Co-planar streams, pancakes, and angular-momentum exchange in high-z disc galaxies

2 MB·English

by  Mark Danovich

Mon.Not.R.Astron.Soc.000,1–20(0000) Printed13January2012 (MNLATEXstylefilev2.2)
Co-planar streams, pancakes, and angular-momentum exchange in
high-z disc galaxies
2
Mark Danovich1 ⋆, Avishai Dekel1 , Oliver Hahn2, Romain Teyssier3,4
1
0 †
2 1RacahInstituteofPhysics,TheHebrewUniversity,Jerusalem91904,Israel
2KavliInstituteforParticleAstrophysicsandCosmology,SLAC/StanfordUniversity,2575SandHillRoad,MenloPark,CA94025,USA
n
3CEA,IRFU,SAp,91191Gif-sur-Yvette,France
a
J 4InstituteforTheoreticalPhysics,UniversityofZurich,CH-8057Zurich,Switzerland

2
1

]
O
ABSTRACT
C We study the feedingof massive galaxiesat high redshift throughstreams from the cosmic
. webusingtheMareNostrumhydro-cosmologicalsimulation.Ourstatisticalsampleconsists
h
p of 350 dark-matter haloes of ≃ 1012M⊙ at z = 2.5. We find that ∼ 70% of the influx
into the virial radius R is in narrow streams covering 10% of the virial shell. On average
- v
o 64% of the stream influx is in one stream, and 95% is in three dominant streams. The
r streams that feed a massive halo tend to lie in a plane that extends from half to a few R ,
t v
s hereafter “the stream plane” (SP). The streams are typically embedded in a thin sheet of
a low-entropy gas, a Zel’dovich pancake, which carries 20% of the influx into R . The
[ ∼ v
filaments-in-a-planeconfigurationaboutthe massive haloesat the nodesof the cosmic web

2 differsfromthelarge-scalestructureofthewebwherethefilamentsmarktheintersectionsof
v slanted sheets. The stream plane is only weakly aligned with the angularmomentum(AM)
9 near R , consistent with the fact that typically 80% of the AM is carried by one dominant
v
0 stream.Thegalacticdiscplaneshowsaweaktendencytobeperpendiculartothelarge-scale
2
SP,consistentwithtidal-torquetheory.Mostinteresting,thedirectionofthediscAMisonly
6
weaklycorrelatedwiththeAMdirectionatR .ThisindicatesasignificantAMexchangeat
. v
0 theinterphasebetweenstreamsanddiscinthegreaterenvironmentofthediscinsidean“AM
1 sphere of radius 0.3R . The required large torques are expected based on the perturbed
v
1 morphologyand∼kinematics within this interaction sphere. This AM exchangemay or may
1 not require a major modification of the standard disc modelingbased on AM conservation,
:
v dependingontheextenttowhichtheamplitudeofthediscAMisaffected,whichisyettobe
i studied.
X
Key words: cosmology:theory — galaxies: evolution — galaxies: formation — galaxies:
r
a haloes — galaxies: kinematics and dynamics — galaxies: spiral — large-scale structure of
Universe
1 INTRODUCTION Adelman-McCarthy 2008). The honey-comb-like structure
consists of big voids surrounded by flat low-overdensity
The
sheets (walls, pancakes), that intersect in narrow, denser
large-scaledistributionofmatterintheuniverse,dominated
filaments, which further intersect in relatively compact,
by the dark matter, exhibits a cosmic web (Bondetal.
virialized, spheroidal dark-matter haloes (clusters) at the
1996; Pogosyanetal. 1998). This has been envisioned
nodes of the web. According the quasi-linear Zel’dovich
based on the Zel’dovich approximation (Zeldovich 1970)
approximation (Zeldovich 1970), each Lagrangian point is
and the theory of Gaussian random fields (Doroshkevich
characterized by the eigenvectors and eigenvalues of the
1970; Bardeenetal. 1986), reproduced in cosmological
deformation tensor, which consists of the second spatial
N-bodysimulations(Klypin&Shandarin1983;Davisetal.
partial derivatives of the gravitational potential field. if we
1985;Springeletal.1996;Klypinetal.2011),andobserved
denotetheeigenvalues(λ ,λ ,λ ),orderedsuchthatλ >
in redshift surveys (Hucraetal. 1983; Colless 1999; 1 2 3 1
λ > λ , a sheet would form due to a one-dimensional
2 3
collapse where λ dominates, which we can crudely
1
approximate by the requirement that the signature of the
⋆ E-mail:[email protected] eigenvalues is (+, , ). A filament would form after
† E-mail:[email protected] − −
2 Danovichet al.
dM˙/dΩ
6
−300
222
4
−200
2
−100 0
c] −2
p 0
k
[
−4
100
−6
200 −8
−10
300

−300 −200 −100 0 100 200 300
[kpc]
Figure1. Coldgasstreams.Shownistheradialfluxdensitypersolidangle(in M⊙yr−1rad−2)intotwotypicalmassivegalaxiesatz = 2.5fromthe
MareNostrumcosmologicalsimulation.Left:A1-kpcthickslicethroughthecentreofahalo,showingthreestreamsthatemergeatadistancemorethan5
timesthevirialradius(blackcircle)andpenetratetotheinnerhalo.Right:athree-dimensionalviewofinflux,extendingtotwicethevirialradius,showing
thatthestreamscontainclumpsandasmoothergascomponent.Theclumpsaremerginggalaxiescontaininggas,starsanddarkmatter,(seeDekeletal.2009;
Ceverinoetal.2010).
field, the fraction of volume and mass associated with
each of the four different signatures of the deformation
tensor is 42% for the filaments and sheets, and 8%
for the haloes and voids (Doroshkevich 1970). In the
non-linear regime, the statistics depend on scale, as the
structures have collapsed bottom-up to increasingly higher
densities occupying smaller and smaller scales. Hahnetal.
