Blowing in the wind: The dust wave surrounding $\sigma$ Ori AB

3.3 MB·

by  B. B. Ochsendorf

Astronomy&Astrophysicsmanuscriptno.sigmaori (cid:13)c ESO2014
July9,2014
Blowing in the wind: The dust wave around σ Ori AB
B.B.Ochsendorf1,N.L.J.Cox2,S.Krijt1,F.Salgado1,O.Berne´4,J.P.Bernard4,L.Kaper3 &A.G.G.M.Tielens1
1 LeidenObservatory,LeidenUniversity,P.O.Box9513,NL-2300RA,TheNetherlands
e-mail:[email protected]
2 InstituutvoorSterrenkunde,K.U.Leuven,Celestijnenlaan200D,bus2401,3001Leuven,Belgium
3 SterrenkundigInstituutAntonPannekoek,UniversityofAmsterdam,SciencePark904,P.O.Box94249,1090GEAmsterdam,The
Netherlands
4 Universite´deToulouse,UPS-OMP,IRAP,31028Toulouse,France
Preprintonlineversion:July9,2014
ABSTRACT
4
1 ObservationsobtainedwiththeSpitzerSpaceTelescopeandtheWISEsatellitehaverevealedaprominentarc-likestructureat50”
0 ((cid:39) 0.1pc)fromtheO9.5V/B0.5VsystemσOriAB.Wemeasureatotaldustmassof2.3±1.5×10−5 M .Thederiveddust-to-gas
(cid:12)
2 massratiois(cid:39)0.29±0.20.
We attribute this dust structure to the interaction of radiation pressure from the star with dust carried along by the IC 434 photo-
l
u evaporativeflowofionizedgasfromthedarkcloudL1630.Wehavedevelopedaquantitativemodelfortheinteractionofadusty
J ionizedflowwithnearby(massive)starswhereradiationpressurestallsdust,pilingitupatanappreciabledistance(>0.1pc),and
8 forceittoflowaroundthestar.ThemodeldemonstratesthatfortheconditionsinIC434,thegaswilldecouplefromthedustand
willkeepitsoriginalflowlines.Hence,wearguethatthisduststructureisthefirstexampleofadustwavecreatedbyamassivestar
] movingthroughtheinterstellarmedium.Ourmodelshowsthatforhighergasdensities,couplingismoreefficientandabowwave
R willform,containingbothdustandgas.
S Our model describes the physics of dust waves and bow waves and quantitatively reproduces the optical depth profile at 70 µm.
Dustwaves(andbowwaves)stratifydustgrainsaccordingtotheirradiationpressureopacity,whichreflectsthesizedistributionand
.
h compositionofthegrainmaterial.ItisfoundthatintheparticularcaseofσOriAB,dustisabletosurviveinsidetheionizedregion.
p Comparisonofourmodelresultswithobservationsimpliesthatdust-gascouplingthroughCoulombinteractionislessimportantthan
- previouslythought,challengingourunderstandingofgraindynamicsinhot,ionizedregionsofspace.
o Wedescribethedifferencebetweendust(andbow)wavesandclassicalbowshockscreatedbytheinteractionofastellarwindwith
tr theinterstellarmedium.TheresultsshowthatforlateO-typestarswithweakstellarwinds,thestand-offdistanceoftheresulting
s bowshockisveryclosetothestar,wellwithinthelocationofthedustwave.Ingeneral,weconcludethatdustwavesandbowwaves
a
shouldbecommonaroundstarsshowingtheweak-windphenomenon,i.e.,starswithlog(L/L )<5.2,andthatthesestructuresare
[ (cid:12)
bestobservedatmid-IRtoFIRwavelengths,dependingonthestellarspectraltype.Inparticular,dustwavesandbowwavesaremost
2 efficientlyformedaroundweak-windstarsmovingthroughahighdensitymedium.Moreover,theyprovideauniqueopportunityto
v studythedirectinteractionbetweena(massive)staranditsimmediatesurroundings.
5
8
1
7 1. Introduction bleineithershockedgas(Brown&Bomans2005;Kaperetal.
. 1997)orwarmdustradiatingatinfraredwavelengths(vanBuren
1 The initial expansion of HII regions is driven by rapid ioniza- & McCray 1988). The Infrared Astronomical Satellite (IRAS;
0
4 tion around a young, massive star. Once the HII region is es- Neugebaueretal.(1984))all-skysurveydetectedmanyextended
tablished, the overpressure of the ionized region will drive the
1 arc-like structures associated with OB-runaway stars, revealing
expansion as the ionizing flux of the star dilutes with distance,
: thatbowshocksareubiquitousaroundstarswithpowerfulstellar
v sweeping up neutral gas in a shell. Dust inside the HII region winds(vanBurenetal.1995;Perietal.2012).However,recent
i will absorb ionizing flux and re-emit in the IR, stalling the ex-
X observations indicate that many late O-type dwarfs have mass-
pansion of the ionized material (Petrosian 1973; Draine 2011).
lossrateswhicharesignificantlylowerthanpredictedbytheory
r
a When the ionization front breaks out of the molecular cloud, a (Bouretetal.2003;Martinsetal.2004),whichraisesquestions
phase of rapid expansion of the ionized gas into the surround-
whethertheobservedscalesizesofbowshocksaroundstarsthat
ing low density medium commences: the so-called champagne
display the weak-wind phenomenon can be accounted for by a
flowphase(Tenorio-Tagle1979;Bedijn&Tenorio-Tagle1981;
wind-drivenbowshockmodel.Ithasalreadybeenproposedby
Yorke1986).
vanBuren&McCray(1988)thatradiationpressuredrivenbow
Massivestarshavestrongwinds(M˙ ∼10−8 -10−6 M(cid:12) yr−1, waves are expected around stars with a low wind momentum
v∞(cid:39)1000-2500kms−1;Kudritzki&Puls(2000)).Ifthesestars flux.Untilnow,nosuchstructurehasbeendetectedintheinter-
move supersonically with respect to their environment, a bow stellarmedium(ISM).
shockwillbecreatedatthestand-offdistancefromthemoving
starwheretherampressureandmomentumfluxofthewindand TheIC434emissionnebulaisprobablyanevolved HIIre-
theinterstellarmediumbalance(vanBurenetal.1990;MacLow gion,wheretheionizingpopulationofthelargeσOrioniscluster
et al. 1991). The swept-up material in the bow shock is heated hasclearedawayitsimmediatesurroundings.Currently,theion-
by the radiation of the OB star, making these structures visi- izationfrontiseatingitswayintotheL1630molecularcloudand
1
B.B.Ochsendorfetal.:ThedustwavearoundσOriAB
theionizedmaterialisstreamingintothe HIIregion.Thecentral Hαimaging
component is a five-star system, found approximately one de- Hα narrow band data from the Hubble Space Telescope
greebelowAltinak,theeasternmoststarinOrion’sBelt.Thisre- (HST), the Mosaic 1 wide field imager on Kitt Peak National
gionalsocontainsthecharacteristicHorseheadNebula(Barnard Observatoy (KPNO) and the Southern H-Alpha Sky Survey
33), emerging as a dark nebula out of the large L1630 molecu- Atlas (SHASSA) are used in this study. The HST image of the
larcloud.Caballero(2008)hasmeasuredadistancesof334+25 Horsehead was taken as part of the Hubble Heritage program
−22
pc, although reported distances vary up to ∼500 pc, as deter- (PI: K. Noll) and is used as a calibrator for the KPNO image.
