Low temperature MIR to submillimeter mass absorption coefficient of interstellar dust analogues I: Mg-rich glassy silicates

2.9 MB·

by  K. Demyk

Astronomy&Astrophysicsmanuscriptno.Demyk2017 (cid:13)cESO2017
January26,2017
Low temperature MIR to submillimeter mass absorption coefficient
of interstellar dust analogues I: Mg-rich glassy silicates
K.Demyk1,C.Meny1,X.-H.Lu1,G.Papatheodorou2,3,M.J.Toplis1,H.Leroux4,C.Depecker4,J.-B.Brubach5,P.
Roy5,C.Nayral6,W.-S.Ojo6,F.Delpech6,D.Paradis1,andV.Gromov7
1 IRAP,UniversitédeToulouse,CNRS,UPS;IRAP;9Av.colonelRoche,BP44346,F-31028Toulousecedex4,France
2 InstituteofChemicalEngineeringSciences,FORTH,P.O.Box1414,GR-26504Patras,Greece
7 3 DepartmentofChemicalEngineering,UniversityofPatras,GR-26504Patras,Greece
1 4 UMET,UMR8207,UniversitéLille1,CNRS,F-59655Villeneuved’Ascq,France
0 5 LigneAILES-SynchrotronSOLEIL,L´OrmedesMerisiers,F-91192Gif-sur-Yvette,France
2 6 UniversitédeToulouse,INSA,CNRS,LPCNO,F-31077Toulouse,France
7 SpaceResearchInstitute,RAS,84/32Profsoyuznaya,117810Moscow,Russia
n
a Received...;accepted...
J

5
ABSTRACT
2

Context.ThesubmillimeterspectraldomainhasbeenextensivelyexploredbytheHerschelandPlancksatellitesandisnowreachable
]
A fromthegroundwithALMA.Awealthofdata,revealingcolddustthermalemission,isavailableforastronomicalenvironmentsrang-
ingfrominterstellarclouds,coldclumps,circumstellarenvelops,andprotoplanetarydisks.Theinterpretationoftheseobservations
G
reliesontheunderstandingandmodelingofcolddustemissionandontheknowledgeofthedustopticalproperties.
. Aims.Theaimofthisworkistoprovideastronomerswithasetofspectroscopicdataofrealisticinterstellardustanaloguesthatcanbe
h
usedtointerprettheobservations.Itpursuestheexperimentaleffortaimedatcharacterizingthespectroscopicpropertiesofinterstellar
p
dustanaloguesatlowtemperatureinthemidinfrared(MIR)tomillimeterspectraldomain.Comparedtopreviousstudies,itextends
-
o therangeofstudieddustanaloguesintermsofcompositionandofstructureofthematerial.
r Methods.Glassy silicates of mean composition (1-x)MgO - xSiO2 with x = 0.35 (close to forsterite, Mg2SiO4), 0.50 (close to
t enstatite,MgSiO )and0.40(closetoMg SiO orMgSiO :Mg SiO =50:50)weresynthesized.Themassabsorptioncoefficient
s 3 1.5 3.5 3 2 4
a (MAC)ofthesampleswasmeasuredinthespectraldomain30-1000µmforgraintemperatureintherange300K-10Kandat
[ roomtemperatureinthe5-40µmdomain.
Results.WefindthattheMACofallsamplesvarieswiththegrainstemperatureandthatitsspectralshapecannotbeapproximatedby

1 asinglepowerlawinλ−β.IntheFIR/submm,andabove30K,theMACvalueatagivenwavelengthincreaseswiththetemperatureas
v thermallyactivatedabsorptionprocessesappear.Thestudiedmaterialsexhibitdifferentandcomplexbehaviorsatlongwavelengths
5 (λ ≥200to700µmdepending onthesamples).Thesebehaviorsareattributedtotheamorphous natureof dustandtotheamount
2 andnatureofthedefectswithinthisamorphousstructure.WedonotobserveMACvariationsinthe10-30Krange.Above20µm,
2 the measured MAC are much higher than the MAC calculated from interstellar silicatedust models indicating that the analogues
7 measuredinthisstudyaremoreemissivethanthesilicatesincosmicdustmodels.
0 Conclusions.TheunderestimatedvalueoftheMACdeducedfromcosmicdustmodelsintheFIR/submmhasimportantastrophysical
. implicationsbecausemassesareoverestimatedbythemodels.Moreover,constraintsonelementalabundanceofheavyelementsin
1
cosmicdustmodelsarerelaxed.
0
7 Keywords. Astrochemistry-Methods:laboratory:solidstate-Techniques:spectroscopic-(ISM:)dust,extinction-submillimetre:
1 ISM-Infrared:ISM
:
v
i
X
1. Introduction where τ is the dust optical depth, and B (T ) is the Planck
λ λ dust
r blackbodyemissionlawatthedustcolortemperatureT ,M is
aInastrophysicalobservations,thefar-infrared(FIR)andsubmil- thedustmassalongthelineofsight,dthedistanceofthdeustsourdce,
limeter (submm) emission (∼ 100 µm - 2mm) is shown to be Ωthebeamsolidangleandκ themassabsorptioncoefficientof
λ
dominated by a componentfrom big nanograins(BG) with ra- the dust along the line of sight(MAC, cm2.g−1). κ is a funda-
λ
diusintherange∼10-15nmto∼100-400nm,bigenoughtora- mental quantity which contains all the informationon dust: its
diateatthermalequilibriumwiththesurroundingradiationfield. composition and structure (amorphous or crystalline, porosity,
Assumingopticallythinemissionwhichisoftenavalidhypoth- coagulation), its size distribution and the way it interacts with
esis in the FIR-submm domain, the dust spectral energy distri- light. Simple semi-classical physical models for bulk material
bution(SED)observedthroughafewbroadbandfiltersappears provide,in the FIR/submmdomain,a temperatureindependent
to be coherent with the following modified blackbody (MBB) asymptoticbehaviorforthedustemissivitywhichiswidelyused
emissionlaw: inastronomicalmodelingandisexpressedasfollows:
λ
Iλ =τλBλ(Tdust)=Mdustd−2Ω−1κλBλ(Tdust) (1) κλ = κλ0 (λ0)−β (2)
Articlenumber,page1of13
A&Aproofs:manuscriptno.Demyk2017
wherethespectralindexβhasaconstantvalue(i.e.temperature est component achieving the submm excess (Finkbeineretal.
andwavelengthindependentvalue)thatrangesfromonetotwo. 1999;Meisner&Finkbeiner2015).(ii)TheTLSmodelinwhich
Thevalueβ=2iscommonlyadoptedbecauseitistheasymptotic the variation of the spectral index (with wavelength and tem-
value toward long wavelengthsof the two most simple models perature) is linked to intrinsic properties of the amorphous
for dust absorption in the FIR-submm : the Lorentz oscillator stateofonlyoneinterstellardustcomponent(Menyetal.2007;
model for absorption in crystals and the Debye model (with a Paradisetal.2011).TheTLSmodelsuccessfullyreproducesthe
constantopticalcouplingcoefficient)forabsorptionin3dimen- dust emission in ultra-compactHII regionsand cold molecular
sionalamorphousstructures(Henning&Mutschke1997). clumpswiththesamedustcomponentinbothtypesofenviron-
Historically, the first observationsby the ballon-bornemis- mentwithouttheneedtoconsidertwodifferentdustcomponents
sions PRONOAS and Archeops in the FIR/submm wavelength associatedwitheachenvironment(andcharacterizedbydifferent
range, revealed an unexpected result : an anticorrelation be- spectralindexvalues)asisthecaseintheMBBemissionmodel
tweentheobservedspectralindexβ andthetemperatureT (Paradisetal.2014).AnanalysisoftheouterGalacticplaneus-
obs dust
(Dupacetal.2003;Désertetal.2008).Morerecently,theobser- ingDIRBE,ArcheopsandWMAPdatarevealsasageneralphe-
vationscarriedoutbythe Herschel(160- 550µm) andPlanck nomenona changein the emissivity aroundλ = 600µm in the
missions(160µm - 3 mmforthe HFI instrument)havegreatly SED,withanemissionsteeperintheFIRthaninthesubmmand
increased the number and precision of available data. Com- mm,bothinmolecularcloudsandatomicphases(Paradisetal.
