Chap.4 Galactic Dark Matter

Transcription

1 Chap.4 Galactic Dark Matter Total mass of a dark halo in a galactic scale Shape of a dark halo Density profile of a dark halo Dark matter substructure 1

2 V circ = If ρ(r) is spherically symmetric V circ (r) = (GM(<r)/r) 1/2 where M(<r) = r 4πρr 2 dr 2

3 Galaxy-sized dark halo from N-body simulations Moore Virial radius ~ 200 kpc 3

4 4.1 Total mass U,V,W velocities of stars near the Sun Escape velocity near the Sun: V esc =500~550km/s Limits on a gravitational potential Φ at R=R sun 4

5 Satellites GCs Sakamoto, Chiba, Beers 2003, A&A, 397, 899 More distant halo tracers HB stars (211 w. pm / 413) Globular clusters (41/137) Satellite galaxies (5/11) confined in a model potential Φ( r) = GM a 2 2 r + a + a log r HBs GCs model 1: a=195kpc, V LSR =220km/s model 2: a= 20kpc, V LSR =211km/s 5

6 Rest-frame velocity: V RF V esc = ( 2 Φ ) 1/2 model 1:a = 195 kpc model 2: a = 20 kpc (rejected for a declining rotation curve) 6

7 Milky Way mass from maximum likelihood Stellar distribution function f(e,l) (velocity anisotropy β) inside a gravitational potential (scale length a total mass M) Max. probability for getting the observed (r i, v i ) i=1,n 2 ( ν vr ) 1 d ν dr β v + 2 r 2 r β = const. ν v 2 r dφ GM ( r) = = 2 dr r = r 2β r νgm ( r) r 2 r 2β dr Total mass = Msun over ~ 200 kpc Visible mass = Msun over ~ 15 kpc We see only 10 % of the total mass 7

8 4.2 Shape Sagittarius dwarf galaxy (Ibata, Gilmore, & Irwin 1994, Nat, 370, 194) Sgr dwarf d r d ~ 24 kpc r ~ 16 kpc 8

9 Field of Streams in SDSS data (Belokurov et al. 2006) Monoceros ring Sgr stream Virgo overdensity 2MASS (M giants) Majewski et a

10 Sgr stream Majewski et al. Stream is confined onto an orbital plane round dark halo at 15 < r < 60 kpc 10

11 Obs. 14<r<58kpc τ=0.9gyr, t=5τ Helmi 04 q Φ =1 q Φ = < q Φ < 0.95 is most likely (0.83<q ρ <0.92) Johnston

12 However, CDM halos are generally triaxial / prolate. (Jing & Suto 2000, 2002) Hayashi+07: (c/a) Φ = 0.72, (b/a) Φ = 0.78 in central parts 12

13 Gas cooling makes CDM halos rounder. (Kazantzidis et al. 2004, ApJ, 611, L73) r / r vir 13

14 4.3 Density profile Virialized CDM halos (Navarro, Frenk, & White 1997, ApJ, 490, 493) ρ = r r s ρ s 1 + r rs 2 ρ r -1 at r << r s ρ r -3 at r >> r s 14

15 NFW or Moore et al. profile? (Navarro et al. 2004, MNRAS, 349, 1039) -γ ρ r -γ at inner parts γ= 1: NFW γ= 1.5: Moore et al. No universal γ 1 < γ < 1.5 Einasto profile: ln ρ( r) / ρ 2 = ( 2 / α) [( / ) 1] α r r 2 15

16 CDM halos are too cuspy? (Moore 1994, Nature, 370, 629) Rotation curves of dwarf galaxies simulation 16

17 NFW isothermal More refined comparison with a CDM profile (Hayashi, E. et al. 2004) Fitting to the rotation curves of LSB galaxies (using Hα observation) NFW isothermal Fitting function: V(r) = V 0 / (1 + x γ ) 1/γ x r / r 0 NFW: γ~0.6 in this expression Isothermal: γ~2 17

18 Fitting to rotation curves of LSB galaxies (Hayashi et al. 2004, MNRAS, 355, 794) A group (good fit!) V(r) = V0 / (1 + x γ ) 1/γ x r / r0 Obs: 0 < γ < 5 Fitting with γ ~ 1 (CDM comparable) looks good. 18

