Table Of ContentMon.Not.R.Astron.Soc.000,1–13(2015) Printed28January2015 (MNLATEXstylefilev2.2)
The 11.2µm emission of PAHs in astrophysical objects
A. Candian1,2⋆ and P.J. Sarre2†
5
1 1Leiden Observatory,Niels Bohrweg 2, 2333 CA Leiden, The Netherlands.
0 2School of Chemistry, The Universityof Nottingham, University Park, Nottingham NG7 2RD, U.K.
2
n
a
J Accepted. Received.
7
2
ABSTRACT
] The 11.2µmemissionband belongs to the family of the ‘Unidentified’ Infrared(UIR)
A emission bands seen in many astronomical environments. In this work we present a
G theoretical interpretation of the band characteristics and profile variation for a num-
ber of astrophysical sources in which the carriers are subject to a range of physical
.
h conditions. The results of Density Functional Theory (DFT) calculations for the solo
p out-of-plane(OOP)vibrationalbending modes oflargepolycyclicaromatichydrocar-
-
bon (PAH) molecules are used as input for a detailed emission model which includes
o
r the temperature and mass dependence of PAH band wavelength, and a PAH mass
t distributionthatvarieswithobject.Comparisonofthemodelwithastronomicalspec-
s
a traindicatesthat the 11.2µmbandasymmetryandprofile variationcanbe explained
[ principallyintermsofthemassdistributionofneutralPAHswithasmallcontribution
from anharmonic effects.
1
v Key words: molecular processes – ISM: molecules – ISM: lines and bands
1
1
8
6
0 1 INTRODUCTION tionofPAHsub-groups,andthusnarrowdownthenumber
. of possible PAHsas carriers of AIBs.
1 ThediscoverybyGillett,Forrest&Merrill(1973)ofanemis-
0 sion feature near 11.2µm in spectra of planetary nebulae Inthispaperwefocusonthe11.2 µmfeature,whichis
5 one of the most distinctive bands in the AIB spectrum. It
opened a new era in the study of interstellar matter. It is
1 has been assigned to the C-H out-of-plane (OOP) bending
now recognised as one of the strongest of the ‘unidentified
v: infrared’ (UIR) or ‘aromatic infrared’ (AIB) bands that lie mode of solo-containing neutral PAHs (Hony et al. 2001;
i between 3 and 20µm and which are generally attributed van Diedenhoven et al. 2004; Bauschlicher, Peeters & Al-
X
lamandola 2008; Ricca et al. 2012), although their precise
to vibrational transitions of polycyclic aromatic hydrocar-
r molecular shapes and size distribution has not been estab-
bon (PAH) molecules (for a review see Tielens 2008, and
a
lished.Weakeremissionfeaturesaround11.0 µmaregener-
referencestherein).However,innocasehasitprovedpossi-
allyattributedtothesametypeoftransitioninPAHcations
bletoidentify aspecificPAHmolecule. Thisis unfortunate
(Sloan et al. 1999; Hudgins & Allamandola 1999; Boersma,
because knowledge of PAH shape, size distribution and de-
Bregman&Allamandola2013).Wepresenthereanemission
gree of hydrogenation and/or ionisation would allow much
model based on Density Functional Theory (DFT) calcula-
greater exploitation of the spectra as probes of astrophys-
tions of vibrational transitions and intensities for a set of
ical conditions and processes. The advent of infrared (IR)
PAH molecules. The model considers the emission process
satellites including ISO, Spitzer (Werner et al. 2004a) and
following optical/UV excitation using the relevant stellar
AKARI(Murakamietal.2007) hasrevealedtherichnessof
spectral energy distribution (SED) and includes the tem-
theAIBspectrumandalsosignificantdifferencesinthepro-
files of individual bands (e.g. van Diedenhoven et al. 2004; perature dependence of the emission wavelength (band po-
sition) as the PAH molecule cools through emission of IR
Bern´eetal.2007;Rosenbergetal.2011,2012;Boersma,Ru-
photons. The results are used to explore the variation of
bin&Allamandola2012;Boersma,Bregman&Allamandola
the 11.2µm profile in a range of astronomical objects with
2013).Interpretationofthesevariationsintermsofthephys-
particularreferencetotheinfluenceofthePAHmassdistri-
ical and chemical properties of PAHs and the astronomical
bution.
objectsinwhichtheyarefoundcouldassistintheidentifica-
Thepaperisarrangedasfollows. InSection2thechar-
acteristicsofthe11.2µmbandarereviewed.Thetheoretical
approachandtheresultsofaseriesofDFTcalculations are
⋆ [email protected] presentedinSection3andtheemissionmodelisdescribedin
† [email protected] Section4.Sections5and6containtheresultsanddiscussion
2 A. Candian and P.J. Sarre
of their astrophysical implications. A possible contribution short-wavelengthsideofthe11.2µmfeaturein16spectraof
from acenes to the 11.0µm feature in the Red Rectangle is class A sources is almost invariant, which we determine
11.2
also discussed. to be 11.171 (2σ = 0.002)µm; the origin of this striking
property is not understood. If the short-wavelength edge
is considered to be part of a Lorentzian profile this would
correspond to a FWHM of only c. 4 cm−1 which is narrow
2 CHARACTERISTICS OF THE 11.2µm BAND
compared with otherUIR bands.
2.1 Classification of the 11.2µm band (b) The peak wavelength of the 11.2µm feature has
been found to depend on the effective temperature, T , of
The 11.2µm feature has an asymmetric shape with a steep eff
theexcitingstar(Sloanetal.2007;Kelleretal.2008).Fig.2
blue side and an extended red tail (Roche, Aitken& Smith
collectstogetherdatafromvariousauthors.Thepeakwave-
1989; Witteborn et al. 1989). Following analysis of ISO ob-
lengthofthe11.2µmbandisindependentoftemperaturefor
servations of objects in the Galaxy, van Diedenhoven et al.
classA objects (squares),butstartingfrom class B (
(2004) proposed two classes of 11.2µm sources (A and 11.2 11.2
11.2 triangle-TheRedRectangle)itshiftstolongerwavelength
B ) and introduced a description using a tail-to-top ra-
11.2 with decrease in stellar temperature. This change has been
tio, i.e. the strength of the red wing relative to the peak
interpretedintermsofrelativelynewlyformedmaterialnear
intensityof theoverall profilewith maximum near11.2µm.
tolowtemperaturecarbon-richorHerbigAe/Bestars(class
Sloanetal.(2007)introducedathirdclass,C .Theclass
11.2 C )comparedwitholderprocessedmaterialinthehigher
characteristics, illustrated with examples in Fig. 1, are: 11.2
temperatureenvironmentsofplanetarynebulaeandHiire-
A -themostcommon,withapeakwavelengthranging gions (Sloan et al. 2007).