minedfromcolour-magnitudediagrams(Caballeroetal.2007). The calibrated KPNO image offers Hα data at a high angular
Previous studies have revealed a vast population of lower-mass resolution(0.26”pix−1),butdoesnotextendtowardsσOriAB.
starsandbrowndwarfsbelongingtothelargerσOriopenclus- Becauseofthis,wecomplementourHαobservationswithdata
ter (Be´jar et al. 2011; Caballero 2007). The dominant ionizing fromtheSHASSAmission.SHASSAprovidesacompletecov-
component of the system, σOri AB, is a 3 Myr old (Caballero erageofthenorthernhemisphereata0.8arcminuteresolution.
2008) close binary of spectral type O9.5V and B0.5V with a
third massive companion (Simo´n-D´ıaz et al. 2011). The ioniz-
Spitzer/IRSspectralmapping
ing flux from the central stars illuminates IC 434 together with
Spitzer/IRS(Houcketal.2004)spectralmapsfromtheSpitzer
themaneoftheHorseheadnebula.Thepresenceofa24µmin-
Science Center Archive were obtained as part of the SPECHII
frared arc-like structure near σ Ori has been noted previously
program (PI: C. Joblin) in April 2008. Both Long-Low mod-
by Caballero et al. (2008) (their Fig. 1, as well as Fig. 2 from
ules(LL)wereusedfromtheobservations,whichcoverthe16-
Herna´ndezetal.(2007)),whodesignatedthebrightestknotasσ
35 µm wavelength region at an angular resolution of 5(cid:48)(cid:48)/pixel.
OriIRS2.Tothebestofourknowledge,wepresentherethefirst
In addition, a dedicated offset position was taken at an IRAS
detailedstudyofthisuniqueandconspicuousinfraredsource.
darkposition.SpectralcubeswerebuiltusingCUBISM(Smith
WearguethatthearcstructureengulfingσOriABpresents
etal.2007).CUBISMusesthe2DBCDdataandallowsforstan-
the first detection of a dust wave in the ISM, where radiation
dardreductionoperationssuchasskysubtractionandbadpixel
pressurehasstalledthedustwhichwascarriedalongbyaphoto-
clipping. Inaddition, slitand apertureloss correction functions
evaporationflowofionizedgas.InSec.2,wepresenttheobser-
appropriateforextendedsourcecalibrationareappliedandsta-
vationsandhowweprocessedthedata;Sec.3reviewsthestellar
tistical errors originating from the IRS pipeline are propagated
propertiesandwederivelocalphysicalparameters;inSec.4the
throughCUBISM.
observablesandtheglobalstructurearepresented;inSec.5we
propose the dust wave scenario to explain the observations; re-
sults are shown in Sec. 6 which we will discuss in Sec. 7. We
3. Stellarpropertiesandlocalphysicalconditions
concludeinSec.8.
Figure 1 displays the mid-IR view of the IC 434 complex.
Although diffuse structures are seen inside the HII region, the
2. Observations imageshows alarge cleared-outregion with σ OriAB slightly
displacedfromitscenter.TheimageshowsthatσOriABisin-
IRphotometry deedthedrivingionizingsourceoftheregionasnumerouspil-
Infrared (IR) photometry of the σ Ori cluster combines data
larsofmaterial,whicharecurrentlybeingphoto-evaporated,are
from the Wide-field Infrared Survey Explorer (WISE; Wright
directedtowardsthestar.ThelowerpanelsinFig.1zoomsinto
et al. (2010)), the Infrared Array Camera (IRAC; Fazio et al. our region of interest: the σ Ori AB - L1630 region. Radiation
(2004)) and the Multiband Imaging Photometer (MIPS; Rieke
from the star is ionizing the boundary of the molecular cloud,
et al. (2004)) on board of the Spitzer Space Telescope and
launching the material into the HII region. Extended emission
the Photodetector Array Camera and Spectrometer (PACS; at24µmandanarcstructure,morepronouncedat12µm,reveals
Poglitsch et al. (2010)) on the Herschel Space Telescope. The
the interaction of the ionized flow with either a stellar wind or
WISE atlas data were extracted from the All-Sky Data release radiationpressureemanatingfromσOriAB.
andweremosaicedusingMontage.IRACdatawereobservedin
March2004aspartofprogramID37andweretakenfromthe
Spitzer Science Center archive as a post-Basic Calibrated Data 3.1. Basicstellarpropertiesandspacevelocities
◦ ◦
(post-BCD)product.Thepost-BCDimagewitha1 ×0.8 field- Table 1 lists basic stellar properties for σOri AB. We calcu-
of-view (FOV) combines BCD images of 30 seconds integra- late the space velocity of σOri AB with respect to the Local
tion time each and was found to be of good quality. The MIPS StandardofRest(LSR).Usingtheseparameters,σOriABhasa
24 µm post-BCD data was also of sufficient quality and give spacevelocityof15.1kms−1,withapositionangleof49.9◦.For
◦ ◦
a 0.75 ×1.5 FOV in medium scan mapping mode with 160(cid:48)(cid:48) comparison, σOri D and σOri E have space velocities of 18.5
steps. PACS 70 µm photometry was taken from the Herschel and13.1kms−1,respectively.
Science Archive (HSA) from the Gould Belt survey (Andre´ The direction of the space velocity of σ Ori AB (see Sec.
