ISO far infrared observations of the high latitude cloud L1642. II. Correlated variations of far-infrared emissivity and temperature of "classical large" dust particles

1.4 MB·English

by  K. Lehtinen

Astronomy&Astrophysicsmanuscriptno.L1642-V5.0 c ESO2008
(cid:13)
February5,2008
⋆
ISO far infrared observations of the high latitude cloud L1642
II. Correlated variations of far-infrared emissivity and temperature of “classical
large” dust particles
K.Lehtinen1,M.Juvela1,K.Mattila1,D.Lemke3,andD.Russeil1,2
7 1 Observatory,Ta¨htitorninma¨ki,P.O.Box14,00014,UniversityofHelsinki,Finland
0 2 Laboratoired’AstrophysiquedeMarseille,2PlaceLeVerrier,13004Marseille,France
0 3 Max-Planck-Institutfu¨rAstronomie,Ko¨nigstuhl17,D-69117Heidelberg,Germany
2
Received/accepted
n
a
ABSTRACT
J

6
Aims.Ouraimistocomparetheinfraredpropertiesofbig,“classical”dustgrainswithvisualextinctioninthecloudL1642.Inpar-
2 ticular,westudythedifferencesofgrainemissivitybetweendiffuseanddenseregionsinthecloud.
Methods.Thefar-infraredproperties of dust arebased onlarge-scale100µmand200µmmaps. Extinctionthrough thecloud has
1
beenderivedbyusingthestarcountmethodatB-andI-bands,andcolorexcessmethodatJ,HandK bands.Radiativetransfercal-
s
v culationshavebeenusedtostudytheeffectsofincreasingabsorptioncross-sectiononthefar-infraredemissionanddusttemperature.
3 Results.Dustemissivity,measuredbytheratiooffar-infraredopticaldepthtovisualextinction,τ(far-IR)/A ,increaseswithdecreas-
V
6
ingdusttemperatureinL1642.Thereisabouttwo-foldincreaseofemissivityoverthedusttemperaturerangeof19K–14K.Radiative
7 transfercalculationsshowthatinordertoexplaintheobserveddecreaseofdusttemperaturetowardsthecentreofL1642anincrease
1 of absorption cross-section ofdust atfar-IRisnecessary. Thistemperaturedecrease cannot beexplained solelybytheattenuation
0 ofinterstellarradiationfield.Increasedabsorptioncross-sectionmanifestsitselfalsoasanincreasedemissivity.Wefindthat,dueto
7 temperatureeffects,theapparentvalueofopticaldepthτ (far-IR),derivedfrom100µmand200µmintensities,isalwayslowerthan
app
0 thetrueopticaldepth.
/
h
Keywords.ISM:individualobjects:Lynds1642–ISM:clouds–dust,extinction–Infrared:ISM
p
-
o
r 1. Introduction Laureijs.AlsoStepniketal.(2003)suggestthatgrain-grainco-
t
s agulation is the reason for changes of dust properties in dense
a Recent observations have indicated that the far-IR emissivity
regions.
: (measured by the ratio τ(far-IR)/A ) increases with decreas-
v V
i ing temperature (Cambre´sy et al. 2001; del Burgo et al. 2003;
X Stepnik et al. 2003; Kramer et al. 2003). Probable reasons for Fortheintroductionofthehighgalacticlatitudedarkcloud
r increasedemissivityarecoagulationofdustparticlesintolarge, L1642werefertoLehtinenetal.(2004,PaperI)andreferences
a
fluffy aggregates, and formation of ices on grain surfaces in therein.PaperIwasbasedonISOPHOTobservationsinthefar-
dense regions (Bazell & Dwek 1990; Preibisch et al. 1993; infrared,andwemadethefollowingconclusions:
Ossenkopf&Henning1994;Dwek1997;Cambre´syetal.2001 Based on the 200µm optical depth map the cloud was divided
andreferencestherein).Variationsofdustopticalpropertiesare into three regions, called A (consists of two cloudlets, A1 and
visibleevenoverascaleofgalacticanticenterhemisphere,any- A2),BandC(seeFig.1).
wherewhere AV > 1mag(Cambresyetal.2005).delBurgo& Region B, the one with the highest dust column density, AV
Laureijs(2005)us∼edobservationsoftheTaurusmolecularcloud 8mag, isrelated to a temperatureminimum,T 13.8K for≈a
d
TMC-2between60µmand200µmtoseparatetheemissioninto ν2emissivity. ≈
acoldandawarmcomponent.Theyfoundthatfar-IRemissiv- This region is close to being gravitationally bound, while the
ity ofthe coldcomponentis a few timeslargerthan thatof the othersarenot.
diffuse interstellar medium, and that the change in the proper- The lower dust temperature in region B cannot be explained
ties of the big dust particles takes place at intermediate densi- solelybythedustattenuationofthegeneralinterstellarradiation
tiesofn(H2) 103cm−3.Theyfavouredgrain-graincoagulation field,butchangesinthepropertiesofdustparticlesarerequired.
≈
overgasaccretionasthereasonforenhancedemissivitybecause
thelatterprocessproducesanincreaseofemissivitybyafactor
of about two at most, less than that observed by del Burgo & Inthispaperwewillcomparetheinfraredpropertiesofbig
grainswithvisualextinction.Bycomparingfar-IRemissiondata
withopticalextinctiondatawecanstudytheinfraredandoptical
Sendoffprintrequeststo:K.Lehtinen(kimmo.lehtinen@helsinki.fi)
⋆ BasedonobservationswithISO,anESAprojectwithinstruments properties of dust grains. In particular, combinationof reliable
funded by ESA Member States (especially the PI countries: France, dusttemperature,far-IRopticaldepthandvisualextinctiondata
Germany,theNetherlandsandtheUnitedKingdom)andwiththepar- enablesus to study the differencesof grain emissivity between
ticipationofISASandNASA diffuseanddenseregionsinthecloud.
2 K.Lehtinenetal.:ISOfarinfraredobservationsofthehighlatitudecloudL1642
A [mag]
0.0 1.1 2.2 V3.4 4.5 5.6 6.7 70
a)
60
-13° 50′ -1y sr] 50
J 40
M
00 m) [ 30
A1
A2 µ
0 20
000) 10 I(20 10
2 B
n ( 0
o 20
clinati 15 b)
De 30 C -1sr]
40 MJy 10
m) [
-14° 50′ µ
0 5
0
1
-15° 00′ I(
0
04h 38m 37 36 35 34 33 0 2 4 6 8
Right Ascension (2000) A [mag]
V
Fig.1. Visual extinction through L1642, derived using J, H Fig.2. a)Relationbetweenvisualextinctionand200µmsurface
and K data from 2MASS archive, smoothing the individual brightness.ThedatapointsoftheregionsA,BandCaremarked
s
extinctions of stars with a gaussian with FWMH=4.5. The with green, yellow and red, respectively. Linear fits to regions
′
IRAS sources, marked with asterisks, are from right to left: A/Band interclumppartof the cloudareshown.We havesub-
IRAS 04325–1419, 04327–1419, 04336–1412, 04342–1444, tractedfromA andI(200µm)thezero-levelvaluesasfixedout-
V
04347–1415and04349–1436.TheFWHMsizesoftheregions sidetheextentofL1642(seeSection2.3.1).b)Relationbetween
A1, A2, B and C as derived by Lehtinen et al. (Paper I) from visual extinction and 100µm surface brightness. Linear fits to
200µmopticaldepthdataareshownasellipsesandcircles.The theregionsA/Bandinterclumppartofthecloudareshown.The
contoursareat1.5,2.5,3.5,4.5and5.5mag fitoftheinterclumpparthasbeenforcedtogothroughtheori-
gin. We have subtracted from A and I(100µm) the zero-level
V
Table 2. Error sources contributing to the pixel-to-pixel vari- valuesasfixedoutsidetheextentofL1642(seeSection2.3.1)
ations of temperature, far-IR optical depth and emissivity. See
Section2.4forexplanations 0 1 2 3 AV [ma4g] 5 6 7
Errorsource Value 1.5
i) <σ(I(200µm))> 0.19MJysr 1
−
]
ii) σ(I(100µm)) 5% -30
iii) σ(flatfield) 0.43MJysr 1 1
− [ 1.0
iv) <σ(PSF)> 0.14MJysr−1 m)
v) <σ(A )> 0.32mag µ
V 0
vi) <σ(zero-level(100µm))> 0.9MJysr−1 20
vviiiii)) <<σ(σze(rzoe-rloe-vleevl(e2l0(A0µ)m)>))> 2.06.4M3Jmyasrg−1 τ(app 0.5
V
0.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
2. Dataanalysis
N(H+H) [1022]
2
ForthedatareductionoftheISOdatawerefertoPaperI.