11.2
between 11.20 and 11.24µm and a relatively short red tail. (c) Barker, Allamandola & Tielens (1987) suggested
Sources belonging to this class have a low value of tail-to- that the long red tail of the 11.2µm band may be due to
top ratio and comprise various types of interstellar matter superimposed transitions between higher vibrational levels
-reflection nebulae,Hiiregions and thegeneral interstellar such as v = 2 → 1. In the absence of laboratory data this
medium. contributionwasincorporatedassumingthatthev=2→1
B -lesscommon,withapeakwavelengthof11.25 µm band falls at an arbitrarily chosen wavenumber 5 cm−1
11.2
and alongtail. Objectsin thisclass, such astheRedRect- lower than for the fundamental transition. More recently,
angle(HD44179), haveahighvalueoftail-to-top ratioand van Diedenhoven et al. (2004) noted that while a feature
are usually associated with circumstellar matter. of class A(B)11.2 could be considered as coming from the
C - only a few examples, with peak wavelength rang- same PAH population distribution as that which gives rise
11.2
ingbetween11.35and11.40µmandanapproximatelysym- to class A11.2 – but with higher internal energy, they com-
metric shape. Bands belonging to this class are found in mented that the difference between the A11.2 and B11.2
carbon-rich objects. classescouldnotreadilybeexplainedbyanharmoniceffects
alone.Acontributiontoemissionintheredtailcouldpoten-
Some objects (mostly planetary nebulae) are classified as
tially come from duo-Hs of compact PAH cations (Hudgins
class A(B) and have a mixture of the characteristics
11.2 &Allamandola1999),C–HOOPtransitionsinPAHanions
of the A and B classes, with a peak wavelength of class
(Bauschlicher, Peeters & Allamandola 2009) or from pro-
A and a tail-to-top ratio of class B objects (see for
11.2 11.2 tonated PAHs (Knorke et al. 2009). In addition Wada et
example BD+30◦ 3639 in Fig.1). Also, within the single al. (2003) have discussed the possible role of 13C isotopic
reflectionnebulaNGC7023,variationinthe11.2µmspectra
substitution. Blind spectral decomposition studies indicate
from type A to A(B) has been found (Boersma, Bregman
that a contribution to the red wing of ‘11.2µm’ emission
& Allamandola 2013). The A/B-type classification has also
arises in carriers well removed from theexciting star in e.g.
been applied to other spectral features in the 3µm and 6-
NGC 7023; this emission has been ascribed to ‘Very Small
9µm regions.
Grains’ (VSGs) (Rapacioli et al. 2006; Bern´e et al. 2007;
Based on a study of mid-IR Spitzer spectra of carbon-
Rosenberg et al. 2011, 2012).
rich post-AGB stars in the LMC, Matsuura et al. (2014)
The shapes of the AIBs have been modelled (Schutte,
have introduced separate classifications for the 6-9µm and
Tielens & Allamandola 1993; Cook & Saykally 1998; Ver-
10-14µmregions,wherethespectraforthelatterregionare
straete et al. 2001; Pathak & Rastogi 2008); the most de-
classified as α,β,γ and δ. As the spectra we consider here
tailed study of the 11.2µm band is that of Pech, Joblin
are high-resolution data from ISO-SWS (de Graauw et al.
& Boissel (2002) and includes both intermode anharmonic-
1996),wehaveelectedtousetheA ,B andA(B)
11.2 11.2 11.2 ity (which from laboratory measurements of Joblin et al.
classification of van Diedenhoven et al. (2004).
(1995) allows the effect of cooling on emission wavelength
andlinewidthtobeestimated),andintramodeanharmonic-
ity which is a contribution from vibrational transitions of
2.2 Asymmetry and peak wavelength of the
thetypev → v−1 with v > 2. A mass distribution for the
11.2µm band
PAHswasincludedoftheformN−3.5 whereN isthenum-
C C
Interpretationoftheshapeandthevariationintheprofileof ber of carbon atoms. This affects theresponse of the PAHs
the11.2µmbandisasignificantchallengewhichrequiresan toopticalexcitationandtheirsubsequentcooling.However,
explanation of (a) the steep short-wavelength side, (b) the in considering molecular diversity, it was assumed that all
variable peak wavelength and (c) the extension to longer PAHs contributing to the 11.2µm band profile had exactly
wavelength. Considering these in turn: the same infrared active mode frequency. It was deduced
(a)Thewavelengthathalfpeakintensity(λ )onthe thattheasymmetricprofileappearedtobecharacteristicof
1/2
The 11.2µm emission of PAHs in astrophysical objects 3
RR
Figure 2. Peak wavelength (λc) and class-type of the 11.2µm
feature vs. effective temperature (Teff) of the central star.
The squares are a sample of type A/A(B)11.2 sources from
Hony et al. (2001): GGD 27-ILL (star formation region), CD-
4211721(HerbigAe/Bestar),NGC7023(reflectionnebula)and
IRAS21282+5050(planetarynebula).ThetrianglesareTheRed
Rectangle (RR) and mostly carbon stars (class B11.2 to C11.2)
from Sloan et al. (2007), the 5-points stars represent Herbig
Figure 1. Comparison of the 11.2µm profiles of class A11.2 Ae/Bestars(classB11.2toB/C11.2)fromKelleretal.(2008)and
(Orion H2S1) – in red (thin line), B11.2 (HD 44179 - the Red the circles are proto-planetary nebulae (class B/C11.2 to C11.2)
Rectangle) and A(B)11.2 (NGC 7027). These ISO spectra are fromZhang, Kwok&Hrivnak(2010).
continuum-subtracted andnormalisedtothepeakintensity.
tionswereperformedusingQ–Chem(Shaoetal.2006)with
the anharmonicity of molecular modes, and that including
the B3LYP functional (Becke 1993; Stephens et al. 1994)
a spread of frequencies according to molecular size and ge-
and the 6–31G* basis set. Secondly, DFT calculations were
ometry would lead to a change in overall band shape and
carriedoutforselectedhighlysymmetriccompactlargesolo-
consequentdifficultyinachievingagood fittotheobserved
containingPAHsandtheseresultsappliedinthefullspectral
band.This contrastswith thework reported herewhere we
profile modelling. Gas-phase laboratory data were used to
find that the dependence of the vibrational transition fre-
obtain mode-specific vibrational scaling factors.
