LCDM Subhalos

1. LCDM Subhalos P.Nurmi, P.Heinämäki, E. Saar, M. Einasto, J. Holopainen, V.J. Martinez, J. Einasto Submitted to MNRAS, Subhalos in LCDM cosmological simulations: Masses and abundances

2. Dark matter cosmological simulations have had considerable success in modeling large-scale-structure in the Universe: CMB to present structures, abundance of massive galaxy clusters… More detail simulations shows that there are still a number of discrepancies on smaller scales: • CDM predicts one-to-two orders of magnitude more satellite galaxies (subhalos) orbiting their host halos.. • In simulations the density profiles of virialized galaxy scale CDM halos are too steep with respect to what is inferred from rotation curves of dwarf spiral and low surface brightness galaxies. Propably mass is more smootly distributed on smaller scales, baryonic physics casuses small halos to remain starless? (Bullock et al. 2000,Somerville 2002, Springel et al. 2001). Galaxies and suhalos represet different population (Gao et al. 2004)? If predicted subhalos exist most of the satellites are completely (or almost completely) dark The predicted mini-halos are not observed Strong gravitational lensing (multiple quasar images and giant arc systems) provides an unique way to study the dark matter content of galaxies.

3. Provide physical understandung: qualitative predictions of theoretical models • Make obsevable predictions for testing models Knebe astro-ph/0412565

4. Different N-body codes are needed • Numerical methods themselves are approximations:limitations in resolution, physics, numerical errors, bugs… • Different halo finding algorithms are needed • FOF, SKID, SO, DENMAX, BDM…. • Large enough volume, sufficient mass resolution • mp=(L/N)3W0 rc

5. N-body code • MLAPM (Multi-Level-Adaptive-Particle-mesh) 1992-1997 (Andrew Green) • First release (Alexander Knebe) • Lightcone package (Enn Saar) • Halo identification, AHF, Amiga Halo Finder (Stuart Gill) AMIGA (2005) Adaptive Mesh Investigations of Galaxy Assembly) Hydrodynamics already Parallelisation under way

6. AMIGA • open source C-code • Tree-code which recursively refines cells – subgrids being adaptively formed in regions where the density exceeds a spesified threshold number of particles). • memory efficient • fast • support for all sorts of input data • analysis tools • integrated halo finder, AHF

8. N-body Grid hierarchy The general goal of a halo finder is to identify gravitationally bound objects. Subhalos are virialized objects inside the virial radius of main halos. Assuming each of density peaks in adaptive grids is the centre of a halo. Step out in (logarithmically spaced) radial bins until the radius rvir 1) where the density reaches rsatellite(rvir) = D vir(z) r b(z), r b is background density and Dvir(z) is overdensity of the viralized objects or 2) radial density profile starts to rise. Each branch of the grid tree represents a single dark matter halo within the simulation From S. Gill thesis (2005)

9. Essential parameter free • Halos on-the fly (uses the adaptive grids of AMIGA to locate the satellites of the host halo.) • Halos, subhalos, sub-sub halos From A.Knebe talk in Helmholtz summer school 2006

10. Merger trees, tracking halos through time

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

12. Mass function Differential 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.

13. Resolution limit 10000 particles Subhalo MF seems to be universal : do not depend on the mass of the main halo. b =-0.9 (Gao et al. 2004, Ghigna et al. 2000 Helmi et al. 2002) Weak dependence suggested by Reed et al. 2005. Reliable regions 100 particles

14. Mass fraction between 0.08-0.2. • Depends slightly on the total halo mass • Might depend on the redshift

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

16. Subhalo mass fraction • Mass fraction varies 0.08-0.33 • Mass fraction larger at earlier redshifts (van de Bosch et al. opposite results with semi-analytical model) • More massive halos have a larger fraction of their mass in substructure: functional dependence:

17. The distribution for logarithm of mass fraction can be approximated by a Weibull distribution. • Distributions at different redshifts are similar but • At earlier times the mass ratio were higher in the mean and small ratio wing not so prominent  Tidal distribution of subhalos - as the main halo evolves, subhalos gradually lose their mass

18. Halo environment

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

20. Conclusions • Number of N-body particles to reliably select a halo: about 100 particles for subhalos, 10000 particles for main haloes harboring subhalos. • Functional form of the mass function agrees well with earlier studies Gao et al. 2004, Kravtsov et al. 2004 • The MF slope is same for main halos and subhalos. Slope is a function of redshift. • 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 fraction is larger at earlier epochs. • The distribution for the logarithm of mass fraction can be approximated by a Weibull distribution. There is a systematic change in the distribution parameters as a function of redshift.’ • 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. • 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, 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 haloes is uniform.

21. 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 double their speed every 18 months (Moore's law) N-body simulations have doubled their size every 16-17 Months. Recently, growth has accelerated further. The Millennium Run should have become possible in 2010 – we have done it in 2004 !

25. RESULTS (White et al.): • Satellite subhalos appear to have softer cores both than their • progenitor halos and than isolated halos of similar mass • ● The normalised halo mass function (1/Mhalo) dN(msub)/dmsub • appears to be universal for msub ≪ Mhalo • ● After correction for the differing definitions of (sub)halo edge, • this function is close to the Sheth-Tormen halo mass function • ● The concentration of a halo is anticorrelated with the amount of • substructure it contains • ● Most z=0 subhalos first became subhalos at low redshift (z < 1) • ● Subhalos with less mass loss were accreted at lower redshift • ● The density profiles for subhalos are shallower than NFW

26. Klypin et al. 1999a, Ghigna et al. 1998). A considerable amount of work has been • done to reconcile this discrepancy, with some suggesting suppressed star formation • is 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; Somerville • 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 Dark • Matter (Knebe et al. 2002; Bode, Ostriker & Turok 2001; Colin et al. 2000). • Recent results from (strong) lensing statistics suggest that the predicted excess • of substructure is in fact required to reconcile some observations with theory • (Dahle et al. 2003, Dalal & Kochanek 2002), although this conclusion has not been • universally accepted (Sand et al. 2003; Schechter & Wambsganss 2002; Evans & • Witt 2003). If, however, the lensing detection of halo substructure is correct and • the overabundant satellite population really does exist, it is imperative to understand • the orbital evolution of these objects and their deviation from the background • dark matter distribution. • While there has been intense interest, from both a theoretical and an observational • perspective, in placing limits on the central dark matter density in galaxies • and understanding the abundances of satellite galaxies, comparatively little attention • has 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.

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

28. The greatest disadvantage is its simple choice of linking length which can lead to a connection of two separate objects via so-called linking \bridges". Moreover, as structure formation is hierarchical, each halo contains substructure and thus the need for dierent linking lengths to identify \halos-within-halos". There have been many variants to this scheme which attempt to overcome some of these limitations (Suto, Cen & Ostriker 1992; Suginohara & Suto 1992; van Kampen 1995; Okamoto

29. From Gill’s thesis • bridging the gap between the picture of the • early Universe (CMB) and today. Examples of which include the prediction of • the 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 et • al. 1997). • While 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. • < Mpc). • The most high prole and contentious of these is the inner density prole of • galaxies. Within cosmological simulations the density proles of virialized CDM • halos (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 dwarf • spiral and low surface brightness galaxies (McGaugh & De Block 1998). • Second, CDM predicts one-to-two orders of magnitude more satellite galaxies • orbiting 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;