(2007)havedemonstratedthisscaledependencebyshowing
how the volume fractions of the four signatures of the
deformationtensordeviatefromthe Gaussian randomfield
values as the smoothing scale is decreased. Using adaptive
filtering, Arago´n-Calvoetal. (2010) found that the mass
fractionsassociatedwith the foursignaturesof theHessian
tensor, consisting of the spatial partial derivatives of the
densityfield,are28.1%inhaloes,39.2%infilaments,5.5%
insheetsand27.2%invoids,whilethesestructuresoccupy
0.4%, 8.8%, 4.9% and 85.9% of the volume, respectively.
The corresponding mean overdensities with respect to the
mean cosmological background are 73, 4.5, 1.1 and 0.3,
Figure2. Gasdensityinthestreamsfeedingthegalaxyshownintheright
respectively. Using an excursion-set model for triaxial
panelofFig.1(314),inaRAMSEStestrunwitharesolution higherby
collapse, Shenetal. (2006) found that at z = 0, when
anorderofmagnitude.Theboxencompassesasphereoftwicethevirial
radius. The stream configuration remains qualitatively similar, with the filtering over scales corresponding to 1010M⊙, typically
99% of the mass has crossed the threshold for collapse
innerstructureofthestreamsbetterresolved(courtesyofD.Tweed).
alongatleastoneaxis,andthusresidesinsheets(including
filamentsandhaloes), while 72%is in filaments(including
haloes) of smaller scales embedded in these sheets, and
collapseintwodirections,whereλ andλ arecomparable
1 2 only 46% is in haloes. Thus, no matter how we look at it,
and much larger than λ , e.g., a signature (+,+, ). A
3 − the filaments containthe largestfractionof mass, and their
halo would form in a node, where the eigenvalues are all
higher density contrast makes them much easier to detect
comparableandpositive,(+,+,+).Thefilamentsthusform
than the sheets. Several other studies have addressed the
intheintersectionsofsheets,andthenodesareintersections
large-scalegeometryofcosmic-webfilamentsinsimulations
of filaments. In the quasi-linear regime, the matter flows
(e.g.,Colbergetal.2005;Hahnetal.2007,2009;Gayetal.
awayfromthevoidsintothesheets,withinthesheetstoward
2010; Arago´n-Calvoetal. 2010; Noh&Cohn 2011), and
thefilaments,andalongthefilamentstowardthenodes.
howtotraceitintheobserveddistributionofgalaxies(e.g.,
Thefilamentsaretheprominentfeaturesofthecosmic
Dekel&West 1985; Arago´n-Calvoetal. 2007; Sousbie
web,bothintermsofmasscontentanddensitycontrast.In
2011; Sousbieetal. 2011). Massive galaxies at redshift
the linear regime of a Gaussian random density fluctuation
Streams,pancakes andgalaxyangularmomentum 3
z > 2 form in dark-matter haloes that are much more thefirstdetectionofpancakesincosmologicalsimulations,
massive than the typical halo at that time, hundreds of to be studied in detail in Hahnetal. (2011). In 4 we
§
times larger than the characteristic Press-Schechter mass investigatethedistributionofinfluxinstreamsandpancakes,
(which is 3 109M⊙ at z = 2.5 for the WMAP7 revealing one dominant stream and a tendency for three
∼ ×
cosmological parameters). They are therefore “high-sigma major streams. In 5 we address the angular momentum
§
peaks” of the initial density fluctuation field, which reside transportbystreamsfromoutsidethehalointotheinnerdisc,
in the nodes of the cosmic web. In each halo, the dark by exploring the degree of alignment between the stream
matterflowingalongthefilamentsfeedsthedarkmatterhalo planeandAMatthevirialradiusandbetweenthemandthe
and fills the entire virial sphere. The baryons that stream disc.In 6wediscussthepossibleoriginofthemainfeatures
§
withthedarkmatteralongthefilamentsintothehalovirial of the cosmic web near a node. In 7 we summarize our
§
radius penetrate through the halo and feed the galaxy at resultsanddiscussthem.Weaddressseveraltechnicalissues
the halo centre, both as merging galaxies and a smoother in the appendices. Of particular interest is C, where we
§
gascomponent(Birnboim&Dekel2003;Keresetal.2005; evaluateapotentialsystematiceffectinouranalysis,namely
Dekel&Birnboim 2006; Ocvirketal. 2008; Dekeletal. the numerical tendency of alignment between the disc and
2009).ThisisillustratedinFig.1,showingtheinfluxdensity theaxesofthesimulationgrid.
per solid angle on the scale of a few virial radii in two
galaxies from the Mare Nostrum cosmological simulation
(Ocvirketal. 2008) used in Dekeletal. (2009) and in the
2 METHOD
currentpaper.