19 B & C groups (bad fit!) 70%: consistent with a CDM profile of γ~1 20%: unable to fit with any smooth curves 10%: inconsistent with a CDM profile 19

20 Density profiles of Galactic dsph satellites (Walker+09) Dark halo model: γ r ρ ρ 1 r = 0 + r0 0 r NFW: γ=α=1 Plummer for stars: ν ( r) α [ 2 ] 2 5/ 2 1+ r / r h γ 3 α Jeans eq. (spherical sym.) l-o-s velocity dispersion profile No strong constraints on cusp/core 20

21 4.4 Dark matter substructure Missing satellites problem Moore 10 6 ~10 9 Msun Cumulative number of halos satellite galaxies Simulation V c / V global 21

22 Via Lactea simulation (Diemand et al. 2007, ApJ, 657, 262) 1 particle ~ 10 4 Msun Within r vir Within 0.1r vir Blue solid line: N(>M sub ) M sub -1 22

23 Current Power Spectrum ΛCDM CDM subhalos Seed of first objects Galaxy morphology Tegmark et al

24 Suppression of satellite formation (Bullock, Kravtsov, Weinberg 2000, ApJ, 539, 517) Extended Press-Schechter formalism + UV feedback Formation of galaxies with V c < 30 km/s is suppressed at z < z reionization 24

25 Probing dark matter substructure Dark matter (WIMP) annihilation Dynamical effects on visible galactic structure Star clusters and stellar streams Thin or thick disks Gravitational lensing Anomalous flux ratios Direct radio imaging 25

26 Dark matter (WIMP) annihilation Moore If dark matter is WIMP (Weakly Interacting Massive Particle), such as neutralino, it annihilates into visible photons. WIMP mass is likely around Gev-Tev, so corresponding γ-ray photons may be detected by MAGIC, Fermi, etc. γ-ray luminosity ρ 2 dv, so subhalos (+ Galactic Center and dwarf spheroidal galaxies) may be detectable because these have high phase-space densities. 26

27 Based on Via Lactea simulation (Diemand et al. 2007, ApJ, 657, 262) 27

28 After 12Gyr smooth Tidal streams of stellar systems Presence of CDM subhalos alters the phase-space structure of tidal streams of stellar systems, such as globular clusters and dwarf satellites (Ibata+02, Johnston+01). GC streams detectable by GAIA. lumpy 28

29 Lens mapping of CDM subhalos Moore Anomalous Flux Ratios for multiply lensed QSOs (Metcalf & Madau 2001, Chiba 2002, Dalal & Kochanek 2002) These are hardly explained by smooth lens models. 29

30 PG (radio quiet) z s =1.72, z L =0.31 C(0.24) Smooth lens model (Singular Isothermal Ellipsoid + External Shear) A2(0.59) source critical curve caustic A1(1.00) B(0.16) Iwamuro et al : obs : model Model: A2/A1 1 (fold caustic) Observed A2/A1 (near-ir): (anomalous) 30

31 B (radio loud) z s =3.62, z L =0.34 Smooth lens model (Singular Isothermal Ellipsoid + External Shear) A(0.90) B(1.00) critical curve D(0.02) C(0.53) caustic source CASTLES : obs : model Model: (A+C)/B 1 (cusp caustic) Observed (A+C)/B (radio): (anomalous) 31

32 Elliptical Lens lens plane source plane lens plane source plane critical lines caustics critical lines caustics Fold singularity Cusp singularity 32

33 Anomalous Flux Ratios Implausible by luminous GCs and satellites, CDM subhalos are most likely (Chiba 2002) Mass fraction of CDM subhalos ~ a few % (Dalal & Kochanek 2002) Flux anomaly depends on image parities, being consistent with substructure lensing (Kochanek & Dalal 2004) Evidence for many CDM subhalos!? 33

34 Unsolved issues Other causes for anomalous flux ratios Differential dust extinction? Stellar microlensing? Limits on the mass of lens substructure Mass of a subhalo? How many subhalos? Magnification of a source with radius R s compared with Einstein radius R E ( M 1/2 ) 34

