Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.stsci.edu/~kgordon/papers/PS_files/dust_scat.ps.gz Äàòà èçìåíåíèÿ: Mon Sep 29 22:52:25 2003 Äàòà èíäåêñèðîâàíèÿ: Tue May 27 07:55:07 2008 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: reflection nebula

Astrophysics of Dust
ASP Conference Series, Vol. ??, 2004
A.N. Witt, G.C. Clayton, & B.T. Draine
Interstellar Dust Scattering Properties
Karl D. Gordon
Steward Observatory, University of Arizona, Tucson, AZ 85721
Abstract. Studies of dust scattering properties in astrophysical objects
with Milky Way interstellar dust are reviewed. Such objects are reflection
nebulae, dark clouds, and the Di#use Galactic Light (DGL). To ensure
their basic quality, studies had to satisfy four basic criteria to be included
in this review. These four criteria significantly reduced the scatter in dust
properties measurements, especially in the case of the DGL. Determina­
tions of dust scattering properties were found to be internally consistent
for each object type as well as consistent between object types. The
2175 š A bump is seen as an absorption feature. Comparisons with dust
grain models find general agreement with significant disagreements at
particular wavelengths (especially in the far­ultraviolet). Finally, unan­
swered questions and future directions are enumerated.
1. Introduction
The scattering properties of dust provide a unique view into the physical prop­
erties of dust grains. This view is di#erent from other probes of dust grains
(eg., extinction, polarization due to di#erential extinction, abundances) as it
allows their absorption and scattering properties to be separated. The scatter­
ing properties of dust grains are indicators of the size and composition of dust
grains.
The scattering of photons by dust grains can be described by a single scat­
tering albedo, a, and a scattering phase function, #(#), where # is the scattering
angle. In most studies, #(#) is approximated by the single parameter Henyey­
Greenstein (1941) phase function
#HG (#) = # 1 - g 2
#
4# (1 + g 2
- 2g cos #) 3/2
(1)
where
g = # #(#) cos # d# = #cos ## . (2)
The g parameter is referred to as the scattering phase function asymmetry and
varies from ­1 (complete back scattering) to 0 (isotropic scattering) to 1 (com­
plete forward scattering). This Henyey­Greenstein phase function is a good ap­
proximation for dust grains, except possible in the far­ultraviolet (Witt 1989).
Other analytic forms of the scattering phase function have been proposed (e.g.,
1

2 Gordon
Cornette & Shanks 1992; Draine 2003b), but have yet to be used in dust scat­
tering studies.
There are three astrophysical objects which are suited for studies of Milky
Way interstellar dust scattering properties. These are reflection nebulae, dark
clouds, and the Di#use Galactic Light (DGL). These objects consist of either
high­density or di#use dust illuminated by su#ciently strong sources to permit
the detection of scattered light. Reflection nebulae usually consist of a single or
small number of stars illuminating their natal cloud. Dark clouds are isolated
dust clouds which are usually illuminated by the interstellar radiation field. The
DGL is the sum of the light of the stars in the Milky Way scattered by dust
in the Galaxy. Other objects which do show scattering light, but which are
not suitable for such studies are circumstellar disks, H II regions, and external
galaxies. These objects have dust which is newly formed, processed, or non­
Milky Way dust.
Each of these three astrophysical objects have di#erent strengths and weak­
nesses with respect to determining dust scattering properties. The strengths of
reflection nebulae are that they are bright, have simple, wavelength indepen­
dent illuminator geometries, and are illuminated by a single or handful of stars.
Their weaknesses are that they often have strong emissions in the red (Extended
Red Emission [ERE]) and near­infrared (non­equilibrium, thermal small particle
emission). In addition, they usually probe high density regions (R V > 3.1) mak­
ing the results harder to compare to most dust grain models. The strengths of
dark clouds are that they have simple, wavelength independent illuminator ge­
ometries and are externally illuminated by the interstellar radiation field and/or
a small number of stars. Dark clouds share the same weakness as reflection
nebulae as they also probe high density regions (R V > 3.1) and, in addition,
they are di#cult to observe as they are faint. The strength of the DGL is that
it probes the di#use interstellar medium (R V = 3.1). The weaknesses of the
DGL are that the illuminator geometry is wavelength dependent and the dust
geometry is complex having a disk density distribution with embedded dust
clouds. In addition, DGL observations are challenging as observations of the
faint DGL signal are needed over a fairly large region of the sky, especially a
range of galactic latitudes, to allow for accurate measurements of a and g. The
combination of the results from all three astrophysical objects should give a
good view of dust scattering properties without undue uncertainties resulting
from each object type's weaknesses.
This review will concentrate on published studies of interstellar dust scatter­
ing properties in the ultraviolet, visible, and near­infrared. The topic of X­ray
scattering by dust is covered elsewhere in these proceedings. A great deal of
work has taken place in this area since the review of dust scattering properties
at the last dust meeting (Witt 1989). At that time, only a handful of studies ex­
isted which made quantitative determinations of dust scattering properties (ie.,
actually determined values for a and g). Since the last dust meeting, a number
of studies have specifically been addressed to this issue.
Brief summaries of these studies, usually in the form of plots of a and g
as a function of wavelength, have been presented in the literature (eg., Gordon
et al. 1994; Mathis 1996; Li & Greenberg 1997; Witt & Gordon 2000; Draine
2003a, 2003b). One drawback to these reviews has been the inclusion of all