Figure 2 shows the gas density in the streams that 2.1 Thecosmologicalsimulation
feed the same galaxy shown in the right panel of Fig. 1,
The cosmological simulation used in this analysis is the
galaxy 314 of the Mare Nostrum simulation, which has
AMR Horizon Mare Nostrum (MN) galaxy formation
been displayed in more detail in Dekeletal. (2009). The
simulation (Ocvirketal. 2008), which utilized the AMR
current map is from a test run using RAMSES with a
code RAMSES (Teyssier 2002) to simulate the dynamics
maximumresolutionof60pc,higherbymorethananorder
ofgasanddarkmatterinacosmologicalbox.Thestandard
ofmagnitudethantheMareNostrumresolution.Thisfigure
ΛCDMcosmologyisassumed,withΩ = 0.7,Ω = 0.3,
demonstratesthatthe generalstream patternis notaffected Λ m
Ω = 0.045,h = 0.7 and σ = 0.95 in a periodic box of
by the resolution, except that the inner structure of the b 8
side50h−1Mpc.Thedark-mattercomponentisrepresented
streamsandthesmallermerginggalaxiesarebetterresolved.
The efficient feeding of galaxies by streams has a boyf 1100224433cpealrlsticilsesproofgr1e.s1s7iv×ely1a0d7aMp⊙tedeawchhe.nAthbeasniucmgbriedr
major impact on the way these galaxies form and evolve
of DM particles in the cell exceeds 8, or when the gas
(Dekel&Birnboim2006; Dekeletal. 2009;Ceverinoetal.
mass exceeds 8 times the initial gas mass resolution.. The
2010; Oseretal. 2010; Ceverinoetal. 2011; Cacciatoetal.
minimumcellsizeis1kpcphysical.Thelargecosmological
2011). The streams bring in most of the baryonic mass
boxandthe1-kpcresolutionallowsforareliablestatistical
and angular momentum, and are thus responsible for
study of the way massive galaxiesare fed fromthe cosmic
the formation of large rotating discs. The continuous
webatthehaloscales.Thisresolutionallowsforidentifying
intense in-streaming allows for high star formation rates
massivediscsthatextendto 10kpc,butthediscthickness
(SFR) in those discs, in most cases not related to ∼
is barely resolved. The MN simulation employs at the
mergers(Genzeletal.2006;Dekeletal.2009).Thestreams
sub-gridlevelphysicalprocessesthatarerelevantforgalaxy
maintain a high gas fraction that is responsible for a
formation, such as star formation, supernovae feedback,
violent disc instability with large transient features and
metalenrichment,metaldependentcoolingandbackground
giantclumps,whichdrivearapidmassinflowtothecentre
UV heating (see appendix A). However, these processes
(independent of whether the clumps disrupt Dekeletal. §
are followedwith a limited accuracythatis dictated by the
2009; Geneletal. 2012; Hopkinsetal. 2012). This may
limitedresolution.
eventually lead to the formation of a central bulge with
a massive black hole (Dekeletal. 2009; Ceverinoetal.
2010;Bournaudetal.2011).Astudyofthebaryonicstream
2.2 DarkMatterhaloesandgalaxies
propertiesis thereforecrucial for a better understandingof
galaxyformationathighredshift.Inaddition,sincethegas We select from the MN snapshot at z = 2.5 all the 351
tendstocondenseinthecentral,denserregionsofthemore dark-matter haloes with virial mass in the range (0.8
dispersivedark-matterfilamentsandsheets,thegascanalso 3) 1012M⊙ (serially numbered 50 to 400 in order o−f
serve as a unique tracer of the cosmic web skeleton in the dec×reasingmass).Thisisthemassrangeofhaloesthathost
vicinityofitshigh-sigmapeaknodes. themassivestar-forminggalaxiesobservedattheseredshifts
In this paper we use a hydrodynamical cosmological (Genzeletal.2006,2008;Tacconi2008;Dekeletal.2009),
simulation, the Mare Nostrum simulation, to study the with a comoving number density of 4 10−4Mpc−3 for
large-scale properties of the streams feeding massive Mv > 1.5 1012M⊙ at z = 2.5.×These haloes are
×
galaxiesathighredshift.Wealsomakeapreliminaryattempt expected to be relatively rare (> 2σ) density peaks at
atrelatingtheangularmomentum(AM)ofdisc galaxiesto the nodes of the cosmic web, and are predicted to have
theAMcarriedbythestreamsfromthecosmicwebintothe shock-heatedhot media penetratedby narrow cold streams
halo.Theoutlineof thepaperis asfollows:In 2(and A) (Dekel&Birnboim2006;Dekeletal.2009).
