Several studies have indicated that the local cosmic velocity field is rather
cold, in particular in the regions outside the massive, virialized clusters of
galaxies. If our local cosmic environment is taken to be a representative
volume of the Universe, the repercussion of this finding is that either we live
in a low-$\Omega$ Universe and/or that the galaxy distribution is a biased
reflection of the underlying mass distribution. Otherwise, the pronounced
nature of the observed galaxy distribution would be irreconcilable with the
relatively quiet flow of the galaxies.
  Here we propose a different view on this cosmic dilemma, stressing the fact
that our cosmic neighbourhood embodies a region of rather particular dynamical
properties, and henceforth we are apt to infer flawed conclusions with respect
to the global Universe. Suspended between two huge mass concentrations, the
Great Attractor region and the Perseus-Pisces chain, we find ourselves in a
region of relatively low density yet with a very strong tidal shear. This tidal
field induces a local velocity field with a significant large-scale bulk flow
but a low small-scale velocity dispersion. By means of constrained realizations
of our local Universe, consisting of Wiener-filtered reconstructions inferred
from the Mark III catalogue of galaxy peculiar velocities in combination with
appropriate spectrally determined fluctuations, we study the implications for
our local velocity field. We find that we live near a local peak in the
distribution of the cosmic Mach number, $|v_{bulk}|/\sigma_v$, and that our
local cosmic niche is located in the tail of the Mach number distribution
function.Comment: Contribution to `Evolution of Large Scale Structure', MPA/ESO
  Conference, August 1997, eds. A. Banday & R. Sheth, Twin Press. 5 pages of
  LaTeX including 3 postscript figures. Uses tp.sty and psfi

Hoffman, Yehuda

van de Weygaert, Rien

English

arXiv

Abstract: Several studies have indicated that the local cosmic velocity field is rather cold, in particular in the regions outside the massive, virialized clusters of galaxies. If our local cosmic environment is taken to be a representative volume of the Universe, the repercussion of this finding is that either we live in a low-$Omega$ Universe and/or that the galaxy distribution is a biased reflection of the underlying mass distribution. Otherwise, the pronounced nature of the observed galaxy distribution would be irreconcilable with the relatively quiet flow of the galaxies. Here we propose a different view on this cosmic dilemma, stressing the fact that our cosmic neighbourhood embodies a region of rather particular dynamical properties, and henceforth we are apt to infer flawed conclusions with respect to the global Universe. Suspended between two huge mass concentrations, the Great Attractor region and the Perseus-Pisces chain, we find ourselves in a region of relatively low density yet with a very strong tidal shear. This tidal field induces a local velocity field with a significant large-scale bulk flow but a low small-scale velocity dispersion. By means of constrained realizations of our local Universe, consisting of Wiener-filtered reconstructions inferred from the Mark III catalogue of galaxy peculiar velocities in combination with appropriate spectrally determined fluctuations, we study the implications for our local velocity field. We find that we live near a local peak in the distribution of the cosmic Mach number, $|v_{bulk}|/sigma_v$, and that our local cosmic niche is located in the tail of the Mach number distribution function.

Weygaert, R. van de

Hoffman, Y.

