Lifting the Dusty Veil II: A Large-Scale Study of the Galactic Infrared Extinction Law

Abstract

We combine near-infrared (2MASS) and mid-infrared (Spitzer-IRAC) photometry to characterize the IR extinction law (1.2-8 microns) over nearly 150 degrees of contiguous Milky Way midplane longitude. The relative extinctions in 5 passbands across these wavelength and longitude ranges are derived by calculating color excess ratios for G and K giant red clump stars in contiguous midplane regions and deriving the wavelength dependence of extinction in each one. Strong, monotonic variations in the extinction law shape are found as a function of angle from the Galactic center, symmetric on either side of it. These longitudinal variations persist even when dense interstellar regions, known a priori to have a shallower extinction curve, are removed. The increasingly steep extinction curves towards the outer Galaxy indicate a steady decrease in the absolute-to-selective extinction ratio (R_V) and in the mean dust grain size at greater Galactocentric angles. We note an increasing strength of the 8 micron extinction inflection at high Galactocentric angles and, using theoretical dust models, show that this behavior is consistent with the trend in R_V. Along several lines of sight where the solution is most feasible, A_lambda/A_Ks as a function of Galactic radius is estimated and shown to have a Galactic radial dependence. Our analyses suggest that the observed relationship between extinction curve shape and Galactic longitude is due to an intrinsic dependence of the extinction law on Galactocentric radius. Comment: Accepted to ApJ

Full text

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arXiv:0910.4403v1 [astro-ph.GA] 22 Oct 2009
ApJ
Preprint typeset using LATEX style emulateapj v. 08/22/09
LIFTING THE DUSTY VEIL II:
A LARGE-SCALE STUDY OF THE GALACTIC INFRARED EXTINCTION LAW
G. Zasowski1, S. R. Majewski1, R. Indebetouw1, M. R. Meade2, D. L. Nidever1,
R. J. Patterson1, B. Babler2, M. F. Skrutskie1, C. Watson3, B. A. Whitney2,4, E. Churchwell2
Accepted to ApJ
ABSTRACT
We combine near-infrared (2MASS) and mid-infrared (Spitzer-IRAC) photometry to characterize
the IR extinction law (1.2-8 µm) over nearly 150◦of contiguous Milky Way midplane longitude.
The relative extinctions in 5 passbands across these wavelength and longitude ranges are derived by
calculating color excess ratios for G and K giant red clump stars in contiguous midplane regions and
deriving the wavelength dependence of extinction in each one. Strong, monotonic variations in the
extinction law shape are found as a function of angle from the Galactic center, symmetric on either side
of it. These longitudinal variations persist even when dense interstellar regions, known a priori to have
a shallower extinction curve, are removed. The increasingly steep extinction curves towards the outer
Galaxy indicate a steady decrease in the absolute-to-selective extinction ratio (RV) and in the mean
dust grain size at greater Galactocentric angles. We note an increasing strength of the 8 µm extinction
inflection at high Galactocentric angles and, using theoretical dust models, show that this behavior
is consistent with the trend in RV. Along several lines of sight where the solution is most feasible,
Aλ/AKs as a function of Galactic radius (RGC) is estimated and shown to have a Galactic radial
dependence. Our analyses suggest that the observed relationship between extinction curve shape and
Galactic longitude is due to an intrinsic dependence of the extinction law on Galactocentric radius.
Subject headings: dust, extinction — Galaxy: disk — infrared: ISM
1. INTRODUCTION
Interstellar extinction presents one of the longest-
standing challenges to observational astronomy. Exten-
sive work has been done to understand the complex and
highly-variable ultraviolet and optical portions of the ex-
tinction curve (see, e.g., reviews by Mathis 1990 and
Whittet 2003); only recently, however, has comprehen-
sive characterization of the infrared (IR) extinction law
become possible, through the influx of near- and mid-
infrared (NIR, MIR) data provided by large-area surveys
like 2MASS, UKIDSS, and GLIMPSE I/II/3D. Not only
does this characterization enable more accurate study of
sources extinguished by dust, but reliable derivation of
the wavelength-dependent IR extinction behavior also fa-
cilitates identification and modeling of the physical prop-
erties (e.g., chemical composition, grain size, crystalliza-
tion fraction) of the interstellar dust itself.
Many dust absorption studies to date have converged
to a treatment of the infrared extinction law in the dif-
fuse interstellar medium (ISM) as nearly constant and
universal. The NIR extinction curve (λ ? 1–4 µm) is of-
ten modeled as a power law (Aλ∝ λ−β), with β ranging
between 1.6 and 1.8 (e.g., Rieke & Lebofsky 1985; Draine
2003, and references therein), but values up to 2 have
1Department of Astronomy, University of Virginia, PO Box
400325, Charlottesville, VA 22904-4325:
srm4n@virginia.edu,remy@virginia.edu,
rjp0i@virginia.edu, mfs4n@virginia.edu
2DepartmentofAstronomy,
sin atMadison, 475North
53706:meade@astro.wisc.edu,
ney@spacescience.org, ebc@astro.wisc.edu
3Manchester College, North Manchester, IN 46962:
son@manchester.edu
4Space Science Institute, 4750 Walnut St., Boulder, CO 80301
gailis@virginia.edu,
dln5q@virginia.edu,
University
Charter
brian@sal.wisc.edu,
ofWiscon-
St.,Madison, WI
bwhit-
cwat-
been reported (Nishiyama et al. 2006, 2009). At longer
wavelengths (λ > 4 µm), however, Aλ deviates from
this relationship and appears to “flatten out” (become
grayer) before increasing towards the peak of the 9.7 µm
silicate feature. The absolute extinction ratios Aλ0/AKs
used to normalize the derived extinction curves are gener-
ally determined for the diffuse ISM using reddened back-
ground standard candles for which intrinsic colors can be
assumed—e.g., red clump stars (Indebetouw et al. 2005;
Nishiyama et al. 2009) or RGB-tip or low-mass-lossAGB
stars (Jiang et al. 2003, 2006).
More recent work has demonstrated that in re-
gions of dense ISM, such as dark cloud cores or star-
forming regions, the MIR Aλ curve becomes even
shallower than in diffuse material, likely due to dust
grain growth through grain coagulation or ice mantle
coating (e.g., Weingartner & Draine 2001; Moore et al.
2005; Rom´ an-Z´ u˜ niga et al. 2007; Flaherty et al. 2007;
McClure 2009; Chapman et al. 2009). The absolute ra-
tios Aλ0/AKs have been determined in these regions
using either stars assumed to be in the background
(Flaherty et al. 2007) or associated gas emission—
e.g., hydrogen recombination spectra (Lutz et al. 1996;
Moore et al. 2005) or H2 rotational and rovibrational
lines (Rosenthal et al. 2000). Infrared extinction behav-
ior as a function of density, beyond a simple “dense” vs.
“diffuse” dichotomy, has only recently begun to be stud-
ied in specific cloud cores (Chapman et al. 2009; McClure
2009). We address the effects of ISM density on the ex-
tinction law here as well, but the present work is also
the first to examine extinction behavior with respect to
overall Galactic ISM density or grain-size gradients.
Given the differences in the extinction law behavior in
dense and diffuse interstellar environments, one may ex-
pect the Galactic extinction law to vary substantially