etal.2010)withobservationIDs1342215984and1342215985. 3.1)suggeststhatitismovingtowardsthemolecularcloud,in-
ThesePACSdatawereobtainedinPACS/SPIREparallelmode creasingtherelativevelocitybetweentheflowandthestar.We
athighscanningspeed(60(cid:48)(cid:48) s−1).Thenominalfullwidthathalf notethatitispossiblethattheobservedspacevelocityoftheσ
maximum (FWHM) of the point spread function (PSF) for this Ori AB (as a member of the σ Ori cluster) represents the ve-
typeofobservationsis5.9(cid:48)(cid:48) ×12.2(cid:48)(cid:48) fortheblue(70µm)chan- locityoftheentireregionwithrespecttotheLocalStandardof
nel.HIPEv.8(Ott2010)andScanamorphosv.15(Roussel2012) Rest(LSR),whichwouldimplythatσOriABisatrestwiththe
were used to make maps of the IC 434 region after which the L1630molecularcloud.Acomparisonofradialvelocities(with
datawasinter-calibratedwithIRAS70µmdata.Contamination respect to the LSR) v of members of the σ Ori cluster (i.e.,
LSR
byzodiacallightwassubtractedusingtheSPOTbackgroundes- σ Ori AB, σ Ori D and Ori σ E) and the L1630 cloud reveal
timator,basedontheCOBE/DIRBEmodel(Kelsalletal.1998). similar velocities: we calculate a mean v of 13 km s−1 for
LSR
2
B.B.Ochsendorfetal.:ThedustwavearoundσOriAB
◦ ◦
Fig.1:(a):Mid-IRviewoftheIC434region.Thetotalfield-of-viewis3.1 ×2.9 .GreenistheWISE-312µmband;redisthe
WISE-422µmband.(b):Blown-uppartoftheupperimagewithdifferentscalingtoaccentuatetheextendedemissionaroundσ
OriAB.TheHorseheadnebulaislocatedatthetopleft.Here,bluerepresentsHαtakenwiththeKPNO4mtelescope,whereasred
isMIPS24µmemission.TheKPNOimagedoesnotextendovertheentirefieldofviewbutcutsoff6(cid:48)eastwardsofσOriAB.(c):
CloseupoftheenvironsofσOriAB.GreenisWISE-3,whileredisMIPS24µm.Overplottedisthepropermotionvectorwhich
displaysthemovementintheplaneofthesky.
3
B.B.Ochsendorfetal.:ThedustwavearoundσOriAB
Table1:StellarparametersforSigmaOriAB(alsoknownas48 closertothetruevaluegiventheextremesensitivityoftheBrα
Ori, HD 37468, and HIP 26549) and calculated space velocity line flux for very low mass-loss rates (Auer & Mihalas 1969;
parameters. L is the luminosity of the star; Q0 is the ionizing Najarroetal.1998;Lenorzeretal.2004).Themodelpresented
photon flux; vrad is the radial velocity; µα and µδ are the proper in this work naturally follows from σ Ori AB being a weak-
motions in RA and DEC, respectively; d is the measured dis- windobject;however,wewilldiscusstheimplicationswhenone
tance;M˙ isthemass-lossrate.Thepropermotionpositionangle woulduseahighermomentumfluxinSec.6.2andinAppendix
θ is measured from north to east; i is the inclination angle with A.
respecttotheskyandv isthetotalspacevelocityofσOriAB.
(cid:63)
RA(J2000) 05:38:44.768 Caballero(2007) 3.3. Photo-evaporationflow
DEC(J2000) -02:36:00.25
Spectraltype O9.5V+B0.5V Hoffleit&Jaschek(1982) TheIC434 HIIregionisaclearexampleofaflowofionizedgas,
L(log(L /L )) 4.78 Lee(1968) whichisinitiatedwhentheionizationfrontbreaksoutofadense
(cid:63) (cid:12)
logQ (s−1) 47.88 Martinsetal.(2005a) confiningmolecularcloudenvironmentintoasurroundingtenu-
0
µ (masyr−1) 4.61±0.88 Perrymanetal.(1997)1 ousmedium.Thedensitycontrastwilldriveastrongisothermal
α
µ (masyr−1) -0.4±0.53 Perrymanetal.(1997) shockintothelowdensityregion,whileararefactionwavewill
δ
µα(kms−1) 6.8 plough into the ionized cloud gas. Material ionized at the edge
µδ(kms−1) 5.7 ofthemolecularcloudisrapidlyacceleratedanddrivenintothe
vrad(LSR)(kms−1) 11.45 Caballero(2008) lowdensityregion,startingtheonsetofaflowofionizedgas(a
d(pc) 334+−2252 Caballero(2008) champagne flow; Tenorio-Tagle (1979); Tielens (2005)). In the
M˙ (M yr−1) 8.0×10−8 Howarth&Prinja(1989)
(cid:12) caseofIC434,itisthedensitycontrastbetweenthetenuous HII
2.0×10−10 Najarroetal.(2011)
regionandthehighdensityL1630cloudthathassetuptheflow
v (kms−1) 1060 Howarth&Prinja(1989)
∞ ofionizedgastowardsσOriAB.
1500 Najarroetal.(2011)
θ(◦) 49.9 Thiswork Figure2showstherootmeansquare(RMS)electrondensity
i(◦) 49.4 derivedfromtheobservedHαemissionmeasure(EM),assum-
v (kms−1) 15.1 ing a path length of the emitting region along the line of sight.
(cid:63) (cid:82)
1 ValuesforpropermotionpublishedinvanLeeuwen(2007)showa The EM is defined as n2edl, where ne is the electron density
largediscrepancybetweendifferentmembersσOricentralcluster. andlthepathlengthoftheemittingregion.Weconsiderthe HII
Therefore,weadoptpropermotionparametersfromPerrymanetal. region to be fully ionized, i.e., n = n , with n the hydrogen
e H H
(1997).Inthiscase,propermotionsbetweenσOriABaresimilar density.
tothevaluesforσOriDandσOriElistedinCaballero(2007). We estimate the electron density in two independent ways.
First,Compie`gneetal.(2007)usedtheS[III]19and33µmfine-
structure lines to determine the electron density just ahead of
the σ Ori cluster members, whereas the L1630 cloud moves at theHorsehead(within∼0.02pcfromtheionizationfront)tobe
a velocity of v ∼ 10 km s−1 as seen through molecular ob- n (cid:39) 100-350 cm−3. Second, the local density at the ionization
LSR e
servations (Maddalena et al. 1986; Gibb et al. 1995). Surely, a front is estimated by calculating the amount of ionizing pho-
comparison of radial velocities alone will not resolve the ques- tons J whichlandonthesurfaceoftheL1630molecularcloud.
tionwhetherbothstructuresaremovingtogetherornot,asthese Assumingadustattenuationofe−τ =0.5,Abergeletal.(2003)
measurements only represent one component of the true space approximated this at J = 0.8 × 108 cm−2 s−1. Dividing this by
velocity. In this work, we will use the measured space velocity theisothermalsoundspeedc =(kT/µm )1/2 =10kms−1 atT
s H e
of σ Ori AB as the relative velocity between the cloud and the = 7500 K (Ferland 2003), we calculate a density of n = n =
H e
star, but we will address the implications on our conclusions if J/c = 80 cm−3, in close agreement with the value derived by
s
thetwostructureswereatrestwithoneanother. Compie`gneetal.(2007).
TheEMoftheflowisderivedusingthecalibratedKPNOHα
intensity together with standard conversion factors taken from
3.2. Windproperties
Osterbrock&Ferland(2006).WemeasureEM=1.8×104cm−6
ThewindsfromearlyO-typestarsandearlyB-typesupergiants pcattheionizationfront.Wecanthenpindownthepathlength
are well described by the mass-loss recipe from Vink et al. l of the L1630 molecular cloud at the cloud surface using the
(2000).However,theaccuracyofthisrecipehasbeenquestioned deriveddensitynH.Inthisway,L1630needstoextend1pcalong
forstarswithluminositylog(L/L )<5.2,inparticularbecause thelineofsightinordertoreproducethederiveddensity.
