Detection and characterization of a 500 mic dust emissivity excess in the Galactic Plane using Herschel/Hi-GAL observations
D. Paradis, R. Paladini, A. Noriega-Crespo, C. Mény, F. Piacentini, M. A. Thompson, D. J. Marshall, M. Veneziani, J.-P. Bernard, S. Molinari
aa r X i v : . [ a s t r o - ph . GA ] N ov Astronomy&Astrophysicsmanuscript no. 17956 c (cid:13)
ESO 2018October 16, 2018
Detection and characterization of a 500 µ m dust emissivity excessin the Galactic plane using Herschel/Hi-GAL observations ⋆ D. Paradis , , R. Paladini , A. Noriega-Crespo , C. M´eny , , F. Piacentini , M. A. Thompson , D. J. Marshall , , M.Veneziani , J.-P. Bernard , , and S. Molinari Universit´e de Toulouse; UPS-OMP; IRAP; Toulouse, France CNRS; IRAP; 9 Av. du Colonel Roche, BP 44346, F-31028, Toulouse, cedex 4, France Spitzer Science Center, California Institute of Technology, 1200 E. California Blvd, Pasadena, CA 91125, USA Dipartimento de Fisica, Universita di Roma 1 La Sapienza, Roma, Italy Centre for Astrophysics Research, Science and Technology Research Institute, University of Hertfordshire, Hatfield, UK INAF-Instituto Fisica Spazio Interplanetario, Via Fosso del Cavaliere 100, I-00133 Roma, ItalyPreprint online version: October 16, 2018
ABSTRACT
Context.
Past and recent observations have revealed unexpected variations in the far-infrared - millimeter (FIR-mm) dust emissivityin the interstellar medium. In the Herschel spectral range, those are often referred to as a 500 µ m emission excess. Several dustemission models have been developed to interpret astrophysical data in the FIR-mm domain. However, these are commonly unable tofully reconcile theoretical predictions with observations. In contrast, the recently revised two level system (TLS) model, based on thedisordered internal structure of amorphous dust grains, seems to provide a promising way of interpreting existing data. Aims.
The newly available Herschel infrared Galactic (Hi-GAL) data, which covers most of the inner Milky Way, o ff ers a uniqueopportunity to investigate possible variations in the dust emission properties both with wavelength and environment. The goal of ouranalysis is to constrain the internal structure of the largest dust grains on Galactic scales, in the framework of the TLS model. Methods.
By combining the IRIS (Improved Reprocessing of the IRAS Survey) 100 µ m with the Hi-GAL 160, 250, 350, and 500 µ m data, we model the dust emission spectra in each pixel of the Hi-GAL maps, using both the TLS model and, for comparison, asingle modified black-body fit. The e ff ect of temperature mixing along the line of sight is investigated to test the robustness of ourresults. Results.
We find a slight decrease in the dust temperature with distance from the Galactic center, confirming previous results. We alsoreport the detection of a significant 500 µ m emissivity excess in the peripheral regions of the plane (35 ◦ < | l | < ◦ ) of about 13-15%of the emissivity, which can reach up to 20% in some HII regions . We present the spatial distributions of the best-fit values for thetwo main parameters of the TLS model, i.e. the charge correlation length, l c , used to characterize the disordered charge distribution(DCD) part of the model, and the amplitude A of the TLS processes with respect to the DCD e ff ect. These distributions illustratethe variations in the dust properties with environment, in particular the plausible existence of an overall gradient with distance to theGalactic center. A comparison with previous findings in the solar neighborhood shows that the local value of the excess is less thanexpected from the Galactic gradient observed here. Key words.
ISM:dust, extinction - Infrared: ISM - Submillimeter: ISM
1. Introduction
The interstellar medium (ISM) is where matter from di ff useclouds is brought into stars. In this context, studying dust evolu-tion is important as variations in the properties of the ISM con-stituents likely a ff ect the star formation process. In addition, un-derstanding the emission from big grains (BGs) is important ininterpreting experiments devoted to the observation of the cos-mic microwave background (CMB) and its fluctuations. Theseexperiments typically operate in the millimeter domain, wherethe cosmological signal is dominated by the Galactic foregroundemission, of which dust is one of the components.The spectral energy distributions (SEDs) of BGs can be ap-proximated by modified black-body emission I ν ( λ ) = ǫ ν B ν ( λ, T d ) N H , (1) ⋆ Herschel is an ESA space observatory with science instrumentsprovided by European-led Principal investigator consortia and with im-portant participation from NASA. where I ν ( λ ) is the brightness, ǫ ν is the dust emissivity per hydro-gen column, B ν is the Planck function, T d is the dust tempera-ture, and N H is the hydrogen column density. When Equation 1is used to interpret the observed emission, ǫ ν is the mean dustemissivity along the line of sight (LOS). This approximation isjustified because the medium is optically thin in the far-infrared(FIR) and submillimeter (submm). The dust temperature is how-ever expected to vary along the LOS (see Section 4.2.2). Thedust emissivity is usually defined as ǫ ν ( λ ) = ǫ ν ( λ ) λλ ! − β , (2)where ǫ ν ( λ ) is the emissivity at wavelength λ , and β isthe emissivity spectral index, usually taken to be equal to2. In recent years, however, an increasing number of stud-ies have found that the emissivity might actually depart froma simple λ − power-law. Indeed, the emissivity spectral indexseems to be temperature-dependent: its value has been shownto decrease with increasing temperature (Dupac et al., 2003; Paradis et al.: Detection and characterization of a 500 µ m excess in the Galactic plane Td (K)A lc (nm) N b o f p i x e l s e
500 (%) (A)(C) (D) N b o f p i x e l s (B) Fig. 1.
