A Case Against Spinning PAHs as the Source of the Anomalous Microwave Emission
DDraft version May 6, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
A CASE AGAINST SPINNING PAHS AS THE SOURCE OF THE ANOMALOUS MICROWAVE EMISSION
Brandon S. Hensley
Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA andJet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
B. T. Draine
Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
Aaron M. Meisner
Berkeley Center for Cosmological Physics andLawrence Berkeley National Laboratory, Berkeley, CA 94720, USA (Dated: May 6, 2018)
Draft version May 6, 2018
ABSTRACTWe employ an all-sky map of the anomalous microwave emission (AME) produced by componentseparation of the microwave sky to study correlations between the AME and Galactic dust properties.We find that while the AME is highly correlated with all tracers of dust emission, the best predictorof the AME strength is the dust radiance. Fluctuations in the AME intensity per dust radiance areuncorrelated with fluctuations in the emission from polycyclic aromatic hydrocarbons (PAHs), castingdoubt on the association between AME and PAHs. The PAH abundance is strongly correlated withthe dust optical depth and dust radiance, consistent with PAH destruction in low density regions.We find that the AME intensity increases with increasing radiation field strength, at variance withpredictions from the spinning dust hypothesis. Finally, the temperature-dependence of the AME perdust radiance disfavors the interpretation of the AME as thermal emission. A reconsideration of otherAME carriers, such as ultrasmall silicates, and other emission mechanisms, such as magnetic dipoleemission, is warranted. INTRODUCTION
High sensitivity, full-sky observations of the far-infrared and microwave sky from WMAP and
Planck have pushed studies of the Cosmic Microwave Back-ground (CMB) to a regime in which contamination fromGalactic foregrounds has become a key uncertainty inthe analysis. Understanding the physical nature of theforeground components and producing better models ofeach are essential for mitigating this uncertainty.The anomalous microwave emission (AME) is perhapsthe least well-understood of the foreground components.Discovered as a dust-correlated emission excess peak-ing near 30 GHz (Kogut et al. 1996; de Oliveira-Costaet al. 1997; Leitch et al. 1997), AME is often ascribedto electric dipole emission from rapidly rotating ultra-small dust grains (Draine & Lazarian 1998a,b; Hoanget al. 2010; Ysard & Verstraete 2010; Silsbee et al. 2011),i.e. “spinning dust emission.” Empirically, this emis-sion component peaks between ∼
20 and 50 GHz (e.g.Planck Collaboration et al. 2014b) and has an emissivityper H of ∼ × − Jy sr − cm H − at 30 GHz (Dobleret al. 2009; Tibbs et al. 2010, 2011; Planck Collabora-tion et al. 2014b,c). Polycyclic aromatic hydrocarbons(PAHs), which give rise to prominent emission features inthe infrared, are considered natural carriers of the AMEdue to their small size and apparent abundance (Draine& Lazarian 1998a).Theoretical spinning dust SED templates based on a [email protected] PAH size distribution that reproduces the infrared emis-sion features have been successful in fitting observationsof the AME both in the Galaxy (Miville-Deschˆenes et al.2008; Hoang et al. 2011; Planck Collaboration et al.2015b) and in the sole extragalactic AME detection inthe star-forming galaxy NGC 6946 (Murphy et al. 2010;Scaife et al. 2010; Hensley et al. 2015).The AME has been observed to correlate well withthe PAH emission features in the infrared. Ysard et al.(2010) found that, over the full sky, the AME was morecorrelated with emission at 12 µ m than with 100 µ m.Likewise, the AME in the dark cloud LDN 1622 was bet-ter correlated with the 12 and 25 µ m emission than witheither the 60 or 100 µ m emission (Casassus et al. 2006).However, studying the AME in a sample of 98 Galacticclouds, Planck Collaboration et al. (2014b) found no sig-nificant differences between the 12, 25, 60, and 100 µ memission in their correlation with the AME. Analysis ofboth the Perseus molecular cloud (Tibbs et al. 2011) andthe H II region RCW175 found no compelling link be-tween the PAH abundance and the AME. Likewise, thelink between the AME and PAH abundance determinedfrom dust model fitting has proven tenuous in NGC 6946(Hensley et al. 2015).In addition to spinning ultrasmall grains, grains con-taining ferro- or ferrimagnetic materials are also pre-dicted to radiate strongly in the microwave and may con-tribute to the AME (Draine & Lazarian 1999; Draine &Hensley 2013). Draine & Lazarian (1999) argued that thespinning dust and magnetic emission mechanisms couldbe distinguished by observing the AME in dense regions a r X i v : . [ a s t r o - ph . GA ] O c t where PAHs would likely be depleted due to coagulation.If the AME per dust mass is constant across both denseand diffuse regions, then spinning dust emission wouldbe disfavored.In this work, we test the spinning PAH hypothesisusing new full-sky observations of the infrared and mi-crowave sky. Planck Collaboration et al. (2015b) decom-posed the Planck sky into foreground components mak-ing use of both the 9-year WMAP data and the Haslam408 MHz survey. The combination of these data allowedthe low frequency foreground components – primarilysynchrotron, free-free, and AME – to be disentangled,producing a full-sky map of the AME.All-sky WISE observations at 12 µ m, a tracer of PAHemission, have natural synergy with the AME map, al-lowing us to test at high significance the link betweenthe AME and PAHs. Additionally, all-sky dust model-ing by Planck Collaboration et al. (2014a) permits deeperexploration into the dust and environmental parametersthat influence the strength of the AME.This paper is organized as follows: in Section 2 we sum-marize the data sets used in our analysis; in Section 3 wedescribe the correlations predicted by our current under-standing of the spinning PAH hypothesis; in Section 4we present the relationships between environmental anddust properties and AME as derived from the data; inSection 5 we discuss the implications of these results onspinning dust theory in particular and AME modeling ingeneral; and we summarize our principal conclusions inSection 6. DATA
Planck Foreground Separation Maps
Combining full-mission all-sky
Planck observations(Planck Collaboration et al. 2015a) with the 9-yr.WMAP data (Bennett et al. 2013) and the Haslam408 MHz survey (Haslam et al. 1982), Planck Col-laboration et al. (2015b) used data from 32 differentdetectors spanning a range of 408 MHz to 857 GHzin frequency to perform foreground component separa-tion within the Bayesian