bined with the FIRAS 100 µm band, these observations allow 2009).Suchwavelengthdependenceofthespectralindexisalso
astronomers to build spectral energy distribution (SED) from well demonstratedby the study of Juvelaetal. (2015) who de-
the FIR to the millimeter range with unprecedentedsensitivity, terminereliableestimatesofthemeanspectralindex(usingthe
spectralresolutionforHerschelobservationsandoverthewhole MBB model) in 116 cold cores selected from the Planck Cold
sky with the Planck mission. In all these observations,the β Clump Catalogue C3PO and mapped with Herschel PACS and
obs
- T anti-correlation is observed (PlanckCollaborationetal. SPIRE instruments. Using differentcombinationsof photomet-
obs
2011a,b, 2014a,b; Malinenetal. 2014; Juvelaetal. 2015). De- ric data, Juvelaetal. (2015) showed that the best fit to the ob-
pending on the environments, this β - T anti-correlation is ob- servationsareobtainedwithtwocomponents.Intheabsenceof
served on a temperature range of 10 to 30 K, up to 60 K if knowledgeofthewavelengthdependenceofthespectralindex,
hotter clouds are considered. Meanwhile, many studies have theyadopteda wavelengththresholdvalueofλ = 700µm, and
been conducted to determine all possible causes for the varia- determinedamillimetricspectralindexβmm =1.66closetothe
obs
tion of β with T : the effectof noise in the data and of the value observed by Planck in the diffuse medium (βmm = 1.51,
obs obs obs
choice of the method used to fit the observations (Shettyetal. PlanckCollaborationetal.2014b),andaFIRspectralindexβFIR
obs
2009; Juvela&Ysard 2012a; Juvelaetal. 2013); the effect of =1.91.UsingonlyHerscheldatatheauthorsfoundthatmanyin-
specific distributions of density and temperature profiles of in- dividualcoldclumpsgivevaluesuptoβFIR ∼ 2.2,andpointed
obs
terstellar grains along the line of sight (Malinenetal. 2011; outthattemperaturegradientsinopticallythicksourcescanonly
Juvela&Ysard2012b;Paganietal.2015);theintrinsicproper- decrease the FIR spectral index value and that in consequence
tiesofgrains(Menyetal.2007;Köhleretal.2012;Paradisetal. theFIRspectralindexvaluemayevenbesteeperinthelimited
2011;Jones2012a,b;Jonesetal.2013). wavelengthrangecoveredbyHerschel.
However,uptonowtheFIRandsubmmobservationsreveal
some facts that remain valid, when interpreted with the MMB From the modeling point of view, dust models aim to re-
emissionlaw: produce astrophysical observables (extinction, emission, MIR
i) The dust spectral index and temperature are statistically bands, polarization, etc.) over the widest spectral range (from
anticorrelated,asdiscussedpreviouslyinthisintroduction. far-ultraviolet, FUV, to the millimeter range). They should be
ii)Thespectralindexvalueβ andthemassabsorptionco- able to propose a coherent scenario of the evolution of dust
obs
efficientκ evolveinthedifferentphasesoftheISM(fromdif- properties (composition, structure, and coagulation, amongst
λ0
fusetodensemedia,fromHIregionstocoldmolecularclouds, others) through various environments (diffuse ISM, molecular
withmetallicity).AttheGalacticscale,Paradisetal.(2012)ob- clouds, PDRs and HII regions, different metallicities, etc.) and
serve in Herschel data that the submm excess (or lowering of beconsistentwiththeexpectedISMabundanceoftheelements
thespectralindex)increaseswiththeGalacticlongitude.Inex- in the various environments. All dust models (see for exam-
tragalactic environments, the Large and especially the Small pleCompiègneetal.2011;Jonesetal.2013;Draine&Li2007)
Magellanic clouds (respectively LMC and SMC) have a pro- consider at least two dust components: a component of very
nounced FIR and submm excess compared to the Milky Way small grains (VSG) with grain radius a ≤ 10-15 nm, and a big
(Gallianoetal. 2011; Botetal. 2010). It is also observed that grain (BG) component. The VSG component is dominated by
theFIR-submmemissivity,normalizedtothevisibleorthenear- carbongrains(eithergraphiteoramorphouscarbonmoreorless
infraredextinction,increasesbyafactorgreaterthan3andthat hydrogenated, denominated hereafter as a-C(:H)), transiently
the temperature decreases by 10-20%, from diffuse medium to heated by the ISRF and dominating the near and mid-infrared
denser ISM (Stepniketal. 2003; Köhleretal. 2012). More re- witharesidualtailintheFIR-submm.TheBGcomponentdrives
cently, Paradisetal. (2014), using 70 - 500 µm Herschel data the FIR-submm emission. Although silicates dominate the BG
combinedwith1.1mmBolocamdata,showthattheFIR-submm component in terms of mass, some mixing with the carbona-
emission in ultra-compact HII regions and in cold molecular ceousphaseisexpected,andthustheFIR-submmSEDsreflect
clumpsarecharacterizedbytwodifferentspectralindexvalues. opticalpropertiesofboththesilicate andcarbonaceousphases.
iii)Thedustspectralindexvarieswithwavelength.Thisob- Accordingtorecentdustmodelssuchmixingcouldoccur,either
servationalfact has been often recognizedand is referred to as byintroducingacomplementarycomponentofpurea-C(:H)big
submm flattening of the SED or submm excess. It has been at grains, or by accretion of mantles or aggregationprocesses in-
the origin of two interpretations : (i) The Finkbeiner two big sideorbetweenthea-Silanda-C(:H)phases(Jonesetal.2013).
grain components model, in which each component gives rise Inthatcase,κ inEq.1isthusaveragedoverthetwoBGcom-
λ
to a FIR emission following equations (1) and (2), the cold- ponents.
Articlenumber,page2of13
K.Demyketal.:LowtemperatureMIR/submmmassabsorptioncoefficientofMg-richglassysilicates
Theinterpretationofthewellestablishedobservationalfacts x = 0.35, 0.40, 0.50. The mean composition x = 0.35 is close
intheFIR-submmdescribedabove,requiresdetailedknowledge to forsterite (Mg SiO , i.e. x = 33.3), while x = 0.50 is close
2 4
of the various expected silicate and carbonaceous components to a mean composition of enstatite (MgSiO ) and x = 0.40 to
3
of the ISM. Furthermore, the robustness of dust models relies anintermediatecompositioninbetweenMgSiO andMg SiO .
