Dark matter. Anne Green University of Nottingham

Transcription

1 Dark matter Anne Green University of Nottingham 1. Observational evidence for DM and constraints on its properties Alternatives to dark matter (modified gravity) 2. The DM distribution on galactic scales (is there a small scale CDM crisis?) 3. Weakly Interacting Massive Particles: theory & detection 4. Other dark matter candidates: theory & detection

2 The DM distribution on galactic scales numerical simulations observations effects of baryons what if the DM is warm rather than cold? Recommended further reading: Galactic searches for dark matter, Strigari, Phys. Rep., arxiv: Numerical simulations of the dark Universe: state of the art and the next decade, Kuhlen, Vogelsberger & Angulo, arxiv:

3 As we ll see in the next lecture the signals expected in DM detection experiments depend on: the local DM density and speed distribution (lab based direct detection experiments) the DM density distribution: density profile of individual (sub)halos & subhalo mass function (indirect detection via annihilation products).

4 Analysis of DM detection data often assumes the standard halo model, a smooth, isotropic, isothermal sphere with / r 2 and a Maxwell- Boltzmann speed distribution: f(v) / exp 3 v = r 3 2 v c with circular speed vc=220 km s -1 and local density ρ0=0.3 GeV cm -3

5 The DM distribution on galactic scales Numerical simulations In CDM cosmologies structure forms hierarchically: small halos (typically) form first and then larger halos form via mergers and accretion. Small scales (re-)enter the horizon, and density perturbations can start growing, earliest. P (k) = k3 2 2 h 2 i Therefore if the initial power spectrum is (close to) scale-invariant small scales go non-linear and collapse first.

6 Simulating Milky Way like halos (a non-expert summary): Chose input cosmological parameters (e.g. h, m,, n s ). Calculate linear power spectrum. Carry out large volume simulation. Select Milky Way like halo ( major mergers). M M, no massive close neighbours or recent Resimulate, using lower mass particles in region that forms halo of interest ( zoom technique ). Carry out convergence tests (do properties change when you change the particle mass or gravitational softening?) and study halo-to-halo scatter. Recent high resolution dark matter only simulations (e.g. Aquarius, GHALO, Via Lactea II) can resolve scales M 10 4 M.

7 Via Lactea I, Diemand, Kuhlen & Madau Not smooth, spherical and isotropic (a la isothermal sphere). Radius (O(200 kpc)), much larger than Solar radius (8 kpc). No well-defined edge.

8 Substructure Since late 90s simulations have been able to resolve large amounts of substructure (sub-halos) within galaxy halos [Klypin et al.; Moore et al.] Aquarius: M/M dn dm ] dn / dm sub [ M O Aq-A-1 Aq-A-2 Aq-A-3 Aq-A-4 Aq-A-5 M 2 dn dm M sub 2 dn / dm sub [ M O ] M sub [ M O ] M sub [ M O ] sub-halo mass function for 5 varying resolution simulations of same halo mass function: dn dm M M =1.90 ± 0.03

9 Radial distribution of sub-halos: Fraction of local mass in (resolved) sub-halos as a function of radius loc f sub r [ kpc ] Aq-A-1 Aq-A-2 Aq-A-3 Aq-A-4 Aq-A-5 ~10% of the total mass is in resolved sub-halos < 0.1 % of the mass at the solar radius is in resolved sub-halos

10 Density profile Aquarius: z = Aq-A-1 (r) / < > Aq-A-2 Aq-A Aq-A Aq-A r [ kpc ] r Navarro, Frenk & White: A universal density profile from hierarchical clustering (r) = crit char (r/r s )[1 + (r/r s )] 2 r s r vir scale radius dln = 2 dlnr r=r s virial radius, radius within which mean density is Δ times background density virial overdensity c = r vir r s concentration (r) / r 1, as r! 0, (r) / r 3, for r r s (r) / r 2 c.f. (singular) isothermal sphere: for all r.

11 How does the density profile behave in r! 0 limit? Aquarius: logarithmic slope of density profile = dln dlnr Einasto _._._._ NFW Einasto profile: (r) = s exp log r [kpc/h] 2 [(r/rs ) 1] n.b. different halos have different best fit parameters scatter between different halos similar to differences between profiles

12 Local velocity distribution Systematic deviations from multi-variate gaussian: more low speed particles, peak of distribution lower/flatter. Stocastic high v features. As well as cold tidal streams, tidal stripping produces spatially extended debris flows (shells, sheets & plumes) that aren t completely phase mixed. [Lisanti & Spergel; Kuhlen, Lisanti and Spergel] Vogelsberger et al. red lines: simulation data, black lines: best fit multi-variate Gaussian Hansen et al.; Fairbairn & Schwetz and Kuhlen et al. have found similar results.