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2 Zasowski et al.
through the widely changing environments across the
disk. Yet the vast majority of infrared extinction law
studies, including those listed above, use no more than
a few specific regions on the sky (?10 deg2) to define
the extinction law and/or are limited to measuring rel-
ative Aλ variations in environmental extremes, such as
dark clouds. Moreover, most efforts are concentrated in
the inner Galaxy, where both starcounts and the over-
all extinction are higher, but where the potential effects
of Galactic-scale gradients (such as ISM metallicity or
density) cannot be easily identified. Thus, there is little
reason for the “universal” extinction law derived from
these observations to be in fact applicable to the Galaxy
as a whole.
In contrast to previous studies, this work tests both the
very assumption of a universal diffuse extinction law and
the pertinence of a simple bimodal dense versus diffuse
description of the ISM with regard to extinction. Our
collected databases allow us to determine coherent pat-
terns of extinction behavior by measuring the IR extinc-
tion law in a consistent way along many different sight-
lines spread over ∼150◦of the Galactic disk. §2 of this
paper contains a description of the data we use in this
new, comprehensive exploration of extinction behavior.
§3 explains our methodology for determining Aλ/AKs,
and §4 examines the question of density as the sole driver
of extinction variations. In §5, we compare our results
to previous observational and theoretical studies and dis-
cuss their similarities and differences with our findings.
We also address the implications of the observed varia-
tions in the 8 µm extinction upturn and the feasibility of
measuring extinction behavior as a function of Galacto-
centric radius. Finally, §6 summarizes our findings and
conclusions.
2. DESCRIPTION OF DATA
To probe the extinction law from 1.2–8 µm throughout
a large portion of the Galactic disk, we combine photo-
metric data from several mid-infrared Spitzer-IRAC sur-
veys with the near-infrared 2MASS Point Source Catalog
(PSC; Skrutskie et al. 2006). The PSC contains photo-
metric measurements at J (1.24 µm), H (1.66 µm), and
Ks (2.16 µm), and is considered complete to a magni-
tude limit of 16.1, 15.5, and 15.1 mag in J, H, and Ks,
respectively.5
At MIR wavelengths, we use data taken with Spitzer’s
IRAC instrument, with imaging channels roughly cen-
tered at 3.6, 4.5, 5.8, and 8 µm. From the Spitzer Legacy
archive, we have used photometry from the GLIMPSE-
I catalog (Benjamin et al. 2003), which consists of 2-sec
IRAC observations of the Galactic plane, contiguously
mapped for |b| ≤ 1◦across 10◦≤ l ≤ 65◦and 295◦≤ l
≤ 350◦.
We supplement the GLIMPSE coverage with our own
Galactic disk observations.
GLIMPSE is a similar survey of the Galactic midplane
covering the Vela molecular ridge and the Vela-Carina
star-forming region (PID 40791).
stretches between 255◦≤ l ≤ 295◦and is 2◦tall in lati-
tude, either centered at the midplane or offset ±0.5◦to
include regions of interest or the expected disk warp at
these Galactic longitudes; the depth of the photometry is
Extending the reach of
The survey region
5http://www.ipac.caltech.edu/2mass/releases/allsky/doc/sec6 5a1.html
very similar to that of GLIMPSE (e.g., m3.6µm? 15.5).
Additional IRAC observations of the disk include a num-
ber of 1◦×1◦fields scattered unevenly between 90◦≤ l ≤
300◦and 0◦≤ |b| ≤ 12◦(the “Argo” survey, PID 20499).
All of these Spitzer-IRAC data have been reduced
and band-merged with the 2MASS PSC using the same
pipeline6, and we begin with the more complete Archive
data for all of the IRAC surveys. In total, we have data
in 7 photometric bands (2MASS JHKsand IRAC [3.6µ],
[4.5µ], [5.8µ], [8µ]) spanning ∼150◦of disk longitude
(∼290 deg2in total area; see Figure 1), observed and
reduced in a consistent manner. Table 1 contains the
sky coverage and references for the IRAC observations.
3. MEASUREMENT OF EXTINCTION
We use the method of color excess ratios to measure
extinction behavior as a function of wavelength. This
procedure consists of making linear fits to pairs of ob-
served colors for numerous stars with varying levels of
extinction, as described in detail in Section 3.2. To min-
imize intrinsic scatter in the stellar colors, which would
make the fits less certain and less physically meaningful,
we desire a sample of stars with homogeneous stellar at-
mospheric properties; we also require the adopted stellar
population be common enough in the disk to comprise
a significant statistical sample. Section 3.1 contains the
details of our sample selection criteria.
3.1. Sample Selection
To ensure the most homogeneous sample of stars for
study, we choose to use G and K type red clump (RC)
stars, a population that is relatively luminous (MKs ∼
−1.54; Groenewegen 2008), homogeneous in color and
absolute magnitude ((J − Ks) ∼ 0.65 ± 0.10, σMKs∼
0.04; Girardi et al. 2002; Groenewegen 2008), and com-
mon in disk populations across a wide range of metallici-
ties and ages. In the color-magnitude diagram (CMD) of
an unreddened region of sky, the RC appears as a promi-
nent vertical stripe, with the counts per magnitude trac-
ing the density of the stellar population along the line
of sight. When dust is present along the line of sight,
its extinction acts to both dim the RC stars and redden
them, resulting in a diagonal shift of their CMD to the
right at fainter magnitudes (Figure 2a). However, even
in highly-reddened disk midplane fields, the RC forms a
distinctive locus, which we utilize to identify the stars
for study.
For our analysis, we selected only those stars detected
in all three of the 2MASS JHKsbands with σ ≤ 0.4 mag;
this requirement removes many intrinsically red sources
(i.e., those not detected in the bluer 2MASS bands) with
low line-of-sight reddening from potentially contaminat-
ing the highly-reddened part of the RC sample.
the four Spitzer-IRAC bands ([3.6µ], [4.5µ], [5.8µ], [8µ]),
we follow Indebetouw et al. (2005) in requiring signal-
to-noise ?10 and paring the catalog to those stars with
σ ? 0.2 mag. To remove sources with possible intrinsic
IR-excesses (e.g., YSOs or evolved stars with circumstel-
lar shells), we adopt color restrictions of ([3.6µ]-[4.5µ])
≤ 0.6 mag and ([5.8µ]-[8µ]) ≤ 0.2 mag (Flaherty et al.
2007). Figure 2b shows the stars remaining after these
photometric quality and color limits are imposed.
For
6http://irsa.ipac.caltech.edu/data/SPITZER/GLIMPSE/doc/glimpse1 data

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Galactic Infrared Extinction Law3
Fig. 1.— Top: 2MASS all-sky image; horizontal lines indicate ± 5◦latitude. Bottom: Close-up of Galactic midplane. The overlaid surveys
on both plots are GLIMPSE (forward-slash shading), Vela-Carina (backward-slash shading), and Argo (filled diamonds), as detailed in
Table 1. For the Argo data, we have only shown the midplane fields used in this study (i.e., with |b| < 1◦), and we have slightly elongated
the points in longitude for visual clarity (the fields are actually 1◦x1◦each).
TABLE 1
Span of IRAC observations used in this analysis.
Survey Galactic Longitude, l
Galactic Latitude, b
Reference
GLIMPSE
10 - 65
295 - 350
255 - 295
90, 135, 180,
225, 270, 280, 290
(-1) - +1
(-1.5) - +1.5a
Benjamin et al. (2003)
Vela-CarinaSpitzer PID 40791
Argo
(-0.5) - (0.5)
Spitzer PID 20499
aSurvey spans 2◦at any given location; center ranges from -0.5 ≤ b ≤ 0.5.
To ensure the purest possible sample of RC stars, we
require that RC sample candidates have the character-
istics of RC stars in both observed and intrinsic color
space. To that end, we deredden the remaining stars
with a new technique, detailed elsewhere (Majewski et
al., in prep), and then select only those stars whose
dereddened colors fall within the expected range of RC
colors. In brief, this dereddening technique takes advan-
tage of the fact that infrared photometry (λ ? 1.5 µm)
measures primarily the Rayleigh-Jeans portion of stel-
lar spectral energy distributions, which has a constant
shape only minimally dependent on intrinsic stellar at-
mospheric variations; this constancy implies a homoge-
neous set of infrared colors, particularly at the longer
wavelengths sampled by the Spitzer-IRAC bands. Thus,
any departure from the nominal infrared colors measures
the amount of reddening and extinction towardseach star
individually. We apply this technique to the sample of
stars remaining after the photometric quality and color
cuts imposed above, and we then retain only stars with
0.55 ≤ (J − Ks)0 ≤ 0.9 mag (Figure 2c). This step is
invoked to help remove marginally-reddened RGB stars
or highly-reddened bluer dwarfs that overlap the RC in
the observed CMD. We note that the potential circular-
ity of selecting stars dereddened with an assumed extinc-
tion law is not a source of concern, because the generous
∆(J − Ks)0= 0.35 mag RC selection bin will still con-
servatively include very nearly all RC stars anyway.
Next, we divide the catalog into ∼2.5◦x2◦blocks (in
Galactic longitude and latitude, respectively) and plot a
CMD for each block; straggler stars lying outside the ob-
vious RC locus, which are primarily redder giant stars, as
well as the brightest (unreddened) RC stars are then re-
moved manually (Figure 2d). Because many fainter stars
unable to be positively associated with the RC locus are
removed, this step has the effect of reducing the over-
all range of 2MASS photometric uncertainties for stars
ultimately used in the sample analysis. Although high
uncertainties in the PSC, particularly in the midplane,
are potential indicators of a flux overestimation bias7,
Figure 3 shows that our final distribution of NIR pho-
tometric uncertainties is well below the limit where this
bias is a concern.
Finally, in order to make reliable color-color linear fits
(Section 3.2), we require an average RC reddening of at
least 0.35 mag and a minimum spread in RC reddening
of at least 0.15 mag (i.e., (J − Ks) ≥ 1 and ∆E(J −Ks)
≥ 0.15 mag) in each block’s CMD. We performed the
color-color fits described below using a variety of photo-
metric quality cuts, and the set of restrictions detailed
here is the most lenient one (i.e., includes the most stars
to provide better statistics) yielding the same fit results
as stricter requirements.
7http://www.ipac.caltech.edu/2mass/releases/allsky/doc/sec5 3a.html