Histograms of the 500 µ m emissivity excess (panel A), results of the TLS modeling: the dust temperature (panel B), the A parameter (panel C) as defined in equation 5, and the l c parameter (panel D), as defined in equation 4.D´esert et al., 2008; Veneziani et al., 2010; Paradis et al., 2010).This T d - β anti-correlation has been extensively debated. Someauthors claim that this behavior is only the consequence ofmis-handling noisy data and / or temperature mixing along theLOS (Shetty et al., 2009). However, all the aforementioned stud-ies have concluded that the e ff ect was not due to noise, andsome analyses have included tests that rejected temperature mix-ing as the cause of the observed trend (Paradis et al., 2009;Malinen et al., 2011). We note that in some extreme cases, theinferred β values can reach up to 3.5-4 at low apparent temper-atures ( ≤
10 K), which appears very di ffi cult to reconcile with asingle value of β and temperature mixing e ff ects. It appears morelikely that actual variations in the dust emissivity are at play.Emissivity variations also appear to be wavelength-dependent with the emission spectrum flattening in the sub-millimeter ( λ > − µ m) relative to a single modifiedblack-body emission (Wright et al., 1991; Reach et al., 1995;Finkbeiner et al., 1999; Galliano et al., 2005; Paladini et al.,2007; Paradis et al., 2009, 2011a). They also appear to beenvironment-dependent (see, for instance, Li, 2005, for a re-view), with an absolute emissivity value in the FIR ( λ < − µ m) that is higher in colder and denser environments(Stepnik et al., 2003; Paradis et al., 2009; Planck collaboration,2011u). Moreover, the analysis of the Planck data in the solarneighborhood and both the Large and Small Magellanic Clouds(Planck collaboration, 2011e,m) indicates that the flattening ofthe emissivity spectrum could be related to the metallicity, be-cause it is more significant in low metallicity environments.From the astrophysical point of view, grain aggregation in thecore of dense clouds could, in principle, explain the observedabsolute FIR emissivity excess, if one assumes that aggregates emit more FIR radiation than individual grains. Nevertheless,this interpretation is only partially satisfactory, since grain ag-gregation may a ff ect only the absolute values and not necessarilythe shape of the emissivity, and the aforementioned excess hasonly been reported for some Galactic molecular clouds, while inthe extragalactic context, such as in the Large Magellanic Cloud(Paradis et al., 2011b), it has not been found at all.In this work, we study the FIR / submm data obtained forthe first and fourth Galactic quadrants through the Herschelinfrared GALactic (Hi-GAL) survey (Molinari et al., 2010a,b),and demonstrate the existence of a submm emissivity excess.Thanks to the sub-arcmin resolution, comprehensive sky cover-age, and broad wavelength range spanned by the Hi-GAL data,we can for the first time perform a systematic investigation ofsuch an excess in our Galaxy. In addition, the Galactic plane isideal for conducting such an analysis because it contains a va-riety of di ff erent environments, from di ff use clouds to compactsources, and from cold to warm structures, which can potentiallyharbor di ff erent dust properties. We also show that we are ableto reconcile the observed excess with theory predictions usingthe two level system (TLS) model, which provides a sophisti-cated analytical description of the disordered internal structureof amorphous dust grains.The paper is organized as follows. In Section 2, we introducethe observational data that we use in this work. Sections 3 and 4focus on the variations in the emissivity spectral shape and theorigin of these variations. Section 5 provides our conclusions. aradis et al.: Detection and characterization of a 500 µ m excess in the Galactic plane 3 Fig. 2.
From left to right: 500 µ m emissivity excess (in percent) and dust temperature derived from a modified black-body emission,and the results of the TLS modeling for dust temperature ( T TLS ) in K, intensity of the TLS processes ( A ), correlation length ( l c ) innm, and reduced χ . Paradis et al.: Detection and characterization of a 500 µ m excess in the Galactic plane e ( % ) (A) T d ( K ) GLON GLON A l c ( n m ) (B)(C) (D) A NormaScutum 3 kpc ring3 kpc ring Perseus Crux
Fig. 3. µ m emissivity excess (panel A), dust temperature (panel B), A parameter (panel C), and l c parameter (panel D), as afunction of Galactic longitudes. The dashed line shows the solar neighborhood value when normalized to c ∆ , s = σ standard deviation. The blue arrows show the tangent directions of the spiral arms at l = -50 ◦ , -33 ◦ ,-21 ◦ , and 31 ◦ (Vall´ee, 2008) and of the 3 kpc ring at | l | = ◦ (Dame & Thaddeus, 2008).