University of Groningen Digital Archive

Cold Flows and Large Scale Tides

University of Groningen

   University of GroningenCold Flows and Large Scale TidesWeygaert, R. van de; Hoffman, Y.Published in:Default journalIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:1998Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Weygaert, R. V. D., & Hoffman, Y. (1998). Cold Flows and Large Scale Tides. Default journal.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 12-11-2019arXiv:astro-ph/9811410 v1   25 Nov 1998Proceedings: Evolution of Large Scale Structure – Garching, August 1998COLD FLOWS AND LARGE SCALE TIDESRien van de Weygaert1 and Yehuda Hoffman1,21Kapteyn Astronomical Institute, P.O. Box 800, 9700 AV Groningen, the Netherlands2Racah Institute of Physics, The Hebrew University, Jerusalem 91904, IsraelABSTRACT. We propose a different view of the dilemma concerning thecoldness of the local cosmic flow and its repercussions for the global Universe.We stress the fact that our cosmic neighbourhood embodies a region of ratherparticular circumstances, whose dynamics and kinematics are substantiallyinfluenced by its location in between the Great Attractor region and thePisces-Perseus chain. On the basis of constrained simulations of our cosmicneighbourhood we indicate through the cosmic Mach number that we live inan extraordinarily cold niche of the Universe.1 Cosmic Chills and UniversalTruthsEarly assessment of the small-scale random motions of galaxies, es-timated on the basis of pairwise ve-locity dispersions, revealed that lo-cally the Universe is rather cold.While we participate in a bulk flowof approximately 600km/s, the ran-dom velocities with respect to themean flow are estimated to be in therange of a mere 200−−300km/s (seee.g. Suto, Cen & Ostriker 1992) Thislow value of the velocity dispersionin combination with the pronouncedstructure displayed by the distribu-tion of galaxies was in fact a strongargument for either a low Ω-Universethe or for the latter being a biasedtracer of the underlying matter dis-tribution. The assumption of bias, inparticular in the form of the oversim-plifying linear bias factor b, wouldthen imply the matter distributionnot to have evolved as far as sug-gested by the pronounced nature ofthe galaxy distribution, and hencewould be in agreement with the lowvalue of the “thermal” motions in thelocal Universe.An interesting elaboration on theassessment of the implications of thecoldness of the local velocity flowfor the properties of the global Uni-verse, in particular for the valueof the cosmological density parame-ter Ω, was suggested by Ostriker &Suzo (1990). They pointed out thata comparison between the proper-ties of the small-scale “dispersion”velocities, σ(v), and the large-scalebulk motions, |v|bulk, would not onlyprovide valuable information on therelative amount of large-scale andsmall-scale power in the spectrumof density- and velocity fluctuations,but that to do this on the basis oftheir ratio, the “cosmic Mach num-ber” M,M≡|v|bulkσ(v). (1)has the additional advantage of pro-viding this information in a way thatis independent of both the – not yetdefinitively settled – amplitude nor-malization of the power spectrum aswell as of a possible – linear, scale-indepent – bias between galaxies andmatter. The only intrinsic assump-tion is that the velocities of galax-ies do form an unbiased tracer of theunderlying velocity field. One of themost striking conclusions reached onthe basis of extensive tests of thediscriminatory virtues of the Machnumber was that the velocity field inour local Universe appeared to ex-clude the viability of the standardCDM model (Ostriker & Suzo 1990).2 Local versus GlobalIn an attempt to interpret the sig-nificance of the coldness of the localcosmic flow, we postulate an alterna-tive view. Rather than interpretingthe coldness of the flow as a propertyof the global Universe, we hold theview that it is our rather uncommoncosmic location that lies at the basisof the issue and that we should becareful in drawing conclusions con-2 van de Weygaert & HoffmanFigure 1.Left: The density distribution in a constrained reconstruction of our LocalUniverse. Based on the Mark III catalogue peculiar motions, smoothed ona Gaussian scale of Rf = 5h−1Mpc, the Wiener filter reconstruction yieldsthe density field in the top left frame, represented by a density contour plotin the central x − y plane. The solid contours correspond to δ > 0.0, thedashed ones to low-density regions with δ < 0.0. The indicated density lev-els range between -0.6 and 1.3, with the linear increment between contourlevels amounting to ∆δ = 0.1. The heavy solid line is the δ = 0.0 contour.We, the Local Group, are at the centre of the box, clearly recognizable are themass concentrations around the Perseus-Pisces complex (lower lefthand side)and the Great Attractor region (upper righthand corner). Superimposed onthe Wiener filtered density field contours are the bars representing the com-pressional component of the tidal shear within the x − y plane (see van deWeygaert & Hoffman 1998). Notice the strength of the tidal field in the un-derdense region near our own cosmic location. Centre: the constrained lineardensity field realization after including a constrained contribution of small-scale waves according to the standard CDM scenario, Gaussian smoothed ona scale of Rf = 5h−1Mpc. The density contours are characterized in the sameway as the ones in the top frame, with the linear increment of the contourlevels amounting to ∆δ = 0.2, ranging in value from δ = −1.6 to δ = 3.0.Right: outcome of the nonlinear evolution of the constrained realization ofour local Universe, as evolved by means of an N-body simulation.cerning the global value of cosmic pa-rameters as well as of the validity ofstructure formation scenarios.Figure 1a contains a reconstruc-tion of the linear density field (Gaus-sian scale Rf = 5h−1 Mpc) in ourlocal Universe, in a slice approxi-mately coinciding with the Super-galactic Plane, based on the set ofmeasured peculiar velocities of galax-ies in the Mark III catalogue (Willicket al. 1997). The Local Group is lo-cated at the center of the box. On theupper lefthand side we can discerna huge positive density complex, theGreat Attractor region, while on theother side, lower righthand corner,we observe the presence of anothermassive density enhancement, corre-sponding to the Perseus-Pisces su-percluster region. Moreover, in per-pendicular directions we have vastregions of lower than average den-sity. Hence, seemingly we find our-selves located right near the centreof a configuration strongly reminis-cent of a canonical quadrupolar massdistribution. The direct dynamicalimplication of this is that we arelocated near the saddle point of astrong field of tidal shear. In fact,when turning to Figure 1b we seethe compressional component of thetidal field corresponding to the den-sity distribution in the local Uni-verse (Van de Weygaert & Hoffman1998), superposed on the isoden-sity contours in the same slice. Thetidal field, illustrated by bars whosesize and direction are proportionalto the strength of the compressionalong the indicated direction is, ev-idently, very strong within the realmof the two huge matter concentra-tions where the density reaches highvalues. In addition, however, we alsoCold Flows and Large Scale Tides 3Figure 2.Notice 90◦ change in figure orientation. The velocity field structure in ourlocal Universe. Central frame: full velocity field at particle locations, repre-sented by velocity vectors of velocity components in central x− y plane. Leftframes contain the bulk velocity component of the velocity field at the par-ticle locations, with the top frame displaying the vector representation, andthe bottom frame the contour plot of the amplitude of the bulk velocity in thecentral x−y plane. The righthand frames display the same for the small-scalevelocity ‘dispersion’ component. The bulk velocity is defined as the velocityafter filtering out the contributions on scales smaller than 5h−1Mpc, whilethe velocity dispersion is the remaining small-scale residual velocity.see that the tidal shear is indeedvery strong at our own location, pre-cisely due to the fact that we arehanging in between the Great At-tractor and the Perseus-Pisces chain.In fact, through the anisotropic na-ture of the induced tidal forces wecan recognize a situation that was forinstance already recognized withinthe context of the Cosmic Web pic-ture (see Bond, Kofman & Pogosyan1997, also see van de Weygaert &Bertschinger, 1996, fig. 4), the col-lapse and formation of filamentaryand tenuous wall-like features in re-gions bordered by massive matterclumps like clusters of galaxies. Thisappears to be the generic outcomeof the evolutionary path of regionsof moderately low overdensities im-mersed in an external tidal fieldwhose strength is of the same orderof magnitude as the selfgravity of theregion. In such situations we may ex-pect the contraction itself to be ac-celerated with respect to the situa-tion of the same initial region hav-ing been spatially isolated. In fact,the shearing nature of the forces willaccelerate the contraction along theshortest axis of the region that willexperience an accelerated contrac-tion, while the longest axis will expe-rience a slow down of its contractionrate. This in turn will very likely im-ply a slower mixing, “thermal” set-tling and virialization of the matterinvolved in the contraction process.It is the preceding sketch of eventsthat prompts us to expect our lo-cal corner of the Universe, becauseof its special location in betweenthe Great Attractor and the Perseus-Pisces complex, to have a substan-tially lower velocity dispersion thanwe may expect to encounter in an av-erage patch of our Universe.3 Wiener filtering the MarkIII Local CosmosIn an attempt to address the im-plications of the coldness of the localcosmic flow, we investigated the dy-namical and kinematical evolution ofcosmic regions resembling as closelyas possible our own local Universe.First issue in this approach is toset a cosmic environment resemblingour local Universe. This is achievedby invoking relevant observationally4 van de Weygaert & Hoffmandetermined properties of the localcosmos. As we are specifically inter-ested in dynamical issues, we baseourselves on a local cosmic primor-dial linear density field that rep-resents an optimally significant re-construction of the prevailing mat-ter distribution in the early Uni-verse. We achieve this by applying aWiener filter algorithm to the sam-ple of measured peculiar velocities ofgalaxies in the Mark III catalogue(Willick et al. 1997, and Zaroubi etal. 1995 for technical aspects). Sucha reconstruction restricts itself to re-gions that arguably are still withinthe linear regime, and whose statisti-cal properties are still Gaussian. Wediscard further observational con-straints on the small-scale clumpi-ness and motions in the local Uni-verse. Instead, we generate and su-perpose several realizations of small-scale density and velocity fluctua-tions according to a specific powerspectrum of fluctuations, global cos-mological background specified byH0 and Ω0, and with the small-scale noise being appropriately mod-ulated by the large-scale Wiener fil-ter reconstructed density field. Tothis end we invoke the technique ofconstrained random fields (see Hoff-man & Ribak 1991, van de Wey-gaert & Bertschinger 1996), with theWiener filtered field playing the roleof “mean field”.4 Small-scale evolution of theLocal CosmosHaving generated a full realizationof a patch of the Universe resemblingthe primordial density field in our lo-cal cosmic neighbourhood, we traceits development by means of an P3MN-body simulation. The outcome ofour simulations is reduced and ana-lyzed with the help of a ‘dynamicalfields’ code. The resulting distribu-tion of the particles in a central slicethrough the simulations box is shownin the central frame of Figure 2.Clearly recognizable are massive con-centrations of matter at the locationswhere in the real Universe we observethe presence of the Great Attractorregion (slightly “north” of the “west”direction) and the Perseus-Pisces re-gion (slightly “south” of the “east”).Interesting is to see how vast and ex-tended these regions in fact are, cer-tainly not to be identified with well-defined singular objects. The corre-sponding velocity field in the sameregion of the simulations is displayedby means of a decomposition in thelarge-scale bulk flow vbulk, top-hatfiltered in a sphere of radius RTH =5h−1Mpc, and the small-scale veloc-ity “dispersion” vσ (for technical de-tails see Van de Weygaert & Hoffman1998). The top-lefthand frame andthe top-righthand frame contain con-tour plots of the amplitude of thesevelocity field components, while thelower lefthand and lower righthandframe show the corresponding vecto-rial representation of the velocities atthe locations of the particles. In par-ticular the bulk flow field provides abeautiful impression of the displace-ment of matter towards the emer-gence of large-scale features like fil-aments and voids. Most interestingthough is that also the small-scaledispersion field appears to bear themarks of underlying large-scale fea-tures: not only do we see large “ther-mal” velocities at the sites of clusterconcentratios, but we can also rec-ognize sizeable small-scale velocitiesnear the locations of filaments (seeVan de Weygaert & Hoffman 1998).When we compare the contourplots of the bulk motion and the dis-persion velocities, we can already dis-cern the fact that while we (i.e. thecentre of the simulation box) are stillembedded in a region of high bulkflow, evidently incited by the GA andthe PP region, we also find ourselvesin a region of exceptional low veloc-ity dispersion. Evidently a nice re-flection of the observed “coldness”of the local cosmos. We should notfail to notice that apparently thesesmall-scale repercussions are the nat-ural outcome of the dynamical evolu-tion of a region possessing the large-scale features (R > 5h−1Mpc) of thelocal universe.Secondly, an inspection of the con-tour map of the spatial comsic Machnumber distribution illuminates thesignificance of the “coldness” of thelocal cosmic flow. A comparison withthe density map in Figure 1 revealsthe interesting aspect of a large co-herent band of high Mach numbervalues running from the lower left-hand side to the upper righthandside of the simulation box, avoid-Cold Flows and Large Scale Tides 5Figure 3.Contour plot of the Mach number distribution in the central x− y slice, to-gether with the probability distribution function of the Mach number (bottomframe). The arrow indicates the location of the value of the Mach numberat our cosmic location (centre of box), equal to M = 2.61 for the presentedLocal Universe simulated realization.ing both the Great Attractor regionand the Pisces-Perseus region, situ-ated approximately in between thosetwo complexes, almost along the bi-secting plane that they define (seevan de Weygaert & Hoffman 1998).Superposed on this large-scale pat-tern are a plethora of small-scale fea-tures. For our purpose the most sig-nificant of these is the fact that weappear to be right near a toweringpeak of the Mach number distribu-tion. In fact, for this N-body real-ization of our Universe we find atthe location of the Local Group abulk velocity of 695.5km/s, a veloc-ity dispersion of 266.5km/s and aMach number of 2.61, correspondingto a percentile level of 82.1%. Thatpoint is stressed further by invokingthe statistical distribution functionof the Mach number in Figure 3b.Clearly we find ourselves somewherein the tail of the distribution, poten-tially rendering it possible that we dolive in a high-density Universe eventhough locally it’s chilly ... Althoughthe exact numbers differs for variousrealizations, and for instance the spa-tial patterns in the Mach number dis-tribution amy display different fea-tures (narrower band, no conspicu-ous peak), the Mach number consis-tently assumes a value in the rangeabove the 80% percentile value.ReferencesHoffman, Y., Ribak, E., 1991, ApJ,380, L5Ostriker, J.P., Suto, Y., 1990, ApJ,348, 378Suto, Y., Cen, R., Ostriker, J.P.,1992, ApJ, 395, 1van de Weygaert, R., Bertschinger,E., 1996, MNRAS, 281, 84van de Weygaert, R., Hoffman, Y.,1998, ApJ, submittedWillick, J.A., Courteau, S.,Faber, S.M., Burstein, D., Dekel, A.,Strauss, M.A., 1997, ApJS, 109,333Zaroubi, S., Hoffman, Y., Fisher,K.B., Lahav, O., 1995, ApJ, 449, 446

