We present the results of three independent analyses in which we show that
IRAS galaxies faithfully trace the underlying distribution the mass in the
local universe. In the first analysis we compare the mass and the galaxy
density fields and show that they are consistent within 60 $h^{-1}$Mpc. In the
second one we show that the tidal velocity field of the Mark III catalog is
consistent with the tidal velocity field predicted from the distribution of
IRAS galaxies, hence indicating that IRAS galaxies trace the mass distribution
well beyond 60 $h^{-1}$Mpc. Finally, a third analysis aimed at determining the
mean biasing relation of IRAS galaxies showed no appreciable deviations from
the linear biasing prescription.Comment: 5 pages including 4 Figures + 1 LaTex macro. Contribution to
  ``Where's the Matter? Tracing Dark and Bright Matter with the New Generation
  of Large Scale Surveys'', June 2001, Treyer & Tresse Eds, Frontier Grou

Branchini, E.

English

arXiv

BRANCHINI, ENZO FRANCO

Archivio della Ricerca - Università di Roma 3

Probing the Mass Distribution with IRAS Galaxies

Branchini E.F.

Archivio istituzionale della ricerca - Università di Genova

arXiv:astro-ph/0110611v1  29 Oct 2001PROBING THE MASS DISTRIBUTION WITH IRAS GALAXIESE. Branchini 11 Dipartimento di Fisica, Universitá di Roma TRE, Via della Vasca Navale 84, 00146, Roma,ItalyAbstract. We present the results of three independent analyses in which we show that IRASgalaxies faithfully trace the underlying distribution the mass in the local universe. In the firstanalysis we compare the mass and the galaxy density fields and show that they are consistentwithin 60 h−1Mpc. In the second one we show that the tidal velocity field of the Mark III catalogis consistent with the tidal velocity field predicted from the distribution of IRAS galaxies, henceindicating that IRAS galaxies trace the mass distribution well beyond 60 h−1Mpc. Finally,a third analysis aimed at determining the mean biasing relation of IRAS galaxies showed noappreciable deviations from the linear biasing prescription.1 IntroductionIRAS redshift surveys are characterized by their considerable depth and almost complete sky coverageand thus have been extensively used to investigate the mass distribution in the local universe. As aresult, most of the local cosmological information is derived under the assumption that IRAS galaxiesare faithful tracers of the underlying mass distribution. Therefore, it is of fundamental importance totest the validity this hypothesis and to quantify the so called biasing relation, i.e. the map betweenthe mass and the galaxy spatial distributions both smoothed with the same filter and on the samesmoothing scale.This problem has been already addressed in several different ways by a number authors. Bakeret al. (1998) and Seaborne et al. (1999) have shown that distribution of IRAS galaxies is consistentwith that of optical galaxies on scales larger that 5 h−1Mpc. This indicates that different types ofobjects trace a common underlying density field. More important, direct comparisons with the massdensity field obtained from the observed peculiar velocities of galaxies using POTENT-like algorithms(Bertschinger & Dekel 1989) or Wiener Filtering techniques (Zaroubi et al. 1995), have shown thatthe distribution of IRAS galaxies is consistent with that of the mass within a region of ≈ 60h−1Mpc(see Sigad et al. 1998 and reference therein).Our aim is to improve the accuracy of the previous analyses, extend them to scales larger than 60h−1Mpc and determine whether the biasing of IRAS galaxies is consistent with a linear relation.2 IRAS Galaxies vs. Mass within 60 h−1MpcIn the first analysis we perform a density-density comparison i.e. we reconstruct the mass densityfield within 60 h−1Mpc from observed galaxy peculiar velocities and compare it with the 3D galaxydistribution obtained from the IRAS redshift surveys. In our analysis we use a new reconstructionmethod, called Unbiased Minimal Variance estimator [UMV, hereafter], a new catalog of peculiarvelocity, called SEcat, and the most recent redshift survey of IRAS galaxies, called PSCz.The UMV estimator proposed by Zaroubi (2001) can be viewed as a compromise between POTENTalgorithm and the Wiener filtering technique. It constitutes an improvement over both these methodssince it provides an unbiased minimum variance reconstruction of the underlying density field fromincomplete, noisy and sparse catalogs of galaxy