3 2 4
onaccurateknowledgeoftheopticalpropertiesofthosecompo- Threesamplesweresynthesizedwiththefirstmethod:X35,X40
nentsoverthewholeFUV-mmwavelengthrange.Theseoptical andX50A,correspondingtox=0.35,0.40and0.50respectively
propertieshavetobedeterminedfromrelevantcombinationsof andonesamplesynthesizedwiththesecondmethod:X50B,cor-
laboratorymeasurementsperformedonwellcharacterized(e.g. respondingto x=0.50.TheX50AandX50Bsampleshavethe
stoichiometry,atomic-structureandgrainsizes)interstellardust samestoichiometrybut,theyweresynthesizedbytwodifferent
analogues(silicates,carbonaceouscompounds,ices)orpureel- methods.Both have been studied to verify that synthesis tech-
ements or compounds(graphite, Fe, Mg, FeS, MgO,...), from niquedoesnotinfluencemicroscopicstructure.
physicalmodelsofinteractionbetweenthesolid-stateandelec- The structural and chemical local order within the network
tromagnetic waves, and from astrophysical observational con- in silicate glasses may be characterized by the amount of Qi
strains. species, with i=0,1,2,3,4 designating the number of bridging
Within this context, this work presents a new experimental oxygensaround a given silicon atom. The Qi value can be de-
studyofsilicatedustanalogues.WehavemeasuredtheMACof rived from Raman or 29Si and 25Mg MAS NMR spectroscopic
magnesium rich glassy silicate grains with composition of en- studies.Q0 speciescorrespondtoisolatedtetrahedra,SiO4−,Q1
4
statite (MgSiO3), of composition close to forsterite (Mg2SiO4) speciestodimersSi O6−,andQ2speciestochains.Aglassmade
and a non-stoichiometric composition (MgSiO :Mg SiO = 2 7
3 2 4 ofQ3 andQ4 speciesishighlyinterconnectedandmayhavedi-
50:50)inthe5µm-1mmspectraldomainandforgraintemper-
verse3-dimensionalstructures(seeFig.5inKalampouniasetal.
aturevaryingfromroomtemperatureto10K.Thisstudyextends
2009).Senetal.(2009)havedeterminedtherelativeproportion
ourworkonmagnesiumrichamorphoussilicatessynthesizedby
of Qi species in 9 glasses from a series of (MgO) (SiO )
solgelmethods,butforwhichspectroscopicmeasurementswere y 2 100−y
glasses with y in the range50-66.7(y=50,60, 66.7 correspond
limited to wavelengths longer than 100 µm (Coupeaudetal.
to x=0.5,0.40,0.33inthenotationadoptedhere).Thesamples
2011). Boudetetal. (2005) also measured the MAC of glassy
X35,X40 andX50Aweresynthesizedbythesame team using
andsolgelsilicatesinthewavelengthrange100µm-1mmwhile
thesametechniqueasthestudyofSenetal.(2009)allowingdi-
Mennellaetal.(1998)measuredironrichamorphoussilicatesin
rectcomparisonofthe resultspresentedherewith thoseofSen
the range 20 µm - 2 mm.All these studiesshow that the MAC
etal.(2009).Fromastructuralpointofviewthestudiedsamples
of dust grains varies with temperature: at a given wavelength
mainlydifferbytheirdegreeofpolymerization,i.e,theiramount
the MAC decreases as T decreases. This decrease of the MAC
ofsharedSiO4− tetrahedra.Senetal.(2009)findthattheX50A
is more pronouncedat long wavelengths and consequently the 4
sample contains Q1, Q2, Q3 and Q4 species in respective pro-
wavelengthdependenceoftheMACcannolongerbedescribed
portionsof25.0,42.0,25.7and7.3%,whereastheX40samples
byanasymptoticpowerlawwithasinglespectralindex,asas-
containsQ0,Q1andQ2speciesinrespectiveproportionsof27.5,
sumedindustmodels.
58.0and14.5%whiletheX35samplecontainsonlyQ0 andQ1
This paper is organized as follows. Sect. 2.1 describes the
speciesinrespectiveproportionsofabout50-60and50-40%.As
studied dustanalogues(synthesisandcharacterization),the ex-
expected,theX35sampleclosetotheforsteritecomposition,is
perimentalsetupsusedforthemeasurements,thesampleprepa-
lesspolymerizedthanthetheX50Asample,ofenstatitecompo-
rationandthedatareductionperformedtoreconstructtheMAC.
sition,theX40beingintermediate.
The MAC measurements of each samples are presented in
Sect. 3. They are compared with previous experimental data
in Sect. 4 and with astronomical dust models in Sect. 5 which
2.2.Spectroscopicmeasurements
also discuss the astrophysical implications of these new mea-
surements. The MAC of the samples were recorded on the ESPOIRS
setup at IRAP (Institut de Recherche en Astrophysique et
Planétologie) and on the AILES (Advanced Infrared Line
2. Experiments Exploited for Spectroscopy) beam line at the synchrotron
SOLEIL (Brubachetal. 2010). The ESPOIRS setup consists
2.1.Samplessynthesisandcharacterization
in a Fourier Transform InfraRed (FTIR) spectrometer (Bruker
ThestudiedsamplesareMg-richsilicateglassessynthesizedby Vertex70V)coupledwithaclosedcycleopticalcryostat(QMC
twodifferentmethods.Thefirstmethodisdescribedindetailsin Instruments)allowingto cooldownthesamplesfrom300K to
Kalampouniasetal. (2009). Briefly, it consists in puttinga sin- 10 K. Thanks to the combination of various sources (Globar,
teredmixtureoftheoxideshavingthedesiredstoichiometryina Hg and tungsten lamps), beam splitters (CaF , CsI, Si) and
2
controlledArgasflowjetandusingaCO laserforheatingand detectors(InGasAs,DLaTGS,closedcycleHecooledtransition
2
melting.Theheatingofthelevitatedsamplemustbecontrolled edge superconducting bolometer from QMC Instrument) the
toavoidoverheating.Thesampleismeltedforlessthan5sand spectrometer covers the spectral domain from 0.7 µm to 1
whenthe laser is shutdownamorphoussphericalsamplesof∼ mm. The sample cryostat contains a rotating wheel on which
1 - 1.5 mm diameter, colorless and transparent, are produced. six samples may be mounted and measured without having
Inthesecondmethod,appropriateproportionsofsilicondioxide to break the vacuum. At SOLEIL, the experimental setup of
andmagnesiumcarbonatepowdersisheatedtogetherina plat- the AILES beam line is composed of a Bruker FTIR 125V
inum crucible in air at 1600◦C for approximately 30 minutes. spectrometer equipped with a Mylar 125 µm beamsplitter, a
Theliquidisquenchedtoglassbydippingthebottomofcrucible 1.6K Si bolometer and a closed-cycle sample cryostat (300K -
in water. Thisglass wasthencrushedandremeltedatthesame 10K). The synchrotronradiation is much brighter than internal
conditionsto ensure homogeneity.The four samplesstudied in lightsourcesand thusallows to obtainmore reliable spectra in
this work have mean compositions of (1-x)MgO-(x)SiO with the 700 - 1000 µm range than internal sources. Measurements
2
Articlenumber,page3of13
A&Aproofs:manuscriptno.Demyk2017
atwavelengthsgreaterthan400µm upto 1mmandmorewere
performedatSOLEILwhichallowedagoodoverlapofthetwo
sets of measurements. For λ ≤ 40µm the measurements were
performed at room temperature and for λ ≥ 30µm they were
performedat300K,200K,100K,30K,and10K.
The X35, X40 and X50A samples obtained by levitation
and CO laser melting are spheres of diameter of ∼ 1mm, the
2
X50B sample is bulk transparent material. The four samples
weregroundbyhandinanagatemortaruntil(sub)micronicsizes
arereached.Forthetransmissionmeasurements,thesamplesare
preparedintheformofpellets.FortheMIRdomain(2-40µm),
∼0.5-1.0mgofsampleweremixedwith300mgofKBrorCsI
(Aldrich)forseveralminutesinanagatemortarandpressedun-
dertentonsforfiveminutestoproducea1.3mmdiameterpellet.