ExtinctionthroughL1642hasbeendeterminedviastarcount Fig.3. Relationbetweenapparent200µmopticaldepthandhy-
method at optical, and color excess method at near-IR wave- drogencolumndensityN(H+H ),derivedfromvisualextinction
2
lengths.Near-IRJ,HandKsbanddatahavebeenextractedfrom (seeSect.3.3).Typicalpixel-to-pixel1–σerrorsareshown.The
the2MASS(2MicronAllSkySurvey)archive.Thetwobinary data points of the regions A, B and C are marked with green,
T Tauri stars near the center of the cloud have been excluded yellowandred,respectively.ThevaluesofA and200µm op-
V
fromthe2MASSdata. ticaldepthhavebeenderivedaftersubtractingfromA andin-
V
tensitiesI(100µm)andI(200µm)thezero-levelvaluesasfixed
outsidetheextentofL1642(seeSection2.3.1).
2.1.B-andI-bandextinctionfromstarcounts
DetailsofthestarcountsaregiveninAppendixA.Westatehere
theconclusionthatextinctionlawinL1642issimilartothatof
K.Lehtinenetal.:ISOfarinfraredobservationsofthehighlatitudecloudL1642 3
Table 1. Values of parametersin L1642, in other clouds and in models. For a description of the differentregions of L1642 see
Section2.3.AllthedataofthecloudL1642applyto4.5 resolution,exceptcolumns4and6whicharefor3.5 resolution.Columns
′ ′
5and6givetheslopesoflinearfitsbetweenI(far-IR)andA .ForadescriptionofmethodsAandBseeSection3.2.Columns2–4
V
forL1642givethevaluesafterthezero-levelsoftheinterclumpdusthavebeensubtracted(seeSection2.3).Columns7–10,inthe
case of methodA, give the valuesafter the backgroundlevelsof each regionhave beensubtracted (see Section 2.3). For L1642,
the columns 2–4 and 7–10 (in the case of ’method A’), give the mean values and 1-σ standard deviations of the corresponding
parameterswithineachregion
Slopeof Slopeof
<A > <I(100µm)> <I(200µm)> I(100µm)vs.A I(200µm)vs.A
V V V
Region [mag] [MJysr 1] [MJysr 1] [MJysr 1mag 1] [MJysr 1mag 1]
− − − − − −
1 2 3 4 5 6
L1642A 2.1 0.6 14 1 34 3 1.6 0.2 4.2 0.4
± ± ± ± ±
L1642B 4.3 1.1 16 1 52 6 0.8 0.1 4.5 0.3
± ± ± ± ±
L1642C 1.5 0.2 16 2 35 3 - -
± ± ±
L1642interclumpdust 1.7 0.1 12 2 28 3 6.7 1.6 17.7 1.2
†
± ± ± ± ±
G300.2–16.8ON1[1] 1.8 0.2 17 9.2 2.1
± ±
G300.2–16.8ON2[1] 1.9 0.2 21 11.0 2.5
± ±
G300.2–16.8ON3[1] 2.9 0.2 35 12.1 2.6
± ±
T <τ(200µm)> τ(200µm)/A σH(200µm)
dust V
Region [K] [10 4] [10 4mag 1] [cm2H-atom 1]
− − − −
[10 25]
−
7 8 9 10
L1642A(methodA) 16.3 0.6 1.3 0.6 1.3 0.5 0.7 0.3
± ± ± ±
L1642A(methodB) 15.9 0.2 - 0.8 0.1 0.4 0.1
± ± ±
L1642B(methodA) 14.2 0.6 4.9 2.5 2.2 0.6 1.2 0.3
± ± ± ±
L1642B(methodB) 13.4 0.3 - 1.9 0.3 1.0 0.2
± ± ±
L1642C(methodA) 18.9 2.6 0.7 0.5 1.1 0.8 0.6 0.4
± ± ± ±
L1642interclumpdust(methodA) 16.3 0.5 4.0 1.0 2.4 0.5 1.3 0.3
‡ ‡
± ± ± ±
L1642interclumpdust(methodB) 17.1 1.0 - 2.2 0.2 1.2 0.1
‡ ‡
± ± ±
G300.2–16.8ON1[1] 17.4 1.9 1.1 0.2 0.6 0.2
± ±
G300.2–16.8ON2[1] 17.4 2.4 1.3 0.2 0.7 0.1
± ±
G300.2–16.8ON3[1] 17.5 4.0 1.4 0.2 0.7 0.1
± ±
TPN[2] 5.3 2.5
G301.2–16.5[3] 0.42-0.95
L183[4] 3.4–3.8
L1780[5] 15.2 2.6 1.4
DiffuseISM[6] 3.2 1.7
DiffuseISM[7] 2.5 1.4
Model[8] 2.7
Model[9] 2.9 1.5
Model[10] 4.7 2.5
Thefithasbeenforcedtogothroughorigin
†
LimitedtovisualextinctionA >1.2mag
‡ V
[1]Rawlingsetal.(2004);[2]Lehtinenetal.(1998);[3]Laureijsetal.(1996);[4]Juvelaetal.(2002);[5]Ridderstadetal.(2006);[6]Cambre´sy
etal.(2001);[7]Dweketal.(1997);[8]Hildebrand(1983);[9]Li&Draine(2001b)fordiffuseISMforR =3.1,interpolatedfromtheirTable6.