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4Zasowski et al.
Fig. 2.— Color-magnitude diagrams (CMDs) demonstrating
red clump (RC) sample selection for a typical field, centered at
(l=310◦, b=0◦). Panel (a): the near-infrared CMD with all stars
shown; the RC locus is clearly visible next to the arrow indicat-
ing a typical reddening vector (AKs= 1.5 mag; Indebetouw et al.
2005). Panel (b): CMD of the stars remaining after photometric
uncertainty and color limits are imposed. Panel (c): dereddened
CMD, with main-sequence, RC, and red giant branch stars visible;
the dotted lines indicate the color range used to remove the dwarfs
and red giant stars. Notice the magnified (J − Ks)0 scale in this
panel. Panel (d): CMD of stars remaining after the dereddened-
color cut; the boxed region indicates the final RC selection.
Fig. 3.— Range of NIR photometric uncertainty in final RC
stellar sample, for comparison to original uncertainty requirements
(σJHKs≤ 0.4 mag).
3.2. Color Excess Ratios
A star’s color excess E(λ1−λ2) is simply the difference
between the intrinsic color (λ1− λ2)0and the observed
color (λ1− λ2); this excess depends on both the col-
umn density of dust along the line of sight to the star
and the difference in extinction (for the same amount of
dust) between λ1and λ2. However, the color excess ra-
tio (CER) removes the total column density dependence
(Appendix A) and reflects the differential behavior of
extinction as a function of wavelength. An example of a
CERλfor a source is
CERλ=
E(H − λ)
E(H − Ks)=
(H − λ) − (H − λ)0
(H − Ks) − (H − Ks)0,
(1)
where (H −λ)0and (H −Ks)0are the intrinsic colors of
the source. Here we have chosen E(H − Ks) to be the
common reference denominator for our CERλ analysis
because (H − Ks)0is a well-defined color for RC giants,
more well-measured in our sample than MIR colors, and
less susceptible to color variations from metallicity, tem-
perature, or non-RC contamination than the other NIR
colors (J − Ks)0and (J − H)0.
Equation 1 can be rearranged as
(H−λ) =
E(H − λ)
E(H − Ks)[(H−Ks)−(H−Ks)o]+(H−λ)o,
(2)
where (H −λ) and (H −Ks) are the observed stellar col-
ors. For this work, we have adopted intrinsic colors for
RC stars from the Padova suite of stellar models, where
(H−Ks)0= 0.10 nearly independently of RC metallicity
(e.g. Girardi et al. 2002). When pairs of observed colors
([H − Ks] and [H − λ], for λ=J, [3.6µ], [4.5µ], [5.8µ],
[8µ]) are plotted against one another for stars spanning
a wide range of extinctions, we find extremely linear cor-
relations; a linear fit to these distributions gives esti-
mates of the CERλvalues as the slope, and the intrinsic
(H − λ)0 colors as the y-intercept when (H − λ) is on
the ordinate. Figure 4 shows an example of these linear
correlations and fits.
Our goal is to measure CERλvalues using RC stars in
many different parts of the Galactic plane and to look
for variations. Before fitting, the data are binned by
Galactic longitude into the same ∼2.5◦×2◦bins used in
the RC sample selection. By adopting only fields meeting
the average-reddening and differential-reddening require-
ments (as before: E(J − Ks) ≥ 0.35 and ∆E(J −Ks) ≥
0.15 mag), we fit 65 longitude bins, spanning from 10◦
to 100◦from the Galactic center (i.e., 10 ≤ l ≤ 65◦, l
= 90◦, and 260 ≤ l ≤ 350◦). For each bin, we fit a set
of five CERλ (i.e., [H − Ks] vs. each of [H − λ], λ ?=
Ks) using a linear weighted least-squares algorithm. We
take the uncertainties in the fits to be 1-σ, where σ is
the standard deviation of the fitted parameters. Because
of the intrinsic stellar density gradient in the disk, the
number of stars in each bin varies (from 820 to >6×104)
across our longitude range. We check for any effects this
variation in sample size has on the fits by “normalizing”
to the number of stars in the least-populated longitude
bin (820); that is, for every other bin, we apply the fit-
ting algorithm to 820 randomly-selected stars a total of
25 times. Though we find no noticeable difference with
the parameters derived by fitting all the stars in each

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Galactic Infrared Extinction Law5
Fig. 4.— Example of CERλfits for a bin centered at (l = 30◦,b =
0◦). The abscissa is (H−Ks)−(H −Ks)0, where we have adopted
(H −Ks)0= 0.10 (Girardi et al. 2002). The slope of each fit gives
the color excess ratio for that bandpass, and the y-intercept gives
the intrinsic (H − λ)0 color for stars in this field.
bin, the results described below are the mean of the 25
fits for each bin, and the quoted uncertainties are either
the average 1-σ or the standard deviation of the 25 fit
parameters, whichever is larger.
3.3. Results
3.3.1. Derived CERλ
Figure 5 shows the derived CERλvalues as a function
of angle from the Galactic center. This figure straight-
forwardly demonstrates the existence of a large-scale lon-
gitudinal variation in the infrared extinction law, sym-
metric about the Galactic center, and that the slopes
of the CERλ trends increase as λ increases (i.e., more
drastic CERλ variations at longer MIR wavelengths).
Because an increased CERλ for λ > H (and decreased
CERλfor λ < H) results from relatively greater redden-
ing E(H −λ), these results indicate a steeper extinction
curve (Aλ/AKs; Section 5.1) in the outer Galaxy. The
CERλvalues, averaged in 5◦bins, are also presented in
Table 2.
CERJappears nearly constant (with large scatter) un-
til the angle ∼ 55◦, when it becomes increasingly nega-
tive, while the MIR CERλvalues have a somewhat flat
distribution only out to ∼25◦. Of all the IR colors under
consideration, (H − J) is the most sensitive to spectral
variations due to differences (spatially-dependent or ran-
dom) in RC metallicity and temperature. Thus the be-
havior of CERJis consistent with the presence of global
extinction law trends, but because it is also the most sus-
ceptible to unaccounted-for RC population variations, we
do not evaluate the significance of the different Galacto-
centric angle of the trend inflection at this time.
3.3.2. Checks on (H-λ)0
In Figure 6, we plot the derived intrinsic RC colors
(H−λ)0against the field Galactocentric angle. Exploring
the y-intercept values of our fits serves as a sanity check
on our results—if our method is viable, then (H − λ)0
Fig. 5.— CERλ= E(H − λ)/E(H − Ks) as a function of angle
from the Galactic center (bins are 2.5◦wide). The filled circles
indicate data with l < 180 (Galactic quadrant I), and the open
circles indicate data with l > 180 (Galactic quadrants III/IV).
There is no obvious difference in CERλbehavior between one side
of the Galaxy and the other. The error bars indicate either the 1-σ
uncertainty on the fit parameter or the standard deviation of the
parameters from the 25 fits, whichever is larger. Notice the near
constancy at 3.6 µm and the increasing steepness of the trend with
increasing λ.
from our fits should uniformly correspond to the intrin-
sic (H − λ)0colors of RC stars. Figure 6 shows that we
indeed find (H − λ)0colors that are not only consistent
across our survey but also in good agreement with the
predictions of the Padova stellar models (Girardi et al.
2002). Some slight differences (≤0.025 mag) compared
to the theoretical colors may be attributable to inconsis-
tencies in bolometric corrections or inaccuracies in the
filter transmission profiles applied to the stellar models.
It is possible, of course, that the true intrinsic colors
of the RC stars in our sample do vary slightly, since the
derived (H − λ)0 values depend on our assumption of
a constant (H − Ks)0. We validate the latter assump-
tion using the recent Milky Way disk abundance gra-
dient of Pedicelli et al. (2009) and the relationship be-
tween [Fe/H] and (H − Ks)0 in the Padova isochrones.
For metallicities spanning -1.22 ≤ [Fe/H] ≤ +0.18, the
intrinsic (H −Ks)0color of RC stars changes steadily by
?0.06mag. Pedicelli et al. (2009) find an [Fe/H] gradient