Commander analysis framework(Eriksen et al. 2004, 2006, 2008). They constructedtheoretically-motivated models for the frequency depen-dence of each component – including the CMB, syn-chrotron, free-free, thermal dust, and AME – while mini-mizing the number of free parameters needed and simul-taneously fitting for calibration offsets. Using a Gibbssampling algorithm, they determined the best-fit valuesfor each model parameter on a pixel-by-pixel basis.In this work, we focus primarily upon the resulting mapof the AME. This component was modeled by the sumof two spinning dust spectra with fixed spectral shape asdetermined by the
SpDust code (Ali-Ha¨ımoud et al. 2009;Silsbee et al. 2011), but differing amplitudes and peakfrequencies. One of the spectra was required to have aspatially fixed peak frequency, fit to be 33.35 GHz, whilethe other peak frequency was allowed to freely vary frompixel to pixel. Thus, the data products consist of anamplitude for each AME component, the peak frequencyof the spatially varying component, and the uncertaintyof each for every pixel on the sky.To facilitate comparisons with the literature, we cal-culate the sum of the two components at 30 GHz. We also calculate the uncertainty in this quantity assumingGaussian errors and ignoring the uncertainty on the peakfrequency of both components.In addition to the AME map, we employ the param-eters from the thermal dust fit to compute the 353 GHzdust optical depth τ . Although this parameter wasalso an explicit data product of the full-sky modifiedblackbody fits performed by Planck Collaboration et al.(2014a), we prefer to use the results from Planck Col-laboration et al. (2015b) for several reasons. First, thefits were performed on more data and with more de-tailed treatment of calibration and bandpass uncertain-ties. Second, the fits were performed at 1 ◦ versus 5 (cid:48) resolution, mitigating the effects of cosmic infrared back-ground (CIB) anisotropies. Finally, a single-temperaturemodified blackbody model has been demonstrated to beinadequate to fit the FIR dust emission from Planck
HFI frequencies to 100 µ m (Meisner & Finkbeiner 2015;Planck Collaboration et al. 2015b). Thus, we prefer touse a τ derived from fits to the Rayleigh-Jeans portionof the dust emission spectrum only. We find τ derivedin this way to be on average 10% lower than that reportedby Planck Collaboration et al. (2014a).Additionally we employ the parameter maps that char-acterize the free-free, synchrotron, and CO emission. Asfree-free and CO emission cannot be fit reliably in regionsof low surface brightness, we exclude all pixels with emis-sion measure of 0.1 cm − pc or less and with no fit COemission when analyzing the former and latter, respec-tively.The Commander parameter maps have a resolution of1 ◦ (FWHM) and are pixellated with HEALPix (G´orskiet al. 2005) resolution of N side = 256. For our analysis,we downgrade these maps to N side = 128, correspondingto pixels of about 27’.5 on a side. Dust Parameter Maps from Modified BlackbodyFitting
A key limitation of the thermal dust fits performed byPlanck Collaboration et al. (2015b) is the omission ofany data at higher frequency than the
Planck
857 GHzband. Without information on the Wien side of the dustemission spectrum, it is difficult to constrain the dusttemperature and luminosity.Thus, we employ the full-sky parameter maps of PlanckCollaboration et al. (2014a), who fit a modified black-body model of the dust emission to the 2013
Planck µ m data from IRAS.For the latter, they employ both the reprocessed IRISmap (Miville-Deschˆenes & Lagache 2005) as well as themap of Schlegel et al. (1998). The fits were performedat 5 (cid:48) resolution and yielded an estimate of τ , the dustradiance R ≡ (cid:82) I dust ν d ν , the dust temperature T d , andthe dust spectral index β ≡ d ln τ / d ln ν for each pixel.We employ R , T d , and β from these fits in our analysis,but use τ from the Commander fits as discussed above.We use the parameter map pixellated with
HEALPix resolution of N side = 2048, then smooth with a Gaus-sian beam of FWHM 1 ◦ and downgrade the resolutionto N side = 128. WISE 12 µ m Map WISE observed the full sky in four infrared bands– 3.4, 4.6, 12, and 22 µ m (Wright et al. 2010). The12 µ m channel ( W µ m, capturesthe strongest of the infrared emission features associatedwith PAHs and thus traces the population of small dustgrains. The full-sky WISE 12 µ m imaging has been re-processed by Meisner & Finkbeiner (2014) to isolate dif-fuse emission from Galactic dust at 15” resolution.Because interplanetary dust models are insufficientlyaccurate to remove zodiacal light from the W P lanck
857 GHz map, essentially replacing 12 µ mmodes on scales larger than 2 ◦ with a rescaling of857 GHz dust emission. Since we wish to study real fluc-tuations in PAH emission per FIR dust radiance on 1 ◦ scales, this zero level procedure has the potential to ar-tificially suppress part of our signal.Our analysis relies on quantifying the PAH abundancein a given pixel through the ratio of the W R , a quantity we designate f PAH (see Section 3.2). Computing f PAH via simple division ofthe Meisner & Finkbeiner (2014) W R is prob-lematic because this method is sensitive to the P lanck
857 GHz-based 12 µ m large-scale zero level.We therefore employ an alternative approach to com-pute f PAH , leveraging the excellent angular resolution ofWISE and
P lanck to render the large-scale zero levelof the W N side = 128 HealPix pixels of ∼ ◦ on a side. Todetermine f PAH , we subdivide each of these pixels intoapproximately 120 subpixels of 2 . (cid:48) on a side and thenderive the best-fit correlation slope of W R across the 120 subpixels. To infer the optimal f PAH value within a single
HEALPix pixel, we employ themodel ( νI ν ) µm i = R i × f PAH + C , (1)where, in the i th subpixel, ( νI ν ) µm i is the W (cid:48) resolution and high-pass filtered at 15 (cid:48) ,and R i is the P lanck radiance map (Planck Collabora-tion et al. 2014a) high-pass filtered at 15 (cid:48) . The high-pass filtering serves to remove large-scale modes fromthe comparison, and the offset C is a nuisance parame-ter. Because linear regression can become sensitive to thechoice of fitting methodology in the limit of poor signal-to-noise (see, e.g., Hogg et al. 2010), we restrict analysesof these f PAH correlation slopes to
HEALPix pixels withvery strong linear correlation between ( νI ν ) µm and R ,using a threshold of Pearson r > f PAH .The f PAH map derived in this way is qualitatively simi-lar to that obtained by simply dividing the 12 µ m map by R , but displays a factor of ∼ f P AH val-ues. Our basic conclusions are unaffected by the choiceof f PAH map, and we employ the map obtained withEquation 1 as the default.Only in the case of Figure 7 do we require a map ofthe 12 µ m emission itself, rather than f PAH . For thispurpose, we generated a custom version of the Meisner& Finkbeiner (2014) W ◦ with a rescaling based on the P lanck
857 GHz emission. This better preserves real fluctuationsin 12 µ m emission per R on (cid:39) ◦ scales.Both our final maps of WISE 12 µ m and f PAH are pixel- lated with
HEALPix resolution of N side = 128.
