Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.stsci.edu/~kgordon/papers/PS_files/upper_sco_ob2.ps.gz Äàòà èçìåíåíèÿ: Thu Apr 24 02:49:35 2003 Äàòà èíäåêñèðîâàíèÿ: Tue May 27 07:57:40 2008 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: molecular cloud

The Far­Ultraviolet Dust Albedo
in the
Upper Scorpius Subgroup of the Sco OB2 Association
Karl D. Gordon and Adolf N. Witt
Ritter Astrophysical Research Center, The University of Toledo
Toledo, OH 43606
and
George R. Carruthers, Susan A. Christensen, and Brian C. Dohne
E. O. Hulburt Center for Space Research, Code 7609
Naval Research Laboratory, Washington, DC 20375­5320
ABSTRACT
During NRL's Far Ultraviolet Cameras experiment on STS­39, four images of the
giant reflection nebula encompassing the Upper Scorpius subgroup of the Sco OB2
association were obtained in two ultraviolet bandpasses with – eff = 1362 š A and 1769
š A. From these images and IUE and TD­1 stellar spectra, the ratio of nebular to stellar
flux was calculated. The ratio ranged from 0.577 to 0.921 at 1362 š A and 0.681 to
0.916 at 1769 š A with the spread in the ratio arising mainly from uncertainties in the
sky background. In order to analyze these images, a model utilizing Monte Carlo
techniques to describe radiative transfer in a spherical nebula with asymmetrically
distributed stars was developed by elaborating on previous work by Witt (1977).
This model was used to determine the range of albedos reproducing the observed
nebular--to--stellar flux ratios while allowing the scattering phase function asymmetry
to vary between 0.0 and 0.8. The resulting albedos were between 0.47 and 0.70 at 1362
š A and between 0.55 and 0.72 at 1769 š A.
Subject headings: dust, extinction -- ISM: individual -- open clusters and associations:
individual (Scorpius OB2) -- radiative transfer -- ultraviolet: ISM
1. Introduction
The dust albedo in the far--ultraviolet (FUV), 912 š A -- 2500 š A, has been studied by many
authors, but agreement on the range of acceptable albedos has yet to be reached. The FUV albedo
has been determined by measuring the spatial distribution of the diffuse galactic light (DGL) and
the scattered light in reflection nebulae and interpreting these observations with radiative transfer

-- 2 --
models. Early work using the DGL concluded that the FUV albedo was approximately 0.6 (Witt
& Lillie 1973; Lillie & Witt 1976). The latest work on the DGL has constrained the FUV albedo
to be less than 0.25 (Hurwitz, Bowyer, & Martin 1991). An extensive multiwavelength study of
the reflection nebula NGC 7023 concluded that the FUV albedo was greater than 0.6 (Witt et al.
1982; Witt et al. 1992; Witt et al. 1993). Bowyer (1991) and Henry (1991) have disagreed on the
solution to the FUV albedo problem in two recent reviews concentrating on determinations using
the DGL. Mathis (1993) gives an excellent general review of interstellar dust including a review of
the two above reviews.
The disagreement surrounding the FUV albedo arises in the DGL from the coupled nature
of the two parameters used to describe the scattering process which produces the scattered light
intensity. The two parameters describing the scattering process are the albedo, the percentage of
light reflected by the dust grain, and the scattering phase function asymmetry, g. The scattering
phase function asymmetry is the weighted average of the cosine of the scattering angle, where
the weight is the scattering phase function. This coupling arises in the interpretation of the
high--latitude DGL intensity which can be produced by a low albedo and low g or a high albedo
and high g. In studying reflection nebulae, this coupling is much weaker, but uncertainties in the
nebula's geometry greatly affect the validity of the resulting FUV albedo.
Two classes of reflection nebulae exist, externally and internally illuminated. The distribution
of surface brightness of an externally illuminated nebula is strongly dependent on g and only
weakly dependent on the albedo (Witt & Stephens 1974; Witt, Oliveri, & Schild 1990). The total
internal flux of internally illuminated nebulae is strongly dependent on the albedo and only weakly
dependent on g. As a result, observing externally illuminated nebulae probes g and internally
illuminated nebulae probes the albedo.
The reflection nebula in the region of the Upper Scorpius subgroup of the Sco OB2 association
is an internally illuminated nebula, thus allowing for a determination of the FUV albedo mostly
independent of g. Studying this nebula avoids the main uncertainty associated with determinations
of the FUV albedo from NGC 7023, namely foreground dust. Gaustad and Van Buren (1993)
examined the IRAS database at the positions of O and B stars for extended objects with excess
emission at 60 ¯m which indicated the presence of interstellar dust at that position. They deduce
that we reside in a low--density ``trough'' in the interstellar medium which, in the direction of
the Upper Scorpius subgroup of the Sco OB2 association, extends out to 60 pc. Examining their
data corresponding to the Upper Scorpius region, we find a hole in their ``trough'' in exactly the
direction of the Upper Scorpius subgroup. There appears to be very little dust between us and the
Upper Scorpius reflection nebula. The internal illumination arises from multiple embedded stars;
thus the uncertainties associated with the physical properties of individual stars are averaged
out. This nebula is in a quite different portion of the sky than previously studied nebulae, so our
results will increase the applicability of comparing the average dust properties of nebulae with the
dust properties of the DGL.