Formeasurementsabove40µm,KBr andCsI are nottranspar-
ent and are replaced by polyethylene (PE, Thermo Fisher Sci-
entific). The PE and sample mixture were heated on a heating
Fig. 1. Mass absorption coefficient of the samples X35, X40, X50A
plateupto130◦C(measuredontopofthedye)forfiveminutes
andX50BatroomtemperatureintheMIR.Thebandlabeledwiththe
beforepressingundertentonsforfiveminutestoproducea1.3
asteriskisnotassociatedwiththesamplesandisduetothePEmatrix.
mmdiameterpellet.BecausetheMACofthesamplesdecreases
at long wavelengths,severalpellets with an increasing mass of
sampleswereused.Typically,pelletscontaining5,20,4080and appliedithere.IthasbeenestimatedinMennellaetal.(1998)to
170mgofsamplesand300mgofPEwereretained. be1.35fortheamorphousfayalitesamples.
The overall MAC curve is built from the transmittances of
pellets having different masses. Before extracting their respec-
2.3.Datareduction
tive response we suppress from the transmittance curves the
The MAC of the pellet (sample and matrix), κ (cm2.g−1), fringesduetointernalreflexionsbetweenthetwointernalfaces
pellet
is related to the transmittance spectrum as follows (e.g. ofthepelletandtothefactthattheblankandsamplepelletsdo
Bohren&Huffman1998): not have the same exact thickness. The procedure to suppress
thefringesissimilartothatusedinCoupeaudetal.(2011).The
S resultingtransmittancesarethenconvertedtoMACandthedif-
κ =− ×ln(T) (3)
pellet m ferentMACare joinedtogetherbyaveragingthe spectra in the
overlappingregions.
whereSisthepelletarea(cm2),mthesamplemassinthepellet The uncertainty on the MAC has two origins. The first is
(g)andTthetransmittancespectrum.TheMACofthegrains,κ, the uncertaintyon the transmittance due the spectrometerther-
isdeducedfromtheMACofthepelletbythefollowingrelation mal stability (∆MAC =(δT/T)∗S/m). It is estimated to be
stab
(Eq.(6)from Mennellaetal.1998): δT/T ∼ 2.5%above 40 cm−1 and δT/T ∼ 5% below. The sec-
ond is the uncertainty on the mass of sample contained in the
pellet,∆MAC =MAC(λ)∗δm/m.Itbecomesimportantinthe
m
κ(λ,f)=g(ǫ,f)∗κpellet(λ,f) (4) MIRsincetheamountofsampleisverylow,typicallylessthan1
mgandtheprecisionoftheweighingscaleisδm≃0.1mg.The
where f is the volume filling factor of the grains within
errorontheMACisthusthequadraticsumofthesetwouncer-
the matrix (f never exceeds 0.15 for all the pellets) and g(ǫ,
tainties.Toestimate thetotalerroronthemeasuredkappaover
f) is the finite concentration reduction factor. g(ǫ, f) is calcu-
the entire spectral range we have taken the highest uncertainty
latedusingtheformulagivenbyMennellaetal.(1998)andus-
on the mass and on the spectrometer stability and applied it to
ing their value for the dielectric function of the host medium
thewholespectralrange.
(PE) and for the grain material. This calculation revealed that
TheabsolutevalueoftheMACwassetinthespectralrange
g(ǫ, f) is always greater than 0.88. The transmittance cor-
wheretheerroronthemassisminimizedwhilethedilutionfac-
rected for reflexion loss, T , is calculated using the formula:
corr torofthesampleinthepelletishighenoughtopreventanysig-
T =T /(1−R)2 with R, the reflectance of the pellet,
corr measured nificantinhomogeneityinthepellet.Thiscorrespondstopellets
expressed as R=(1−n )2/(1+n )2. The effective refractive
eff eff containingabout2-5mgof sampleanda spectralregionin the
indexofthepellet,n ,isrelatedtotheaveragedielectricfunc-
eff 40-50µmrange.
tionofthepellet,ǫeff,bytheformulaneff = pRe(ǫeff).Thecor-
rectionfactorforreflexionloss,(1-R)2,islargerthan0.9forall
the pellets.Such correctionis basedonthe assumptionthatthe 3. MIRandFIR/submmmassabsorptioncoefficient
grains are spherical. However this is not the case even though
asafunctionofthetemperature
SEMimagesshowthatthegrainshaveaspheroidalshapeclose
to a sphere. To correctfor the shape effect one has to make an IntheMIRdomain,thespectrashowthetwovibrationalbands
assumptiononthegrainshapedistributionandtomodelthere- characteristic of amorphous silicates: the stretching mode of
sultingMACspectrumfromtheopticalconstantsofsomemate- theSi-Obondat∼10µmandthebendingmodeoftheO-Si-O
rialclosetothestudiedone.Thedrawbackofsuchanapproach bond at ∼ 19 µm (Fig. 1). The broadness and the absence of
isthatthecorrectionfactorwillbedependentontheshapedis- structure of the bands confirm the amorphous state of all four
tribution and on the optical constants chosen and we have not samples.Thepeakpositionofthestretchingbandshiftstoward
Articlenumber,page4of13
K.Demyketal.:LowtemperatureMIR/submmmassabsorptioncoefficientofMg-richglassysilicates
1000.0 1000.0
100.0 100.0
2m/g) 2m/g)
MAC (c 10.0 X35 MAC (c 10.0 X40
10 K 10 K
100 K 100 K
200 K 200 K
1.0 1.0
300 K 300 K
0.1 0.1
10 100 1000 10 100 1000
λ (µm) λ (µm)
1000.0 1000.0
100.0 100.0
2m/g) 2m/g)
MAC (c 10.0 X50A MAC (c 10.0 X50B
10 K 10 K
100 K 100 K
200 K 200 K
1.0 1.0
300 K 300 K
0.1 0.1
10 100 1000 10 100 1000
λ (µm) λ (µm)
Fig.2.MassabsorptioncoefficientofthesamplesX35(upperleftpanel),X40(upperrightpanel),X50A(lowerleftpanel)andX50B(lowerright
panel).Foreachsampleweshowthespectrameasuredforagraintemperatureof300K(red),200K(orange),100K(green)andat10K(blue).
Theshadedarearepresentstheuncertaintyontheexperimentaldata(seeSect.2.2).Thesharpbandat7.2µmisnotassociatedwiththesamples
andisduetothePEmatrix.
long wavelengths from the X50A and X50B samples (9.87 410 cm−1 (24.39µm) to rotation modes of the SiO tetrahedra
4
µm) to the X40 and X35 samples (10.10 µm and 10.34 µm, in crystalline forsterite. This assignment is compatible with
respectively). In addition, the stretching band of the X40 and ourresults for glassy samples and the factthat this band is not
X35 samples exhibits a shoulder at respectively 11.68 µm and observed in the X50 samples which contains no Q0 species
11.93 µm, that is not observed in the two X50 samples. The (isolatedtetrahedra,SiO4−).TheX50AandX50Bsampleshave
4
bendingmodepeaksat19.42µmforX50AandX50Bsamples verysimilar MIRspectra as expectedsince theyhave the same
whereas it shows two peaks for the X40 and X35 samples: the stoichiometry but this also seems to show that they also have
firstoneat18.55µmandthesecondoneat24.39µm,thelatter similarstructuralstates. We notethatthepolymerizationofthe
beingmorepronouncedinthespectrumoftheX35samplethan samples also has an impact on the FIR MAC as proposed by
in the one of the X40 sample.The position and width of the Coupeaudetal.(2011)(seeSect.5).
vibrational bands depends on the polymerization of the SiO
4
tetrahedra within the sample which is related to the metal/Si
ratioandtoNBO/T,theaveragenumberofnonbridgingoxygen Figure 2 presents the MAC of the studied samples in the
in each SiO tetrahedra. The sample X35 containing the most wholespectralrangemeasuredand at 10,100,200 and 300K.
