Boughn, Stephen P.

de Oliveira-Costa, Angelica

Page, Lyman A.

Tegmark, Max

English

Haverford College: Haverford Scholarship

Haverford College Haverford Scholarship Faculty Publications Astronomy 1998 Galatic emission at 19 GHz Angelica de Oliveira-Costa Max Tegmark Lyman A. Page Stephen P. Boughn Haverford College, sboughn@haverford.edu Follow this and additional works at: https://scholarship.haverford.edu/astronomy_facpubs Repository Citation Galactic Emission at 19 GHz. Angélica de Oliveira-Costa et al. 1998 ApJ 509 L9 This Journal Article is brought to you for free and open access by the Astronomy at Haverford Scholarship. It has been accepted for inclusion in Faculty Publications by an authorized administrator of Haverford Scholarship. For more information, please contact nmedeiro@haverford.edu. L9The Astrophysical Journal, 509:L9–L12, 1998 December 10q 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A.GALACTIC EMISSION AT 19 GHzAnge´lica de Oliveira-Costa,1,2 Max Tegmark,2,3 Lyman A. Page,1 and Stephen P. Boughn4Received 1998 August 4; accepted 1998 October 8; published 1998 October 29ABSTRACTWe cross-correlate a 19 GHz full sky cosmic microwave background survey with other maps to quantify theforeground contribution. Correlations are detected with the DIRBE 240, 140, and 100 mm maps at high latitudes( ), and marginal correlations are detected with the Haslam 408 MHz and the Reich & Reich 1420 MHzCFbF 1 30synchrotron maps. The former agree well with extrapolations from higher frequencies probed by the COBEDifferential Microwave Radiometer and Saskatoon experiments and are consistent with both free-free and rotatingdust grain emission.Subject headings: cosmic microwave background — methods: data analysis1. INTRODUCTIONOne of the major challenges in any cosmic microwave back-ground (CMB) anisotropy analysis is to determine the fractionof the observed signal due to diffuse Galactic emission. Threecomponents of Galactic emission have been firmly identified:synchrotron and free-free radiation, which are important mainlyat frequencies below 60 GHz, and thermal emission from dustparticles, which is important mainly at frequencies above60 GHz (see, e.g., Weiss 1980; Bennett et al. 1992; Brandt etal. 1994; Tegmark & Efstathiou 1996). In principle, these threecomponents can be discriminated by their frequency depen-dence and morphology. In practice, however, there is no emis-sion component for which both the frequency dependence andthe spatial template are currently well known (see, e.g., Kogutet al. 1996a, and references therein).The cross-correlation technique allows one to estimate therms level of Galactic emission present in a CMB map. Forinstance, an analysis of high-latitude Galactic emission in theCOBE Differential Microwave Radiometer (DMR) map gaverms estimates of ( ) mK for synchrotron and (3.4 5 3.7 2.7 5) mK for dust emission at 53 GHz on a 77 scale (Kogut et1.3al. 1996b, hereafter K96b). A third component, correlated withthe DIRBE maps but decreasing with frequency, was detectedat the level of ( ) mK and was tentatively identified as7.1 5 1.7free-free emission (K96b). Although this component was alsodetected in the Saskatoon maps (de Oliveira-Costa et al. 1997)on a 17 scale, at a level ( ) mK at 40 GHz, it is still17.5 5 9.5not clear if it is due to free-free emission. An analysis of OwensValley Radio Observatory data at 14.5 GHz showed such acomponent at the level of 203 mK in a small sky region onscales of 79–229 (Leitch et al. 1997, hereafter L97), but thislevel is substantially higher than free-free emission estimatesbased on Ha images (Gaustad et al. 1996; Simonetti et al.1996). Suggested explanations include the presence of high-temperature gas (L97) and rotating dust grains (Draine & La-zarian 1998), but more observational data is needed to settlethis