V
Valueofemissivityτ(far-IR)/A hasbeenderivedfromtheirvalueofσH(far-IR)bymultiplyingitwiththeratio
V
N(H+H )/A =1.871021cm 2mag 1(seesection3.3);[10]De´sertetal.(1990)fordiffusemedium.ValueofσH(far-IR)hasbeenreadfrom
2 V − −
theirFig.3withabout20%accuracy.Valueofemissivityτ(far-IR)/A hasbeenderivedfromvalueofσH(far-IR)bymultiplyingitwiththeratio
V
N(H+H )/A =1.871021cm 2mag 1(seesection3.3)
2 V − −
thediffuseinterstellarmatter,correspondingtoR = A /E = 2.2.Extinctionfromnear-IRcolorexcess
V V B V
3.1(seeFig..2). −
In order to derive extinctions from near-IR color excesses of
starsvisiblethroughL1642wehaveappliedtheoptimizedmulti-
band technique of Lombardi & Alves (2001) called NICER,
4 K.Lehtinenetal.:ISOfarinfraredobservationsofthehighlatitudecloudL1642
6 -1g]
ma 15
-1ag] 5 -4 [10 V 10 τ /A
-4 [10 mV 34 µ200m)/A 5 true V τapp/AV
A τ(
m)/ 2 16
µ
0
20 1 K] 15
τ(app 0 T [dust 14

-1 13
12 14 16 18 20 22 24
T [K] 1 2 3 4 5
dust
absorption cross-section multiplication factor
Fig.4. The ratio τ (200µm)/A as a function of dust tem- Fig.6. Modelclouds:Apparentdusttemperatureandemissivity
app V
peratureforthe regionsA, B andC (green,yellowandred,re- (τ (200µm)/A )asafunctionofmultiplicationfactorkforthe
app V
spectively), as derived with the method A in Section 3.2. The absorption cross-section of dust grains at far-IR (see Sect. 4.2
errorbarsshowtypicalpixel-to-pixelerrorswithineachregion. for details). The dots are values of apparent temperature and
Thevectorsshowtypicaldirectionandmagnitude(1-σstandard emissivity as derived from the 100µm and 200µm intensities
deviation) of the movementof a data point within each region given by the model. The observed mean values of temperature
duetotheinverserelationbetweenT andτ(far-IR),basedon andemissivityinthecenterofregionBaremarkedashorizontal
dust
MonteCarlocalculations(seeSect.4.2.) lines,shadedareasshowthe1-σuncertainties.Thetrianglesare
truevaluesofemissivity
5
]
-1ag 4 imum, but the angular resolutionis not high enoughto resolve
m
-410 3 tvhiesucalluemxptisncAti1oannodnAth2e.Ionnegesnideeraal,ntdhtehceo2r0re0sµpmondsuernfcaecebebtrwigehetn-
[
V nessandopticaldepthmaps(seePaperI)ontheothersideisvery
A
m)/ 2 good.Thereare,however,somedifferences.The200µmsurface
µ brightnessandopticaldepthofregionsAandCareaboutequal.
00 However, the maximum extinction of region C ( 2.0mag) is
2 ∼
τ(app 1 cthleeaerxlytinlocwtioenr tohvaenrrthegatioonfCredgoioensnAot(h∼av3e.0amsiamg)il.aFrurertghuelramrodrise-,
tributionwithasinglemaximumasthefar-IRsurfacebrightness
0
andopticaldepthmapsdo.
15.0 15.5 16.0 16.5 17.0 17.5 18.0
T [K] TherearedifferencesbetweentheUSNObasedand2MASS
dust
based extinctions. Firstly, the maximum visual extinction de-
Fig.5. Theratioτ (200µm)/A asafunctionofdusttemper- rived from star counts is about half of the maximum derived
app V
ature for the interclump part of the cloud, as derived with the fromnear-IRcolorexcesses.Thiscanbeatleastpartlyexplained
method A in Section 3.2. To suppress noise, we have included bythelowerresolutionandlowerpenetrationpowerofthestar
only those datapointsfor which A > 1.2mag. The error bars countmap.Secondly,therelativevaluesofextinctioninregions
V
show typicalpixel-to-pixelerrors.The straightline has a slope AandCaredifferent;intheUSNObasedextinctionmapregion
of-1.210 4. Thevectorshowstypicaldirectionandmagnitude ChasalargerextinctionthanregionA,butinthe2MASSbased
−
(1-σstandarddeviation)ofthemovementofadatapointdueto mapthesituationisreversed.Thereasonforthisisunknown.For
theinverserelationbetweenT andτ(far-IR),basedonMonte allsubsequentanalyseswewillusethe2MASSbasedextinction
dust
Carlocalculations(seeSect.4.2.) map.
In the following data analysis of this paper, we have used
only those datapoints for which the signal-to-noise ratio of A
V
whichisageneralisationofthetraditionalcolorexcessmethod
is greater than two. In practice, this limit sets the lowest A to
V
usingdataoftwobandsonly.OurdataforL1642compriseJ,H
about0.5mag.
and K bandmagnitudesfromthe2MASSarchive.Thesurface
s
density of stars detected at all three bandsis constantthrough-
out the map, with an averageof about0.9 stars/ ′. The details 2.3.Zero-levelofextinctionandfar-IRintensity
⊔⊓
of our extinction determination are given in Appendix B. The
resulting visual extinction map, weighted with a FWHM=4.5 When deriving the emissivity of dust, it is important to avoid
′
Gaussian, is shown in Fig. 1. Region B has a maximumvisual biasescausedbyimproperdeterminationofzerolevelofextinc-
extinctionof 6.7mag.AtFWHM=3 resolutionthemaximum tion and far-IR emission. We have determined the zero levels
′
∼
extinctionrisesto 8.2mag.RegionA isseenasa localmax- differentlyfortheinterclumpdustandthedenseregions.
∼
K.Lehtinenetal.:ISOfarinfraredobservationsofthehighlatitudecloudL1642 5
2.3.1. Interclumpdust thezero-levelvaluesofeachregionasestimatesofthelastthree
errorcomponents.
Wedefinethe’interclumpdust’astheareasinthe200µmmap
which are outside the regions A/B/C, and which have A <
V
2.0mag. We expect that interclump dust is low density mate- 3. Results
riallocatedaroundthe denserregionsof L1642,andextending
beyondour200µmmap.Forinterclumpdustthezero-levelhas 3.1.Relationbetweenvisualextinctionandfar-IRsurface
tobedeterminedatlocationssufficientlyfarawayfromL1642, brightness
outside our 200µm map. Fortunately, in the context of another
The relations between 200µm and 100µm surface brightness
project,wehaveobservedwithISOat200µmseveralpositions
andA areshowninFig.2.Thereisacleardifferencebetween
in the vicinity of L1642. Here we have utilized the six posi- V
the overall relations; the I(200µm) vs. A relation shows less
tionswiththelowest200µmintensityvalues,locatedabout2.5 V
◦ scatter, andthe changeof slope at A 2 3mag is less pro-
South-West from the center of L1642 (TDT (Target Dedicated V ≈ −
nouncedthanforI(100µm)vs.A .
Time)numbers85500550–55). V
TheparametersoflinearfitstothedatapointsI(100µm)vs.
The 100µm intensities at the same positions have been
A andI(200µm)vs.A ofdifferentregionsaregiveninTable1.
derived from IRAS/ISSA data. To obtain a sufficiently low V V
For region C, there is no clear correlation between far-IR in-
noise for these zero-level positions in the A maps, we used
V tensity and A , mainly because the A -range in this region is
a Gaussian with FWHM=12 as a smoothing function, giving V V
′ rathersmall(see Fig.1).Itisnotablethatthehighestvaluesof
about 0.12mag standard deviation per map pixel. In these six
I(100µm) are located in region C where the visual extinction,
zero-levelpositions,thevalueofI(100µm)=3.4 0.6MJysr 1,
− A 1.5mag, is lower than in regionsA and B (see Fig. 2b).