Abstract: Several studies have indicated that the local cosmic velocity field is rather cold, in particular in the regions outside the massive, virialized clusters of galaxies. If our local cosmic environment is taken to be a representative volume of the Universe, the repercussion of this finding is that either we live in a low-$Omega$ Universe and/or that the galaxy distribution is a biased reflection of the underlying mass distribution. Otherwise, the pronounced nature of the observed galaxy distribution would be irreconcilable with the relatively quiet flow of the galaxies. Here we propose a different view on this cosmic dilemma, stressing the fact that our cosmic neighbourhood embodies a region of rather particular dynamical properties, and henceforth we are apt to infer flawed conclusions with respect to the global Universe. Suspended between two huge mass concentrations, the Great Attractor region and the Perseus-Pisces chain, we find ourselves in a region of relatively low density yet with a very strong tidal shear. This tidal field induces a local velocity field with a significant large-scale bulk flow but a low small-scale velocity dispersion. By means of constrained realizations of our local Universe, consisting of Wiener-filtered reconstructions inferred from the Mark III catalogue of galaxy peculiar velocities in combination with appropriate spectrally determined fluctuations, we study the implications for our local velocity field. We find that we live near a local peak in the distribution of the cosmic Mach number, $|v_{bulk}|/sigma_v$, and that our local cosmic niche is located in the tail of the Mach number distribution function