issue. The purpose of this Letter is to evaluate the Galacticcontribution in the 19 GHz full sky map (see Fig. 1) by cross-correlating it with the DIRBE dust maps and with the Haslamand Reich & Reich synchrotron maps.1 Princeton University, Department of Physics, Princeton, NJ 08544;angelica@ias.edu.2 Institute for Advanced Study, Olden Lane, Princeton, NJ 08540.3 Hubble Fellow.4 Haverford College, Department of Astronomy, Haverford, PA 19041.2. METHODThe 19 GHz map consists of pixels with skyN 5 24,576temperatures yi and noise ni. We assume that this map is asuperposition of CMB fluctuations and a Galactic componentwhose angular distribution is traced in part by an external dataset. Representing these contributions by N-dimensional vectors,y 5 n 1 x 1 ax 1 y , (1)CMB Gal Galwhere is the contribution of the fluctuating component ofixCMBthe CMB, is the brightness fluctuations of the GalacticixGaltemplate map (not necessarily in temperature units), a is thecoefficient that converts units of the Galactic template intoantenna temperature, and represents any residual GalacticiyGalcontribution which is uncorrelated with . We consider nixGaland to be random variables with zero mean, i.e.,xCMB, and and to be constant vectors. Thus,Ax S 5 AnS 5 0 x yCMB Gal Galthe data covariance matrix is given byT T T TC { A yy S 2 A ySA y S 5 Ax x S 1 Ann S, (2)CMB CMBwhere is the covariance matrix of the CMB andTAx x SCMB CMBis the noise covariance matrix. The noise in the 19 GHzTAnn Smap is approximately uncorrelated and has a known rms am-plitude of mK. Therefore, the covariance matrix of thisj ∼ 2imap is2C ≈ An n S ≈ j d . (3)ij i j i ijMinimizing yields the2 T 21x { ( y 2 ax ) C ( y 2 ax )Gal Galminimum-variance estimate of a, i.e.,T 21x C yGalaˆ 5 (4)T 21x C xGal Galwith variance12ˆDa 5 . (5)T 21(x C x )Gal GalNote that unlike the case in de Oliveira-Costa et al. (1997),there is little contribution from chance alignments between theCMB and the various template maps, since the CMB contri-bution to C is negligible. If the noise is correlated or the an-L10 DE OLIVEIRA-COSTA ET AL. Vol. 509Fig. 1.—The 19 GHz survey (top), 408 MHz Haslam synchrotron template(middle), and DIRBE 100 mm dust template (bottom).TABLE 1Correlations with the 19 GHz MapTemplate aaˆ ˆDa ˆDaM ˆDaTdTb(mK)CFbF 1 20100 mm . . . . . . . . . 38.5 3.3 5.8 8.3 138.6 5 29.9140 mm . . . . . . . . . 29.8 2.5 4.0 6.3 146.0 5 30.9240 mm . . . . . . . . . 46.2 3.9 6.0 10.0 143.2 5 31.0408 MHz . . . . . . . 13.4 3.1 3.4 4.4 52.3 5 17.21420 MHz . . . . . . 0.9 0.1 0.2 0.3 86.5 5 28.8CFbF 1 30100 mm . . . . . . . . . 47.1 9.0 16.2 17.3 65.9 5 24.2140 mm . . . . . . . . . 31.6 6.3 10.2 10.3 66.4 5 21.6240 mm . . . . . . . . . 38.9 8.4 12.8 12.9 66.1 5 21.9408 MHz . . . . . . . 7.6 3.7 4.7 6.2 25.1 5 20.51420 MHz . . . . . . 0.4 0.2 0.2 0.3 29.8 5 22.3a has units mK (MJy sr21)21 for the DIRBE templates, mK/Kaˆfor the 408 MHz template, and mK/mK for the 1420 MHz template.b.ˆ ˆdT { (a 5 Da )jT Galisotropy signal is significant, then our C used above will differfrom the true covariance matrix, denoted C9. Although equation(4) still provides a reasonable and unbiased estimate of a,5 itsvariance will be larger than implied by equation (5), given byT 21 ′ 21(x C C C x )Gal Gal2ˆDa 5 . (6)T 21 2(x C x )Gal GalIn the next section, an estimate of C9 is made from the dataand the corresponding variance of is evaluated.aˆ3. DATA ANALYSIS AND RESULTSThe 19 GHz map has an angular resolution of 37 FWHMand is stored in pixels (Cottingham 1987; Boughn17.3 # 17.3et al. 1992). The template maps are convolved with a 37 Gaus-sian beam, and regions within 207 and 307 of the Galactic planeare excluded. To avoid contamination by zodiacal dust emis-sion, data within 107 of the ecliptic plane are also excludedfrom the analysis, although the results are found to