4
MgO is the least polymerized sample whereas the samples The MAC measured at 30 K is similar to that at 10 K. In the
X50 containingthe least MgO are the most polymerized.Such FIR, all the spectra show the now well-known temperature de-
a shift of the stretching mode toward long wavelengths with pendence characteristic of amorphous materials. (i) The MAC
increasing content of MgO and the opposite behavior for the decreaseswith decreasing grain temperature.(ii) Consequently
bendingmodeisinagreementwithpreviousstudies(Jägeretal. the spectral index (defined as the local slope of the spectrum)
2003; McMillan 1984). Hofmeister (1987) attributes a peak at varies with the temperature: (iii) at a given wavelength, it in-
creaseswhenthetemperaturedecreases.ThisisevidentinFig.3
Articlenumber,page5of13
A&Aproofs:manuscriptno.Demyk2017
4. Comparaisonwithpreviousexperimentaldata
Assuggested,foragivencomposition,thestructureatnanome-
terscaleoftheproducedanaloguesdependsonthemethodsused
forthesynthesis.Inthatsense,eachsampleisuniqueandhasa
structuredifferentfromtheothers.Glassymaterialsproducedby
quenchingof high temperature liquids have a higher degree of
polymerizationofthesilicatesnetworkthanmaterialsproduced
via solgel methods. Solgel samples are characterized by their
watercontent(whichcanbehigh)andbytheirsignificantporos-
ityduetoalargeamountofdefectsintheirstructure.Theythus
havehigherspecificsurfaceandcontainsalotofdanglingbonds.
Onthecontrary,quenchedglassescontainalmostnowater,have
fewer defects and are more compact than solgel samples. All
these structural differences may impact the spectral properties
ofthematerial.Wemustusecautionwhenrelatingthespectro-
scopicandphysicalpropertiesofagivenmaterial.Therearesev-
eral reasonsfor this. During the synthesis processit is difficult
Fig. 3. Spectral index as afunction of thewavelength for the studied topreciselycontrolthestoichiometrichomogeneityatnm-scale,
samples:X35(upperleftpanel),X40(upperrightpanel),X50A(lower theporosityanddefectspresentinthesample.Inadditionthese
leftpanel)andX50B(lowerrightpanel).Foreachsample,thespectral
quantitiesaredifficulttomeasure.
indexisdisplayedfordifferenttemperatures:300K(red),100K(green)
ans10K(blue).Thevalueofthespectralindexwasderivedfroma6th Despite the differences of the dust analogues retained in
orderpolynomialfitofthemeasuredMAC. previous studies (Mennellaetal. 1998; Boudetetal. 2005;
Coupeaudetal.2011)andinthepresentone,thespectroscopic
properties and temperature dependent behavior of all these
analogues remain qualitatively similar: the MAC value is
correlatedwiththedusttemperatureandhasacomplexspectral
shapedifferingfromasimpleasymptoticbehaviorinλ−2.Atthe
whichshowsthevalueofβcalculatedateachwavelength.This sametime,becauseofthesedifferencesbetweenthesamplesin
temperatureeffectis observedwhen the temperaturedifference termsofinternalstructure,composition,porosity,homogeneity,
betweenthemeasurementsishighenough,thatis,forthespec- theshapeoftheMACintheFIRvaries.Consequently,theMAC
tra measured at 300, 200, 100 and 10K. However we observe value at a given wavelengthof all samples from this study and
notemperaturevariationoftheMACbetween10Kand30Kin frompreviousstudiesspansalargerangeofvalues(seeTable1
thestudiedspectralrange.TheMACvariationswiththetemper- fortheMACvalueofthesamplesstudiedhereandTable1from
ature are more pronouncedat long wavelengths. They become Demyketal. (2013) for previous studies at 1 mm). It must be
detectableabovedifferentwavelengthsaccordingtothesamples: noted that the MAC in Boudetetal. (2005) has been corrected
from∼ 300µm fortheX35samplesupto500µm fortheX40 for grain shape effect whereas in Coupeaudetal. (2011) and
andX50Bsamples(Fig.2).Belowthesewavelengths,theMAC Mennellaetal. (1998) and in the present study this correction
ismoreorlessinvariablefromroomtemperatureto10K.Inad- was not applied (see Sect 2.3). This partly explains why the
dition,foreachsample,thewavelengthatwhichthesevariations MAC value are smaller in Boudet’s study, together with the
aredetectable,thatis, thewavelengthatwhichthe temperature effect of differences in the samples in terms of composition
activatedabsorptionappears,dependsonthegraintemperature: and structure. At 100 µm, the MAC values of all the samples
itdecreaseswithincreasingtemperatureofthesample.Inaddi- from this study and from previous work are similar at 300 K
tion, to the T-β anticorrelation,Fig. 3 also illustrates the wave- and 10 K (50 - 300 cm2.g−1 at 300 K and 40 - 260 cm2.g−1 at
lengthdependenceof the MACof the samples. It is clear from 10 K). At 500 µm, the MAC is greater at 300 K than at 10 K
Fig.3thatthemeasuredMACcannotbefittedwithapowerlaw (2 - 20 cm2.g−1 at 300 K and 0.7 - 13 cm2.g−1 at 10 K). This
andasinglespectralindexoverthewholespectralrangeandin is also the case at 1 mm where the MAC is in the range 0.1
particularabove100µm,inthespectraldomainwheretheMBB -11 cm2.g−1 at 300 K and 0.12 - 7 cm2.g−1 at 10 K. We note
modelsisusuallyadoptedinastronomicalstudies. that for each sample the MAC at 300K is always greater than
at 10 K. Furthermore, the fact that the range of values of the
TheMACofthefoursamplesarecomparedat10Kand300 MAC at 300 K and 10 K overlaps results from the dispersion
KinFig.4.Upto100µmallMACaresimilar,ascanbeseenin of the measured spectra. This diversity of the MAC value and
Fig.1.Above100µm,theMACofthefoursamplespresentdif- spectral shape that vary as a function of the materials studied
ferentspectralshapesandthe differencesare morepronounced canbeproblematicforastrophysicalapplicationssinceonehas
at 10 K than at 300 K. The X35 sample is the least absorbent todecidewhatanalogisthemostrelevantandshouldbeusedin
whereas the X40 sample is the most absorbent. The two X50 themodeling.ThisisconsideredinmoredetailinSect5.
samples have very similar spectra up to 300 µm at 300 K and
up to 200 µm at 10 K but are different at longer wavelengths. The comparison of the four samples at 300 K and 10 K
In the FIR, as in the MIR, the spectrumof amorphoussilicates (Fig. 4) shows that, above 100 µm and at any temperature,the
dependsonthestructuralstateofthematerial.Howeveritisalso MAC are very different from one sample to the other. In their
affectedbythepresenceofdefectsinthematerial.Hence,these studyofsolgelMg-richsilicatesdustanalogues,Coupeaudetal.
differencesmightcome fromthe factthatthe X50Aand X50B (2011)proposethatthespectralshapeoftheMACdependspri-
samples,beingsynthesizedusingdifferentmethods,donotcon- marilyonthecation/Siratioandthatthetemperaturevariations
tainthesamedistributionofdefectsorthesametypeofdefects. of the MAC may be related to the connectivity of the SiO4−
4
Articlenumber,page6of13
K.Demyketal.:LowtemperatureMIR/submmmassabsorptioncoefficientofMg-richglassysilicates
1111000000000000....0000 1111000000000000....0000
111100000000....0000 111100000000....0000
2m/g) 2m/g)
MAC (c 11110000....0000 T = 300 K MAC (c 11110000....0000 T = 10 K
X50B X50B
X50A X50A
X40 X40
1111....0000 1111....0000
X35 X35
0000....1111 0000....1111
11110000 111100000000 1111000000000000 11110000 111100000000 1111000000000000
λ(µm) λ(µm)
Fig.4.MassabsorptioncoefficientofthesamplesX35,X40,X50AandX50Batroomtemperature(leftpanel)andat10K(rightpanel).Thesharp
bandat7.2µmisnotassociatedwiththesamplesandisduetothePEmatrix.