IRAS 100 µ m Map As our analysis is performed on scales of (cid:39) ◦ , wefollow Planck Collaboration et al. (2014a) in employingthe IRAS 100 µ m map of Schlegel et al. (1998). We donot however employ the reprocessed IRIS maps (Miville-Deschˆenes & Lagache 2005) on small scales as was done inPlanck Collaboration et al. (2014a). We note that usingthe IRIS map instead in our analysis somewhat degradesthe tightness of the correlation between the 100 µ m emis-sion and the AME, particularly in regions of low surfacebrightness. The effect is small and has limited impact onour conclusions.We smooth the IRAS 100 µ m map of Schlegel et al.(1998) to a FWHM of 1 ◦ and pixellate with N side = 128. Masks
Zodiacal light in the ecliptic plane can dominate thesignal from PAH emission at 12 µ m even on small an-gular scales, thereby biasing our primary PAH tracer.We therefore exclude all pixels within five degrees of theecliptic plane (8.7% of the sky) to mitigate this effect.Likewise, artifacts from moon contamination are alsopresent in the 12 µ m map. We therefore mask all pixelsflagged for moon contamination by Meisner & Finkbeiner(2014), totaling 16% of the sky. Since our analysis re-quires that both R and I µ m ν measure true dust emis-sion, and since these quantities will closely correlatewhen they do, we require every pixel in our analysis tohave a Pearson r > . R and I µ m ν acrossits 2.5’ subpixels as described in Section 2.3. This cutalone eliminates 42% of the sky, mostly at low surfacebrightness and high Galactic latitude where WISE lackssufficient sensitivity to measure diffuse dust emission.Though nominally a full-sky mission, IRAS did nothave 100% sky coverage. We therefore mask the regionsIRAS did not observe (Wheelock et al. 1994), totaling2% of the sky, as the 100 µ m emission in these regionsestimated using lower resolution DIRBE data (Schlegelet al. 1998) may not be reliable.To mitigate the effects of point sources, we employthe Planck point source masks in intensity at each HFI and LFI band (Planck Collaboration et al. 2015a).These masks eliminate point sources with signal-to-noisegreater than 5 at resolution N side = 2048. We downgradethese masks to N side = 128 by rejecting any pixel con-taining a point source, resulting in 39% of the sky beingmasked due to point sources.Finally, we use the Planck
Galactic plane mask cov-ering 1% of the sky based on the 353 GHz HFI data (Planck Collaboration et al. 2015a). This eliminates theregions in the Galactic plane with the most complicatedand highest intensity emission and where the relativelysimple foreground models are most likely to break down.After applying the masks described above, 51,579 pix-els covering 26% of the sky remain. The total mask is http://irsa.ipac.caltech.edu/data/Planck/release_2/ancillary-data/masks/HFI_Mask_PointSrc_2048_R2.00.fits http://irsa.ipac.caltech.edu/data/Planck/release_2/ancillary-data/masks/LFI_Mask_PointSrc_2048_R2.00.fits http://irsa.ipac.caltech.edu/data/Planck/release_2/ancillary-data/masks/HFI_Mask_GalPlane-apo0_2048_R2.00.fits Fig. 1.—
Top : The Mollweide projection full-sky map of R as derived by Planck Collaboration et al. (2014a) with the mask described inSection 2.5 overlaid in gray. The unmasked area comprises 26% of the sky. Bottom : The full-sky map of f PAH ≡ ( νI ν ) µ m / R with thesame mask overlaid. illustrated in Figure 1 on the full-sky R map. This com-bination of masks is used in all analysis, although wediscuss the sensitivity of our results to various additionalmasking (e.g. masking the Galactic plane) in Section 4.6. TESTS OF AME THEORY
AME Theory
The AME has been suggested to be electric dipoleemission from ultrasmall, rapidly-rotating grains thathave been torqued up through interactions with both thegas and radiation field (Draine & Lazarian 1998b; Hoanget al. 2010; Ysard & Verstraete 2010; Silsbee et al. 2011).The observed peak frequency of the emission requiresthat the grains be small (radius a (cid:46)
10 ˚A), leading to anatural association with the PAHs that produce emissionfeatures in the infrared.If so, we might expect a linear relation between thetotal PAH surface density Σ
PAH and the AME intensity.Adopting an empirical 30 GHz spinning dust emissivityof 3 × − Jy sr − cm H − , and assuming this corre-sponds to typical Galactic values of M d /M H = 0 .
01 andΣ
PAH / Σ d = 0 .