ARTS repository - University of Groningen

   University of GroningenCold Flows and Large Scale TidesWeygaert, R. van de; Hoffman, Y.Published in:Evolution of large scale structure : from recombination to GarchingIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:1998Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Weygaert, R. V. D., & Hoffman, Y. (1998). Cold Flows and Large Scale Tides. In Evolution of large scalestructure : from recombination to Garching : proceedings of the MPA-ESO Cosmology Conference :Garching, Germany, 2-7 August 1998 ESO.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 10-09-2023arXiv:astro-ph/9811410 v1   25 Nov 1998Proceedings: Evolution of Large Scale Structure – Garching, August 1998COLD FLOWS AND LARGE SCALE TIDESRien van de Weygaert1 and Yehuda Hoffman1,21Kapteyn Astronomical Institute, P.O. Box 800, 9700 AV Groningen, the Netherlands2Racah Institute of Physics, The Hebrew University, Jerusalem 91904, IsraelABSTRACT. We propose a different view of the dilemma concerning thecoldness of the local cosmic flow and its repercussions for the global Universe.We stress the fact that our cosmic neighbourhood embodies a region of ratherparticular circumstances, whose dynamics and kinematics are substantiallyinfluenced by its location in between the Great Attractor region and thePisces-Perseus chain. On the basis of constrained simulations of our cosmicneighbourhood we indicate through the cosmic Mach number that we live inan extraordinarily cold niche of the Universe.1 Cosmic Chills and UniversalTruthsEarly assessment of the small-scale random motions of galaxies, es-timated on the basis of pairwise ve-locity dispersions, revealed that lo-cally the Universe is rather cold.While we participate in a bulk flowof approximately 600km/s, the ran-dom velocities with respect to themean flow are estimated to be in therange of a mere 200−−300km/s (seee.g. Suto, Cen & Ostriker 1992) Thislow value of the velocity dispersionin combination with the pronouncedstructure displayed by the distribu-tion of galaxies was in fact a strongargument for either a low Ω-Universethe or for the latter being a biasedtracer of the underlying matter dis-tribution. The assumption of bias, inparticular in the form of the oversim-plifying linear bias factor b, wouldthen imply the matter distributionnot to have evolved as far as sug-gested by the pronounced nature ofthe galaxy distribution, and hencewould be in agreement with the lowvalue of the “thermal” motions in thelocal Universe.An interesting elaboration on theassessment of the implications of thecoldness of the local velocity flowfor the properties of the global Uni-verse, in particular for the valueof the cosmological density parame-ter Ω, was suggested by Ostriker &Suzo (1990). They pointed out thata comparison between the proper-ties of the small-scale “dispersion”velocities, σ(v), and the large-scalebulk motions, |v|bulk, would not onlyprovide valuable information on therelative amount of large-scale andsmall-scale power in the spectrumof density- and velocity fluctuations,but that to do this on the basis oftheir ratio, the “cosmic Mach num-ber” M,M ≡|v|bulkσ(v). (1)has the additional advantage of pro-viding this information in a way thatis independent of both the – not yetdefinitively settled – amplitude nor-malization of the power spectrum aswell as of a possible – linear, scale-indepent – bias between galaxies andmatter. The only intrinsic assump-tion is that the velocities of galax-ies do form an unbiased tracer of theunderlying velocity field. One of themost striking conclusions reached onthe basis of extensive tests of thediscriminatory virtues of the Machnumber was that the velocity field inour local Universe appeared to ex-clude the viability of the standardCDM model (Ostriker & Suzo 1990).2 Local versus GlobalIn an attempt to interpret the sig-nificance of the coldness of the localcosmic flow, we postulate an alterna-tive view. Rather than interpretingthe coldness of the flow as a propertyof the global Universe, we hold theview that it is our rather uncommoncosmic location that lies at the basisof the issue and that we should becareful in drawing conclusions con-2 van de Weygaert & HoffmanFigure 1.Left: The density distribution in a constrained reconstruction of our LocalUniverse. Based on the Mark III catalogue peculiar motions, smoothed ona Gaussian scale of Rf = 5h−1Mpc, the Wiener filter reconstruction yieldsthe density field in the top left frame, represented by a density contour plotin the central x − y plane. The solid contours correspond to δ > 0.0, thedashed ones to low-density regions with δ < 0.0. The indicated density lev-els range between -0.6 and 1.3, with the linear increment between contourlevels amounting to ∆δ = 0.1. The heavy solid line is the δ = 0.0 contour.We, the Local Group, are at the centre of the box, clearly recognizable are themass concentrations around the Perseus-Pisces complex (lower lefthand side)and the Great Attractor region (upper righthand corner). Superimposed onthe Wiener filtered density field contours are the bars representing the com-pressional component of the tidal shear within the x − y plane (see van deWeygaert & Hoffman 1998). Notice the strength of the tidal field in the un-derdense region near our own cosmic location. Centre: the constrained lineardensity field realization after including a constrained contribution of small-scale waves according to the standard CDM scenario, Gaussian smoothed ona scale of Rf = 5h−1Mpc. The density contours are characterized in the sameway as the ones in the top frame, with the linear increment of the contourlevels amounting to ∆δ = 0.2, ranging in value from δ = −1.6 to δ = 3.0.Right: outcome of the nonlinear evolution of the constrained realization ofour local Universe, as evolved by means of an N-body simulation.cerning the global value of cosmic pa-rameters as well as of the validity ofstructure formation scenarios.Figure 1a contains a reconstruc-tion of the linear density field (Gaus-sian scale Rf = 5h−1 Mpc) in ourlocal Universe, in a slice approxi-mately coinciding with the Super-galactic Plane, based on the set ofmeasured peculiar velocities of galax-ies in the Mark III catalogue (Willicket al. 1997). The Local Group is lo-cated at the center of the box. On theupper lefthand side we can discerna huge positive density complex, theGreat Attractor region, while on theother side, lower righthand corner,we observe the presence of anothermassive density enhancement, corre-sponding to the Perseus-Pisces su-percluster region. Moreover, in per-pendicular directions we have vastregions of lower than average den-sity. Hence, seemingly we find our-selves located right near the centreof a configuration strongly reminis-cent of a canonical quadrupolar massdistribution. The direct dynamicalimplication of this is that we arelocated near the saddle point of astrong field of tidal shear. In fact,when turning to Figure 1b we seethe compressional component of thetidal field corresponding to the den-sity distribution in the local Uni-verse (Van de Weygaert & Hoffman1998), superposed on the isoden-sity contours in the same slice. Thetidal field, illustrated by bars whosesize and direction are proportionalto the strength of the compressionalong the indicated direction is, ev-idently, very strong within the realmof the two huge matter concentra-tions where the density reaches highvalues. In addition, however, we alsoCold Flows and Large Scale Tides 3Figure 2.Notice 90◦ change in figure orientation. The velocity field structure in ourlocal Universe. Central frame: full velocity field at particle locations, repre-sented by velocity vectors of velocity components in central x − y plane. Leftframes contain the bulk velocity component of the velocity field at the par-ticle locations, with the top frame displaying the vector representation, andthe bottom frame the contour plot of the amplitude of the bulk velocity in thecentral x−y plane. The righthand frames display the same for the small-scalevelocity ‘dispersion’ component. The bulk velocity is defined as the velocityafter filtering out the contributions on scales smaller than 5h−1Mpc, whilethe velocity dispersion is the remaining small-scale residual velocity.see that the tidal shear is indeedvery strong at