APS Conf. Ser. Style 3
literature results without consideration of the quality of each study. This has
lead to a misplaced notion that our knowledge of dust scattering properties is
quite uncertain in some wavelength regions. This has been especially pronounced
in studies of the DGL in the far­ultraviolet (around 1500 š A). In a handful of
these studies, preliminary analyses have been revised in later papers resulting
in significantly higher determinations of both a and g. Thus, it is important to
apply a uniform set of criteria when reviewing dust scattering studies to ensure
the basic quality of the results. This has been done in this review.
2. Literature Results
The literature was searched for determinations of dust scattering properties in
objects possessing Milky Way interstellar dust. Astrophysical objects which
satisfy this constraint are reflection nebulae, dark clouds, and the DGL.
For inclusion in this review, each study had to satisfy four criteria. These
criteria are:
1. Determine albedo & g : This requires that specific values be quoted for
the two quantities. Studies which were only sensitive to one of the two
quantities were included as long as a realistic range of the other quantity
was probed. Usually, the albedo (a) was the quantity determined with
calculations performed for g values between zero and one. While this
criteria means that the large number of early studies which only put limits
on a and/or g are neglected, their limits are usually consistent with the
values determined from later studies.
2. Determine uncertainties: The importance of this criteria cannot be un­
derstated. The uncertainties presented here are either the uncertainties
quoted in the original paper or reflect the range of a & g values allowed by
models presented in each study. This can mean that multiple models (with
di#erent assumptions) have been combined into a single measurement with
larger uncertainties than a single model.
3. Refereed Publication: This ensures that the full details of the work have be
presented. In addition to the usual journals (eg., ApJ, AJ, A&A, PASP,
MNRAS, etc.), theses were counted as refereed publications.
4. Not be superseded by other work : A number of studies are superseded by
newer work which usually used better radiative transfer models (especially
the case for DGL studies). This usually results in significantly di#erent
determinations of a & g.
The studies satisfying the first three criteria are listed in Table 1, separated
by astrophysical object studied. These tables give the study reference, a brief
description, a model code, and whether the study satisfied the fourth criteria
and, as such, was included in Figs. 1­4. Each model code is explained in Table 2
where the method of calculation, sources, and dust geometry are summarized.
Ideally, the model used to interpret the observations of a specific object would
include realistic illuminators (location and spectrum), a realistic dust distribu­
tion, and calculate the full multiple scattering of photons. This ideal is unlikely

