The Current Status of Too Big To Fail problem! based on Warm Dark Matter cosmology 172th Astronomical Seminar Dec.3 2013 Chiba Lab.M2 Yusuke Komuro
Key Word s Too Big To Fail TBTF Cold Dark Matter CDM Warm Dark Matter WDM Mixed Dark Matter MDM MDM=CDM+WDM
Abstract Although the nature of dark matter is still unknown, the CDM model describe large scale structure successfully. However, the result of N-body simulations based on the CDM model show shortcomings on galactic and sub-galactic scales, for example Missing Satellite Problem e.g. A.R.Klypin et al.1999, Cusp-Core Problem e.g. R.A.Swaters et al.2001 and so on. In the recent year, M.Boylan-Kolchin et al.2011 suggest a new problem called as Too Big To Fail Problem. If we change the model of the dark matter, what kind of influence is reflected on this problem? In today s talk, I want to talk mainly on items of the next page.
Outline of today s talk! Introduction The CDM theory Too Big To Fail problem! The properties of WDM and WDM halo Free-Streaming damping The differences between CDM halo and WDM halo! The results of simulation based on MDM The possibility of MDM from Satellites distribution and TBTF! Summary Related paper: M.Boylan-Kolchin et al.2012,mnras,422,1203-1218 D.Anderhalden et al.2013,arxiv:1212.2967v2 M.R.Lovell et al.2012,mnras,420,2318-2324
Introduction
The current picture of our universe Best fit value http://map.gsfc.nasa.gov/ http://www-supernova.lbl.gov/! Our universe consist of Dark Energy 71.4%, Dark Matter 24%, Baryons 4.6%.! Our universe is flat. Cosmological constant. What is the nature of Dark Matter?
Cold Dark Matter The basis of the CDM theory was established by White & Rees 1978, they assumed the following items about the CDM 1) The velocity dispersion of the CDM particle is dynamically cold. 2) The influence except the gravitational interaction is small so as to be able to ignore it. =>The CDM particle is Collisionless. The scenario of structure formation based on the CDM model is hierarchical Press & Schechter 1974. This means that small scale structure is formed earlier than large scale structure. time Mass of halo
Jing & Suto 2000,2002 The CDM theory Large scale Small scale Dark Matter halo formed by collapse of density fluctuation. The self gravitational equilibrium system in the universe. The prediction about Dark Matter halo with the CDM theory: The shape of density profile is cuspy in the central region Navarro,Frenk&White 1997. Dark Matter halo has triaxiality Jin&Suto 2000. Dark Matter halo contains many Dark Matter subhalos Moore et al.1999.
The comparison between! the CDM model and the observation Tegmark et al.2004 Linear region Large Scales >1[Mpc] >success! Solid red line is predicted with CDM P( k) = δ all k,t today ( ) 2 = 2π 2 h 3 k 3 2 δ all ( k,t today )P ini ( k) Observed values Below galactic scale Small Scales <1[Mpc] > Non-linear region
The structure on small scale <1[Mpc] Grebel et al.1998 The Local Group is a galaxy group to which the Milky Way and M31 belongs. The Local Group is an excellent laboratory as a test of the Dark Matter model on small scales. Many satellites are around the Milky Way and M31. * The currently known members are about sixty galaxies in the Local Group. The bird s-eye view of the Local Group
Aquarius Project V.Springel et al.2008 subhalo Aquarius Project is N-body simulation with the CDM. This project is the simulation with high-resolution to investigate the merging history of Milky Way sized halo. They have simulated six different haloes Aq-A Aq-F, each at several different numerical resolution. Milky Way sized halo This panel shows the result of Aq-B halo. As for Aq-B halo, Virial Mass of halo Mvir and Virial Radius Rvir is consistent with the observed values of Milky Way halo.
The CDM theory small scale crisis! Angular Momentum Problem e.g. Navarro & Steinmetz 2000 The size of simulated disk galaxy is smaller than the real size of disk galaxy at the same stellar mass.! Cusp-Core Problem e.g. de Block et al.2001 The central densities of CDM haloes in simulations show a cusp, whereas the density profiles of Low Surface brightness galaxies show core-like structure.! Missing Satellite Problem e.g. Klypin et al.1999 The amount of Dark Matter subhalos in Milky Way sized haloes is overpredicted by roughly one order magnitude.
New problem?
Too Big To Fail problem What is TBTF problem?! When we compare the theoretical value of V r with the observed value of V 1/2, V 1/2 is smaller than V r. This means that subhalos simulated with the CDM model more concentrate than the real dsph. dsph r 1/2 dsph=dwarf spheroidal galaxy The circular velocity at half-light radius r 1/2 is calculated by the following way: 1) The density profile of dsph is modeled with spherical symmetric NFW profile. 2) We suppose that a test particle perform circular motion at r 1/2. Observed value ρ ( r) = ρ s r s 3 ( ) 2 r r s + r V 1/2 V circ r 1/2 ( ) = GM ( < r 1/2 ) r 1/2 M 1/2 = 3G 1 2 σ los r 1/2
Too Big To Fail problem The velocity profile of the spherical symmetric NFW subhalo is shown in the following equation V 2 2 c ( r) = V vir vir g( c vir ) g( x) x g( x) = ln( 1+ x) x 1+ x V r becomes maximum velocity V max at r=r max =2.16r s 2 V max 2 c = 0.216V vir vir g( c vir ) V max is sensitive to concentration parameter c vir. Therefore, if subhalo s Virial Mass is given, V max is a good parameter to express the degree of the central concentration of subhalo.
