News Concerning MOND Laws
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News concerning MOND laws Astro Seminar November 2016 MOND basic tenets • A theory of dynamics (gravity/inertia) involving a new constant a0 (beside G; :::) • Standard limit (a0 ! 0): The Newtonian limit • Scale invariance: (t; r) ! λ(t; r) MOND limit : a0 ! 1; A0 ≡ Ga0 fixed (G ! 0): a0 is analog to c in relativity or ~ in QM 1 Scale invariance X ma = F;F = mMG=r2 2 2 V ma =a0 = F; F = mMG=r , 1=2 or ma = F; F / m(MGa0) =r 2 MOND laws of galactic dynamics • Essentially follow from only the basic tenets of MOND • Are independent as phenomenological lawse.g., if interpreted as eects of DM (just as the BB spectrum, the photo electric eect, H spectrum, superconduc- tivity, etc. are independent in QM) • Pertain separately to properties of the DM alone (e.g., asymptotic atness, universal Σ), of the baryons alone (e.g., M − σ, maximum Σ), relations between the two (e.g., M − V ) • Revolve around a0 in dierent roles 3 Phenomenological lows derived from basic tenets alone In QM, many laws were derived before the Schr. equation: BB spectrum, photoelecic eect, H-like atomic spectra, specic heat of solids, Induced and spontaneous emission/absorption. All involve ~. In pre GR: equivalence principle ) gravitational redshift, light bending (c). 4 MOND: Baryonic density ) dynamical one (not in DM) r ) g r ) r ≡ − −1r~ · g . ρb( ) M ( ) ρD( ) (4πG) M 5 Some of the MOND laws • Asymptotic constancy of orbital velocity: V (r) ! V1 (H) • Light-bending angle becomes asymptotically constant (H) 4 • The velocity mass relation: V1 = MA0 (H-B) 4 • DML virial relation: σ ∼ MA0 2 • Discrepancy appears always at V =R = a0 (H-B) • Isothermal spheres have surface densities Σ¯ . a0=G (B) • The central surface density of dark halos is ≈ a0=2πG (H) • Universal baryonic-dynamical central surface densities relation (H-B). • Full rotation curves from baryon distribution alone (H-B) 6 A universal Halo central surface density? Dashed line [best t log(Σ0) = 2:15 ± 0:2] From Salucci et al. 2012 −2 ΣM ≡ a0=2πG = 138M⊙pc [log(ΣM ) = 2:14] 7 Spiral galaxies (open red circles); dwarf irregulars (full green circles), spirals and ellipticals (weak lensing black squares); Milky Way dSphs (pink triangles); nearby spirals in THINGS (small blue triangles); early-type spirals (full red triangles). 8 A universal Halo central acceleration? a. b. c. d. The parallel lines correspond to gmax(halo) =, 0:2a0 (dashed), 0:3a0 (solid), 0:4a0 (dotted). gmax(halo)=a0 ≈ 0:46ρ0Rc=ΣM 9 From Milgrom and Sanders et al. 2006 10 Maximal Halo acceleration Brada and Milgrom 1999: We have recently discovered that the modied Newtonian dynamics (MOND) implies some universal upper bound on the acceleration that can be produced by a dark halo, which, in a Newtonian analysis, is assumed to account for the eects of MOND. Not surprisingly, the limit is on the order of the acceleration constant of the theory. gH=a0 = ν(y)y − y; y = gN =a0 . ν(y ≫ 1) ≈ 1; ν(y ≪ 1) ≈ y−1=2 11 MOND prediction ΣM is a universal accumulation value of ΣH, for high-surface density galaxies. 1=2 For low-surface-density systems ΣH ≈ 2:4(ΣbΣM ) , Σb = ρR. R 1 −1r~ · g − g ΣH = 2 0 (4πG) ( N )dr = R 1 −2 @ f 2 − g ΣM 0 r @r r y[ν(y) 1] dr: y(r) ≡ gN (r)=a0. 12 Baryonic and dynamical central Surface densities Milgrom 2016, data: Lelli et al. 2016. `Scatter largely driven by obs. uncertainties'. `virtually no intrinsic scatter'. 13 Nonrelativistic theories Nonlinear Poisson equation: r~ · [µ(jr~ ϕj=a0)r~ ϕ] = 4πGρ The deep-MOND limit is conformally invariant Quaslinear MOND (QUMOND): ∆ϕN = 4πGρ, ∆ϕ = r~ · [ν(jr~ ϕN j=a0)r~ ϕN ] Derivable from actions Limits of relativistic theories (TeVeS, BIMOND, Einstein Aether) 14 central-surface-densities relation (CSDR) R 0 0 , ≡ , y 0 0 ΣD = ΣM S(ΣB=ΣM ) ΣM a0=2πG S(y) = 0 ν(y )dy Asymptotes: 0 0 for 0 ≫ , ΣD = ΣB ΣB ΣM 0 0 1=2 for 0 ≪ ΣD = (4ΣM ΣB) ΣB ΣM Quite unrelated to the mass-asymptotic-speed relation. 