046 (Draine & Li 2007), we would expect I AME ν,
30 GHz = 0 . (cid:18) Σ PAH M (cid:12) kpc − (cid:19) Jy sr − . (2)In the context of the spinning dust model, environmen-tal factors can influence both the peak frequency of theemission and the emissivity itself. The importance of col-lisions with ions depends on the fractional ionization andthe charge state of the ultrasmall grains. In regions withvery intense radiation fields, drag forces from IR photonemission become important. Damping by the rotationalemission generally causes the ultrasmall grains to havesub-LTE rotation rates.The electric dipole moment distribution of the dustpopulation will also strongly influence the emissivity,though we have no a priori estimates of the systematicvariations of this quantity from one region to another.We expect spinning dust emission to be relatively in-sensitive to the strength of the radiation field, whichis an important source of excitation only in fairly ex-treme environments such as reflection nebulae and photo-dissociation regions (PDRs). However, the emissivityper unit gas mass should increase with increasing localgas density, which may correlate with the radiation fieldstrength.The impact of these factors on the 30 GHz AME fluxdensity was estimated by Draine & Lazarian (1998b) tobe only about a factor of two between the Cold Neu-tral Medium, Warm Neutral Medium, and Warm Ion-ized Medium environments. In our study, these effectsare mitigated by the low angular resolution of the maps,which are likely to be sampling dust emission from dif-ferent environments within each pixel.These caveats notwithstanding, the spinning PAHmodel for the AME predicts:1. A linear correlation of the PAH surface density andthe AME flux density at 30 GHz.2. Relatively constant AME per PAH surface densityover a range of radiation field strengths. Data Model τ is equal to the product of the dust mass columndensity and the dust opacity at 353 GHz. Because dustgrains are much smaller than the wavelength of light atthis frequency, the dust opacity is insensitive to the sizedistribution of the grains and τ is thus a reliable in-dicator of the total dust column density. There is evi-dence, however, that the dust optical properties changesomewhat in different environments (Planck Collabora-tion et al. 2014d).The dust radiance R is the frequency-integrated dustintensity. R is estimated using the best-fit single temper-ature modified blackbody with τ ν ∝ ν β , and is a tracerof both the dust column density and the strength of theradiation field heating the dust.Finally, the 12 µ m flux density is effectively a measureof the total power emitted by PAHs, i.e., the starlightpower absorbed by PAHs. Thus, the ratio of the 12 µ memission to the dust radiance is a proxy for the fractionof dust in PAHs (see Equation 1). The product f PAH τ is then a proxy for the PAH column density. It is thisquantity which the spinning dust model predicts to bethe most accurate predictor of the strength of the AME.We assume that τ , f PAH τ , R , I µ m ν , and I µ m ν correlate with the AME intensity in a linear way, i.e., foreach pixel i and each observable A i , the AME intensity inthat pixel is given simply by α i A i where α i is a constantto be determined.To identify the physical quantity which is the best pre-dictor of the AME intensity, we wish to quantify the in-trinsic dispersion in α i across all pixels. We assume thateach pixel samples a Gaussian distribution with mean α and standard deviation σ α .The likelihood of this model given the data over allpixels is: L ∝ (cid:89) i (cid:113) σ I,i + ( A i σ α ) × exp (cid:34) − (cid:0) I AME ν,
30 GHz ,i − αA i (cid:1) σ I,i + ( A i σ α ) (cid:35) , (3)where σ I,i is the uncertainty on I AME ν,
30 GHz ,i . We thusseek the maximum likelihood values of α and σ α for eachobservable A . In practice, we employ the emcee Markovchain Monte Carlo code (Foreman-Mackey et al. 2013)to derive the best fit values and confidence intervals foreach parameter assuming uninformative priors.If there are zero point errors in any of the maps usedin this analysis, then I AME ν,
30 GHz = αA + b is a more ap-propriate functional form for the relationship, where b isa parameter to be fit. We find that the introduction ofan intercept has little impact on the results, such as theordering of the σ α /α , or the value of α . RESULTS
Correlation with PAH Abundance
We test the predictions of the spinning PAH hypoth-esis laid out in Section 3.1 by relating the observationaldata to physical properties of the dust through the modeldescribed in Section 3.2.In Figure 2 we plot the AME flux density at 30 GHzagainst τ , f PAH τ , the dust radiance R , and the100 µ m flux density I µ m ν . All four correlate highly Fig. 2.—
The 30 GHz AME intensity is plotted against (a) τ , (b) f PAH τ , (c) R , and (d) I µ m ν . We divide the plot area intohexagons of equal area in log-space and color each according to the number of pixels that fall within that hexagon. Each panel has thesame logarithmic area allowing for straightforward comparisons between panels. In doing this, we have restricted the range of each plot toexclude some outlying points. In each panel we also plot (solid blue) the line with slope equal to the best-fit value of α . All four quantitiesare excellent tracers of the AME, but it is clear that R traces the AME with the greatest fidelity and least dispersion. TABLE 1Correlation Analysis I AME ν,
30 GHz = αAA α ± σ α σ α /α σ A /A (0 . R ± − sr − MJy sr − I µ m ν (7 . ± . × − I µ m ν (2 . ± . × − τ ±
72 MJy sr − f PAH τ ±
487 MJy sr − Note . — α and σ α are the best fit values ob-tained from Equation 3 for each observable A such that I AME ν,
30 GHz = αA . The formal uncertainties on α and σ α are less than the quoted accuracy in the table, generallyof order 0.1%. σ A /A (0 .
2) denotes the value of σ A /A such that σ α /α = 0 .
2, indicating the level of observa-tional uncertainty needed in A to produce a relationshipwith I AME ν,
30 GHz comparably tight as that observed with R . with AME as expected, and we present the fit slope ofthe relation with each in Table 1. The tightness of eachcorrelation is indicated by σ α /α , with R having the tight-est correlation (see Figure 2c).If the AME arises from spinning PAHs, we would ex-pect the emission to correlate better with f PAH τ than τ . While it is clear that both are good tracers of AME, f PAH τ has a larger dispersion about the best-fit rela-tion than τ . Maximizing Equation 3, A = τ yieldsa relation with σ α /α = 0 .
33 while A = f PAH τ yields σ α /α = 0 .
43 (see Table 1). Thus, f PAH does not appearto contain additional information about the strength ofthe AME not already present in τ .The spinning PAH model predicts that variations inthe AME intensity per unit dust mass should arise fromvariations in the abundance of small grains. Therefore,as a second test of the link between the AME and PAHs,we look for correlations between f PAH and the AME per τ .In Figure 3a we plot the AME intensity normalized by ατ against f PAH , but we find no evidence for the ex-pected positive correlation. We quantify this with theSpearman rank correlation coefficient r s which, unlikethe Pearson correlation coefficient, does not assume afunctional form for the relationship between the two vari-ables. We find r s = − .
15, suggesting anti -correlation.Similarly, quantifying the correlation between f PAH and the AME intensity normalized instead by α R (seeFigure 3b) yields r s = − .
