Modelling Dust Scattering in our Galaxy

9.4 MB·

by  Jayant Murthy

MNRAS000,1–12(2015) Preprint12April2016 CompiledusingMNRASLATEXstylefilev3.0
Modelling Dust Scattering in our Galaxy
Jayant Murthy,1(cid:63)
1Indian Institute of Astrophysics, Bangalore 560 034
AcceptedXXX.ReceivedYYY;inoriginalformZZZ
6
1
ABSTRACT
0
2
I have used Monte Carlo models with multiple scattering to predict the dust

r scattered light from our Galaxy and have compared the predictions with data in two
p
UV bands from the GALEX spacecraft. I find that 90% of the scattered light arises
A
from less than 1000 stars with 25% from the 10 brightest. About half of the diffuse

1 radiation originates within 200 pc of the Sun with a maximum distance of 600 pc.
1 Multiple scattering is important at any optical depth with 30% of the flux being
multiply scattered even at zero reddening. I find that the global distribution of the

] scattered light is insensitive to the dust distribution with grains of 0.3<a<0.5 and
A
g<0.6. There is an offset between the model and the data of 100 and 200 ph cm−2
G s−1 sr−1 ˚A−1 in the FUV and NUV, respectively, at the poles rising to 200 — 400 ph
h. cm−2 s−1 sr−1 ˚A−1 at lower latitudes.
p The Monte Carlo code and the models of diffuse radiation for different values of
- the optical constants are available for download.
o
r Key words: surveys - dust - local interstellar matter - ultraviolet: general - ultravi-
t
s olet: ISM
a
[

4
v 1 INTRODUCTION al.2001;Seon2015).Theavailabilityoftheall-skyGALEX
0
data provides a powerful incentive to revisit the nature of
3 The diffuse ultraviolet (UV) background was first detected
the diffuse background with a consistent set of data and a
4 byHayakawaetal.(1969)butitsfaintnessandtheneedfor
unifiedmodellingapproach.Suchdeviationsfromdustscat-
0 space-borneobservationsrenderedprogressslowforthenext
tered predictions may have important consequences for our
0 few decades (reviewed by Bowyer (1991) and Henry (1991)
. understanding of the evolution of galaxies and the dynami-
1 with a recent review by Murthy (2009)). There have been
calhistoryoftheUniverse(Overduin&Wesson2004).Iwill
0 three large scale surveys of the diffuse ultraviolet sky over
describehereanewmodelofthedustscatteredbackground
6 the last two decades. The first was the NUVIEWS (Nar-
and its application to the GALEX observations in its two
1 rowband Ultraviolet Imaging Experiment for Wide-Field
ultraviolet bands.
: Surveys) rocket flight (Schiminovich et al. 2001) which ob-
v
i servedabout25%oftheskyandnotedthestrongenhance-
X
menttowardtheGalacticplanewithotherbrightspotsnear
r star forming regions such as Ophiuchus. More recently, the 2 DATA
a
SPEAR/FIMS mission carried out a spectroscopic UV sur-
The GALEX spacecraft and its mission has been described
vey of the sky (Edelstein et al. 2006) and the Galaxy Evo-
by Martin et al. (2005) and Morrissey et al. (2007). The
lutionExplorer(GALEX)observedabout75%oftheskyin
spacecraftwasoperationalfrom2003June7until2013June
two ultraviolet bands (Murthy 2014b).
28andobservedmostoftheskywitharesolutionof5–10(cid:48)(cid:48)
Thegreatestpartofthediffusebackground,particularly
in two UV bands. The FUV (1521 ˚A) detector was plagued
at low latitudes, is thought to be due to starlight scattered
with intermittent failures of the high voltage power supply
by interstellar dust grains (Draine 2003) and models of the
(HVPS) and finally ceased to work after 2009 May while
backgroundhavetakentheincomingstarlightandscattered
theNUV(2361˚A)instrumenttookdatauntilthespacecraft
itfromthegrainswithdifferentassumptionsforthedistribu-
wasshutdown.Mostoftheobservationsweremadeathigh
tionoftheexcitingstarsandthescatteringdust(Jura1979;
Galacticlatitudestoavoiddamagetothedetectorsfromthe
Murthy &Henry 1995; Gordonetal.2001; Schiminovichet
bright diffuse background but there was a concerted effort
tomapbrighterregions,includingatlowGalacticlatitudes,
(cid:63) E-mail:[email protected] neartheendofthemission.Unfortunately,theFUVdetector
(cid:13)c 2015TheAuthors
2 Jayant Murthy
3.0
pro F
it T
R
IA
L version
2.0
V)
B -
E(
el
d
o
M
1.0
0.0
0.0 1.0 2.0 3.0
Observed E(B - V)
Figure 2.ThecorrelationbetweentheE(B-V)fromSchlegelet
al.(1998)andthemodelledE(B-V)isshownasadensityplotfor
Model1(redlines)andModel2.