I(200µm) = 4.8 0.6MJysr 1 and A = 0.14 ±0.11mag(the V ≈
− V ThisisduetothehighertemperatureinregionC(seeFigs.3and
± ±
givenuncertaintyisthestandarddeviationoftheparameter).
4ofPaperI).
Thegeneraldistributionof the data pointsis more linearat
2.3.2. RegionsA,BandC 200µm than at 100µm. This can be explained by the fact that
the temperature drop in region B influences the 100µm inten-
We consider the regions A/B/C as separate clumps which are sitymorestronglythanthe200µmintensitybecausethe100µm
seeninexcessoverthegeneralbackgroundofL1642.Thezero- intensityisontheshort-λsideoftheemissionmaximum.
levelsofregionsA/B/Chavebeendeterminedintheimmediate
surroundings of each of the regions. In this way, we measure
emissionandextinctionwhichisoriginatingsolelyfromthere- 3.2.Determinationofapparentemissivityτapp(200µm)/AV
gioninquestion.Anyforground/backgroundemissionbyinter-
Wheninvestigatingthepossiblevariationsofthedustemissivity
clumpdustisinthiswayeliminated,atleastapproximately.
inL1642itisimportanttorecognizethattheopticaldepthasde-
ForregionsAandBthevalueofemissivitycanalsobede- rivedfromthefar-infraredobservationsat100µm and200µm,
rivedusingtheslopesof I(100µm)vs. I(200µm)and I(200µm)
i.e.
vs. A , which are independentof any backgroundand/or fore-
V
groundzero-levelsubtraction.Thismethodwillbedescribedin τ(200µm)= I (200µm)/B (T ) (1)
ν ν dust
Section3.2.
isingeneralnotthetrueopticaldepthofdustintegratedover
the line of sight. We designate the two quantities by apparent
2.4.Errorestimates
opticaldepth,τ (200µm),andtrueopticaldepth,τ (200µm)
app true
Inthispaperourmainobjectiveistostudythevariationsofthe (seeSection4.3foradetaileddiscussion).
dust properties over the uniformly mapped L1642 cloud area. Therelationbetweenapparent200µmopticaldepthandA
V
Thedifferenterrorsourcescontributingtothepixel-to-pixelvari- is shown in Fig. 3. At 100µm the relation is exactly the same
ations of temperature, far-IR optical depth and emissivity are except that the τ (100µm) values are higher by a factor of
app
listed in Table 2. They are: i) the intrinsic error of each pixel (200/100)2 = 4.ThePearsoncorrelationcoefficientsforthere-
ofthe 200µm intensity map,as givenbythe dataanalysispro- lationare0.85and0.91fortheregionsAandB,respectively.
gramPIA(ISOPHOTInteractiveAnalysis),ii)thepixel-to-pixel
Wehavedeterminedtheapparentemissivitiesusingtwodif-
variationofthe100µm IRASmap,estimatedtobe5%,iii)the
ferentmethods.
errorduetothe incompleteflatfieldcorrectionoftheISO map.
Thishasbeenestimatedfromthedeviationsoftheintensitiesof MethodA.Inthismethodwefirstsubtractfromthe100µmand
adjacentpixels,inawaysimilartotheactualflatfieldcorrection 200µmintensitiesandvisualextinctionthezerolevelvaluescor-
estimation (see Paper I), iv) the error due to the non-matching respondingtoeach region(see Section2.3).Thenthetempera-
pointspreadfunctionsofthe100µmIRASmapandthe200µm ture and 200µm optical depth are derived, on a pixel-by-pixel
intensity map which has been convolved to the IRAS resolu- basisbyusingEq.1.Withinthedifferentregionswederivethe
tion.Thiserrorhasbeenestimatedbyconvolvingthe ISOmap followingmeanvaluesofapparentemissivity:
to 5.0 resolution instead of the 4.5 resolution. As expected, regionA:1.3 0.510 4mag 1
′ ′ − −
the largest differences, about 1.6MJysr 1, are at the positions regionB:2.2±0.610 4mag 1
− − −
of the largestgradientsat regionB. This error source has been regionC:1.1±0.810 4mag 1
− −
appliedto the 200µm map only,v) the errorof the A map as interclumpdu±st(A >1.2mag):2.4 0.510 4mag 1
V V − −
±
givenbytheNICERprogram,vi)theerrorrelatedtouncertainty The A values of interclump dust have been limited to values
V
of zero-level subtraction of 100µm intensity (see Section 2.3), greaterthan1.2maginordertosuppressnoise.Thegivenerror
vii) the error related to uncertainty of zero-levelsubtraction of of emissivity is the 1-σ standard deviation of individual data-
200µm intensity, viii) the error related to uncertainty of zero- pointswithineachregion.Thevaluesofemissivityat100µmare
levelsubtractionofA .Wehaveusedthestandarddeviationsof afactoroffour((200/100)2)higherthanthevaluesat200µm.
V
6 K.Lehtinenetal.:ISOfarinfraredobservationsofthehighlatitudecloudL1642
Method B. From the slope of the I(200µm) vs. I(100µm) re- perature(τ I/B )thex-andy-axesinFigs.4and5arenot
dust
∝
lation we derivethe dusttemperatureT , notaffectedby any independent.Any overestimation of temperature causes under-
dust
constant foreground and/or background emission components. estimationofopticaldepthandviceversaandasaconsequence
Thistemperaturerepresentsatypicaltemperatureineachregion, arelationlikethatinFigs.4or5mayoccur.Wehaveestimated
andisgivenincolumn7ofTable1.Then,theI(200µm)vs.A the uncertainty of the emissivity via Monte Carlo calculations,
V
relation(Fig.2a)givestheslopebetweenthesequantities,called consideringthe eighterrorsourcesas listed in Table 2. Forde-
k. The apparent emissivity ǫ is then ǫ = k/B(T ). This tailsseeAppendixC.Weconcludethattheincreaseofemissiv-
app app dust
methodhasbeenappliedtoregionsAandBandinterclumpdust itywithdecreasingT withinregionB(yellowpointsinFig.4)
dust
forwhichwecanmakeareliablelinearfitofI(200µm)vs.A . can be partly caused by errors in the T estimates. However,
V dust
Wederivethefollowingmeanvaluesofapparentemissivity: the increased emissivity in region B relative to regions A and
regionA:0.8 0.110 4mag 1 C cannot be explained this way. It is found to be a real effect
− −
regionB:1.9±0.310 4mag 1 caused by the change of dust properties. On the other hand, in
− −
interclumpdu±st:2.2 0.210 4mag 1 thecaseofinterclumpdusttherangeoftemperatureinFig.5is
− −
±
Thesevaluesareabouta factorof0.6–0.9lowerthanthosede- rather small, and thus the change of emissivity is only slightly
rivedwithmethodAabove.Moreimportantly,bothofthesein- largerthanthederiveduncertainty.
dependentmethodsgivethesamerelativedifferencebetweenre-
gionsA,B,andinterclumpdust.
