LCDM SubhalosLCDM Subhalos

P.Nurmi, P.Heinämäki, E. Saar, M. P.Nurmi, P.Heinämäki, E. Saar, M. Einasto, J. Holopainen, V.J. Einasto, J. Holopainen, V.J.

Martinez, J. EinastoMartinez, J. Einasto

Submitted to MNRAS, Submitted to MNRAS, Subhalos in LCDM Subhalos in LCDM cosmological simulations: Masses and cosmological simulations: Masses and

abundancesabundances

Dark matter cosmological simulations have had considerable Dark matter cosmological simulations have had considerable success in modeling large-scale-structure in the Universe: success in modeling large-scale-structure in the Universe: CMB CMB to present structures, abundance of massive galaxy clusters…to present structures, abundance of massive galaxy clusters…

More detail simulations shows that there are still More detail simulations shows that there are still a number of a number of

discrepancies on smaller scales:discrepancies on smaller scales: CDM predicts one-to-two orders of magnitude more satellite CDM predicts one-to-two orders of magnitude more satellite

galaxies (subhalos) orbiting their host halos..galaxies (subhalos) orbiting their host halos.. In simulations the density profiles of virialized galaxy scale CDM In simulations the density profiles of virialized galaxy scale CDM

halos are too steep with respect to what is inferred from rotation halos are too steep with respect to what is inferred from rotation curves of dwarf spiral and low surface brightness galaxies.curves of dwarf spiral and low surface brightness galaxies.

Propably mass is more smootly distributed on smaller scales, Propably mass is more smootly distributed on smaller scales,

baryonic physics casuses small halos to remain starless? (Bullock baryonic physics casuses small halos to remain starless? (Bullock et al. 2000,Somerville 2002, Springel et al. 2001). Galaxies and et al. 2000,Somerville 2002, Springel et al. 2001). Galaxies and suhalos represet different population (Gao et al. 2004)? suhalos represet different population (Gao et al. 2004)?

If predicted subhalos exist If predicted subhalos exist most of the satellites are completely most of the satellites are completely

(or almost completely) dark(or almost completely) dark

The predicted mini-halos are not observed Strong gravitational The predicted mini-halos are not observed Strong gravitational lensing (multiple quasar images and giant arc systems) provides lensing (multiple quasar images and giant arc systems) provides an unique way to study the dark matter content of galaxies. an unique way to study the dark matter content of galaxies.

Provide physical understandung: Provide physical understandung: qualitative predictions of theoretical qualitative predictions of theoretical modelsmodels

Make obsevable predictions for testing Make obsevable predictions for testing modelsmodels

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Different N-body codes are neededDifferent N-body codes are needed Numerical methods themselves are approximations:limitations in Numerical methods themselves are approximations:limitations in

resolution, physics, numerical errors, bugs… resolution, physics, numerical errors, bugs…

Different halo finding algorithms are Different halo finding algorithms are neededneeded

FOF, SKID, SO, DENMAX, BDM….FOF, SKID, SO, DENMAX, BDM….

Large enough volume, sufficient Large enough volume, sufficient mass resolutionmass resolution

mmpp=(L/N)=(L/N)3300cc

N-body codeN-body code MLAPM (MLAPM (Multi-Level-Adaptive-Particle-mesh) 1992-Multi-Level-Adaptive-Particle-mesh) 1992-

1997 (Andrew Green)1997 (Andrew Green) First release (Alexander Knebe)First release (Alexander Knebe) Lightcone package (Enn Saar)Lightcone package (Enn Saar) Halo identification, AHF, Amiga Halo Finder (Stuart Halo identification, AHF, Amiga Halo Finder (Stuart

Gill)Gill)

AMIGA (2005) AMIGA (2005) Adaptive Mesh Investigations of Adaptive Mesh Investigations of Galaxy Assembly)Galaxy Assembly)

Hydrodynamics alreadyHydrodynamics alreadyParallelisation under way Parallelisation under way

AMIGAAMIGA

open source C-codeopen source C-code Tree-code which recursively refines cells – Tree-code which recursively refines cells –

subgrids being adaptively formed in regions subgrids being adaptively formed in regions where the density exceeds a spesified where the density exceeds a spesified threshold number of particles).threshold number of particles).

memory efficientmemory efficient fastfast support for all sorts of input datasupport for all sorts of input data analysis toolsanalysis tools

• • integrated halo finder, AHFintegrated halo finder, AHF

The general goal of a halo finder is The general goal of a halo finder is to identify gravitationally bound to identify gravitationally bound objects.objects.