Figure 1.ObservedfluxesintheFUV(top)andNUV(bottom)
GALEXbands.Thebrighteststarsareplottedas+symbolswith the grains scatter isotropically and g=1 implies fully for-
thewidthofthesymbolproportionaltothelogofthebrightness
ward scattering grains. Draine (2003) has pointed out that
at the respective wavelength. Black areas were not observed by
thescatteringmaybemorecomplexwithapossiblereverse
GALEX.
scattering component but the data have not yet been good
enoughtosupportaddedcomplexityinthescatteringfunc-
had already failed by this time so there are very few FUV
tion.
observations at low latitudes.
Henry(1977)showedthattheinterstellarradiationfield
Murthy (2014b) used the GALEX data to construct
in the UV could be calculated through an integration over
maps of the diffuse background in both the FUV and NUV
the stars in a standard catalog. In this work, I have used
bandsat0.1◦spatialresolutionwiththeforegroundemission the Hipparcos catalog (Perryman et al. 1997) which con-
(airglow and zodiacal light) subtracted (Fig. 1). The 1000
tains over 100,000 stars with the spectral type, B and V
brighteststarsareoverplottedontheimagesas+signswith
magnitude and distance of each star. I modelled the spec-
the size of the symbol proportional to the log of the bright-
trum of each star using template spectra from Castelli &
ness. Gould’s Belt is prominent in both bands as are halos
Kurucz (2004) with the translation from spectral type to
around a number of bright stars (Murthy & Henry 2011). model number as per their instructions2. I then calculated
A full description of the methodology in the production of
the observed E(B - V) from the cataloged B and V magni-
thesemapsisgiveninthepaperandthemapsareavailable
tudes and the intrinsic (B - V) and finally the unreddened
from the High Level Science Products (HLSP) data reposi-
fluxfromeachstarassumingtheMilkyWayextinctioncurve
tory1 at the Space Telescope Science Institute.
of Draine (2003). This is the source function in my model:
the number of photons from each star at the wavelength of
interest.
3 MODELLING I have tried two dust distributions in order to explore
their effects on the scattered light. In the first (Model 1),
Theradiativetransferproblemingalaxieshasbeenreviewed
I have assumed that the gas density at the Galactic plane
by Steinacker et al. (2013) with the much simpler problem
(n[H])is1atomcm−3,independentoflongitude.Inthesec-
of scattering only addressed in their Section 5.1. The prob-
ond(Model2),IscaledthedusttomatchtheobservedE(B
lem can be broken into three parts: the stellar distribution;
- V) fromSchlegel et al.(1998) inModel 2. Inbothcases, I
the dust distribution; and the scattering function. Photons
assumedthattherewas acavity of radius 80pcaroundthe
areemittedbythestarsandarescatteredbytheinterstellar
Sun,correspondingtotheLocalBubble(Welshetal.2010),
dust to the detector. The scattering function is commonly
and that the dust fell off from the Galactic plane with a
assumed to be the Henyey-Greenstein function (Henyey &
scale height of 125 pc (Marshall et al. 2006). I have plot-
Greenstein 1941) which is dependent on two free parame-
ted the correlation between the observed and the modelled
ters: the albedo or reflectivity (a) and the phase function
E(B - V) for the two models in Fig. 2. My purpose in im-
asymmetry factor (g≡<cos(θ)>), where g=0 implies that
1 https://archive.stsci.edu/prepds/uv-bkgd/ 2 http://www.stsci.edu/hst/observatory/crds/castelli kurucz atlas.html
MNRAS000,1–12(2015)
Diffuse Galactic Light 3
pathffleeemcdAteiisnnttfgruiindbllguurtstahtiodesnsicaeaottdiftvieieffnretitnrerergansntrteasmlftleharoerdrmdetluohssdatwen.latsiostoaccoecmxuprplaoletrexelytbhreeecpafaruecssteeonristt 1.5×1010 pro Fit TRIAL version aaaaaa ====== 000000......774447;;;;;; ggggg g ===== = 00000 0......360360
is non-linear, non-local and multiwavelength in its formu- s) a = 0.1; g = 0.0
nit 1.0×1010 a = 0.1; g =0.3
lation (reviewed by Steinacker et al. 2013). However, I am n u a = 0.1; g =0.6
onlyconcernedwiththescatteringofphotonsatsinglewave- oto
h
lengths which is a much simpler problem (Steinacker et al. s (P
2013, Section 5.1). I have written a set of routines in ANSI xe
u
C which are available from the ASCL (Murthy 2015). The Fl 5.0×109
programisintendedforuseintheUVwherethesourcedis-
tribution is well characterized and the volume of space is
limited because of the high optical depth to UV radiation.
However, the code is modular and documented and may be 0.0×100
0 20 40 60 80 100
freely modified for other purposes.