4. Discussion
3.3.ApparentabsorptioncrosssectionperH-atomσH (λ)
app
4.1.Dustemissivityvariations
Inthissectionweshallderivetheratiobetweenthefar-infrared
optical depth τ (λ) and the hydrogencolumn density, i.e. the
app The relatively large area of 1.6 which we have mapped in
◦
apparentaverageabsorptioncrosssectionperH-nucleus, ⊓⊔
and around L1642 contains both dense and more diffuse areas
with different dust populations. The 200µm and 100µm emis-
τ (λ)
H app
σ (λ)= (2) sion, dominated by the large particles, and the 60µm, 25µm
app N(H)
and 12µm emissions, dominated by smaller particles, peak at
We can use the near-IR extinction for estimation of the to- separate positions in the cloud (see e.g. Laureijs et al. 1987).
tal hydrogen column density, N(H + H ). We adopt the value Comparedwith the situation where a sample of distinct clouds
2
N(H + H )/E(B V) = 5.81021cm 2mag 1 valid for diffuse have been studied to cover a range of different dust properties
2 − −
clouds (Bohlin et−al. 1978) together with A /E(B V) = 3.1 (seee.g.delBurgoetal.2003)wehavetheobservationaladvan-
V
to obtain N(H + H )/A = 1.871021cm 2mag 1−. The rela- tagethatamoreaccurate(relative)calibrationacrossoursingle,
2 V − −
tion between N(H + H ) and τ (200µm) is shown in Fig. 3. uniformlymappedareacanbeachieved.Thus,thevariationsof
2 app
Within the differentregionswe derive the following mean val- thedustpropertiesoverthemappedareaaremoreaccuratelyde-
H termined.
ues of σ (200µm), calculated with the method A above (see
app
Section3.2): We have found in Sect. 3.4 that the emissivity of the dust,
regionA:0.7 0.310−25cm2H-atom−1 τapp(200µm)/AV, is notconstantbutdecreasesas a functionof
regionB:1.2±0.510−25cm2H-atom−1 dusttemperature,Tdust.Partofthisvariationiscausedbythefact
regionC:0.6±0.410 25cm2H-atom 1 thatthex-andy-axesarenotindependent.Ourerroranalysisin
− −
interclumpdu±st:1.3 0.310 25cm2H-atom 1 AppendixChasshown,however,thatonthelargescaleoverthe
− −
±H wholecloudareathesetendenciesarereal.
Thegivenerrorofσ (λ)is1-σstandarddeviationofindivid-
app
Basedonthetemperatureonly,theemissivityofinterclump
H
ual datapoints within each region. The values of σ (100µm)
app dust(Tdust 16.3 17.1K)isexpectedtobeataboutthesame
H ≈ −
arefourtimesashighasthevaluesofσ (200µm). level as the emissivity of region A (T 15.9 16.3K).
app dust ≈ −
However, it is abouttwo times higher,at the same level as the
emissivityinregionB.Thiscanbeexplainedintermsofdiffer-
3.4. τ (200µm)/A asafunctionofT
app V dust ent contributionsby large grains in differentregionsof L1642.
Figure4showstheemissivityτ (200µm)/A asafunctionof ThemapsofLaureijsetal.(1987)showthat25µmemissionhas
app V
dusttemperaturefortheregionsA/B/C,asderivedwithmethod localmaximaatregionsAandC,while60µmemissionhasalo-
A (see Section 3.2). The emissivity appears to increase as the calmaximumatregionC. Thisindicatesthatverysmallgrains
temperature decreases. Taken from Table 2, there is two-fold (VSGs)havealargerabundanceinregionsAandCascompared
increase of emissivity in the temperature range 19–14K, the to other regions. One possible explanationfor the lower far-IR
rangedeterminedbythemeantemperaturesofreg∼ionsCandB. emissivity of big grains as observed in these regions A and C
Attheverylowesttemperaturevalues,12–14K,thereisindica- couldbethefollowing:thebiggrainsandVSGsarepartofthe
tion of a further increase of emissivity, but the number of data same grain size distribution; decrease in the number of VSGs
pointsisnotsufficienttoconfirmthat. meansanincreaseinthenumberofbiggrains,e.g.viacoagula-
Theemissivityasafunctionofdusttemperaturefortheinter- tionormantleformation.
clumpdustisshowninFig.5.Theemissivityappearstoincrease Thereis,inaddition,thequestionwhetherthe100µmemis-
by a factor of about 1.5 when the dust temperature decreases sion in regions A and C contains a contribution from tran-
from17Kto15.5K. sientlyheatedverysmallgrains,whichwouldmakethederived
Inordertoconfirmthevalidityoftherelationbetweenemis- temperature an ill-defined quantity. This has been discussed in
sivityanddusttemperature,wemustexcludethepossibitythat AppendixD,andtheconclusionisthatthereisnotevidencefor
the relation is due to uncertaintiesin the deriveddusttempera- substantialemissionat100µmfromtransientlyheatedVSGsin
ture: because the optical depth depends inversely on dust tem- regionsAorC.
K.Lehtinenetal.:ISOfarinfraredobservationsofthehighlatitudecloudL1642 7
4.2.Dustemissivityversustemperature:modelling 4.3.Thedifferencebetweentrueandapparentemissivity
Asdiscussedintheprevioussection,theapparentvalueofemis-
In PaperI we showedthatthe decreaseof dusttemperatureto-
sivityisalwayssmallerthanitstruevalue.Theunderlyingrea-
wards the centre of region B in L1642 can not be explained
sonisthatthecolortemperatureisbiasedtowardstoohighval-
solely by the attenuation of the radiation field. In the denser
ues,leadingtoanapparentopticaldepthwhichistoosmall.This
parts of a cloud the dust grains are expected to stick together,
bias is caused by the following facts: i) there is a temperature
forming grains with a bigger cross-section. We have used the
gradienttowardsthecloudcenterwithlowertemperaturesatthe
radiativetransfer programof Juvela & Padoan(2003) to test if
centre than at the edge (see eg. Zucconi et al. 2001 and Galli
anincreasedvalueofabsorptioncross-section(thatis,increased
et al. (2002) for a theoretical discussion), ii) graphite particles
emissivity) of dustgrainscan explainthe observeddecreaseof
arewarmerthansilicateparticleswhichfurthermoreextendsthe
dusttemperatureinL1642.
temperature range of dust particles, iii) the very small grains,
Theparametersofthemodelcloudwhicharebasedonobser- which have a larger temperature fluctuation range than the big
vationsarethecloudsize,radialdensitydistribution,andvisual grains, have a noticeable contribution at 100µm. The net re-
extinction AV at the cloud center. Our model is tailored for re- sult of the above effects is that the emission is to some degree
gionBinL1642.TheFWHMsizeofτ(200µm)ofthemodelis dominatedbythewarmerdustparticles;theycontributealarger
equaltotheobservedone.Thedensityisconstantupto0.2times fractionofthetotalemissionthanwhatshouldbeaccountedfor
the cloudradius, outside of which it has the form ρ(r) r−1.5. by their relative mass. This is especially true at 100µm. The
∝
This density distribution is in agreementwith the CO observa- colour temperature derived from 100µm and 200µm observa-
tions(Russeiletal.2002)andthefar-IRobservations(PaperI). tionsisthereforelargerthantheproper,mass-weightedtemper-
Thecloudis heatedbythe Solar neighbourhoodinterstellarra- ature. Thus, the apparent optical depth τ (200µm) is always
app
diation field (Mathis et al. 1983). The grain properties used in smallerthanthetrueopticaldepthτ (200µm).Consequently,
true
themodelarethoseofLi&Draine(2001b).Wehavecalculated theapparentemissivityisalwayssmallerthanthetrueemissiv-
asetoffivemodels,multiplyingthevaluesofabsorptioncross- ity.