02, suggesting that f PAH car-ries no information on the AME intensity not alreadypresent in the dust radiance.We note that f PAH is itself correlated with both τ Fig. 3.— f PAH is plotted against the AME intensity normalized by (a) ατ and (b) α R . Here and in subsequent plots, the isodensitycontours corresponding to 25, 50, and 75% of the pixels enclosed are plotted in green. There is no apparent correlation between f PAH andthe AME, at variance with the spinning PAH hypothesis. and R as demonstrated in Figure 4. f PAH (measured on ∼ ◦ scales) varies from ∼ . − .
30 over most of theunmasked sky, so that variations in the PAH abundancemight have been expected to account for a factor of ∼ . R with f PAH .The observed strong correlation between f PAH and τ is evidence for PAH destruction in the diffuse ISM (low τ ). Depletion of PAHs by a factor of ∼ α tofree-free emission (Dong & Draine 2011) and is roughlyconsistent with the range of f PAH we observe.A study of the H α -correlated AME by Dobler et al.(2009) found the AME to be a factor of ∼ ∼ f PAH and τ also sheds lighton the apparent negative correlation observed between f PAH and I AME ν /τ in Figure 3a. Figures 2a and 5cdemonstrate that ατ tends to underpredict the trueAME intensity at low values of τ and to overpredict athigh values. Since f PAH is positively correlated with τ ,it is not surprising that assuming a linear relationshipbetween the AME and f PAH τ only exacerbates thosediscrepancies. Correlation with the Radiation Field
Figure 2 and Table 1 also indicate the surprising re-sult that the AME is more tightly correlated with R than τ . We would expect R and τ to be relatedthrough the strength of the radiation field– a fixed quan-tity of dust will radiate more when exposed to more ra-diation. The most straightforward conclusion is that theAME is enhanced by a stronger radiation field, whichruns counter to the predictions of the spinning dust hy-pothesis (Ali-Ha¨ımoud et al. 2009; Ysard & Verstraete2010).A positive correlation between the radiation fieldstrength and the AME intensity has been noted in boththe Perseus molecular cloud (Tibbs et al. 2011) and theH II region RCW175 (Tibbs et al. 2012b). This trendwas also noted by Planck Collaboration et al. (2014b),who attribute the correlation to a positive correlationbetween the radiation field and the local gas density.The relationship between the AME/ R and T d , illus-trated in 5a, is best-fit by a power-law of index -0.97.If the AME were thermal emission in the Rayleigh-Jeanslimit, we would expect I AME ν to scale linearly with T d , i.e I AME ν,
30 GHz ∝ τ T d . Since R ∝ T βd if τ ν ∝ ν β , I AME ν / R should therefore scale as T − β − d ≈ T − . d if the AME isthermal emission and β ≈ .
65. Fitting the data with apower T − . d yields a substantially worse χ (10.2 vs.4.6). The data suggest then that the AME is nonthermalemission, unless the dust opacity at 30 GHz has a steeptemperature dependence (e.g. τ /τ ∝ T . d , where τ is the dust optical depth at 30 GHz.). We caution thatsystematic effects arising from fitting a single- T d mod-ified blackbody to the thermal dust emission may alsoalter the correlation with T d and we thus cannot rule outa thermal emission mechanism completely based uponthese data alone.If the fit AME component is contaminated with emis-sion from other low-frequency foregrounds, then this mayalso induce correlations with T d . Indeed, Figure 6 re-veals some coherent large-scale structures in the map ofAME/ R that are likely related to strong synchrotronemission (see Planck Collaboration et al. 2015b, Fig- Fig. 4.—
Plotting f PAH against both (a) τ and (b) R , it is clear that a strong positive correlation is present with both, consistent withdepletion of PAHs in the diffuse ISM. The majority of the pixels have 0 . < f PAH < .
30, suggesting that fluctuations in PAH abundancecould account for a scatter of a factor of at most ∼ . Fig. 5.—
The 30 GHz AME intensity normalized by α R is plotted against (a) T d and (b) β determined by modified blackbody fits to thedust SED (Planck Collaboration et al. 2014a), and against τ determined from component separation (Planck Collaboration et al. 2015b)in panel (c). Since PAHs are depleted in dense regions, the spinning PAH hypothesis predicts that the AME per R should be smaller indenser regions. These regions are likely to have more cold dust and thus a smaller β , but no correlation is observed between β or τ and the AME intensity per R . The data do suggest a possible correlation with T d . We find a best-fit power-law of T − . d (blue solid)and plot also the best fit relation assuming the AME is thermal emission with τ ∝ τ , i.e. I AME ν ∝ τ T d , hence I AME ν /R ∝ T − . d (black dashed). The latter relationship is disfavored relative to the former ( χ = 10 . T d and β determined by Planck Collaboration et al. (2015b). Fig. 6.—
The Mollweide projection full-sky map of the 30 GHz AME intensity normalized by α R . Although some large-scale featuresassociated with strong synchrotron emission are present, overall the map has little correlation with the synchrotron intensity ( r s = 0 . Fermi bubbles (Su et al. 2010).We discuss this possibility further in Section 5, thoughaside from a few clear structures, contamination appearsto be minimal.For pixels containing regions with both high and lowradiation intensities, fitting the λ ≥ µ m emission bya single-temperature modified blackbody will lead to sys-tematic errors, tending to overestimate T d and underes-timate both β and τ . Thus, if the correlation betweenthe AME and the dust radiance is driven by the corre-lation between the radiation field intensity and the localgas density, we might expect the AME per R to correlatewith β . We find no evidence for such a correlation (seeFigure 5b). Correlation with I µ m ν The ratio of I AME ν,