our own location, pre-cisely due to the fact that we arehanging in between the Great At-tractor and the Perseus-Pisces chain.In fact, through the anisotropic na-ture of the induced tidal forces wecan recognize a situation that was forinstance already recognized withinthe context of the Cosmic Web pic-ture (see Bond, Kofman & Pogosyan1997, also see van de Weygaert &Bertschinger, 1996, fig. 4), the col-lapse and formation of filamentaryand tenuous wall-like features in re-gions bordered by massive matterclumps like clusters of galaxies. Thisappears to be the generic outcomeof the evolutionary path of regionsof moderately low overdensities im-mersed in an external tidal fieldwhose strength is of the same orderof magnitude as the selfgravity of theregion. In such situations we may ex-pect the contraction itself to be ac-celerated with respect to the situa-tion of the same initial region hav-ing been spatially isolated. In fact,the shearing nature of the forces willaccelerate the contraction along theshortest axis of the region that willexperience an accelerated contrac-tion, while the longest axis will expe-rience a slow down of its contractionrate. This in turn will very likely im-ply a slower mixing, “thermal” set-tling and virialization of the matterinvolved in the contraction process.It is the preceding sketch of eventsthat prompts us to expect our lo-cal corner of the Universe, becauseof its special location in betweenthe Great Attractor and the Perseus-Pisces complex, to have a substan-tially lower velocity dispersion thanwe may expect to encounter in an av-erage patch of our Universe.3 Wiener filtering the MarkIII Local CosmosIn an attempt to address the im-plications of the coldness of the localcosmic flow, we investigated the dy-namical and kinematical evolution ofcosmic regions resembling as closelyas possible our own local Universe.First issue in this approach is toset a cosmic environment resemblingour local Universe. This is achievedby invoking relevant observationally4 van de Weygaert & Hoffmandetermined properties of the localcosmos. As we are specifically inter-ested in dynamical issues, we baseourselves on a local cosmic primor-dial linear density field that rep-resents an optimally significant re-construction of the prevailing mat-ter distribution in the early Uni-verse. We achieve this by applying aWiener filter algorithm to the sam-ple of measured peculiar velocities ofgalaxies in the Mark III catalogue(Willick et al. 1997, and Zaroubi etal. 1995 for technical aspects). Sucha reconstruction restricts itself to re-gions that arguably are still withinthe linear regime, and whose statisti-cal properties are still Gaussian. Wediscard further observational con-straints on the small-scale clumpi-ness and motions in the local Uni-verse. Instead, we generate and su-perpose several realizations of small-scale density and velocity fluctua-tions according to a specific powerspectrum of fluctuations, global cos-mological background specified byH0 and Ω0, and with the small-scale noise being appropriately mod-ulated by the large-scale Wiener fil-ter reconstructed density field. Tothis end we invoke the technique ofconstrained random fields (see Hoff-man & Ribak 1991, van de Wey-gaert & Bertschinger 1996), with theWiener filtered field playing the roleof “mean field”.4 Small-scale evolution of theLocal CosmosHaving generated a full realizationof a patch of the Universe resemblingthe primordial density field in our lo-cal cosmic neighbourhood, we traceits development by means of an P3MN-body simulation. The outcome ofour simulations is reduced and ana-lyzed with the help of a ‘dynamicalfields’ code. The resulting distribu-tion of the particles in a central slicethrough the simulations box is shownin the central frame of Figure 2.Clearly recognizable are massive con-centrations of matter at the locationswhere in the real Universe we observethe presence of the Great Attractorregion (slightly “north” of the “west”direction) and the Perseus-Pisces re-gion (slightly “south” of the “east”).Interesting is to see how vast and ex-tended these regions in fact are, cer-tainly not to be identified with well-defined singular objects. The corre-sponding velocity field in the sameregion of the simulations is displayedby means of a decomposition in thelarge-scale bulk flow vbulk, top-hatfiltered in a sphere of radius RTH =5h−1Mpc, and the small-scale veloc-ity “dispersion” vσ (for technical de-tails see Van de Weygaert & Hoffman1998). The top-lefthand frame andthe top-righthand frame contain con-tour plots of the amplitude of thesevelocity field components, while thelower lefthand and lower righthandframe show the corresponding vecto-rial representation of the velocities atthe locations of the particles. In par-ticular the bulk flow field provides abeautiful impression of the displace-ment of matter towards the emer-gence of large-scale features like fil-aments and voids. Most interestingthough is that also the small-scaledispersion field appears to bear themarks of underlying large-scale fea-tures: not only do we see large “ther-mal” velocities at the sites of clusterconcentratios, but we can also rec-ognize sizeable small-scale velocitiesnear the locations of filaments (seeVan de Weygaert & Hoffman 1998).When we compare the contourplots of the bulk motion and the dis-persion velocities, we can already dis-cern the fact that while we (i.e. thecentre of the simulation box) are stillembedded in a region of high bulkflow, evidently incited by the GA andthe PP region, we also find ourselvesin a region of exceptional low veloc-ity dispersion. Evidently a nice re-flection of the observed “coldness”of the local cosmos. We should notfail to notice that apparently thesesmall-scale repercussions are the nat-ural outcome of the dynamical evolu-tion of a region possessing the large-scale features (R > 5h−1Mpc) of thelocal universe.Secondly, an inspection of the con-tour map of the spatial comsic Machnumber distribution illuminates thesignificance of the “coldness” of thelocal cosmic flow. A comparison withthe density map in Figure 1 revealsthe interesting aspect of a large co-herent band of high Mach numbervalues running from the lower left-hand side to the upper righthandside of the simulation box, avoid-Cold Flows and Large Scale Tides 5Figure 3.Contour plot of the Mach number distribution in the central x − y slice, to-gether with the probability distribution function of the Mach number (bottomframe). The arrow indicates the location of the value of the Mach numberat our cosmic location (centre of box), equal to M = 2.61 for the presentedLocal Universe simulated realization.ing both the Great Attractor regionand the Pisces-Perseus region, situ-ated approximately in between thosetwo complexes, almost along the bi-secting plane that they define (seevan de Weygaert & Hoffman 1998).Superposed on this large-scale pat-tern are a plethora of small-scale fea-tures. For our purpose the most sig-nificant of these is the fact that weappear to be right near a toweringpeak of the Mach number distribu-tion. In fact, for this N-body real-ization of our Universe we find atthe location of the Local Group abulk velocity of 695.5km/s, a veloc-ity dispersion of 266.5km/s and aMach number of 2.61, correspondingto a percentile level of 82.1%. Thatpoint is stressed further by invokingthe statistical distribution functionof the Mach number in Figure 3b.Clearly we find ourselves somewherein the tail of the distribution, poten-tially rendering it possible that we dolive in a high-density Universe eventhough locally it’s chilly ... Althoughthe exact numbers differs for variousrealizations, and for instance the spa-tial patterns in the Mach number dis-tribution amy display different fea-tures (narrower band, no conspicu-ous peak), the Mach number consis-tently assumes a value in the rangeabove the 80% percentile value.ReferencesHoffman, Y., Ribak, E., 1991, ApJ,380, L5Ostriker, J.P., Suto, Y., 1990, ApJ,348, 378Suto, Y., Cen, R., Ostriker, J.P.,1992, ApJ, 395, 1van de Weygaert, R., Bertschinger,E., 1996, MNRAS, 281, 84van de Weygaert, R., Hoffman, Y.,1998, ApJ, submittedWillick, J.A., Courteau, S.,Faber, S.M., Burstein, D., Dekel, A.,Strauss, M.A., 1997, ApJS, 109,333Zaroubi, S., Hoffman, Y., Fisher,K.B., Lahav, O., 1995, ApJ, 449, 446