2. Data
The reference database for our investigation consists of the Hi-GAL dataset, a collection of 56 tiles of 2 ◦ × ◦ , with the longi-tude range -70 ◦ < l < ◦ , and an extension of 2 ◦ in latitude,following the Galactic warp. The Hi-GAL PACS (70 and 160 µ m) and SPIRE (250, 350, and 500 µ m) data (Pilbratt et al.,2010; Poglitsch et al., 2010; Gri ffi n et al., 2010) were processedusing the ROMAGAL software, described in Traficante et al.(2011). We also used ancillary IRIS (Improved Reprocessing ofthe IRAS Survey, see Miville-Deschˆenes & Lagache, 2005) datato constrain the peak of the BG emission. We corrected the gainsand zero-level in the SPIRE and PACS images by applying gainsand o ff sets derived from the comparison to a combination of thePlanck-HFI (High Frequency Instrument) and the IRIS observa-tions, using the same procedure as in Bernard et al. (2010). Aforthcoming paper will be dedicated to the intercalibration ofthe Hi-GAL data with existing photometric data (Bernard et al.,2011). A full description of the Planck mission is provided inTauber et al. (2010) and the Planck collaboration (2011a). TheHi-GAL data ( θ = ′′ to 37 ′′ from 160 to 500 µ m) were con-volved to a 4 ′ angular resolution to match the resolution ofthe IRIS data. In addition, each tile was re-projected using theHEALPIx pixelization scheme (Hierarchical Equal Area isoLat-itude Pixelization) with nside = ′ , i.e. adequate for Shannon sampling of theadopted resolution. We used the surface area of the intersectionbetween the HEALPix and the native pixel as a weight to re-project the data. After reprojecting, all the fields were combinedinto a single HEALPix file covering the entire inner Galactic http: // lambda.gsfc.nasa.gov / plane. We adopted the same absolute calibration accuracy as forthe SDP fields in the PACS data, i. e. 20%, and 13.5% for IRIS100 µ m. The calibration of the SPIRE data was recently revisedleading to an accuracy of 7%. As a conservative approach, wedid not include the PACS 70 µ m data in the analysis becauseat this wavelength we are probably most sensitive to emissionfrom very small grains (VSGs), which are stochastically heatedby photon absorption (Compi`egne et al., 2010). This contribu-tion can only be roughly evaluated and can severely bias thederivation of the BG temperature (especially for T d <
25 K).
3. Emissivity excess at 500 µ m A break in the observed emissivity law around 500 µ m hasbeen identified in the outer Galaxy (Paradis et al., 2009) fromthe analysis of DIRBE (Hauser, 1993), Archeops (Benoˆıt et al.,2002), and WMAP (Bennett et al., 2003) data, as well as in theLarge Magellanic Cloud based on Herschel data (Gordon et al.,2010; Galliano et al., 2011). However, in the two Hi-GALScience Demonstration Phase (SDP) fields (centered at l = ◦ and l = ◦ ), Paradis et al. (2010) did not find any significantemissivity excess at 500 µ m, even when taking calibration un-certainties into account. The goal of the present work is to in-vestigate the existence of this break. For this purpose, we fit theHi-GAL / IRIS emission in the range 100 µ m < λ < µ m ineach pixel with a single modified black body, adopting a leastsquares fit method. We assume that calibration uncertainties aredistributed following a Gaussian function. The dust temperatureis set as a free parameter. We then compare the observed emis-sivity at 500 µ m ( ǫ obs ) with the value predicted by extrapolating aradis et al.: Detection and characterization of a 500 µ m excess in the Galactic plane 5 Fig. 4.
Temperature derived using the TLS model ( T TLS ), as afunction of temperature derived from a modified black-body fitwith β = T fit ).the best-fit emissivity power-law to 500 µ m ( ǫ fit ). We define the µ m excess as the quantity e = ǫ obs − ǫ fit ǫ obs . (3)To perform the fit described above, we need to adopt a value forthe emissivity spectral index β . A recent analysis of the Planckdata (Planck collaboration, 2011e) has found, for 100 µ m < λ < µ m, a median β value of 1.8 over the entire sky. In contrast,Paradis et al. (2010) obtained, for 100 µ m < λ < µ m, amedian β value of 2.3 in both of the Hi-GAL SDP fields. In thelight of these results, we decide to keep β fixed and equal to 2.We note that this assumption is a matter of how the excess isdefined and only a ff ects the amplitude of the excess and not itsspatial distribution.In Figure 1 (panel A), we show the pixel distribution of theemissivity excess at 500 µ m ( e ) derived from the fitting pro-cedure. The distribution is clearly not centered at zero (as wouldbe the case for pure noise), but instead visibly skewed towardspositive values. The median of the distribution is 0.8%, with a σ of 4.2%. Excess values larger than 13.4% exceed the 3- σ stan-dard deviation of the distribution and are significantly larger thanthe calibration uncertainty of the SPIRE data (cf. Section 2).We emphasize that this result, i.e. the existence of a signifi-cant excess of emission at 500 µ m, does not depend on the par-ticular value adopted for β in the modified black-body fit. If werepeated the analysis with a di ff erent spectral emissivity value,for example β equal to 1.8 instead of 2, the shape of the excessdistribution would remain unchanged, although it would shifttowards more negative values, suggesting that, for the majorityof the pixels, the model overestimates the data. Incidentally, wenote that this also corroborates the hypothesis that, at least alongthe inner Galactic plane, β is indeed larger than 1.8.Figure 2 illustrates the spatial distribution of the 500 µ m ex-cess across the Galactic plane. Inspection of the map reveals amore pronounced excess in the peripheral regions ((35 ◦ < | l | < ◦ )) than in the central ones ( | l | < ◦ ). This e ff ect also appearsin Figure 3, panel A, where we have plotted the median valueof the excess at each Galactic longitude, and its associated 1- σ standard deviation. In particular, for − ◦ < l < − ◦ the excess becomes significant, contributing to as much as 16 - 20% of thetotal emissivity, and even reaching values larger than 23% to-ward some HII regions. Regions in the proximity of the Galacticcenter, where a ring of dense and cold clouds has been identi-fied at the Herschel resolution (Molinari et al., 2011), however,do not exhibit any excess. The spatial distribution of the excessdoes not display any particular symmetry either: for instance,the significant increase in the fourth Galactic quadrant aroundl < -50 ◦ is not mirrored by a corresponding increase within thesame longitude range in the first quadrant. Remarkably, the mor-phological behavior that characterizes the 500 µ m excess is -per se - an indication that this e ff ect is not related to calibrationuncertanties, as these would have an equal impact on di ff erentregions of the plane. In the specific fields of l = ◦ and l = ◦ ,the median value of the excess is 1% and 3%, which does notcorrespond to any significant detection, in agreement with thefindings in Paradis et al. (2010).The submm excess could, in principle, be induced by the fit-ting procedure. To test this hypothesis, we carried out two tests:first, we included in the fit all data points for 100 µ m ≤ λ ≤ µ m; second, we performed the fit by replacing the 350 µ m datapoint with the 500 µ m data. Both tests provided larger reduced χ than the original fit (on average, by a factor of 2.3 and 2.6),thus supporting the idea that this excess has an astrophysical ori-gin.In the following, we investigate in detail the 500 µ m excessin the framework of the TLS model, by analyzing variations inthe model parameters.