peculiar velocities and also account for the correlationproperties of the underlying velocity field. The recent SEcat catalog of peculiar velocities results fromthe merging of the SFI catalog of spiral galaxies (Giovanelli et al. 1997) and the ENEAR catalog ofearly type galaxies (da Costa et al. 2000). The large number of objects, homogeneous sky coverageand composite nature of the catalog guarantee dense, uniform and unbiased sampling of the cosmicFigure 1: Scatterplot showing the UMV reconstructed mass density it vs. the PSCz galaxy density.The size of the symbols is inversely proportional to the errorsvelocity field. Finally, the PSCz catalog (Saunders 1996) constitutes the largest and deepest all-skyredshift survey of IRAS galaxies to date.The preliminary results of the comparison between the UMV-reconstructed mass and the IRASPSCz galaxy density fields are shown in Fig. 1. Each point displayed in the scatter-plot shows thecomparison between the UMV and PSCz overdensities smoothed with a Gaussian filter of radius 12h−1Mpc and measured at the same location. The correlation between the two fields is linear andthus consistent with a biasing relation on the scale of the smoothing. The slope of the solid linereturns β ≡ Ω0.6/b = 0.56+0.12−0.10, where Ω and b indicate the mass density and linear bias parameters,respectively. The distribution of the density residuals is consistent with Gaussian, hence indicating thatthe PSCz density field is an adequate model for the underlying mass density field within a radius of 60h−1Mpc under the assumption of linear biasing and on a scales larger than the smoothing length. It isworth stressing that, due to the regularization properties of the UMV estimator and the unprecedentedquality of the SEcat and PSCz datasets, the statistical significance of this density-density match isgreater than in previous comparisons of this type.The UMV estimator can be also used to reconstruct the underlying continuous velocity field.The comparison with the linear model velocity field predicted from the distribution of PSCz galaxiesreturns a value of β = 0.51+0.04−0.04, consistent with the one obtained from densities (Zaroubi et al. inprep.).3 IRAS Galaxies vs. Mass beyond 60 h−1MpcTo determine the mass distribution on scales larger than 60 h−1Mpc and compare it to that of IRASgalaxies we have used the tidal field decomposition technique proposed by Hoffman et al. (2001).In this method the Wiener filtering technique is applied to the Mark III peculiar velocity catalog(Willick et al. 1997) to reconstruct the full density and velocity fields (top-left panel of Fig. 2).The density field within 60 h−1Mpc is used to determine, via linear theory, the divergent part of thevelocity field (top-right). The tidal velocity field (bottom-left) is obtained by subtracting the divergentcomponent to the full velocity field. This tidal field is only determined by the mass distribution beyond60 h−1Mpc and is dominated by its dipole and quadrupole moments. The velocity field shown in theFigure 2: Decomposition of the MARK III velocity field in the Supergalactic plane in a sphere of60 h−1Mpc about the Local Group. Top left: full velocity field. Top Right: divergent component.Bottom left: Tidal component. Bottom right: Tidal component - dipole moment. The long arrowsshow the directions of the dipole (bottom-left) and of the dilational and compressional eigenvectors ofthe shear (bottom-right).Figure 3: Same as Fig. 2 but for the PSCz linear velocity field.Figure 4: Large dots: PSCz mean biasing function. The results refer to a Top Hat smoothing of 8h−1Mpc and to σ8 = 1.025 The two solid lines show the expected stochasticity of the bias relation fromthe SAM predictions. The shaded region shows the biasing relation determined by Feldman (2000)bottom-right panel was obtained after subtracting the dipole component from the tidal field and isclearly characterized by a quadrupole pattern. The direction of the Mark III dipole vector is displayedas long arrows in the bottom-left panel of Fig. 2. The long arrows in the bottom-right panel show thedirections of the compressional and dilational eigenvectors of the shear tensor.A similar decomposition was applied to the linear velocity field obtained from the distribution ofIRAS PSCz galaxies. The full velocity field and its divergent part are obtained, via linear theory,from the distribution of PSCz galaxies within 200 h−1Mpc and 60 h−1Mpc, respectively (upper plotsof