(cid:12)
of wind clumping and the weak-wind problem as described in We are particularly interested in the gas density further
Najarro et al. (2011); Puls et al. (2008), but see Huenemoerder downstream,wheretheionizedflowinteractswithσOriAB(see
et al. (2012). This is because traditional mass-loss indicators Fig.1).Forthis,weneedtoadoptadensitylawbetweenthestar
(UV, Hα) become insensitive at low mass-loss rates. Thus far, andthemolecularcloud.AsdiscussedinSec.1andabove,the
there are wind parameters for only a handful of late O-dwarf density contrast between the tenuous HII region and the dense
stars(Bouretetal.2003;Martinsetal.2004;Najarroetal.2011). molecularcloudL1630setsupachampagneflowstreaminginto
Table 1 includes two different values for the mass-loss rate M˙ the HII region (Tenorio-Tagle 1979). Strictly speaking, on a
andtheterminalwindvelocityv ofσOriAB.Earliermeasure- largescalethesurfaceoftheL1630cloudwillbeconvex,which
∞
mentsbyHowarth&Prinja(1989)wereinterpretedintermsof will lead to a photo-evaporation flow following the nomencla-
amuchhighermomentumflux.However,itisnowwellappreci- turedescribedinHenneyetal.(2005).However,astheradiusof
atedthatthediagnosticuseofUVwindlinesislimited(Martins curvatureoftheionizationfrontismuchlargerthanthedistance
etal.2005b;Pulsetal.2008).Najarroetal.(2011)categorized to the ionizing source and as we are focussing on the material
σOri AB as a weak-wind candidate after careful modeling of passingclosetothestar(whichwilloriginatefromasmallpart
spectral lines in the L-band. We believe that the latter value is ofL1630),theanalysisofHenneyetal.(2005)suggestthatwe
4
B.B.Ochsendorfetal.:ThedustwavearoundσOriAB
canapproximatethestructureoftheflowasachampagneflowin
aplane-parallelgeometry.Forthiswewilladopttheresultsfor
anisothermalshocktubeasdescribedinBedijn&Tenorio-Tagle
(1981)andTielens(2005).
The initial velocity of the gas leaving the cloud surface is
assumedtobecomparabletothesoundspeed(i.e.,aD-critical
ionizationfront).Therarefactionwavemovingintotheionized
cloud gas sets up an exponential density gradient along which
the gas is accelerated into the HII region. The continuity and
momentumequationscanthenbeusedtoshowthatthegasfol-
lowsalinearvelocitylawdefinedas
dρ
dv =c g. (1) Fig.2:Densityprofileoftheionizedphoto-evaporationflowin-
g s ρg sideIC434.ThecontributionoftheHorseheadisplottedinred,
whichisonlyasmalldisturbanceatthestartoftheflow.Small
Here, v and ρ are the velocity and density of the flow.
g g artifactsintheobserveddensityprofilepersistaftersubtraction
Rewritingthisintermsofthenumberdensityn,Eq.1integrates of background/foreground stellar features not associated with
to(Bedijn&Tenorio-Tagle1981)
theflow.Theobservedprofilerevealsanexponentialdensitygra-
(cid:32) (cid:33) dientandisfittedusinganappropriatedensitylaw(dashedline;
J r−R
n(r)= exp s , (2) seetext).σOriABislocatedatadistanceof3.2pc.
c c t
s s
whereristhedistancefromthestar(r≤R );R istheStro¨mgren
s s gasstayscoupled.Thissectionwillelaborateoninformationex-
radius (Stro¨mgren 1939) (in our case: the distance between σ
tractedfromtheIRobservations,whileSec.5willdealwiththe
Oriandthemolecularcloud),andtisthetimewhichhaspassed
physicsofbowwavesanddustwaves.
since the material at the head of the flow had been ionized and
startedtomoveintoIC434.
Weadopt anexpansionlaw todescribe theevolutionof the 4.1. Dustdistribution
pathlengthlwithdistancefromthemolecularcloud.Whilethe
Thedustcolortemperatureisderivedfromthe24µmand70µm
flow expands into the HII region, we increase the path length
intensitiesafterconvolvingthePACS70µmimagetotheMIPS
linearly. When the flow has reached σOri AB, we assume that
24µmbeamusingtheconvolutionkernelsdescribedinAniano
thescalesizeoftheemittinggasalongthelineofsightisequalto
et al. (2011). According to the Herschel PACS Instrument
thetraverseddistance,i.e.,theprojecteddistancebetweenL1630
Calibration Centre (ICC), photometric measurements between
and σOri AB of d = 3.2 pc at a distance of 334 pc. The ion-
PACSandMIPSareconsistentwithin17%2.Thedependenceof
izedflowthenshowsasmoothdropinhydrogendensity,rang-
dust emissivity on wavelength, β, is of little importance in our
ing from n = 100 cm−3 at the cloud surface to n = 10 cm−3
H H study as we are extrapolating towards long wavelengths where
nearσOriAB.TheresultisshowninFig.2.Wefindthat,due
theintensityislow.Inthiswork,wefixtheemissivityatβ=1.8.
to the pressure gradient, the gas near σ Ori AB is accelerated
FollowingHildebrand(1983),thedustopticaldepthisestimated
to 35 km s−1 which is 3.5 times the local sound speed c . The
s by
timescalefortheionizedgastoreachthestaristhenroughly1.5
×105yr.TakingintoaccountthespacevelocityofσOriAB,we
I
calculateamaximumrelativevelocitybetweenthestarandthe τ = ν , (3)
ν B
ionizedflowof50kms−1.Insummary,Fig.2demonstratesthat ν,Td
thedensitylawiswelldescribedbyanexponentialdensitylaw
where I is the surface brightness and B is the Planck func-
with a scale height of 1 pc at the cloud surface. As the density ν ν
tion for dust temperature T . We evaluate Eq. 3 at 70 µm. The
attheionizationfrontiswelldeterminedfromtheintensityratio d
dustcolortemperaturemapandtheopticaldepthmapat70µm
oftheS[III]finestructurelines,theonlyassumptionthatenters
areplottedinFig.3.Dusttemperaturesrangefrom50±10Kto
intothiscomparisonisthelinearexpansionoftheflowalongthe
75±14KnearσOriABwhiletheopticaldepthτ aheadofthe
lineofsightfrom1pcattheionizationfrontto∼3pcatσOri. 70
star increases by a factor of 2-3 compared to the region behind
σOriAB.