4. Towards an understanding of the nature of theexcess
We now provide a brief description of the TLS model. We referthe reader to M´eny et al. (2007) for a fuller description.Our revised TLS model is based on both solid state physicsand laboratory measurements, and provides an accurate descrip-tion of the physical properties of amorphous grains. It consistsof two parts: (1) the disordered charge distribution (DCD) one,which describes the interaction between the electromagneticwave and acoustic oscillations in the disordered charge of theamorphous material (Vinogradov, 1960; Schl¨omann, 1964); and(2) the actual TLS part, which takes the interaction of the elec-tromagnetic wave with the simple distribution of an asymmetricdouble-well potential into account. This second part correspondsto a theory originally developped by Phillips (1972, 1987) andAnderson et al. (1972). The first e ff ect (DCD) is temperature-independent, occurs on the grain scale and is the most dominante ff ect in the FIR. Moreover, it has two types of asymptotic be-haviors at both lower and higher frequencies than ω : ǫ ν ∝ λ − in the short wavelength range, i. e. ω > ω , and ǫ ν ∝ λ − in thelong wavelength range, i. e ω < ω . This DCD e ff ect is charac-terized by the so-called correlation length l c , which determinesthe wavelength at which the inflection point between the twoasymptotic behaviors occurs. This parameter is defined in the ω term by ω = v t / l c , (4)where v t is the transverse sound velocity in the material. TheTLS e ff ects, which consist of three mechanisms (a resonant ab-sorption and two relaxation processes, thermally activated), areinstead temperature-dependent, take place on the atomic scale,and start to be important in the submm domain, becoming the Paradis et al.: Detection and characterization of a 500 µ m excess in the Galactic plane
16 K20 K24 K28 K32 K l ( m m) e ( no r m a li ze d t o un it y a t m m )
16 K20 K24 K28 K32 K
TLS modelModified black-body fit e n l - e n l - Fig. 5.
Average emissivity spectra in five bins of temperature andtheir 1- σ uncertainty: 16 K in red (solid), 20 K in dark blue(dash), 24 K in light blue (dot), 28 K in green (dash-dot), and32 K in orange (dash-dot-dot). The emissivities have been com-puted using the best-fit with the TLS model (top panel) and witha modified black body with β = λ − is overplotted as a continuous gray line, forcomparison.predominant e ff ects in the mm wavelength range. The amplitudeof the TLS e ff ects with respect to the DCD part is determinedby the intensity parameter denoted with A . This means that allTLS processes are multiplied by the same intensity A . The totalemission deduced from the TLS model ( I tot ) is then the sum ofthe emissions coming from the DCD ( I DCD ) and TLS processes( I TLS ), such as I tot = I DCD + X I TLS . (5)Paradis et al. (2011a) performed a comparison between themodel predictions and astrophysical data to determine the modelparameters. They analyzed both the FIR / mm SED of the solarneighborhood using FIRAS and WMAP data, and of Galacticcompact sources observed with the Archeops experiment. Thepurpose of their analysis was to constrain the four key parame-ters of the TLS model, namely: (1) the charge correlation length l c for the DCD absorption; (2) the amplitude A of the TLS ef-fects, with respect to the DCD process; (3) a parameter c ∆ de-scribing the double-well potential for one of the TLS processes;and (4) the dust temperature T TLS . The combined fit of the SEDsfor the solar neighborhood and the compact sources provided ageneral description of Galactic dust in terms of these parameters, whose best-fit values are l c , s = A s = c ∆ , s =
475 (seealso Table 1), which were referred to as the standard values.In the following, we repeat the fitting procedure described inSection 3, using this time the TLS model rather than a modifiedblack body. The best-fit values for the TLS parameters derivedfrom the fit are then compared to the standard ones, and those ob-tained for the solar neighborhood and compact sources. Beforedescribing the results we obtained, a few considerations need tobe made. First, we note that the c ∆ parameter is, to first order, de-generate with the A parameter. In addition, c ∆ cannot be tightlyconstrained in our study because we are limited to wavelengthsshorter than 500 µ m. For this reason, following Paradis et al.(2011a), we set c ∆ to be equal to the standard value, ( c ∆ , s = l c , we adopt 36 nm as an upper limit. For l c ≥
36 nm,the DCD process indeed reaches an asymptotic behavior in λ − from FIR to mm wavelengths. Values of l c of the order of a fewnanometers, combined with either small or null values of A , al-low β to be instead close to 4. The slope of the spectra increaseswith decreasing l c , in the absence of significant TLS processes.As analyzed in Paradis et al. (2011a), for the range 100-550 µ m, A = l c = β is expected to beconstant with a value of 3.4 (2.0), regardless of the dust temper-ature (see their Figure 7, middle panel). However, for A =
10 and l c = β varies from 2.45 ( ≃ To minimize the computing time, we pre-calculated the bright-ness in the IRIS 100 µ m and Herschel bands using the TLSmodel, taking into account the color-correction to be applied toeach instrument. In this way, we generated a multi-dimensionalgrid, for di ff erent T TLS between 10 K and 40 K (with a 0.5 Kstep), l c in the range 1-36 nm (with a 1 nm step), and 50 valuesof A between 0 and 50. We then compared the brightness ex-pected from the TLS model with the observed brightness in eachpixel of the map. The χ value was computed for each value ofthe grid, and we chose the value of the parameters ( p ) that min-imizes the χ . Calibration uncertainties were included in the fitas described in Section 3. To allow interpolation between indi-vidual entries of the table, the best-fit parameter values ( p ⋆ ) arecomputed for the ten smallest values of χ using p ⋆ = P i = p i × χ i P i = χ i . (6)Since Planck data are not yet available, we are unable to placetight constraints on the A parameter using only Herschel data.A normalization of the dust emission predicted by the TLSmodel is required. We adopt the normalization I TLS , norm = I TLS × < I obs >< I TLS > , (7)where I TLS and I TLS , norm are the emission spectrum from the TLSmodel before and after the normalization, while < I obs > and < I TLS > are the emission averaged in wavelength between 100 µ m and 500 µ m, corresponding, respectively, to the observationsand the TLS model. aradis et al.: Detection and characterization of a 500 µ m excess in the Galactic plane 7 Fig. 6.
