Matching dust emission structures and magnetic field in high-latitude cloud L1642: comparing Herschel and Planck maps
J. Malinen, L. Montier, J. Montillaud, M. Juvela, I. Ristorcelli, S. E. Clark, O. Berné, J.-Ph. Bernard, V.-M. Pelkonen, D. C. Collins
MMNRAS , 1–14 (2015) Preprint 10 October 2018 Compiled using MNRAS L A TEX style file v3.0
Matching dust emission structures and magnetic field inhigh-latitude cloud L1642: comparing
H erschel and
P lanck maps (cid:63)
J. Malinen, † L. Montier, , J. Montillaud, M. Juvela, I. Ristorcelli, , S. E. Clark, O. Bern´e, , J.-Ph. Bernard, , V.-M. Pelkonen, and D. C. Collins Department of Physics, Florida State University, Tallahassee, FL, USA Universit´e de Toulouse, UPS-OMP, IRAP, F-31028 Toulouse cedex 4, France CNRS, IRAP, 9 Av. colonel Roche, BP 44346, F-31028 Toulouse cedex 4, France Institut Utinam, CNRS UMR 6213, OSU THETA, Universit´e de Franche-Comt´e, 41bis avenue de l’Observatoire, 25000 Besan¸con, France University of Helsinki, P.O. Box 64, FI-00014 Helsinki, Finland Department of Astronomy, Columbia University, New York, NY, USA
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
The nearby cloud L1642 is one of only two known very high latitude ( | b | >
30 deg)clouds actively forming stars. It is a rare example of star formation in isolated con-ditions, and can reveal important details of star formation in general, e.g., of the ef-fect of magnetic fields. We compare
Herschel dust emission structures and magneticfield orientation revealed by
P lanck polarization maps in L1642. The high-resolution( ∼ (cid:48)(cid:48) ) Herschel data reveal a complex structure including a dense, compressed cen-tral clump, and low density striations. The
P lanck polarization data (at 10 (cid:48) resolution)reveal an ordered magnetic field pervading the cloud and aligned with the surroundingstriations. There is a complex interplay between the cloud structure and large scalemagnetic field. This suggests that the magnetic field is closely linked to the formationand evolution of the cloud. CO rotational emission confirms that the striations areconnected with the main clumps and likely to contain material either falling into orflowing out of the clumps. There is a clear transition from aligned to perpendicularstructures approximately at a column density of N H = 1 . × cm − . Comparingthe Herschel maps with the
P lanck polarization maps shows the close connectionbetween the magnetic field and cloud structure even in the finest details of the cloud.
Key words:
Submillimetre: ISM – Polarization – ISM: dust, magnetic fields, clouds
The major physical processes involved in molecular cloudand star formation are gravitation, turbulence, magneticfields, and thermal pressure, but the full picture is not clear,especially regarding the relative importance of turbulenceand magnetic fields (e.g., McKee & Ostriker 2007; Bergin &Tafalla 2007; Crutcher 2012; Andr´e et al. 2014). The Galac-tic magnetic field covers our whole Galaxy and takes part inthe dynamics of the interstellar medium (ISM) and in thedifferent phases of the star formation process, from molecu-lar clouds to filaments and cores where stars are born. (cid:63)
Herschel is an ESA space observatory with science instrumentsprovided by European-led Principal Investigator consortia andwith important participation from NASA. † E-mail:[email protected].fi
Magnetic fields can be studied using several methods,including Zeeman splitting of spectral lines, and polarizationof starlight or thermal dust emission. In this paper we use thelast method, polarized dust emission. Because dust grainsare not spherical, their radiation is polarized along the maingrain axis. When grains are aligned with a magnetic field,the observed thermal radiation is linearly polarized (e.g.,Davis & Greenstein 1951; Vaillancourt 2007). The grainsalign with their long axis perpendicular to the magnetic fieldorientation. Therefore, if the polarization vectors are rotatedby 90 degrees, the dust observations reveal the magnetic fieldorientation in the plane of the sky (POS).Ground-based observations of polarized starlight in dif-fuse areas (e.g., Myers & Goodman 1991; Pereyra & Mag-alh˜aes 2004) and dust emission in dense areas (e.g., Ward-Thompson et al. 2000; Crutcher et al. 2004) have shown c (cid:13) a r X i v : . [ a s t r o - ph . GA ] M a y J. Malinen, L. Montier et al. that the POS magnetic field lines are linked to the cloudstructures.Recently,
P lanck satellite has observed the whole skyin submm-mm wavelengths, including the polarization withhigh enough sensitivity to map magnetic fields both in denseand diffuse areas (Planck Collaboration I 2014). PlanckCollaboration Int. XIX (2015) presented an overview ofthe
P lanck polarization data, and reported a systematicdecrease of the polarization fraction with increasing col-umn density. Planck Collaboration Int. XX (2015) comparedthe polarization observations with magnetohydrodynamical(MHD) simulations, and came to the same conclusion thatthe polarization fraction is highest in the most diffuse areas.Planck Collaboration Int. XXXII (2014) studied large, lo-calized filamentary structures, which they called ”ridges”, inthe Galaxy having hydrogen column densities ( N H ) between10 and 10 cm − , and found that these structures can beseen also in the polarization data (Stokes Q and U maps).The structures are usually aligned with the magnetic field,especially at lower column densities. Planck CollaborationInt. XXXIII (2014) analysed and modelled three filaments inmore detail. Planck Collaboration Int. XXXV (2015) madea quantitative analysis of the orientation of the magneticfield and column density structures in ten nearby clouds,finding that the relative orientation is likely to change frompreferentially parallel or without a preferred orientation toperpendicular with increasing column density, the changeoccuring at N H ∼ . cm − .Several observational studies have revealed more detailsin the diffuse ISM structure. Goldsmith et al. (2008) andPalmeirim et al. (2013) compared earlier magnetic field ob-servations with CO data and Herschel dust emission maps,respectively, concluding that striations in the diffuse ISMtend to be parallel to magnetic field lines and perpendicularto denser filaments. Clark et al. (2014, 2015) found linear,several degrees long structures, ”fibers”, at high Galactic lat-itude in neutral hydrogen (HI) maps at 4 (cid:48) resolution. Theycompared HI to polarized starlight and
P lanck dust polar-ization, and concluded that the ”fibers” are closely alignedwith magnetic fields.As observations reveal more and more details of elon-gated structures at different size scales of the interstellarmedium (ISM) and molecular clouds, the nomenclature isstill developing and sometimes ambiguous between differentsubfields. Here, we use the following definitions for differenttypes of structures, most of them elongated or ”filamentary”.By ”filament” we mean an elongated, medium-low columndensity structure (approximately at N H > × cm − ,but this is not a strict limit) linked to low-mass star form-ing regions. By ”fiber” we mean elongated sub-structure offilaments (as used in Andr´e et al. 2014). By ”striation” wemean any low column density structure (approximately at N H < × cm − ) which is either linear or curving, andeither at diffuse areas or connected to denser filaments orother structures. By ”blob” we mean an irregular structureof relatively dense matter which is more round than filamen-tary.Malinen et al. (2014) presented Herschel dust emissionmaps of molecular cloud L1642, which showed clear stria-tions in the diffuse matter surrounding the cloud. L1642 isone of only two high-latitude ( | b | > ◦ ) clouds confirmedto have active star formation. The high galactic latitude ( − . ◦ ) with very low line-of-sight contamination, smalldistance (140 pc or less, Hearty et al. (2000); Schlafly et al.(2014)), and relatively low column density make the clouda good object for studying low-mass star formation (seeMcGehee 2008; Malinen et al. 2014).Our aim in this paper is to study the magnetic fieldsrevealed by P lanck dust polarization maps and comparethem to the striations and other structures shown in thehigher resolution
Herschel maps of L1642. Previous
P lanck papers have used the polarization maps only in combinationwith the
P lanck intensity maps, at best at ∼ (cid:48) resolution,but usually convolved to lower resolution ( ∼ (cid:48) ). We willshow that the P lanck magnetic field maps can be very usefuleven when compared to higher resolution intensity maps, like
Herschel at ∼ Herschel maps and compare it to the magnetic fields and kinematicdata in Sect. 4. We discuss the implications of the results inSect. 5 and draw our conlusions in Sect. 6.