4. Bowwavesanddustwaves
Figure1revealsanincreaseinemissionatmid-IRwavelengths 4.2. Dustmass
nearσOriAB,peakingatadistanceofd=0.1pcaheadofthe
The spectral energy distribution (SED) of the emission is ex-
star. Given that σ Ori AB is classified as a weak-wind candi-
tracted using an aperture which encapsulated the IR emission
date,weproposethattheextendedemissionsurroundingσOri
while minimizing stellar contamination by σ Ori AB. This al-
AB represents the first detection of a radiation-pressure driven
lowsustostudytheaveragedustpropertieswithintheaperture.
structure around a massive star moving through the ISM (van
Subsequently,anaverageofseveralbackgroundpositionsabsent
Buren & McCray 1988). The radiation pressure of σ Ori AB
of obvious emission is subtracted. A two-component modified
actsonthedust,stallingitatadistanceaheadofthestarwhere
blackbodyfunctionisthenfittedtotheIRAC8.0µm,WISE12
therampressureoftheISMmaterialisbalanced.Weadjustthe
µm, MIPS 24 µm and PACS 70 µm integrated intensities. We
nomenclatureasdescribedbyvanBuren&McCray(1988)and
distinguishbetweenadustwave,wheredustisstoppedandde- 2 PICC-NHSC-TN-029:https://nhscdmz2.ipac.caltech.edu/pacs/docs/
couplesfromthegas,andabowwave,wheredustisstoppedand Photometer/PICC-NHSC-TN-029.pdf
5
B.B.Ochsendorfetal.:ThedustwavearoundσOriAB
Fig.3:Left:MIPS24µmversus70µmPACSdustcolortemperaturemap.Thescalesizeis16.5(cid:48) ×16.5(cid:48).Onlypixelswithvalues
>3σinthePACS70µmimageareplotted.Northisup,eastistotheleft.Right:70µmopticaldepthmap.
we have S = 3.4±0.5 × 1035 cm2 and thus L = 8.3±1.6 L .
IR (cid:12)
ThestellarluminosityistakenfromLee(1968)andequalsL =
∗
0.6 × 105 L . The energy absorbed by the dust grains through
(cid:12)
UV photons is subsequently re-emitted in the IR. Therefore, a
goodestimatefortheopticaldepthatUVwavelengthsisgiven
by the ratio L /L = τ = 1.4±0.3 × 10−4. From the optical
IR ∗ UV
depth at UV wavelengths, we can estimate the total dust mass
M byassumingagrainopacityatUVwavelengthsκ and
d,UV UV
bymultiplyingwiththesurfaceareaofashelllocatedatr=0.1
pc:
τ
M =4πr2 UV. (4)
d,UV κ
UV
Fig.4: A two-component modified black body is fitted to SED We take κ = 1 × 104 cm2 g−1 (Weingartner & Draine 2001).
oftheextendedIRemissionaroundσOriAB. InthiswayU,VwecalculateatotaldustmassofM =8.4±1.6×
d,UV
10−6 M .
(cid:12)
minimize the temperature variation across the aperture by fo-
4.2.2. IRderivedmass
cussingonthebrightemissiononly.TheIRAC3.4,4.6and5.8
µm images are heavily affected by diffraction patterns from σ Itispossibletoobtainanestimateofthetotaldustmassthrough
Ori AB and could therefore not be used to extract reliable flux theIRobservations.Md,IRisdirectlyproportionaltothedetected
values. The two components are believed to represent different far-IRemission:
dustpopulations.Theemissioncomponentpeakingnear45µm, τ
radiatingatatemperatureT =68K,isthoughttooriginatefrom Md,IR = κνS. (5)
largedustgrainsorBigGrains(BGs),whichareinthermalequi- ν
libriumwiththeradiationfield.Theothercomponentemittingat Here, κ = 60 cm2 g−1 at 70 µm (Weingartner & Draine 2001)
shorterwavelengths,radiatingatT =197K,probablyoriginates and theνaverage dust optical depth within the aperture is τ =
70
fromVerySmallGrains(VSGs).IntypicalISMconditions,the 1.3±0.2×10−5.Wederiveatotaldustmass M =3.7±0.7×
d,IR
VSGsarestochasticallyheated.Here,itissafetoassumethatthe 10−5 M .
(cid:12)
intensityoftheradiationfieldishighenoughfortheVSGstobe
inthermalequilibriumandcanthereforebefittedbyamodified
blackbodyfunction. 4.2.3. Summaryontheobservations
The total dust mass is approximated both through energy ab-
4.2.1. UVderivedmass sorbedintheUV(Md,UV)ordirectlythroughtheIR70µmemis-
sion(M ).Ourcalculationsshowadiscrepancybetweenboth
d,IR
ThetotalsurfacebrightnessItot isfoundbyintegratingtheSED deriveddustmasses,i.e.,Md,IR/Md,UV=4±0.8.Thisdiscrepancy
overfrequency,yieldingItot=7.6×10−3ergs−1cm−2sr−1.The maysimplyreflectthatthedustopacitiesatUVandfar-IRwave-
totalluminosity LIR isthen LIR = 4πItotS,whereS istheemit- lengthsfordustin HIIregionsisverydifferentfromthatcalcu-
tingsurfaceareaoftheIRstructure.Withd=334+25 pcandan latedfor(average)interstellardust.Inparticular,Weingartner&
−22
aperturewhichsubtends1.3×104squarearcsecondsonthesky, Draine(2001)useastandardMathis-Rumpl-Nordsieck(MRN)
6
B.B.Ochsendorfetal.:ThedustwavearoundσOriAB
sizedistribution(Mathisetal.1977),althoughthesizedistribu- and σ and Q¯ are the geometrical cross section and the flux
d rp
tioncanbeheavilyaffectedduringcoagulationinthemolecular weighted mean radiation pressure efficiency of the grains. The
cloud.Asizedistributionwithrelativelymorelargedustgrains firsttermontherighthandsideofEq.6describestheradiation
wouldreducetheopacityatUVwavelengths.Adiscrepancybe- pressureforceF .ThetermF istheLorentzforceandis
rad Lorentz
tween far-IR and UV derived dust abundances has been noted describedbelow.F isthedragforceduetointeractionsofthe
drag
bySalgadoetal.(2012)fordustin HIIregions.Consideringthe dustwithatomicorionicspeciesiandequals(Draine&Salpeter
discrepancybetween valuesderived inboth methods,we adopt 1979):
atotaldustmassofM =2.3±1.5×10−5 M ,whichisthemean
d (cid:12)
value of both earlier derived values (with the 1σ uncertainty). F =2πa2kTn (cid:16)G (s)+z2φ2ln(Λ/z)G (s)(cid:17). (7)
Thetotaldust-to-gasmassfractioncanthenbeapproximatedby drag i 1 i i i 2 i
comparingM withtheamountofgasM containedinthesame
d g (cid:113)
volume. We adopt a geometry of a spherical shell with thick- Here, s = mv2 /2kT,m andz arethemassandchargeof
ness dr ≈ 25(cid:48)(cid:48) = 1.3 × 1017 cm. The S[III] spectra show that i i drift i i
theinteractingatomsorions;aisthegrainradiusandv isthe
there is no clear detection of an enhanced density structure in drift
relativevelocitybetweenthegasandthedustcalledthedriftve-
the gas coinciding with the observed dust arc (although high-
locity.Thedragforceincludesboththedirectdragthroughcol-
resolutionimagingisneededtoconcludeonthe(non-)existence
lisionsandtheplasmadragthroughlongrange Coulombinter-
of a gaseous structure around σ Ori AB; see the discussion in
actionswithionicspeciesandelectrons.Theelectrostaticgrain
Sec. 6.2). Here, we opted to extrapolate the large scale density
potentialisdefinedbyφ=Z e2/kT,whereZ isthegraincharge
distribution measured from the KPNO Hα data. The gas den- d d
andeistheelementarycharge.ΛrepresentstheCoulombfactor
sity at the location of the dust arc is then about 10 cm−3 (Sec.
