Statistics of WMAP ILC map temperature fluctuations towards distant radio galaxies
aa r X i v : . [ a s t r o - ph . C O ] A ug Bull. Spec. Astrophys. Obs., 2011, 66, 199–206 c (cid:13) Special Astrophysical Observatory of the Russian AS, 2018
Statistics of WMAP ILC Map Temperature FluctuationsTowards Distant Radio Galaxies
O.V. Verkhodanov a , M.L. Khabibullina a a Special Astrophysical Observatory of the Russian AS, Nizhnij Arkhyz 369167, Russia
Received September 6, 2010; accepted February 1, 2011.
For 2442 galaxies of the catalog, compiled based on the NED, SDSS, and CATS survey datawith redshifts z > . T max = 0 .
012 mK is located within the σ interval, estimated byMonte Carlo simulations for the Gaussian fluctuations of the CMB signal in the ΛCDM model.The low amplitude of the dipole indicates that it is impossible to confirm this hypothesis from theWMAP data. In addition, we studied the statistics of the fluctuation amplitude of the microwavesignal in the direction to radio galaxies. A weakening of the absolute value of the mean signal inthe corresponding fields was discovered. Key words:
Radio lines: galaxies—techniques: radar astronomy
1. INTRODUCTION
The studies of properties of the large-scale structure,reflected in the statistics of the Cosmic MicrowaveBackground (CMB), are of particular interest in con-nection with the advent of new high-accuracy obser-vations in the millimeter and submillimeter ranges[1, 2, 3, 4]. Using the data on galaxy clusters andthe magnitude of the CMB signal fluctuations in thedirection to their centers, where the signal fluctu-ations are caused by the Sunyaev-Zel’dovich effect(SZ) [5], we can estimate the cosmological parame-ters (the Hubble constant H , and the density pa-rameter Ω ) [6]. In addition, one of the componentsof the SZ effect—the kinematic SZ effect, caused bythe proper motion of the cluster as a whole with re-spect to the CMB reference system—opens the pos-sibility of studying the large-scale fluxes of matter.In particular, [7, 8] describe the study of large-scale“dark bulk flows” in motion of clusters of galaxies,based on the WMAP5 data and the catalog, com-piled from the X-ray data and containing more than1000 clusters. The authors have calculated the dipolefrom the CMB pixel values. The dipole is determined,in their opinion, by the kinematic SZ effect; it revealsa constant velocity, at least on the scale of 800 Mpc. Note that despite the low WMAP sensitivity tothe SZ effect due to the relatively poor resolution ofthe final map of the isolated CMB signal (the lim-iting spherical harmonics—a multipole—in the firstWMAP releases for the ILC CMB map there is ℓ max ∼ θ ∼ ′ and inthe seven-year release it is ℓ max ∼
150 ( θ ∼ ′ ), whilethe SZ effect for most of galaxy clusters is stronglymanifested on the small scale: θ < ′ ), the discussedeffect is of great interest in terms of its manifestationin the ongoing Planck mission .Also note that despite the limitations on reso-lution (channel W has a better resolution of 12 . ′ with the frequency of 94 GHz) and on the sensitiv-ity of WMAP maps, various attempts to measurethe SZ effect statistically have been made both inthe population averaging (“stacking”) (see, e.g., re-cent papers [9, 10]), and directly for individual brightclusters, such as Coma [10], where the effect wasobserved. Diego and Partridge [9] used three chan-nels: Q (43 GHz, FWHM = 0 . ◦ ), V (61 GHz,0.35 ◦ ) and W (94 GHz, 0.22 ◦ ) and obtained aver-aged profiles in the direction to known clusters. In O.V. Verkhodanov,M.L. Khabibullina particular, besides the presence of the desired signaland the growth of its amplitude with frequency, theauthors found that the signal’s value is lower than ex-pected from the X-ray data, the fact that they linkedwith the presence of a point source in the cluster. TheWMAP team [10] has conducted a similar study, us-ing two channels: V and W. They also applied the av-eraging of different regions in the direction to knownclusters with X-ray emission and evidenced the ef-fect. In addition, they discovered that the effect canbe traced down to the scales of θ = 1 . ◦ . The sig-nal