L1642 (G210.90-36.55) was observed by
Herschel (Pil-bratt et al. 2010) as part of the Galactic Cold Coresproject (Juvela et al. 2012). The data were presented anddescribed in Malinen et al. (2014). Here, we use
Herschel µ m dust emission map, which shows striations of thediffuse material surrounding the cloud, and hydrogen col-umn density map for separating dense and diffuse areas. Wehave calculated the column density N H by assuming thatemissivity spectral index β is 1.8, and dust opacity κ is0.1 cm /g ( ν /1000 GHz) β , which is assumed to be valid inhigh density environments (Hildebrand 1983; Beckwith et al.1990). We use the polarized dust signal measured by the
P lanck -HFI 353 GHz channel, where the signal-to-noise ratio (S/N)of the dust emission is maximum, as a tracer of the mag-netic field (B). The
P lanck observations provide Stokes I , Q , and U parameter maps. The total polarized intensity P ,polarization fraction p , polarization angle ψ , and plane ofthe sky (POS) magnetic field orientation angle θ B can bederived from the Stokes parameters using the equations P = (cid:112) Q + U , (1) p = P/I, (2) ψ = 0 . − U, Q ) , (3) θ B = ψ + π/ . (4) MNRAS000
P lanck observations provide Stokes I , Q , and U parameter maps. The total polarized intensity P ,polarization fraction p , polarization angle ψ , and plane ofthe sky (POS) magnetic field orientation angle θ B can bederived from the Stokes parameters using the equations P = (cid:112) Q + U , (1) p = P/I, (2) ψ = 0 . − U, Q ) , (3) θ B = ψ + π/ . (4) MNRAS000 , 1–14 (2015)
In Eq. 3, arctan( − U, Q ) gives the angle arctan( − U/Q )in the correct quadrant, and the minus sign converts the
P lanck data from
Healpix to IAU convention, where thepolarization angle is counted positively from the GalacticNorth to the East. See, e.g., Planck Collaboration Int. XIX(2015) for more details.Since our object, L1642, is located at high latitude,
P lanck data have to be processed further to increase theS/N of the polarization quantities and to avoid any bias is-sues, as recommended by Montier et al. (2015a). Hence the
P lanck maps at 353 GHz have been smoothed to 10 (cid:48) in or-der to reach a S/N > (cid:48) radius centredon the cloud. Moreover, the modified asymptotic estimator(hereafter MAS, Plaszczynski et al. 2014) has been chosen toprovide a robust estimate of the polarization fraction, p MAS ,as described in Montier et al. (2015b). With this setup theuncertainty of the polarization angle remains below 5 ◦ inthe cloud and in most of the surrounding areas.For the analysis of the regularity of the B field, we willalso use the polarization angle dispersion function, as definedin Planck Collaboration Int. XIX (2015) with the followingquantity: S ( (cid:126)x, δ ) = (cid:32) N N (cid:88) i =1 (∆ ψ xi ) (cid:33) / (5)where ∆ ψ xi = ψ ( (cid:126)x ) − ψ ( (cid:126)x + (cid:126)δ i ) is the angle difference be-tween ψ ( (cid:126)x ), the polarization angle at a given sky position (cid:126)x (the central pixel), and ψ ( (cid:126)x + (cid:126)δ i ) the polarization angle at asky position displaced from the centre by (cid:126)δ i . The average iscomputed over an annulus of radius δ = | (cid:126)δ | and width ∆ δ .We use value 3.4 (cid:48) for both radius and width. We examine the dynamics of the cloud with the CO obser-vations of Russeil et al. (2003), used also in Malinen et al.(2014). The SEST radio telescope mapped L1642 in the J = 1 − J = 2 − CO, CO andC O. The half-power beam widths of the data are 45 (cid:48)(cid:48) for J = 1 − (cid:48)(cid:48) for J = 2 −
1. The grid has 3 (cid:48) spacing.Typical noise levels are ∆ T rms = 0 .
06 K for C O(2–1) and ∼ In order to visualize the B field orientation on other inten-sity maps, such as
P lanck or Herschel emission maps, weuse the Line Integral Convolution (LIC, Cabral & Leedom1993) filtering technique. The method filters (’blurs’) an in-put image texture along local vector field lines, in our caseshowing the orientation of the magnetic field lines.When applying the LIC algorithm based on
P lanck in-formation at 10 (cid:48) on the 250 µ m Herschel map at ∼ (cid:48)(cid:48) reso-lution, we make the assumption that the orientation of the Bfield is not changing inside the P lanck beam. This is a strongassumption which ignores any kind of small scale patterns,which could come for example from turbulence. Hence, thisprocess is valid only when comparing large scale features.