Number of Scatters
MycodeisverysimilartootherMonteCarloprograms
300
tGooprdreodnicetttahle.s(c2a0t0t1e)r)e.dIliwghiltl(ilelgu.stWraotoedt&heRperyongroaldms(fl1o9w99i)n; pro Fit TR aaa === 000...111;;; ggg === 000...036
mmyulitmipplelesmcaetntteartiinogns.bIygfeonlleorwaitnegaanseiwngrlaenpdhoomtonnutmhrboeurgfhroimts 250IAL version aaa === 000...444;;; ggg === 000...136
a = 0.7; g = 0.1
a uniform distribution in each step below except in Steps a = 0.7; g = 0.3
a = 0.7; g = 0.6
2 and 5 where two numbers are needed to determine the s)
direction of the photon. I have used the genunf (generate a me ( 200
randomnumberfromauniformdistribution)functionfrom Ti
the randlib library3 to generate the random numbers and,
if necessary, weighted the distribution to match the desired
probabilities. 150
(i) A photon is emitted from a random star, where the
probability of selecting a given star is weighted by the rel-
100
ative number of photons from that star, in a random direc- 0 20 40 60 80 100
tion. Each photon begins with a unit weight which will be Number of Scatters
reduced at each scattering.
(ii) Two random numbers are generated to calculate the Figure3.Thetotalflux(phcm−2s−1sr−1˚A−1)inthesimulation
direction of motion, one for theta (in the range from 0 —
is shown on the top and the amount of time per 10 million in-
π, measured from the z axis) and one for phi (in the range putphotons(ona3.7GHzQuad-CoreIntelXeonE5MacPro)is
from 0 — 2π). The position of the star is known (from the shownonthebottom.Inboth,themaximumnumberofscatter-
Hipparcoscatalog)inCartesiancoordinates(x,y,z)andthe ingsperinputphotonbeforeterminatingtherunisplottedonthe
anglesareconvertedintoadirectionvectorassumingastep x axis. Each point represents a run of 10 million input photons
size of 1 bin. withdifferentvalueofaandg.
(iii) Another random number is generated to determine
the optical depth the photon travels. I have divided the
Galaxy into 1000 x 1000 x 1000 cells with a side of 1 pc step2.Thezdirectionisnowtheoriginaldirectionofmotion
and filled each cell with dust as per the individual model. with the change of reference back to the original Cartesian
Thecross-sectionofthedustwastakenfromDraine(2003), coordinates using a rotation angle matrix.
whichisaparametrizationofthecanonicalextinctioncurve (vi) Theprocedureisrepeatedfromstep3untiltheeffec-
with R (=AV/E(B−V))=3.1, the so-called Milky Way dust. tiveweightofthephotondropsbelowapredeterminedfactor
I then follow the photon along until the cumulative optical orthenumberofscatteringsexceedsaspecifiedlimit(nscat-
depthalongthepathexceedsthepredeterminedvalue.This ter). Note that single scattering corresponds to nscatter=0.
yieldstheCartesiancoordinatesx,y,andzofthescattering Inthatcase,thephotonstopsatthefirstinteractionbutthe
location. effective peeling method results in a flux at the detector.
(iv) I use the“effective peeling”technique (Yusef-Zadeh
et al. 1984) to send a fraction of the photon back to the
detectorandsubtractthis(small)amountofenergyfromthe
effective weight of the photon. The detector in this case is 4 RESULTS
assumedtoobservetheentireskywithanangularresolution
of 0.1◦ per square bin. I have plotted the total flux in the Galaxy at 1500 ˚A as
a function of the number of scatterings for different values
(v) The effective weight of the photon is reduced by the
of the optical constants along with the time taken for each
albedo and a new scattering direction is determined as in
run in Fig. 3. The flux saturates at about 5 scatterings per
photon and I have therefore capped the number of scatters
3 http://hpux.connect.org.uk/hppd/hpux/Maths/Misc/randlib- at that level leading to a significant savings in execution
1.3/readme.html time without affecting the total flux. These numbers are
MNRAS000,1–12(2015)
4 Jayant Murthy
1.5 2.0×1010
ggg === 000...012 pro Fit TR
1.4 units)1.5×1010 ggggg ===== 00000.....34567 IAL version
n g = 0.8
1.3 oto
o h
Rati x (p1.0×1010
u
Fl
1.2 al
Tot
5.0×109
1.1
0.0×100
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1.0
0 1 2 3 4 Albedo
E(B – V)
Figure5.Thetotalfluxovertheentireskyisshownas
Figure4.Ratiobetweenmultipleandsinglescatteringasafunc- afunctionofalbedoforarangeofg.Thelinerepresents
tionofE(B-V)witha=0.4andg=0.3. a quadratic fit to the g=0 points and is shown for
comparisononly.
1.00
a=0.1
from runs at 1500 ˚A with the dust distributed as in Model a=0.2
2; similar results are obtained at 2300 ˚A and for Model 1. a=0.3
a=0.4
Itistemptingtoassumethatsinglescatteringprovides a=0.5
0.95 a=0.6
a reasonable estimate of the diffuse flux, especially in re- a=0.7
gions of low optical depth (Murthy & Henry 1995; Henry a=0.8
x
u
et al. 2015) because the solution may be derived exactly Fl
e
wthiethroauttiorebceotuwreseentothMeotnwtoe fCoarrlao=m0e.4thoandds. gI=ha0v.3e pinlotFtiegd. elativ0.90
R
4. Even at the lowest reddening, multiple scattering gives
about25%morefluxrisingtoabout40%morebyE(B-V)
=1.5,althoughtheexactvaluewilldependonthelocalge- 0.85
ometrybetweenthestarsandthedust.Muchofthisexcess
is simply because the photon still carries energy after the
firstinteractionwhichisdisregardedinthesinglescattering
0.80
0.0 0.2 0.4 0.6 0.8 1.0
assumption.