quenciesonthemassesofthe11.2µmcarriersandtheirrel-
InthefirstpartofthestudyPAHstructuresarelabelled
ative abundance are key factors in determining the overall
(x, y) where x is the number of 6-membered rings in a row
11.2µm band profile and its variation between objects.
and y is the number of rows. Examples include anthracene
(C H ) for which x = 3 and y = 1 and anthanthrene
14 10
(C H ) for which x = 3 and y = 2 (see Fig.3(a) and
22 12
3 DFT CALCULATIONS Tab.1(a)).VibrationalfrequenciescomputedinDFTcalcu-
lations are systematically high and a scaling factor is often
3.1 Theoretical Approach
invokedtobringcalculationandexperimentintoagreement.
AlargenumberofDFTcalculationsofPAHvibrationalfre- HereascalingfactorforthespecificsoloOOPmodewasem-
quencies have been reported. Attention has generally been ployed. For y = 1, 2 and 3 PAHs a scaling factor of 0.987
focused on neutral and singly ionised (i.e. radical cation) wasadoptedinthemodelling,determinedbycomparingthe
PAH molecules, with extension to hydrogenated, proto- high-resolutiongas-phaseexperimentalvalueforanthracene
nated,irregular and otherclosed-shell charged PAHs(Hud- of 876.7 cm−1 (Can´e et al. 1997) with the unscaled DFT
gins,Bauschlicher&Allamandola2001;Beegle,Wdowiak& result of 888.2 cm−1.
Harrison 2001; Pathak & Rastogi 2005, 2006; Bauschlicher, Thesecondpartofourstudyfocussedonlargecompact
Peeters&Allamandola2008,2009;Bauschlicheretal.2010; PAHs (see Fig.3(b) and Tab.1(b)). These molecules were
Ricks, Douberly & Duncan 2009; Hammonds, Candian & chosen to investigate whether the OOP frequency shares a
Sarre2011; Ricca,Bauschlicher &Allamandola 2011; Ricca similar mass-dependent behaviour as for low-medium mass
et al. 2012; Boersma et al. 2014; Candian, Sarre & Tielens PAHs. The 11.2µm band is generally attributed to large
2014).Theworkreportedhereisintwocloselyrelatedparts: neutral PAHs (Hony et al. 2001; Bauschlicher, Peeters &
First, we report the results of DFT calculations on a Allamandola 2008; Ricca et al. 2012), their compactness
set of medium-sized PAHs, inspired in part by the work of andhighsymmetrymakingthemoptimalcandidatestosur-
Pathak & Rastogi (2005) on a series of acenes up to hep- vive in harsh astronomical environments. The study was
tacene (see their fig. 7 which shows convergence of the solo again undertaken with B3LYP/6-31G*, using Gaussian 03
OOPwavelength at highmass). Wehaveundertakenasys- (Frisch et al. 2004). A scaling factor of 0.975 was used for
tematic investigation to explore how the frequency and in- these molecules, deduced by reference to the experimental
tensity of the out-of-plane (OOP) bending solo modes of gas-phase data for the solo OOP bending mode of ovalene
neutral PAHs vary with PAH size and shape. The calcula- (C H ) (Joblin et al. 1994).
32 14
4 A. Candian and P.J. Sarre
a) y=1 y=2 y=3
Table 1. Computed scaled DFT (B3LYP/6-31G*) C–H out-of-
plane(OOP)vibrationalwavenumbersfor(a)aceneswithx=3-
8,y=1andmulti-rowPAHswithx=3-7,y=2and3(sf=0.987,
x=3
see text), and for (b) large compact PAHs (sf=0.975, see text)
showninFig.3.
C14H10 C22H12 C32H14
x=4 (x,y) Molecule Wavenumber Wavelength Intensity
(cm−1) (µm) (kmmol−1)
C18H22 C28H14 C40H16 (a)
(3,1) C14H10 876.7 11.410 55.0
b) (4,1) C18H12 895.3 11.169 69.3
(5,1) C22H14 901.7 11.090 87.8
(6,1) C26H16 905.7 11.041 106.7
(7,1) C30H18 906.6 11.030 124.8
(8,1) C34H20 906.6 11.030 146.2
C42H16 C54H18
(3,2) C22H12 875.2 11.426 96.9
(4,2) C28H14 881.8 11.340 109.3
(5,2) C34H16 886.5 11.280 123.4
(6,2) C40H18 888.1 11.300 133.7
(7,2) C46H20 888.1 11.300 172.0
(3,3) C32H14 884.2 11.310 123.0
C66H20 C80H22 (4,3) C40H16 890.5 11.230 155.4
(5,3) C48H18 891.3 11.220 185.0
Figure 3. Molecular structures (a) for PAHs with x = 3-4 and
(6,3) C56H20 891.3 11.220 204.6
y = 1-3, where x is the number of six-membered rings in a row
(7,3) C64H22 891.3 11.220 231.8
and y isthe number of rows.For y = 3, x indicates the number
ofedgeringsinthe topandbottom rows.In(b)fourlargePAH (b)
structureswithD2h andD6h symmetryareshown. C32H14 877.0 11.403 120.3
C42H16 882.2 11.328 154.3
C54H18 885.0 11.300 190.6
Theuseofascalingfactorisnormalpracticewhencom- C66H20 887.9 11.262 203.61
paringlaboratoryandDFTresults.Typically,ascalingfac- C80H22 889.3 11.245 234.31
tor of 0.958 for B3LYP/4-31G is used for simplicity for the C96H24 891.1 11.222 265.16
entirespectrum,basedoncomparison withmatrix-isolation
data. However, it is known that this technique introduces
unpredictable shifts in the band positions (Langhoff 1996).
frequency on PAH mass is found in the computed data of
In contrast to previous studies, the scaling factor employed
Bauschlicher, Peeters & Allamandola (2008) who used the
inthisworkisreferencedtogas-phasedataandisspecificto
B3LYP functional and a (smaller) 4-31G basis set; the val-
the vibrational mode (solo OOP transitions of PAHs). For
ues for C H and C H are 11.061 and 10.959µm, re-
54 18 96 24
ouranalysis,thisispreferabletotheuseofagenericscaling
spectively.
factor. At the present time there is insufficient laboratory
Larger PAH molecules with N > 100 are needed
C
gas-phase data on a range of PAHs to evaluate the appli-
to determine the value at the asymptotic limit but this
cability of the same scaling factor for all PAHs. However,
wasbeyondourcomputationalcapacity.Henceafunctional
the use of the well characterised B3LYP/6-31G* and the
form was used to fit the available data (once scaled) from
mode-specific scaling factor should reduce the uncertainty
Tab.1(b) and so deduce the asymptotic wavelength limit
significantly. for the largest PAHs: ω = (b+a/N 2)−1, where ω is the
C
mode wavenumber and N the number of carbon atoms.