Left panel: α parameter from the Dale et al. (2001) model. Right panel: reduced χ deduced from the comparison betweendata and the Dale et al. (2001) model. Paradis et al.: Detection and characterization of a 500 µ m excess in the Galactic plane The spatial distribution of the dust temperature, as well as thereduced χ obtained through the TLS modeling are presentedin Figure 2. The temperature histogram is shown in Figure 1(panel B). We note that the reduced χ values are systematicallysmaller than 1, suggesting that the uncertainties in the observa-tional data are probably overestimated, particularly for the PACSdata. The median temperature along the Galactic plane is 18.6 K,while the Galactic center exhibits temperatures in the range 18-25 K. As reported in Molinari et al. (2011), some cold clumpscan be found in this region, with temperatures of about 16-18K. However, with respect to Molinari et al. (2011), we do notfind any evidence of temperatures above 25 K. This may be forseveral reasons. First, our temperature map was generated at 4 ′ angular resolution, instead of 25 ′′ as in Molinari et al. (2011).Secondly, the 70 µ m was not included in our analysis, whichmight have caused the underestimation of the warmest dust tem-peratures.In general, temperatures appear to be higher in the cen-tral regions of the Galaxy ( T TLS = | l | < ◦ ),and to decrease with increasing longitude ( T TLS = ◦ < | l | < ◦ ), as one can clearly see in Figure 3 (panelB). This general behavior has been seen before using DIRBE(Sodroski et al., 1994), FIRAS (Reach et al., 1995), and Planckdata (Planck collaboration, 2011e). Temperatures span the range16 K - 26 K (Figure 1, panel B). A the IRIS resolution, theGalactic plane remarkably does not show dust temperaturesbelow 15 K. Some warm spots with T TLS ≥
30 K are, however,visible in the peripheral regions, probably owing to HII regions.These warm spots also show the largest 500 µ m emissivityexcess. The comparison between temperatures estimated withthe TLS model and those derived from the modified black-bodyfit in the range 100-350 µ m with β = T fit ) is provided inFigure 4. As described in Paradis et al. (2011a), there is goodagreement between the two methods up to ≃
25 K, where adeparture from a one-to-one correlation becomes noticeable.The dust temperature is only taken into account in the Planckfunction in the case of a modified black-body fit, whereas theTLS processes are temperature-dependent and increase withtemperature. As a consequence, the di ff erence in the temperaturecontribution in the two methods could explain the departure inthe T TLS -T fit correlation at high temperatures, and especially thefaster increase in T TLS compared to T fit for temperatures higherthan 25 K. The outlier points ( T fit >
20 K) correspond either topixels with a low quality χ for the modified black-body fit, orto edges of the map.In Figure 5, we have plotted the average dust emissivities,for 100 µ m < λ < µ m, in five dust temperature bins cen-tered at 16, 20, 24, 28, and 32 K. The plots have been createdfor both the TLS model and a modified black-body fit with β = T TLS , A , and l c ) foreach pixel, that we averaged per temperature bin. We derivedthe averaged emissivity in the photometric bands by applyingthe adequate color-correction for each instrument. In the secondcase (modified black-body fit), we divided the brightness com-ing from the data by the Planck function at the temperature T fit .The emissivity spectra were normalized to unity at 100 µ m. Theuncertainties in the emissivity were computed using ∆ ǫ ν ǫ ν = ∆ B ν ( T d ) B ν ( T d ) + ∆ I ν I ν . (8) The relative error ∆ B ν ( T d ) / B ν ( T d ) is related to the error on T d ( ∆ T d ) as ∆ B ν ( T d ) B ν ( T d ) = h ν kT d e h ν kTd e h ν kTd − ∆ T d T d (9)The figure highlights the existence, for both models, of aclear trend in the emissivity spectra with the dust temperature,with the spectra being flatter with increasing dust temperature.This observed flattening behavior with T d cannot be accountedfor by the calibration error at 500 µ m. If the brightness at 500 µ m were systematically o ff by 7% owing to calibration uncer-tainties, all emissivity spectra would be a ff ected but this shouldnot induce a change in the dust temperature. Another e ff ect hasto be considered. Given that we conducted our analysis along theGalactic plane, where temperature mixing is expected along theLOS, one may argue that we can introduce an artificial bias byfitting the data points with a single dust temperature. To addressthis question, following Dale et al. (2001), we computed the pre-dicted brightness in each IRIS and Herschel band for di ff erentvalues of the interstellar radiation field intensity, X IS RF , relativeto the intensity of the ultraviolet field in the solar neighborhood(Mathis et al., 1983).The Dale et al. (2001) model describes a temperature distri-bution using the concept of local SED combination, and assumesa power-law distribution of dust mass subjected to a given heat-ing intensity dM d ( X IS RF ) dM d ( X IS RF ) ∝ X α IS RF dX IS RF , (10)where α and X IS RF are in the range 1 < α < < X IS RF < . With this representation, the di ff use medium has α close to2.5, whereas active star-forming regions have α of 1. We esti-mated the emission spectra ( I mod ν ( X IS RF )), for di ff erent values of α , using the DustEM package (Compi`egne et al., 2008, 2011)and assuming β =