on the scale of θ = 0 . ◦ is considered as true,and that on the scale of θ = 1 . ◦ —as a statisticalfluctuation. At that, the authors [10] have concludedthat the apparent effect for the averaged sources isconsistent with that, expected from the X-ray obser-vations. Let us emphasize that the evaluations aremade for the source, producing the SZ effect, and av-eraged over the sky. Recent experiments, such as thethe one conducted on the Atacama Cosmology Tele-scope (ACT) [11] and Planck mission [12] already al-low to isolate and see this effect directly.Despite the fact that for most clusters the SZ ef-fect is not directly visible in the WMAP data, it isestimated statistically. We believe that the approachproposed in [7, 8] deserves special attention. We de-velop it in this paper, using the amplitude of temper-ature fluctuations in the points, corresponding to thedirection to distant radio galaxies from our survey forthe analysis. To detect the possible “dark bulk flow”we need to evaluate the signal towards distant radiogalaxies. A useful moment is the fact that the CMBsignal in the ILC map of fluctuations is isolated usingthe channels, in which the SZ effect, if existing, willhave a negative signal. Fortunately, the angular scaleof the SZ effect, discovered by the WMAP team [10]corresponds to the resolution of the ILC map of seven-year observations.In the standard scheme of galaxy formation, theradio source lights up as a result of a merger of galax-ies, and formation of an accretion disk and jets, ob-served at radio and other wavelengths. As a rule (seereviews in [13, 14]), the most powerful radio galax-ies, visible at large redshifts are identified with gi-ant elliptical galaxies, which are mainly the centralgalaxies of clusters and are formed by merging. Thisproperty (radio emission) can be used to find dis-tant clusters and protoclusters of galaxies. For ex-ample, [15] presents the results of a program, con-ducted with the ESO VLT telescope, searching forthe emerging clusters of galaxies near the powerfulradio galaxies at redshifts 2 < z < . B . > erg s − Hz − sr − . Theauthors have selected 150 objects and examined thefields around nine of them. In the fields the authors have selected the galaxies, emitting in Ly α (the so-called Ly α -emitters), the redshifts of which were mea-sured. Using the data on spatial density of objects itwas concluded whether they belong to protoclusters.The size of such protoclusters is at least 1.75 Mpc. Itwas shown that 75% of radio galaxies with z > × − of the forming clusterslay in the interval of 2 < z < . z > .
2. DATA ANALYSIS
A sample of radio galaxies with z > . , CATS [21, 22],SDSS [23] with the aim to use it in various statisti-cal and cosmological tests [13, 24, 25], which requirean analysis of a large sample of objects of the samenature. The NED database was used to constructthe primary list of objects. We selected from it theobjects with required parameters, mainly based onredshift ( z > .
3) and morphological properties ofradio galaxies. The initial catalog contained 3364objects. Such a sample of galaxies is contaminatedwith objects with incomplete information, or objectswith other properties. Therefore, special attentionwas paid to clean the original sample from the oddsources: galaxies (1) with redshifts, determined bythe photometric method; (2) those with quasarproperties from the available literature data. Thefinal catalog contains 2442 sources with spectroscopicredshifts, the photometric values and flux densitiesin the radio range, the sizes of radio sources, as wellas radio spectral indices, which were calculated basedon the results of cross-identification with the radiocatalogs, stored in the CATS, in the frequency range http://cats.sao.ru TATISTICS OF WMAP ILC MAP TEMPERATURE FLUCTUATIONS (Wilkinson Microwave AnisotropyProbe). To construct the WMAP map, the datain five bands were used: 23 GHz (K-band), 33 GHz(Ka-band), 41 GHz (Q-band), 61 GHz (V-band), and94 GHz (W-band). The ILC map contains informa-tion on the distribution of the microwave backgroundfor not very high harmonics ( ℓ ≤ T ( θ, φ ), describing the tem-perature anisotropy on the sphere, with two limit-ing values (by angular resolution) of the multipoles ℓ max ≤