§ §
we describe the simulation and the method of analysis. In For each halo, we define the centre as the peak of the
3westudythetendencyofthestreamstobeco-planarand gasdensitysmoothedwithaGaussianofstandarddeviation
§
4 Danovichet al.
5.4kpc. We then use the gas density and velocity in 2563 radius, we sometimes consider the sum of all the spherical
cells of a cubic grid about the galaxy centre. For a study shells in the radius range (1 2)R . This stacking
v
−
on the halo scale at the highest resolution, the cell side is improvesthestatisticsbyincludingmoreinformation,andin
1.246 kpc (= 50/2ℓh−1Mpc comoving at adaptive level particularitemphasizeselongatedradialstreamsthatstretch
ℓ = 14)andthe correspondingboxside is319kpc,almost overavirial-radiusscale.Itproperlysmoothesoverthelocal
encompassing a 2R sphere. For a study of the greater fluctuations due to merging galaxies, putting them in the
v
environmentof the halo, we use boxes and cells twice and contextofthestreamsthattheybelongto.
fourtimesaslarge(adaptivelevelsℓ=13and12),reaching
to 5.5R .
v
∼Thegasvelocitiesarecorrectedtotherestframeofthe 2.4 NumericalAlignment
centre of mass of the cold gas with T < 105K within a A potential caveat in our analysis of preferred planes
sphere of radius 0.1Rv 10kpc about the density peak, is the numerical tendency for artificial alignment of
∼
mimicking the centre of mass of the disc. In most cases planes of matter with the simulation grid. A grid-based
this correction is smaller than one resolution element and Poissonsolver,andinparticularthehydrodynamicalsolver,
ithasanegligibleeffectontheresults.AHubbleflow(H = create non-physical forces along the preferred Cartesian
254kms−1Mpc−1 at z = 2.5) is added to the comoving directions of the simulation grid, which act to align the
velocities used in the simulation. Angular momentum is mass distribution with the grid (Hahnetal. 2010). This is
computed about the position of this centre of mass. Our especiallyrelevantforthegalacticdiscplane,whichinvolves
resultsconcerninginflowsandangularmomentaweretested scales not much larger than the resolution scale, but it
nottobesensitivetotheexactchoiceofdisccentreandrest would also be useful to verify that no artificial alignment
frame,whichcanbedeterminedatanaccuracylevelthatis propagates to the sheets on larger scales (to be defined
comparabletothesimulationresolution. below). The artificial alignment is expected to be stronger
We excludefromthe analysis15haloeswherethereis at lower redshifts, where the discs might have had enough
no obvious central galaxy in the halo, presumably due to timeto relaxto theclosestgriddirection,so we expectour
ongoingmajormergers.Thisleavesuswithasampleof336 analysisofmassivegalaxiesatz =2.5tobelessvulnerable
haloes. tothisnumericaleffect,despitethe1-kpcresolution.
We address this potential numerical alignment in
appendix C.Wefindthatitislimitedto 20%ofthediscs.
§ ∼
2.3 Identificationofstreams Forcaseswheretheoriginalcosineoftheanglebetweenthe
normaltothediscandtheclosestgridaxiswascosθ >0.8,
The streams consist in principle of dark matter, stars and
ithasbeenpushedupby∆(cosθ) 0.08.Thisis a rather
gas, but our previous attempts to quantify stream statistics ∼
small effect, associated with a negligible shift in the mean
based on the dark matter led to noisy results, that got
of cosθ. This is the level of error that we should assign to
worse at smaller radii inside the haloes where the dark
anymeasureofalignmentbetweenthediscandotherplanes.
matter is virialized. Here we identify the streams and
As expected, the stream plane at R does not show any
study their properties based on the cold gas, which, due v
measurablenumericalalignmentwiththesimulationgrid.
to dissipative processes, traces much more cleanly the
filamentaryskeletonofthecosmicweb.
The mainquantityused ateverypoint~r on a spherical
grid about the galaxy centre is the radial flux density per 3 STREAMCO-PLANARITY
solidangle, In the large-scale cosmic web, where the filaments bridge
between the nodes to form a three-dimensional network,
dM˙
=ρv r2, (1) thereisnoobviousapriorireasonforthefilamentsthatfeed
r
dΩ a nodeto lie in one plane.We findbelow thattheydotend
where ρ is the gas density, v the radial velocity and r the to lie in a plane that contains the galaxy centre, which we
r
radialdistancefromthegalaxycentre.Weuseintheanalysis term “the stream plane” (SP). Figure 3 shows the influx in
thinsphericalshellsofone-cellthicknessortheaverageover a thick shell at (1 2)Rv for twelve different simulated
−
severalthin shells inside a thick shell. The scalars given in galaxies. The haloes shown were selected from the large
the cells of the cubic grid are interpolated into a spherical sampleofhaloesthathaveatleastthreestreams(according
gridof5122equal-areaangularcells,witharadialthickness toourdefinitionofstreamnumberdescribedbelow)andthey
of√3 50/2ℓh−1Mpc,whereℓistheadaptivelevelused areverywellconfinedtoagreatplane(namelyaplanethat
forthe×cubicgridthatsamplesthatshell(see 2.2). containsthegalaxycentre).Thecoordinatesarerotatedsuch
In each shell, we identify streams by fi§rst applying a thatthebest-fitstreamplaneisattheequator.Wefindusing
giveninfluxdensitythreshold,atagivenoverdensityabove the goodnessof fit measure (described below) that 60% of
theaverageinfluxdensityintheentireshell.Wethenapply the galaxiesfit a plane better than the worst case shown in
an angular friends-of-friendsalgorithm to the influx above thefigure(halo145).Examplesofgalaxiesinwhichthefit
thethresholdonthesphericalshellgrid.Thismeansthatwe toaplaneisworseareshowninappendix D.