Several different methods have been used for identifying lin-ear structures and quantifying their orientation. For exam-ple, Peretto et al. (2012) and Palmeirim et al. (2013) usedthe DisPerSE method (Sousbie 2011) to extract the crests oflinear structures, and calculated their average orientations.Other methods include column density gradients (Soler et al.2013; Planck Collaboration Int. XXXV 2015), inertia ma-trix (Hennebelle 2013), and Hessian matrix (Planck Collab-oration Int. XXXII 2014).As our interest here is mostly in diffuse striations, we usethe Rolling Hough Transform (RHT, Clark et al. 2014). TheRHT is a machine vision method based on the Hough trans-form (Hough 1962). It calculates the intensity as a functionof angle in a circular region around every pixel of image data.The RHT thus quantifies the orientation of linear structures,rather than simply identifying them. By contrast, the Dis-PerSE method (Sousbie 2011), originally developed for cos-mic web data, defines filaments as structures that connectlocal density maxima. This requirement is not well suitedfor characterizing striations. Indeed, we find that in orderfor DisPerSE to locate the faintest striations, the persistencethreshold must be set so low that many spurious structureswere also returned. Even then, the RHT-defined structuresare a better representation of the striations seen by eye.We quantify the orientations of linear structures, andthe orientation uncertainties, from the RHT output usingthe equations defined in Clark et al. (2015). The RHT ap-proach enables a direct pixel-by-pixel comparison of thestructure orientation with the magnetic field orientation. Weuse the default parameter values of the RHT.The RHT output is three-dimensional: intensity as afunction of angle for every pixel in the input image. Inte-grating the RHT output over all possible angles producesthe RHT backprojection, a visualization of the linear inten-sity in the image (see Clark et al. 2014, for details).
Soler et al. (2013) (and Planck Collaboration Int. XXXV2015) use the name Histogram of Relative Orientations(HRO) to refer to their method of using column densitygradients to extract linear structures. Confusingly, they usethe same name to refer to the end result, the actual his-togram comparing the relative orientation of structures andmagnetic field. We take the same approach as Planck Col-laboration Int. XXXVIII (2015) and use the name HRO torefer just to the histogram in general, regardless of how theorientation of the structures has been determined.We perform an HRO analysis to quantify the alignmentbetween the magnetic field and the
Herschel µ m elon-gated structures traced by the RHT method. We build theangle difference between the B field orientation θ B and thestructure orientation θ RHT in each pixel by∆ θ = θ B − θ RHT . (6)This angle difference is only computed where the uncertaintyof the B field and the RHT orientations are simultaneouslybelow 10 ◦ . MNRAS , 1–14 (2015)
J. Malinen, L. Montier et al.
We want to examine how the relative alignment of duststructure and magnetic field changes with column density.It is expected that the two are preferentially aligned in lowcolumn density environments, and perpendicular in high col-umn densities (e.g., Planck Collaboration Int. XXXV 2015).We want to go a step further to build a robust quantificationto reveal the transition between the two modes, without anya priori knowledge on the components. This is why we usemultivariate analysis methods to determine the basic waysin which the HROs vary as a function of column density.We use a two step method to analyze quantitavely theHROs described in the previous section. In the first step, weuse a variant of Principal Component Analysis (PCA, seee.g., Jolliffe 2002) to estimate the number of componentsin the HROs. PCA is a statistical method used to find theprincipal components of the data, i.e., the directions withthe most variance. The method is often used to reduce thedimensions of the data. First, we divide the
Herschel mapinto 18 continous bins of column density, all containing thesame number of pixels. The HRO analysis described above isthen performed on each column density bin separately, yield-ing a set of 18 HROs. Then, we create the matrix M , whosecolumns contain the 18 HROs. We compute the principalcomponents of matrix M using PCA. The principal compo-nents constitute a basis to the set of histograms containedin M . Since the components are orthogonal by definition itis difficult to interpret them in physical terms (in particularbecause they contain negative elements). Therefore, we onlyuse PCA to estimate the number of main components.In the second step we apply non-negative matrix factor-ization (NMF, Lee & Seung 1999) to the matrix M . NMFis a multivariate analysis technique, which is used to fac-torize a matrix M of dimension ( m × n ) into two matrices W ( m × p ) and H ( p × n ), where p is usually notably lowerthan m or n . All the matrices can have only non-negative el-ements. Usually, the problem must be approximated numer-ically forming V = W × H + U , where U is a residual matrix.The dimensions of W and H must be defined. m is definedby the number of rows in M , i.e., the number of differentangle bins in our case. n is defined by the number of columnsin M , i.e., the number of HROs ( n = 18) in our case, while p , the number of rows in H , or elementary histograms wewish to extract, must be set by the user. We use the numberof the main components in M obtained with PCA in stepone. The algorithm to compute W and H was presented inLee & Seung (1999). It is initialized with random W and H matrices and it uses iterative update rules to minimisethe Euclidian distance between M and W × H . It shouldbe noted that NMF is similar in many regards to “positivematrix factorization” (PMF), introduced by Paatero & Tap-per (1994), which differs mainly in terms of optimizationalgorithm. Both NMF and PMF have been applied in as-tronomy (see, e.g., Bern´e et al. 2007; Juvela et al. 1996).The solution to NMF is not unique and can depend onthe initialization, hence we run NMF 1000 times on M toempirically verify that the solution is constant in our spe-cific case. The resulting components in H extracted by NMFare elementary histograms. The NMF method produces di-rectly the weights contained in W , i.e., the contribution of each component to the histograms of M , which can then beshown as a function of the column density. This analysis isperformed in Sect. 4.5. P lanck polarization and magnetic fieldorientation
The
P lanck