Table1.ValueoftheMACoftheglassysamplesX35,X40,X50AandX50B.
MassAbsorptionCoefficient(cm2.g−1)
100µm 250µm 500µm 850µm 1mm
10K 300K 10K 300K 10K 300K 10K 300K 10K 300K
X35 194.6 217.2 19.2 30.1 2.0 5.2 0.4 1.8 0.2 1.4
X40 200.9 216.9 68.6 74.7 25.4 31.3 7.9 14.0 5.0 11.2
X50A 153.4 160.2 27.9 36.5 3.9 8.1 1.7 3.5 1.7 3.1
X50B 136.8 152.2 36.5 39.9 10.2 12.8 2.9 4.8 2.0 3.5
<MAC1>(1) 171.4 186.4 38.1 45.3 10.4 14.3 3.2 6.03 2.2 4.8
<MAC2>(2) 169.8 186.7 25.7 34.1 4.5 7.8 1.3 3.0 1.0 2.3
MACsphere0.1µm(3) 33.5 5.1 1.2 0.48 0.36
MACdistribsphericalgrains(3) 36.9 4.9 1.1 0.45 0.34
MACdistribprolategrains(3) 50.3 6.8 1.5 0.6 0.47
MACCDE(3) 74.0 11.5 2.6 1.05 0.81
Notes.
(1)<MAC1>representstheMACaveragedoverthefoursamplesX35,X40,X50AandX50B,seeSect.5.1.
(2)<MAC2>representstheMACaveragedoverthesampleX35andthemeanoftheX50AandX50Bsamples,seeSect.5.1.
(3)TheseMACarecalculatedusingtheopticalconstantsofthe"astrosilicates"fromLi&Draine(2001),seeSect.5.1.
tetrahedra.FromthevaluesoftheratiooftheMACathightem- SiO4− tetrahedra, estimated by the population of Qi, seems to
4
perature(300K,200K,100K)totheMACatlowtemperature be the most appropriate parameter for describing the material
(10K), we findthattheamplitudeofthe variationof theMAC structuralstate.
withtemperatureincreasesfromthemostpolymerizedsamples
(X50AandX50B)totheleastpolymerizedsample(X35).Inthe
wavelength range 800-1000 µm, the MAC of the X35 sample
(which contains only isolated SiO4− tetrahedra and bridged 5. Discussion
4
Si O6−dimericstructures,seeSect.2.1),variesbyafactorthree
2 7 5.1.Comparaisonwithcosmicdustmodels
to four from 10 K to 200 K as comparedto a factor 1.3 to 1.6
for the X40sample (whichcontainsisolated tetrahedra,dimers InordertocomparethemeasuredMACwithcosmicdustmodels
and chains), and from 1 to 1. 4 for the two X50 A and X50B we have calculated the MAC of their silicate componenteither
samples (which contains mainly chains and three-dimensional using Mie theory for spherical grains or using the DDA code
structures). These results are consistent with the interpretation DDSCAT 7.3 developedby Draine&Flatau (2013) for prolate
that the temperature-activated processes responsible for the grains (with an axis ratio of two). We calculated the MAC for
MACvariationsarelinkedtothestructuralstateofthematerial differentcases:forasphericalgrainof0.1µmdiameter,typical
(Menyetal. 2007). The connectivity or polymerization of the of interstellar silicate size; for two populations of grains char-
acterized by a log-normaldistribution of size with a mean size
Articlenumber,page7of13
A&Aproofs:manuscriptno.Demyk2017
andreferencetherein).Itisthusimportanttoemphasizethatthe
observedspectraldifferencesintheMIRdonotquestiontherel-
evanceofthestudiedanalogues.
At longer wavelengths and in the temperature range of
astrophysical interest 10 K - 30 K (where T-independent
processesfully dominate the absorption)the laboratoryspectra
and the modeled ones are very different. The measured MAC
for the X40, X50A and X50B samples are much higher than
themodeledMACinthewholespectralrange.Thisisalsotrue
for the X35 samples for λ ≤ 700 µm but for λ ≥ 700 µm the
measured MAC is similar to the modeled one. The increase
of the measured MAC with respect to the MAC modeled for
sphericalgrainscanbecalculatedatsomespecificwavelengths
fromTable1(aswellasforothershapesandsizedistributions).
TheX40sample,themostabsorbent,is4timesmoreabsorbent
at 100 µm than the models and about 10 to 17 times at longer
wavelengths. The two X50 samples are 3 to 7 times more
absorbent than the models over the entire spectral range. For
Fig.5.ComparisonofthemeasuredMACofthesamplesX50A,X50B, the X35 samples the MAC is 1 to 3 times more absorbent in
X40,X35at10KwiththeMACcalculatedfromcosmicdustmodelsus- the100- 600µm rangeandbecomesasabsorbentorevenless
ingMieTheoryforsphericalgrainof0.1µmsize:"astrosilicates"from absorbent at longer wavelengths. At wavelengths greater that
(Li&Draine2001)(redcurve)andthetwosilicatesfromthe"Themis"
20 µm, the "astrosilicates" and the "Themis" silicates are not
dust model (Jonesetal.2013):amorphous enstatite(greencurve) and
basedonexperimentalmeasurementsoronobservationsbuton
amorphousforsterite(cyancurve).
the extrapolation of the optical constants derived in the MIR.
ThedifferencesbetweenthemeasuredMACandtheMACfrom
cosmic dust thus do not reflectdifferencesin terms of material
of 1 µm (to represent the grain size distribution of the studied but rather in terms of theory of the absorption processes (see
samples)andfortwodifferentgrainshapes,sphericalgrainsand Sect.5.2).
prolategrainswith an axisratio of2;andfor a continuousdis-
tributionofellipsoids(CDEmodelwhichassumesthatallellip- As highlighted in Sect. 4 and as seen in Fig. 5, the diver-
soidalshapesareequiprobable,Bohren&Huffman(1998)).For sity of the MAC from one sample to another raises the ques-
comparisonoftheMACintensity,itisbesttocomparewiththe tion of the relevant dust analogues to be used in astronomi-
MACmodeledforadistributionofellipsoidsasitistheclosest cal models. To investigatethis questionit is interesting to con-
totheexperimentalgrainsdistributionwithinthepellets. sider what we can learn from the many (about one thousand)
Figure 5 shows the comparison between the MAC of the presolar silicate grains that have been identified (Nguyenetal.