Subhalos are virialized objects Subhalos are virialized objects inside the virial radius of main inside the virial radius of main halos.halos.

Assuming each of density peaks in Assuming each of density peaks in adaptive grids is the centre of a adaptive grids is the centre of a halo. Step out in (logarithmically halo. Step out in (logarithmically spaced) radial bins until the radius spaced) radial bins until the radius rrvir vir 1) where 1) where the density reaches the density reaches satellite(rsatellite(rvirvir) = ) = virvir(z) (z) bb(z), (z), bb is is background density and background density and virvir(z) is (z) is overdensity of the viralized objects overdensity of the viralized objects or 2) radial density profile starts to or 2) radial density profile starts to rise.rise.

Each branch of the grid tree represents a Each branch of the grid tree represents a single dark matter halo within the single dark matter halo within the simulationsimulation

From S. Gill thesis (2005)

N-body Grid hierarchy

Essential parameter freeEssential parameter free Halos on-the fly (Halos on-the fly (uses the adaptive grids of AMIGA uses the adaptive grids of AMIGA

to locate the satellites of the host halo.)to locate the satellites of the host halo.)

Halos, subhalos, sub-sub halos Halos, subhalos, sub-sub halos

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Merger trees, Merger trees, tracking halos tracking halos through timethrough time

to reach the mass resolution we have in our B10 simulation for a single 80 Mpc/h cube would require 20483 particles,

Mass functionMass functionDifferential mass functions of all haloes in three simulations at two different redshifts z= 0 and z = 5 (see the legend in the Figure). The theoretical Press-Schechter (PS) and Sheth & Tormen (ST) predictions are also shown.

Resolution limit Resolution limit 10000 particles10000 particles

Subhalo MF seems to be universal : Subhalo MF seems to be universal : do not depend on the mass of the do not depend on the mass of the main halo. main halo. -0.9 (Gao et al. -0.9 (Gao et al. 2004, Ghigna et al. 2000 Helmi et 2004, Ghigna et al. 2000 Helmi et al. 2002)al. 2002)

Weak dependence suggested by Weak dependence suggested by Reed et al. 2005.Reed et al. 2005.

Reliable regions 100 particlesReliable regions 100 particles

Mass fraction Mass fraction between 0.08-0.2.between 0.08-0.2.

Depends slightly Depends slightly on the total halo on the total halo massmass

Might depend on Might depend on the redshift the redshift

Evolution of the subhalo Evolution of the subhalo mass functionmass function

Hints that slope of Hints that slope of the subhalo MF is the subhalo MF is a function of a function of redshift. (Subhalo redshift. (Subhalo MF might be MF might be steeper)steeper)

Subhalo mass fractionSubhalo mass fraction Mass fraction varies Mass fraction varies

0.08-0.330.08-0.33 Mass fraction larger Mass fraction larger

at earlier redshifts at earlier redshifts ((van de Bosch et al. van de Bosch et al. opposite results with semi-opposite results with semi-analytical model) analytical model)

More massive halos More massive halos have a larger have a larger fraction of their fraction of their mass in mass in substructure: substructure: functional functional dependence: dependence:

The distribution for The distribution for logarithm of mass logarithm of mass fraction can be fraction can be approximated by a approximated by a Weibull distribution. Weibull distribution.

Distributions at different Distributions at different redshifts are similar but redshifts are similar but

At earlier times the mass At earlier times the mass ratio were higher in the ratio were higher in the mean and small ratio mean and small ratio wing not so prominent wing not so prominent

Tidal distribution of Tidal distribution of subhalos - as the main subhalos - as the main halo evolves, subhalos halo evolves, subhalos gradually lose their gradually lose their mass mass

Halo environment Halo environment

Total mass fraction + subhalo MF + Total mass fraction + subhalo MF + spatial distribution can be used to spatial distribution can be used to find the radial mass density find the radial mass density distributions of subhalos, and the distributions of subhalos, and the surface mass densities necessary for surface mass densities necessary for gravitational lensing studies.gravitational lensing studies.