857 GHz intensity map with POS magnetic fieldorientation of the area surrounding L1642 is shown in Fig. 1.L1642 is located at the head of a large, over 5 ◦ long pillarstructure visible in HI and infrared/submillimeter dust emis-sion maps. We use the LIC method described in Sect 3.1 tovisualize the POS magnetic field. The magnetic field orien-tation is shown at 30 (cid:48) resolution, since, at full resolution, theS/N of the polarization data in the surrounding low columndensity region is low, as there is not much material to emitpolarized radiation. We use Equatorial coordinates and referto directions North (N, up), South (S, down), East (E, left),and West (W, right) in this and all other images.The large scale POS magnetic field in Fig. 1 shows alot of turmoil in this region. The areas discussed below aremarked with letters a − d in the figure. The large pillar lead-ing to L1642 appears to be a turning point to the large scalemagnetic fields. On the E part of the pillar ( a ), the mag-netic field is oriented approximately midway between theE-W and NE-SW directions. On the NW side of L1642 ( b )the B field is oriented in the NW-SE direction, that is ap-proximately perpendicular to the E side. In the center of thepillar ( c ), where there are two dense, elongated structures,these perpendicular B fields meet and the field lines bend.However, at the W part of the pillar and at the head whereL1642 is situated ( d ), the B field is again at E-W orientation.Thus, the NW part of L1642 faces again a perpendicular Bfield. The impact of the surrounding region to the L1642cloud is discussed more in Sect. 5.Fig. 2 shows maps of the P lanck
353 GHz intensity I ,polarization angle dispersion function S , the MAS estimateof polarization fraction p MAS , magnetic field orientation an-gle θ B , S/N of the p MAS , and the dispersion of the orienta-tion angle σ ( θ B ) of the L1642 cloud, all at 10 (cid:48) resolution.The magnetic field orientation θ B shows a sharp transitionbetween the NW and SE regions, as the B field orientationchanges abruptly near the densest part of L1642.The polarization fraction p MAS is very low at the dens-est parts of the cloud. The polarization fraction is high onlyin the N part of L1642, where striations are more visible.There is clear anti-correlation between S and p MAS . In theN area of the striations, the S level is low, and p MAS rel-atively high, which is consistent with a well ordered mag-netic field in this part. As shown in the Planck observationsoverview (Planck Collaboration Int. XIX 2015) and relatedsimulations (Planck Collaboration Int. XX 2015), variationsof the B field direction within the beam or along the line ofsight (e.g. due to tangling), would result in a decrease of theobserved polarization fraction. The relatively high value of p MAS , coinciding with a low S level indicates that the fieldis uniform in this area. MNRAS000
353 GHz intensity I ,polarization angle dispersion function S , the MAS estimateof polarization fraction p MAS , magnetic field orientation an-gle θ B , S/N of the p MAS , and the dispersion of the orienta-tion angle σ ( θ B ) of the L1642 cloud, all at 10 (cid:48) resolution.The magnetic field orientation θ B shows a sharp transitionbetween the NW and SE regions, as the B field orientationchanges abruptly near the densest part of L1642.The polarization fraction p MAS is very low at the dens-est parts of the cloud. The polarization fraction is high onlyin the N part of L1642, where striations are more visible.There is clear anti-correlation between S and p MAS . In theN area of the striations, the S level is low, and p MAS rel-atively high, which is consistent with a well ordered mag-netic field in this part. As shown in the Planck observationsoverview (Planck Collaboration Int. XIX 2015) and relatedsimulations (Planck Collaboration Int. XX 2015), variationsof the B field direction within the beam or along the line ofsight (e.g. due to tangling), would result in a decrease of theobserved polarization fraction. The relatively high value of p MAS , coinciding with a low S level indicates that the fieldis uniform in this area. MNRAS000 , 1–14 (2015)
Figure 1.
Region surrounding L1642 in
P lanck
857 GHz intensity map with POS magnetic field orientation shown by the LIC textureat 30 (cid:48) resolution (see main text for details). Structures discussed in the text are marked with letters a − d . L1642 ( α = 4 h m and δ = − ◦ (cid:48) ) is located at the SW corner of the image (marked with a square), at the head of an over 5 ◦ long HI pillar orientedtowards NE. There are also two smaller dense blobs at the center of the pillar, at approximately α = 4 h m , marked with c . Thedetails of the figure are best seen in the electronic version. Herschel submm maps
Malinen et al. (2014) examined the general structure andstar formation activity of molecular cloud L1642 using es-pecially
Herschel dust emission maps. Their data showeddifferences in the different parts of the cloud. In this paper,we continue with a more detailed analysis of the cloud struc-ture. Fig. 3 ( left ) shows the
Herschel column density mapwith named regions A, B, C, and D. Although the cloud isshaped more like a blob than a filamentary structure, it con-tains several elongated features. As noted in Malinen et al.(2014), there are clear striations in the diffuse cloud sur-rounding the star-forming, dense area, e.g, in the N side ofthe cloud (S1 in the figure). There are also interesting struc-tures that may fall between the concepts of ”filament” and”striation”, for example the spiraling ”tail” in the East (S2in the figure). There are also striations directly connected tothe main parts of the cloud, especially in the W part, wherethey form part of the A structure (S3). All these striationshave column densities of typically N H < × cm − . Also,the two elongated, straight structures (S4) between regionsB and C are not typical filaments or striations. S5 marksanother linear feature almost perpendicular to the S4 struc-tures.The previously known objects, including three YoungStellar Objects (YSOs) binary B-1, binary B-2, and B-3, anda cold clump B-4, inside the densest cloud (Malinen et al.2014), together with the submillimetre clumps from Mon-tillaud et al. (2015) have been marked in Fig. 3 ( right ).Galaxies and non-reliable objects have been removed fromthe list. In the densest central part of the cloud, there isalso an elongated extension, resembling a finger (marked N in the figure), towards North. This type of structure wouldnot usually be considered filament or striation.To extract structures in the Herschel map, we use theRHT method (described in Sect. 3.2). We analysed the RHTresults separately for the whole area and for selected regions.We used the column density N H map to define a threshold incolumn density to separate diffuse ( N H < . × cm − )and dense ( N H > . × cm − ) regions. We then di-vided the dense medium into four regions: A, B, C, and D.The region B is defined as the region of highest column den-sity, N H > . × cm − , shown in Fig. 3 ( left ) with acontour. The other regions are defined as belonging to therespective ellipse shown in Fig. 3 ( left ), and having columndensity values 1 . × cm − < N H < . × cm − .Fig. 4 shows the linear stuctures extracted with theRHT method, and the reliability of the detections. The re-sults match the structures seen in the map very well, reveal-ing detailed, linear structures both in the diffuse regions andin the denser parts of the cloud. We note that in additionto these, the RHT map shows two structures resembling thebody of a fishbone, with linear ”spine” and approximatelyperpendicular ”bones”, marked in the Fig. 4 ( top ). The relia-bility map does not show notable difference in the structuresbetween diffuse and dense regions. P lanck and
Herschel data
Fig. 3 ( right ) shows the magnetic field lines derived from
P lanck polarization map (at 10 (cid:48) resolution) plotted withvectors on the
Herschel µ m intensity map (at ∼ (cid:48)(cid:48) resolution) of the cloud L1642. The length of the vectors MNRAS , 1–14 (2015)
J. Malinen, L. Montier et al.
Figure 2.