(Spitzer1978):
3.3). With n = 10 cm−3, we calculate a total gas mass of M
H g
= 6.9±1.3 × 10−5 M(cid:12). The total dust-to-gas mass ratio is then (cid:32) (cid:33)
Md/Mg =0.29±0.20,significantlyhigherthanthestandardratio Λ= 3 kT . (8)
in the ISM (∼ 0.01). The derived dust-to-gas ratio implies that 2ae|φ| πne
the dust number density has increased; we attribute this to ra-
diation pressure acting on the dust grains, creating a dust wave The functions G and G are approximated by (Baines et al.
1 2
aheadofσOriAB. 1965;Draine&Salpeter1979)
5. Physicsofbowwavesanddustwaves G (s)≈ 8√s (cid:32)1+ 9πs2(cid:33)1/2 (9)
1
3 π 64
The dust wave around σ OriAB is continuously fed by the
photo-evaporation flow emanating from the L1630 molecular
and
cloud. This flow is considered to be a two-component fluid of
dustandgasparticles,eachofthecomponentscontainingitsown
(cid:18) (cid:19)−1
density, temperature and velocity structure. We follow the flow G (s)≈ s 3π1/2+s3 . (10)
from L1630 to σ OriAB. As the gas is being accelerated and 2 4
approaches the star, it will drag along the dust grains through
collisions.Insidetheflow,dustgrainswillabsorbphotonenergy Grains with a velocity component perpendicular to the local
andphotonmomentumfromtheionizingstar:whiletheenergy magnetic field B will gyrate around the field lines due to the
isradiatedaway,theabsorbedmomentumcausesthedusttobe LorentzforceFLorentz:
decelerated.Wedonotconsiderinteractionwiththestellarwind;
it is assumed that the momentum flux of the wind is negligible F =m v×ω . (11)
Lorentz d B
comparedtotheradiationpressure.Theionizedgascomponent
oftheflowhasanegligiblecrosssectionforphotonabsorption, Theangularvelocityω isgivenby
B
butexchangesmomentumwiththedustthroughdrag.Through
collisionsofgasatomswithadustgrain,asignificantamountof z e
ω = d B. (12)
momentumfromthedustcanbetransferredtothegas.Thismo- B m c
d
mentumisthendistributedoverallgasparticlesbyinternalcol-
lisions. Depending on the magnitude and efficiency of the mo-
The drift velocity between the gas and the dust component can
mentumtransfer,thegasandthedustcomponentcanstaycou-
leadtotheejectionofatomsfromthesurfaceofthedustintothe
pled in the flow. The dust wave around σ OriAB is caused by
gas phase. Grain-grain collisions will be negligible in the flow
abalancebetweenradiationpressureandthedragforce.Below,
duetothelownumberdensityofgrainscomparedtothegas.At
we present a quantitative model describing the physics of this
lowenergiesandforlightprojectiles,sputteringiscausedbythe
interaction.
reflectionofanioninadeeperlayerofthegrain.Aftertheion
gets reflected, it knocks a surface atom into the gas phase. The
5.1. Dustcomponent rateofdecreaseingrainsizeisgivenby(Tielensetal.1994)
Wewritetheequationofmotionfordustas(Tielens1983)
da m
= spv nY, (13)
m dvd =−σdQ¯rpL(cid:63) +F +F , (6) dt 2ρs drift i i
d dt 4πcr2 drag Lorentz
wherem andρ arethemassofthesputteredatomsandthespe-
sp s
wherem isthemassofthedustgrain;risthedistancefromthe cificdensityofthegrainmaterial;andn andY arethenumber
d i i
star;L andcaretheluminosityofthestarandthespeedoflight; densityofthegasparticlesandthesputteringyield.
(cid:63)
7
B.B.Ochsendorfetal.:ThedustwavearoundσOriAB
5.2. Gascomponent Table2:Parametersusedincalculatingthetwodifferentmodels
showninFig.5.aistheradiusofthegrainandρ isthespecific
s
Thegasmomentumequationdoesnotcontaintheradiativede- densityofthegrainmaterial.Thesecombinationsofparameters
celeration term as the ionized hydrogen has a negligible cross representafiducialgrainanddonotnecessarilyrepresentgrains
section for photon absorption. We neglect gravitational attrac- takenfromexistingdustmodels.
tion and therefore the equation of motion of gas consists of a
balancebetweenthepressurefactor(Eq.1)andthemomentum
ModelA ModelB Units
transferthroughinteractionswithdustgrains: κ 7×103 7×104 cm2g−1
rp
a 3000 300 Å
dvg =v cs dρ + ndF . (14) nd/ng 1.8×10−13 1.7×10−11
dt gρ dr ρ drag
g g
The term on the right hand side represents the amount of mo- forsterite(3.21gcm−3)andfayalite(4.39gcm−3).Forcompar-
mentum transferred per second to a unit mass of gas. The dust ison, ideal graphite has a specific density of 2.24 g cm−3. We
numberdensitynd istakenfromtheMRNsizedistributionand setQ¯rp =1throughouttheflowinbothmodels.Inreality,Q¯rp is
the gas density ρ is adopted from Eq. 2. The ratio n /ρ is not dependentonrbecauseitisaveragedoverthephotonspectrum.
g d g
constant,butwilldependontherelativevelocityofthegasand This spectrum is altered due to attenuation of dust inside the
dustthroughthecontinuityequation. HIIregion.Thetotaldustopticaldepthisestimatedate−τ=0.5
(Abergeletal.2003)andtheeffectofthedustwaveontheUV
radiation field is negligible (see Sec. 4). The radiation pressure
5.3. ModelingtheinteractionbetweentheflowandσOriAB becomes important close to the star where the dust attenuation
islow,whichmakes Q¯ independentofr plausible.Theinitial
To determine the velocity structure of the photo-evaporation rp
flow, we integrate the coupled differential equations 6, 13 and dust number densities per H atom (nd/nH) are estimated using
the MRN size distribution (Mathis et al. 1977) where we con-
14simultaneouslyusingafourth-orderRunge-Kuttamethodin
siderboththecontributionofgraphiteandsilicategrains.Inthis
threedimensions.Asweneglectgrain-graincollisions,wecould
way, small grains have an abundance of 5.7 × 10−11 H-atom−1
replaceEq.6withasetofequationsforeachgrainsize.Thedrag
forabinsizerangingfrom100Åto500Å.Forthebiggrains,
force in Eq. 14 should then be rewritten to account for the size
distribution. For simplicity, we assume a single dust size dis- weuseabinsizerangingfrom1000Åto5000Å.Thesegrains
tribution, but we will investigate the influence of grain size by haveanabundanceof1.8×10−13H-atom−1.Thegascomponent
solvingtheequationsforseveralvaluesofa.First,weconsider followsthesamedensityandvelocitylawasderivedinSec.3.3.
a flow without grain charge and show that this reproduces the We calculate a posteriori the amount of momentum which the
observations. Afterwards, we will discuss the inclusion of the gashasacquiredthroughcollisionswiththedust.