§
assign to the same stream all the adjacent grid cells with
influxdensityabovethethreshold(see 4formoredetails).
§ 3.1 Thebest-fitStreamPlane
Foreachstream,werecorditsflux-weightedaverageangular
positiononthesphereanditstotalmassinflowrate. We definethebest-fitstreamplaneandmeasurethequality
In our analysis of the streams flowing into the virial of the fit based on the angular positions of the centres
Streams,pancakes andgalaxyangularmomentum 5
Figure3. Co-planarinflowingstreamsandpancakesinathickshellat(1−2)Rv.Shownaswhole-skyHammer-Aitoffmapsofinfluxdensityaretwelve
different simulated galaxies in haloes of∼ 1012M⊙ at z = 2.5. They are selected to represent the many galaxies with at least 3 streams that almost
perfectlylieonagreatplane.Thecoordinates arerotatedsuchthatthebest-fitstreamplanecoincides withtheequator.Thecolorrepresents radialinflux
ofgas masspersolidangle. Thecentres ofthethree streams with thehighest influxaremarked bygreendots. Typical fluxdensities inthestreams are
(50−150)M⊙yr−1rad−2withthehigherfluxesvalidinthemoremassivehaloes.Thinpancakesof∼10−15M⊙yr−1rad−2areseenbetweenthe
streams,mostfrequentlycoincidingwiththestreamplane,butsometimesshowingpancakesegmentsthatdeviatefromthestreamplane.
of the three streams with the largest influx at (1 2)R . points.Fora similarreason,whenwe fita planewe donot
v
−
One or two streams always lie on a plane that containsthe weighthethreestreamsbytheirindividualinfluxes.
galaxy centre, so three is the smallest number of streams
forwhichco-planarityisnontrivial.Wethuseliminatefrom The three streams for the fit of a plane are determined
the analysis of co-planarity the haloes with less than three after applying the two following procedures. First, if two
streams(seebelow).Wewillshowthattypicallymorethan streams are separated by less than a minimum angular
90%of theinfluxin streamsiscarriedbythe threeleading separationsmin,wecombinethemintoone,withthesumof
streams, so using these three for the fit and ignoring any themassinflowratesandanewinflow-weightedcentre.This
additionalstreamsisquitesensible.Welimitthefittoafixed is in order to avoid confusion with two apparently nearby
numberofstreams(3)inordertoproperlycomparetoanull streams that may actually be part of one stream and may
hypothesis of random angular positions without worrying lead to a trivial co-planarity. Second, and what turns out
aboutthe dependenceof the co-planarityon the numberof to make a stronger effect, we eliminate from the analysis
haloes in which the ratio of inflow rate in the third stream
6 Danovichet al.
1 1
0.9 0.9
0.4R
v
0.8 0.8 0.8R
v
1R
0.7 p=8×10−11 0.7 1.5vR
0.6 0.6 v
2.5R
F F v
D0.5 D0.5 3.5R
C C v
random
0.4 0.4
0.3 0.3
0.2 0.2
0.1 0.1
0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
d[rad] d[rad]
Figure4. Thesignificanceofthestreamco-planarityinashell(1−2)Rv(left)andinshellsofdifferentradii(right).Shownisthecumulativeprobability
distribution(CDF)ofthermsdeviationofthethreelargeststreamsfromthebest-fitplane,d,basedon235haloes(color).ItiscomparedtothesameCDF
forthenullhypothesisofarandomangulardistributionof3points,basedon5,000realizations(black).Thesamethresholdsminisappliedtothedataand
thenullmodel.AKStestrevealsthatatRvthenullhypothesisisstronglyrejectedwithapvalueof8×10−11.Thecorrespondingp-valuesforshellsfrom
0.4Rvto3.5Rvare:0.12,7×10−5,2×10−12,2×10−8,4×10−6,0.38.
D−statistic
1 0 0.28
0.9
5 0.26
0.8
0.7
10 0.24
0.6
F n
D0.5 mi15 0.22
C S
0.4
20 0.2
0.3
0.2
25 0.18
0.1
0 30 0.16
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1/5 1/10 1/15 1/20 1/25 0
d[rad] f31
Figure5. Sensitivitytotheprocedureofidentifyingthestreams.Left:ShownaretheCDFsofdfordifferentvaluesofsminandf31,forthesimulatedhaloes
(red)andtherandom-positionnullmodel(blue).Right:TheDstatisticoftheKS-test(incolor)fordifferentcombinationsofsminandf31.Theresultsare
insensitivetothechoiceofparametersinthegivenrange.
comparedtothefirststreamissmallerthanathresholdf . d in radians, is used as a measure of the deviation from a
31
If this ratio is below the threshold,we consider the halo to plane.