P lanck
353 GHz intensity, polarization angle dispersion function S , MAS estimate of polarization fraction p MAS , magneticfield orientation angle θ B , S/N of p MAS , and σ ( θ B ) maps at 10 (cid:48) resolution. The white (and green) contours are from the P lanck
353 GHzintensity map. B field is visualized with vectors on the intensity map. The blue, cyan, magenta, red, and black contours on the p MAS and S/N of p MAS maps show the column density based on
Herschel data at 5.22, 3.0, 2.0, 1.74, and 1.0 × cm − , respectively. The Herschel data are shown at 10 (cid:48) resolution (on the p MAS map) and at the original 40 (cid:48)(cid:48) resolution (on the S/N of p MAS map). The highest(blue) contour is not seen at 10 (cid:48) resolution. MNRAS000
Herschel data at 5.22, 3.0, 2.0, 1.74, and 1.0 × cm − , respectively. The Herschel data are shown at 10 (cid:48) resolution (on the p MAS map) and at the original 40 (cid:48)(cid:48) resolution (on the S/N of p MAS map). The highest(blue) contour is not seen at 10 (cid:48) resolution. MNRAS000 , 1–14 (2015)
Figure 3. ( Left ) Herschel column density map with regions A, B, C, and D, and contours at 1 . × cm − and 5 . × cm − usedfor RHT analysis (see text for details). Other structures discussed in the text are marked with dashed white (or red) ellipses. S1, S2, andS3 mark striations, S4 marks elongated structures between regions B and C, and S5 marks another linear feature almost perpendicularto the S4 structures. ( Right ) Herschel µ m intensity map with sources from Malinen et al. (2014): YSOs B-1, B-2, and B-3, coldclump B-4, and an elongated structure N marked with black ellipses. The YSOs are also marked with red stars. Bound and unboundsubmillimetre clumps from Montillaud et al. (2015) are marked with blue and red ellipses, respectively. B field is visualized with vectors.The grey arrow shows the location of the cut used in the CO analysis in Fig. 11. are proportional to the polarization fraction. For compari-son, Fig. 5 shows the B fields with a LIC map (described inSect. 3.1). There are clear differences in the magnetic fieldorientations in the different areas of the cloud. In the NWpart of the cloud, the magnetic field lines are oriented be-tween NE-SW. In the S and E parts of the cloud, the linesare oriented mostly between E-W. However, when the linesreach the W point of the dense region, they turn abruptlyapproximately 90 ◦ , almost towards S, along with the lines inthe W part. Similarly, when the lines at the E and N regionsmeet at NE at the outskirts of the cloud, they turn towardsthe same orientation, almost to S. The densest part of thecloud is exactly where the B field is bending the most.The Eastern, filamentary curving tail (S2) of the cloudis located in the area where B field lines with different ori-entations meet. The orientation of the two linear structures(S4) between the regions B and C differs by ∼ ◦ . As thefield lines curve in this region, both structures are in fact ap-proximately perpendicular to the local magnetic field. Thelargest elongated structure (N) of the main cloud point-ing towards NE is approximately aligned with the magneticfield. Some of the structures extracted by the RHT method,especially in region A and West of region B, resemble fish-bones, with an elongated structure as the spine, and perpen-dicular smaller structures or striations on both sides. Com-paring to the LIC texture, these structures are not exactlyperpendicular or aligned with the magnetic field, but couldbe moving and evolving. Especially region A looks as if it isbend and shaped by the magnetic field. The roundish gen-eral structure is revealed to be formed of thin slices whenlooked in more detail. Comparing the magnetic field linesto the Herschel map, it is evident how well the field lines follow the general structure of the cloud even to the finerdetails, and the diffuse striations surrounding the cloud.
Fig. 6 shows the polarization fraction p MAS as a functionof the column density (derived from
Herschel maps), fordata at 10 (cid:48) resolution. The sample points are taken ev-ery 5 (cid:48) . The polarization fraction is notably reduced above N H = 2 × cm − . The upper envelope of the polarisationfraction distribution begins to decrease already below thiscolumn density value. Reduced polarization fraction is ob-served over a large area where the magnetic field orientationis still mainly uniform (see Fig. 2). For comparison, the mid-dle left frame of Fig. 2 shows the column density contours(at 10 (cid:48) resolution) on the p MAS map. Although most of thehigh column density pixels originate in the central regionB, also region A has a significant number of pixels above N H = 2 × cm − . All of the highest column density pix-els N H > × cm − originate in the central region Bwithin a few P lanck resolution elements. The high columndensity points in Fig. 6 are therefore highly correlated andcome from a relatively small area.Part of the depolarisation (and most of the scatter)could be related to changes in magnetic field orientation,either at small scales not resolved by
P lanck or in regionsalong the line of sight where POS orientation of the magneticfield differs. However, it is possible that the column densitydependence is caused by a partial loss of grain alignment inthe densest parts of the cloud. If grain alignment is assumedto be caused by radiative torques (see review by Lazarian2007), the change would be directly related to the attenua-
MNRAS , 1–14 (2015)