g
Ihaveaddedthefluxovertheentiremodelskyforeach
combinationoftheopticalconstantsinFig.5and6.Unlike
the single scattering case where the total flux should rise Figure 6. The flux over the entire sky is shown as
linearlywiththealbedo,thetotalfluxrisesasapproximately a function of g for different values of the albedo (see
the square of the albedo when multiple scattering is taken legend). The fluxes for each albedo have been divided
into account. The flux decreases with increasing g as the bythefluxatg=0.
photonismorelikelytostaywithintheGalaxyforisotropic
scattering and there are more scatterings per photon.
Table 1.FiveBrightestStars
The above results depend little on the distribution of
the dust. On the other hand the distance of the scattering
StarName HIPNo. PercentageofTotalFlux
locationsfromtheSundependsonthedustdistributionbut
notontheopticalparameters.Ihaveplottedthepercentage Model1
of flux originating in 10 pc bins as a function of distance βCen 68702 3.5
fromtheSuninFig.7.Abouthalfoftheobservedradiation ζ Ori 26727 3.1
originates within 100 - 200 pc from the Sun and none from (cid:15) Ori 26311 2.8
cells more than 600 pc away. The average distance between αCru 60718 2.7
ζ Pup 39429 2.0
scatters is also dependent on the dust distribution (Fig. 8).
Model2
About 60% of the photons are scattered within 200 pc of
αCru 60718 5.6
their origin in Model 1 and more than 90% in Model 2.
βCru 62434 4.2
Virtuallyallthephotonstravellessthan500pcbeforebeing
ζ Ori 26727 2.7
scattered. The optical depth per bin is higher in Model 2 ζ Oph 81377 2.6
(Fig. 2) and most photons will not travel more than one (cid:15) Ori 26311 2.3
optical depth before interacting with a dust grain.
The diffuse flux from our Galaxy is dominated by a
MNRAS000,1–12(2015)
Diffuse Galactic Light 5
10
Model 1
Model2
8
al
of Tot 6
e
g
a
nt
e
erc 4
P
2
0
0 200 400 600 800 1000
Distance from Sun (pc)
Figure 7. The percentage of the flux in each 10 pc
bin is shown as a function of distance from the Sun
for a=0.4 and g=0 for the two models. Both models
includeacavityof80pcradiusaroundtheSun.
1.0
Model 1
Model 2
0.8
n
o
Fracti0.6
e
ativ
ul
m0.4
u
C
0.2
0.0
0.0 100.0 200.0 300.0 400.0 500.0
Distance between Scatterings (pc)
Figure8.Thepercentageofthetotaldiffusefluxasa
functionofdistancebetweenscatteringsisshown.
100.0
Model 1
Model 2
80.0
e
g
a
nt
e
erc 60.0 Figure 10. Model 2 predictions at 1500 ˚A for a=0.4 and g=0
e P (top), g=0.4 (middle), and g=0.8 (bottom). The brightest stars
v
ati are plotted as circles with the radius proportional to the log of
mul 40.0 thebrightnessat1500˚A.Similarresultsareobtainedat2300˚A
Cu andforModel1.
20.0
handfulofstars(Table1)with23%and27%ofthetotalflux
coming from only 10 stars for Models 1 and 2, respectively,
and 90% of the total observed flux (Fig. 9) from the 1000
0.0
0.0 200.0 400.0 600.0 800.0 1000.0 brightest stars. I have plotted the predictions from Model
Number of Stars 2 at 1500 ˚A in Fig. 10 for a=0.4 and g=0 (isotropic scat-
tering),g=0.5andg=0.8.Thediffuselightisconcentrated
Figure 9. The cumulative contribution of the brightest stars is in Gould’s Belt following the stars, plotted as circles with
shownforModels1and2. a radius proportional to the log of the star brightness. As
thegrainsbecomemoreforwardscattering,thediffuselight
becomes more localized near the stars.