4 Gordon
to be fully met by any specific model, but models which come closest have the
best chance of producing good dust scattering properties. The original study
reference should be consulted for the full details of each study.
The a and g values for the studies which satisfy all four criteria are plotted
separate in Figs. 1­3 for reflection nebulae, dark clouds, and the DGL. In addi­
tion, predictions for di#erent dust grain models are included in these figures (see
§3.1. for model details). The results have been divided between object classes
to highlight their di#erences. It would not be surprising to find real di#erences
in the a and g values between object classes. For example, reflection nebulae
and dark clouds possess, on average, larger dust grains than the DGL. This is
seen from the di#erent R V values measured for these objects as R V is a rough
measure of the average grain size. Examining the results separately also allows
for the impact of the di#erent strengths and weaknesses of each object on the
derived scattering parameters to be examined. The final reason to separate the
results is to check if the assumptions in the modeling based on object type signif­
icantly a#ect the resulting scattering values. All of the a and g values have been
plotted together in Fig. 4 to check the consistency of determinations between
the three astrophysical object types.
3. Discussion
The brightness and relative compactness of reflection nebulae have led to de­
terminations of dust scattering properties with a finer wavelength sampling and
smaller uncertainties than in either dark clouds or the DGL (see Fig. 1). Due to
the usual presence of strong emissions (ERE and non­equilibrium emission), re­
flection nebulae have only provided scattering information in the ultraviolet and
blue­optical. While dark clouds are faint, their relative compactness and usual
lack of strong emissions has made them valuable as probes of dust scattering
properties in the red­optical and near­infrared (Fig. 2). The one drawback to
both reflection nebulae and dark cloud studies is that they probe higher density
media than di#use interstellar medium. This leads to questions to the general
applicability of reflection nebulae and dark clouds results.
The faintness and large extent of the DGL makes it the most challenging
object to both observe and model. The importance of measuring dust scat­
tering properties in the di#use interstellar medium and determinations of the
extragalactic background has resulted in considerable e#ort being expended on
the study of the DGL. Determinations of DGL dust scattering properties in the
blue­optical and near­ultraviolet have been fairly uncontroversial, while such
determinations in the far­ultraviolet have been quite controversial. This contro­
versy is highlighted by the back­to­back reviews on the ultraviolet background
in which it was argued that the majority of the ultraviolet background is from
dust scattered light (Bowyer 1991) or extragalactic light (Henry 1991). The
di#culties in both observing and modeling the DGL in the far­ultraviolet has
led to studies in the literature with conflicting results, either low a and g values
or high a and g values. This is the area which was most a#ected by the fourth
criteria (not superseded by a more recent study). A number of initial analyses
giving low a and g values were superseded by subsequent studies using more
sophisticated models which found higher a and g values. As a result, the scatter