J. Malinen, L. Montier et al.
Figure 4. ( T op ) Structures extracted by RHT analysis of
Her-schel µ m map. The ellipses show two structures resembling afishbone with ”spine” and approximately perpendicular ”bones”.( Bottom ) Uncertainty of the RHT orientation angle θ RHT . TheHRO analysis is restricted to regions where the uncertainty isbelow 10 ◦ . The grey background shows the POS magnetic fieldorientation with LIC texture. tion of the radiation field. This increases the lower size limitof the dust grains that remain aligned in the magnetic field.Thus, Fig. 6 could point to an almost complete loss of grainalignment in the cloud center and the minimum values of p MAS could be attributed to polarised emission from diffuseregions along the line of sight.The column density dependence of the polarization frac-tion has been discussed in the recent
P lanck papers (PlanckCollaboration Int. XIX 2015; Planck Collaboration Int. XX2015; Planck Collaboration Int. XXXIII 2014). Planck Col-laboration Int. XIX (2015) concluded that the general de-crease of p with N H , at the resolution of 1 ◦ , was mainly dueto fluctuations in the B field orientation along the line ofsight, probing various components in particular toward re-gions close to the galactic plane. This was supported by theanti-correlation observed between p and S . In our case of a high-latitude cloud, there is not as much confusion along theLOS. However, we see an increase of S toward the centralpart associated with the highest N H values. In this paper,we are only looking at one cloud and not making a statisticalanalysis of several regions. Therefore, it is not clear what isthe cause of the decrease of p in our particular case. Herschel structures
We perform a Histogram of Relative Orientations (HRO)analysis (as described in Sect. 3.3) to quantify the align-ment between the magnetic field and the
Herschel µ melongated structures traced by the RHT method. The re-sulting histograms are shown in the top frame of Fig. 7 forthe entire region, and split between the diffuse and denseregions. There are two peaks in this distribution, approxi-mately centred at 0 ◦ and 90 ◦ . The HRO computed on thediffuse regions is mainly associated to the first peak at 0 ◦ ,while the HRO of the denser regions is more complex.When splitting the denser areas into four physical re-gions, A, B, C, and D (as defined in Sect. 4.2), it appears thatthe structures in C are clearly perpendicular to the mag-netic field, while the A and D regions have structures mainlyaligned with the magnetic field (see Fig. 7 lower frame). Inthe densest region B, there is no clear distinction anymore.This is mainly due to the fact that the distribution of theRHT angles (tracing the matter) is much more flat becauseof confusion along the line of sight. Fig. 2 shows that the ori-entation of the magnetic field is reliable and very uniform inthe full region. We also note that the distribution peaks arenot exactly at 0 ◦ and 90 ◦ , but slightly above those values.Region A also shows another, smaller peak at ∼ ◦ . The”fishbone” like structures shown in Fig. 4 ( top ) are in the Aregion, and are likely to contain most of the pixels causingthis peak. We analyze the column density dependence of relative ori-entation using the method described in Sect. 3.4. We havedivided the
Herschel map into 18 continuous bins of columndensity between 0 . × cm − and 9 . × cm − , allcontaining the same number of pixels. The HRO analysis de-scribed above is then performed on each column density binseparately, yielding a set of 18 HROs, which are combinedin matrix M , and shown in Fig. 8. We run an initial PCAanalysis on this set, and find that 95% of the power in M can be expressed with the first two components.In the second step, we apply NMF to factorize matrix M into the product W × H , where the dimensions of H are ( p × n ), and n = 18. As we have seen above in the PCAanalysis, the data is contained in a dimension 2 subspace andhence we can apply NMF directly with p = 2. We then runNMF 1000 times on M to empirically verify that the solutionis constant. The two final averaged components found inthe Monte Carlo runs are shown in Fig. 9. As expected, onecomponent has a clear peak at 0 ◦ , while the other componenthas two main peaks, near 0 ◦ and 90 ◦ .The weights contained in W , i.e. the contribution of MNRAS000
Herschel map into 18 continuous bins of columndensity between 0 . × cm − and 9 . × cm − , allcontaining the same number of pixels. The HRO analysis de-scribed above is then performed on each column density binseparately, yielding a set of 18 HROs, which are combinedin matrix M , and shown in Fig. 8. We run an initial PCAanalysis on this set, and find that 95% of the power in M can be expressed with the first two components.In the second step, we apply NMF to factorize matrix M into the product W × H , where the dimensions of H are ( p × n ), and n = 18. As we have seen above in the PCAanalysis, the data is contained in a dimension 2 subspace andhence we can apply NMF directly with p = 2. We then runNMF 1000 times on M to empirically verify that the solutionis constant. The two final averaged components found inthe Monte Carlo runs are shown in Fig. 9. As expected, onecomponent has a clear peak at 0 ◦ , while the other componenthas two main peaks, near 0 ◦ and 90 ◦ .The weights contained in W , i.e. the contribution of MNRAS000 , 1–14 (2015)
Figure 5.
L1642 in
Herschel µ m map (at 18.3 (cid:48)(cid:48) resolution) with P lanck magnetic field orientation (at 10 (cid:48) resolution) visualized byLIC texture. The details of the figure are best seen in the electronic version.
Figure 6.
Polarization degree p MAS (based on
P lanck data) asa function of the column density (based on
Herschel data). Thedata are at a resolution of 10 (cid:48) , and the samples are taken every5 (cid:48) . each component to the 18 histograms of M are shown asa function of the column density in Fig. 10. This confirmsthat one component is associated with diffuse regions andone with dense regions. We see a clear transition arounda column density at N H ∼ . × cm − . Planck Col-laboration Int. XXXV (2015) derived a threshold value of N H = 10 . cm − ∼ × cm − in their analysis, but us-ing another convention for the dust opacity κ . To comparewith our estimate, we need to divide their value by 3 lead-ing to N H ∼ . × cm − , which is in good agreementwith our result. The other way, our estimate corresponds to N H ∼ . × cm − ∼ . cm − using their conventionfor κ . We use the CO data presented and analysed by Russeil et al.(2003) to compare with the
Herschel map and magneticfield orientations in terms of morphology and kinematics.The general morphology of the cloud revealed by the COdata is very similar to the
Herschel data shown in Fig. 3( left ). It is dominated by the bright clumps A, B and C(Fig. 11a). The Eastern parts of the main filamentary struc-tures in the North (S1) and East (S2) of L1642 are also visi-ble. The Western parts of these structures are overwhelmedby the emission of the main cloud and can be partly revealedwhen selecting the larger velocities (Fig. 11b). However, therelatively low resolution of the CO data does not enable toresolve the striations in these structures, similarly to
P lanck data.The large scale kinematics was studied by Russeil et al.(2003). Their figure A.1 shows channel maps of CO(1 − V LSR = − . − , while another part, includingmostly the West (A) and North regions of the cloud, hasvelocities between V LSR = 0 . − . The Northand East filamentary structures (S1 and S2) are connectedto this second, more red-shifted, structure. In Fig. 11c weshow the map of peak velocity obtained by a Gaussian fit ofthe CO(1 −
0) line.Interestingly, at V LSR > − , the emission of allCO transitions is dominated by the northern part of clumpA, at the root of the striations of the northern structureS1 (Fig. 11b). Fig. 11d shows the position-velocity (PV) di- MNRAS , 1–14 (2015) J. Malinen, L. Montier et al.
Figure 7.
