Mid-Infrared Extinction Law in the Spitzer IRAC (3.6-8 μm) and MIPS 24 μm Photometric Bands:
A Summary of Recent Literature

Eric Mamajek (U. Rochester)

Last updated: 22 March 2010


For the purposes of modelling the spectral energy distributions of stars plus their debris disks, it is important to adopt an extinction curve that stretches into the infrared wavelength range. Optical and ultraviolet extinction curves have been discussed at length in classic reviews, however I have not found a brief review of the IR extinction curves given the recent photometric results from the Spitzer Space Telescope. Here I briefly survey the literature specifically on the measured extinction laws in the Spitzer photometric bands, ranging from IRAC-1 (3.6 μm) to the MIPS 24 μm band.

General Comment on Estimating RV, the Ratio of Reddening to Extinction at V-band

The ratio of reddening to extinction RV (= AV/E(B-V)) demonstrates real scatter along lines of sight in the Milky Way, ranging from RV ~ 2 to 5, with RV = 3.1 used as a commonly adopted mean value (e.g. Rieke & Lebofsky 1985, Mathis 1990). Cardelli, Clayton, & Mathis 1990 demonstrated that in the optical and infrared that multi-parameter fits to extinction curves could be parameterized by the single parameter R_V, and of course, wavelength. Mathis 1990 refers to dust with RV ~ 3.1 as "diffuse dust" and dust with larger values of RV (~5) as "outer-cloud dust". Whittet et al. 1988 found evidence for the formation of ice mantles on dust in regions with AV > 3.3, which leads to variations in the mid-IR extinction curve (specifically he measured the change in optical depth of the 3.1 μm O-H stretching mode from solid ice).

As extinction studies probe different environments (dense molecular clouds vs. diffuse interstellar medium), it is helpful to quantify which RV value is appropriate for your sample. Perhaps the most convenient way of quantifying RV using commonly available photometry is through the ratio of E(V-K) vs. E(B-V), that is:

RV = -0.26 + 1.19(E(V-K)/E(B-V)) [Equation (8) of Fitzpatrick & Massa 2007]

For a sample of all F0V stars in the Hipparcos catalog with Johnson BV photometry and 2MASS K_s photometry, I estimated the reddening slope to be E(V-Ks)/E(B-V) = 2.92+-0.09, I estimated a mean RV value of 3.29, similar to the commonly adopted value of 3.1.

Pre-Spitzer Extinction Laws in the 3.6-24 μm Range

The well-cited extinction law survey of Cardelli, Clayton, & Mathis 1990 specically only discussed extinction blueward of 3.5 μ.

Draine 1989 show that in both the Galaxy and Magellanic clouds, the extinction law between 0.7 and 7 μm goes as Aλ ∝ &lambdaβ (where β ~ 1.75), more specifically Aλ/E(J-K) = 2.4(λ/μm)-1.75 between 0.7 and 5 μm. More recently, Draine 2003 provided an updated review on published estimates of the power-law index β. The median β index from among 7 studies is β ≈ 1.7.

Mathis 1990 tabulated an extinction law table with Aλ/AJ where the assumed J-band effective wavelength is 1.25 μms (their Table 1). They list AJ/A0.55 μ = AJ/AV = 1/3.55 = 0.282 for RV = 3.1 ("diffuse dust"), and AJ/AV = 1/3.06 = 0.327 for RV = 5.0 ("outer-cloud dust").

Cohen et al. 1982 reports AL/AV = 0.050+-0.010, where L band is on the CIT photometric system.

Rieke & Lebofsky 1985 tabulate Aλ/AV values from U-band through 13.0 μm (at bands corresponding to the Arizona-Johnson system), most relevantly to this discussion with AJ/AV = 0.282, AH/AV = 0.175, AK/AV = 0.112, AL/AV = 0.058, AM/AV = 0.023, and A8μm/AV = 0.020 +- 0.003.

Extinction Laws Measured in Spitzer Surveys in the 3.6-24 μm Range

I will briefly review the major Spitzer extinction studies that I have found in the literature.

Flaherty et al. 2007 (F07) report estimates of the IR extinction law in the Spitzer IRAC bands and MIPS 24 μm band towards the nearby Ori A, NGC 2068/2071, NGC 2024/2023, Serpens, and Ophiuchus star-formation regions. Hence their extinction curves may be representative of lines-of-sight through dense, local interstellar medium within <0.5 kpc. Their individual measurements of Aλ/AKs for the five star-forming clouds are listed in Table 3 of Flaherty et al. 2007. The values are very consistent with one another, with the exception of Ophiuchus. Below I list only the median values from among the 5 regions (and two regions for A[24μm]/AKs, namely Serpens and NGC 2068/2071).
EH-Ks/EKs-[3.6μm]1.49 F07 median (N=5)
EH-Ks/EKs-[4.5μm]1.17 F07 median (N=5)
EH-Ks/EKs-[5.8μm]1.08 F07 median (N=5)
EH-Ks/EKs-[8.0μm]1.07 F07 median (N=5)
AH/AKs 1.55 F07 adopted

Indebetouw et al. 2005 (I05) reports extinction law data for two line of sights in the Galactic plane towards l = 42 deg and 284 deg (towards an "relative quiescent and unremarkable region" and the other including the H II region RCW 49 H II). I05 fit the average Aλ/AK curve for their regions over λ = 1.25 to 7.75 μm as:

log(Aλ/AK) = 0.61(±0.04) - 2.22(±0.17)log λ + 1.21(±0.23)[log λ]2

E[3.6μm]-K/EJ-K -0.30 ± 0.01 I05 average (N=3)
E[4.5μm]-K/EJ-K -0.37 ± 0.02 I05 average (N=3)
E[5.8μm]-K/EJ-K -0.38 ± 0.04 I05 average (N=3)
E[8.0μm]-K/EJ-K -0.37 ± 0.04 I05 average (N=3)
AKs/AV 1/8.8 adopted for RV = 3.1 (from Cardelli et al. 1989)
AKs/AV 1/7.5 adopted for RV = 5 (from Cardelli et al. 1989)

Chapman et al. 2009 (C09) examined the extinction curve in the IRAC 3.6 through 8 μm bands, MIPS 24 μm, plus near JHKs bands, in the Ophiuchus, Perseus, and Serpens regions (dense molecular cloud regions within 300 pc). They find that Aλ/AKs varies as a function of AKs. As with Flaherty et al. 2007, they find that none of their comparison models accounts for the large A24μm/AKs values (~1) observed in the diffuse ISM (AKs < 0.5).

Rel. Extinction F07 C09 C09 C09 C09 I05
AKs<0.50.5 < AKs < 1 1 < AKs < 2 AKs > 2
A[3.6μm]/AKs0.632 0.41 ± 0.190.49 ± 0.10 0.60 ± 0.05 0.64 ± 0.03 0.56 ± 0.06
A[4.5μm]/AKs0.53 0.26 ± 0.180.35 ± 0.10 0.46 ± 0.05 0.53 ± 0.03 0.43 ± 0.08
A[5.8μm]/AKs0.49 0.28 ± 0.180.35 ± 0.10 0.44 ± 0.05 0.46 ± 0.03 0.43 ± 0.10
A[8.0μm]/AKs0.49 0.21 ± 0.170.35 ± 0.10 0.43 ± 0.05 0.45 ± 0.03 0.43 ± 0.10
A[24μm]/AKs 0.48 1.08 ± 0.320.75 ± 0.14 0.61 ± 0.08 0.34 ± 0.13
AH/AKs 1.55 1.55 ± 0.08
AJ/AKs 2.5 ± 0.2