MNRAS000,1–12(2015)
6 Jayant Murthy
Table 2.BestFitParameters
Model a g y0 χ2 r
FUV
Model1(allτ) 0.3 0.0 -68 3.91 0.750
Model1(τ<1) 0.2 0.1 253 2.75 0.721
Model1(τ>1) 0.25 0.0 978 14.96 0.591
Model2(allτ) 0.36 0.0 391 2.99 0.861
Model2(τ<1) 0.50 0.3 224 1.91 0.888
Model2(τ>1) 0.30 0.1 1026 13.64 0.681
NUV
Model1(allτ) 0.40 0.3 356 4.48 0.810
Model1(τ<1) 0.30 0.1 367 2.74 0.733
Model1(τ>1) 0.40 0.2 732 14.81 0.699
Model2(allτ) 0.39 0.2 859 4.89 0.769
Model2(τ<1) 0.50 0.4 627 2.10 0.857
Model2(τ>1) 0.31 0.4 1818 16.74 0.592
20.0 g = 0.0
g = 0.1
g = 0.2
g = 0.3
g = 0.4
FMiogduerle21(b1o.ttSocmat)tearted15l0i0gh˚At pforredai=ct0io.3n6safnodr Mg=od0.e5l.1 (top) and V Model 1)15.0 gggg ==== 0000....5678
U
F
2Reduced χ( 10.0
5.0
0.0
0.0 0.2 0.4 0.6 0.8
Albedo (a)
10.0 g = 0.0
g = 0.1
g = 0.2
g = 0.3
g = 0.4
UV Model 2) 8.0 ggggg ===== 00000.....56789
F
2 Reduced χ( 6.0
4.0
2.0
0.0 0.2 0.4 0.6 0.8
Albedo (a)
Figure 13.Reducedχ2 plottedasafunctionoftheopticalcon-
stantsintheFUVbandforModel1(top)andModel2(bottom).
NUV:r=0.360)wheretheopticaldepthislowandthescat-
tered light is dependent on the dust distribution. The total
output from the Galaxy is dominated by the low latitude
Figure 12.FUV(top)andNUV(bottom)plottedversusmodel dust and hence will not be sensitive to the details of the
predictionsforModel1(red)andModel2(blue). dust distribution in the Galaxy.
Alsosuperficiallysimilararethecalculateddiffuseback-
5 COMPARISON WITH DATA
groundsovertheentireskyforeachoftwodustdistributions
(Fig.11)withbothshowingagoodcorrelationwiththedata The main motivation for this study was the availability of
(Fig.12).Thecorrelationbetweenthetwomodelsisbestat theall-skyGALEXdatawhichallowstestsofthescattering
low latitudes (FUV: r = 0.841; NUV: r= 0.808) where the onbothsmall andlarge scales. Ihave comparedthe output
opticaldepthishighandthescatteredlightisconcentrated oftheMonteCarlomodelsforbothdustdistributionsfora
nearthestarsandispoorathighlatitudes(FUV:r=0.441; rangeofopticalconstantsintheFUVband(Fig.13)andin
MNRAS000,1–12(2015)
Diffuse Galactic Light 7
20.0 g = 0.0 5000
g = 0.1
g = 0.2
g = 0.3
g = 0.4 4000
2 Reduced χ(NUV Model 1)1105..00 gggg ==== 0000....5678 FUV (photon units) 23000000
5.0
1000
0.0
0.0 0.2 0.4 0.6 0.8
Albedo (a) 00.0 0.2 0.4 0.6 0.8 1.0
20.0 g = 0.0 E(B - V)
g = 0.1
g = 0.2
g = 0.3 Figure 15. Observed FUV flux plotted versus E(B - V) for
UV Model 2)15.0 gggggg ====== 000000......456789 |rGbe|As<pLo3En0◦Xd.sTbtahonedassno.lTiodphtleiincNaeUlreVdperppetlsohetnoitsfss1aimniniEla(brBoatn-hdVtI)hheoafFv0eU.1nV5otwasnhhdiochwNncUoiVrt-.
N
2Reduced χ (10.0 feuvseenbmaockregraopupnadreinstdautesttiolltshheorstteerllwaravdeilsetnrgibthustio(Mn.uTrthhiys &is
5.0
Sahnow 2004) where there are many fewer bright stars.
I will look more closely at the distribution of the back-
ground in different sections of the Galaxy in the following
0.0
0.0 0.2 0.4 0.6 0.8
Albedo (a) paragraphsbutwillfocusonModel2,wherethedustdistri-
butionismorecloselyreproduced.Thesignal-to-noiseofthe
Figure 14.Reducedχ2 plottedasafunctionoftheopticalcon-
MonteCarlorunsisalimitingfactorathighlatitudesandI
stantsintheNUVbandforModel1(top)andModel2(bottom).
haveusedasinglelongrunof8×109 photonswithfixedop-
ticalconstantsof(a=0.36;g=0.5).Thesevaluesfallnearthe
χ2 minimum and are consistent with other determinations
Table 3.LatitudinalFits(a=0.36;g=0.5) in the literature (reviewed by Draine (2003)). I have found
thebestfitofthemodeltothedatainthedifferentlatitude
Range Slope y0 χ2 r intervals and tabulated these in Table 3. I have allowed for
aslopeandanoffsetbetweenthemodelandthedatawhere
FUV
|b|<30;τ<1 1.24 741 5.03 0.846 the slope may indicate either differences in the albedo from
|b|<30;τ>1 0.72 1430 13.74 0.724 a=0.36oranadditionalcomponentwiththesamedistribu-
30<b<60;τ<1 1.79 359 1.93 0.917 tion as the scattered light. The offset represents additional
−60<b<−30;τ<1 1.01 457 2.17 0.856 contributorstothediffusebackgroundperhapsincludingan
60<b 1.15 325 1.26 0.468 airglow component and will be discussed further below.