be of two streams or less, where the fit to a plane should In appendix B, we describe a different algorithm for
§
betrivial,andeliminateitfromtheanalysisofco-planarity. definingthestreamplane,whichmaximizestheinflowrate
These proceduresreduce the numberof haloes that we use throughabeltofwidth π/9radiansaboutagreatcircleon
±
in ourstatistical analysisconcerningthe stream planefrom the spherical shell. We find that in the vast majority of the
336to 235.The main selection is due to the thresholdf , haloes,atR ,thestreamplanesdefinedbythetwomethods
31 v
whichwithf =0.1filtersout92ofthe101haloesthatare practicallycoincide,with a medianofcosθ = 0.96forthe
31
eliminatedfromtheco-planarityanalysis. angle between the planes as defined by the two methods
Thedeviationofthethreestreamsatagivenconcentric (Fig.20).
shell from a given great plane is defined by the sum in
quadrature of the angular distances between the stream
3.2 Thesignificanceoftheco-planarity
centre angular positionsand the greatcircle of intersection
between the plane and the shell. The best-fit plane is The statistical significance of the stream co-planarity is
determinedbyminimizingthissum,andtheminimumvalue, evaluated by comparing the data from the simulations to a
Streams,pancakes andgalaxyangularmomentum 7
andthe68%percentilesforthecosineoftheanglebetween
1 these planes as a function of r, compared to a random
0.9 distributionwhere themedianis 0.5.The averagecosine is
above0.75intherange0.5 2.5R ,indicatingasignificant
v
0.8 −
alignment of the SP in this range. Note that R itself is
v
0.7 not a special physical radius, as the virial shock and the
dark-mattervirializationradiuscouldactually be anywhere
0.6
θ in this range. The figure would therefore be qualitatively
os0.5 similar had we anchored the curve at some other radius
c
0.4 slightlydifferentfromRv.
Outsidethevirialradius,theSPextendstobeyond5R .
0.3 v
KS-tests yield p values that range from 3 10−49 at r =
0.2 1.5R , through 5 10−11 at r = 3.5R ,×to 6 10−4 at
nˆ ·nˆ(r) v × v ×
0.1 Rv r = 5.5Rv. This plane connects the neighborhood of the
halototheglobalcosmicweb.
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 Inside the halo, the SP penetrates to 0.4R , with
r/Rv the KS p values ranging from 10−53 at r∼ = 0.8vR to
v
4 10−7 at r = 0.4R . However, at r = 0.2R , the SP
Figure6. Extensionofthestreamsplane.Shownisthemedianofthecosine × v v
nolongercorrelateswiththeSPatR ,withaKSp=0.92.
oftheanglebetweentheSPat1RvandtheSPatdifferentradiifrom0.2Rv v
This argues that the stream plane practically disappears at
to5.5Rvcomparedtoarandomdistributioninwhichthemedianis0.5.It
showsasignificantalignmentfrom0.5Rvto2.5Rvandaweakalignment r = 0.2Rv andinsideit,the20kpcvicinityofthedisc.We
forshellsinside0.5Rvandintherange2.5−5.5Rv. willgetbacktothisinthediscussionofangularmomentum
in 5.
§
A complementarywaytoexaminetheextensionofthe
null hypothesis where the streams represent three random SP is by evaluating the goodness of fit to a plane in each
pointsonthesky,obeyingthesameselectioncriteriabased radius. We apply a KS test similar to 3.2 to the streams
on smin and f31. We use a Kolmogorov-Smirnov(KS) test at radii from 0.4Rv to 3.5Rv. Figure 4§ (right) shows the
to compare the cumulative distribution functions (CDF) of CDFs for the different radii, and the caption quotes the
the deviation from a plane, d, in the sample of simulated corresponding KS p values. We see that the co-planarity
haloescomparedtothenullhypothesis.TheKS-testallows is highly significant for radii from 0.8R to 2.5R , and it
v v
todeterminethestatisticallikelihood(p-value)thatthetwo becomes much less significant both at r 6 0.4R and at
v
data sets are drawn form the same distribution. For the r >3.5R .