sectionsgivenbyLi&Drainebyafactorofk=1.0,1.5,2.0,3.0, Irrespectiveof the dust temperature,an increase of absorp-
4.0,and5.0,atallwavelengthslongerthananarbitrarilychosen tioncross-sectionofdustparticlesproducesanincreaseofopti-
thresholdwavelengthof50µm. caldepthbythesameamount.InFig.6,theapparentemissivity
isseentoincreaseonlybyafactorofabout3.5whenkincreases
The starting point of the model is the observed maximum
fromonetofive.Thisisduetothefactthattheabovementioned
visualextinctionof A = 6.7magat4.5 resolution.Firstly, in
V ′ effectsaremorepronouncedwhenthetemperatureislower.
the case of k=1.0, the column density of dust is modified until
the model gives a value of A which is equal to the observed
V
one; A (model) is derived by integrating the extinction coeffi-
V 4.4.Comparisonwithgrainmodelsandotherclouds
cient along the line of sight throughthe modelcloud. Then, in
subsequentcalculations,withincreasingvaluesofk,thetruecol- The observed two-fold increase of emissivity in L1642 is sim-
umndensityofdustinthemodeliskeptthesameasinthecase ilar to that observed in other regions; increase at 850µm by a
k=1.0.Thevalueofvisualextinctiongivenbythemodelisthe factor of 4 over a temperature range 20K–12K in the dark
∼ ∼
sameforallvaluesofk becausecolumndensityofdustiscon- cloudIC5146(Krameretal.2003)andbyafactorof 2inB68
∼
stant, and the properties of dust particles are changed only at (Bianchietal.2003);increaseintheFIRbyafactorof 3.4in
∼
λ>50µm. adensefilamentinTaurus(Stepniketal.2003),andincreaseby
afactorof>4inhigh-latitudeclouds(delBurgoetal.2003).
Themodelgivesthe100µmand200µmintensitiesatdiffer-
Table1givesacompilationofsomeobservedandtheoretical
ent radial distances from the cloud center. The intensities are
propertiesof dust. The theoreticalvalues for τ(200µm)/A and
convolved to 4.5 resolution. The optical depth derived from V
′ σH(200µm) in Table 1 are “true” values in our nomenclature.
100µmand200µmintensitiesgivenbythemodelcloudisanap-
Becausethe“apparent”valuesofσH(far-IR)andemissivityare
parentopticaldepth,becauseitisobtainedbymimikingtheac-
alwayssmallerthanthetruevalues(seeSect.4.3),acomparison
tualISOobservations.Thetrueopticaldepth,ontheotherside,
withthemodelresultsisnotstraightforward.Infact,oneshould
isderivedbyintegratingtheabsorptioncoefficientalongtheline
use a certain modelto derive intensity valuesat the two far-IR
ofsightthroughthemodelcloud.Wethenderivemapsofcolor
wavelengths, 100µm and 200µm, and use them to derive the
temperatureandapparentopticaldepthτ (200µm).Thevalues
app apparentopticaldepthandemissivityaswehavedoneinSection
oftemperatureandemissivity,τ (200µm)/A ,atthecentreof
app V
4.2.
the model cloud are shown in Fig. 6 as dots for different val-
H
ues of k. The observed dust temperature and emissivity at the The value of apparent σapp(200µm) of region B is slightly
center of region B are marked as horizontal lines. The shaded lower than the true value obtained for diffuse ISM by Li &
areas show 1-σ uncertainty of the observed values, derived by Draine (2001a) for their carbonaceous-silicate grain model in
assuming 20% absolute uncertainty for the 100µm and 200µm the case RV=3.1. By using Fig. 6 we can transform the value
H
intensities.Clearly,valuesofabsorptioncross-sectionsatfar-IR ofσ (200µm)ofregionBintoitstruevalue.Byassumingthat
app
enhancedby a factor of about2–3are requiredto explainboth themultiplicationfactorforemissivityk = 2.5,theratiooftrue
the observed temperature and apparent emissivity towards the emissivitytoapparentemissivityforthemodelisabout2.5.The
centerofthecloud.Thetruevaluesofemissivity,at4.5′ resolu- valueofσHtrue(200µm)ofregionBwouldthenbeabout3.010−25.
tion,areshownastriangles. ThisishigherthananyvaluefordiffuseISMinTable1.
In the case k = 2 the model predicts intensities at the The regions A and C have < AV >=1.5–2.1mag, slightly
cloudcenterofabout15MJysr 1and64MJysr 1at100µmand higherthan theextinctionthroughtypicaldiffuse dust.In these
− −
H
200µm, respectively, at 4.5 resolution. These values compare regions the value of apparent σ (200µm) (as measured with
′ app
wellwiththeobservedones, 14MJysr 1and 60MJysr 1. method A) is clearly less than the true value obtained for dif-
− −
∼ ∼
8 K.Lehtinenetal.:ISOfarinfraredobservationsofthehighlatitudecloudL1642
fuse ISM by Li & Draine. However, we can not compare the A [mag]
H 0.0 0.5 1.0 B1.5 2.0 2.5 3.0
estimatedvaluesoftrueσ (200µm)ofregionsAandCtothe
true
truevalueofthemodelbyLi&Drainebecausewelackradiative
transfercalculationsforregionsAandC.