C
The parameters of the best fitting are a = 0.021 ±0.002
3.2 Results & Discussion
and the asymptotic value b = 11.2139 ± 0.0007µm (or
Tab.1 collects together the computed intensities and un- 891.75±0.06cm−1).Thus,theinferredasymptoticlimitfor
scaled vibrational wavenumbers of the studied molecules. large PAHs falls to shorter wavelength compared with low-
Fig.4showsthatfortheacenes(x= 3−8,y = 1)thewave- medium mass PAHs, i.e. PAHs with multiple rows with y
length decreases with increase in x (or number of carbon = 2and3asshowninFig.3(a).Thevalueof11.21µmfalls
atoms), converging towards a high-mass asymptotic value within the range of peak wavelengths (11.20 to 11.24µm)
of 11.03µm. A similar characteristic holds for zig-zag edge in class A objects (van Diedenhoven et al. 2004) and
11.2
moleculeswithtworows(stars)andthreerows(filledtrian- falls very close to the observed value of λ of 11.171µm
1/2
gles), but they reach thehigh-mass limiting value at longer discussed in Section 2.2(a).
wavelength(Fig.4,lowerpanel).Inallcases,thewavelength Key resultsfrom these calculations area) themore ex-
forthesoloOOPbendingmodemovestoshorterwavelength tended (acene) and larger PAH molecules have solo out-of-
asthenumberofcarbonatoms(i.e.themass)increases(see plane modes at the shortest wavelengths, b) the transition
Tab.1 (a) and (b)). A similar dependence of the CH OOP wavelengthsforacenesandforlargePAHsreachasymptotic
The 11.2µm emission of PAHs in astrophysical objects 5
bewritten:
n
hcω
U(T)= i
exp(hcω /k T)−1
X i B
i=1
where ω is the wavenumber of the ith vibrational mode
i
and n is the total number of modes of the molecule. The
PAH molecule cools through its various vibrational modes,
through a so-called radiative cascade. For the ith mode the
emission rate φ is given by:
i
A1,0
φ = i
i exp(hcω /k T)−1
i B
wheretheEinsteincoefficientsA1,0forspontaneousemission
i
canbecalculatedfromtheDFTtransitionintensities(Cook
& Saykally 1998).
The fractional energy emitted in the ith mode, corre-
sponding toa fall in internal energy δU, is:
φ ×ω
δE (T)= i i δU(T)
i n φ ×ω
i=1 i i
P
Figure 4. Upper panel: ISO-SWS spectrum of the 11.0 and Thetotalemittedenergyisobtainedbyintegrationover
11.2µmbandcomplexinOrionH2S1,anexampleofclassA11.2. the temperature range from Tp to 50 K, and weighted by
Lower panel: wavelength behaviour of the OOP bending transi- therate of photon absorption
tion with respect to number of carbon atoms for y = 1 (filled
circles - acenes), y = 2 (stars) and y = 3 (filled triangles) - see 13.6 Bdσ
R = ν νdν
Fig.3(a)andTab.1(a). abs Z hν
0
where ν is the frequency of the absorbed photon, σ is
ν
valuesathighmass,c)increasingthenumberofrows(larger thefrequency-dependentphoto-absorptioncross-sectionand
PAHs) results in a faster approach to the asymptotic limit 13.6 eV represents the high-energy cut-off in the radiation
than for the single-row acenes, d) the higher-mass acenes field.Foreachmoleculeσ wastakenfromtheFrench-Italian
ν
maycontributeto11.0µmemission.Thepresenceofahigh- database1 (Malloci, Joblin & Mulas 2007). For a molecule
massasymptoteforthewavelengthofthelargestPAHspro- (PAH1) for which there was no entry,the cross-section was
vides an attractive explanation for the steepness and wave- estimatedusingdataavailableforthemoleculeclosestinsize
lengthinvarianceoftheshort-wavelengthside(λ )among (PAH2), scaled by NPAH1/NPAH2 (Mulas et al. 2006). The
1/2 C C
classA objects.Inthefollowing sectionsweexplorethis excitationsourceisrepresentedbyadilutedPlanckfunction
11.2
furtherusing a detailed theoretical model. Bd (see Tab.2). At high photon energy, photoionisation of
ν
the neutral PAH can also be significant and leads to a re-
duction in the quantum yield for IR emission. To take this
process into account, we incorporated in our modelling the
4 EMISSION MODEL
energy-dependentphoto-yieldusingtheempirical lawgiven
In this section we describe how the DFT results for fre- byLePage,Snow&Bierbaum(2001)andionisationenergies
quencies and intensities are incorporated into a model for (IE) from the French-Italian database. When experimental
the AIB emission occurring in astrophysical environments. valueswerenotavailable,atheoreticalverticalIEwasused.
As far as we are aware this is the first attempt to include
mass-dependence of the PAH emission wavelength into a
modelandusing,whereavailable,referencetoexperimental 4.2 Experimental input
results. We have chosen to employ a model based on the
Joblinetal.1995studiedtheinfluenceoftemperatureonIR
thermalapproximation(asemployedbye.g.Pech,Joblin &
absorptionspectraofgas-phasePAHsinthelaboratoryand
Boissel 2002; Pathak & Rastogi 2008).
found a linear dependence on temperature for both band
position and band width, arising mostly from anharmonic
couplingbetweenmodes.Thefollowingrelationsforthefre-
4.1 Theoretical Approach
quencyω(T),andwidth∆ω(T),wereusedinthemodelling:
L´eger, d’Hendecourt & Defourneau (1989) proposed that
ω(T)=ω +∆ω +χ′T (1)
the thermal approximation can be used to describe the in- 0 RS
fraredcoolingofPAHswherethistreatmentassumesthata
and
molecule can be considered as a heat bath with an average
molecular energy U and temperature T. Following absorp- ∆ω(T)=∆ω(0)+χ′′T (2)
tionofaUVphoton,aPAHmoleculehasaninternalenergy
U(T ), where T is the(initial) peak temperature.
p p
Intheharmonicapproximation,theinternalenergycan 1 http://astrochemistry.oa-cagliari.inaf.it/database.