ConclusionsConclusions Number of N-body particles to reliably select a halo: about 100 particles for Number of N-body particles to reliably select a halo: about 100 particles for

subhalos, 10000 particles for main haloes harboring subhalos. subhalos, 10000 particles for main haloes harboring subhalos.

Functional form of the mass function agrees well with earlier studies Gao et al. Functional form of the mass function agrees well with earlier studies Gao et al. 2004, Kravtsov et al. 2004 2004, Kravtsov et al. 2004

The MF slope is same for main halos and subhalos. Slope is a function of The MF slope is same for main halos and subhalos. Slope is a function of redshift.redshift.

Subhalo mass fraction depends on the main halo mass – more massive halos have Subhalo mass fraction depends on the main halo mass – more massive halos have larger mass fraction. Within the same main halo mass range, the subhalo mass larger mass fraction. Within the same main halo mass range, the subhalo mass fraction is larger at earlier epochs.fraction is larger at earlier epochs.

The distribution for the logarithm of mass fraction can be approximated by a The distribution for the logarithm of mass fraction can be approximated by a Weibull distribution. There is a systematic change in the distribution parameters Weibull distribution. There is a systematic change in the distribution parameters as a function of redshift.’as a function of redshift.’

The dependence of the number of subhaloes on the main halo mass can be The dependence of the number of subhaloes on the main halo mass can be described by a simple relation <Nh >∝ M1.1. MH, independent of the resolution.described by a simple relation <Nh >∝ M1.1. MH, independent of the resolution.

The number density of haloes surrounding main haloes drops quickly as we move The number density of haloes surrounding main haloes drops quickly as we move beyond the virial radius of the halo. However, the slope stays the same after that, beyond the virial radius of the halo. However, the slope stays the same after that, up to distance about 3 *rvir. The sphere of influence of a halo reaches out to the up to distance about 3 *rvir. The sphere of influence of a halo reaches out to the distance of 16 times of its virial radius. Beyond this limit the number density of distance of 16 times of its virial radius. Beyond this limit the number density of haloes is uniform.haloes is uniform.

From V. Springel’s talk:From V. Springel’s talk:

Will require an extremely efficient code on the largest available machines, and result in a cosmological simulation with extremely large dynamic range.

Computers doubleComputers doubletheir speed everytheir speed every18 months18 months(Moore's law)(Moore's law)

N-bodyN-bodysimulations havesimulations havedoubled their sizedoubled their sizeevery 16-17every 16-17Months.Months.

Recently, growthRecently, growthhas acceleratedhas acceleratedfurther. further. The Millennium RunThe Millennium Runshould have becomeshould have becomepossible in 2010 –possible in 2010 –we have done it inwe have done it in2004 !2004 !

1.1. RESULTS (White et al.):RESULTS (White et al.): Satellite subhalos appear to have softer cores both than theirSatellite subhalos appear to have softer cores both than their progenitor halos and than isolated halos of similar massprogenitor halos and than isolated halos of similar mass ● ● The normalised halo mass function (1/Mhalo) The normalised halo mass function (1/Mhalo)

dN(msub)/dmsubdN(msub)/dmsub appears to be universal for msub Mhalo≪appears to be universal for msub Mhalo≪ ● ● After correction for the differing definitions of (sub)halo edge,After correction for the differing definitions of (sub)halo edge, this function is close to the Sheth-Tormen halo mass functionthis function is close to the Sheth-Tormen halo mass function ● ● The concentration of a halo is anticorrelated with the amount The concentration of a halo is anticorrelated with the amount

ofof substructure it containssubstructure it contains ● ● Most z=0 subhalos first became subhalos at Most z=0 subhalos first became subhalos at low low redshift (z < redshift (z <

1)1) ● ● Subhalos with less mass loss were accreted at lower redshiftSubhalos with less mass loss were accreted at lower redshift ● ● The density profiles for subhalos are shallower than NFWThe density profiles for subhalos are shallower than NFW