CoulombdragtermdescribedinEq.18andtheLorentzforce.
In our model, the x-axis is directed along the flow, which
6. Results
representstheprojecteddistancefromL1630toσOriAB.The
star is placed at the origin. The y-axis and z-axis represent the In Fig. 5 we plot trajectories along which a specific dust grain
directions perpendicular to the flow, i.e., the direction in the will travel. Model A represents a 3000 Å grain (κ = 7 × 103
rp
plane of sky and the direction along the line of sight, respec- cm2 g−1), while model B represents a 300 Å grain (κ = 7 ×
tively.Theflowstartsatthemolecularcloud,positionedat x = 104cm2g−1)withidenticalvaluesforρ (=3.5gcm−3)rpandQ¯
3.2 pc. We define the impact parameter b as the distance along (=1).Theeffectofdustparticlesizeissclearlyseen.Forlargerpr
they-axis(seeFig.5)atthestartoftheflow.Adustgrainwhich
values of κ , radiation pressure is able to alter the direction of
approachesthestarhead-on(b=0)willlosemomentumbyab- rp
the grain further away from the star, even for trajectories with
sorbingphotonsandbestoppedatthepointwherethedragforce
smallinitialb.Whilethedistancewhichtheparticleovershoots
F balances the radiation pressure force F . More specifi-
drag rad is far less compared to model A, the stopping distance of the
cally,anincomingdustgrainwilltendtoovershootitsstopping
grainincreaseswithhighκ .Wecalculatethatadustgrainwith
distance,reachingaminimumdistancetothestarr depending rp
min κ =6.7×103 cm2 g−1 (3300Å)willbestoppedatd=0.1pc,
on its momentum. Subsequently, it is pushed back by the radi- rp
which coincides with the peak emission of the dust wave at 24
ation pressure force until an equilibrium radius r is reached
eq
where|F /F |equalsunity.Thisresultsinadampedoscilla- µm.
rad drag
Figure6showsresultsforonespecifictrajectorywithinitial
tion around r . Particles with b > 0 will have similar trajecto-
eq impactparameterb=0.01pc.Ourcalculationsshowthata300
ries,butwillgainmomentumintheydirectionandthereforebe
pushedpastthestarinashell-likestructure.Wedefinetheradi- Ågrainwillbeacceleratedonashorttimescale,reachingtheve-
ationpressureopacityκ ,whichdeterminestheexacttrajectory locityofthegasatt=2.5×103yr.Momentumislostgradually
rp
ofaparticle andrminisreachedafter1.5×105yr,wheretherelativeincrease
innumberdensitypeaksat17timestheinititalnumberdensity
κ =σ Q¯ /m . (15) (nd,0).Figure6alsoshowstheratiobetweenthevelocityofthe
rp d rp d
gas with (v ) and without (v ) momentum transfer with the
g,c g,uc
Weevaluatethemodelfortwodifferentvaluesofκ .Forsmall dust.Thegaswillflowatavelocityof0.97vg,ucpastthestarand
rp
willthereforelose3%ofitsinitialmomentum.Fig.6showsthat
grains,κ ishigherbecausetheratioofsurfaceareaovervolume
rp
increases with smaller a. We have chosen the values of κ in a the large grains (3000 Å) will be decelerated by the radiation
rp
waytoclearlydemonstratetheinfluenceofgrainsize.Themo- pressureforcebeforereachingthegasvelocity.Eventhoughthe
mentumoftheincomingparticleisdeterminedbythegrainsize 3000Ågrainshavelowervelocitiesrelativetothestarcompared
and the specific density ρ . In both models we choose ρ = 3.5 to 300 Å grains, they have significantly more momentum and
s s
gcm−3,intermediatebetweenthespecificdensityofcrystalline willthereforeapproachthestarmoreclosely.Thetimespentat
8
B.B.Ochsendorfetal.:ThedustwavearoundσOriAB
(a) Dusttrajectoriesfora3000Åsilicategraintrajectoriesfor (b) Same,butforadifferentvalueofκ ,whichrepresentsa300
rp
differentvaluesofimpactparameterb. Åsilicategrain.
Fig.5: Two dimensional plots of dust grain streamlines, evaluated for different grain sizes a. The x-axis represents the projected
distance from L1630 to σ Ori, while the y-axis is the direction perpendicular to the line connecting L1630 and σ Ori AB, in the
planeofthesky.
(a) Thevelocity,densityincreaseandtheamountofmomentum (b) Samefigures,butforadustgrainwitha300Åradius.
transfer,evaluatedfora300Ådustgrainwithimpactparameter
b=0.01.
Fig.6: Upper panels: The radial velocity v of a dust grain (solid) and a gas particle (dotted, evaluated at the position of the dust
r
grainintheframeofthestar)asafunctionoftime.Attimet=0,thegasisionizedandentersthe HIIregion.Middlepanels:The
relativedensityincreaseindustalongthetrajectory.Thisvalueapproachesunitywhenthegasanddustarecoupled.Lowerpanels:
Thevelocityratioofagasparticlev ,aftermomentumtransferwiththedust,toanuncoupledgasparticlev ,whichreflectsthe
g,c g,uc
amountofmomentumtransferredfromthedusttothegas.
r issmallerbecausetheradiationpressureforceisfargreater factorofthreetogeteffectivesputteringofthegrains.Therefore,
min
closetothestar.However,wecalculatethatthetotalmomentum weconcludethatthermalsputteringofdustgrainsintheionized
transferredtothegasissmall:gasflowsat0.96v pastthestar. flowisnegligible.
g,uc
Themomentumofagraindependsonitssizeandcomposi-
Wecalculatethevelocityofthedustandgasateachxyzpoint
tion,whichwillultimatelydeterminethetrajectoryoftheparti-
inspace.Weconsidertheproblemtobeaxisymmetricalongthe
cle.Largergrainswilltendtomoveclosertothestarcompared
y and z axes. Subsequently, we collapse the three-dimensional
tosmallergrains.Consequently,dustwillbestratifiedaccording
data cube along the line of sight and estimate the density in-
totheirsizeandspecificproperties.Figure7plotstheminimum crease using continuity: ρ v = C, where C is a constant. The
radiusrminversustheradiationpressureopacityκrp.Whencom- resultforgrainswithκ =d6d.7×103 cm2 g−1 isthencompared
paringsilicateandgraphitegrainsofsimilarsizes,graphitepar- rp
againsttheobservationsinFig.8.Wescalethemodeltotheob-
ticlesarestoppedfurtheroutfromthestarbecauseoftheirlow servedvalueofτ atx=0.8pc.Inthisway,themodelgivesan
specificdensity. 70
absoluteincreaseindensityalongthelineofsight.InFig.8we
Thethresholdenergyforsputteringofhydrogenatomsfrom alsoshowthesolutionofthemodelwithoutradiationpressure.