6 A. Candian and P.J. Sarre
Table 2.Physicalconditions forobjects considered inthe mod-
elling.Teff representstheeffectivetemperatureofthecentralstar
inK,Ltheluminosityinunitsofsolarluminosity(L⊙),Wdilthe
geometric dilution factor and D the distance inkpc. In the case
oftheHD44179,thetwocomponentsofthebinarystellarsystem
aretakenintoaccount.
Object OrionH2S1 NGC7027 HD44179
Class(a) A11.2 A(B)11.2 B11.2
Teff(K) 4·104b 1.6·105d 8250f 6·104f
L(L⊙) 1.35·107c 10e 6·103f 100f
Wdil 2.09·10−11 2.8·10−17 4.8·10−6 3.7·10−13
D(kpc) 0.45b 1e 0.71f
Figure5.EmissionprofilecomputedforC54H18exposedtostel-
References: (a) van Diedenhoven et al. 2004, (b) O’Dell 2001,
(c)Verstraeteetal.2001,(d)Beintemaetal.1996,(e)Bujarrabal lar radiation with Teff = 8,250 K (dotted line) and 160,000 K
(full line). The linewidthis taken to be constant with aFWHM
etal.2001, (f)Men’shchikovetal.2002. of5cm−1.
Table 3. Empirical coefficients for the temperature-dependent
wavenumberandlinewidthofthesoloOOPmode(seeequations
(1)and(2). (a) the peak wavelength is red-shifted and (b) the redward
sideextendstolongerwavelengthforaPAHwithahighini-
Large† Acenes‡ tial internal temperature (i.e. irradiation as in NGC 7027).
However,thisisnotinagreementwithobservation.Theob-
χ′ (cm−1/T) -0.0114 -0.0065
served peak wavelength in NGC 7027 is lower and the red
∆ωRS (cm−1) -12.91 -9.54 wing is no more extended than in HD 44179 (see Fig.6).
χ′′ (cm−1/T) 0.0157 – We also remark that a red tail originating from ‘hot-band’
∆ω(0)(cm−1) 0.54 – emission from higher vibrational levels is difficult to rec-
oncile with thepresence of Class A features (with a low
11.2
Note: †Measurements on neutral gas-phase ovalene in the 550- tail-to-topratio)inmanycompactandextendedHiiregions
820KrangeandinaNematrixat4K(Joblinetal.1994,1995; (van Diedenhovenet al. 2004).
Pech,Joblin&Boissel2002). Weconcludethatafactorotherthantheradiationtem-
‡Measurementsonneutralgas-phaseanthracene(Semmler,Yang perature is responsible for the change in 11.2µm profile
&Crawford1991; Califano1962; Can´eetal.1997)andinanAr between objects and, given the DFT results of Section 3.,
matrix at 10K (Hudgins & Sandford 1998). No information is
proposethatthedependenceoftheemission wavelength on
availableonthetemperaturedependenceofthelinewidth;avalue
PAH mass is the largest single factor in determining the
foranthracene inthegasphase(at370K)isknown(Can´eetal.
differences in the 11.2µm profiles between objects. This is
1997).
now explored through modelling of astronomical emission
profiles which includes the wavelength dependenceon PAH
where ∆ω = ω (0) − ω can be considered to be
RS L 0 mass.
an empirical red-shift (RS) between the calculated DFT
frequency (at zero Kelvin) ω(0) and the frequency ω (0),
L
at zero Kelvin inferred from the experimental (laboratory)
studies (Cook & Saykally 1998). Tab.3 collects the coef-
ficients for the solo out-of-plane mode. We consider ova- 4.4 Summary of calculations
lene and anthracene to be representative of large and small
The procedure to calculate the energy E(T) emitted in a
(acene) PAHmolecules, respectively.Inthecaseof ovalene,
band is described in Sec. 4.1. Each E(T) is then associated
χ′′ was derived after removing the rotational contribution
withaLorentzianprofilesothatthetotalenergyemittedin
(see Fig.8 of Pech, Joblin & Boissel 2002). For a molecule
thesolo out-of-plane bendingmode is described by:
such as ovalene and based on experiments in absorption,
it is expected that the emission will move to longer wave- (Γ/2)E (T)
E (ω)= α m
length(lowerω)asthecoolingcascadeoccurs,andthatthe solo m π((Γ/2)2+(ω−ω (T))2)
X X m
linewidth will increase. m T
where Γ = ∆ω (T) is the FWHM, α is a multiplica-
m m
tive coefficient and m is summed over the molecules con-
4.3 Single molecule calculation: influence of
sidered. This calculation is then weighted by R and a
temperature? abs
χ2−minimisation routine employed to determine the best
We consider here the emission profile resulting from the fit to the astronomical ISO spectra of the three sources -
cooling cascade for a single PAH molecule, circumcoronene Orion H2S1, NGC 7027 and HD 44179 (see Tab.2) - with
(C H , Fig.3 b), in radiation fields with T = 8,250 K thesmallestpossiblenumberofcontributingmolecules.The
54 18 eff
and 160,000 K corresponding to HD 44179 and NGC 7027, only variable in the χ2−minimisation is α which is the
m
respectively. The results are given in Fig.5 and show that numberof molecules of typem included in the fitting.
The 11.2µm emission of PAHs in astrophysical objects 7
5 ASTRONOMICAL PROFILE MODELLING
In this section we describe the results of modelling the
11.2µm band for three profile classes: (A , A(B) and
11.2 11.2
B ). It was found that only four very symmetrical solo-
11.2
containingmolecules(C H ,C H ,C H andC H ,
32 14 42 16 54 18 66 20
Tab.1 b) were needed to produce acceptable fits, the sole
variable in the χ2 optimisation being the relative propor-
tionsofthesePAHs(α )whicharetakentoberepresenta-
m
tive of the PAH mass distribution. However, we emphasise
thatthisdoesnotrepresentidentificationoftheseparticular
fourPAHs;rathertheresultsshowthatsolo-containingneu-
tral PAHsin this absolute and relative size range providea
goodfittothe11.2µmfeatureanditsprofilevariationwith
object. This aspect is discussed further in Section 6.1. Two
closely related models were developed.