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TABLE 1
Observational Details
Image Camera Exposure Time
[s]
1 1 300
2 1 100
3 2 100
4 2 30
In x2 we describe the observations of this nebula and the calculation of the nebular to stellar
flux ratio for this object. The model used in this study is explained in x3. The application of the
model to this specific nebula is detailed in x4. In x5 we discuss the ramifications of our results,
and a summary of this paper appears in x6.
2. Observations
Images of the Upper Scorpius subgroup of the Sco OB2 association were obtained during the
Far UV Cameras experiment (NRL­803), which was part of the Air Force Space Test Program's
AFP­675 payload that flew aboard the space shuttle in 1991 May (STS­39). The instrument
consisted of two electrographic Schmidt cameras with opaque alkali halide photocathodes. The
cameras had collecting aperture diameters of 75 mm with f/1 focal ratios. The first camera
covered the wavelength range 1230--1600 š A using a CaF 2 filter. The second camera covered the
range 1650--2000 š A using a SiO 2 filter and was equipped with a microchannel intensifier stage,
which yielded an intensity gain of approximately 100. Each image extended over a circular area of
20 ffi diameter with an angular resolution of approximately 3' (Carruthers 1986). The images were
digitized with a PDS model 1010ms microdensitometer and calibrated using pre­ and post­flight
measurements (Carruthers et al. 1992). The conversion from image pixels to galactic coordinates
was accomplished separately for each image by using the pixel coordinate of the intensity maxima
of three unsaturated stars with known galactic coordinates.
Four images were obtained with exposures between 30 and 300 s (Table 1). Image 4 taken
with camera 2 for 30 s is displayed in Figure 1 (Plate 1). These images were centered on the star ae
Oph and contained a majority of the Upper Scorpius subgroup of the Sco OB2 association. In all
four images, the light from the ultraviolet stars is scattered by the surrounding interstellar dust,
producing a giant reflection nebula. These images are the first detailed FUV observations of this
nebula and show a great deal of detail, including numerous dust lanes (Carruthers et al. 1992).
In order to compare these images with theoretical computations, the nebular to stellar flux

-- 4 --
360 355 350 345
galactic longitude
10
15
20
25
galactic
latitude
360 355 350 345
10
15
20
25
Fig. 1.--- Image of the giant reflection nebula encompassing the Upper Scorpius subgroup of the Sco
OB2 association in an ultraviolet bandpass with camera 2 and an exposure of 30 s. The isophotes
are of log (S N =F S ) and they begin with ­0.5 sr \Gamma1 , increase in steps of 0.3 sr \Gamma1 , and end with 1.9
sr \Gamma1 . The image has been corrected for the maximum possible sky background, 1.8\Theta10 6 photons
(cm 2 s bandpass sr) \Gamma1 . The parallel linear streaks are trailed bright star images or scratches made
as the film advanced.