APS Conf. Ser. Style 5
Table 1. Literature Dust Scattering Studies
Reference Description Model Inc.
Reflection Nebulae
Witt et al. 1982 NGC 7023; IUE 1200--3000 š A RN1 Yes 1
& ground­based 3470--5515 š A
Witt et al. 1992 NGC 7023; UIT 1400 & 2800 š A RN1 Yes
Witt et al. 1993 NGC 7023; RN1 Yes
Vogager 2 1000--1300 š A
Gordon et al. 1994 Sco OB2; 1365 & 1769 š A RN2 Yes
Calzetti et al. 1995 IC 435; IUE 1200--3100 š A & RN1 Yes
ground­based B & V
Burgh et al. 2002 NGC 2023; FOT 900--1400 š A RN1 Yes
Gibson et al. 2003 Pleiades; WISP 1650 & 2200 š A RN3 Yes
Dark Clouds
Matilla 1970 Coalsack and Libra dark DC1 Yes
cloud; UBV
Fitzgerald et al. 1976 Thumbprint Nebula; B DC1 Yes
Laureijs et al. 1987 L1642; 3500--5500 š A DC1 Yes 2
Witt et al. 1990 Bok globule; 4690--8560 š A DC1 Yes
Hurwitz 1994 Taurus molecular cloud; DC2 Yes
Berkeley UVX 1600 š A
Haikala et al. 1995 G251.2+73.3 cirrus cloud; DC1 Yes
FAUST 1400--1800 š A
Lehtinen & Mattila 1996 Thumbprint Nebula; JHK DC1 Yes 2
Di#use Galactic Light
Witt 1968 ground­based 3600, 4350, DGL1 No 3
& 6100 š A
Mathis 1973 ground­based 3600 & DGL2 Yes 2
4350 š A
Witt & Lillie 1973 OAO­2 1500--4200 š A DGL3 No 4
Lillie & Witt 1976 OAO­2 1500--4200 š A DGL2 Yes
Morgan et al. 1976 TD­1 2350 & 2740 š A DGL3 Yes 2
Toller 1981 Pioneer 10 4400 š A DGL4 Yes
Hurwitz et al. 1991 Berkeley UVX 1625 š A DGL5 No 5
Murthy et al. 1993 Voyager 2 1050 š A DGL6 Yes 2
Murthy & Henry 1995 Berkley UVX & others DGL6 Yes 2
Sasseen & Deharveng 1996 FAUST 1565 š A DGL7 No 6
Petersohn 1997 DE 1 1565 š A DGL8 Yes
Witt et al. 1997 FAUST 1564 š A DGL8 Yes
Schiminovich et al. 2001 NUVIEWS 1740 š A DGL9 Yes
1 UV g determinations not included, not enough radial data for unique g solution
2 No g determination possible
3 Superseded by Mathis 1973
4 Superseded by Lillie & Witt 1976
5 Superseded by Murthy & Henry 1995
6 Superseded by Witt et al. 1997

6 Gordon
Table 2. Radiative Transfer Models
Name Method Sources Dust Geometry
RN1 Monte Carlo single star homogeneous sphere
RN2 Monte Carlo multiple stars homogeneous sphere
RN3 analytic multiple stars approximated
single scattering clumpy slab
DC1 Monte Carlo MW ISRF & homogeneous sphere
specific stars
DC2 numerical int. MW ISRF 2D distribution
DGL1 analytic Galaxy model homogeneous slab
DGL2 numerical int. MW ISRF infinite cylinder
n=8 scatterings boundary condition
DGL3 analytic constant infinite slab
DGL4 numerical int. star counts non­homogeneous
n=2 scatterings
DGL5 numerical int. TD­1 star catalog clumped dust
DGL6 numerical int. SKYMAP catalog dust based on
HI survey
DGL7 Monte Carlo star catalogs dust based on
HI survey
DGL8 Monte Carlo TD­1 star catalog dust cloud spectrum
based on HI survey
DGL9 Monte Carlo 3D TD­1 star catalog dust cloud spectrum
based on HI survey

APS Conf. Ser. Style 7
Figure 1. Determinations of the albedo and g in reflection nebulae
are plotted versus wavelength. In addition, predictions from dust grain
models are plotted for comparison.

8 Gordon
Figure 2. Determinations of the albedo and g in dark clouds are
plotted versus wavelength. In addition, predictions from dust grain
models are plotted for comparison.

APS Conf. Ser. Style 9
Figure 3. Determinations of the albedo and g in the DGL are plotted
versus wavelength. In addition, predictions from dust grain models are
plotted for comparison.

10 Gordon
Figure 4. The combined determinations of the albedo and g in reflec­
tion nebulae, dark clouds, and the DGL are plotted versus wavelength.
The plot symbols are not identified and do not correspond to legends
in previous figures, see Figs. 1­3 for information about specific stud­
ies. In addition, predictions from dust grain models are plotted for
comparison.