   University of GroningenCold Flows and Large Scale TidesWeygaert, R. van de; Hoffman, Y.Published in:Evolution of large scale structure : from recombination to GarchingIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:1998Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Weygaert, R. V. D., & Hoffman, Y. (1998). Cold Flows and Large Scale Tides. In Evolution of large scalestructure : from recombination to Garching : proceedings of the MPA-ESO Cosmology Conference :Garching, Germany, 2-7 August 1998 ESO.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 01-11-2023arXiv:astro-ph/9811410 v1   25 Nov 1998Proceedings: Evolution of Large Scale Structure – Garching, August 1998COLD FLOWS AND LARGE SCALE TIDESRien van de Weygaert1 and Yehuda Hoffman1,21Kapteyn Astronomical Institute, P.O. Box 800, 9700 AV Groningen, the Netherlands2Racah Institute of Physics, The Hebrew University, Jerusalem 91904, IsraelABSTRACT. We propose a different view of the dilemma concerning thecoldness of the local cosmic flow and its repercussions for the global Universe.We stress the fact that our cosmic neighbourhood embodies a region of ratherparticular circumstances, whose dynamics and kinematics are substantiallyinfluenced by its location in between the Great Attractor region and thePisces-Perseus chain. On the basis of constrained simulations of our cosmicneighbourhood we indicate through the cosmic Mach number that we live inan extraordinarily cold niche of the Universe.1 Cosmic Chills and UniversalTruthsEarly assessment of the small-scale random motions of galaxies, es-timated on the basis of pairwise ve-locity dispersions, revealed that lo-cally the Universe is rather cold.While we participate in a bulk flowof approximately 600km/s, the ran-dom velocities with respect to themean flow are estimated to be in therange of a mere 200−−300km/s (seee.g. Suto, Cen & Ostriker 1992) Thislow value of the velocity dispersionin combination with the pronouncedstructure displayed by the distribu-tion of galaxies was in fact a strongargument for either a low Ω-Universethe or for the latter being a biasedtracer of the underlying matter dis-tribution. The assumption of bias, inparticular in the form of the oversim-plifying linear bias factor b, wouldthen imply the matter distributionnot to have evolved as far as sug-gested by the pronounced nature ofthe galaxy distribution, and hencewould be in agreement with the lowvalue of the “thermal” motions in thelocal Universe.An interesting elaboration on theassessment of the implications of thecoldness of the local velocity flowfor the properties of the global Uni-verse, in particular for the valueof the cosmological density parame-ter Ω, was suggested by Ostriker &Suzo (1990). They pointed out thata comparison between the proper-ties of the small-scale “dispersion”velocities, σ(v), and the large-scalebulk motions, |v|bulk, would not onlyprovide valuable information on therelative amount of large-scale andsmall-scale power in the spectrumof density- and velocity fluctuations,but that to do this on the basis oftheir ratio, the “cosmic Mach num-ber” M,M ≡|v|bulkσ(v). (1)has the additional advantage of pro-viding this information in a way thatis independent of both the – not yetdefinitively settled – amplitude nor-malization of the power spectrum aswell as of a possible – linear, scale-indepent – bias between galaxies andmatter. The only intrinsic assump-tion is that the velocities of galax-ies do form an unbiased tracer of theunderlying velocity field. One of themost striking conclusions reached onthe basis of extensive tests of thediscriminatory virtues of the Machnumber was that the velocity field inour local Universe appeared to ex-clude the viability of the standardCDM model (Ostriker & Suzo 1990).2 Local versus GlobalIn an attempt to interpret the sig-nificance of the coldness of the localcosmic flow, we postulate an alterna-tive view. Rather than interpretingthe coldness of the flow as a propertyof the global Universe, we hold theview that it is our rather uncommoncosmic location that lies at the basisof the issue and that we should becareful in drawing conclusions con-2 van de Weygaert & HoffmanFigure 1.Left: The density distribution in a constrained reconstruction of our LocalUniverse. Based on the Mark III catalogue peculiar motions, smoothed ona Gaussian scale of Rf = 5h−1Mpc, the Wiener filter reconstruction yieldsthe density field in the top left frame, represented by a density contour plotin the central x − y plane. The solid contours correspond to δ > 0.0, thedashed ones to low-density regions with δ < 0.0. The indicated density lev-els range between -0.6 and 1.3, with the linear increment between contourlevels amounting to ∆δ = 0.1. The heavy solid line is the δ = 0.0 contour.We, the Local Group, are at the centre of the box, clearly recognizable are themass concentrations around the Perseus-Pisces complex (lower lefthand side)and the Great Attractor region (upper righthand corner). Superimposed onthe Wiener filtered density field contours are the bars representing the com-pressional component of the tidal shear within the x − y plane (see van deWeygaert & Hoffman 1998). Notice the strength of the tidal field in the un-derdense region near our own cosmic location. Centre: the constrained lineardensity field realization after including a constrained contribution of small-scale waves according to the standard CDM scenario, Gaussian smoothed ona scale of Rf = 5h−1Mpc. The density contours are characterized in the sameway as the ones in the top frame, with the linear increment of the contourlevels amounting to ∆δ = 0.2, ranging in value from δ = −1.6 to δ = 3.0.Right: outcome of the nonlinear evolution of the constrained realization ofour local Universe, as evolved by means of an N-body simulation.cerning the global value of cosmic pa-rameters as well as of the validity ofstructure formation scenarios.Figure 1a contains a reconstruc-tion of the linear density field (Gaus-sian scale Rf = 5h−1 Mpc) in ourlocal Universe, in a slice approxi-mately coinciding with the Super-galactic Plane, based on the set ofmeasured peculiar velocities of galax-ies in the Mark III catalogue (Willicket al. 1997). The Local Group is lo-cated at the center of the box. On theupper lefthand side we can discerna huge positive density complex, theGreat Attractor region, while on theother side, lower righthand corner,we observe the presence of anothermassive density enhancement, corre-sponding to the Perseus-Pisces su-percluster region. Moreover, in per-pendicular directions we have vastregions of lower than average den-sity. Hence, seemingly we find our-selves located right near the centreof a configuration strongly reminis-cent of a canonical quadrupolar massdistribution. The direct dynamicalimplication of this is that we arelocated near the saddle point of astrong field of tidal shear. In fact,when turning to Figure 1b we seethe compressional component of thetidal field corresponding to the den-sity distribution in the local Uni-verse (Van de Weygaert & Hoffman1998), superposed on the isoden-sity contours in the same slice. Thetidal field, illustrated by bars whosesize and direction are proportionalto the strength of the compressionalong the indicated direction is, ev-idently, very strong within the realmof the two huge matter concentra-tions where the density reaches highvalues. In addition, however, we alsoCold Flows and Large Scale Tides 3Figure 2.Notice 90◦ change in figure orientation. The velocity field structure in ourlocal Universe. Central frame: full velocity field at particle locations, repre-sented by velocity vectors of velocity components in central x − y plane. Leftframes contain the bulk velocity component of the velocity field at the par-ticle locations, with the top frame displaying the vector representation, andthe bottom frame the contour plot of the amplitude of the bulk velocity in thecentral x−y plane. The righthand frames display the same for the small-scalevelocity ‘dispersion’ component. The bulk velocity is defined as the velocityafter filtering out the contributions on scales smaller than 5h−1Mpc, whilethe velocity dispersion is the remaining small-scale residual velocity.see that the tidal shear is indeedvery strong at our own location, pre-cisely