v
purposeofidentifyingthecentersofthestreams,thefiducial We note that the apparentdisappearance of the stream
valuesfortheselectionparametersarechosentobeaninflux planeintheinnerhalomaypartlybeattributedtothemethod
densitythresholdforthestreamidentificationof5timesthe of identification of streams, which becomesless reliable at
mean influx density in the shell, and then smin = 15◦ and smallradii,wherethe streamsoccupya largerangulararea
f31 = 0.1. The choice of an overdensity threshold of 5 andthevelocityfieldbecomesmuchmorecomplex(see 5.6
helps sharpening the definition of the stream centers, but andFig.18below). §
the results for thresholds of 3 and even 2 do not make a
significantdifferenceto the resultant co-planarity.Figure 4
(left)showsthetwoCDFs,revealingasignificantdifference
3.4 Pancakes
betweenthesimulateddataandtherandomnullmodel.With
a sample of 235 simulated haloes, the maximum vertical While the qualitative tendency of the streams to be
separation between the CDFs is D = 0.234,implying that co-planar has been noticed already in Dekeletal. (2009),
the null hypothesis is strongly rejected with a p value of the Hammer-Aitoff projections at and outside R , like the
v
8 10−11. ones shown for a sample of galaxies in Fig. 3, also reveal
×
Figure 5 (left) shows the same CDFs for different thin sheets of inflowing gas, typically filling the same
values of smin in the range 0 30◦ and f31 in the range plane defined by the streams, and sometimes hinting to
−
0 0.2. The value of D for each combination of values additional planes or plane segments. This is a low-entropy
−
for these parameters is also shown in Fig. 5 (right). The gas, inflowing toward the central galaxy with a typical
small variations in the KS-test results demonstrate that the influx density 10M⊙yr−1rad−2, as opposed to
significanceofthestreamco-planarityisnotsensitivetothe 100M⊙yr−1ra∼d−2inthestreams.Figure7highlightsthes∼e
exactchoiceof valuesforthe parametersused to selectthe
sheetsinthree-dimensionalimagesofgasinfluxdensityand
streamsforthefit.
gasdensityinthreedifferenthaloes.Ineachcase,theintense
streams are embedded in a well-defined sheet of gas with
influxdensityjustabovethethreshold,extendingto5R and
3.3 Spatialextentofthestreamsplane v
beyond. These are the pancakes envisioned by Zel’dovich
Inordertoaddressthespatialextentofthestreamplaneboth (Zeldovich1970),showingupforthefirsttimesoclearlyin
outsidethevirialradiusandinsidethehalo,wefirstinspect thegasdistributionofcosmologicalsimulations,astheyare
thealignmentbetweentheSPatR andtheSPatotherradii low-densityfeaturesthatare normallyoverwhelmedby the
v
rintherange0.2R to5.5R .TheSPisidentifiedusingthe denser,moremassivefilaments.
v v
sameselectioncriteriaatallradii.Figure6showsthemedian Figure 8 shows three examples of haloes in which
8 Danovichet al.
Figure7. Coldstreamsembeddedinpancakes,flowingintothreedifferentsimulatedgalaxies.Theboxsideismarkedineachcase.Notemperaturethreshold
isapplied.Top:loginfluxdensity(in M⊙yr−1rad−2).Bottom:loggasdensity(ingcm−3).Theplanarpancakesandelongatedstreamsbecomeapparent
inthisray-castingmaximum-intensityprojection,whichshowsthemaximumintensityvolumetricpixelalongthelineofsight.
Figure8. PancakesatRv.Shownaremapsofinfluxdensity(top)andlogentropyS=Tρ−2/3(bottom)inthreesimulatedgalaxieswithdominantpancakes.
Notemperaturethresholdisapplied.Thecoordinatesarerotatedsuchthatthemaximuminfluxisabouttheequatorialplane(appendix§B).Morethan90%
oftheinfluxisinthe±π/9equatorialbelt.Thepancakeandstreamsareoflowentropy,boundedbyhigh-entropyregionsindicativeoftheplanarshocksthat
resultedfromtheinflowofgasfromthevoidsintothepancakes.
Streams,pancakes andgalaxyangularmomentum 9
4 INFLUXIN3STREAMSANDPANCAKES
Wenowaddressthedistributionofinfluxamongthestreams
and in the pancakes. We explore the effective number
of dominant streams, and justify our focus on the three
dominantstreamsin the analysisof the stream planein the
previoussection.
Figure 9 shows Hammer-Aitoff maps of influx
overdensity with respect to the mean for each of three
galaxies( 2.3),withanemphasisontheinfluxdensitylevels
§
associated with the streams and the pancakes. One can see
thatthestreamsaretypicallyseparatedoutforthresholdsof
2 times the mean influx density. Higher levels of influx
∼
overdensity define the central regions of the streams. We
therefore use an overdensity threshold of 3 or 5 to define
the stream centres. The pancakes are typically confined
to influx overdensities in the range 0.5 to 2. The small
angularareacontainedwithinaninfluxoverdensityoforder
unitydemonstratesthehighlyanisotropicpatternofcoldgas
streaming(seealsoAubertetal.2004).
Once the streams are identified for a given influx
overdensitythreshold,theyarerankorderedbyinflux,from
high to low. Figure 10 (left) shows the influx in the first
N streamsrelativeto the totalinfluxin the shell atR , for
v
differentvaluesoftheinfluxoverdensitythreshold,averaged
over all 336 haloes. As described in 3.2, nearby streams
have been merged based on s =§ 15◦, and streams
min
with influx much below the influx of the first stream were
eliminated based on f = 0.1, but here the analysis was
31
not restricted to haloes of three streams. With the lowest
influx overdensity threshold, 0.5 of the mean, the influx is
effectivelyinasinglemeta-stream,orapancake,thatcarries
morethan90%ofthetotalinfluxinthatshell.Withaninflux
overdensityof 2 times the mean, forwhich the streams are
already well separated, the first stream carries on average
49%ofthetotalflux,thefirstthreestreamscarry68%,and
allthestreamscarry70%.Thethresholdoverdensityof2is
usefulforcapturingmostofthe influxin thestreamswhile
avoidingmostoftheoffstreaminfluxinthepancakes.In
∼
Figure9. Influxdensityinstreamsandpancakes.Shownisinfluxdensity 90%ofthehaloesthedominantstreamisthedenseststream,
in Hammer-Aitoff maps of three haloes at Rv. The contours refer to andin67%ofthehaloesthedominantstreamhasthehighest
iso-influx-overdensitywithrespecttothemeaninfluxdensityintheshell, inflowvelocity.Inmostcasesthedenseststreamisalsothe
at levels of 0.5 (grey), 1 (orange), 2 (purple), 3 (blue), 5 (red), and 8 one with the highestvelocity, but in 30% of the haloes the
(darkred).Thepancakesareconfinedtoinfluxoverdensities intherange
densest stream does not have the highest inflow velocity.