anamorphouscarbonandsilicatesurfaceisE=0.5mv2 ∼22 In this case, the dust will be accelerated as it is dragged by the
i drift
eV(Tielens2005).Thisenergyisnotreachedintheflow,evenat gas and will follow the gas velocity law given by Eq. 1. When
thestagnationpointwherethedriftvelocityismaximal.Indeed, theradiationpressureforceisincluded(i.e.,Eq.6),thedustwill
theimpactenergy E shouldexceedthethresholdenergywitha pile up in front of the star, resulting in a peak optical depth at
9
B.B.Ochsendorfetal.:ThedustwavearoundσOriAB
recombination. Under typical ISM conditions, this results in a
positivegrainchargeduetotheharshconditionsoftheinterstel-
lar radiation field combined with low electron densities. In an
HII region like IC 434, the electron density far exceeds that of
thediffuseISM.Agoodinsightinthelocalphysicalparameters
isneededinordertoconstrainthenatureandmagnitudeofthe
graincharge.
Thephoto-ejectionrate J isdependentontheincidentra-
pe
diationfieldandthephoto-ionizationyieldY ,
ion
(cid:90) νmax J(ν)
J =σ Q Y (Z ,ν)dν, (16)
pe d hν abs ion d
νZd
whereJrepresentsthemeanradiationintensitycalculatedusing
aFtiigo.n7:pTrehsesuproeinotpoafcictylosκerpstfoaprptrraojaecchtotroietshewsittahrbrm=in0v,earssususmraidnig- athOe9ab.5sVorpKtiuornucezffimcioedneclyaotmftohsepghrearien(mKautreurciazl.1W99e3)taaknedQQabasbsfoisr
Q¯rp=1independentofgrainsizea.Labeledabovethecurveare silicatesfromLaor&Draine(1993).Thephoto-ionizationyield
typicalgrainsizesinangstromsforsilicates.Belowthecurveare Y has been measured in laboratory experiments for energies
ion
thecorrespondinggrainsizebutforgraphitegrains. up to 20 eV (Abbas et al. 2006), but experiments with higher
energyphotonsarelackingandareveryuncertain.Weingartner
et al. (2006) investigated the role of extreme ultraviolet radia-
tionandX-raysandconcludedthathigherenergyphotonsdonot
contributesignificantlytothechargestateofdustgrainsin HII
regions ionized by OB stars. We follow Weingartner & Draine
(2001) and take the ionization yield Y as has been described
ion
there.
The photo-ejection rate is balanced by the electron recom-
bination rate. Assuming a Maxwellian velocity distribution of
thegas, thecollisional rate J betweenelectrons anda grainof
e
positivechargeZ isestimatedwith(Tielens2005)
d
Fiziogn.t8a:llAy cthrorosusgchutthoeftshtaegonpattiicoanlpdoepintht omfatpheinduFsigt.w3avtaeke(snohliodr)-. Je(Zd)=nese(cid:32)8πkmT(cid:33)1/2πa2(cid:32)1+ |ν(cid:15)|(cid:33)1+(cid:32)(cid:15)+22|ν|(cid:33)1/2. (17)
i
Overplottedisamodelwithoutradiationpressureforce(dashed)
andamodelwithradiationpressureforce(dotted). Here we define the reduced temperature, (cid:15) = akT/q2 (with q
e e
being the charge of the electron), and the charge ratio between
thedustandanelectron,ν = Z /q .Ifν<0,thecollisionalrate
d e
x = 0.1 pc. The observed optical depth at 0.5 > x > 0.1 pc is increases because of electrostatic focussing. The charge distri-
significantly above the model value, which we attribute to the butionfunctionisthencalculatedwithEq.16and17,
presence of a population of smaller grains which are deflected
atlargerradii.At x<0pc,theopticaldepthislowercompared f(Zd+1) = Jpe(Zd) , (18)
to the model without radiation pressure force. This cavity can f(Z ) J (Z +1)
d e d
notbeexplainedbymereaccelerationofdustpastthestar(see
Fig. 6). The decrement in optical depth is only reproduced by where f isthefractionalabundanceofadustgrainwithcharge
the model if we take trajectories with |z| < 0.5 pc into account. Z . The maximum charge of a dust grain is calculated at a dis-
d
Inotherwords,theobservedopticaldepthat70µm(Fig.3)only tance d = 0.1 pc from the star. At these conditions, the peak
traces dust at a distance of r < 0.5 pc from σ Ori AB. This is ofthechargedistributionfunctionliesatZ =195fora300 Å
d
because the 24 µm and 70 µm emission traces dust grains at a grain,whereasfora3000ÅgrainthisisZ =1809.
d
temperatureof∼30-100K. Achargedgrainwillnotonlyhavedirectcollisionswiththe
Insummary,weattributethemainpeakintheopticaldepth gas(directdrag),butwillalsohavelongrangeCoulombencoun-
map to large grains with κ > 1 × 104 cm2 g−1 (a > 1500 Å ters with both electrons and ions (Coulomb drag). In addition,
rp
for silicates). The enhanced optical depth in front of the main a grain will gyrate around the local magnetic field through the
dust wave is then aresult of grains with κ < 1 × 104 cm2 g−1 Lorentz force if it has a velocity component perpendicular to
rp
andistracingsmallerdustgrainsordifferentgraincomposition the field lines. The magnitude of both the Coulomb and the di-
(graphiteversussilicate).Therefore,dustwaves(aswellasbow rectdragforceishighlydependentonv .Atsubsonicspeeds,
drift
waves)arenaturalgrainsortersseparatingdustgrainsaccording bothdirectandCoulombdragforcesareproportionaltov .In
drift
totheirradiationpressureopacities. thesupersonicregime,thedirectdragforceincreaseswithv2 ,
drift
whiletheCoulombdragisproportionaltov−2 .Figure9relates
drift
the drag forces for a charged particle at 0.1 pc as a function of
6.1. Coulombinteractions
theMachnumberM=v /c .InSec.3,wehaveshownthatthe
drift s
Thusfarwehaveneglectedgrainchargingofthedustgrains.The maximumdriftspeedintheflowisM∼5.Asaresult,itseems
chargeofaninterstellargrainisdeterminedbyphoto-ionization notjustifiedtoneglecttheCoulombdragforceasitshoulddom-
andpositiveionrecombinationbalancedwithnegativeelectron inatethetotaldragforcethroughouttheentireflow.
10