2. We then summed these contributions overthe same X IS RF range proposed by Dale et al. (2001) I tot ν = P i = P j = I mod ν ( X IS RF , i ) × X − α j IS RF , i P i = P j = X − α j IS RF , i . (11)We then compared the observational data with the predictedSEDs, and searched for the optimal α value that minimizes thedi ff erence between the two. As a result of this process, each pixelof the map has an emission that incorporates temperature mix-ing along the LOS. Figure 6 is an illustration of the pixel-to-pixel map of the recovered α values. The central regions of theGalactic plane are characterized by values of α in the range [1.9,2.5], while for | l | > ◦ , α appears to be systematically equal tothe asymptotic value of 2.5. At the same type, inspection of thereduced χ spatial distribution (also shown in Figure 6) revealsthat the SEDs for most of the peripheral regions are not well re-produced by the Dale et al. (2001) model. In these regions, tem-perature mixing is probably less important than in the centralregions of the Galaxy.We considered only pixels with reduced χ < .
5. Modelingwith a reduced χ ≥ . χ is provided in Figure 6. Thisselection removes 39% of the pixels, and in particular the pe-ripheral parts or the map, corresponding essentially to the cold-est parts of our map. We then proceeded as before, with thedi ff erence that we treated the brightness derived from the best-fit Dale et al. (2001) model for the selected pixel (61% of theGalactic plane) as “real” data: we performed a χ minimization, aradis et al.: Detection and characterization of a 500 µ m excess in the Galactic plane 9 l ( m m) TLS modelModified black-body fit e ( no r m a li ze d t o un it y a t m m ) e n l - e n l - Fig. 7.
Emissivity spectra in five bins of temperature and their1- σ uncertainty, assuming temperature mixing along the LOS(with the use of the Dale et al. (2001) model): 19.1 K in red(solid), 22.3 K in dark blue (dash), 25.5 K in light blue (dot),28.7 K in green (dash-dot), and 31.9 K in orange (dash-dot-dot).The emissivities have been computed for the best-fit TLS model(top panel) and a modified black body with β = λ − is overplotted for comparison incontinuous gray line.using the TLS model and a modified black-body emission modelwith β =
2, to derive the best-fit parameters and the emissivityspectra for di ff erent temperature bins. Since the coldest regionshad been rejected from the analysis, the temperature bins rangedfrom 19.1 K to 31.9 K.If temperature mixing did indeed account for the flatteningof the spectra with increasing dust temperature, we would expectto observe the same type of behavior with this test. However,as shown in Figure 7, the spectra do not show any sign of adependence on dust temperature, regardless of the model usedto derive the dust emissivities. Thus, temperature mixing is notlikely to be responsible, and we are confident that the emissiv-ity changes are instead related to the intrinsic properties of dustgrains. A and l c Unlike in Paradis et al. (2011a), we explored both cold andwarm / hot regions of the Galaxy, to systematically investigate thevariation in the TLS model parameters with environment.Figure 8 shows the median values derived from this study forthe l c and A parameters in the case of, respectively, the whole Galactic plane region covered by Hi-GAL and, the central andperipheral parts of the plane. We have also displayed, for com-parison, the best-fit values deduced by Paradis et al. (2011a) forthe solar neighborhood, for Archeops compact sources, and forthe combination of both. In this analysis, the uncertainties in theparameters are assumed to be equal to their standard deviation.Since the error bars in the data are likely to be overestimated,as already discussed in Section 4.2.2, the parameters cannot bestrongly constrained.The distribution of points in the figure reveals that di ff er-ent environments are likely associated with di ff erent dust grainproperties. From the fitting procedure discussed in Section 4.2.1,we estimated that the most representative values of l c and A forthe Galactic plane are 7.5 nm and 11.0. For l c , this is close tothe value derived for Archeops sources, but smaller than for thesolar neighborhood. We also note (Figure 1, panel D) that l c isglobally characterized by values much lower than the standardone ( l c , s = A , this is larger by a factor of 1.9 inthe Galactic plane than the standard value ( A s = . c ∆ di ff ers signifi-cantly from the standard value. Therefore, to be able to performa proper comparison between these results, we needed to nor-malize A to c ∆ , s = A equal to 4.8and 10.9 for, respectively, the solar neighborhood and the com-pact sources. Again, A in the Galactic plane is di ff erent from thevalue derived in the solar neighborhood. This result indicatesthat grains within the plane might have a larger degree of amor-phization than in the solar neighborhood on the atomic scale,where the TLS processes occur.The spatial variation across the Galactic plane of l c and A isprovided in Figure 2. Important variations in the two parameters,on both small scales (pixel to pixel) and large scales (from thecentral to the peripheral parts of the Galaxy), are visible. The A parameter exhibits high values in regions with significantlyhigh e (especially in peripheral regions, see Figure 3, panelC), which suggests that the excess does not depend on l c , butrather on A . This explains the large fluctuations in the l c pa-rameter in the peripheral regions (see Figure 2), which inducelarge standard deviations in the longitude profile of this parame-ter (see Figure 3). In contrast, l c is more accurately characterizedin regions of negative excess. In that