150 ( θ ≥ ′ ) and ℓ max ≤
20 ( θ ≥ ′ )according to the decomposition into sphericalharmonics:∆ T ( θ, φ ) = ∞ X ℓ =2 m = ℓ X m = − ℓ a ℓm Y ℓm ( θ, φ ) , where the spherical harmonics is Y ℓm ( θ, φ ) = s (2 ℓ + 1)4 π ( ℓ − m )!( ℓ + m )! P mℓ ( x ) e imφ ,x = cos θ P mℓ ( x ) are the associated Legendre poly-nomials, ℓ and m are the multipole number and itsmodes, respectively. For the expansion of sphericalharmonics, we used the GLESP package [26]. To analyze the Gaussianity of the distribution in thefirst order and compare it with the model, we tookthe amplitude of CMB signal fluctuations in the mappixels, onto which the radio galaxies are projected(Fig. 2), and constructed the histograms of its distri-bution (Fig. 3). One of the rules of galaxy selectionin our sample was the presence of a spectroscopicredshift, measured, as a rule, in objects outside theGalactic plane, hence the lack of sources in the cen-tral band of Fig. 2 (the Galactic plane) is a selectioneffect. The pixel size of maps, used for the analysis,at resolutions of ℓ max ≤
150 and ℓ max ≤
20 amountsto 36 ′ × ′ and 260 ′ × ′ , respectively. The analysis http://lambda.gsfc.nasa.gov was carried out for maps with ℓ max ≤ σ -spread, calculated by two methods on the pixelstatistics: (1) for the given 100 realizations of the mi-crowave background maps in the ΛCDM cosmologi-cal model with homogeneous and isotropic Gaussianrandom fields, resulting in the corresponding CMBfluctuations, and (2) for 100 realizations of a randomarrangement of 2442 points in the ILC WMAP7 mapitself. The value of the histogram bean is 0.02 mK.Note the particularities of the distributions shownin Fig. 3. All the signal variation distributions in thestudied pixels are close to normal. The distributionmaximum N is located strictly in the region of zeroamplitude fluctuations. Its value exceeds the mean ex-pected level by more than 3 σ for the maps with a res-olution of ℓ max ≤
150 and about 2 σ with ℓ max ≤ σ for the estimates, obtained in randomlyselected pixels of the ILC map. The estimates are pre-sented in the Table.In addition, for both resolutions ℓ = 150, and ℓ = 20, the ratio ( T max /T min ) lcdm > ( T max /T min ) ilc ,indicating a lower dispersion of signal variations inthe map than that, expected in the ΛCDM model. Using the value of temperature fluctuations in pixelsin the map with a resolution of ℓ = 150, applying theleast-squares method we estimated the correspondingdipole in the form T ( l, b ) = T x cos( l ) cos( b ) + T y sin( l ) cos( b ) + T z sin( b ) , where ( l, b ) are the galactic coordinates: longitudeand latitude, T ( l, b ) is the value of CMB temperaturefluctuations in mJy, taken in the pixels correspondingto the positions of radio galaxies, and ( T x , T y , T z ) arethe dipole components, which are found to be equalto (0.0116, 0.0036, 0.0026), respectively.Hence, we obtain the following for the extrema: T extrem = ± q T x + T y + T z ,b = ± arctan( T z / q T x + T y ) ,l = arctan( T y /T x ) , O.V. Verkhodanov,M.L. Khabibullina
Figure 1:
Position of selected radio sources on the celestial sphere in galactic coordinates. White circles markthe SDSS objects, gray crosses—the remaining sources.
Figure 2:
Position of selected galaxies (black circles) in the CMB WMAP map with a resolution of ℓ max = 20 in galactic coordinates. Dark spots in the map correspond to the cold signal, while light spots—to the hot signal. or in the maximum T max = 0 . l max , b max ) = (17 ◦ . , ◦ . T min = − . l min , b min ) = (197 ◦ . − ◦ . T max = 0 .
012 mK. This value lays within the σ -scatter from the mean, i.e. within the noise, estimatedby modelling of 50 CMB signal realizations in theΛCDM model, and determining the parameters of the dipole in each of the realizations for the coordinates ofthe radio galaxy catalog. The modelling results yieldan average estimate of the parameters ( T x , T y , T z ) =(0 . ± . , . ± . , − . ± .
3. RESULTS
We investigated the properties of the CMBWMAP7 signal in the fields of distant ( z > .