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6Zasowski et al.
TABLE 2
Derived CERλvalues for use in Equation 3. For the contiguous data,
the results have been averaged over 5◦.
Galactic Longitude, l
CERJ
CER[3.6µ]
CER[4.5µ]
CER[5.8µ]
CER[8µ]
10–15
15–20
20–25
25–30
30–35
35–40
40–45
45–50
50–55
55–60
60–65
90
260–265
265–270
270–275
275–280
280–285
285–290
290–295
295–300
300–305
305–310
310–315
315–320
320–325
325–330
330–335
335–340
340–345
345–350
-1.97
-1.95
-1.98
-2.01
-1.99
-1.97
-2.00
-1.96
-2.01
-2.06
-2.07
-2.18
-2.16
-2.10
-2.14
-2.13
-2.02
-2.11
-2.06
-2.13
-2.05
-2.03
-2.02
-2.04
-2.05
-2.00
-2.00
-2.01
-1.98
-2.00
1.79
1.78
1.80
1.80
1.82
1.83
1.83
1.81
1.83
1.83
1.82
1.94
1.83
1.77
1.77
1.80
1.81
1.82
1.80
1.85
1.81
1.82
1.81
1.82
1.84
1.81
1.81
1.80
1.79
1.80
1.92
1.92
1.93
1.94
2.01
2.02
1.99
2.00
2.03
2.02
2.00
2.38
2.11
2.05
2.01
2.06
2.06
2.01
1.98
2.05
2.00
2.02
2.02
2.02
2.03
2.01
1.99
1.95
1.97
1.93
2.08
2.07
2.08
2.09
2.16
2.19
2.19
2.21
2.30
2.30
2.30
2.78
2.54
2.39
2.43
2.51
2.40
2.43
2.36
2.38
2.27
2.21
2.20
2.22
2.24
2.18
2.15
2.11
2.12
2.10
2.00
1.99
2.01
2.05
2.10
2.15
2.11
2.13
2.20
2.20
2.19
2.49
2.42
2.29
2.34
2.35
2.29
2.42
2.31
2.28
2.21
2.12
2.08
2.09
2.12
2.07
2.05
2.02
2.00
2.01
of ∼−0.13 dex/kpc inside the solar circle and ∼−0.042
dex/kpc outside of it. Given the approximate range of
RGCof our RC sample (see Section 5.5), this corresponds
to a maximum ∆[Fe/H] of 0.46 dex along any single line
of sight, resulting in a maximum intrinsic (H − Ks)0
scatter of ≪0.06 mag in any single fitted field. Since the
measured E(H −Ks) values are so much larger (usually
≥0.8 mag), this possible scatter does not affect the de-
rived CERλvalues. This conclusion is further supported
by the very tight linear color-color correlations observed
(Figure 4), indicating no significant intrinsic color varia-
tions within any single field.
4. EXTINCTION AND DENSITY
4.1. Defining the Diffuse ISM
Recent studies of dark molecular clouds have shown
that theMIRextinction
ingly shallow with increasing local dust density (e.g.,
Flaherty et al. 2007; Rom´ an-Z´ u˜ niga et al. 2007; McClure
2009; Chapman et al. 2009). Theoretical models predict
this behavior as an effect of grain growth, from either
the coagulation of grains or the accumulation of refrac-
tory ice mantles in dense clouds (Li & Greenberg 2003;
Draine 2003). In either case, the growth of grains serves
both to remove small particles (including PAHs) and to
add larger ones, leading to an overall flatter (“grayer”)
extinction. In addition, the presence of certain ices may
lead to enhanced extinction around their solid-state res-
onance bands (e.g., CO at 4.7 µm and H2O at 3.1 and
6.0 µm).However, neither the specific environmental
conditions producing this grain growth, nor the detailed
behavior of Aλ/AKs as a function of grain size, is yet
well-constrained. Chapman et al. (2009) approach these
curvebecomesincreas-
questions by using AV as a proxy for density to probe
specific molecular clouds and find a steady progression
towards shallower 3.6-8 µm extinction curves as <AV>
increases in the cloud. The 2.5◦-wide longitude bins and
the large total spatial extent of our stellar sample mean
that any density variations potentially driving the ex-
tinction law variations seen here are likely dominated by
the large-scale density gradient of the Galactic disk, not
the small-scale filamentary structure of dark clouds.
This density gradient may be understood as either a
change in the density of the mean ISM or a changing
fractional contribution of molecular cloud material. One
of the stated goals of this study is to test the commonly
used description of a simple, bimodal ISM comprising
individually homogeneous “dense” regions (dark clouds
and cores) and “diffuse” regions (everything in between).
Thus, we must examine what we mean hereafter in this
analysis when we refer to “diffuse” material and attempt
to distinguish its reddening effects from those of denser
clouds.
Here, we explore the diffuse ISM using two separate
methods to identify those stars tracing it.
these—the “RPD” and “13CO” methods—lead to their
own implicit definition of interstellar diffusivity, and we
will discuss the relative merits of each method and defi-
nition.
Each of
4.1.1. The RPD Method
One approach to selecting stars reddened only by dif-
fuse foreground material is to approximate the distance
to each star and impose a maximum “reddening per unit
distance” (RPD; e.g., E[H − Ks]/kpc) limit on the stel-
lar sample; stars with RPD values greater than this limit

Page 7

Galactic Infrared Extinction Law7
Fig. 6.— The intrinsic colors of RC stars, measured as the
y-intercepts in our color excess ratio fits, assuming a constant
(H − Ks)0=0.10 mag. The error bars indicate either the 1-σ un-
certainty on the fit parameter or the standard deviation of the pa-
rameters from the twenty-five fits, whichever is larger. Also shown
are the mean values for all longitudes (dashed lines) and the pre-
dicted intrinsic colors from the Padova stellar models (solid lines;
Girardi et al. 2002).
would then be identified as being within or behind a
“dense cloud” and removed from the analysis. The major
complication of this method is the uncertainty in the as-
sumptions required to calculate the RPD limit for diffuse
material.
In the first place, one must know the distance to each
star individually. We estimate these values as described
later in this paper (Section 5.5), but we need to note a
critical source of systematic uncertainty. Choosing an
extinction law for each star is neither practical nor reli-
able, so a single law (extrapolated from RV = 3.1) is used
for the entire RC sample. For lines of sight containing
dense ISM (e.g., with RV ∼ 4-5), this choice has the end
result of overestimating the stellar distances, thus under-
estimating the RPD values (by up to ∼30%). Given the
relatively narrow range of RPD values observed in our
sample (0–0.5), this is a significant uncertainty. So stars
behind dense clouds are systematically more likely to be
included in a diffuse ISM subsample defined by an upper
RPD limit.
In addition, there is the process of even defining an
appropriate RPD limit. One can either select character-
istic values for the ISM with regard to number density
(n[H]) and to
N(H)(or the more common
conversion factor) or adopt a published RPD value. The
extant literature contains ranges of values for all of these
quantities such that the “diffuse” RPD may be said to
span 0.05–0.22 mag kpc−1(a range of more than a fac-
tor of four), depending on results given by Cardelli et al.
(1989), Dickey & Lockman (1990), Madsen & Reynolds
(2005), Indebetouw et al. (2005), Misiriotis et al. (2006),
or Pineda et al. (2008).
Given this wide range of realistic RPD values, and the
open question of how the constituent factors may vary
with Galactic radius, the choice of a single RPD upper
limit becomes tricky, even arbitrary. Imposition of a par-
ticular limit has the potential to artificially skew the de-
rived extinction law behavior by not accounting for den-
sity variations along the line of sight. Moreover, making
a priori assumptions about the homogeneous properties
of a likely heterogeneous ISM risks obscuring the very
intrinsic characteristics of interstellar dust targeted by
this study.
AKs
AV
N(H)and a
4.1.2. The13CO Method
An alternative method of exploring the diffuse ISM
is to identify (and remove) the effects of dense ISM on
our extinction curves is through use of an appropriate
tracer of high ISM density, such as molecular gas emis-
sion. The J=1→0 transition of13CO (ν0= 110.2 GHz) is
one such tracer, with an emission threshold correspond-
ing to a cloud density wherein there is only 1–2 mag of
AV extinction. For a typical molecular cloud with r ∼
200 pc, this corresponds to a number density of roughly
n(H) ∼ 1-5 cm−3. Comparison to the commonly used
range of diffuse n(H) (0.5–few cm−3; Dickey & Lockman
1990; Misiriotis et al. 2006; Whittet 2003) demonstrates
13CO to be a highly sensitive tracer of interstellar mate-
rial dense enough to exhibit the known shallower extinc-
tion curves described above.
Given the ambiguities inherent in distances derived
from molecular gas emission maps, we cannot conclu-
sively match the13CO emission to specific foreground
dust clouds and remove only the stars behind them. The
most direct approach is then to remove all stars coinci-
dent in sky position with a13CO detection. A disadvan-
tage of this method is the exclusion of useful stars in in-
trinsically diffuse regions, in the foreground of denser ma-
terial; nevertheless, the low optical depth and low emis-
sion threshold of13CO means that the resulting “diffuse”
subsample is very conservatively defined and highly un-
likely to be contaminated by stars in intrinsically dense
regions. Another potential problem with using molecular
gas as a tracer of dense ISM is the clumpy, filamentary
structure of dark clouds and molecular cloud cores, which
may prevent efficient filtering of dense ISM on a star-by-
star basis. This obstacle, however, may be countered by
using gas emission maps with resolution appropriate to
trace molecular cloud structure at the median distance
of our stellar sample.
4.2. Derived CERλfor Diffuse ISM
To assess the effects of high-density clouds on our
average ISM extinction curves, we sort our dataset