latter case, variations in thespectral shape of the SEDs can only be accounted for by vari-ations in the correlation length, since this parameter allows usto produce emission spectra with a spectral index larger than 2.This explains why the l c standard deviation is smaller closer tothe Galactic center. The correlation between the 500 µ m excessand the A parameter is shown in Figure 9. Disorder in the grainstructure on the atomic scale, i. e. the TLS part of the model, thusappears to be the main contributor to the emissivity variations at500 µ m. The l c parameter is indeed almost constant along theGalactic plane, as one can discern in Figure3 (panel D).The A values (or excess values) are higher over most of theinner Galactic plane than in the solar neighborhood. If the originof the variations is a general Galactic gradient, this would in-dicate that the solar neighborhood is an atypical place. It mightalso suggest that the spatial distribution of the excess is not de-scribed by simply an overall Galactic gradient but a more com-plicated structure.The relation between A and l c is illustrated in Figure 10. Theplots are very noisy, especially for the whole and the peripheral µ m excess in the Galactic plane Full GP (this work)
35 <|l|<70 (this work)Solar neighborhoodCompact sourcesSolar neighb. & Compact sourcesA l c ( n m ) |l|<35 (this work) Fig. 8.
Best-fit model parameters l c and A and their 0.5- σ standard deviations, derived from the TLS model for di ff erentGalactic environments. The arrows indicate values of the param-eter to first order, when fixing c ∆ to the standard value equal to475.regions of the Galactic plane. Nevertheless, they reveal a weakanti-correlation between the two parameters, which disappearsat large values of A . We also see that, in the central regions ofthe Galactic plane, most of the points cluster in the region de-limited by A ≃ −
10, whereas the peripheral regions is ratheraccurately characterized by A ≃ −
22. This shift in A is likelyassociated with variations in the dust properties, while the disap-pearance of the anti-correlation between A and l c confirms thatspectral variations at wavelengths equal to or larger than 500 µ mcould be entirely due to variations in the intensity of the TLSprocess. A significant flattening of the spectra in the submm / mmdomain is indeed expected if the TLS e ff ects are responsible forthe observed excess. We remind the reader, however, that longerwavelength observations are required to confirm the results ob-tained for this parameter. We note that the calibration uncertaintyin the 500 µ m measurement does not a ff ect the spatial distribu-tion of the TLS parameters. The calibration error would indeedonly induce a variation in the absolute value of A . For instance,a decrease in the SPIRE 500 µ m data by 7% would cause a cor-responding decrease in A by a factor of 1.6, but the peripheralregions of the plane would still have the largest values of A . Asfor l c , its median value - and standard deviation - would be lower( l c ≃ l c ≃ ff erence of 1.4 K between the average dust temperature in thecentral and peripheral regions of the Galaxy would be preserved(see Section 4.2.2). According to Greenberg & Li (1995), the spiral arms regions andthe interarm regions might have di ff erent dust properties. Thiscould explain the variations with Galactic longitude observed inthe extinction data of Gao et al. (2009). The latter authors ar-gued that these variations could be caused by the larger grainsproduced by coagulation, a higher dust density and a strongerradiation field in the spiral arms regions. Bernard et al. (2010)also showed the existence of warmer dust in regions of the LOScorresponding to the intersection with spiral arms. In Figure 3,we have marked the tangent positions of the spiral arms taken Fig. 9. A parameter derived from the TLS model as a functionof the 500 µ m emissivity excess. The overplotted contours, withlevels at 50, 200, 350, 600, and 1000, represent the density ofpixels.from Vall´ee (2008) (l = -50 ◦ , -33 ◦ , -21 ◦ , and 31 ◦ for the Crux-Scutum, Norma, Perseus, and Scutum-Crux arms, respectively),as well as the position of the 3-kpc molecular ring defined inDame & Thaddeus (2008) ( | l | = ◦ ).From Figure 3, one can observe a direct link between thetangent positions of the spiral arms with some peaks in the dusttemperature profile. Variations in the 500 µ m emissivity excesslinked to the arms are also visible but are less significant thanthe general trend with distance from the Galactic center. For the A parameter, the relationship with spiral arms is less obvious. Ahint of a relationship can be discerned between the spiral armsand the correlation length, which is enhanced in these regions,although by an amount that is smaller than the standard devia-tion.Variations in the optical properties predicted by the TLSmodel replace or are complementary to the predicted variationsin emissivity caused by either aggregation or flu ffi ness. Dustgrowth is expected in dense molecular clouds, and aggregationlikely produces both an increase in emissivity with respect to thegas column (for a given dust to gas ratio) and a decrease in dusttemperature. The increase in the absolute emissivity with respectto the gas cannot be measured here because we do not directlycompare the emissivity with the gas column density. From dipolediscrete approximations calculations, the emissivity increase foraggregates is expected to be roughly constant in the range 100-500 µ m. This does not change the spectral shape of the emis-sivity and cannot reproduce any significant 500 µ m emissivityexcess. Similarly, the changes in apparent dust temperatures aredi ffi cult to interpret in terms of aggregation at the scales ana-lyzed here, and are probably determined mainly by variations inthe local radiation field intensity, which may obscure any tem-perature decrease caused by dust aggregates.