3) radiogalaxies. In general, the signal distribution over theareas corresponds to normal. Moreover, in this dis-tribution the histogram amplitude is higher than ex-pected (more than by a σ -scatter) both for the ΛCDM TATISTICS OF WMAP ILC MAP TEMPERATURE FLUCTUATIONS
The histograms of the distribution of the microwave background signal value (the thick solid line)in the ILC map, measured in pixels, corresponding to the direction to radio galaxies. Above: histograms forthe pixel map resolution of ℓ max ≤ . Bottom: histograms for the pixel map resolution of ℓ max ≤ . Left:the dotted and dashed lines show the levels of σ and σ -spreads, respectively, calculated from the data of 100realizations of the Λ CDM cosmological model. Right: The dotted and dashed lines show the levels of σ and σ -spreads, respectively, calculated from the data of 100 realizations of a random distribution of points in theILC WMAP seven-year map. Figure 4:
The position of the dipole on the sphere, determined with the least-squares method from the CMBpixel values in the locations of distant radio galaxies, in galactic coordinates. O.V. Verkhodanov,M.L. Khabibullina
Table 1:
Table.
Parameters of normal distribu-tion (the amplitude N and the width parameter s = θ . (8 ln 2) − / ), corresponding to the distribu-tion of the CMB temperature fluctuation amplitudein the pixels of galaxy positions for maps with res-olutions ℓ = 150 and ℓ = 20 . The estimates of thedistribution of temperature minima and maxima atthe σ -scatter are obtained when modeling the back-ground fluctuations in 100 realizations of a randomsignal in the Λ CDM cosmological model (marked as lcdm ), and in the simulations of 100 realizations ofa random scatter of galaxy locations in the ILC map(noted as ilc ). Value Amplitude s ,Distribution N mK T ( ℓ = 150) 319.2 0.060 T min ( ℓ = 150) lcdm T max ( ℓ = 150) lcdm T min ( ℓ = 150) ilc T max ( ℓ = 150) ilc T ( ℓ = 20) 552.6 0.035 T min ( ℓ = 20) lcdm T max ( ℓ = 20) lcdm T min ( ℓ = 20) ilc T max ( ℓ = 20) ilc s distribution is smaller than expected in mod-els, which also indicates an increased number of pix-els with zero signal in the fields of radio galaxies. Andif the correlation ( T max /T min ) lcdm > ( T max /T min ) ilc can be explained by an underestimated value of theamplitude of the ILC quadrupole, then the cause ofthe effect of signal attenuation in the fields of radiogalaxies is as yet unclear.We as well tried to test the effect of existence ofa dipole in the CMB data in the regions of galaxyclusters, discovered in [7, 8]. It is determined, as theauthors suppose, by the kinematic SZ effect, and asso-ciated with the “dark bulk flow” of matter. To verifythis phenomenon, we constructed a dipole using thevalues in the pixels of galaxy positions, and foundthat this dipole’s amplitude is below the σ noise levelof model variations.Note that the size of the ILC map pixel in generaldoes not allow to valuably investigate the SZ effect. Inaddition, it is clear that the nonzero dipole can almostalways be defined for a finite sample of pixels withnonzero values, what the models are demonstrating.Although we do not rule out the possibility that forthe nearby clusters of galaxies the background fluctu-ations can show the existence of a common movement,distinct from the known CMB kinematic dipole, butfor distant objects, as in our case, the Hubble flow willbe dominating. We shall be able to check this effectafter the publication of maps of the Planck mission.