Fig. 3). The PSCz tidal velocity field, obtained from the galaxy distribution between 60 and200 h−1Mpc is shown in the two bottom panels with its dipole component (bottom-left) and withoutit (bottom-right). As in Fig. 2, the long arrows shown in Fig. 3 indicate the directions of dipole(bottom-left) and shear eigenvectors (bottom-right) of the PSCz tidal velocity field.The preliminary results of our quantitative analysis indicate that the dipole and quadrupole mo-ments of the Mark III and PSCz tidal velocity fields agree within the errors (Hoffman et al. in prep.).This match strongly suggests that the distribution of the mass beyond 60 h−1Mpc is consistent withthat traced by IRAS galaxies, at least in term of dipole and quadrupole moments.4 The Mean Biasing Function of IRAS galaxiesFinally, we have used the method of Sigad, Branchini & Dekel (2000) to determine the mean biasingfunction of IRAS galaxies from their observed one point probability distribution function [PDF]. Themethod assumes that the bias is deterministic and monotonic and that the the mass PDF is lognormalon the scales of interest. To apply this technique we have extracted a volume limited subsample fromthe PSCz galaxy survey and applied a spherical Top Hat filter of radius 8 h−1Mpc to estimate thePDF of galaxies. Then the mean biasing function has been determined by mapping the galaxy PDFinto that of the mass, modeled by a lognormal distribution. Extensive numerical tests have shownthat the method is very effective to measure deviations from linear biasing. However, the slope ofthe mean biasing function is sensitive to the rms density fluctuations, σ8, which fully characterizes alognormal distribution and needs to be assumed a priori.The preliminary results are shown in Fig. 4. The large dots show the PSCz mean biasing functionobtained assuming σ8 = 1.025. The function is clearly consistent with a linear biasing scheme. The twosolid lines indicate the 1σ uncertainty interval around the mean biasing, associated to the stochasticityof the biasing relation. as predicted by the Semianalytic Model [SAM] of Somerville et al. (2000).The dashed region is plotted for reference and shows the biasing function of IRAS galaxies determinedby Feldman et al. (2001) that, however, refers to scales much larger than those of our analyses.5 ConclusionsThe preliminary results presented here corroborate the common assumption that IRAS galaxies arefaithful tracers of the mass distribution. In the first analysis we have applied the new UMV estimatorto show that the distribution of IRAS galaxies matches that of the mass within 60 h−1Mpc. Thisconfirms the results of similar comparisons previously performed using a number of different techniquesand datasets. In the second analysis we take advantage of the nonlocal properties of the galaxy peculiarvelocities to infer the mass distribution beyond 60 h−1Mpc and found that is consistent with that ofIRAS PSCz galaxies. Finally, we use the inverse-mapping method of Sigad, Branchini & Dekel (2000)to quantify the biasing relation between galaxies and mass. Combined with the result of the likelihoodanalysis of Tegmark et al. (2000), our results show that on a scale of 8 h−1Mpc IRAS PSCz galaxiesobey a mean linear biasing relation with a biasing parameter b consistent with unity.Acknowledgements. EB is grateful to Y. Hoffman and S. Zaroubi for kindly providing unpublishedresults and figures.References[1] Baker, J., Davis, M., Strauss, M., Lahav, O., Santiago, B., 1998, ApJ, 508, 6[2] Bertshinger, E., Dekel, A., 1989, ApJ, 335, L5[3] da Costa et al., 2000, AJ, 120, 95[4] Feldman, H., Frieman, J., Fry, J., Scoccimarro, R., 2001, astro-ph/0010205[5] Giovanelli, R., et al., 1997, AJ, 113, 22[6] Hoffman, Y., Eldar, A., Zaroubi, S., Dekel A., 2001, (astro-ph/0102190)[7] Saunders, W., 1996, web site: http://www-astro.physics.ox.ac.uk/∼wjs/pscz.html[8] Seaborne, M., et al., 1999, MNRAS, 309, 80[9] Sigad, Y., Dekel A., Strauss, M., Yahil, A., 1998, ApJ, 495, 516[10] Sigad, Y., Branchini, E., Dekel A., 2000, ApJ, 540, 62[11] Somerville, R., et al., 2000, MNRAS, 320, 289[12] Tegmark, M., Zaldarriaga, M., 2000, ApJ, 544, 30[13] Willick, J., et al., 1997, ApJS, 109, 333[14] Zaroubi, S., Hoffman, Y. Fisher, K., Lahav, O., 1995, ApJ, 449, 446[15] Zaroubi, S., 2001, (astro-ph/0010561)

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Probing the Mass Distribution with IRAS Galaxies

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