be inde-pendent of this cut. Off the Galactic plane, the 19 GHz map5 Note that the diagonal approximation of eq. (3) reduces eq. (4) to a simplenoise-weighted least-squares fit.is dominated by the CMB dipole ( ). On the other hand,ø 5 1because of its planar structure, emission associated with theGalaxy has a strong quadrupole ( ) component. Therefore,ø 5 2the monopole, dipole, and quadrupole moments are removedfrom both the 19 GHz and template maps. As a consequence,the computed depends only on correlated structure in theaˆmaps on angular scales &907.3.1. Correlations and Their Error BarsThe 19 GHz map was cross-correlated with five differenttemplates: two for synchrotron emission—the 408 MHz (Has-lam et al. 1981) and 1420 MHz (Reich & Reich 1988) sur-veys—and three to study dust and free-free emission—the 100,140, and 240 mm DIRBE sky maps (Boggess et al. 1992). Table1 lists the coefficients derived from equation (4) with errorsaˆcomputed from equation (5). All three DIRBE templates showsignificant correlations with the 19 GHz map, while the twosynchrotron templates are found to be only marginallycorrelated.Also listed in Table 1 are the implied fluctuations in antennatemperature in the 19 GHz map, i.e., , where jGal isˆdT 5 ajGalthe rms of the template map. If a template map includes adistinct component that is uncorrelated with the 19 GHz map,then dT is underestimated by a factor , where is′ ′j /j jGal Gal Galthe rms of the correlated component of the template map. Forthis reason, the dT’s in Table 1 should be considered lowerlimits.As mentioned above, the errors listed in Table 1 were com-puted from equation (5) and are therefore lower limits to theerror. We now describe a series of tests, performed to estimatethe uncertainty in due to correlated noise and otheraˆsystematics.3.1.1. The Noise Correlation FunctionIf the true noise correlation matrix is isotropic, ′C 5ij, where vij is the angle between pixels i andAn n S 5 R(v )j ji j ij i jj, then we can estimate the noise correlation function R(v) ofthe 19 GHz data (after removing the monopole, dipole, andquadrupole) by , where yi is the antenna21R(v) 5 N O y y /j jv ij i j i jtemperature of the ith pixel and the sum is over all Nv pairs ofpixels separated by v. Substituting these relations into equation(6) gives estimates of that are from 6% to 17% larger thanˆDathose in Table 1.No. 1, 1998 GALACTIC EMISSION AT 19 GHz L11Fig. 2.—Dependence of on Galactic latitude for the 100 mm map.aˆ FbFThe error bars are given by .ˆDaT Fig. 3.—CCF(v) between 19 GHz and 140 mm map for a 307 Galactic cut,together with the 140 mm autocorrelation.3.1.2. Monte Carlo SimulationsAs another test of the robustness of the estimates of , weaˆemployed Monte Carlo simulations in which the template mapsare sliced into 18 regions of equal area, each corresponding toa range of Galactic latitude . Inside each of these regionsFbFthe pixels are rearranged in random order, so that the latitudedependence is preserved but the longitudinal correlations aredestroyed. Repeating this procedure 1000 times yields distri-butions of ’s consistent with zero mean and with standardaˆdeviations times larger than the formal errorsˆ ˆDa ∼ 1.6 DaM(see Table 1).3.1.3. Sky RotationsBecause of the approximate axial symmetry of the Galaxy,it is natural to ask if the correlations are simply due to overalllarge-scale Galactic structure common to all emission com-ponents. To test this hypothesis, we repeated the analysis withtransformed maps, rotated around the Ga-2 # 2 # 36 5 144lactic axis by multiples of 107 and/or flipped vertically and/orhorizontally.For a 207 Galactic cut, the correct template map has thehighest of all 144 correlations, while the distribution of thesecorrelations has standard deviation times larger thanˆDa ∼ 2.5Tthe formal errors . Likewise, the correct