-- 5 --
ratio, FN =F S , was determined. The technique used to extract the nebular surface brightness,
SN , from the images was as follows: (1) each image was sliced along 16 parallel lines of constant
galactic latitude equally spaced in galactic latitude, (2) the slices from images taken with the
same camera were graphed together on a semi log plot increasing the visibility of the difference
in the slopes of the stellar light and SN , (3) a SN curve was drawn removing the stellar light in
the process, and (4) the SN was determined at 16 points equally spaced in galactic longitude.
Two of these plots are displayed in Figures 2a and 2b. By plotting the slices from images taken
with the same camera together, saturation problems were dealt with easily. Saturation was seen
in some regions of images 1 and 3 and compensated for by using the corresponding unsaturated
regions of images 2 and 4, respectively. For camera 1 an average shift of 2.4\Theta10 6 photons (cm 2
s bandpass sr) \Gamma1 between images 1 and 2 was found. This shift is most likely due to changes
in the airglow, specifically O I ––1304 \Gamma 1356, as the shuttle moved around earth in orbit. The
saturation problems in addition to the lack of an accurate point--spread function for either camera,
necessitated the visual extraction of SN . This method of extraction introduced little error in the
measurement of SN as the angular size of these images relegated the majority of the image to pure
nebular surface brightness. A generous estimate of the error in determining SN from the semi log
plots was 5\Theta10 5 photons (cm 2 s bandpass sr) \Gamma1 .
The outcome of the extraction process was a 16 \Theta 16 array of the nebular surface brightness
for each camera. Each 16 \Theta 16 array was expanded to fill a 512 \Theta 512 array by linear interpolation
between pixels and extrapolation on the very edges. This expansion was carried out simply to
make the calculation of the nebular flux easier, i.e. each pixel was then small enough that its
position alone determined if it was part of the nebula. The calculation of the nebular flux, FN ,
was then simply a matter of converting each pixel's surface brightness to a flux, subtracting the
sky background, and adding up the fluxes within 9:9 ffi of the center of the image, l = 354:5 ffi
and b = 17:9 ffi . Since the nebula almost entirely filled the images, the sky background could
not be determined precisely. Instead, constraints on the sky background were determined using
the minimum nebular surface brightness as the maximum possible sky background and zero as
the minimum sky background. For each camera, the range in FN was calculated by using the
512 \Theta 512 nebular surface brightness array and the constraints on the sky background (Table
3, cols. [5]--[6]). The error in the determination of the SN translates into an error in FN of
\DeltaF N = \DeltaS N
\Theta\Omega = 4.68\Theta10 4 photons (cm 2 s bandpass) \Gamma1
where\Omega is the solid angle of the nebula.
The composite stellar flux for each bandpass was determined by identifying the bright
ultraviolet stars, convolving their spectral energy distributions with each camera's sensitivity
function (Carruthers 1986), and summing the resulting fluxes. Using the ANS catalog of point
sources (Wesselius et al. 1982), the bright stars were defined as stars with magnitudes brighter
than 6 in the ANS bandpasses' 15W or 18. Basic data on these stars was collected from the
literature (Table 2). The stars' spectra were taken from the IUE archives or the TD­1 catalog
(Thompson et al. 1978), giving preferences to large­aperture low­dispersion IUE spectra, then
large­aperture high­dispersion IUE spectra, and finally TD­1 data. While there is some question

-- 6 --
Fig. 2.--- Nebular surface brightness slices (S N ) at b = 17:22 ffi . (a) Images 1 and 2 both taken with
camera 1. Note the variable background for this camera apparent in the shift of 2.4\Theta10 6 photons
(cm 2 s bandpass sr) \Gamma1 . (b) Images 3 and 4 both taken with camera 2. Note the saturation of image
3 between l = 346 ffi and 355 ffi .