13 Local density: Observations Mass modelling: e.g. Widrow et al., Catena & Ullio, Weber and de Boer, Fornasa & Green model for the MW (luminous components + halo) + multiple data sets (rotation curve, velocity dispersions of halo stars, local surface mass density, total mass...). ~10% statistical errors, central values vary in range 0 =( ) GeV cm 3. Systematic errors larger e.g. flattening of halo increases density in disc. Model independent/minimal assumption methods e.g. Salucci et al. Gabari et al. give consistent values, but with significantly larger errors.

14 Local circular speed: Reid & Brunthaler proper motion of Sgr A*: v, (250 ± 10) km s 1 Bovy et al. APOGEE data (l.o.s. v of 3000 stars): v, = ( )kms 1 v c = (218 ± 6) km s 1 implies φ component of Sun s motion wrt Local Standard of Rest (LSR) larger than thought or LSR orbit non-circular. McMillan & Binney dropping flat rotation curve assumption: v c = ( ) km s 1 n.b. Standard halo has one-to-one relationship between circular speed and velocity dispersion & peak speed, but in general this isn t the case.

15 density profiles (the core-cusp problem) [see de Block for overview] as r! 0 core:! const i.e. =0 cusp: / r NFW =1 Rotation curves of low surface brightness (dark matter dominated) galaxies: [THINGS, Oh et al.] =0.29 ± 0.07 Half light radius & velocity dispersion of multiple stellar populations in MW dwarf Spheroidal galaxies: [Walker & Penarrubia] < Galaxy cluster Abell 383: strong & weak lensing data combined with stellar kinematics [Newman et al.] =

16 substructure: the missing satellites problem [see Bullock and Kravtsov for overviews] In the late 1990s: MW had ~10 known satellite galaxies ( classical dwarfs such as Draco & Fornax) semi-analytic models and simulations find MW-like galaxies contain ~1000 subhalos massive enough to host dwarf galaxies. [Kaufmann, White & Guiderdoni; Klypin et al.; Moore et al.] mass function in terms of M300 (mass within central 300 pc, can be accurately determined for both observed and simulated satellites) Via Lactea observed MW dwarf Spheroidals [Bullock]

17 Since then: ~10 new dwarfs found (by searching for overdensities in SDSS and SEGUE data) [e.g. Willman et al.] majority less luminous and more dark matter dominated than previously known dwarfs ( ultra-faint ) Segue 1 [Geha]

18 Since then: ~10 new dwarfs found (by searching for overdensities in SDSS and SEGUE data) [e.g. Willman et al.] majority less luminous and more dark matter dominated than previously known dwarfs ( ultra-faint ) taking into account limited sky coverage and detection limits MW could contain ~ of these ultra-faint dwarfs [Tollerud et al.] Luminosity of MW dsphs observed corrected for SDSS sky coverage with luminosity correction [Tollerud et al.]

19 the too big to fail problem [Boylan-Kolchin, Bullock & Kaplinghat] The most massive sub-halos in simulated galactic mass halos are inconsistent with the dynamics of the brightest Milky Way dwarf Spheroidals. i.e. there are big sub-halos that would be expected to host visible galaxies, but the visible galaxies correspond to smaller sub-halos. Rotation curves of subhalos from Aquarius simulation and 9 bright MW dsphds.

20 Effects of baryons Galaxy formation is a very complicated process (involving messy sub grid physics). Central density profile Adiabatic contraction (due to cooling and contraction of baryons) would steepen central density profile while supernovae feedback or infall of baryon clumps can make it shallower. Substructure Various physical processes (e.g. Supernovae feedback, heating from photoionization, ability of gas to cool) can suppress galaxy formation on dwarf galaxy scales.

21 Dark disc Sub-halos merging at z<1 preferentially dragged towards disc, where they re destroyed leading to the formation of a co-rotating dark disc. [Read et al., Bruch et al., Ling et al.] Detailed properties (& existence?) of dark disc are very uncertain. Purcell, Bullock and Kaplinghat argue that to be consistent with the observed properties of thick disc, MW s merger history must be quiescent compared with typical ΛCDM merger histories, hence the DD density must be relatively low. Bidin et al. measure surface density with 2-4 kpc of Galactic plane (using kinematics of thick disc stars), consistent with visible mass.