DIRBE maps haveˆDathe highest of all 144 correlations, and the standard deviationsare , even for a 307 Galactic cut (see Table 1). Inˆ ˆDa ∼ DaT Mcontrast, we find no significant correlation between the 100 mmand Haslam maps, indicating that synchrotron and dust emis-sion are not strongly correlated at high latitudes.Since both and have correlated signals contributingˆ ˆDa DaM Tto the noise, they constitute overestimates of the true error bars.3.2. Latitude DependenceTo investigate the dependence of the correlation on Galacticlatitude, we sliced the maps into six regions of equal area, eachcorresponding to a range of latitude . Figure 2 shows theFbFresults for the 100 mm map. Note that from the 19 GHzaˆDIRBE correlation stays almost the same at each latitude band,indicating that this correlation is not dominated by one or twonearby clouds. The 19 GHz Haslam correlation is found to bemore concentrated in the Galactic plane.66 In order to test how important spatially localized features are for thecorrelation, we cross-correlated 19 GHz with Haslam using only one hemi-sphere. Most of the correlation was found to come from the northern hemi-sphere, presumably because of emission features such as the North Polar Spur.3.3. Scale DependenceOne way to determine angular scale of the correlation is tocompute the angular cross-correlation function (CCF) of the19 GHz map with the template maps. We computed this ac-cording to , where the2 22CCF(v) 5 [O x y /j ] [O j ]Zij Gal, j i i ij isums are again over all pairs of pixels separated by v.As an example, Figure 3 shows the CCF(v) of the 19 GHzand 140 mm maps as well as the autocorrelation function ofthe 140 mm map. It is clear that the correlated structure in thetwo maps is on small angular scales ( ) and that theCv & 10CCF is well-behaved on all angular scales. The latter gives usadditional confirmation that there are no large, unknown sys-tematics that compromise the analysis. Similar results are foundfor the other two DIRBE maps. The lower signal-to-noise ratiofor the correlation of the two radio templates result in CCFswhich are less demonstrative. Note that .ˆCCF(0) ∝ aAs another way to investigate the dependence of the cor-relation on the angular scale, we repeated the analysis afterhigh-pass filtering the 19 GHz map using a partial sky multipoleremoval technique (see Tegmark & Bunn 1995). Only afterremoving spherical harmonic components with does theø * 8correlation significantly decrease, which again indicates thatlarge-scale Galactic structure is not the source of the correla-tion. Both types of filtering therefore indicate that the bulk ofthe correlations are caused by fluctuations on scales of severaldegrees, which is consistent with the shape of the CCF in Figure3.4. CONCLUSIONSThe two synchrotron templates are found to be marginallycorrelated with the 19 GHz map, while all three DIRBE far-infrared templates show a significant correlation. When a syn-chrotron and a DIRBE template are simultaneously fit to the19 GHz map (via linear regression), the correlation coefficientsdo not change significantly from those listed in Table 1 and,in addition, the two fit parameters are essentially uncorrelated( . We conclude that the correlations with DIRBEFrF & 0.05)dust emission are independent of the correlations with syn-chrotron emission. The amplitude of the signal is much largerthan expected for ordinary (vibrational) dust emission, asshown in Figure 4. Moreover, there is now good agreementbetween different experiments that this correlated componentis brighter at lower frequencies.So what physical component is this? Two contenders havebeen proposed. Kogut et al. (1996a; K96b) argue on physicalgrounds that free-free emission might be spatially correlatedL12 DE OLIVEIRA-COSTA ET AL. Vol. 509Fig. 4.