-- 7 --
TABLE 2
Basic Stellar Data
HD Name l II b II MK a Flux b Flux b Flux origin
[ ffi ] [ ffi ] [1362 š A] [1769 š A]
141637 1 Sco 346.099 21.706 B1.5Vn 15150 10770 swp42216 & lwp20988
142096 – Lib 350.72 25.38 B3V 7929 5644 swp42326 & lwr10778
142114 2 Sco 346.879 21.614 B2.5Vn 14710 9847 TD­1
142165 \Delta \Delta \Delta 347.519 22.148 B5V 3066 2598 swp42217 & lwp17717
142184 \Delta \Delta \Delta 347.934 22.545 B2V 5028 3731 swp36741 & lwp15993
142250 \Delta \Delta \Delta 345.570 20.005 B7V 1845 1546 swp36742 & lwp15994
142301 3 Sco 347.1 21.51 B8III/IV 2227 2094 swp21092 & lwr16825
142315 \Delta \Delta \Delta 348.982 23.299 B9V 422 393 swp36837 & lwp16118
142378 47 Lib 351.648 25.658 B2/3V 3178 2457 swp9236 & lwr7996
142883 \Delta \Delta \Delta 350.886 24.086 B3V 2404 1904 swp42218 & lwp20990
142884 \Delta \Delta \Delta 348.965 22.254 B8/9III 595 601 swp36743 & lwp15995
142990 \Delta \Delta \Delta 348.121 21.197 B5V 4843 4099 swp42227 & lwp20991
143018A­B ú Sco 347.217 20.231 B1V+B2V 183800 115200 swp35530 & lwp15011
143275 ffi Sco 350.099 22.491 B0.2IV 226100 148300 swp35532 & lwp15012
144217­8 fi1­2 Sco 353.195 23.600 B0.5V+B2V 169400 99370 swp36791
144334 \Delta \Delta \Delta 350.349 20.855 B8V 2350 2157 swp21083 & lwr16819
144470 !1 Sco 352.752 22.773 B1V 34040 23220 swp42228 & lwp20992
144661 \Delta \Delta \Delta 349.996 19.969 B8IV/V 1418 1222 swp13953
144844 \Delta \Delta \Delta 350.736 20.368 B9V 1240 1156 swp36828 & lwp16109
145482 13 Sco 348.118 16.836 B2V 25220 17130 swp19351
145483 12 Sco 347.747 16.498 B9V 1113 1209 swp16306
145501 š Sco C 354.616 22.711 B8/9V 723 661 swp7901 & lwr6884
145502 š Sco A 354.611 22.701 B2IV 26937 16074 swp29140
145792 \Delta \Delta \Delta 351.012 19.029 B6IV 1444 1089 swp36749 & lwp16002
146001 \Delta \Delta \Delta 350.389 18.118 B8V 1414 1146 swp38567 & lwp16003
146416 \Delta \Delta \Delta 353.983 20.598 B9III/IV 450 466 swp36831 & lwp16112
147165 oe Sco 351.315 16.999 B1III 47550 26160 swp45517 & lwp23843
147933--4 ae Oph A & B 353.688 17.687 B2/3V+B2V 9564 6396 swp6588 & lwr5639
148184 ü Oph 357.677 20.677 B2Vne 8827 5955 swp15059
148479 ff Sco B 351.95 15.06 B2.5V 3449 2471 swp41472 & lwp20233
148605 22 Sco 353.100 15.796 B3V 13970 10100 swp9221 & lwr7977
149438 Ü Sco 351.536 12.808 B0V 321300 193800 swp33008 & lwp12766
a Houk 1982; Houk & Smith--Moore 1988.
b units; photons (cm 2 s bandpass) \Gamma1 .

-- 8 --
TABLE 3
Calculated Quantities from Observations
Camera – eff \Delta– eff F \Lambda (FN ) min
a (FN ) max
b (FN /F \Lambda ) min (FN /F \Lambda ) max
[ š A] [ š A] [photons/(cm 2 s filter)]
1 1362 270 1.142\Theta10 6 6.587\Theta10 5 1.052\Theta10 6 0.577 0.921
2 1769 278 7.190\Theta10 5 4.897\Theta10 5 6.583\Theta10 5 0.681 0.916
a derived from the maximum possible sky background
b derived from a sky background of zero
as to the accuracy of the faint TD­1 fluxes (Gondhalekar 1990; Bowyer et al. 1993), the only star
in this study needing TD­1 fluxes was bright enough to avoid this difficulty. The composite stellar
flux for each bandpass was computed by simply summing the individual stars' fluxes (Table 3,
col. [4]). The effective wavelength, – eff , and bandpass, \Delta– eff , for each camera was calculated by
weighting each star's – eff and \Delta– eff by the effective flux at – eff and the effective bandpass flux,
respectively (Table 3, cols. [2]--[3]). The composite stellar of each bandpass was combined with the
range of nebular fluxes yielding a range of FN =F S for each bandpass (Table 3, cols. [7]--[8]). The
error in the FN =F S was 0.041 for camera 1 and 0.065 for camera 2.
3. Model
Our model uses Monte Carlo techniques in determining the transfer of radiation through a
spherical dust geometry. The dust geometry is broken into spherical shells allowing any radial
distribution of dust, such as a geometry with a spherical dust shell and an inner dust­free region.
The amount of dust is specified by the radial optical depth. The sources of emission are specified
by their positions and luminosities , i.e. allowing multiple stars with an asymmetric distribution.
In determining when and how a photon and a dust grain interact, the methods described in Witt
(1977) are used.
The total number of photons in a particular model calculation is divided up among the stars
in the nebula according to each star's unreddened luminosity. Thus, each photon starts its journey
from one of these stars. The photon experiences forced first scattering, with the appropriate
reduction in its weight, and any subsequent scatterings are determined via Monte Carlo techniques.
Throughout the photon's journey, the effects of all scatterings are noted by keeping a weight.
Thus, when we speak of a photon and its weight we are speaking of a conceptual tool useful in
determining the behavior of radiation as it travels though the dust cloud. The final weight of the