APS Conf. Ser. Style 11
in the plots of a and g for the DGL (Fig. 3) is now within the quoted uncer­
tainties. The values of a and g derived from DGL measurements are similar to
those derived from reflection nebulae and dark clouds.
By examining Figs. 1­3, it can be seen that the a and g values derived for
each object type are internally consistent. For example, the measurements of
a and g from di#erent reflection nebulae all are consistent with a single wave­
length dependence. When examing these figures, it is important to remember
that they include results from broad­band filters along with those derived from
spectroscopy. Comparing the results for all three object types in Fig. 4, it can
be seen that the same may be true in general and not just internal to an object
type. The only area where the data from di#erent object types may disagree is
in the far­ultraviolet region for a measurements only. The uncertainties are large
enough to make a strong statement either way di#cult. The high level of agree­
ment between object types implies that their di#erent strengths and weaknesses
as well as model assumptions are not severely biasing our view of dust scatter­
ing properties. This result goes a long way in answering the concerns raised
by Mathis, Whitney, & Wood (2002) about possible biases in reflection nebulae
measurements of the dust albedo caused by ignoring the known clumpiness of
dust.
In fact, it is not unreasonable to say that the current data (see Fig. 4) indi­
cates the wavelength dependence of the albedo is #0.6 in the near­infrared/optical
with a dip to #0.4 for 2175 š A bump, a rise to #0.8 around 1500 š A, and a drop
to #0.3 by 1000 š A. The wavelength dependence of g is simpler with a mono­
tonic rise from 0.6 to 0.8 from 10000 to 1000 š A. The uncertainties do allow for
significant real variation in the a and g values around these qualitative averages
of at least 0.1.
The study of dust scattering properties has shed light on the nature of
the 2175 š A bump and the far­ultraviolet rise features of extinction curves. Early
work on the 2175 š A bump indicated that it was likely an absorption feature with
no scattered component (eg., Lillie & Witt 1976). Subsequently, evidence for a
scattered component in the 2175 š A bump was found in two reflection nebulae,
CED 201 and IC 435, by Witt, Bohlin, & Stecher (1986). This results was found
to definitely be spurious for IC 435 when much more sensitive observations were
taken and analyzed by Calzetti et al. (1995). By inference, the observations
of CED 201 are also likely to be spurious. As a result, all evidence currently
supports a 2175 š A extinction bump which is only due to absorption. Similarly,
examining the results of reflection nebulae (see Fig. 1) gives good evidence that
a significant portion of the far­ultraviolet rise in extinction curves (1700 š A and
shorter wavelengths) is due to absorption.
3.1. Comparisons with Dust Grain Models
One way to synthesize our knowledge of dust is to fit di#erent observations of
dust to a dust grain model. The main observational constraints for dust grain
models are usually the di#use ISM dust extinction curve and dust abundances
(Weingartner & Draine 2001; Clayton et al. 2003). In addition, some dust grain
models also fit the dust polarization (Kim & Martin 1994; Li & Greenberg 1997)
and infrared emission spectrum (Zubko et al. 2003; Li & Draine 2001). Some
dust grain models also have been fit to the denser dust extinction curves (Kim,