Klypin et al. 1999a, Ghigna et al. 1998). A considerable amount of work has beenKlypin et al. 1999a, Ghigna et al. 1998). A considerable amount of work has been done to reconcile this discrepancy, with some suggesting suppressed star formationdone to reconcile this discrepancy, with some suggesting suppressed star formation is due to the removal of gas from the small protogalaxies by the ionising radiationis due to the removal of gas from the small protogalaxies by the ionising radiation from the rst stars and quasars (Bullock et al. 2000; Tully et al. 2002; Somervillefrom the rst stars and quasars (Bullock et al. 2000; Tully et al. 2002; Somerville 2002) thus leaving most of the satellites completely (or almost completely) dark.2002) thus leaving most of the satellites completely (or almost completely) dark. Others suggest that the form of dark matter is incorrect appealing to Warm DarkOthers suggest that the form of dark matter is incorrect appealing to Warm Dark Matter (Knebe et al. 2002; Bode, Ostriker & Turok 2001; Colin et al. 2000).Matter (Knebe et al. 2002; Bode, Ostriker & Turok 2001; Colin et al. 2000). Recent results from (strong) lensing statistics suggest that the predicted excessRecent results from (strong) lensing statistics suggest that the predicted excess of substructure is in fact required to reconcile some observations with theoryof substructure is in fact required to reconcile some observations with theory (Dahle et al. 2003, Dalal & Kochanek 2002), although this conclusion has not been(Dahle et al. 2003, Dalal & Kochanek 2002), although this conclusion has not been universally accepted (Sand et al. 2003; Schechter & Wambsganss 2002; Evans &universally accepted (Sand et al. 2003; Schechter & Wambsganss 2002; Evans & Witt 2003). If, however, the lensing detection of halo substructure is correct andWitt 2003). If, however, the lensing detection of halo substructure is correct and the overabundant satellite population really does exist, it is imperative to the overabundant satellite population really does exist, it is imperative to

understandunderstand the orbital evolution of these objects and their deviation from the backgroundthe orbital evolution of these objects and their deviation from the background dark matter distribution.dark matter distribution. While there has been intense interest, from both a theoretical and an observationalWhile there has been intense interest, from both a theoretical and an observational perspective, in placing limits on the central dark matter density in galaxiesperspective, in placing limits on the central dark matter density in galaxies and understanding the abundances of satellite galaxies, comparatively little and understanding the abundances of satellite galaxies, comparatively little

attentionattention has been paid to the study of the evolution of the spatial and kinematicalhas been paid to the study of the evolution of the spatial and kinematical properties of these satellite galaxy populations. This thesis aims to ll that void.properties of these satellite galaxy populations. This thesis aims to ll that void.

Simulations predict Simulations predict

Theory and observation agree well on Theory and observation agree well on

LIDDLE:LIDDLE: In a galaxy cluster, there are perhaps thousands of knots of darkIn a galaxy cluster, there are perhaps thousands of knots of dark matter making up the galaxies, which survive assimilation into thematter making up the galaxies, which survive assimilation into the galaxy cluster..galaxy cluster.. However, in the cold dark matter scenario the same predictionHowever, in the cold dark matter scenario the same prediction should be true of galaxies; they should contain thousands of dwarfshould be true of galaxies; they should contain thousands of dwarf galaxies.galaxies. The Milky Way actually has around ten. Even if the baryons wereThe Milky Way actually has around ten. Even if the baryons were stripped from these, the dark halos should remain and wouldstripped from these, the dark halos should remain and would disrupt the disks of spiral galaxies.disrupt the disks of spiral galaxies. This has become known as the halo substructure problem, andThis has become known as the halo substructure problem, and has only been recognised recently thanks to high-resolutionhas only been recognised recently thanks to high-resolution simulations, especially by Moore and collaborators. However itsimulations, especially by Moore and collaborators. However it remains controversial (and arguably is becoming less compelling).remains controversial (and arguably is becoming less compelling). Halo structure problemsHalo structure problems In fact there are now three worrying ways in which the cold darkIn fact there are now three worrying ways in which the cold dark matter paradigm appears to have difficulty matching observations.matter paradigm appears to have difficulty matching observations. 1) Halo substructure: the predicted mini-halos are not observed.1) Halo substructure: the predicted mini-halos are not observed. 2) Dwarf galaxy cores: theory predicts that the density diverges2) Dwarf galaxy cores: theory predicts that the density diverges towards the centre of halos, whereas in well-observed dwarftowards the centre of halos, whereas in well-observed dwarf galaxies a uniform-density core is favoured.galaxies a uniform-density core is favoured. 3) Bulge constitution: enough microlensing events have been seen3) Bulge constitution: enough microlensing events have been seen towards the galaxy bulge to suggest that they explain towards the galaxy bulge to suggest that they explain all all thethe dark matter in the central regions of our galaxy, leaving no roomdark matter in the central regions of our galaxy, leaving no room for particle dark matter.for particle dark matter. Perhaps the dark matter is not cold. How about annihilating,Perhaps the dark matter is not cold. How about annihilating, self-interacting, condensated or warm? All have been suggested.self-interacting, condensated or warm? All have been suggested. Are existing treatments ofAre existing treatments of inflation oversimplistic?inflation oversimplistic?