−60>b 0.92 313 1.09 0.592
NUV
|b|<30;τ<1 1.57 895 5.75 0.822 5.1 Mid and Low Latitudes
|b|<30;τ>1 0.63 2241 17.43 0.589
30<b<60;τ<1 1.85 592 1.53 0.890 The range of E(B - V) is greatest at low latitudes with the
−60<b<−30;τ<1 1.12 717 3.52 0.592 expected areas of high extinction near the plane but with
60<b 1.20 590 1.12 0.437 surprisingly low values even short distances away from the
−60>b 0.54 637 1.29 0.266 plane. I have plotted the observed FUV as a function of
E(B-V)inFig.15anddividedtheobservationsintotwore-
gions:E(B−V)<0.15andE(B−V)>0.15,approximatelycor-
theNUV(Fig.14).Ineachcase,therewasanoffsetbetween responding to an optical depth of 1 inbothGALEXbands.
the modelandtheobservationsrepresentingcomponentsof Thereisacorrelationbetweentheobservedbackgroundand
the diffuse background other than dust scattered light and the reddening for τ<1 (FUV: r = 0.583; NUV: r = 0.489)
Iaddedtheseoffsetstothemodeloutputbeforecalculating andthemodeldoesagoodjobofpredictingthebackground
the reduced χ2 of the fit between the models and the data with correlations of 0.846 and 0.822 in the FUV and NUV
(Table 2). These tests were carried out assuming a 500× (Fig. 16). The better correlations of the model to the data
500×500 grid for the Galaxy with each run incorporating arebecausethediffusebackgroundisdependentonthedis-
5×108 photons. tributionofthedustandofthestars,whichisaccountedfor
The predictions of both models for the dust distribu- by the modelling.
tion are generally consistent with the data suggesting that, The slope in both bands is somewhat greater than 1
atleastonaglobalscale,anaccurateknowledgeofthedust suggesting that the albedo was underestimated by a factor
distribution may not be critical in determining the diffuse equal to the square root of the slope (Fig. 5) implying that
background. Rather, much of the structure seen in the dif- a=0.4 in the FUV and a=0.45 in the NUV. There is an
MNRAS000,1–12(2015)
8 Jayant Murthy
10000 τ < 1 2000 North
τ > 1 South
UV (photon units) 68000000 UV (photon units) 11050000
F F
Observed 4000 Observed 500
2000
00 2000 4000 6000 8000 10000 00 200 400 600 800 1000
Model FUV (photon units) Model FUV (photon units)
10000 τ < 1 2000 North
τ > 1 South
UV (photon units) 68000000 UV (photon units) 11050000
N N
Observed 4000 Observed 500
2000
00 2000 4000 6000 8000 10000 00 200 400 600 800 1000
Model NUV (photon units) Model NUV (photon units)
Figure16.ObservedfluxatlowGalacticlatitudesplottedversus Figure 17. Observed flux at mid-latitudes plotted versus pre-
predictedfluxforτ<1(red)andτ>1(blue)forFUV(top)and dicted flux for FUV (top) and NUV (bottom). The Northern
NUV(bottom)bands.Theredlinerepresentsthebestfitbetween hemisphere points are plotted in blue and the Southern hemi-
the model and the data. I have not plotted the best fit line for sphereinred.Theblueandredlinesrepresentlinearfitstoboth
τ>1becauseofthescatterinthedata. hemispheres.
offset of 740 and 900 ph cm−2 s−1 sr−1 ˚A−1 in the FUV spheres in both bands, this is largely because the model
under-predicts the brightest points in the Northern hemi-
and the NUV bands, respectively, of which Murthy (2014a)
attributed 200 — 300 ph cm−2 s−1 sr−1 ˚A−1 to unresolved sphere. The reason for this is unclear and I will defer an
explanation pending further modelling.
airglow.Othercontributorstothediffusebackgroundatlow
latitudesmayincludemolecularhydrogenfluorescenceinthe
FUV (Hurwitz 1994; Lim et al. 2013) or other more exotic
5.2 High Latitudes
sources(Henryetal.2015).Ihavenotincludedthesesources
in my model but will do so in a future version. Thedustscatteredlightathighlatitudesisduetotheback
There is considerable scatter between the observations scatteringoflightfromGalacticplanestars(Jura1979)and
and the reddening for τ>1 (FUV: r = -0.001; NUV: r = would be expected to be proportional to the reddening at
0.120) because only the front layers of the dust contribute these low column densities. However, there is considerable
to the observed background (Fig. 15). The models fit the scatter in a plot of the observed background as a function
data reasonably well (FUV: r = 0.724; NUV: r = 0.589) of the reddening (Fig. 18) perhaps due to uncertainties in
but with considerable scatter although the models should the Schlegel et al. (1998) reddening derivation. This must
include self-extinction by the dust. This is because the dis- be added to the scatter in the Monte Carlo models because
tribution of dust in these line of sight is likely to be more of the relatively small number of photons at high latitudes
complexandlocaleffectsmaydeterminetheobservedback- andtothesmallrangeinthefluxestobefitted.Giventhese
ground. One example of this was seen in the vicinity of the uncertainties, it appears that the data are consistent with
CoalsackNebulawhereMurthyetal.(1994)foundthatthe an a=0.36 and g=0.5 but a better understanding of the
intensediffuseemissionwasduetothescatteringofthelight statistics is needed before a firm conclusion may be drawn.