Page 8

8Zasowski et al.
into rough divisions of “dense” and “diffuse” lines
of sight, separately for each of the two methods de-
scribed above. For the13CO-emission method, we use
the integrated-intensity maps of the Boston University-
FCRAO Galactic Ring Survey (GRS, spanning 18◦≤ l
≤ 54◦; Jackson et al. 2006) as tracers of high ISM den-
sity. These maps have resolution high enough (∼ 0.75’)
to distinguish filamentary structures of potentially dense
ISM at the median distances of our stellar sample (where
distances are estimated using the technique detailed in
Section 5.5). As the most conservative selection of “dif-
fuse” material, we consider only those stars with no mea-
sured13CO emission at their projected position on the
sky (comprising ∼55% of the RC stars in the longitudes
covered by the GRS). As described above, this should
eliminate any typically-sized molecular clouds with n(H)
? 1-5 cm−3from affecting our derived extinction law.
For the RPD method, we consider two choices of max-
imum reddening-per-distance for “diffuse” ISM — RPD
≤ 0.22 and RPD ≤ 0.15 mag kpc−1— to assess the ef-
fects of the particular limiting value. These cuts retain
∼79% and ∼57%, respectively, of the RC stars in the
longitudes covered by the GRS.
We apply the CERλ fitting process as before (Sec-
tion 3.2) to these various “diffuse” subsamples. The GRS
coverage limits the13CO-selection method to 18◦≤ l
≤ 54◦, and we show results for the RPD method both
with and without this longitude limitation. The num-
ber of randomly selected stars for the 25 CERλfits per
field (i.e., the minimum starcount in any longitude bin)
changes from 820 (Section 3.2) to 14000 for RPD ≤ 0.22
mag kpc−1, 5700 for RPD ≤ 0.15 mag kpc−1, and 8000
for W(13CO) = 0 K; this increase in the number of fit-
ted stars, compared to the original fits, occurs because
we are now considering only fields no further than 54◦
from the Galactic center. The increased counts are re-
sponsible for the smaller errorbars throughout Figure 7
(compared to Figure 5).
In the case where CERλvalues are derived from stars
with no13CO emission detected at their positions (Fig-
ure 7a), we observe very nearly the same behavior with
Galactic angle as seen in the case where no distinction
between “dense” and “diffuse” lines of sight is made (i.e.,
Figure 5). That is, even with the likeliest sites of larger
dust grains explicitly removed, the ISM extinction be-
havior continues to depend on Galactocentric angle, with
the reddening curve becoming steeper toward the outer
Galaxy.
For comparison, in the case where stars are filtered us-
ing the RPD method, the distribution of CERλ shows
significant variation with longitude (Figure 7b), though
no global trends are apparent. In addition, we find the
counterintuitive result that the departure from canon-
ical “diffuse ISM” values (e.g., Indebetouw et al. 2005)
actually increases as the restriction on maximum RPD
is lowered from 0.22 to 0.15 mag kpc−1. Moreover, the
extinction curves that derive from these “pure” diffuse-
only samples are difficult to explain physically, as they
are steeper than even a simple power law or RV = 3.1
dust model (e.g., Section 5.3). At least part of the larger
scatter in CERλis due to the uncertainties inherent to fit-
ting a straight line (as in Figure 4) to the increasingly in-
coherent color-color distributions that are obtained when
the high-reddening stars are preferentially removed and
the color-colorplots become dominated by the photomet-
ric errors of the stars. If one considers the lower CERλ
values near l ∼ 28◦and 50◦to be troughs, rather than
attributing the values at l ∼ 37◦to a peak, these depres-
sions do correspond roughly with the expected positions
of the tangencies of the Scutum and Sagittarius spiral
arms (e.g., Englmaier & Gerhard 1999). This might be
one possible explanation for the troughs since decreased
CERλ values indicate a shallower extinction curve (see
Section 5.1), consistent with what would be expected in
a dense spiral arm.
However, ascribing this behavior to the spiral arms has
many problems. First, because the removal of stars with
high RPD estimates is explicitly intended to filter out all
stars in or behind molecular clouds, it is unlikely that
features caused by molecular clouds would become in-
creasingly prominent as the RPD limit is lowered (in the-
ory producing an even purer diffuse-only stellar sample).
Second, while the precise heliocentric distances of these
spiral arm tangent points are not tightly constrained, re-
cent models place them near or beyond the range of our
RC stars (e.g., Hou et al. 2009), making it impossible for
the stars with low RPD values in our dataset to probe
spiral arm tangencies. Third, we can check for the cor-
responding spiral arm tangencies in the fourth Galactic
quadrant (Carina, l ∼ 284◦and Crux, l ∼ 310◦), since
the RPD method is not limited to the longitude range im-
posed by the13CO maps. Figure 7c shows CERλvalues
derived from stars with RPD < 0.22 mag kpc−1over the
entire longitude span of our data—no dips correspond-
ing to the Crux and Carina arms are visible. In light
of these inconsistencies, we cannot ascribe the CERλbe-
havior for 18◦≤ l ≤ 54◦to any known Galactic structure.
The physical reality of the observed features themselves
(Figures 7bc) are called into question by (a) the number
and type of assumptions that must be made to select a
diffuse RPD limit from a wide (and potentially varying)
range of possibilities, (b) the increasing departure from
realistic CERλvalues as the RPD limit is tightened, and
(c) the strong dependence of the calculated RPD val-
ues on the stellar distance estimates, which themselves
require an assumed extinction law to calculate.
Given this wide range of complications, we conclude
that the13CO selection filter, while not perfect, has fewer
systematic uncertainties than does the RPD filter, and
we therefore adopt the lack of13CO emission as the pre-
ferred tracer of diffuse, intra-cloud interstellar material.
The similarity in behavior between this “diffuse” extinc-
tion and the “all stars” extinction derived in Section 3
indicates that the environments probed by our full set of
RC stars are dominated by ISM too thin to harbor13CO
molecules; the following analyses, therefore, are not lim-
ited to the available longitudes of the13CO data and are
able to explore the extinction behavior across the largest
possible span of the Galactic disk. The persistence of
the trends between relative extinction and longitude in
the diffuse ISM, particularly at 5.8 and 8 µm, indicates
effects on the reddening law of either the mean Galac-
tic density gradient (beyond the known growth effects
in very dense clouds) or of secondary factors that vary
throughout the Galactic disk, such as the chemical com-
position, size, or crystalline fraction of the dust grains.
These secondary factors, particularly grain size and crys-