-- 9 --
scattered photon is
W scattered = \Gamma
1 \Gamma e \GammaÜ \Delta
a n OE(cos `; g)dw: (1)
The term (1 \Gamma e \GammaÜ ) accounts for the amount of the photon forced to scatter at the first scattering
site where Ü is the optical depth to the dust cloud's surface along the photon's initial direction.
The term a n accounts for the amount of the photon reflected from a dust grain for the total n
scatterings, i.e. (1 \Gamma a) n is the amount of the photon absorbed by the dust. The term OE(cos `; g)dw
accounts for the amount of the photon actually impinging on a detector. It is composed of the
normalized Henyey­Greenstein scattering phase function (Henyey & Greenstein 1941), where `
is the angle from the final scattering site such that the photon impinges on the detector, and
dw the solid angle of the detector. Each photon's final weight, W scattered , is binned according
to its exit position on the surface of the dust cloud. This array of binned weights, which is an
uncalibrated image of the nebular flux, is transformed into an image of the uncalibrated nebular
surface brightness by dividing each array position by its solid angle. Summing all the elements of
the uncalibrated nebula flux array results in the total nebula flux.
The weight of the part of the each photon escaping the dust cloud without undergoing a
single scattering is
W stellar = e \GammaÜ dw
4ú : (2)
The term e \GammaÜ accounts for the amount of the photon exiting the dust cloud without scattering at
all where Ü is the optical depth to the dust cloud's surface in the direction of the detector. The
term dw=4ú accounts for the amount of the photon impinging on the detector. Each escaping
photon's weight is summed to produce a composite stellar flux weight (F S ). The ratio FN =F S is
a unitless number making it ideal for comparing observations with model calculations. Using the
distribution of the nebular surface brightness and the composite stellar weight, the distribution of
the ratio of the nebular surface brightness to stellar flux, SN =F S , is computed. This has units of
sr \Gamma1 , making it an excellent way to compare the distribution of the nebular surface brightness
with observations.
Our model has inputs of the albedo, phase function asymmetry, radial distribution of the
dust, radial optical depth, and positions and luminosities of individual stars. The model produces
the FN =F S and the distribution of the log (S N =F S ). With slightly more work, a calibrated FN and
distribution of SN can be also produced by knowing F S in absolute units.
4. Analysis
The result of this investigation was a derivation of the FUV albedo from the ratio FN =F S .
We chose to study an optically thick nebula with embedded stars because the ratio FN =F S varies
weakly with g. The actual distribution of scattered light does depend on g quite strongly, but the
small variation of the total nebular flux with g is a direct result of the fact that the scattered

-- 10 --
light from the embedded stars emerges somewhere. The remaining inputs needed are the radial
distribution of dust, the total optical depth, and the positions and luminosities of the embedded
stars.
In an extensive survey of gas and dust in the Sco OB2 association by de Geus & Burton (1991)
and de Geus (1992) the distribution of interstellar matter in the Upper Scorpius subgroup was,
in a broad sense, found to be a roughly spherical shell with a projected radius of approximately
15 ffi with a finger of denser matter piercing the shell. Our observations correspond to the lower
portion of this shell, where this finger disrupts the shell. Thus, this conceptual picture is most
uncertain in just the region of interest to us. Other studies have dealt with the ae Oph molecular
cloud in great detail, but as this cloud is only a small part of the Upper Scorpius subgroup these
studies were of marginal use for our purposes. In the absence of good spatial detail of the whole
Upper Scorpius subgroup dust, the dust distribution was assumed to have a constant density, be
spherically distributed, and centered on our observations. The radius was set to 9:9 ffi to correspond
to the area in common to all of our observations. In an attempt to reconcile this simple dust
distribution with the actual distribution, the stars were embedded in our spherical model nebula
by their optical depths as detailed below.
In order to determine the radial optical depth of the nebula and the positions and luminosities
of our stars, the effective optical depth toward each star was computed for both cameras'
bandpasses. The effective optical depth was computed by,
Ü eff =
R
Ü(–)Filter(–)Flux(–)d–
R
Filter(–)Flux(–)d– ; (3)
where Filter(–) is the camera sensitivity as a function of wavelength, and
Ü(–) = EB \GammaV
1:086
Ÿ
E –\Gamma2740 (–)
EB \GammaV
+ A 2740
EB \GammaV
–
: (4)
E –\Gamma2740 (–)=EB \GammaV for each star was taken from Papaj, Wegner, & Krelowski (1991) for 15 of our
stars and for the remaining stars an average constructed from these 15 stars was used (Table 4,
col. [1]). Figure 3 plots this average along with the average for general interstellar matter. The
EB \GammaV values were taken from de Geus, de Zeeuw, & Lub (1989) with the exception of HD 142096
and HD 142301, which were taken from Krelowski & Strobel (1983), and HD 148479 which was
taken from Corbally (1984) (Table 4, col. [2]). The value of A 2740 =EB \GammaV was determined from a
characterization of extinction curves by their R V values (Cardelli, Clayton, & Mathis 1988). In
the absence of good R V values for more than just a few of our stars, the value of R V was chosen
to be 3.5 using the logic that the majority of our stars possess the normal R V , 3.2 and a minority
possess much higher R V 's -- notable those near the ae Oph molecular cloud. The effective optical
depths for each star are tabulated in Table 4, cols. [3]--[4].
Using these optical depths, the radial optical depth and the stars' positions and luminosities
were computed by the following procedure. The distance to the center of the nebula was assumed
to be the average of the distances to the stars (de Geus et al. 1989), resulting in a distance of 149

