values for the galaxies are summarized in Table 1 but presented in earlier work. The E(B-V) values measured in these nebular regions are systematically higher than the galaxy-wide average value, which is the quantity they actually want for predicting the attenutation of the stellar continuum (this is what they call E_s(B-V)) -- in this case, they say that the stellar continuum color excess E_s(B-V)) is 44% of the nebular color excess.

I think our implementation is fine because the conversion between the two has to be made by the user after we've provided them with A(lambda) / A(V). In order to calculate a final attenuation in magnitudes A(lambda), a user must determine what A(V) is for their region, which requires assuming an E(B-V) and an RV. It is at this point that the definition of the color excess becomes relevant, which is after we have already calculated A(lambda) / A(V).

[icweaver]

Really interesting, thanks for taking the time to explain the distinction to me! That also clears up for me why Karl made both a dust_extinction and dust_attenuation package 😄

[cgarling]

Looks good to merge