Too Big To Fail problem M.Boylan-Kolchin et al.2012 The square symbols are observed V 1/2 value of dsphs with error bars. Each size of symbol is proportional to logl V Walker et al.2009. The various color rotation curves correspond to NFW subhaloes. The shading region indicates the 1 scatter in r max at fixed V max. V circ ( ) ( r) = GM < r r The Milky Way s 9 bright dsphs L V >10 5 L sun are consistent with NFW subhaloes of V max =12~24[km/s].
Too Big To Fail problem M.Boylan-Kolchin et al.2012 V circ ( ) ( r) = GM < r r Aq-B halo contain at least 10 subhalos with V max > 25[km/s] Left-hand panel Circular velocity profiles at redshift zero for subhalos of the Aq-B halo M vir =9.5 10 11 M sun that have V infall > 30 [km/s] and V max z=0 > 10 [km/s]. Right-hand panel Circular velocity profiles for subhalos from left-hand panel with the 10 highest values of V max z=0.
Too Big To Fail problem The physical process which moderate the concentration in subhalos is necessary. Candidate to solve TBTF problem! The baryonic process e.g. SN feedback S.Garrison-Kimmel et al.2013 shows that SN feedback alone can t solve TBTF problem.! The dynamical evolution of subhalo e.g. mass-loss by tidal-stripping. tidal-heating >My study theme.! The Dark Matter model except the CDM model e.g. WDM
The property of WDM and WDM halo
Free-Streaming damping When we think about the structure formation, we take the matter content of the universe to be an ideal fluid. This approximation breaks down for wavelengths smaller than a particular critical value. The energy of matter is drained by certain dissipative process at smaller wavelengths of density fluctuations. In baryons, it arises due to coupling between radiation and matter. In collisionless Dark Matter which is dynamically hot or warm, dissipation occurs through a process called as Free-Streaming. =>Free-Streaming damping Free-Streaming damping is important physical process that WDM wipe out the small density fluctuations.
Free-Streaming damping λ FS ( t) = a(t) 0 ( ) ( ) da' υ t ' a' 2 H t ' ( υ << c) FS t is Free-Streaming scale of dark matter particle at t or redshift z. We assume that the particle decoupled from other energy content in the early universe. L hor ( t) = L hor t is a particle horizon scale. ( ) a t 0 c a' 2 H ( t ') da' Relativistic particle can run to a particle horizon scale at t. However, non-relativistic particle can t run. Particle horizon scale It is important when a particle becomes nonrelativistic to affect the structure formation.
Free-Streaming damping The zero-th component of geodesic equation on Robertson-Walker metric dp 0 dλ + Γ 0 µνp µ P ν = 0 P a 1 The momentum of free-streaming particle is decaying as the universe expands. If Free-Streaming particle becomes non-relativistic by the epoch of equality, the particle can affect the structure formation. # λ FS 0.11 Ω WDMh 2 & % ( $ 0.15 ' 1 3 # mwdm $ % kev & ' ( 4 3 [ Mpc] M FS = 4 3 π! λ $ fs # & 2 % Free-Streaming damping wipe out the density fluctuation on scales below FS. 3 ρ m ( z) The formation epoch of WDM halo is delayed and the size becomes small.
The property of WDM halo CDM WDM
The property of WDM halo M.R.Lovell et al.2012 The left panel shows systematic differences in the formation epoch of the 12 most massive WDM and CDM progenitors which survive to z=0 as distinct subhalos in their sample. In this paper, they define the formation time as the first time at which the progenitor mass exceeds the mass within 1[kpc] at infall. past The WDM subhalos tend to form later than the CDM subhalos.
The property of WDM halo M.R.Lovell et al.2012 CDM WDM The left panel shows the circular velocity profile at z=0 for the 12 subhalos which had the most massive progenitor at infall. As can be inferred from the left panel, the WDM subhalos have similar central masses to the observed satellite galaxies, while the CDM subhalos have central masses lager than the Milky Way satellite galaxies. The red solid line represent subhalos with the most massive progenitors. The concentration of WDM subhalo moderate.
The results of simulation based on MDM
Simulation based on MDM MDM!!!! f W = Ω WDM Ω WDM + Ω CDM = Ω WDM Ω DM WDM fraction All simulations have been performed with the parallel treecode PKDGRAV J.stadel 2001. The cosmological parameters taken from WMAP7 E.Komatsu et al.2011 8 =0.8,h=0.7, DM =0.227, b =0.046, =0.727,n s =0.961 Initial conditions are generated with the GRAFIC package E.Bertschnger 2001.
The possibility of MDM 1 D.Anderhalden et al.2013 N(>Vmax) The left panel shows the cumulative velocity function for all subhalos with a value of V max > 9[km/s] as well as a sample of observed Milky Way satellites black open circles. The difference get larger since V max is sensitive to the concentration of the subhalo. Depending on a combination of fraction f W and mass, the simulated result may reproduce the observed result. V max [km/s] Massive
The possibility of MDM 2 Circular velocity profiles at redshift z=0 for the 12 subhalos which had the most massive progenitor at infall.
Summary of today s talk Due to the reduced power at small scales, structure formation is delayed, leading to slightly smaller halo and subhalo concentrations. Pure 2kev WDM model does not suffer from the Too Big To Fail problem. In the MDM model, both fraction and mass of the WDM may be constrained from satellite distribution and velocity profile. The overall mass profiles of Dark Matter dominated objects like dsph are not mainly changed by baryons. Another possibility is that the satellite population of the Milky Way is not typical of the average to which the model predictions apply. Liu et al.2011, Guo et al. 2011
End.