5.1 Model 1: 11.2µm modelling using
temperature-dependent linewidths
Inthefirstapplicationoftheaboveapproach(short-dashed
line in Fig.6), the experimentally-based temperature-
dependence for the band frequency and width (Eq. 1. and
2. respectively - see Section 4.2) for ovalene were taken to
hold for the larger molecules in the set (i.e. independent
of PAH mass). However, as each molecule has a different
initial peak temperature (determined by the stellar SED)
and a different vibrational solo-OOP frequency accord-
ing to molecular size, the cooling cascade and resultant
emission profile necessarily differs in each case. A χ2
minimisation was undertaken with the only variable being
the relative adundance of the four PAHs. This model
provides a reasonable match with the peak wavelength and
long-wavelength tails of the bands, but it does not account
very well for the steep short-wavelength side seen in many
astronomical spectra includingOrion H2S1and NGC 7027.
This discrepancy falls in the part of the profile where
high-mass PAHs are expected to contribute most strongly
andliesneartotheasymptoticlimitdiscussedinSection3.2.
Considering the experimental observations for the
widths of the infrared active C–H stretch transitions in
naphthalene,pyreneandcoronene2 (Equation2),thenfora
Figure 6. Continuum subtracted ISO-SWS spectra of objects
giventemperaturethewidthofthebandisfoundtodecrease
of class A11.2 - Orion H2S1, A(B)11.2 - NGC 7027 and B11.2 -
withincreaseinPAHmass(seeTab.2andFig.4inJoblinet HD44179,theRedRectangle(greyline),superimposedwiththe
al.1995);forexampleat600Kthelinewidthvaluesfornaph- emission model results using (Model 1) temperature-dependent
thalene,pyreneandcoroneneare40,26and15cm−1,respec- ∆ω(T) (short dashed line) and (Model 2) molecule-specific con-
tively.Thesolo-OOPtransitionlinewidthbehavessimilarly; strainedwidths ∆ω (longdashedline)-seetext fordetails.The
at 370 K the experimental solo-OOP linewidths in absorp- lower panel shows the (scaled) wavelength behaviour of the solo
tion for anthracene (Can´e et al. 1997) and ovalene (Joblin, OOPmodeoflargePAHsfromTable.1b.
C., personal communication) are 25 cm−1 and 6 cm−1, re-
spectively. Additionally, as higher mass PAHs do not reach
5.2 Model 2: molecule-dependent
ashighaninternaltemperature–forthesameexcitingSED,
temperature-independent linewidths
high-mass PAHs have narrower absorption (and emission)
band widths than their lower mass counterparts. This as- AssumingthataLorentzianprofiledescribestheshortwave-
pect is addressed in Model 2. lengthsideofthe11.2µmbandforClassA andA(B)
11.2 11.2
objects,thenfromprofilefittingoftheshort-wavelengthpart
of the profile we obtain a Lorentzian peak wavelength of
11.198µm (or 893.02cm−1) and a FWHM of only 0.05µm
2 Ovalenewasnotconsideredbecausethelawwasdeducedfrom (or4cm−1).This FWHMrepresentstheupperlimit on the
onlytwoexperimental points. widthofasinglecontributiontotheshorterwavelengthside
8 A. Candian and P.J. Sarre
of the11.2µm band.A similar valuehas beensuggested by
Cami (2011). Using this information, Fig.6 shows the best
χ2− minimised fit with constrained FWHM values of 10,
7.5,5and4cm−1 forC H ,C H ,C H andC H ,
32 14 42 16 54 18 66 20
respectively. The value of 10 cm−1 was taken for ovalene
withreferencetothelaboratory absorption data(at600K)
and the 4 cm−1 value as constrained by the observational
data(seeaboveandSection5.1).Thefittothesteepshort-
wavelength side ofthe11.2µm band for theclass A and
11.2
A(B) objectsisimproved,whilethelong-wavelengthtail
11.2
does not change significantly. Thus an accurate description
of the shorter wavelength side of the11.2µm band requires
lower linewidths than experimentally found for theFWHM
ofe.g.ovalene.WealsonotetheRedRectangle,andinpart
NGC 7027, has a discrepancy in the 11.45-11.65µm region
in both models. Wereturn to this in Section 6.2.
5.3 Effect of SED on computed 11.2µm profiles
In section 4.3 it was shown that for a single PAH molecule,
C H ,thecalculatedemissionprofilewithalowT SED
54 18 eff
is narrower than for higher T . To explore the effect of
eff
the excitation SED on computed 11.2µm profiles, we have
takenthe(fixed)massdistributionwhichwasdeterminedfor
NGC7027usingtheSEDforNGC7027,andcalculatedthe
profileusingalowerT SED-thatoftheRedRectangle.
eff
The calculated result in Figure 7. (upperpanel, full line) is
qualitatively similar to the single-molecule calculation and
Figure 7. Upper Panel. Calculated results for the 11.2µm in
gives a very poor match to the astronomical spectrum for
thespectrumofNGC7027(grey)usingthemassdistributionin-
NGC 7027 when compared with Figure 6. middle panel,
ferredforthisobjectfromModel2andusingtheSEDfortheRed
Model 2. Similarly, taking the (fixed) mass distribution as Rectangle. Lower Panel. Calculated results for the astronomical
deduced for the Red Rectangle, using a high-temperature 11.2µmbandintheRedRectangle(grey)usingthemassdistri-
SED (that of NGC 7027) also yields a poor match (Figure bution inferredfor this object from Model 2 and usingthe SED
7.lowerpanel,fullline).Clearly theSEDusedinthecalcu- ofNGC7027.
lation plays a role in determining a computed 11.2µm pro-
filebuttheSEDisfixedforagivenobjectandtheobserved
at longer wavelength suggests that the PAH mass distribu-
profileisdeterminedprincipallybythesolo-containingPAH
tion is skewed towards lower masses than in class A ob-
11.2
mass distribution.
jects.TheclassA(B) objectNGC7027thenfallsbetween
11.2
the class A and B extremes with a broad spread of PAH
masses as suggested by the intermediate value of the mass
6 ANALYSIS AND DISCUSSION distribution indicator introduced above. Using Spitzer ob-
servationsofNGC7023,Boersma,Bregman&Allamandola
6.1 PAH mass distribution and the 11.2µm profile (2013) fittedthe PAHemission spectra as a function of off-
setfromthestarHD200775usingtheNASAAmesPAHIR
Taking the sum of the contributions of the two lower mass
PAHs(C H andC H )tothe11.2µmbandfitinModel SpectroscopicDatabase(PAHdb)(Bauschlicheretal.2010).