-- 11 --
TABLE 4
Stellar Optical Depths and Luminosities
HD EB\GammaV Ü eff Ü eff L c L c
[1362 š A][1769 š A] [1362 š A] [1769 š A]
141637 a 0.153 0.885 1.068 65.2 42.2
142096 a 0.23 1.684 1.591 76.6 38.6
142114 a 0.113 0.985 0.802 63.0 26.9
142165 b 0.113 0.806 0.782 10.7 6.8
142184 a 0.153 1.172 1.116 26.6 14.5
142250 b 0.050 0.357 0.346 4.0 2.6
142301 b 0.07 0.499 0.485 5.4 3.9
142315 b 0.117 0.832 0.810 1.5 1.0
142378 a 0.138 0.972 0.907 13.4 7.5
142883 a 0.172 1.344 1.196 14.9 7.8
142884 b 0.159 1.128 1.100 2.9 2.2
142990 a 0.091 0.816 0.760 16.4 10.1
143018A­B a 0.072 0.507 0.489 444.9 209.6
143275 a 0.147 1.123 1.068 1069.7 509.1
144217­8 a 0.172 1.228 1.154 889.9 375.3
144334 b 0.081 0.578 0.561 5.7 4.0
144470 a 0.219 1.469 1.510 237.0 132.2
144661 b 0.097 0.692 0.672 3.9 2.6
144844 b 0.116 0.826 0.803 4.0 2.8
145482 b 0.044 0.316 0.304 46.4 24.1
145483 b 0.059 0.418 0.409 2.3 2.0
145501 b 0.247 1.757 1.709 6.9 5.2
145502 a 0.247 1.682 1.581 234.7 109.4
145792 b 0.169 1.207 1.168 7.2 4.0
146001 b 0.153 1.091 1.058 6.2 3.8
146416 b 0.075 0.532 0.520 1.0 0.8
147165 a 0.375 2.579 2.410 1158.2 417.6
147933­4 a 0.453 2.856 2.864 317.5 171.5
148184 a 0.569 3.728 3.776 821.7 466.1
148479 b 0.06 0.430 0.415 6.9 3.7
148605 b 0.069 0.495 0.478 29.6 16.3
149438 b 0.034 0.244 0.235 535.1 246.6
a extinction curve from Papaj
b average extinction curve from above curves
c units are 1.559\Theta10 53 photons/(s bandpass)

-- 12 --
Fig. 3.--- Extinction curves for the Upper Scorpius subgroup of the Sco OB2 association and the
general interstellar dust (Whittet 1992). The extinction curve for the Upper Scorpius subgroup is
an average of 15 stars in the subgroup (Papaj et al. 1991).
pc. The stars were placed in the nebula along the line of sight defined by their galactic coordinates
to a depth corresponding to their optical depths. The nebular radial optical depth was taken to
be the optical depth where all the stars just fit into our spherical model nebula. The nebular
radial optical depths were 2.12 and 2.14 for camera 1 and camera 2, respectively. Thus, the stars
are embedded correctly in optical depth space, but their physical depth position is not generally
correct. Since nebular light depends more heavily upon the optical depth than the physical
position of the stars, this should give an accurate result. The luminosities were then calculated
from the distances to the stars' positions, as determined above, and dereddened fluxes calculated
from the stars' observed spectral energy distribution (x2) and their extinction curves, detailed
above. This ensured that the flux calculated from the model would be equivalent to the observed
flux. In order to verify that our derived luminosities were not unreasonable, the luminosities at
1362 š A were converted to absolute ultraviolet magnitudes (M 1362 š A
) and compared to Carnochan's
(1982) M 1400 š A
indicated by the stars' MK classifications. As expected, the correspondence was
not perfect, it produced a well­defined linear correlation with an average dispersion of 1.0 mag.
With the necessary model inputs determined, we ran our model for an appropriate range of
g's, 0.0--0.8, and calculated the albedo necessary to reproduce the observed range of the FN =F S for
both cameras. The results are plotted in Figure 4. For camera 1 (– eff = 1362 š A), the FUV albedo
ranged from 0.47 to 0.55 for the minimum FN =F S and from 0.64 to 0.70 for the maximum FN =F S
resulting in a total range of 0.47--0.70. For camera 2 (– eff = 1769 š A), the FUV albedo ranged from