of only three bright stars by a thin layer of dust in front of The offset between the model predictions and the data
the dense molecular cloud. is much better defined at a level of about 300 and 600 ph
There is much less dispersion in E(B - V) at mid- cm−2 s−1 sr−1 ˚A−1 in the FUV and the NUV, respectively
latitudes (30<|b|<60) and there is a good correlation be- (Fig. 19). The offsets are consistent between both poles at
tweenthemodelledandtheobservedfluxes(Fig.17)inboth both bands. There have been a number of measurements
the FUV and the NUV (Table 3) with an offset of 350 — of the diffuse Galactic light at high latitudes which have
450 and 600 — 700 ph cm−2 s−1 sr−1 ˚A−1 in the FUV and determined the offset at zero reddening to be about 300 ph
NUVbands.Althoughthereisadifferenceintheslopeofthe cm−2s−1sr−1˚A−1(Andersonetal.1979;Paresceetal.1979,
best fit lines between the Northern and the Southern hemi- 1980; Zvereva et al. 1982; Joubert et al. 1983; Jakobsen et
MNRAS000,1–12(2015)
Diffuse Galactic Light 9
800 North al.1984;Tennysonetal.1988;Onakaetal.1989;Hamdenet
South
al. 2013), which is generally thought to be due to an extra-
galactic background (see Bowyer (1991); Henry (1991) for
UV (photon units) 460000 3dco5isn0ctuprsihbsiucotmnio−an2nssd−o1fre2sfr2e−r01enp˚Ach−e1sc)mi.n−(2Mthsue−r1NthsUyr−V210u˚A1s4i−na1g)inadedtrhiiffveeeFdreUnaVtir(gealomnwd-
F pirical)methodofanalysisoftheGALEXdata,whichwould
Observed 200 ilneatvheeaFrUesVidaunadl oNfUaVbo,urtes1p0e0ctaivnedly2.5I0tipshdciffimc−u2lts−t1ossre−p1ar˚Aa−te1
airglow from the other contributors without spectral diag-
nosticsandIwilldeferaself-consistentdeterminationofthe
0 offsets for a future work.
0.00 0.01 0.02 0.03 0.04 0.05
E(B – V)
1000
North
South
V (photon units) 680000 6IduhsatSvesUcapMtrteMesreenAdtResdYtaarliMghotntoeveCratrhloemenotdireel fGoralacaxlyc.uTlahtiengmtahine
U conclusions are as follows:
N
Observed 400 flu(xi)byAambouulttip3l0e%scoavtetrertihnegsimngoldeelsciantctreerainsegsatphperosxciamttaetrioend
200
regardless of the optical depth.
(ii) Thetotalscatteredfluxisproportionaltothesquare
00.00 0.01 0.02 0.03 0.04 0.05 of the albedo and is greatest for isotropically scattering
E(B – V) grains.
Figure 18. Observed flux for FUV (top) and NUV (bottom) (iii) 90%ofthediffusefluxoriginatesfromlessthan1000
at high latitudes plotted versus the reddening. The red points stars and 25% from only 10 stars.
areSouthernhemisphereandthebluepointsareNorthernhemi- (iv) AbouthalfofthediffuseradiationseenattheEarthis
sphere. scatteredwithin200pcoftheSunwithnoradiationarising
fromfurtherthan600pcaway.Mostphotonstravellessthan
800 200 pc before another interaction.
North
South (v) Theall-skydiffuseradiationisfitwellwith0.3<a<0.5
andg<0.6.Thealbedoisconstrainedbythetotalfluxwhile
UV (photon units) 460000 gsuteai(ssrvasci.t)onloTswthreaainmndeodmdebidly-pltarheteditiaucmdtieoosnufsnotraroloefwscclooapstettiectraoinltgdheefpaotrhbfsrs.oeTrmvhebedrfiivgtahilst-
F
Observed 200 pcoomorpelrexa.t larger optical depths where the geometry is more
(vii) There is reasonable agreement between the model
(a=0.36;g=0.5) and the data at high latitudes but with
considerable scatter.
0
0 50 100 150 200 (viii) There is an offset of 300 — 700 ph cm−2 s−1 sr−1
Model FUV (photon units)
1000.0 ˚A−1 inbothbandsandatalllatitudeswhichcannotbedue
North
South to dust scattered radiation. Murthy (2014a) estimated that
the residual airglow was 220 ph cm−2 s−1 sr−1 ˚A−1 in the
V (photon units) 680000..00 stFhrU−a1Vt˚Atha−ne1doinff3s5te0htepaFthUhciVmgh−a2lnasdt−it1NuUsdreV−s1ibs˚Aa1−n01d0si,narnetdhspe2e5Nc0tUivpVehlyci.mmTp−hl2yisisn−ig1s
NU the component that is usually identified with extragalactic
Observed 400.0 lliogwhtla(tBitouwdeyseran1d99m1;ayHbeenrdyue19to91u)n.aTcchoeuonfftesdetssoaurrecelsasrugechr aast
200.0 molecularhydrogenemissionorasyetundeterminedsources
(Henry et al. 2015).