measured samples and the MAC of silicates from astronomi- 2016, and referencestherein). The detailed study, using Trans-
cal dust models: the "astrosilicates" from Li&Draine (2001) missionElectronMicroscopy(TEM),ofthesepresolarsilicates
and the silicates from the "Themis" model (Jonesetal. 2013). grains shows that they have a wide range of microstructure,
IntheMIRrange(2.8-17.5µm),the"Themis"modelisbased shape and composition. They are mostly amorphousand often
on the laboratory work from Scott&Duley (1996), that is, on non-stoichiometricwith sometimes internalnm-scale composi-
amorphous enstatite (MgSiO ) and forsterite (Mg SiO ) pro- tional variations(Nguyenetal. 2016). Boseetal. (2012) found
3 2 4
duced by laser ablation. The optical constants of the "astrosil- intheCO3chondriteALHA77307manypresolargrainshaving
icates" are constructed from observations of dust emission in intermediate stoichiometry between olivine-like and pyroxene-
the Trapeziumregionforthe 9.7µm bandand fromdustemis- likematerial(seetheirFig.6),similartotheX40sample.These
sionfromcircumstellardustshellsaroundO-richstarsaswellas presolar grains come from AGB circumstellar envelops, su-
fromdust absorptiontowardthe Galactic Center for the 18 µm pernovae, novae: they are the interstellar grains that emit in
band(Draine&Lee 1984).In theMIRdomain,upto ∼ 20µm the FIR/submm domain. Ideally, this diversity of composition
the laboratoryspectra and the "Themis" modeledspectra agree shouldbetakenintoaccountininterstellardustmodelsandthe
reasonably well in terms of band shape and MAC value, even silicate component of these models should be built from vari-
thoughdifferencesareexpectedsincethesamplesonwhichthe ousdustanalogues,includingnon-stoichiometricanalogues,for
"Themis"modelisbasedaredifferentfromthefourglassysam- examplebyaveragingtheiropticalconstantsorMAC.
ples. The comparison with the "astrosilicates" shows that the We have calculated the average MAC, <MAC1>, from the
stretching mode at ∼ 9.7 µm of the "astrosilicates" is broader foursamplesX35,X40andX50AandX50Bbysimplyadding
and more intense than the one of the studied analogues, inde- thefourspectraanddividingthesum byfour(Fig.6). Suchan
pendently of assume grain size and shape distribution adopted averagedMAChasa Mg/Siratioof1.18,veryclose tothe one
forthemodel.Becausethe"astrosilicates"areconstructedfrom givenbythecosmicelementalabundanceofmagnesiumandsil-
astrophysicalobservations,thesedifferencescannotbediscussed icon which is in the range 1 - 1.15 depending on the adopted
in terms on material properties. They may be explainedby the reference(Jenkins2009;Przybillaetal.2008).Theresultingav-
factthatadditionalsilicatecomponentsareneededtoreproduce eragedMACpresentsthesamecharacteristicsaseachindividual
thelineofsightfromwhichthe"astrosilicates"areconstructed. sample:variationoftheMACspectralshapeandintensitywith
It is known that the observedMIR silicate bands vary with the the temperature. However, as expected, the amplitude of these
environmentsandthatnouniquesilicates,fromlaboratorydata variations are lower than those of each sample taken individu-
or derived from observations, can reproduce the MIR silicate ally.Inadditionthespectralshapeof<MAC1>issmoothedby
bandsinallastrophysicalenvironments(seeFogertyetal.2016, the average and the β(λ) value varieson a narrowerrange than
Articlenumber,page8of13
K.Demyketal.:LowtemperatureMIR/submmmassabsorptioncoefficientofMg-richglassysilicates
1000
2m/g) 100
C (c
MA Mg rich glasses averaged MAC
10 K
100 K
10
200 K
300 K
Fig.7.SpectralindexasafunctionofthewavelengthfortheMACaver-
ageoverthefourstudiedsamples,<MAC1>.Thevalueofthespectral
indexwasderivedfroma6thorderpolynomialfitofthemeasuredMAC.
1
10 100 1000 Itisdisplayedfordifferenttemperatures:300K(red),100K(green)ans
λ (µm)
10K(blue).
Fig.6.MassabsorptioncoefficientaveragedonthefoursamplesX35,
X40, X50A and X50B for agraintemperature of300 K (red),200 K
(orange),100K(green)andat10K(blue).Theshadedarearepresents
theuncertaintyontheexperimentaldata(seetext).
Mg rich glasses averaged MAC
1000.0 10 K
foreachsample(Fig.7).At300K,the<MAC1>curveiswell 300 K
approximatedbyasinglepowerlawλ−βwithβ=1.6forλ≥100
µmwhereasat10K,twopowerlawsareneededwithβ=1.8for 100.0
150µm≤ λ ≤ 500µm andβ= 2.2forλ ≥ 500µm. Ifwe cal- 2m/g)
culatethe averagein termsofcomposition- takingthe average C (c
of the X50A and X50B sample for the MgSiO3 pole - the re- MA 10.0
Astrosilicates
sultsarecloseto<MAC1>becausethesampleX40,muchmore
sphere 0.1 µm
absorbentthanthe others,dominatesthe averageMAC. On the spheres
contrary,ifwedonotconsidertheX40sampleandaveragesthe spheroids
1.0
samplesX35andthemeanofthetwoX50AandX50B(Mg/Si CDE
=1.12,<MAC2>),theresultsaredifferent.Inthiscaseatleast
fourpowerlawsareneededtoreproducedtheaveragedMAC(β
0.1
=1.8,2.4,2.3,1.6inthespectralranges100-180µm,180-500 10 100 1000
λ (µm)
µm,500-800µmand800-1000µm,respectively).
Fig. 8 shows that the averaged MAC, <MAC1>, is much
more absorbing than that MAC from cosmic dust models. The Fig. 8. Comparison of averaged experimental mass absorption coeffi-
comparisonoftheMACofcosmicdustmodelswith<MAC1> cientswiththeMACcalculatedfromcosmicdustmodel.Thesolidline
showsthatatλ=100µmthemeasuredMACis3.4timeslarger curves with the uncertainty represent the MAC averaged on the four
than the dust model calculated for a size distribution centered samplesX35,X40,X50AandX50B:(red)MACat300K,(blue)MAC
at 1 µm of prolate grains (Table 1). At λ = 1mm <MAC1> is at10K. TheMACofthe"astrosilicates"from(Li&Draine2001)are
calculatedusingMieTheoryfora0.1µmsizegrain(black),foralog-
4.6 timeslargerthan the cosmic silicates dustmodelsforgrain
normalgrainsizedistributionwithameandiameterof1µmforspheri-
temperatureof10K.ThecomparisonwiththeCDEmodelleads
calgrains(magenta)andforprolategrains(cyan)andforaCDEmodel
to a factor of2.3 and2.7respectivelyat 100µm and 1 mmfor
(green).Seetextformoredetails.
<MAC1> measured at 10 K. If one compares with <MAC2>,
then, at 10K, <MAC2> is higher than the modeled one by a
factorof3.5at100µmandbyafactorof2.5at1mm.
The measured MACs correspond to a population of grains
with a certain shape (not spherical) and size distribution (un-
known) and this has to be taken into account when comparing
with the MAC calculated from dust models. The typical sizes
5.2.Absorptionprocesses
whichcanbereachedbymanuallygrindingmineralsinanagate
ThedifferencebetweentheMACscalculatedfromcosmicdust mortararearound1µm,sizethatwasadoptedforthemeansize
models and from experimental data has important astrophysi- for the size distribution. Increasing the grain size broadensthe
calimplicationsintermsofmassandtemperaturedetermination vibrational bands and changes their peak position and relative
whichneedstobeunderstood.Itcouldarisefromexperimental strength. The stretching and bending modes thus constrain the
artefacts(suchastheeffectofsizedistribution,theeffectofco- amountoflargegrainsandthewidthofthechosensizedistribu-
agulationwithinthepellets)oritmaybeduetoabsorptionpro- tion. However, despite these constraints, the solution is degen-
cessesintrinsicofthematerial.Inthefollowing,weinvestigate eratedandseveralgrainsizedistributionscangiveareasonable
thesepossibilities. fittotheexperimentalspectraintheMIRrange.However,none
Articlenumber,page9of13
A&Aproofs:manuscriptno.Demyk2017
of these size distributionscan explain the discrepancybetween measurementsshowthatinthewavelengthrangefrom10to100
astronomicaldustmodelsandourexperimentaldataforλ ≥70 µm,theMACismorecomplexthanexpectedfromsimplesemi-
µm, althoughsize distribution effects may contribute to the in- classicalmodels(LorentzandDebye)orwithTLSmodels.
creaseoftheMACvalueandtothebroadeningoftheredwing The largervalueand the spectralshapeof the experimental
ofthebendingO-Si-Ovibrationalmodein the20-70µm range MAC may be related to the so-called Boson peak (BP) which
(Fig.8).Thisconclusionholdsforadistributionofnonspheri- appears to be a universal feature of solid state of very differ-
cal grainsthat doesnotchange muchthe MAC comparedwith entamorphousmaterialssuchasoxideglasses,amorphousices,
sphericalgrains, althoughit slightly increases the MAC at λ ≥ polymers (Champagnonetal. 2009). The BP has been widely
100µm(Fig.8). observed in the FIR in Raman spectroscopy (Kojimaetal.