Mantleaccretionondustgrainscanincreaseemissivitybya
factorofabouttwoatmost(Preibischetal.1993),whilegrain-
graincoagulation(Bazell&Dwek1990)canincreasetheemis- 00
sivity by a largeramount.Thus, either of these modelscan ex- A2 A1
plaintheobservedincreaseofemissivitybyafactoroftwobe- 0)
0
tweenregionsBandC. 20 15 B
n (
o
ati
5. Conclusions clin 30 C
e
D
Basedonalargescale200µmISOPHOTmappingofthecloud
Lynds 1642, combined with 100µm IRAS/ISSA map, and an
extinctionmapwedrawthefollowingmainconclusions: -14° 45′
– We have found that one has to make a distinction between
apparent values of parameters such as temperature, optical
-15° 00′
depthandemissivity,andtheirtruevalues.Theapparentval-
ues are those which have been derived from the intensity
maps at 100µm and 200µm. We find that the apparentop- 04h 38m 37 36 35 34 33
ticaldepthandemissivityarealwayssmallerthantheirtrue Right Ascen sion (2000)
values because the apparent temperature is biased towards
Fig..1. ExtinctionthroughL1642inB-band.TheIRASsources,
largervalues
marked with asterisks, are from right to left: IRAS 04325–
– The apparent emissivity τ (far-IR)/A increases with de-
app V 1419,04327–1419,04336–1412,04342–1444,04347–1415and
creasingdusttemperature.Thereisabouttwo-foldincrease
04349–1436.TheFWHMsizesoftheregionsA1,A2,BandC
of apparent emissivity when dust temperature decreases
asderivedbyLehtinenetal.(PaperI)from200µmopticaldepth
from19Kto14K
data are shown as ellipses and circles. The contoursare at 1.0,
– Radiative transfer modelling shows that an increase of ab-
1.5,2.0and2.5mag
sorptioncrosssectionofdustatfar-IRiscapableofexplain-
ing two phenomenaobservedin L1642:i) decrease of dust
temperaturetowardsthe centreofthedenseregionB byan
HeartyT.,Ferna´ndezM.,Alcala´J.M.etal.2000,A&A357,681
amount that is more than what can be explained solely by HildebrandR.H.1983,QJRAS24,267
the attenuation of interstellar radiation field, ii) increase of JuvelaM.,MattilaK.,LehtinenK.etal.2002,A&A382,583
apparentemissivitytowardsthecolderregions.Wefindthat JuvelaM.&PadoanP.2003,A&A397,201
KramerC.,RicherJ.,MookerjeaB.etal.2003,A&A399,1073
an increaseofthe far-IRcrosssectionsbyafactorofabout
KesslerM.F.,SteinzJ.A.,&AndereggM.E.1996,A&A315,L27
2–3isrequiredtoexplainboththetemperaturedropandthe LaureijsR.J.,MattilaK.,&SchnurG.1987,A&A184,269
observedemissivityincreaseinregionB LaureijsR.J.,HaikalaL.,BurgdorfM.etal.1996,A&A315,L317
LaureijsR.J.,HerbstmeierU.,A´braha´mP,KlaasU.&LemkeD.2000,In:ISO
Acknowledgements. TheworkofK.L.,M.J.andK.M.hasbeensupportedbythe Beyond Point Sources: Studies of Extended Infrared Emission, Laureijs
FinnishAcademythroughgrantsNos.1204415,1210518and1201269,which R.J.,LeechK.&KesslerM.F.(eds.),ESASP-455,131
isgratefullyacknowledged. Thispublication makesuseofdataproductsfrom LehtinenK.,LemkeD.,MattilaK.,&HaikalaL.K.1998,A&A333,702
the Two Micron All Sky Survey, which is a joint project of the University LehtinenK.,RusseilD.,JuvelaK.,MattilaK.&LemkeD.2004,A&A423,975,
of Massachusetts and the Infrared Processing and Analysis Center/California PaperI
Institute of Technology, funded by the National Aeronautics and Space LemkeD.,KlaasU.,AbolinsJ.etal.1996,A&A315,L64
Administration and theNational Science Foundation. Thisresearch hasmade LiA.&DraineB.T.2001a,
useoftheUSNOFSImageandCatalogueArchiveoperatedbytheUnitedStates http://www.astro.princeton.edu/˜draine/dust/dustmix
NavalObservatory,FlagstaffStation(http://www.nofs.navy.mil/data/fchpix/). LiA.&DraineB.T.2001b,ApJ554,778
LombardiM.&AlvesJ.2001,A&A377,1023
MathisJ.S.,MezgerP.G.&PanagiaN.1983,A&A128,212
MathisJ.S.1990,ARA&A28,37
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K.Lehtinenetal.:ISOfarinfraredobservationsofthehighlatitudecloudL1642 9
Wewereforcedtouseareferencearearelativelyclosetothe
L1642 (at R.A.(J2000)=4h35m00s, Dec.(J2000)=-16 0000 ,
◦ ′ ′′
l=212.90 , b=-37.26 ,a circularregionof1 radius)in orderto
3 ◦ ◦ ◦
have the reference stars on the same plate as most of the field
]
ag stars, and thus with the same magnitude calibration.The value
m
[ ofE(B V)atthereferencepositionisabout0.12magaccording
n −
o 2 R =5.0 tothedustmapofSchlegeletal. (1998),whichcorrespondsto
cti V A 0.4mag.Starcountingwasperformedincircleshavinga
n V
exti R =3.1 radi≈usof 3′. Extinctionswere derived fromthe logN(m) vs. m
d V curvesinthecloudandreferenceareasusingthemethodofWolf
n 1
a (1923).Thepixelsizeoftheextinctionmapwaschosentobe3.
b ′
I- Figure.1showstheB-bandextinctionmap,aftersmoothing
theoriginalmapwitha Gaussianwith FWHM=4.5. Themax-
′
0 imum extinction in the smoothed map, A(B) 3.0mag, occurs
≈
0 1 2 3 4 close to the center of region B. In the center of region C the
B-band extinction [mag] extinctionisabout1.8mag,whileinregionsA1andA2theex-
tinctionsareabout0.8magand1.0mag,respectively.
Fig..2. RelationbetweenstarcountbasedB-andI-bandextinc- TherelationbetweentheB-andI-bandextinctionsisshown
tion.ThedatapointsofregionA,BandCareplottedingreen, in Fig. .2. The extinction ratios at B- and I-bands(470nm and
yellowandred,respectively.Theslopesofthedashedlinescor- 810nm) for the cases RV = 3.1 (diffuse dust) and RV = 5.0
respond to the ratios of total to selective extinction R = 3.1 (“outer-cloud”dust)havebeenadoptedfromTable1ofMathis
V
and R = 5.0. The solid line is a linear fit for A < 3.5mag. (1990), and are shown in Fig. .2 as dashed lines. These values
V B
Thetrianglesaremeanvaluesofextinctionsin0.5mag B-band ofRV correspondtoslopesof0.48and0.58inFig..2.Thesolid
intervalsupto4.0mag,andthedottedlineisalinearfitoftype lineisafitoftypey = a+bxforallthedatapointswhichhave
y = bxtothesemeanvaluesforAB < 3.5mag.Someexamples AB < 3.5mag, weighting by the error of extinction, giving a
of1–σerrorsareshown slope0.54 0.02.
±
Thetrianglesaremeanvaluesofextinctionswithin0.5mag
B-bandintervalsfrom A =0.0–0.5mag up to 3.5–4.0mag, and
B
Wavelength [µm] thedottedlineisalinearfitoftypey =bxtothesemeanvalues
200 120 100 forA <3.5mag.Thederivedslopeis0.49 0.02.Wemaythus
B
±
conclude that the extinction law in L1642 is similar to that of
30
diffuseinterstellarmatter.
25 ThereisindicationinFig..2thatregionChasalowervalue
]
-1r of R than region B. In addition, at A > 3mag the relation
s V B
y 20 indicates a higher value for R inside re∼gion B. The number
MJ V
andaccuracyofdatapointsisnotsufficientforfirmconclusions,
sity [ 15 though.
en 10
nt
I AppendixB: Extinctionfromnear-IRcolorexcesses
5
0 As reference fields, representing areas with “no extinc-
tion”, we have selected two 40 diameter circular areas
1.0 1.5 2.0 2.5 3.0 3.5 4.0 ′
Frequency [1012 Hz] located closely at the same galactic latitude as L1642,
at R.A.(J2000)=4h32m6s, Dec.(J2000)=-12 5027 , and
◦ ′ ′′
R.A.(J2000)=4h41m22s,Dec.(J2000)=-16 4144 .
Fig..3. The intensities measuredata positioninside regionC, ◦ ′ ′′
Theobservedcolorsofstarsinthereferenceareashavethe
at 100µm, 120µm and 200µm. The solid curve is a modified
meanvaluesandstandarddeviationsof(J H)=0.52 0.17and
black-bodywithaν2emissivity,fittedtothe120µmand200µm − ±
(H K)=0.19 0.19.Theywillbeusedasestimatesoftheintrin-
data points. The thick vertical errors at 100µm show the 1-σ − ±
siccolors(J H) ,(H K) andtheirvariances.Fortheratioof
uncertaintyofthefittedblack-body,assuming10%errorforthe − 0 − 0
visualextinctiontocolorexcesswe haveused A /E(J H) =
120µm and 200µm intensities. The thin verticalbarsshow the V −
8.86andA /E(H K )=15.98,whichcorrespondtoR =3.1
estimatederrorsoftheobservedintensities,10%fortheISOdata V − s V
(Mathis1990).
at 120µm and 200µm, and 20% for the IRAS data at 100µm.