due to the fact that we arehanging in between the Great At-tractor and the Perseus-Pisces chain.In fact, through the anisotropic na-ture of the induced tidal forces wecan recognize a situation that was forinstance already recognized withinthe context of the Cosmic Web pic-ture (see Bond, Kofman & Pogosyan1997, also see van de Weygaert &Bertschinger, 1996, fig. 4), the col-lapse and formation of filamentaryand tenuous wall-like features in re-gions bordered by massive matterclumps like clusters of galaxies. Thisappears to be the generic outcomeof the evolutionary path of regionsof moderately low overdensities im-mersed in an external tidal fieldwhose strength is of the same orderof magnitude as the selfgravity of theregion. In such situations we may ex-pect the contraction itself to be ac-celerated with respect to the situa-tion of the same initial region hav-ing been spatially isolated. In fact,the shearing nature of the forces willaccelerate the contraction along theshortest axis of the region that willexperience an accelerated contrac-tion, while the longest axis will expe-rience a slow down of its contractionrate. This in turn will very likely im-ply a slower mixing, “thermal” set-tling and virialization of the matterinvolved in the contraction process.It is the preceding sketch of eventsthat prompts us to expect our lo-cal corner of the Universe, becauseof its special location in betweenthe Great Attractor and the Perseus-Pisces complex, to have a substan-tially lower velocity dispersion thanwe may expect to encounter in an av-erage patch of our Universe.3 Wiener filtering the MarkIII Local CosmosIn an attempt to address the im-plications of the coldness of the localcosmic flow, we investigated the dy-namical and kinematical evolution ofcosmic regions resembling as closelyas possible our own local Universe.First issue in this approach is toset a cosmic environment resemblingour local Universe. This is achievedby invoking relevant observationally4 van de Weygaert & Hoffmandetermined properties of the localcosmos. As we are specifically inter-ested in dynamical issues, we baseourselves on a local cosmic primor-dial linear density field that rep-resents an optimally significant re-construction of the prevailing mat-ter distribution in the early Uni-verse. We achieve this by applying aWiener filter algorithm to the sam-ple of measured peculiar velocities ofgalaxies in the Mark III catalogue(Willick et al. 1997, and Zaroubi etal. 1995 for technical aspects). Sucha reconstruction restricts itself to re-gions that arguably are still withinthe linear regime, and whose statisti-cal properties are still Gaussian. Wediscard further observational con-straints on the small-scale clumpi-ness and motions in the local Uni-verse. Instead, we generate and su-perpose several realizations of small-scale density and velocity fluctua-tions according to a specific powerspectrum of fluctuations, global cos-mological background specified byH0 and Ω0, and with the small-scale noise being appropriately mod-ulated by the large-scale Wiener fil-ter reconstructed density field. Tothis end we invoke the technique ofconstrained random fields (see Hoff-man & Ribak 1991, van de Wey-gaert & Bertschinger 1996), with theWiener filtered field playing the roleof “mean field”.4 Small-scale evolution of theLocal CosmosHaving generated a full realizationof a patch of the Universe resemblingthe primordial density field in our lo-cal cosmic neighbourhood, we traceits development by means of an P3MN-body simulation. The outcome ofour simulations is reduced and ana-lyzed with the help of a ‘dynamicalfields’ code. The resulting distribu-tion of the particles in a central slicethrough the simulations box is shownin the central frame of Figure 2.Clearly recognizable are massive con-centrations of matter at the locationswhere in the real Universe we observethe presence of the Great Attractorregion (slightly “north” of the “west”direction) and the Perseus-Pisces re-gion (slightly “south” of the “east”).Interesting is to see how vast and ex-tended these regions in fact are, cer-tainly not to be identified with well-defined singular objects. The corre-sponding velocity field in the sameregion of the simulations is displayedby means of a decomposition in thelarge-scale bulk flow vbulk, top-hatfiltered in a sphere of radius RTH =5h−1Mpc, and the small-scale veloc-ity “dispersion” vσ (for technical de-tails see Van de Weygaert & Hoffman1998). The top-lefthand frame andthe top-righthand frame contain con-tour plots of the amplitude of thesevelocity field components, while thelower lefthand and lower righthandframe show the corresponding vecto-rial representation of the velocities atthe locations of the particles. In par-ticular the bulk flow field provides abeautiful impression of the displace-ment of matter towards the emer-gence of large-scale features like fil-aments and voids. Most interestingthough is that also the small-scaledispersion field appears to bear themarks of underlying large-scale fea-tures: not only do we see large “ther-mal” velocities at the sites of clusterconcentratios, but we can also rec-ognize sizeable small-scale velocitiesnear the locations of filaments (seeVan de Weygaert & Hoffman 1998).When we compare the contourplots of the bulk motion and the dis-persion velocities, we can already dis-cern the fact that while we (i.e. thecentre of the simulation box) are stillembedded in a region of high bulkflow, evidently incited by the GA andthe PP region, we also find ourselvesin a region of exceptional low veloc-ity dispersion. Evidently a nice re-flection of the observed “coldness”of the local cosmos. We should notfail to notice that apparently thesesmall-scale repercussions are the nat-ural outcome of the dynamical evolu-tion of a region possessing the large-scale features (R > 5h−1Mpc) of thelocal universe.Secondly, an inspection of the con-tour map of the spatial comsic Machnumber distribution illuminates thesignificance of the “coldness” of thelocal cosmic flow. A comparison withthe density map in Figure 1 revealsthe interesting aspect of a large co-herent band of high Mach numbervalues running from the lower left-hand side to the upper righthandside of the simulation box, avoid-Cold Flows and Large Scale Tides 5Figure 3.Contour plot of the Mach number distribution in the central x − y slice, to-gether with the probability distribution function of the Mach number (bottomframe). The arrow indicates the location of the value of the Mach numberat our cosmic location (centre of box), equal to M = 2.61 for the presentedLocal Universe simulated realization.ing both the Great Attractor regionand the Pisces-Perseus region, situ-ated approximately in between thosetwo complexes, almost along the bi-secting plane that they define (seevan de Weygaert & Hoffman 1998).Superposed on this large-scale pat-tern are a plethora of small-scale fea-tures. For our purpose the most sig-nificant of these is the fact that weappear to be right near a toweringpeak of the Mach number distribu-tion. In fact, for this N-body real-ization of our Universe we find atthe location of the Local Group abulk velocity of 695.5km/s, a veloc-ity dispersion of 266.5km/s and aMach number of 2.61, correspondingto a percentile level of 82.1%. Thatpoint is stressed further by invokingthe statistical distribution functionof the Mach number in Figure 3b.Clearly we find ourselves somewherein the tail of the distribution, poten-tially rendering it possible that we dolive in a high-density Universe eventhough locally it’s chilly ... Althoughthe exact numbers differs for variousrealizations, and for instance the spa-tial patterns in the Mach number dis-tribution amy display different fea-tures (narrower band, no conspicu-ous peak), the Mach number consis-tently assumes a value in the rangeabove the 80% percentile value.ReferencesHoffman, Y., Ribak, E., 1991, ApJ,380, L5Ostriker, J.P., Suto, Y., 1990, ApJ,348, 378Suto, Y., Cen, R., Ostriker, J.P.,1992, ApJ, 395, 1van de Weygaert, R., Bertschinger,E., 1996, MNRAS, 281, 84van de Weygaert, R., Hoffman, Y.,1998, ApJ, submittedWillick, J.A., Courteau, S.,Faber, S.M., Burstein, D., Dekel, A.,Strauss, M.A., 1997, ApJS, 109,333Zaroubi, S., Hoffman, Y., Fisher,K.B., Lahav, O., 1995, ApJ, 449, 446