Page 9

Galactic Infrared Extinction Law9
Fig. 7.— CERλ= E(H −λ)/E(H −Ks) as a function of angle from the Galactic center for various definition of “diffuse” environments.
The error bars are as in Figure 5. Panel (a)—Using stars selected as having no13CO emission at their projected position on the sky.
Panel (b)—Using stars from the same sight-lines as in (a), but with calculated reddening-per-distance (RPD) of ≤0.22 mag kpc−1(black
diamonds) or ≤0.15 mag kpc−1(gray diamonds). Panel (c)—Using stars with RPD ≤ 0.22 mag kpc−1with l < 180◦(filled circles) and l
> 180◦(open circles). The solid and dashed lines indicate the expected positions of spiral arm tangencies in Galactic quadrants I and IV,
respectively.
tallinity, may of course be at least partially due to the
overall Galactic ISM density gradient (see the beginning
of Section 4.1).
For now, we adopt a working definition of “diffuse
ISM” to refer to interstellar matter with a hydrogen num-
ber density too low to shield13CO molecules from disso-
ciation (i.e., n(H) ? 1–5 cm−3). We believe that this def-
inition is not only close to what is normally envisioned as
“diffuse ISM” but also that which is most useful in terms
of practical and immediate applicability of our results
to common dereddening problems. In the 4-phase ISM
model (e.g., Whittet 2003), material defined thusly cor-
responds to a mixture of the “warm” and “cool (atomic)”
phases. We recognize that this thin matter is likely to
have a large-scale radial density gradient throughout the
disk, since it probably contains the outskirts of molecu-
lar clouds, which have a varying filling factor throughout
the disk. However, we emphasize that by our (or nearly
any) definition this ISM would not be considered “dense
cloud” material and so, prior to this study, would have
been assigned a constant “diffuse” extinction law, regard-
less of its location in the Galaxy. Our results here show
that this constant extinction law does not accurately de-
scribe the extinction behavior along all lines of sight,
and any reddening corrections applied without consider-
ing the varying nature of the diffuse extinction law could
be potentially subject to severe systematic errors.
5. DISCUSSION
5.1. Conversion to Aλ/AKs
To convert the derived CERλ into the more familiar
IR extinction law format Aλ/AKs, we use the relation
Aλ
AKs
=AH
AKs
−
?AH
AKs
− 1
?
· CERλ.
(3)
Deriving the true, longitude-dependent extinction law
requires an independent determination of AH/AKsalong
each line of sight for which we have measured CERλ.
Unfortunately, this is an extremely challenging measure-
ment to make. Nishiyama et al. (2006, 2009) have done it
towardsthe Galactic center by assuming that all RC stars
are at the same distance; we can make no such assump-
tion for our lines of sight. Indebetouw et al. (2005) fit
the RC locus in NIR CMDs to directly extract AH/AKs,
leaving distance as a free parameter and assuming that
the amount of extinction in those bands is constant per
unit distance along the line of sight, the equivalent of as-
suming a smooth, homogeneous dust distribution. This
assumption is not generally applicable, and in our more
extensive disk survey we see many lines of sight with
CMDs containing shifts and kinks in the RC locus that
provide definitive evidence for a nonhomogeneous extinc-
tion and dust distribution. Thus, given no currently re-
liable method for determining AH/AKsaround the disk,

Page 10

10Zasowski et al.
we cannot provide an absolute, independently calibrated
set of Aλ/AKscurves at this time.
Nevertheless, to facilitate comparison of Aλ/AKs
behavior with other studies, we use the commonly-
adopted value AH/AKs = 1.55 as determined by
Indebetouw et al. (2005), which corrresponds to an Aλ∝
λ−βpower law with β = 1.66. The range of typical β
values (1.6–1.8) give AH/AKs= 1.52–1.6; when applied
to our observed CERλwith Equation 3, this range adds
a ∼3-15% uncertainty to the calculated Aλ/AKsvalues.
This uncertainty is several times smaller than the per-
centage change in Aλ/AKs with Galactic angle due to
the intrinsic CERλtrends we observe here. In addition,
we note that the choice of AH/AKsonly sets the abso-
lute value scale for the relative extinction law; it is not
sensitive to variations in extinction law shape.
5.2. Comparison to Other Observational Studies
InFigure8,wecompare
curve,derived using the total RC sample at all
Galactocentric angles, with the results of Lutz et al.
(1996), Indebetouw et al. (2005, fit from their Equa-
tion 4), Jiang et al. (2006), Flaherty et al. (2007), and
Chapman et al. (2009). We find very similar values and
overall curve shape to the extinction laws found by many
of these authors, but a closer inspection reveals that
our data yield slightly lower relative extinction values in
the mid-infrared (i.e., a steeper MIR extinction curve).
This is entirely in accordance with the difference in en-
vironments probed by these various studies: the shal-
lowest curve results (Lutz et al. 1996; Jiang et al. 2006;
Flaherty et al. 2007) are derived using stars in the Galac-
tic Center and behind dense star-forming regions, where
dust grains are expected to be significantly different than
in the disk’s diffuse ISM (Section 4).
Our results moreclosely
Indebetouw et al. (2005), which was derived using three
lines of sight comprising both diffuse ISM and an HII
region, with Galactocentric angles ∼ 42◦and 76◦. The
fact that our mean curve lies below these data is en-
tirely consistent with our relatively larger inclusion of
diffuse and outer-Galaxy regions. Another comparable
match to our data comes from the two lowest-AKsbins
of Chapman et al. (2009), probing regions where AKs≤
1. The least-extinguished stars in this dark-cloud survey
are likely to be either foreground dwarfs unaffected by
the molecular cloud material or stars observed through
the low-density cloud edges.
our mean
Aλ/AKs
match thecurve of
5.3. Comparison to Theoretical Models
Because our study finds evidence for variations in the
extinction law with longitude, it is useful to compare
extinction curves from different sightlines with curves
extracted from theoretical dust models to attempt ex-
planation of the observed differences. Figure 9 shows
such a comparison between the most current suite of
dust models of Weingartner & Draine (2001)8and our
extinction curves sampled from various Galactocentric
angles, ranging from the innermost GLIMPSE data (10◦–
15◦from Galactic center) to dust entirely beyond the
solar circle (>90◦). The Case A and Case B models of
8http://www.astro.princeton.edu/∼draine/dust/dust.html
Fig. 8.— Mean extinction values (Aλ/AKs) for this work (filled
circles), compared to the Galactic center work of Lutz et al. (1996,
diamonds) and Jiang et al. (2006, triangles), the ISM study of
Indebetouw et al. (2005, thin line), and the dark cloud analy-
ses of Flaherty et al. (2007, squares) and Chapman et al. (2009,
their AKs≤ 1 regions, pluses). The reported uncertainties in the
Chapman et al. (2009) data are large and have been excluded for
clarity.
Weingartner & Draine (2001) differ slightly in their car-
bon abundances (see below) and grain size restrictions—
Case A contains grains only up to 1 µm while Case B
grains can be as large as 10 µm.
As in the case with the observational studies listed
above, our results clearly show a shallower extinction law
than either the RV = 3.1 theoretical model or any power
law that could be extrapolated from the three NIR mea-
surements alone (e.g., the solid line in Figure 9). The
Case B models with RV = 4.0 and RV = 5.5 provide the
closest overall matches to the “inner” Galactic sightlines,
though these are nearly indistinguishable from each other
bluewards of ∼3 µm; we note that if we had scaled the
theoretical curves using AH/AKs= 1.55, as we did for
our derived extinction curves, the MIR range of the Case
B models would shift downwards and align more closely
with the |l| ∼ 30–60◦data points. The original carbon
abundances of the Weingartner & Draine (2001) models
has been called into question by observational constraints
(see discussion in Draine 2003), but only those with RV =
3.1 or a Case A size distribution have subsequently been
modified (with a change in C/H on the order of ?15%).
These Case A models more closely follow the RV = 3.1
curve, but all three yield MIR extinction curves too steep
to explain our inner Galaxy observations.
Thus there is a clear relationship between Galactocen-
tric angle and best-matched dust model: though the in-
ner fields correspond to the higher RV values, the outer
fields are increasingly similar to the highly-diffuse RV =
3.1 and the small-grain Case A models. The diffuse na-