32 14 42 16
Theshapeofthe11.2µmfeatureevolvesfromclassA rel-
2, and similarly taking C H and C H as representa- 11.2
54 18 66 20 ativelynearthestar(c.20′′offset)towardsB asadenser
tiveofhighermassPAHs,anindicativelowmass:highmass 11.2
region isapproached at higher offset.It was concludedthat
abundance ratio can be determined with the break falling
atN ∼50.Usingtheχ2 fittedresults,thisratiois1.8:1for the overall PAH spectra result from approximately equal
C
proportions of large and small PAHs at Position I (a dense
OrionH2S1,2.4:1forNGC7027and3.7:1fortheRedRect-
region) with larger PAHs being more prominent in the dif-
angle.FromthisweinferthattheRedRectanglePAHpop-
fuse region (Position II). Our interpretation of the 11.2µm
ulationcompriseslowermassPAHsthanforNGC7027and
band shape is consistent with these results, though our ap-
OrionH2S1.Wededucethattheshapeandpeakwavelength
ofthe11.2µmfeaturecanbedescribedprincipallyinterms proach differs in that our inferred mass distributions hold
specifically for neutral solo-containing PAHs.
ofthePAHmassdistribution,wherehigh-massPAHsarere-
sponsible for thesteep short wavelength side. Thelow vari-
anceofλ andthesteepbluesideinA objectsariseas
1/2 11.2 6.2 Emission in the 11.4-11.7µm region
anaturalconsequenceoftheasymptoticlimitreachedbythe
solo OOP mode in high-mass PAHs. In class B objects The Red Rectangle and to a lesser extent Orion H2S1 and
11.2
such as the Red Rectangle, the less steep short-wavelength NGC7027,haveexcessemissionrelativetothemodelsinthe
side, themore extendedredward tail and aband maximum 11.4-11.7µmwavelengthregion.BasedontheresultsofDFT
The 11.2µm emission of PAHs in astrophysical objects 9
position for thesolo C-Hout-of-plane bendingmode(Hsin
the9,10positions)tolongerwavelength.Inamajorstudyof
infraredspectraofhydrogenatedPAHsinanargonmatrixit
was found that aromatic C-H stretching bands near 3.3µm
weakenandarereplaced withstrongeraliphaticbandsnear
3.4µm, and that aromatic C-H out-of-plane bending mode
bands in the 11-15µm region shift and weaken (Sandford,
Bernstein&Materese2013).However,veryfewPAHsinthe
sample set had solo-hydrogens. Wetentatively suggest that
a signal identified by Rosenberg et al. (2011) could be due
tosolo-containinghydrogenatedPAHmoleculesratherthan
‘VerySmallGrains’-VSGs(seetheirFig.6);furtherassess-
ment of this will be described elsewhere. Significantly, ob-
jectsclassifiedasA(B) andB ,showaliphaticbandsat
11.2 11.2
3.4 and 3.52µm (Geballe et al. 1985) as would be expected
to appear when PAH hydrogenation levels are high; these
bands appear in the experimental spectra of hydrogenated
anthracene,butemissioninthe6-9µmregionremainsweak
as for otherneutral PAHs.
6.3 The 11-15µm and wider spectral region
Themoleculesconsideredheregiveastrongcontributionto
theUIRbandsinthe11-15µmrange(Schutte,Tielens&Al-
lamandola 1993). Fig.9shows thefingerprint region for the
three prototype objects compared with the emission model
results. Due to the lack of T-dependent experimental data
fortheposition ofandwidthofthebandsinthefingerprint
region,asinglescalingfactorof0.979andafixedFWHMof
Figure 8. Experimental gas-phase absorption spectra 12 cm−1 were applied for all bands. To combine the fit for
(T∼ 500 K) of anthracene (C14H10, top panel), 1,2,3,4- the 11.0-11.2µm band region and the remaining bands in
tetrahydroanthracene(C14H14,middlepanel)and1,2,3,4,5,6,7,8- the fingerprint region, we assumed that the molecular con-
octahydroanthracene (C14H18, bottom panel). The data are tribution for the solo mode in a PAH can be modelled as a
taken from NIST MS Data Center / S. E. Stein (2011). As the Lorentzian function peaking at thescaled (sf=0.979) DFT
numberofattachedhydrogensincreases,thepeakpositionofthe frequency but with a FWHM of 10 cm−1. The predictions
soloC-Hout-of-planebendingmodemovestolongerwavelength.