University of Groningen Research Database

  
 University of Groningen
Cold Flows and Large Scale Tides
van de Weijgaert, Marinus; Hoffman, Y.
Published in:
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Document Version
Publisher's PDF, also known as Version of record
Publication date:
1998
Link to publication in University of Groningen/UMCG research database
Citation for published version (APA):
Weygaert, R. V. D., & Hoffman, Y. (1998). Cold Flows and Large Scale Tides. Default journal.
Copyright
Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the
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Download date: 11-02-2018
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99
8
Proceedings: Evolution of Large Scale Structure – Garching, August 1998
COLD FLOWS AND LARGE SCALE TIDES
Rien van de Weygaert1 and Yehuda Hoffman1,2
1Kapteyn Astronomical Institute, P.O. Box 800, 9700 AV Groningen, the Netherlands
2Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
ABSTRACT. We propose a different view of the dilemma concerning the
coldness of the local cosmic flow and its repercussions for the global Universe.
We stress the fact that our cosmic neighbourhood embodies a region of rather
particular circumstances, whose dynamics and kinematics are substantially
influenced by its location in between the Great Attractor region and the
Pisces-Perseus chain. On the basis of constrained simulations of our cosmic
neighbourhood we indicate through the cosmic Mach number that we live in
an extraordinarily cold niche of the Universe.
1 Cosmic Chills and Universal
Truths
Early assessment of the small-
scale random motions of galaxies, es-
timated on the basis of pairwise ve-
locity dispersions, revealed that lo-
cally the Universe is rather cold.
While we participate in a bulk flow
of approximately 600km/s, the ran-
dom velocities with respect to the
mean flow are estimated to be in the
range of a mere 200−−300km/s (see
e.g. Suto, Cen & Ostriker 1992) This
low value of the velocity dispersion
in combination with the pronounced
structure displayed by the distribu-
tion of galaxies was in fact a strong
argument for either a low Ω-Universe
the or for the latter being a biased
tracer of the underlying matter dis-
tribution. The assumption of bias, in
particular in the form of the oversim-
plifying linear bias factor b, would
then imply the matter distribution
not to have evolved as far as sug-
gested by the pronounced nature of
the galaxy distribution, and hence
would be in agreement with the low
value of the “thermal” motions in the
local Universe.
An interesting elaboration on the
assessment of the implications of the
coldness of the local velocity flow
for the properties of the global Uni-
verse, in particular for the value
of the cosmological density parame-
ter Ω, was suggested by Ostriker &
Suzo (1990). They pointed out that
a comparison between the proper-
ties of the small-scale “dispersion”
velocities, σ(v), and the large-scale
bulk motions, |v|bulk, would not only
provide valuable information on the
relative amount of large-scale and
small-scale power in the spectrum
of density- and velocity fluctuations,
but that to do this on the basis of
their ratio, the “cosmic Mach num-
ber” M,
M≡
|v|bulk
σ(v)
. (1)
has the additional advantage of pro-
viding this information in a way that
is independent of both the – not yet
definitively settled – amplitude nor-
malization of the power spectrum as
well as of a possible – linear, scale-
indepent – bias between galaxies and
matter. The only intrinsic assump-
tion is that the velocities of galax-
ies do form an unbiased tracer of the
underlying velocity field. One of the
most striking conclusions reached on
the basis of extensive tests of the
discriminatory virtues of the Mach
number was that the velocity field in
our local Universe appeared to ex-
clude the viability of the standard
CDM model (Ostriker & Suzo 1990).
2 Local versus Global
In an attempt to interpret the sig-
nificance of the coldness of the local
cosmic flow, we postulate an alterna-
tive view. Rather than interpreting
the coldness of the flow as a property
of the global Universe, we hold the
view that it is our rather uncommon
cosmic location that lies at the basis
of the issue and that we should be
careful in drawing conclusions con-
2 van de Weygaert & Hoffman
Figure 1.
Left: The density distribution in a constrained reconstruction of our Local
Universe. Based on the Mark III catalogue peculiar motions, smoothed on
a Gaussian scale of Rf = 5h
−1Mpc, the Wiener filter reconstruction yields
the density field in the top left frame, represented by a density contour plot
in the central x − y plane. The solid contours correspond to δ > 0.0, the
dashed ones to low-density regions with δ < 0.0. The indicated density lev-
els range between -0.6 and 1.3, with the linear increment between contour
levels amounting to ∆δ = 0.1. The heavy solid line is the δ = 0.0 contour.
We, the Local Group, are at the centre of the box, clearly recognizable are the
mass concentrations around the Perseus-Pisces complex (lower lefthand side)
and the Great Attractor region (upper righthand corner). Superimposed on
the Wiener filtered density field contours are the bars representing the com-
pressional component of the tidal shear within the x − y plane (see van de
Weygaert & Hoffman 1998). Notice the strength of the tidal field in the un-
derdense region near our own cosmic location. Centre: the constrained linear
density field realization after including a constrained contribution of small-
scale waves according to the standard CDM scenario, Gaussian smoothed on
a scale of Rf = 5h
−1Mpc. The density contours are characterized in the same
way as the ones in the top frame, with the linear increment of the contour
levels amounting to ∆δ = 0.2, ranging in value from δ = −1.6 to δ = 3.0.
Right: outcome of the nonlinear evolution of the constrained realization of
our local Universe, as evolved by means of an N-body simulation.
cerning the global value of cosmic pa-
rameters as well as of the validity of
structure formation scenarios.
Figure 1a contains a reconstruc-
tion of the linear density field (Gaus-
sian scale Rf = 5h
−1 Mpc) in our
local Universe, in a slice approxi-
mately coinciding with the Super-
galactic Plane, based on the set of
measured peculiar velocities of galax-
ies in the Mark III catalogue (Willick
et al. 1997). The Local Group is lo-
cated at the center of the box. On the
upper lefthand side we can discern
a huge positive density complex, the
Great Attractor region, while on the
other side, lower righthand corner,
we observe the presence of another
massive density enhancement, corre-
sponding to the Perseus-Pisces su-
percluster region. Moreover, in per-
pendicular directions we have vast
regions of lower than average den-
sity. Hence, seemingly we find our-
selves located right near the centre
of a configuration strongly reminis-
cent of a canonical quadrupolar mass
distribution. The direct dynamical
implication of this is that we are
located near the saddle point of a
strong field of tidal shear. In fact,
when turning to Figure 1b we see
the compressional component of the
tidal field corresponding to the den-
sity distribution in the local Uni-
verse (Van de Weygaert & Hoffman
1998), superposed on the isoden-
sity contours in the same slice. The
tidal field, illustrated by bars whose
size and direction are proportional
to the strength of the compression
along the indicated direction is, ev-
idently, very strong within the realm
of the two huge matter concentra-
tions where the density reaches high
values. In addition, however, we also
Cold Flows and Large Scale Tides 3
Figure 2.
Notice 90◦ change in figure orientation. The velocity field structure in our
local Universe. Central frame: full velocity field at particle locations, repre-
sented by velocity vectors of velocity components in central x− y plane. Left
frames contain the bulk velocity component of the velocity field at the par-
ticle locations, with the top frame displaying the vector representation, and
the bottom frame the contour plot of the amplitude of the bulk velocity in the
central x−y plane. The righthand frames display the same for the small-scale
velocity ‘dispersion’ component. The bulk velocity is defined as the velocity
after filtering out the contributions on scales smaller than 5h−1Mpc, while
the velocity dispersion is the remaining small-scale residual velocity.
see that the tidal shear is indeed
very strong at our own location, pre-
cisely due to the fact that we are
hanging in between the Great At-
tractor and the Perseus-Pisces chain.
In fact, through the anisotropic na-
ture of the induced tidal forces we
can recognize a situation that was for
instance already recognized within
the context of the Cosmic Web pic-
ture (see Bond, Kofman & Pogosyan
1997, also see van de Weygaert &
Bertschinger, 1996, fig. 4), the col-
lapse and formation of filamentary
and tenuous wall-like features in re-
gions bordered by massive matter
clumps like clusters of galaxies. This
appears to be the generic outcome
of the evolutionary path of regions
of moderately low overdensities im-
mersed in an external tidal field
whose strength is of the same order
of magnitude as the selfgravity of the
region. In such situations we may ex-
pect the contraction itself to be ac-
celerated with respect to the situa-
tion of the same initial region hav-
ing been spatially isolated. In fact,
the shearing nature of the forces will
accelerate the contraction along the
shortest axis of the region that will
experience an accelerated contrac-
tion, while the longest axis will expe-
rience a slow down of its contraction
rate. This in turn will very likely im-
ply a slower mixing, “thermal” set-
tling and virialization of the matter
involved in the contraction process.
It is the preceding sketch of events
that prompts us to expect our lo-
cal corner of the Universe, because
of its special location in between
the Great Attractor and the Perseus-
Pisces complex, to have a substan-
tially lower velocity dispersion than
we may expect to encounter in an av-
erage patch of our Universe.
3 Wiener filtering the Mark
III Local Cosmos
In an attempt to address the im-
plications of the coldness of the local
cosmic flow, we investigated the dy-
namical and kinematical evolution of
cosmic regions resembling as closely
as possible our own local Universe.
First issue in this approach is to
set a cosmic environment resembling
our local Universe. This is achieved
by invoking relevant observationally
4 van de Weygaert & Hoffman
determined properties of the local
cosmos. As we are specifically inter-
ested in dynamical issues, we base
ourselves on a local cosmic primor-
dial linear density field that rep-
resents an optimally significant re-
construction of the prevailing mat-
ter distribution in the early Uni-
verse. We achieve this by applying a
Wiener filter algorithm to the sam-
ple of measured peculiar velocities of
galaxies in the Mark III catalogue
(Willick et al. 1997, and Zaroubi et
al. 1995 for technical aspects). Such
a reconstruction restricts itself to re-
gions that arguably are still within
the linear regime, and whose statisti-
cal properties are still Gaussian. We
discard further observational con-
straints on the small-scale clumpi-
ness and motions in the local Uni-
verse. Instead, we generate and su-
perpose several realizations of small-
scale density and velocity fluctua-
tions according to a specific power
spectrum of fluctuations, global cos-
mological background specified by
H0 and Ω0, and with the small-
scale noise being appropriately mod-
ulated by the large-scale Wiener fil-
ter reconstructed density field. To
this end we invoke the technique of
constrained random fields (see Hoff-
man & Ribak 1991, van de Wey-
gaert & Bertschinger 1996), with the
Wiener filtered field playing the role
of “mean field”.
4 Small-scale evolution of the
Local Cosmos
Having generated a full realization
of a patch of the Universe resembling
the primordial density field in our lo-
cal cosmic neighbourhood, we trace
its development by means of an P3M
N-body simulation. The outcome of
our simulations is reduced and ana-
lyzed with the help of a ‘dynamical
fields’ code. The resulting distribu-
tion of the particles in a central slice
through the simulations box is shown
in the central frame of Figure 2.
Clearly recognizable are massive con-
centrations of matter at the locations
where in the real Universe we observe
the presence of the Great Attractor
region (slightly “north” of the “west”
direction) and the Perseus-Pisces re-
gion (slightly “south” of the “east”).
Interesting is to see how vast and ex-
tended these regions in fact are, cer-
tainly not to be identified with well-
defined singular objects. The corre-
sponding velocity field in the same
region of the simulations is displayed
by means of a decomposition in the
large-scale bulk flow vbulk, top-hat
filtered in a sphere of radius RTH =
5h−1Mpc, and the small-scale veloc-
ity “dispersion” vσ (for technical de-
tails see Van de Weygaert & Hoffman
1998). The top-lefthand frame and
the top-righthand frame contain con-
tour plots of the amplitude of these
velocity field components, while the
lower lefthand and lower righthand
frame show the corresponding vecto-
rial representation of the velocities at
the locations of the particles. In par-
ticular the bulk flow field provides a
beautiful impression of the displace-
ment of matter towards the emer-
gence of large-scale features like fil-
aments and voids. Most interesting
though is that also the small-scale
dispersion field appears to bear the
marks of underlying large-scale fea-
tures: not only do we see large “ther-
mal” velocities at the sites of cluster
concentratios, but we can also rec-
ognize sizeable small-scale velocities
near the locations of filaments (see
Van de Weygaert & Hoffman 1998).
When we compare the contour
plots of the bulk motion and the dis-
persion velocities, we can already dis-
cern the fact that while we (i.e. the
centre of the simulation box) are still
embedded in a region of high bulk
flow, evidently incited by the GA and
the PP region, we also find ourselves
in a region of exceptional low veloc-
ity dispersion. Evidently a nice re-
flection of the observed “coldness”
of the local cosmos. We should not
fail to notice that apparently these
small-scale repercussions are the nat-
ural outcome of the dynamical evolu-
tion of a region possessing the large-
scale features (R > 5h−1Mpc) of the
local universe.
Secondly, an inspection of the con-
tour map of the spatial comsic Mach
number distribution illuminates the
significance of the “coldness” of the
local cosmic flow. A comparison with
the density map in Figure 1 reveals
the interesting aspect of a large co-
herent band of high Mach number
values running from the lower left-
hand side to the upper righthand
side of the simulation box, avoid-
Cold Flows and Large Scale Tides 5
Figure 3.
Contour plot of the Mach number distribution in the central x− y slice, to-
gether with the probability distribution function of the Mach number (bottom
frame). The arrow indicates the location of the value of the Mach number
at our cosmic location (centre of box), equal to M = 2.61 for the presented
Local Universe simulated realization.
ing both the Great Attractor region
and the Pisces-Perseus region, situ-
ated approximately in between those
two complexes, almost along the bi-
secting plane that they define (see
van de Weygaert & Hoffman 1998).
Superposed on this large-scale pat-
tern are a plethora of small-scale fea-
tures. For our purpose the most sig-
nificant of these is the fact that we
appear to be right near a towering
peak of the Mach number distribu-
tion. In fact, for this N-body real-
ization of our Universe we find at
the location of the Local Group a
bulk velocity of 695.5km/s, a veloc-
ity dispersion of 266.5km/s and a
Mach number of 2.61, corresponding
to a percentile level of 82.1%. That
point is stressed further by invoking
the statistical distribution function
of the Mach number in Figure 3b.
Clearly we find ourselves somewhere
in the tail of the distribution, poten-
tially rendering it possible that we do
live in a high-density Universe even
though locally it’s chilly ... Although
the exact numbers differs for various
realizations, and for instance the spa-
tial patterns in the Mach number dis-
tribution amy display different fea-
tures (narrower band, no conspicu-
ous peak), the Mach number consis-
tently assumes a value in the range
above the 80% percentile value.
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Ostriker, J.P., Suto, Y., 1990, ApJ,
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