Page 11

Galactic Infrared Extinction Law11
Fig. 9.— Mean extinction curves for the indicated ranges of
Galactic angle (smallest—circles; mid-range—triangles and dia-
monds; beyond the solar circle—squares), compared to the current
suite of theoretical dust models of Weingartner & Draine (2001),
with RV and size distribution case (A or B) as indicated. Also
shown for comparison is an Aλ∝ λ−βpower law, for β = 1.66
(solid line).
ture of outer disk Galactic dust is one of the reasons a
large-scale extinction law survey of this type has not be-
fore been conducted—a diffuse ISM produces small red-
denings that are difficult to study, particularly in the rel-
atively transparent MIR portion of the curve (compared
to shorter, more dust-sensitive wavelengths); our exten-
sive disk coverage and high-quality MIR photometry al-
low us to make headway on overcoming these obstacles.
After determining extinction behavior in a consistent way
across a wide swath of the Galactic disk and comparing
the results to theoretical dust models, we interpret the
variation in extinction law as a consequence of a decrease
in mean dust grain size toward the outer Galaxy.
5.4. 8.0 µm Inflection
The presence of increased relative extinction in the
IRAC-4 channel at ∼8 µm is generally attributed to
the broad 9.7 µm resonance of amorphous silicates.
Indebetouw et al. (2005) estimate this absorption band
has a ?20% effect on the expected flux through the
[8µ] filter (but a negligible effect on the [5.8µ] channel).
Though the exact behavior of the absorption band is
loosely constrained (Whittet 2003), generally the band
strength appears to decrease with both increasing grain
size and increasing crystallinity (Figure 9; models of
Weingartner & Draine 2001). Thus, one may expect a
general trend of more dramatic 8 µm inflections with
decreasing ISM density (loosely, with increasing Galac-
tic angle), and as shown in Figure 10, we see just that.
This figure shows the mean A[8µ]/A[5.8µ]from our data
for each 10◦bin in Galactic angle, and this ratio clearly
Fig. 10.— Ratio between extinction at 8 and 5.8 µm.
points are the mean values of the 2.5◦fields in each 10◦longi-
tudinal bin, the horizontal bars indicate the degree span of each
bin, and the vertical bars indicate the standard deviation of this
ratio for the fields in each bin. The dashed line represents a truly
“flat” extinction curve at these wavelengths, and the dotted lines
represent approximate ratios for the theoretical dust models of
Weingartner & Draine (2001), with RV and size distribution case
as indicated.
increases towards the outer Galaxy. Also included for
comparison are the approximate corresponding ratios for
the five dust models in Figure 9 (Weingartner & Draine
2001). These latter ratios are approximate because they
do not take into account the true filter transmission pro-
files of the two IRAC channels; we use the FWHM and
isophotal wavelength of each bandpass (convolved with
a K2 giant star) to calculate the relative extinction val-
ues. This analysis again suggests decreasing ISM grain
size towards the outer Galaxy via the observed increas-
ing 8 µm relative extinction and is further evidence for
the variable nature of the ISM constituents on Galactic
scales.
The
5.5. Aλ/AKsas a Function of Galactocentric Radius
Because each line of sight analyzed here thus far probes
a range of Galactocentric radii (RGC), the observed lon-
gitudinal variations in CERλ demonstrate that the as-
sumption of a universal infrared extinction law, even for
diffuse material, is incorrect—if it were otherwise, then
the same extinction curve would be measured in all direc-
tions in the Galactic plane and at all distances. Given
that RC stars are good standard candles and that the
factors affecting Aλ/AKs (e.g., dust composition, grain
size) are likely to have a radial dependence, the possibil-
ity of measuring the IR extinction law as a function of
Galactocentric radius is a tantalizing one. The difficulty,
of course, lies in the fact that the reddening we observe
towards each star is caused by dust spread along the line
of sight to the star, so that the observed extinction be-

Page 12

12Zasowski et al.
havior cannot be assigned to the dust at one particular
RGC.
On the other hand, for certain lines of sight, we can
make simple assumptions regarding the dust distribu-
tion that allow reasonable estimates of trends in Aλ/AKs
with RGC. First, we assume that the large-scale Galac-
tic dust distribution has a strong radial density gradi-
ent (scalelength ∼ 2–3 kpc; Drimmel & Spergel 2001;
L´ opez-Corredoira et al. 2002; Misiriotis et al. 2006) from
the Galactic center to the outer disk. In this case, for
sightlines towards the Galactic center (|l| ≤ 13◦), we
can assign the majority of the dust to the approximate
RGCof the farthest concentration of stars in our sample,
where the dust is presumably thickest (for our RC sam-
ple, RGC∼ 5.5 kpc, assuming RGC,⊙= 8 kpc). Likewise,
for large-angle sightlines (≥150◦, including the Galactic
anti-center), we estimate most of the dust to lie in the
foreground of the survey stars nearest the sun (for our
sample, RGC∼ 10.4 kpc), where we expect the dust den-
sity to be highest. Note that we discard the minimum
reddening requirements (§3.1) in order to use these outer
Galaxy fields; the small stellar reddenings at these lon-
gitudes are responsible for the increased uncertainties in
the linear color-color fit parameters. Finally, there ex-
ists an optimal Galactic longitude at which the majority
of the observed stars, at varying heliocentric distances,
fall along the same Galactocentric ring (with a constant,
well-defined RGC). To calculate this, we recognize that
each line of sight (with |l| ≤ 90◦) intersects the tangent
point of a Galactocentric ring, where a concentration of
stars (and the intervening dust) have the same RGC; gen-
erally there will also be stars and dust with larger RGC
on the near and far sides of the tangent point (as seen
from the sun’s position). But as Figure 11 demonstrates,
there are longitudes at which other factors serve to re-
move stars in front of and behind the tangent point—at
these longitudes, nearer stars are either too bright for
2MASS/Spitzer or are blue main sequence stars, and far-
ther stars are actually extinguished out of our database
altogether. For our particular sample’s heliocentric dis-
tance distribution, this critical angle is 58◦(i.e., l = 58◦
and 302◦), corresponding to the ring at RGC ∼ 6.8 kpc
and indicated by the dotted line in Figure 11.
Distances to the RC stars are estimated using the
extinction-measurement technique mentioned in Sec-
tion 3.1 (to be detailed in Majewski et al., in prep); the
law of cosines is applied to convert the midplane helio-
centric distances (d) into RGC:
RGC=
?
d2+ R2
GC,⊙− 2dRGC,⊙cos(l),
(4)
where l is a star’s Galactic longitude and RGC,⊙ is as-
sumed to be 8 kpc. In converting reddenings to extinc-
tion, we must assume an absolute magnitude MKs for
red clump stars (MKs∼ −1.54; Groenewegen 2008) and
a NIR+MIR extinction law, for which we choose that
of Indebetouw et al. (2005) for all three lines of sight
described above. We realize that this introduces a sig-
nificant systematic uncertainty into our calculated RGC
values, which varies depending on the relative molecular
cloud filling factor along the line of sight (Section 4.1.1);
however, we note that in choosing a consistent law for all
three cases, the systematic differences in CERλ among
them are still highly informative. The approximate RGC
Fig. 11.— The distribution of approximate Galactocentric radii
(RGC) for our RC sample, as a function of angle from the Galactic
Center (§5.5; assuming RGC,⊙= 8 kpc). The dotted line indicates
the longitude (|l| ∼ 58◦) at which the spread in RGCis smallest—
that is, at which most stars along the line of sight are at a consis-
tent, well-defined RGC. The solid line indicates the limit of radii
geometrically excluded from the sun’s position.
values themselves are sufficient for our illustrative goals
here, as we are not attempting to “fit” a global relation-
ship but rather to show relative trends.
Figure 12 shows the fitted mid-infrared CERλ values
(i.e., no AH/AKsassumed) for the three ranges of Galac-
tic angle described above. The doubled points for the
inner angles correspond to the sightlines on either side of
the Galactic center. We clearly see a trend with Galac-
tic radius, evidence for an intrinsic Aλ/AKs radial de-
pendence underlying the apparent dependence of the in-
frared extinction law on Galactic angle. The behavior
with RGC is as expected from both the analyses in this
section and theoretical predictions: the presumably more
diffuse ISM in the outer disk produces higher CERλval-
ues (which appear as a steeper extinction curve) relative
to the inner disk. Comparison to theoretical models sug-
gests consistency with the presence of larger grains and
a higher selective-to-relative extinction ratio in the in-
ner Galaxy, decreasing to almost exclusively sub-micron
particles in the outer disk.
Interstellar dust grain size is a function of both the ini-
tial size distribution at formation and the ongoing pro-
cesses that further affect grain size, crystallinity, and
even composition.The formation size distribution of
Galactic dust, and indeed the formation mechanism(s)
itself, is not yet definitively understood (e.g., Speck et al.
2009; Zhukovska & Gail 2009), and layered on top of
these are multiple complex processes, including grain co-
agulation, gas accretion, thermal annealing, collisional
shattering, and gas-grain sputtering, which depend on
local ISM phase and conditions.
sions from the various analyses presented here regard-
ing the mean grain size spatial distribution—larger (at
least micron-sized) grains at small Galactocentric radii,
decreasing steadily to sub-micron ones past the solar
circle—provide an observational constraint on the con-
volved patterns of grain size formation distribution and
the relative importance of local conditions and process-
ing mechanisms at different locations in the disk.
Our initial conclu-