HRO analysis comparing the relative orientation ofmagnetic field and cloud structure in the case of the whole dataor dense and diffuse areas ( top ), and in the case of separate regionsdefined in the main text and shown in Fig. 3 ( left ). N gives thenumber of pixels. Vertical dashed lines show the values 0 ◦ and90 ◦ . The lines for dense and diffuse areas in the ( top ) figure areshifted slightly to the right. agram in CO(2 −
1) along a cut through Clump A (greyarrows in Fig. 11). We find a velocity gradient of ∼ − over the ∼ (cid:48) (0.6 pc) width of Clump A (between offsetsof 5 (cid:48) and 20 (cid:48) ). The velocity then tends to stabilize around1.1 km s − when penetrating the striation region, on thewestern edge of S1 (offsets > (cid:48) ). The cut is shown also onthe Herschel map in Fig. 3 ( right ), revealing that it goesthrough the Western head of Clump A, and parallel to thestriations (S3) on the Northern part of Clump A. For com-parison, we also made a slightly different cut, aligned withthe striations of S3 and the B lines. This does not notablychange the properties of the PV cut.
Figure 8.
The elementary histograms of angle difference builtper bin of column density, so that all histograms contain the samenumber of pixels. Each histogram is normalised by its integral.
Figure 9.
The two principal components found with the NMFalgorithm applied on the 18 histograms of angle difference builtper column density bin. The horizontal axis shows the relativeorientation of magnetic field and cloud structure. Each componentis normalised by its integral.
L1642 is one of the Orion outlying clouds located at thehead of a long HI pillar structure. The cloud itself is elon-gated in the Equatorial E-W direction, forming a complex,partly cometary shaped structure. As shown in Malinenet al. (2014), there are three cores with YSO systems (twobinary and one single) with approximately equal distancesbetween the cores, along a straight line, and apparently inage order from the youngest one (B-2) in the west to theoldest (B-3) in the east. For a cloud with such low mass
MNRAS000
MNRAS000 , 1–14 (2015) Figure 10.
The weights of the components in NMF analysis,i.e., the contribution of each component to the 18 histograms as afunction of column density. The image shows the transition wherethe relative orientation of density structures and magnetic fieldlines changes from preferentially aligned to perpendicular. Thedashed vertical line shows the similar result obtained by PlanckCollaboration Int. XXXV (2015), see main text for details. ( ∼ M (cid:12) ) and high latitude, L1642 has unusually high starformation efficiency, ∼
7% (Malinen et al. 2014).The
P lanck polarization data shown in Figs. 3 ( right )and 5 reveal an ordered magnetic field that pervades thecloud from NE to S. In the smallest scales of the
Herschel map, magnetic field is nearly perpendicular to the line con-necting the YSOs, at least at the western part of the denseregion B. The magnetic field orientation is also closely cor-related with the diffuse material surrounding the cloud, asthe low density striations are aligned with the magnetic fieldorientation. There clearly is a complex interplay between thecloud structure and large scale magnetic fields revealed by
P lanck polarization data. This suggests that the large scalemagnetic field is closely linked to the formation and evolu-tion of the cloud. However, it is an open question whethermagnetic fields shape the cloud, or if the cloud materialshapes the magnetic field, or if they both are simultaneouslyaffected by some physical force.Already Taylor et al. (1982) predicted that a shear-ing flow of material is shaping the cloud. Malinen et al.(2014) discussed the connections between L1642 and itslarger surroundings. To summarise, L1642 appears to be af-fected mostly by a flow coming from the NW/W, or thecloud itself is travelling to NW/W. Both the large scaleFig. 1 and the smaller scale Fig. 5 LIC maps show bend-ing magnetic fields at the NW side of L1642, correspondingto the findings of Malinen et al. (2014) that the cloud seemsto be affected by a compressing force from the NW direc-tion. The cloud morphology and the apparent compressionthat is shaping the cloud from the west suggest that starformation in L1642 may be externally triggered. The openquestion is, what is causing the force shaping the cloud andbending the magnetic field. Lee & Chen (2009) studied starformation in a group of clouds (not including L1642) aroundthe Orion-Eridanus Superbubble, and concluded that com- pression from the Superbubble can potentially have a long-range triggering influence causing star formation in affectedclouds. L1642 is located between two large Bubbles, theOrion-Eridanus Superbubble and the Local Bubble (see Al-cal´a et al. 2008; Malinen et al. 2014, for a summary). It ispossible that this extreme location is enough to cause theobserved phenomena and be the trigger of star formation inthis cloud.This study clearly shows the connection between thelarge scale magnetic field and small scale cloud structurein L1642. However, the conditions affecting the cloud couldmean that magnetic field has more effect here than in otherregions. Also, the geometry of this object can be favourableto reveal such features, as it is quite isolated, in high lat-itude, and shows clear magnetic field orientation. Statisti-cal studies comparing other regions combining
P lanck and
Herschel data would be useful to determine how commonthese features are. Also, high-resolution polarization obser-vations would reveal more details of the small-scale connec-tions between density structures and magnetic fields.
In Section 4.6 we reported the detection of a clear veloc-ity gradient through Clump A with a continuous variationin velocity from the south edge of Clump A to the North-East, parallel to the close-by striation (S3). Since the anglebetween the striation and the plane of the sky remains un-known, it is unclear whether the red-shifted gas is approach-ing Clump A or escaping from it.One possibility is that gas is photoevaporating fromClump A due to the surrounding interstellar radiation field.However, the dust temperature determined from
Herschel data in this part of the cloud, ∼ −
16 K, (Malinen et al.2014; Montillaud et al. 2015) does not support the idea ofUV-rich region, and no ionizing star is known in the vicinityof L1642. On the other hand, the gas may well be much hot-ter than dust at the diffuse cloud surface. Assuming 100 Kgas temperature, the sound speed is ∼ years, which iscompatible with the extent of the striations and the typicallifetime of molecular clouds.Alternatively, the gas north of Clump A could be in-falling into Clump A along the striations and following themagnetic field lines. In Russeil et al. (2003), the total massof the cloud was estimated to be ∼ M (cid:12) based on the COdata. In Malinen et al. (2014), the total mass was estimatedto be slightly higher, ∼ . M (cid:12) , based on dust emission. Ifone assumes accretion onto a 10 M (cid:12) clump, the free-fall ve-locity at the distance of 5 (cid:48) should be ∼ . M (cid:12) anda radius of 0 . ∼ . MNRAS , 1–14 (2015) J. Malinen, L. Montier et al.