for the bands in the fingerprint region are consistent with
theastronomical spectraof thethreeobjects, with nomore
thanasmallcontributiontothe12.7µmfeature.Themodel
calculations and thegas-phase experimental OOPvalue for slightly overestimates the flux of the 12.0µm band for the
anthracene of 11.4µm (at 373 K, see Fig.6), it is suggested RedRectangle,whichisgenerallyascribedtoduohydrogen
theexcessintheRedRectangleisduetoemission fromrel- modes (Hony et al. 2001). However, in SWS-ISO data, the
ativelylow-massPAHswhichwerenotincludedinthemod- regionaround12µmissensitivetothewayspectraarecom-
ellingofthe11.2µmfeaturepresentedhere.ThescaledDFT bined, thus introducing extra uncertainty of 20-30 percent
out-of-plane bending modes for anthracene C H (x = 3; (Hony et al. 2001). A further issue is placement of thecon-
14 10
y = 1) and anthanthrene C H (x = 3; y = 2) fall at tinuuminthesubtractionappliedtothespectra.Thelackof
22 12
11.4µm. This too is consistent with a PAH population of adetailed treatment ofanharmonicity (temperaturedepen-
lower mass for the Red Rectangle deduced separately in dence)mayalsoaffectthismodelledspectrum.Itisnotable
section 6.1. Noting the usual redward shift that occurs in thatthemodelbuiltontreatmentofthe11.2µmregiondoes
emission, these and similar molecules probably contribute not introduce features which are not present in astrophysi-
to emission in the 11.4-11.7µm region. cal spectra of the 11-15µm region; this is also the case for
A second possible contribution to the ‘excess’ could the 6-11µm region. For example, the strongest calculated
arisefromhydrogenatedPAHs.Additionofhydrogenatoms vibration of C H in the 6-9µm region has a strength of
54 18
toPAHmolecules (H-PAHs)perturbstheC-Hout-of-plane 50kmmol−1 (Candian2012) comparedwith191kmmol−1
bending mode frequency, thus affecting the peak position. for the solo OOP mode, i.e. an intensity ratio of 0.3. The
Fig.8 shows gas-phase absorption spectra in the 11.4µm effectoftheradiativecascadeduringthePAHemission will
region, recorded at ∼500 K (NIST MS Data Center / reducethis ratio even more. Also, the6-9µm region is gen-
S. E. Stein 2011) for the closely related molecules: an- erally attributed to ionised PAHs, which show very strong
thracene (C H ), 1,2,3,4-tetrahydroanthracene (C H ) C-C and C-H in plane stretching modes, compared to their
14 10 14 14
and 1,2,3,4,5,6,7,8-octahydroanthracene (C H ). Starting neutralcounterparts(Hudgins&Allamandola1999).Asfor
14 18
with anthracene (upper panel), increasing the number of the3.3µm band,it is known that DFT calculations overes-
hydrogen atoms (middle and lower panels) moves the peak timate the intensity of theC-H stretching modes (Langhoff
10 A. Candian and P.J. Sarre
feature. Inafew cases asomewhat higher11.0/11.2 ratio is
found: two Herbig Ae/Be stars, MWC 1080 (Sakon et al.
2007) and HD 37411(Boersma et al. 2008), in the Hii re-
gion IRAS 18434-0242 (Roelfsema et al. 1996) and in two
reflection nebulae, NGC 1333 SVS3 (Sloan et al. 1999) and
NGC 7023 (Werner et al. 2004b; Boersma, Bregman & Al-
lamandola 2013).
Emission features in the 11.0µm region have been de-
scribed as ‘blue outliers’ of the 11.2 µm band by Sloan et
al. (1999). On increasing distance from the hot star SVS3
it was found that a shorter wavelength part at ∼ 10.8 µm
disappeared first, whereas ∼ 11.0 µm emission was more
persistent. Using the results of theoretical calculations by
Langhoff (1996), Sloan etal. (1999) considered whetherthe
‘11.0 µm’ emission might be due to neutral acenes, such
as anthracene or pentacene, but following comparison with
IR matrix data they concluded that this was unlikely and
PAH cations were preferred as carriers. Hudgins & Alla-
mandola (1999) discussed this in some detail and extended
consideration across the 11-14 µm region. The idea of a
cationic origin gained support from DFT calculations on
large solo-containing PAHs (Bauschlicher, Peeters & Alla-
mandola 2008; Ricca et al. 2012) where the (scaled) solo
wavelengths for the cations were found to fall to wave-
lengthsshorterthanthatforneutrals.Werneretal.(2004b)
and Sakon et al. (2007) found that the c. 11.0 µm emis-
sion reduces in intensity moving away from the exciting
star in NGC 7023 and MWC 1080, respectively, a result
for NGC 7023 recently reinforced by Spitzer observations
(Boersma, Bregman & Allamandola 2013).
Themostcommonlydiscussedcarrierofthec.11.0µm
emission carrier is PAH cations. However, Povich et al.
(2007) observed a lack of variation in the shape and/or in-
tensityof the11.0 µm bandin thephotodissociation region
M17-SW, even where the level of the ionisation in the gas
varied with position. Moreover, in recent work on the evo-
lutionofthe11.2µm and11.0 µmfeatures SEoftheOrion
Bright Bar (Boersma, Rubin & Allamandola 2012), the in-
Figure 9. Emission model in the fingerprint region for the as- tegrated strength of the main 11.2 µm feature dropped by
tronomical objects as in Fig. 6. A scaling factor of 0.979 and a a factor of 5.7 between 2’.6 and 5’.7 whereas the 11.0µm
fixed FWHM of 12 cm−1 were applied. To combine the fit for featuredroppedbyafactorof2.7.Thisresultwasdescribed
the 11.0-11.2µm band complex and the remaining bands in the
as ‘counterintuitive’ in terms of the 11.0µm emission being
fingerprint region, the molecular contribution for the solo mode
dueto PAH cations but rationalised as being influenced by
inaPAHwasassumedtobeaLorentzianfunctionpeakingatthe
scaled(sf=0.979)DFTfrequencyandwithFWHMof10cm−1. thedegreeofhydrogenation.InarecentSpitzer studyofthe
mid-infrared structure of the massive star-formation region
W49A further puzzles have emerged; the 11.0/11.2 ratio is
1996),makingitdifficulttodirectlycompareourmodelwith foundtobeconstantacrossthewholeregionandwithavery
theastronomical spectra. low value of ∼0.01 (Stock et al. 2014). The ratio is more
commonly intherange0.02-0.2 asdiscussed byStock etal.
(2014). In arecent studyfittingthespectrumof NGC 7023
6.4 Emission in the 11.0µm region withtheNASAAMESPAHdatabase,Boersma,Bregman&
Allamandola (2013) noted that the 11.0 µm band could be
6.4.1 Emission in the 11.0µm region - a summary
reproduced by ionised nitrogen-containing PAHs. In sum-
Given the proximity of 11.0 µm emission to the 11.2 µm mary there are many questions as to the origin(s) of fea-
band, we review here whether there is significant evidence ture(s) in the11.0 µm region.
forarelatedorigin.Roche,Aitken&Smith(1991)firstiden-
tified a faint feature on the short-wavelength side of the
6.4.2 Red Rectangle emission in the 11.0µm region
11.2µmbandwhichappearsquiteprominentlyinspectraof
anumberofobjects(Honyetal.2001).Themostcommonly ItwasinferredearlierthattheRedRectanglehasapopula-
occurringbandhasanapproximatelysymmetricshapecen- tionoflower-massPAHsthanforOrionH2S1andNGC7027
tered at 11.05 µm, a rather narrow FWHM of 0.1 µm and (Section6.1),soitisofinteresttoexplorewhetherlow-mass
anintensitywhichrangesbetween2and10%ofthe11.2µm PAHs including acenes might contribute to the 11.0µm re-