Page 13

Galactic Infrared Extinction Law 13
Fig. 12.— CERλvalues for the three ranges of Galactocentric
angle (≥150◦, 57◦–59◦, and ≤13◦, shown by squares, diamonds,
and circles, respectively) dominated by dust at specific radii RGC.
The double points for RGC = 5.5 kpc and RGC = 6.8 kpc cor-
respond to the sightlines on either side of the Galactic center.
Also shown are three curves extrapolated from the dust models
by Weingartner & Draine (2001), with RV and size distribution
case as indicated.
6. SUMMARY AND CONCLUSIONS
Using data from 2MASS (Skrutskie et al. 2006) and
three extensive Spitzer-IRAC surveys (Benjamin et al.
2003, PID 20499, and PID 40791), we have studied the
interstellar relative extinction as a function of wavelength
through the near- and mid-infrared (1.2-8 µm) for con-
tiguous lines of sight covering ∼150◦of the Galactic disk.
Using G and K spectral type red clump (RC) stars,
we have calculated color excess ratios and derived the
wavelength-dependent extinction behavior as a function
of angle from the Galactic center. We find the IR extinc-
tion law becomes increasingly steep as the Galactocentric
angle increases, with identical behavior between l < 180◦
and l > 180◦.
Aware that dense molecular clouds scattered through-
out the disk have recently been shown to exhibit MIR
extinction behavior quite different from that of the dif-
fuse ISM (e.g., Flaherty et al. 2007; Rom´ an-Z´ u˜ niga et al.
2007; McClure 2009; Chapman et al. 2009), we culled
from our sample those stars spatially associated with
lines of sight having detectable13CO (J=1→0) emission
(Jackson et al. 2006), here used as an indicator of high
ISM density (n(H) ? 1–5 cm−3). After doing so, we find
that the derived Aλ/AKstrend with Galactic angle per-
sists, in what should be diffuse ISM only. This behavior
suggests that, apart from high density molecular clouds,
at least one secondary factor that varies throughout the
Galactic disk is at work, such as grain size, composition,
or crystalline fraction. As these factors themselves de-
pend on local ISM conditions (including density), and
that even within the diffuse ISM there are likely to be
density gradients, we see clearly that the previous sim-
ple, bimodal division of the ISM into “dense” and “dif-
fuse” environments is not adequate to characterize the
displayed variation in extinction behavior.
We find close matches to our empirical extinction
curves (as derived from our diffuse-only and total RC
samples) in the diffuse-ISM study of Indebetouw et al.
(2005) and the lowest-density cases of Chapman et al.
(2009), but not in the work of Lutz et al. (1996),
Jiang et al. (2006), and Flaherty et al. (2007), who fo-
cus on regions of known high dust density. Our results
are consistent with several of the theoretical dust models
presented by Weingartner & Draine (2001), and we use
this comparison to characterize the dust at different po-
sitions in the Galaxy. We find that the best-matched RV
decreases (from 5.5 to 3.1) at increasingly greater angles
from the Galactic Center, and the input size distribu-
tions of the best-fit models suggest a decrease in mean
grain size (from super- to sub-micron) towards the outer
Galaxy.
We characterize the extinction “upturn” at ∼8 µm in
each field’s extinction law with the ratio A[5.8µ]/A[8µ],
and we find a clear increase in the strength of this in-
flection at greater Galactocentric angles. The 9.7 µm
silicate absorption, to which we attribute this increased
relative extinction, is strengthened by certain changes in
dust grain characteristics (e.g., to a smaller mean size
and/or lesser crystalline fraction); because these changes
are consistent with the trends between Galactic longitude
and dust grain property derived from the model compar-
isons above, we interpret the 8 µm extinction inflection
behavior as further evidence for the varying nature of
ISM dust grains from the inner to the outer Galaxy
We consider the problem of calculating extinction
curves as a function of true Galactic radius RGC. This is
the ideal, more natural approach to parameterizing the
factors that cause the observed variations in extinction
behavior, but assigning the dust spread out along the line
of sight to a particular RGC is difficult to do. To make
a first attempt, we select three lines of sight for which
we can make good approximations of the dust’s typical
RGC (at ∼5.5, ∼6.8, and ∼10.4 kpc), and we find that
the trend in extinction behavior strongly supports a de-
crease in mean dust grain size (and in RV) at greater
Galactic radii.
Careful measurements of the extinction in the outer
part of the Galaxy are difficult to make because of the
smaller numbers of observed stars and the weaker extinc-
tion to those stars. Nevertheless, large-scale surveys of
the outer disk, such as the approved GLIMPSE-360 Cy-
cle 6 Spitzer-IRAC survey, will provide stellar photom-
etry (at [3.6µ]and [4.5µ]) of the most distant, reddened
stars to the edge of the disk. A better understanding of
the Milky Way extinction law as a function of Galactic
position is crucial not only to a complete description of
the varying dust grain characteristics but also to photo-
metric and spectroscopic corrections made for observa-
tions of sources within or beyond our Galaxy that are
affected by dust reddening and extinction.
We are grateful to P. Arras for useful discussions, to
J. K. Carlberg for comments on the manuscript, and
to the anonymous referee for help with improvements
and clarifications within the paper. We also thank the
Spitzer Science Center for hosting GZ as a guest and

Page 14

14 Zasowski et al.
SRM as a Distinguished Visiting Scientist in June 2008,
during which period some of this research was conducted.
This work is based in part on observations made with
the Spitzer Space Telescope, and has made use of the
NASA / IPAC Infrared Science Archive, which are oper-
ated by the Jet Propulsion Laboratory, California Insti-
tute of Technology under a contract with NASA. Support
for this work was provided by NASA through awards
1276756 and 1316912 issued by JPL/Caltech. We ac-
knowledge use of data products from the Two Micron
All Sky Survey, a joint project of the University of Mas-
sachusetts and the Infrared Processing and Analysis Cen-
ter / California Institute of Technology, funded by NASA
and the NSF. This publication also makes use of molecu-
lar line data from the Boston University-FCRAO Galac-
tic Ring Survey (GRS). The GRS is a joint project of
Boston University and Five College Radio Astronomy
Observatory, funded by the National Science Founda-
tion under grants AST-9800334, AST-0098562, & AST-
0100793. GZ acknowledges support from the Virginia
Space Grant Consortium.
APPENDIX
COLUMN DENSITY INDEPENDENCE OF COLOR EXCESS RATIOS
The extinction Aλat wavelength λ is the difference between the source’s intrinsic intensity I0,λand the observed,
extinguished intensity Iλ=I0,λe−τλ:
Aλ=−2.5log
Iλ
I0,λ
=−2.5loge−τλ
∴ Aλ∼1.086τλ.
(A1)
For a given color (λ1−λ2), the reddening E(λ1−λ2) is the difference in extinction (in magnitudes) between λ1and
λ2:
E(λ1− λ2) = Aλ1− Aλ2= 1.086(τλ1− τλ2)(A2)
Recalling that τλ= N · κλ, where N (cm2) is the column density of extinguishing material along the line of sight
and κλ(cm−2) is the extinction cross-section, the color excess ratio (CERλ) can be expressed as
CERλ=
E(H − λ)
E(H − Ks)
=τH− τλ
τH− τKs
=N (κH− κλ)
N (κH− κKs)
CERλ=κH− κλ
κH− κKs;(A3)
i.e., CERλis independent of the line of sight’s particular column density N. The CERλis a function of the wavelength-
dependent extinction cross-section per particle, which is governed by the grain composition, size, and shape, but not
the total column density (or for this work, the potentially vastly different column densities towards each star in the
sample).
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