4. ACKNOWLEDGMENTS
The authors are grateful to P. D. Naselsky for help-ful discussions, to S. A. Trushkin for valuable com-ments that allowed to improve the text and to O. Na-sonova for her aid with the calculations in the MAT-LAB package. In the study we used the NED databaseof extragalactic objects The authors also used the CATS[27] database of radio astronomy catalogs, the FADPS [28, 29] system for processing the radio astronomy data,and the GLESP package data analysis of microwave ra-diation on the sphere [30, 31]. This work was supportedby the Leading Scientific Schools of Russia (S. M. Khaikinschool) grant, and the RFBR grants (project nos.09-02-00298, 08-02-00486). O.V.V. is also grateful for thepartial support of the Dmitry Zimin Dynasty Foundation. References
C. L. Bennett, M. Halpern, G. Hinshaw, et al., Astrophys.J. Supp. , 1 (2003), astro-ph/0302207.G. Hinshaw, D. N. Spergel, L. Verde, et al., Astrophys. J.Supp. , 288 (2007), astro-ph/0603451.G. Hinshaw, J. L. Weiland, R. S. Hill, et al., Astrophys.J. Supp. , 225 (2009), astro-ph/0803.0732.N. Jarosik, C. L. Bennett, J. Dunkley, et al., Astrophys.J. Supp., submitted (2010), arXiv:1001.4744.Ya. B. Zeldovich and R. A. Sunyaev, Astrophys. SpaceSci. , 301 (1969). http://sed.sao.ru/ ∼ vo/fadps e.html TATISTICS OF WMAP ILC MAP TEMPERATURE FLUCTUATIONS
G. De Zotti, R. Ricci, D. Mesa, et al., A&A , 893(2005), astro-ph/0410709.A. Kashlinsky, F. Atrio-Barandela, H. Ebeling, et al., As-trophys. J , 81 (2010), astro-ph/0910.4958.F. Atrio-Barandela, A. Kashlinsky, H. Ebeling, et al., As-trophys. J , 77 (2010), astro-ph/1001.1261.J. M. Diego and B. Partridge, MNRAS , 1179 (2010).E. Komatsu, K. M. Smith, J. Dunkley, et al., Astrophys.J. Supp. , 18 (2011), astro-ph/1001.4538.A. D. Hincks, V. Acquaviva, P. A. R. Ade, et al. Astro-phys. J. Supp. , 423 (2010).N. Aghanim, M. Arnaud, M. Ashdown, et al. (PlanckCollaboration), A&A, submitted (2011), astro-ph/1101.2043.O. V.Verkhodanov and Yu. N. Parijskij,
Radiogalaktikii kosmologija (Radio Galaxies and Cosmology) , (Fiz.Math. Lit., Moscow, 2009) [in Russian].G. Miley and C. De Breuck, Astron. Astroph. Rev , 67(2008).B. P. Venemans, H. J. A. R¨ottgering, G. K. Miley, et al.,A&A , 823 (2007).M. L. Khabibullina and O. V.Verkhodanov, Astrophys.Bull. , 123 (2009), astro-ph/0911.3741.M. L. Khabibullina and O. V.Verkhodanov, Astrophys.Bull. , 276 (2009), astro-ph/0911.3747.M. L. Khabibullina and O. V.Verkhodanov, Astrophys. J.Suppl. , 340 (2009), astro-ph/0911.3752.O. V.Verkhodanov and M. L. Khabibullina, Pis’ma As-tron. Zh. , 9 (2010), astro-ph/1003.0577.M. L. Khabibullina and O. V.Verkhodanov, Astron. Zh. , 333 (2011).O. V. Verkhodanov, S. A. Trushkin, H. Andernach andV. N. Chernenkov, ASP Conf. Ser. , 322 (1997),astro-ph/9610262.O. V. Verkhodanov, S. A. Trushkin, H. Andernach andV. N. Chernenkov, Bull. Spec. Astrophys. Obs. ,118 (2005), astro-ph/0705.2959.D. P. Schneider, P. B. Hall, G. T. Richards, et al., AJ , 102 (2007).O. V. Verkhodanov and Yu. N. Parijskij, Bull. Spec. As-trophys. Obs. , 66 (2003).O. V. Verkhodanov and Yu. N. Parijskij, in Proc. 14thInternat. School Particles and Cosmology , Ed. byS. V. Demidov, V. A. Matveev, and V. A. Rubakov(INR, Moscow, 2008), p. 109.A. G. Doroshkevich, P. D. Naselsky, O. V. Verkhodanov,et al., Int. J. Mod. Phys. D , 275 (2003), astro-ph/0305537.O. V. Verkhodanov, S. A. Trushkin, H. Andernach andV. N. Chernenkov, Data Science Journal , 34 (2009),astro-ph/0901.3118.O. V. Verkhodanov, ASP Conf. Ser. , 46 (1997).O. V. Verkhodanov, B. L. Erukhimov, M. L. Monosov, etal., Bull. Spec. Astrophys. Obs. , 132 (1993).O. V. Verkhodanov, A. G. Doroshkevich, P. D. Naselsky,et al., Bull. Spec. Astrophys. Obs.58