The pixel size in the extinction map was chosen to be the
Thehorizontalbarsshowthebandwidthofeachfilter
sameasthepixelsizeofISOC200detector,i.e.1.5.Theextinc-
′
tion valuefor eachmap pixelwas derivedby using a Gaussian
as a weighting function for the extinction values of individual
AppendixA: B-and I-bandextinctionfrom stars, and applying the sigma-clipping smoothing technique of
starcounts Lombardi & Alves (2001). The size of the Gaussian function
dependson whetherwe comparevisualextinctionwith 200µm
Data for star counting at B- and I-bands have been extracted ISO map or with maps from IRAS data. In the case of ISO
fromtheUSNO-B1.0archive(Monetetal.2003).Wehaveused map we use a Gaussian with FWHM=3.5, limited by the ne-
′
data fromthe secondepochSERC-J (B -band)and SERC-I (I- cessity of having a sufficient signal-to-noise ratio for the ex-
J
band)surveys.FortheeffectivewavelengthsoftheBandIbands tinction. The point-spread profile of ISO at 200µm can be de-
wehaveused470nmand810nm,respectively(seeEvans1989). scribed by a Gaussian functionhaving FWHM=86 . Thus, the
′′
10 K.Lehtinenetal.:ISOfarinfraredobservationsofthehighlatitudecloudL1642
ISOmaphasbeenconvolvedwithaGaussianhavingFWHM= 100µm.Weassumethat100µmisthelongestwavelengthwhich
√(210 2 86 2) = 192 when comparing with the visual ex- maybeaffectedbynon-equilibriumgrains.Thisissupportedby
′′ ′′ ′′
tinctionm−aphavingFWHM=3.5 resolution. the observationsof L1780 (Ridderstad et al. 2006), which is a
′
The temperature and optical depth maps have been made high latitude cloud similar to L1642,and the translucent/cirrus
by utilizing IRAS data which have a FWHM=4.5 resolution, cloudasstudiedbyLaureijsetal.(2000).Inboththeseclouds,
′
measured from intensity profiles of point sources in the IRAS the intensities at 100µm, 120µm, 150µm and 200µm are all
map. For these maps the 200µm ISO data have been con- well fitted with a single black-body function, even in the po-
volved with a Gaussian having FWHM= √(270 2 86 2) = sitions where 12µm and 60µm emission have their maximum
′′ ′′
256 . Consequently, we use the visual extinction−map with values.Ontheotherhand,at80µmthereisasignificantexcess
′′
FWHM=4.5 resolution in the context of temperature and op- overtheblack-bodyemissionfromthermalequilibriumgrains.
′
ticaldepthmaps. In Fig. .3 we plot 120µm and 200µm intensities at the po-
Thereare twosourcesoferrorforthe extinctionmap;vari- sitioninregionC,togetherwithamodifiedblack-bodyfunction
ance of the intrinsic colors (J H) and (H K) , and vari- fitted to them, and an estimated error of the black-body func-
0 0
anceoftheobservedmagnitude−softheprogram−mestars.Inthe tionat100µm.Whentakingtheerrorsintoaccount,thereisno
A mapmadewithaFWHM=4.5 Gaussiantheformersource evidenceforanexcessemissionat100µm.Webelievethatany
V ′
dominateswitha 0.29mag1-σerrorperpixel,whilethelat- excessemissioninregionAisevensmaller,becauseregionAis
tersourcecontribu∼testypically 0.08mag1-σerrorperpixel, colderthanregionC.
givingatypicaltotalerrorof 0∼.32magperpixel. The 120µm and 200µm points in Fig. .3 are from ISO
∼ data, the 100µm point is from IRAS data (scaled to DIRBE
calibration as in Lehtinen et al. 2004). The ON-source po-
AppendixC: Erroranalysisoftheemissivity sition in region C is at coordinates R.A.(J2000)=4h36m7.2s,
Dec.(J2000)=-14 363 . From the ON-source (ISO TDT
Wehaveestimatedtheuncertaintyofthe200µmemissivityvia ◦ ′ ′′
numbers 83901895, 83901887) intensities we have subtracted
MonteCarlocalculations,consideringtheeighterrorsourcesas
the mean values of intensities at two reference positions,
listed in Table 2. For the emissivity estimation, the largest er-
locatedatcoordinatesR.A.(J2000)=4h33m17.3s,Dec.(J2000)=-
ror source is the error of A because it is a large fraction of
V 15 5812 (ISOTDTnumbers83901881,83901882,83901890,
theextinction( 10–75%forA =6–1mag).Ontheotherhand, ◦ ′ ′′
∼ V 83901889,83901885,83901893)andR.A.(J2000)=4h28m59.4s,
the error of A does not cause any inverse emissivity vs. T
V dust Dec.(J2000)=-15 0011 (ISO TDT numbers 83901896,
relation.Typicalerrorsofemissivityandtemperature,basedon ◦ ′ ′′
83901888).
Monte Carlo calculations, are plotted in Fig. 4 for each of the
regionA/B/C,andforinterclumpdustinFig.5.
We haveused the MonteCarlo methodto study intowhich
direction and how much a datapointmovesin a T vs. τ(far-
dust
IR) plot due to pixel-to-pixelerrors in the 100µm and 200µm
intensitymaps.Letusfirstconsiderthenon-realisticcasewhere
only one of the intensity maps has errors. In this case there is
always a negative correlation between T and τ(far-IR), just
dust
as expected.In the case where both of the intensity maps have
errors, also positive correlation between T and τ(far-IR) is
dust
possible.Thishappenswhen100µmand200µmintensitiesei-
ther increase or decrease simultaneously. For example, if both
ofthemincreasebya suitableamount,thederivedtemperature
may increase just slightly, and then the optical depth increases
toobecausetherelativeincreaseofintensitymaybegreaterthan
theinfluenceoftheincreaseoftemperature.However,apositive
correlation between T and τ(far-IR) happens only when the
dust
change of temperatureis minuscule. When taking into account
alltheerrorsofTable2,wefindthattheslopeoftheinverserela-
tionbetweenT andemissivityhasavalueof 0.5 0.210 4,
dust −
1.1 0.310 4and 0.4 0.310 4inregionA,B−and±C,respec-
− −
− ± − ±
tively.Thus,thevalueoftheslopeincreasesasthetemperature
decreases.Forinterclumpdustthepredictedslopehasavalueof
1.0 0.410 4,closetotheobservedvalueof 1.210 4.
− −
− ± −
The vectors in Figs. 4 and 5 show the direction and mag-
nitude (1-σ standard deviation)of the movementof datapoints
caused by the inverse relation between T and emissivity,
dust
whentakingalltheerrorsourcesofTable2intoaccout.
AppendixD: Existenceofemissionfrom
non-equilibriumverysmallgrains
Becausetheabundanceofverysmallgrains(VSGs)isenhanced
in regions A and C, we have to investigate whether there is
anysignificantemissionfromthese transientlyheatedgrainsat