—Frequency dependence of the fluctuating component of the Galacticemission for . The DMR correlations are represented by circlesCFbF 1 30(K96b), Saskatoon data by pentagons (de Oliveira-Costa et al. 1997), and19 GHz by a square with error bar given by (this work). Dust emissionˆDaT(vibrational modes only) is normalized using the DMR correlation at 90 GHz(Kogut et al. 1996a). The free-free model is normalized to the DMR correlationat 31.5 GHz (the rms free-free emission derived from Ha is much smallerthan this DIRBE-correlated component). The synchrotron emission is nor-malized to the correlation between the 19 GHz map and the 408 MHz Haslammap (see Table 1) and is consistent with the 31.5 GHz upper limits from K96b.The thickness of each curve corresponds to the normalization uncertainty. Thedashed line is an example of emission from rotating dust grains (Draine &Lazarian 1998). All fluctuations have been converted to DMR angular scalesas , where is the rms of each template map and the correctioni iˆdT 5 «aj jGal Galfactor is . Here is DMRb DMR b i 1/2 DMR« 5 ([O (2ø 1 1)ø W ] [O (2ø 1 1)ø W ]) WZø ø øwindow function, is the window function of the experiment to be converted,iWøand we assume a power spectrum slope.b 5 23with dust. However, the correlations between Ha (which isnormally a good tracer of free-free emission) and CMB maps,and between Ha and the DIRBE maps, are weak (L97; Kogut1997; McCullough 1997). One possibility is the presence ofan extremely hot (*106 K), ionized plasma (L97); however,Draine & Lazarian (1998) have argued that this cannot be trueacross the whole sky on energetic grounds. These results mo-tivated Draine & Lazarian to suggest that perhaps it is dustafter all but emitting through rotational rather than vibrationalexcitations. As shown in Figure 4, this can give a spectrumquite similar to that of free-free emission in the relevant fre-quency range.Ha maps with better accuracy are currently being made bythe Dennison, Gaustad, and Reynolds groups and should helpto settle the issue. Another test is indicated by Figure 4: al-though both the rotating dust and the free-free models appearconsistent with the available data,7 the former predicts a bumpand a downturn around 10–20 GHz, while the latter predictsa continued rise toward lower frequencies. A cross-correlationanalysis with lower frequency data like the 10 GHz Tenerifemap may be able to discriminate between these two models.We would like to thank Ed Cheng, Dave Cottingham, BruceDraine, Dale Fixsen, Ken Ganga, Ed Groth, Al Kogut, AlexLazarian, George Smoot, and David Wilkinson for helpful com-ments. Support for this work was provided by NASA grantsNAG5-6034 and NAG5-3015, by NSF grant PHY-9600015,by a David and Lucile Packard Foundation Fellowship (toL. P.), and by NASA through Hubble Fellowship HF-01084.01-96A from STScI, operated by AURA, Inc. under NASA con-tract NAS5-26555.7 We compute the spectral index between 19 and DMR 53 GHz to be ∼22.4and that between 19 GHz and 1420 MHz to be ∼22.8.REFERENCESBennett, C. L., et al. 1992, ApJ, 396, L7Boggess, N. W., et al. 1992, ApJ, 397, 420Boughn, S. P., et al. 1992, ApJ, 391, L49Brandt, W. N., et al. 1994, ApJ, 424, 1Cottingham, D. A. 1987, Ph.D. thesis, Princeton Univ.de Oliveira-Costa, A., et al. 1997, ApJ, 482, L17Draine, B. T., & Lazarian, A. 1998, ApJ, 494, L19Gaustad, J. E., et al. 1996, PASP, 108, 351Haslam, C. G. T., et al. 1981, A&A, 100, 209Kogut, A. 1997, AJ, 114, 1127Kogut, A., et al. 1996a, ApJ, 460, 1———. 1996b, ApJ, 464, L5 (K96b)Leitch, E. M., et al. 1997, ApJ, 486, L23 (L97)McCullough, P. R. 1997, AJ, 113, 2186Reich, P., & Reich, W. 1988, A&AS, 74, 7Simonetti, J. 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Galatic emission at 19 GHz

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Galatic emission at 19 GHz

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