30 GHz to I µ m ν is often quoted in theliterature. We obtain a value of (2 . ± . × − (see Table 1), consistent with other determinations. Forinstance, performing component separation on WMAPobservations at intermediate Galactic latitudes, Davieset al. (2006) derived a ratio of 3 × − . Alves et al.(2010) likewise find a ratio of 3 × − combining obser-vations of radio recombination lines in the Galactic planewith WMAP data. Studying H II regions in the Galacticplane with the Very Small Array at 33 GHz, Todorovi´cet al. (2010) find a ratio of 1 × − . Analyzing a sampleof 98 Galactic clouds with Planck observations, PlanckCollaboration et al. (2014b) derived a ratio of 2 . × − .Thus, the AME component identified by Planck Collabo-ration et al. (2015b) has a strength relative to the 100 µ mdust emission in good agreement with what has been ob-served in other studies.However, as discussed in detail by Tibbs et al. (2012a),this ratio is subject to significant variability. While the100 µ m emission is a reasonable proxy for the total dustluminosity, its sensitivity to the dust temperature intro-duces significant non-linearities in the relationship. Thiseffect is evident at particularly low and high values of I µ m ν in Figure 2d as evidenced by the somewhat non-linear shape of the scatter plot. As expected, the tight-ness of the correlation between the AME and 100 µ mincreases when the analysis is restricted to a set of pixelswith similar T d . Correlation with I µ m ν Finally, we find that the 12 µ m emission is also tightlycorrelated with the AME with dispersion only slightlyless than that of R . While it is tempting to read this asa vindication of the spinning PAH model, the foregoinganalysis suggests that this tight correlation is merely theproduct of the 12 µ m emission being an excellent tracerof both the dust column and the radiation field strength. f PAH , i.e. the 12 µ m emission per unit R , does not cor-relate with the AME intensity (see Figures 3b and 8).Thus, while the PAH emission is an excellent predictorof the AME strength, this appears to be by virtue ofbeing an excellent predictor of the dust radiance ratherthan the result of an inherent link between the AME andPAHs. Emission from Magnetic Dust
Fig. 7.—
As in each panel of Figure 2, we plot the WISE 12 µ mintensity against the 30 GHz AME intensity. The correlation iscomparably tight as observed with R . If the AME is not spinning PAHs, could it be emis-sion from magnetic grains? Draine & Lazarian (1999)predicted that, unlike spinning PAH emission, magneticdust emission would be equally strong per dust mass inboth dense and diffuse regions. Since the dust in denseregions will be cooler than that in diffuse regions, pix-els with significant dust emission from both diffuse anddense regions will have broader SEDs and thus are fittedby smaller values of β relative to diffuse regions whenfitting the SED with a modified single T d blackbody.Thus, the AME per dust mass is predicted to be neg-atively correlated with β in the spinning PAH model anduncorrelated in the magnetic dust model. In Figure 5bwe demonstrate that AME/ R and β are largely uncorre-lated ( r s = 0 . I AME ν / R and T d favors anon-thermal emission mechanism. In addition, thermalemission from magnetic dust seems likely to be polarized(Draine & Hensley 2013) whereas observations find theAME to be minimally polarized (see Section 5 for furtherdiscussion of polarization observations). Dependence on Masks
The lack of correlation between f PAH and the AME in-tensity per τ or R is a potentially serious problem forthe spinning PAH hypothesis. We thus test the sensitiv-ity of this result to the region of the Galaxy examined.In Figure 8, we perform the same analysis as in Figure 3band quantify the degree of correlation with the Spearmancorrelation coefficient r s .Starting with the N = 51579 pixels remaining un-masked following the cuts discussed in 2.5, in Figure 8awe consider only the pixels with Galactic latitude | b | > ◦ . The behavior very much mimics that observed inFigure 3b, with no compelling evidence of a correlation.In Figure 8b, we examine pixels with | b | < ◦ . Thesepixels have more PAH emission per dust radiance (i.e.higher values of f PAH ) than those at higher latitudes,as would be expected from PAH destruction in diffuseregions. Again, however, there is no indication of a cor-relation of the AME intensity per R with f PAH .We next examine in Figure 8c only those pixels inwhich one or both of the AME components are signif-1
Fig. 8.—
As in Figure 3, f PAH is plotted against the 30 GHz AME intensity normalized by α R . We examine four different masks: (a)considering only higher Galactic latitudes | b | > ◦ , (b) considering only lower Galactic latitudes | b | < ◦ , (c) considering only pixels inwhich at least one AME component was significant at > σ , and (d) using the standard mask only. For reference, the dashed lines markthe median values in the standard mask. In all cases, there is no evidence for positive correlation between the AME and f PAH . icant at greater than 5 σ . The cut on AME significancedoes not change significantly the behavior observed inFigure 8a other than to eliminate some pixels with low f PAH values. As illustrated in Figure 4, the pixels withlow f PAH also tend to have low surface brightness, whichmay be responsible for inducing the slight negative corre-lation observed. Finally, Figure 8d shows for comparisonthe same analysis performed on the standard mask (Fig-ure 3a).The non-correlation of the AME intensity and f PAH is therefore robust to assumptions either on the AMEsignificance or the region of the sky analyzed. We nowturn to the implications of this result in the followingsection. DISCUSSION
One of the largest sources of uncertainty in this analy-sis is the fidelity of the AME spectrum recovered from de-composition. Due to a lack of data between the WMAP23 GHz band and the Haslam data at 408 MHz, it is dif-ficult to constrain the relative contributions of the AME,synchrotron, and free-free in the frequency range of in-terest. Planck Collaboration et al. (2015b) notes thattheir estimates of synchrotron emission are lower thanthe 9 yr. WMAP analysis (Bennett et al. 2013) by about70% at high Galactic latitudes and factors of several inthe Galactic plane, with the AME component estimate being larger as a result. It is therefore possible that theAME map has a non-negligible synchrotron component.The presence of contamination in the AME map, suchas free-free or synchrotron, would of course mean that f PAH is not related to the inferred AME intensity in aperfectly linear way even if the AME comes from spin-ning PAHs. Further, since f PAH correlates with τ and R , it is also expected to correlate with the free-free andsynchrotron emission, which increase with increasing gas(and therefore dust) column density.As illustrated in Figure 9a, I AME ν /α R is weakly anti-correlated with the 30 GHz free-free emission per R ( r s = − . I AME ν /α R against the 30 GHzsynchrotron intensity per R . The two quantities showevidence of a weak positive correlation ( r s = 0 . I AME ν /α R against the CO(1-0)line intensity per R . The two quantities show possibleevidence of a weak positive correlation ( r s = 0 . Fig. 9.—
The 30 GHz AME intensity normalized by α R is plotted against (a) the 30 GHz free-free intensity, (b) the 30 GHz synchrotronintensity, and (c) the CO(1-0) line emission all normalized by R . There is evidence for weak correlation in all panels. Fig. 10.—