A second effect is the aggregation of sample grains within 2000; Kalampouniasetal. 2009), inelastic neutron-scattering
the pellets. This phenomenon may occur when preparing spectroscopy(Buchenauetal.1984;Nakayama2002),terahertz
the pellets but it is difficult to control during fabrication and time-domain(Kojimaetal.2005;Parrottetal.2010)oracombi-
impossibletoprobeafterwards.Thiseffectisinprincipletaken nationofreflectionandtransmissiontechnicsandspectroscopy
intoaccountinthedatareductionanalysisthankstoanEffective in the FIR/submm (Schneideretal. 2001; Parrottetal. 2010).
MediumTheoryapproach.Thecorrespondingcorrection,which HowevertheexactoriginandnatureoftheBPhasbeenthesub-
applies to the whole spectrum, is small (a factor in the range ject of many debatesover morethan three decades. Severalat-
0.88 - 1, see Sect.2.1). Using more sophisticated modeling tempts, frequently self-contradictory, have appeared so far for
approaches like the DDA (Discrete Dipole Approximation) theexplanationoftheBPinnon-crystallinesolids.Thesecanbe
approach, it has been shown that the maximum factor of en- groupedinto two main categories. On one side, the BP is con-
hancementduetocoagulationshouldnotexceedtwo,whatever sideredtoarisefromlocalizedorquasi-localizedmodes;theex-
computational method used, and whatever shape, compactness istence of weak interatomic forces into the glass create the so-
and size of the aggregates are considered (Stognienkoetal. calledsoftpotential(Klinger1988;Gurevichetal.2003).From
1995; Köhleretal. 2011; Mackowski 2006; Minetal. 2016). anotherpointofview,theBPisamanifestationthatthedisorder
Thus,althoughcoagulationmayoccurwithinthepelletitcannot impactsonthevibrationaldensityofstates(VDoS)ofthecorre-
explainenhancementfactorsgreaterthanthreeas observednor spondingcrystallinesolid.Dependingonthecompositionofthe
the different enhancement factor at 1 mm relative to the one glass, the BP has been observed in a broad optical wavelength
at 100 µm. This is because coagulation of grains of identical range,extendingroughlyfromλ=100to1000µm.
material do not change the slope of the MAC, meaning that Very few physical and analytical models exist that de-
the enhancement factor does not vary with wavelength, in the scribe BP observations. In the analytical model developed by
FIR/submm. Gurevichetal.(2003),theBPoriginatesfromquasi-localvibra-
tions (QLVs) characterized by large vibrational amplitudes of
All this indicates that for λ ≥ 100 µm our samples are in- some groupsof atoms, which is a typicalfeature of disordered
trinsicallymoreabsorbentthanthesilicatesusedincosmicdust systems and very similar to the well known TLS. These QLVs
models.Forλ ≥ 20µm,bothdustmodelsuse theDebyemodel canbemodeledaslocallowfrequencyharmonicoscillatorscou-
to extrapolate the optical constants of the material. The MAC pled with the acoustic vibrations. In turn, this leads to dipole-
thushasanasymptoticbehaviorin λ−2. However,severalother dipole interactions between the different harmonic oscillators.
absorption processes may occur in the FIR range. In the TLS TheimportantresultsofthismodelarethatgBP(ω),thedensity
model,builttoexplainastronomicalobservationsatλ≥ 100µm of states of the BP, dependson a single parameterωBP charac-
wheretheemissionofbiggrainsdominatestheinterstellarradi- terizing the position of the BP and that the g (ω) excess over
BP
ationfield(Menyetal.2007),twoabsorptionprocessesarecon- the gDebye(ω) (the density of states of the Debye model) varies
sidered,theDCDandtheTLSprocesses.TheDCDmodel(Dis- following g (ω) ∝ ω4 at long wavelengths and g (ω) ∝ ω
BP BP
order in Charge Distribution, Schlömann 1964) describes the at short wavelengths on both sides of the BP maximum. This
FIRabsorptioninadisorderedchargeddistributionsimplychar- modelthus explainsthe occurenceof spectral index values be-
acterizedbythecorrelationlengthl thatrepresentstheaveraged lowtheexpectedasymptoticvalueβ=2inthefar-infraredwings
c
lengthoverwhich chargeneutralityis brokenin the disordered oftheMIRbands(∼30-100µm).ThefitoftheBPrequiresan
material. Such a model induces a dependence of the MAC in other parameter: the amplitude of the corresponding excess of
λ−2 inthevicinityofλ>100µmandanasymptoticbehaviorin vibrationsdensityofstatesovertheunderlyingdensityofstates,
thelongwavelengthlimitinλ−4.Itisatemperature-independent whatever Debye density of states or DCD density of states is
absorption. The TLS (Two Level System, Phillips 1987) com- chosen. We fit the experimental MAC curves with underlying
ponentofthemodeldescribestemperatureactivatedabsorption Debye density of states with constant optical coupling coeffi-
processeswhichareaddedtotheDCDabsorptions.Inthismodel cient,andthebestfitofthemeasuredMACarepresentedinthe
theatomicdisorderednetworkisdescribedbyanordereddistri- Appendix A. The fits are quite good over at least an order of
butionofasymmetricdoublepotentialwells(theTLS),eachof magnitudeinwavelength,fromλ=30µmforallsamples,toλ
whichcanbeviewedastwoconfigurationsofatomsorgroupsof = 400 µm (sample X35), 900 µm (X40), 600 µm (X50A), 700
atoms. Transitionswithin each TLScan occurvia resonnantor µm(X50B).
relaxational temperature-dependent processes (see Menyetal. It is important to keep in mind that these results are pre-
2007,andreferencethereinformoredetails). liminary.Amoredetailedwork,takingintoaccounttheabsorp-
In the absence of experimental measurements of the MAC tionprocessthatoccurintheFIRrange,willbepublishedelse-
in the wavelength range 25 - 100 µm in previous studies, the where.HoweveranalyzingtheMACofoursamplesusingphys-
TLSmodelwassimplyexpectedtoslightlymodifytheslopeof icalmodels,insteadofpureempiricallawssuchasapowerlaw
theFIR/submmMACofthesilicatescalculatedfromastronom- withdifferentspectralindexesdefinedoverdifferentFIRwave-
icaldustmodels.Inparticular,theabsolutevalueoftheMACat length ranges appears to be important for several reasons. If a
λ=100µmwasexpectedtobethesamefortheamorphoussili- physical model can fit the data over an extended wavelength
catesandfortheastronomicaldustmodels.Howeverthepresent range with very few free parametersspecific to the material or
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