12 Gordon
Martin, & Hendry 1994; Weingartner & Draine 2001). No dust grain models
have used the measured dust scattering properties as fitting constraints, but
most do use the scattering properties as a consistency check.
In Figs. 1­4, predictions for a and g from recent dust grain models are
plotted. The Zubko et al. (2003) model plotted is described as BARE­NC­B. All
but one of the five model predictions plotted are for di#use ISM dust (R V = 3.1)
and are then only directly comparable to the DGL dust scattering results. As
can be seen from Fig. 3, the dust grain models are in fairly good agreement with
the results for g, but most of the models underpredict a for most wavelengths.
All the models have a small dip in a at the 2175 š A bump, but the dip is not
as large as indicated by the DGL measurements. The models all predict lower
far­ultraviolet albedos than have been measured in the DGL.
The one dust grain model for denser dust (Weingartner & Draine; R V = 5.5)
is directly comparable to the dust scattering measurements in reflection nebulae
(Fig. 1) and dark clouds (Fig. 2) as these objects have similar R V values. Similar
to the DGL comparison, the g values predicted by the model are in reasonable
agreement for reflection nebulae and dark clouds, except possible in the optical
for dark clouds. The model predictions for a agree with the measurements for
dark clouds which mainly probe the optical and near­infrared. The a predictions
for reflection nebulae are generally too high in the optical and too low in the
far­ultraviolet. The albedo dip at 2175 š A is much smaller in the model than the
well measured values indicate. Basically, the recovery of the albedo at around
1500 š A is not seen in any of the dust grain models.
4. Summary and Future
This review of dust scattering determinations has concentrated on giving a criti­
cal examination of results presented in the literature for reflection nebulae, dark
clouds, and the DGL. Unlike previous such reviews, each study was required to
pass four simple criteria for inclusion in this review. There were a total of 23
studies passing the four criteria with 7 on reflection nebulae, 7 on dark clouds,
and 9 on the DGL.
A great deal of progress has been made since the last review of this area
(Witt 1989). The uncertainty in far­ultraviolet albedo from DGL studies has
been resolved with the help of better observations and more sophisticated mod­
eling. The 2175 š A bump has been shown to be an absorption feature; earlier
indications of scattering in the bump have been traced to bad data. The mea­
surements in reflection nebulae, dark clouds, and the DGL are roughly consistent
alleviating earlier worries about the e#ects of the modeling assumptions specific
to the object being studied (eg. reflection versus the DGL).
While much progress has been made in measuring dust scattering properties,
there are a number of questions which are outstanding.
1. Does the assumption of the Henyey­Greenstein single parameter scattering
phase function significantly bias the resulting dust scattering parameters
(a and g)? This question is probably best answered with models of images
of reflection nebulae and dark clouds which include either more compli­
cated analytical phase functions (eg., a double Henyey­Greenstein phase

APS Conf. Ser. Style 13
function; eq. 4 of Witt 1977) or scattering phase functions computed from
dust grain models.
2. What are the a and g values in the near­infrared? Currently, there is only
a measurements for a single dark cloud and no g measurements. The a
and g values in the near­infrared probe the larger dust grains, information
about which is di#cult to determine from extinction curve measurements
alone.
3. What are the a and g values in the red­optical and near­infrared for re­
flection nebulae? Is it even possible to determine a and g in reflection
nebulae for these wavelengths? There are reflection nebulae in which ERE
has not been detected (Witt & Boroson 1990). Are there nebulae without
near­infrared, non­equilibrium emission?
4. Is it possible to measure dust scattering properties in the red­optical and
near­infrared from DGL measurements?
5. What does it mean to measure dust scattering properties in objects with­
out ERE or near­infrared, non­equilibrium emission if the di#use ISM has
been shown to have ERE (Gordon, Witt, & Friedmann 1998) and probably
also has near­infrared, non­equilibrium emission.
6. Is it possible to use the full multiwavelength appearance of reflection neb­
ulae and dark clouds to alleviate lingering concerns about the geometrical
assumptions inherit in modeling such objects? Specifically, the inclusion
of ultraviolet through far­infrared would provide direct measurements of
the direct, scattered, and re­emitted light and thus require many fewer
assumptions.
7. Is it feasible to consider using the full multiwavelength appearance of the
DGL to reduce number of assumption necessary to model the DGL? Or
is this still too complex of a problem, especially in light of the need for
accurate 3D star positions of all stars important for the DGL (eg., hot
stars in the ultraviolet and cooler stars at longer wavelengths)?
8. What are the real di#erences between dust scattering properties in reflec­
tion nebulae, dark clouds, and the DGL? The current evidence indicates
they are consistent with each other at the #20% level.
9. Are the dust scattering properties in other galaxies di#erent than those
derived for Milky Way dust? The Large and Small Magellanic Clouds
o#er environments which have lower metallicities and high star formation
rates than the Milky Way. In addition, dust extinction curves in the
Magellanic Clouds have been measured to be quite di#erent from Milky
Way extinction curves (Gordon et al. 2003).
Finally, the author would like to encourage readers who find studies which
have not been included in this review to email them to the author (currently

14 Gordon
kgordon@as.arizona.edu). The author is committed to continuing to update the
web­based version of this review 1 .
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