As in Figure 8, f PAH is plotted against the 30 GHz AME intensity normalized by α R . We examine four different sets of pixels:(a) pixels with T d between 19 and 21 K (typical of the high-latitude sky), (b) pixels with β between 1.55 and 1.65, (c) pixels meetingboth the criteria of panels (a) and (b), and (d) using the standard mask only. For reference, the dashed lines mark the median values inthe standard mask. Thus even when the conditions of the local environment are held relatively fixed, there is no evidence for a positivecorrelation between the AME and f PAH . R and theother low frequency components are rather weak, mak-ing it unlikely that these components are driving the ob-served non-correlation between the AME and f PAH .Even assuming no contamination in the fit AME com-ponent, correlations with the synchrotron emission areplausible. For instance, if the AME arises from spinningultrasmall grains, it might be affected in synchrotron-bright supernova remnants where it may be enhancedif shattering in grain-grain collisions increases the ultra-small grain population, or suppressed if ultrasmall grainsare destroyed by sputtering.The theoretical uncertainties in the models for theseemission components underscore the need for obtainingancillary data at lower frequency. Upcoming 5 GHz ob-servations from the C-Band All-Sky Survey (C-BASS)(King et al. 2014) and 2.3 GHz observations from the S-Band Polarized All-Sky Survey (S-PASS) (Carretti et al.2009) will play an invaluable role in disentangling thelow-frequency components.A second source of uncertainty is the ability of f PAH ≡ ∆ ( νI ν ) µ m / ∆ R to trace the PAH abundance. In par-ticular, the fraction of the PAH emission appearing in theWISE 12 µ m band can depend on the ionization state ofthe PAHs and other properties of the local environment(e.g. Draine & Li 2007; Draine 2011). Thus it may bepossible to “wash out” a correlation between f PAH andthe AME intensity even if the AME arises from spinningPAHs.To test the plausibility of such a scenario, in Figure 10we correlate the AME intensity per R with f PAH onlyin pixels with similar environmental conditions as de-termined by their fit dust temperature and β . We findno significant differences from our primary analysis andthus no evidence that variations in the local environmentare driving the lack of correlation between f PAH and theAME intensity per R .In addition to the uncertainties discussed above, eachobservable A also has an associated observational uncer-tainty σ A which we have not included in Equation 3. σ A is highly degenerate with σ α and thus it is difficult toquantify their relative contributions to the total uncer-tainty. Instead, we ask what assumed fractional uncer-tainty on A would be required for the data to be consis-tent with an intrinsic relationship with σ α /α = 0 .
2, com-parably tight as found with R . We denote this quantity σ A /A (0 .
2) in Table 1, finding that for τ and f PAH τ , σ A /A would need to be larger than 25% for the observa-tions to be consistent with an intrinsic relationship withso narrow a dispersion. The small uncertainties on thethermal dust emission at 353 GHz reported by (PlanckCollaboration et al. 2015b) are inconsistent with whatwould be required for the data to be compatible with atight intrinsic relationship between AME and either τ or f PAH τ . Thus, it does not seem plausible to attributethe entirety of our findings to the relative uncertaintiesof the observables.Finally, Planck Collaboration et al. (2015c) demon-strate that the correlation between AME/ R and f PAH can be affected by systematic errors in the determinationof R . Although an analysis using the Commander -derived R and f PAH determined by straight division of the W R maps is inappropriate for the reasons discussed inSection 2.3, it remains possible that the R map producedby Planck Collaboration et al. (2014a) is biased in waysthat affect the correlation with f PAH . Dust modelingemploying additional data, such as 60 µ m dust emission,will help clarify this issue. In the meantime, we notethat R , being the integral of the FIR dust intensity, israther insensitive to the specifics of modeling as long asthe model provides a reasonable fit to the data. Thus,particularly when 100 µ m data is employed, R is straight-forward to determine and we have no reason to suspectstrong systematic biases.If indeed the AME is not correlated with the PAHabundance and is correlated with the strength of the ra-diation field, what are the implications for the origin ofthe emission? We present two possibilities:1. The AME is spinning dust emission that arises pri-marily from ultrasmall grains that are not PAHs.Li & Draine (2001) have shown that as much as ∼
10% of the interstellar silicate mass could be inultrasmall grains. However, it remains to be seenwhether these grains could produce enough rota-tional emission to account for the AME.2. The AME is predominantly thermal dust emis-sion, such as magnetic dipole emission from mag-netic materials. However, the relationship be-tween AME/ R and T d does not appear consistentwith thermal emission (see Figure 5). Addition-ally, current models of magnetic dipole emissiondo not predict behavior that could emulate the ob-served AME SED without invoking highly elon-gated (e.g., 5:1 prolate spheroids) Fe inclusions(Draine & Hensley 2013). Furthermore, thermaldust emission from an aligned component of thegrain population is expected to be significantly po-larized, including magnetic dipole emission fromferromagnetic inclusions (Draine & Hensley 2013),at odds with current non-detections of AME po-larization. Nevertheless, the theoretical calcula-tions of the emissivities of these magnetic mate-rials are still quite uncertain, and more laboratorydata is needed to assess the behavior of magneticmaterials at microwave frequencies to determinewhether such grains could be a potential source ofthe AME. It remains conceivable that some inter-stellar grain component might produce the AMEby non-rotational electric dipole radiation, but weare not aware of materials that could do this.Invoking an alternative explanation for the AME alsorequires explaining why the PAHs are not a substantialsource of spinning dust emission. Because the PAHs areclearly present and must be rotating, this would requirethat the electric dipole moments of the PAHs have beensignificantly overestimated (the spinning dust emissionscales as the square of the dipole moment). The elec-tric dipole moments of selected hydrocarbon moleculescompiled by Draine & Lazarian (1998b) have a scatter ofnearly an order of magnitude. Further, harsh UV irradia-tion more easily destroys asymmetric molecules, perhapspreferentially selecting for a population of more symmet-ric PAHs with smaller dipole moments. Thus it is plau-sible that the dipole moment distributions adopted in4spinning dust models may significantly overestimate thetrue electric dipole moments of interstellar PAHs.Lazarian & Draine (2000) estimated the polarizationfraction of spinning dust emission to be p (cid:46) .