-- 13 --
Fig. 4.--- Plotted are albedos determined from our radiative model calculations. Note the small
change in the albedo arising from allowing g to range between 0.0 and 0.8.
0.55 to 0.62 for the minimum FN =F S and from 0.66 to 0.72 for the maximum FN =F S resulting in a
total range of 0.55--0.72. The error in the albedo from errors in determining the observed nebular
surface brightness was 0.02 for camera 1 and 0.03 for camera 2. Notice that this error is much
smaller than the uncertainty in the albedos introduced by the uncertainties in the sky background.
For completeness, we attempted to fit the observed distribution of SN =F S with the distribution
of SN =F S calculated from our model. The calculated log(S N =F S ) was compared to the observed
log(S N =F S ) by the linear least­squares method with a good fit defined as a slope of 1 and a
y­intercept of 0. In Figure 5 we plotted the curves for a slope = 1, for a y­intercept = 0, and
for a FN =F S = 0.681 (max background) for camera 2. This turned out to be the only case
where the slope curve and the FN =F S curve intersected. For the other three cases (camera 1,
max background; camera 1, zero background; and camera 2, zero background) none of the curves
intersected. The intersect in Figure 5 between the slope and FN =F S curves occurs at a g of 0.6
and an albedo of 0.56. Figure 6 shows the observed versus calculated log(S N =F S ) for this case.
This result was quite surprising given our choice of such a simple geometry, i.e. a constant density
sphere. The fact that none of the curves intersected for camera 1 might be related to the problems
in the calibration of that camera but primarily reflects the fact that all these curves are only
weakly dependent on g and are more or less parallel to each other within a narrow range of albedo
values.

-- 14 --
Fig. 5.--- Curves for three different methods of determining the best fit to the observations for
camera 2 with the maximum background. The solid line was determined by requiring the FN =F S of
the model to match the observed FN =F S . The dashed line was determined from requiring the slope
equal one of a linear least squares fit between the observed and calculated values of log(S N =F S ).
The dot­dashed line was determined by requiring the y­intercept equal zero.
Fig. 6.--- The plot of the observed vs. the calculated log(S N =F S ) distribution and the linear least
squares fit. The y­intercept is not zero, but not far from zero.

-- 15 --
5. Discussion
The main conclusion of this paper is that the FUV albedo is high. Specifically, at 1362 š A
the range in albedos is 0.47--0.70 and at 1769 š A the range in albedos is 0.55--0.72. This result is
independent of the choice of g, but dependent on our choice of a spherical nebula with constant
density and the absence of any foreground dust. The choice of such a simple nebular geometry
was necessitated by the lack of sufficient observations. The fact that a good fit to the distribution
of SN =F S is possible for even one case (camera 2, max background) allows us to conclude that
while this may not be the actual geometry of the nebula, it is a good approximation. While we
assumed a constant density for the nebula, this assumption was partially corrected by embedding
the stars to a depth equal to their observed optical depths. The assumption of no foreground
dust is realistic as we reside in a low­density ``trough'' in the interstellar medium (Gaustad & Van
Buren 1993). The presence of any foreground dust would increase the albedo since more light
would have to be reflected at each scattering to get the same FN =F S from a nebula with less dust,
i.e. fewer scatterings imply a larger albedo. Thus, the FUV albedo must be high.
Assuming that the albedo of this nebula is not radically different than the albedo elsewhere
in our galaxy allows us to use the results of FUV DGL investigations. These investigations
have concluded that either there is a high albedo and high g or a low albedo and low g. As we
have shown that albedo is high, it immediately follows that g is also high. A high value of g,
increasing with decreasing wavelengths in the FUV, was also indicated by the analysis of data for
the reflection nebula NGC 7023 (Witt et al. 1992, 1993). This is born out by our attempt to fit
the distribution of SN =F S with our model. The case where this was possible resulted in a high
g (Figs. 5--6). Using the results of this fit, we ran our model to obtain an image of the nebula
for comparison to the observations at – eff = 1769 š A (Fig. 7) [Plate 2]. Comparison between the
observed image (Fig. 1) and the calculated image (Fig. 7) is not one­to­one as the observed image
contains both stellar and nebular light while the calculated image contains only the nebular light.
Overall, the distribution of nebular surface brightness corresponds fairly well. The bright stars are
the same on both images and so is the general shape of the nebula.
In Figure 8, we compare our results with the results of other investigations which have also
concluded that the FUV albedo is high. In addition, Figure 8 also contains both the normalized
general interstellar extinction curve (Whittet 1992) and the normalized average extinction curve
for the Upper Scorpius subgroup of the Sco OB2 association. The decrease in the albedo in the
wavelength range of the 2200 š A ``bump'' implies that the ``bump'' is definitely an absorption
feature. In addition, note that our result for the slightly higher albedo at 1769 š A (– \Gamma1 = 5:6
¯m) implies there is no additional absorption from the ``bump'' which is expected based on the
narrower 2200 š A ``bump'' seen in the extinction curve for our region. The correspondence between
the albedo and the extinction curve is discussed in Witt et al. (1993).