5. Conclusions
We have performed an analysis of the emissivity variations alongthe Galactic plane using the newly released Herschel / Hi-GALdata (160 µ m < λ < µ m) combined with the IRIS 100 µ mdata, at 4 ′ angular resolution. Changes in the emissivity spectraare interpreted in terms of the TLS model, which includes the aradis et al.: Detection and characterization of a 500 µ m excess in the Galactic plane 11 T TLS (K) l c (nm) A c ∆ Full Hi-GAL data 18.6 ± ± ± ∗ Peripheral Hi-GAL data (35 ◦ < | l | < ◦ ) 18.0 ± ± ± ∗ Central Hi-GAL data ( | l | < ◦ ) 19.4 ± ± ± ∗ Solar neighborhood 17.5 ± ± ± ± ∗∗ ∗ Compact sources - 5.1 ± ± ± ∗∗ ∗ Solar neighborhood + Compact sources 17.3 ± ± ± ± Table 1.
Parameters of the TLS model and their 1- σ standard deviation: median values of the best-fit parameters for the Galacticplane (this work) and best-fit parameters for the other environments (from Paradis et al., 2011a). ∗ set to the standard value defined in Paradis et al. (2011a). ∗∗ A normalized to c ∆ , s = l c ), and theTLS e ff ects, whose intensity ( A ) with respect to the DCD e ff ectis left as free parameter. Our results can be summarized as fol-lows: – A 500 µ m emissivity excess, with respect to the predictionsof a modified black-body model with β =
2, has been found inthe peripheral parts of the Galactic plane (35 ◦ < | l | < ◦ )covered by the data. This excess can represent up to 16% to20% of the total emission in some HII regions. – The dust temperature, derived from the TLS model, appearsto be slightly warmer in the central (by 1.4 K, for | l | < ◦ )than the peripheral Galactic regions covered by the data.Regions near the Galactic center have temperatures in therange 17-25 K, whereas the median temperature across therest of the Galactic plane covered is close to 18.6 K. – We have found a flattening of the emissivity spectra inthe range 100-500 µ m with increasing dust temperature. Amodel using a mixture of temperatures along the LOS hasbeen used to verify wether this could be responsible for theobserved behaviour. The results strongly suggest that thechanges in the observed emissivity spectra with dust tem-perature cannot be accounted for by an LOS e ff ect only, andthat they must be caused instead by intrinsic variations in thedust properties with environment. These results are indeedcompatible with the predictions of the TLS model with dusttemperature, and suggest variations in the degree of amor-phisation of the grains, i. e. the disorder at the atomic and / ornanometer scales. – The 500 µ m emissivity excess can be explained by the in-tensity produced by the TLS processes. Indeed, the spatialvariations in the A parameter (i.e. the amplitude of the TLSe ff ects) follow the distribution of the excess. – Dust properties along the Galactic plane seem to di ff er fromthose of the solar neighborhood, the excess being smaller inthe latter than expected from an extrapolation of the Galacticplane behavior. – The spatial distribution of l c (i.e. the correlation length ofthe DCD e ff ect) does not present significant variations alongthe Galactic plane. Statistically, l c is three times lower thanin the solar neighborhood, although it is close to the valueobtained for compact sources. – Results in the framework of the TLS model indicate that dustgrains are characterized by a degree of amorphization thatis larger along the Galactic plane than in the solar neigh-borhood. In particular, the degree of amorphization tends toincrease in the peripheral part of the plane covered by theHi-GAL data. This work shows that specific variations in themechanical structure of the material constituting the grains are likely to vary from the Galactic center towards the pe-ripheral regions of the plane. – Variations in the dust temperature and the 500 µ m emissivityexcess as a function of Galactic longitude appear to correlatewith the locations of Galactic spiral arms. In the context ofthe TLS model, this may suggest that changes in the mechan-ical structure of the grains occur in the spiral arms.The combination of Planck and Herschel data will providethe opportunity to improve the current constraints on the dustproperties. Acknowledgements.
We would like to thank the anonymous referee for his in-valuable comments. D. P. acknowledges grant support from the Centre Nationald’Etudes Spatiales (CNES).
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