22 Eris simulation [Guedes et al. & Kuhlen et al.] DM density in disc plan enhanced by 30% (~20% due to baryonic contraction, ~10% dark disc). Features in high speed tail of f(v) less pronounced than in DM only simulations. Density profile DM only Eris DM Eris disk DM Eris stars & gas Smoothed f(v) DM only Eris disk

23 What if the dark matter is warm rather than cold? m ~ O(keV), became non-relativistic during radiation domination. Concrete candidates: sterile neutrino, gravitino (more in lec. 4) Differences from CDM: i) free-streaming erases perturbations on scales < O(Mpc) therefore power spectrum, and hence halo mass function, suppressed on galactic and smaller scales Power spectrum for sterile neutrinos with mass between 0.3 kev and 140 kev SDSS 3d power spectrum of galaxies Lymanα forest [Abazajian]

24 ii) maximum value of fine grained phase space density therefore halo density profiles have cores Maccio et al. To produce a ~1 kpc core in dwarf galaxies thermally produced WDM must have m < 0.1 kev, but then free-streaming would erase perturbations on these scales (i.e. no dwarf galaxies would form!). [Maccio et al.] (In my opinion) the extent to which CDM has small scale problems isn t 100% clear and neither is whether or not WDM (or other nonstandard DM) can resolve these problems.

25 Summary Simulated DM halos have cuspy density profiles and contain large amounts of substructure. Speed distribution deviates systematically from Maxwell-Boltzmann dist (of standard halo model ). Non-negligible observational uncertainties in local density and circular speed (related to velocity dispersion). Some tension between observations and simulations. Not clear whether this is due to baryonic or DM physics. Next lecture: WIMP theory and detection

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27 Caveat: scales resolved by simulations are many orders of magnitude larger than those probed by direct detection experiments zoom x10 zoom x10 8 ~300 kpc ~30 kpc ~0.3 mpc Resolution of best Milky Way simulations is many orders of magnitude larger than the mass of the first WIMP microhalos to form microhalo simulation Diemand, Moore & Stadel

28 fine structure in ultra-local DM velocity distribution? Vogelsberger & White: Follow the fine-grained phase-space distribution, in Aquarius simulations of Milky Way like halos. From evolution of density deduce ultra-local DM distribution consists of a huge number of streams (but this assumes ultra-local density= local density). At solar radius <1% of particles are in streams with ρ > 0.01ρ0. Schneider, Krauss & Moore: Simulate evolution of microhalos. Estimate tidal disruption and heating from encounters with stars, produces streams in solar neighbourhood. number of streams Aq-A-5 (harm.) Aq-A-4 (harm.) Aq-A-3 (harm.) Aq-A-5 (median) Aq-A-4 (median) Aq-A-3 (median) r/r 200 number of streams as a function of radius calculated using harmonic mean/median stream density not-so fine structure: Purcell, Zentner & Wang DM component of Sagittarius leading stream may pass through the solar neighbourhood (as originally suggested by Freese, Gondolo & Newberg).

29 How small are the smallest (WIMP) microhalos? [Hofmann, Schwarz & Stocker; Berezinsky, Dokuchaev & Eroshenko; Green, Hofmann & Schwarz; Loeb & Zaldarriaga; Bertschinger; Profumo, Sigurdson & Kamionkowski; Bringmann & Hofmann; Martinez et al.; Bringmann] After freeze-out (chemical decoupling) at T~O(1-10 GeV) WIMPS carry on interacting kinetically with radiation: +, X + X + X ) + X X At T~O(1-10 MeV) WIMPS kinetically decouple and free-stream, erasing perturbations on co-moving scales < O(1 pc). [Hofman, Schwarz & Stocker] For a typical 100 GeV WIMP, first smallest halos to form have [Green, Hofmann & Schwarz] R 0.01 pc M 10 6 M but in MSSM minimum mass can vary by many orders of magnitude. (most recent calculations M <M<10 3 M [Bringmann] 10 9 M <M<10 6 M [Martinez et al.] )

30 Simulations of microhalos formation Diemand, Moore and Stadel Input power spectrum with cut-off at k~1pc. Re-simulate a small typical region starting at z=350 up until z=26 (when the high resolution region begins to merge with surrounding low resolution regions). Smallest microhalos have, as expected, M 10 6 M and profiles similar to larger halos shortly after formation (NFW with low concentration). Mass function: Subsequent dynamical evolution? dn dlnm M 1 (same slope as on larger scales) Initial box size (3 kpc) 3 both zooms are x100. In addition to tidal stripping etc. microhalos on disc crossing orbits with be heated by encounters with stars and lose mass. [Diemand, Moore & Stadel; Zhao, Taylor, Silk & Hooper x2; Moore, Diemand, Stadel & Quinn; Berezinsky, Dokuchaev & Eroshenko; Angus & Zhao; Green & Goodwin; Goerdt et al; Schneider, Moore & Krauss] Earth mass microhalos in the solar neighbourhood will typically lose most of their mass but may retain a dense central core.