35 Panoramic views of a QSO center 1. Mid-IR imaging of a dust torus (Near-IR at rest) Extinction free Microlensing free Radio quiet QSOs are available Source size is available Hot dust torus at sublimation T of ~1800K Size (inner radius) R s (~1pc) L 1/2 from dust reverberation mapping Einstein radius R E ( M 1/2 ) vs R s limits on M R E R S 35

36 Dust reverberation mapping Minezaki et al dust torus nucleus dust torus lag time ( L 1/2 ) day logδt (UV or optical vs. K) = 2.15 Mv / 5.0 (Δt L 1/2 ) 36 then, Mv Δt Rs = cδt

37 Panoramic views of a QSO center 2. Spectroscopy of NLR and BLR NLR: microlensing free BLR: affected by microlensing NLR BLR Hβ [OIII] Selective magnification Moustakas & Metcalf 2003 depending on R E vs R s limits on M 37

38 Subaru observations of quadruple lenses Mid-IR imaging with COMICS (Chiba et al. 2005; Minezaki et al. 2009) FOV=38 30, /pix N band, λ=11.7μm, continuum emission from dust torus IFS observation with Kyoto 3DII (Sugai et al. 2007) FOV=3 3, lenslet -1,37 37lenslets <λ< 0.915μm, line emission from NLR and BLR 38

39 Subaru 11.7μm PG B Chiba et al A2 C A B A1 B C Total flux = 17.5 mjy A2/A1 (Mid-IR) = 0.93±0.06 (model) 0.92 fold caustic (near-ir) = 0.59 ~ 0.67 Total flux = 19.2 mjy (A+C)/B (Mid-IR) = 1.51±0.06 (model) 1.25 cusp caustic 39 (radio) = 1.42 ~ 1.50

40 Subaru 11.7μm MG Q Minezaki et al Total flux = 39.2 mjy A2/A1 (Mid-IR) = 0.90±0.04 (model) 1.1 fold caustic (near-ir) = 0.4 ~ 0.8 Total flux = 22.2 mjy B/A (Mid-IR) = 0.84±0.05, C/A=0.46±0.02, D/A=0.87±0.05 B/A (model) = 0.87, 40 C/A=0.46, D/A=0.86

41 IFS data of RXJ Sugai et al B A C Selective Magnification! Model: B ~ C ~ 0.5A A B C Wavelength 41

42 Hβline flux A/B=1.74 C/B=0.46 [O III] line flux A/B=1.63 C/B=1.19 Smooth model A/B 1.7 C/B 1.0 NLR([OIII]) is OK BLR (Hβ) of Image C is microlensed [O III] line flux (point source subtracted) R s (NLR) 90pc 42

43 Limits on substructure lensing microlens PG (A1, A2) R s ~ 1 pc Mid-IR flux ratio M E < 16 Msun subhalo B (A, B, C) R s ~ 3 pc Mid-IR flux ratio M E > 200 Msun subhalo MG (A1, A2) R s ~ 2 pc Mid-IR flux ratio M E > 200 Msun microlens Q (A, B, C, D) R s ~ 2 pc Mid-IR flux ratio M E < 10 Msun microlens RXJ R s (BLR) ~ 0.01 pc, R s (NLR) ~ 100pc M E < 10 5 Msun for NLR 43

44 ALMA observation of gravitationally-lensed, extended images Direct imaging of subhalo-lensed images with high resolution observation (10mas) Determination of subhalo masses Spatial distribution of subhalos Source image: sub-millimeter continuum radiation from dust T=30~60 K, L=10 2 ~10 3 pc S at 850μm=several tens mjy Test for CDM models 44

45 Gravitational lensing of an extended image Lens system B SIE macrolens + SIS perturber Resolution Source size Radius 10 mas (ALMA) 250 pc (1σ) tidal radius Mass 2*10 8 Msun 45

46 Msun subhalo at resolution 0.01 arcsec ~0.4mJy image contrast a few 10min exposure@5σ(full operation) 3d position & mass 46 Inoue & Chiba 2005

47 source image 47 when there s no subhalo Ohashi, Chiba, Inoue 08

48 ALMA: 重力レンズ銀河 SDP.81 Hezaveh et al Subhalo with 10 9 Msun? Inoue, K. T., Minezaki, Matsushita, Chiba 2016: 銀河間空間にある負の密度摂動の効果決着は付いていない 48