(ix) I have tabulated results from the literature in Table
0.0
0.0 50.0 100.0 150.0 200.0
Model NUV (photon units) 4.Inmostcases,Ihavetakentheresultsasspecifiedbythe
authors which are difficult to translate into the 1σ results
Figure 19. Observed flux at high latitudes plotted versus pre-
moreoftenseen.Inallcases,thereisenoughuncertaintyin
dictedflux.ColoursarethesameasFig.17.
the data and the modelling that the formal limits are sug-
gestiveratherthandefinitive.Therearearangeofpreferred
values for the optical constants and the offset but I hope
MNRAS000,1–12(2015)
10 Jayant Murthy
Table 4.Opticalconstantsandoffsetsintheliterature.
References Wavelength a g Offset
˚A phcm−2 s−1 sr−1 ˚A−1
Witt&Lillie(1973) 1500 >0.6 <0.5 -
Lillie&Witt(1976) 3000 0.7±0.1 0.6–0.9 -
2200 0.35±0.05 0.6–0.9 -
1550 0.6±0.05 0.6–0.9 -
Morganetal.(1976) 2740 0.65±0.1 0.75 -
Morganetal.(1978) 2740 0.68 0.5 -
2350 0.51 0.5 -
1950 0.53 0.5 -
1550 0.5 0.5 -
Andersonetal.(1979) 1230–1680 - - 285±32
Paresceetal.(1980) 1350–1550 0.5 0.5 <300
Feldmanetal.(1981) 1200–1670 - - 150±50
Henry(1981) 1565 >0.5 >0.7 -
Wittetal.(1982) 1400 0.6 0.25 -
2000 0.42 0.4 -
Joubertetal.(1983) 1690–2200 - 0.6–0.7 -
Holberg(1986) 500–1200 - 100–200
Tennysonetal.(1988) 1700–2850 - - 300±100
Fixetal.(1989) 1500 - >0.9 530±80
Hurwitzetal.(1991) 1415–1835 0.13–0.24 <0.4 50
Murthyetal.(1991) 912–1216 <0.1 >0.95 -
Onaka&Kodaira(1991) 1500 ≥0.32 ≥0.5 200–300
Wittetal.(1992) 1400–2200 0.65 0.75 -
Henry&Murthy(1993) 1500 0.5 0.7 300±100
Wittetal.(1993) 1000–1600 0.42±0.04 0.75 -
Murthyetal.(1993a) 912–1150 >0.3 <0.8 -
Murthyetal.(1993b) 1100–1860 0.5–0.7 - -
Gordonetal.(1994) 1362 0.47–0.7 <0.8 -
1769 0.55–0.72 <0.8 -
Hurwitz(1994) 1600 0.6±0.1 0.5±0.15 -
Witt&Petersohn(1994) 1500 0.5 0.9 -
Calzettietal.(1995) 1200–1600 0.7–0.8 0.75±0.05 -
2300 0.4 0.6 -
Murthy&Henry(1995) 1250–2000 0.3–0.6 - 100–400
Sasseen&Deharveng(1996) 1400–1800 0.3 0.8 -
Wittetal.(1997) 1400–1800 0.45±0.05 0.68±0.1 160±50
Schiminovichetal.(2001) 1740 0.45±0.05 0.77±0.1 200±100
Burghetal.(2002) 900–1400 0.2–0.4 0.85
Henry(2002) 1500 0.1 - -
Mathisetal.(2002) 1300 ≥0.5 0.6–0.85 -
Gibson&Nordsieck(2003) <2600 0.22±0.07 0.74±0.06 -
Weller(1983) 1220–1500 - - 200–300
Shalima&Murthy(2004) 1100 0.4±0.2 - -
Sujathaetal.(2005) 1100 0.4±0.1 0.55±0.25 -
Shalimaetal.(2006) 900–1200 0.3–0.7 0.55–0.85 -
Sujathaetal.(2007) 900–1200 0.28±0.04 0.61±0.07 -
Leeetal.(2008) 1370–1670 0.36±0.2 0.52±0.22
Sujathaetal.(2009) 1350–1750 0.4 0.7 -
1750–2850
Puthiyaveettiletal.(2010) 1400–1900 0.6 0.8 500
Sujathaetal.(2010) 1350–1750 0.32±0.09 0.51±0.19 30±10
1750–2850 0.45±0.08 0.56±0.10 49±13
Murthy&Henry(2011) 1521 - 0.58±0.12 -
2320 0.72±0.06
Joetal.(2012) 1350–1750 0.39±0.45 0.45±0.2 -
Choietal.(2013) 1330–1780 0.38±0.06 0.46±0.06 -
Hamdenetal.(2013) 1344–1786 0.62±0.04 0.78±0.05 300
Limetal.(2013) 1360–1680 0.42±0.05 0.20–0.58 -
Jyothyetal.(2015) 1521 0.6–0.7 0.2–0.4 -
2317
MNRAS000,1–12(2015)