frombelow1toabout2.Thestreamsaredefinedbyinfluxoverdensities
Once the streams are separated, namely for thresholds of
of 2 (purple) and above. The mean values for the three examples are:
9.8,5.8,2.9M⊙yr−1rad−2.SeeFig.10andFig.11. 2 and above, the shape of the curves seem to be rather
independentof threshold,indicatingthatthe distributionof
fluxinthestreamsrelativetoeachotherisrobust,whilethe
the high influx density is largely confined to one obvious totalinfluxinstreamsisobviouslyadecreasingfunctionof
pancake and its embedded streams. In these cases the belt thethresholdlevel.
of π/9 about the best-fit plane ( B), encompassing a Figure 11 (left) shows the fraction of the shell area
± §
third of the shell area, contains more than 90% of the coveredbythefirstN streams.Foraninfluxoverdensityof
total influx at R . The entropy maps, where log entropy 2, the coveringfraction by streams is about10%. The area
v
is measured from the gas temperature and density as S = covered by the denser parts of the streams that carry more
Tρ−2/3, demonstrate that the pancakes are regions of low thanhalfthetotalinflux,definedbyaninfluxoverdensityof
entropy,hostingthedenser,coldstreams.Thepancakesare 4,isonaverage5%.Thisiscomparabletotheareacoverage
boundedfromaboveandbelowbyregionsofhigherentropy, estimatedforLyman-alphaabsorptionbycoldstreamsfrom
indicativeofplanarshocksthatresultedformthegasflowing a central source, using simulations of higher resolution
fromthevoidsintothepancakes.Thegaspancakesbetween (Fumagallietal.2011;Goerdtetal.2011).
the streams are explored in more detail in a companion Figure 11 (right) shows the fractional angular area
paper using cosmological simulations of higher resolution coveredbystreamsandpancakesasafunctionofthefraction
(Hahnetal.2011). of influx carried by these streams and pancakes, at R .
v
10 Danovichet al.
1 1
0.5
0.9
1 0.9
0.8
1.5
˙/Mtotal00..67 23 ˙Mstreams00..78 Streams only
˙M0.5 5 ˙M/
0.6
0.4
0.3 0.5
0.2
0.4
1 2 3 4 5 6 1 2 3 4 5 6
N-Number ofstreams N-Number ofstreams
Figure10. FractionalcontributionofthefirstN streamstothetotalinfluxatRv(left)andtothetotalinfluxinstreams(right).Shownaretheaveragesand
standarddeviationsoverthesampleof336simulatedhaloes.Theleftpanelcomparesdifferentthresholdsofinfluxoverdensity.Forexample,withathreshold
ataninfluxoverdensityof2,thefirst3streamscarryonaverage68%ofthetotalinflux.Intherightpanelthestreamsaredefinedbyaninfluxoverdensityof
3.Thefirststreamcarriesonaverage64%oftheinfluxinstreams,andthefirstthreestreamscarry95%.
0.14 1
0.9
0.12
n n0.8
o 2 o
cti 0.1 cti0.7
a a
Fr Fr0.6
e0.08 e
g g
a 3 a0.5
r r
ve0.06 ve pancakes
o o0.4
C C
ea0.04 ea0.3 streams
Ar 5 Ar
0.2
0.02
0.1
0 0
1 2 3 4 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
N-Number ofstreams FluxFraction
Figure11. FractionalareacoveragebystreamsandpancakesatRvaveragedoverthe336haloes.Left:areacoveredbythefirstNstreamsforfluxoverdensity
thresholds2,3,5.Withathresholdoverdensityof2,thefirst3streamshaveanaveragingcoveringfractionof10%.Right:areacoverageasafunctionofthe
correspondingfractionalinflux.Thethresholdofinfluxoverdensityisvaryingalongthecurve,from≫ 1to2forstreams,andfrom2to0.5forpancakes.
Thestreamscarryonaverageabout70%oftheinfluxandcover10%oftheangulararea.Thepancakesbringinabout20%oftheinfluxin20%ofthearea.
Figure12.OutflowingversusinflowinggasatRv.ShownareHammer-Aitoffprojectionsofthefluxdensitypersolidangleforthreehaloes,outflowing(red)
andinflowing(yellowtoblue)gas.Whiletheinflowisconfinedtonarrowstreamsandthinpancakes,theoutflowscover∼50%oftheshell.