Figure 11. CO data of L1642, based on the observations of Russeil et al. (2003). ( a ) Total integrated intensity, ( b ) intensity integratedbetween 0 . < v LSR < . c ) peak velocity obtained by a Gaussian fit of the CO(1 −
0) line, ( d ) position-velocity diagram of CO(2 −
1) along a cut through Clump A and a striation. The cut is shown with grey arrow in the other figures. v LSR is the radialvelocity relative to the local standard-of-rest (LSR) frame. Here, T is the antenna temperature, i.e., it represents the intensity of theemission. The black contours show the total integrated intensity. fore the combination of infall and rotation could explain theobserved velocity gradient.A last alternative we consider here is the collision be-tween two gas streams. We mentioned in Sect. 4.6 that L1642presents two structures with separated velocity ranges, themost blue-shifted including the densest part of the cloud(Clump B) and the southern part (Clump C), while thered-shifted part includes the North and West regions (in-cluding Clump A), as well as the two filamentary structuresS1 (North, connected to Clump A) and S2 (East, connectedto Clump B). This scenario offers the advantage of a com-plete and consistent view of the evolution, morphology andkinematics of the cloud. The cloud would originate from thematerial of the two flows jammed at their meeting point, andwould naturally be cometary shaped. The red-shifted struc-ture would correspond to one stream that is flowing aroundthe North edge of the blue-shifted structure. The striations and the velocity gradient observed in Fig. 11 would originatefrom the shearing between the two streams, and would beinterpreted as a flow of gas away from Clump A. This wouldfit into the notion of Malinen et al. (2014) that Clump Aappears to be compressed from the SW, as the striations(S3) are seen only on the Northern side of the clump. Thealignment between the striations and the magnetic field lineswould also originate from the shearing, assuming that mag-netic field lines are frozen in the gas. Finally, this would alsoexplain the unusually high star formation efficiency of thecloud (Malinen et al. 2014), considering its low mass andhigh latitude. MNRAS000
1) along a cut through Clump A and a striation. The cut is shown with grey arrow in the other figures. v LSR is the radialvelocity relative to the local standard-of-rest (LSR) frame. Here, T is the antenna temperature, i.e., it represents the intensity of theemission. The black contours show the total integrated intensity. fore the combination of infall and rotation could explain theobserved velocity gradient.A last alternative we consider here is the collision be-tween two gas streams. We mentioned in Sect. 4.6 that L1642presents two structures with separated velocity ranges, themost blue-shifted including the densest part of the cloud(Clump B) and the southern part (Clump C), while thered-shifted part includes the North and West regions (in-cluding Clump A), as well as the two filamentary structuresS1 (North, connected to Clump A) and S2 (East, connectedto Clump B). This scenario offers the advantage of a com-plete and consistent view of the evolution, morphology andkinematics of the cloud. The cloud would originate from thematerial of the two flows jammed at their meeting point, andwould naturally be cometary shaped. The red-shifted struc-ture would correspond to one stream that is flowing aroundthe North edge of the blue-shifted structure. The striations and the velocity gradient observed in Fig. 11 would originatefrom the shearing between the two streams, and would beinterpreted as a flow of gas away from Clump A. This wouldfit into the notion of Malinen et al. (2014) that Clump Aappears to be compressed from the SW, as the striations(S3) are seen only on the Northern side of the clump. Thealignment between the striations and the magnetic field lineswould also originate from the shearing, assuming that mag-netic field lines are frozen in the gas. Finally, this would alsoexplain the unusually high star formation efficiency of thecloud (Malinen et al. 2014), considering its low mass andhigh latitude. MNRAS000 , 1–14 (2015) We have compared the large scale magnetic field revealedby
P lanck polarization maps and
Herschel submm dustemission maps in the high-latitude cloud L1642. We concludethat(i) there is a close connection between the cloud struc-ture and the large scale magnetic field in L1642 and thesurrounding region, suggesting that magnetic field is closelylinked to the formation and evolution of the cloud(ii) the connection between cloud structure and largescale magnetic field is seen even at the finest details of thecloud, most notably in the striations(iii) the distribution of relative orientation between cloudstructure and magnetic field lines in diffuse medium has onepeak centered at ∼ ◦ , indicating that diffuse striations andB field are clearly aligned(iv) dense medium presents a bimodal distribution of rel-ative orientation centered at ∼ ◦ and 90 ◦ , but separate re-gions have different behaviours: the dense South part (C) isperpendicular to the B field, West (A) and North (D) exhibitstructures aligned on the B field, and in the densest region(B), we cannot make any distinction on the orientation(v) there is a clear transition from aligned to perpen-dicular structures approximately at a column density of N H = 1 . × cm − (this equals ∼ . cm − when usingthe same convention for dust opacity as Planck Collabora-tion Int. XXXV (2015))(vi) comparison to large scale P lanck polarization dataat ∼ (cid:48) resolution is very useful even when looking at thefinest structures in higher resolution data, e.g. Herschel at ∼ (cid:48)(cid:48) (vii) CO rotational emission confirms that the striationsare connected with the main clumps and likely to containmaterial either infalling to or flowing out of the clumps(viii) Rolling Hough Transform, which was developed toextract linear features in large scale diffuse HI regions, is avery useful and practical method also when studying denserregions with more complex structure ACKNOWLEDGEMENTS
We thank the referee for useful comments which improvedthe paper. We thank Kimmo Lehtinen and Delphine Rus-seil for providing us the CO data from their earlier studies.MJ acknowledges the support of the Academy of Finlandgrants No. 285769 and 250741. S.E.C. was supported by aNational Science Foundation Graduate Research Fellowshipunder grant No. DGE-11-44155. The development of Planckhas been supported by: ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASAand DoE (USA); STFC and UKSA (UK); CSIC, MICINNand JA (Spain); Tekes, AoF and CSC (Finland); DLR andMPG (Germany); CSA (Canada); DTU Space (Denmark);SER/SSO (Switzerland); RCN (Norway); SFI (Ireland);FCT/MCTES (Portugal); and The development of Planckhas been supported by: ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASAand DoE (USA); STFC and UKSA (UK); CSIC, MICINNand JA (Spain); Tekes, AoF and CSC (Finland); DLRand MPG (Germany); CSA (Canada); DTU Space (Den- mark); SER/SSO (Switzerland); RCN (Norway); SFI (Ire-land); FCT/MCTES (Portugal); and PRACE (EU).
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