-- 16 --
360 355 350 345
galactic longitude
10
15
20
25
galactic
latitude
360 355 350 345
10
15
20
25
Fig. 7.--- Image of the giant reflection nebula encompassing the Upper Scorpius subgroup of the
Sco OB2 association calculated from our Monte Carlo model with albedo = 0.56 and g = 0.60. The
isophotes are of log (S N =F S ) and they begin with ­0.5 sr \Gamma1 , increase in steps of 0.4 sr \Gamma1 , and end
with 1.9 sr \Gamma1 . Note this image only includes nebular light while the image in Fig. 1 includes both
nebular and stellar light. A total of 2.13\Theta10 9 photons were involved in calculating this image (512
\Theta 512 pixels).

-- 17 --
Fig. 8.--- Our results plotted with the results of other investigations also finding the albedo to be
high. The results for NGC 7023 are from Witt et al. (1982, 1992, 1993). The results for the diffuse
galactic light are from Lillie & Witt (1976). The results for the TD­1 diffuse galactic light are from
Morgan, Nandy, & Thompson (1976). The general ISM extinction curve is from Whittet (1992).

-- 18 --
6. Summary
Four far­UV images of the giant reflection nebula encompassing the Upper Scorpius subgroup
of the Sco OB2 association were obtained during the STS­39 Far Ultraviolet Cameras experiment
in 1991 May. The images were obtained in two ultraviolet bandpasses with – eff = 1362 š A and – eff
= 1769 š A. The distribution of the nebular surface brightness was extracted from two of the images
in each wavelength range and the stellar flux from the bright ultraviolet stars was obtained from
the IUE or TD­1 archives. The nebular to stellar ratio was calculated for both bandpasses. Due
to the fact that the reflection nebula extended over almost the entire image, it was possible to put
constraints only on the sky background. This gave rise to a significant uncertainty in the observed
nebular to stellar flux ratio derived from these images.
A radiative transfer model based on Monte Carlo techniques which allowed for an asymmetric
distribution of stars inside a spherical nebula was created. The specific geometry of the Upper
Scorpius reflection nebula was assumed to be a constant density sphere due to the lack of
observations with sufficient detail. The stars were embedded in this geometry to a depth equal to
their optical depths which were determined from known EB\GammaV and extinction curves from Papaj
et al. (1991).
As the ratio of nebular to stellar flux of an internally illuminated reflection nebulae is strongly
dependent upon the albedo and only weakly dependent upon g, the model was run for a range of
g's, 0.0--0.8, and the albedo fitting the observed nebular to stellar flux ratio was determined. The
albedo was high and ranged from 0.47 to 0.70 for – eff = 1362 š A and from 0.55 to 0.72 for – eff =
1769 š A. The range in the albedos arose primarily from the uncertainty in the sky background. In
an attempt to fit the observed distribution of SN =F S , we found that only one case resulted in a
good fit, – eff = 1769 š A with the maximum background. This fit was for a g of 0.60 and an albedo
of 0.56.
We would like to thank J. Krelowski for providing us with the digital form of the extinction
curves from Papaj et al. (1991). K. D. G. and A. N. W. acknowledge the support from NASA
LTSAP grant NAGW­3168. We also thank the Air Force Space Test Program, NASA, The
Office of Naval Research, and our co­workers at NRL for their support of the Far UV Cameras
development and flight.

-- 19 --
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