01 near30 GHz. This estimate would also apply to spinning dustemission from non-PAH grains. However, if the AME isthermal emission from large aligned grains, it should besignificantly polarized with E ⊥ B for electric dipoleradiation or E (cid:107) B for magnetic dipole radiation frommagnetic inclusions (Draine & Hensley 2013).Observations of known AME sources in polarizationsuggest minimal polarization of the AME. In the Perseusmolecular cloud, the polarization fraction of the totalemission was found to be 3 . +1 . − . % at 11 GHz (Battistelliet al. 2006), less than 6.3% at 12 GHz (G´enova-Santoset al. 2015), less than 2.8% at 18 GHz (G´enova-Santoset al. 2015), and less than ∼
1% at 23 GHz (L´opez-Caraballo et al. 2011; Dickinson et al. 2011). Likewise,observations of the ρ Ophiuchi molecular cloud haveyielded upper limits of (cid:46)
1% at 30 GHz (Casassus et al.2008; Dickinson et al. 2011). Mason et al. (2009) placedan upper limit of 2.7% on the 9.65 GHz polarization frac-tion in the dark cloud Lynds 1622. 21.5 GHz observationsof the H ii region RCW175 yielded a polarization fractionof 2 . ± .
4% (Battistelli et al. 2015), though it is unclearwhether this polarization is arising from the AME or asub-dominant synchrotron component.These upper limits on polarization in the 10 - 30 GHzemission appear to favor spinning dust emission from anon-PAH population of ultrasmall grains. CONCLUSION
We have combined the
Planck foreground componentmaps,
Planck modified blackbody dust parameter maps,and WISE 12 µ m maps to test key predictions of thespinning PAH hypothesis. The principal conclusions ofthis work are as follows:1. τ , the dust radiance R , and I µ m ν are all excel-lent predictors of the 30 GHz AME intensity. R ex-hibits the tightest correlation, suggesting that theAME is sensitive to the strength of the radiation field.2. Neither AME/ τ nor AME/ R show any correla-tion with the PAH emission whether consideringthe full sky, regions close to the Galactic plane, orhigher Galactic latitudes.3. We find that f PAH is correlated with both τ and R , consistent with PAH destruction in low densityregions.4. Taken together, these facts pose a serious chal-lenge to the spinning PAH paradigm as the expla-nation for the AME. Alternative explanations, suchas magnetic dipole emission from ferro- or ferri-magnetic grains, should be more thoroughly inves-tigated.5. More low frequency constraints are needed to breakdegeneracies between the AME, free-free, and syn-chrotron to enable more accurate decompositionand to better constrain the AME spectrum. Up-coming all-sky observations from C-BASS and S-PASS will thus facilitate deeper investigations intothe origin of the AME.6. Further measurements of AME polarization willhelp clarify the nature of the grains responsible forthe AME.We thank Kieran Cleary, Hans Kristian Eriksen, DougFinkbeiner, Chelsea Huang, Alex Lazarian, Mike Peel,David Spergel, Ingunn Wehus, and Chris White for stim-ulating conversations. BSH and BTD acknowledge sup-port from NSF grant AST-1408723. The research wascarried out in part at the Jet Propulsion Laboratory, Cal-ifornia Institute of Technology, under a contract with theNational Aeronautics and Space Administration. Thiswork was supported in part by the Director, Office ofScience, Office of High Energy Physics, of the U.S.Department of Energy under contract No. DE-AC02-05CH11231. REFERENCESAli-Ha¨ımoud, Y., Hirata, C. M., & Dickinson, C. 2009, MNRAS,395, 1055Alves, M. I. R., Davies, R. D., Dickinson, C., et al. 2010,MNRAS, 405, 1654Battistelli, E. S., Rebolo, R., Rubi˜no-Mart´ın, J. A., et al. 2006,ApJ, 645, L141Battistelli, E. S., Carretti, E., Cruciani, A., et al. 2015, ApJ, 801,111Bennett, C. L., Larson, D., Weiland, J. L., et al. 2013, ApJS, 208,20Carretti, E., Gaensler, B., Staveley-Smith, L., et al. 2009, S-bandPolarization All Sky Survey (S-PASS), ATNF ProposalCasassus, S., Cabrera, G. F., F¨orster, F., et al. 2006, ApJ, 639,951Casassus, S., Dickinson, C., Cleary, K., et al. 2008, MNRAS, 391,1075Davies, R. D., Dickinson, C., Banday, A. J., et al. 2006, MNRAS,370, 1125de Oliveira-Costa, A., Kogut, A., Devlin, M. J., et al. 1997, ApJ,482, L17Dickinson, C., Peel, M., & Vidal, M. 2011, MNRAS, 418, L35Dobler, G., Draine, B., & Finkbeiner, D. P. 2009, ApJ, 699, 1374Dong, R., & Draine, B. T. 2011, ApJ, 727, 35 Draine, B. T. 2011, in EAS Publications Series, Vol. 46, EASPublications Series, ed. C. Joblin & A. G. G. M. Tielens, 29–42Draine, B. T., & Hensley, B. 2013, ApJ, 765, 159Draine, B. T., & Lazarian, A. 1998a, ApJ, 494, L19—. 1998b, ApJ, 508, 157—. 1999, ApJ, 512, 740Draine, B. T., & Li, A. 2007, ApJ, 657, 810Eriksen, H. K., Jewell, J. B., Dickinson, C., et al. 2008, ApJ, 676,10Eriksen, H. K., O’Dwyer, I. J., Jewell, J. B., et al. 2004, ApJS,155, 227Eriksen, H. K., Dickinson, C., Lawrence, C. R., et al. 2006, ApJ,641, 665Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J.2013, PASP, 125, 306G´enova-Santos, R., Mart´ın, J. A. R., Rebolo, R., et al. 2015,MNRAS, 452, 4169G´orski, K. M., Hivon, E., Banday, A. J., et al. 2005, ApJ, 622, 759Haslam, C. G. T., Salter, C. J., Stoffel, H., & Wilson, W. E. 1982,A&AS, 47, 1Hensley, B., Murphy, E., & Staguhn, J. 2015, MNRAS, 449, 809Hoang, T., Draine, B. T., & Lazarian, A. 2010, ApJ, 715, 1462Hoang, T., Lazarian, A., & Draine, B. T. 2011, ApJ, 741, 875