The greatest disadvantage is its simple choice of The greatest disadvantage is its simple choice of linking length which can leadlinking length which can lead

to a connection of two separate objects via so-to a connection of two separate objects via so-called linking \bridges". Moreover,called linking \bridges". Moreover,

as structure formation is hierarchical, each halo as structure formation is hierarchical, each halo contains substructure and thus thecontains substructure and thus the

need for dierent linking lengths to identify \halos-need for dierent linking lengths to identify \halos-within-halos". There have beenwithin-halos". There have been

many variants to this scheme which attempt to many variants to this scheme which attempt to overcome some of these limitationsovercome some of these limitations

(Suto, Cen & Ostriker 1992; Suginohara & Suto (Suto, Cen & Ostriker 1992; Suginohara & Suto 1992; van Kampen 1995; Okamoto1992; van Kampen 1995; Okamoto

From Gill’s thesisFrom Gill’s thesis bridging the gap between the picture of thebridging the gap between the picture of the early Universe (CMB) and today. Examples of which include the prediction ofearly Universe (CMB) and today. Examples of which include the prediction of the abundance of massive galaxy clusters (e.g. Eke, Cole & Frenk 1996), and thethe abundance of massive galaxy clusters (e.g. Eke, Cole & Frenk 1996), and the magnitude of large-scale ows of galaxies (e.g. Strauss & Willick 1995; Zaroubi etmagnitude of large-scale ows of galaxies (e.g. Strauss & Willick 1995; Zaroubi et al. 1997).al. 1997).

While we possess some condence in the basic model of structure formation onWhile we possess some condence in the basic model of structure formation on the largest scale, there still remain a number of discrepancies on smaller scales (i.e.the largest scale, there still remain a number of discrepancies on smaller scales (i.e. < Mpc).< Mpc). The most high prole and contentious of these is the inner density prole ofThe most high prole and contentious of these is the inner density prole of galaxies. Within cosmological simulations the density proles of virialized CDMgalaxies. Within cosmological simulations the density proles of virialized CDM halos (Navarro et al. 1996, 1997, 2004; Power et al. 2002) (which are equated withhalos (Navarro et al. 1996, 1997, 2004; Power et al. 2002) (which are equated with galaxies) are too steep with respect to what is inferred from rotation curves of dwarfgalaxies) are too steep with respect to what is inferred from rotation curves of dwarf spiral and low surface brightness galaxies (McGaugh & De Block 1998).spiral and low surface brightness galaxies (McGaugh & De Block 1998). Second, CDM predicts one-to-two orders of magnitude more satellite galaxiesSecond, CDM predicts one-to-two orders of magnitude more satellite galaxies orbiting their host halos. For example, we would expect signicantly more dwarforbiting their host halos. For example, we would expect signicantly more dwarf galaxies than are observed in systems such as the Local Group (Moore et al. 1999;galaxies than are observed in systems such as the Local Group (Moore et al. 1999;