15 How is 0 measured? ΣD Toomre (1963): R 2 0 1 1 V (r) ΣT = 2πG 0 r2 dr 16 Discrepancy-acceleration correlation for rotationally-supported systems Scale invariance ) V (r ! 1) ! V1. 4 MOND acceleration ) V1 = MGa0. 2 2 1=2 1=2 On the asymptote g(r) = V (r)=r = (a0MG=r ) = (a0gN ) . Elsewhere on the rotation curves of any galaxy? Modied inertia ) g = gN ν(gN =a0) at all radii. ν(y) is universal. ν(y ≫ 1) ≈ 1. ν(y ≪ 1) ≈ y−1=2 (scale invariance). Also true in modied gravity for spherical systems. Predicted by MOND, Approximately, in general. 17 Discrepancy-acceleration correlation for rotationally-supported systems η ≡ g=gN vs. gN for 73 disc galaxies (points with δV=V ≤ 0:05) McGaugh (2015). −2 η ! λη, gN ! λ gN 18 Discrepancy-acceleration correlation for rotationally-supported systems 19 Discrepancy-acceleration correlation for pressure-supported systems g vs. gN , Scarpa (2006) 20 DM? The unexpected diversity of dwarf galaxy rotation curves Oman, Kyle A.; Navarro, Julio F.; Fattahi, Azadeh; Frenk, Carlos S.; Sawala, Till; White, Simon D. M.; Bower, Richard; Crain, Robert A.; Furlong, Michelle; Schaller, Matthieu; Schaye, Joop; Theuns, Tom: (2015) "...The shape of the circular velocity proles of simulated galaxies varies systematically as a function of galaxy mass, but shows remarkably little variation at xed maximum circular velocity. This is especially true for low-mass dark-matter-dominated systems, ... This is at odds with observed dwarf galaxies, which show a large diversity of rotation curve shapes, even at xed maximum rotation speed..." "...We conclude that one or more of the following statements must be true: (i) the dark matter is more complex than envisaged by any current model; (ii) current simulations fail to reproduce the diversity in the eects of baryons on the inner regions of dwarf galaxies; and/or (iii) ... data are incorrect..." Moti: "And, despite the diversity, they all sit on very tight "baryon-DM" relations." 21 Mass-asymptotic-speed relation McGaugh (2011) V (M) from scale invariance. Power 4 from acceleration 22 23 Galaxy-galaxy lensing Data from Brimioulle et al. 2013, analysis from Milgrom 2013. 24 Crater II: Discovery The feeble giant. Discovery of a large and diuse Milky Way dwarf galaxy in the constellation of Crater G. Torrealba, S. E. Koposov, V. Belokurov, M. Irwin (Submitted on 26 Jan 2016 (v1), last revised 1 Aug 2016 (this version, v4)) We announce the discovery of the Crater 2 dwarf galaxy, identied in imaging data of the VST ATLAS survey. Given its half-light radius of 1100 pc, Crater 2 is the fourth largest dwarf in the Milky Way, surpassed only by the LMC, SMC and the Sgr dwarf. With a total luminosity of MV -8, this satellite galaxy is also one of the lowest surface brightness dwarfs. Falling under the nominal detection boundary of 30 mag arcsec−2, it compares in nebulosity to the recently discovered Tuc 2 and Tuc IV and UMa II. Crater 2 is located ∼ 120 kpc from the Sun and appears to be aligned in 3-D with the enigmatic globular cluster Crater, the pair of ultra-faint dwarfs Leo IV and Leo V and the classical dwarf Leo II. We argue that such arrangement is probably not accidental and, in fact, can be viewed as the evidence for the accretion of the Crater-Leo group. 25 The velocity dispersion of Crater II: MOND prediction MOND Prediction for the Velocity Dispersion of the `Feeble Giant' Crater II (McGAugh arXiv:1610.06189) Abstract: Crater II is an unusual object among the dwarf satellite galaxies of the Local Group in that it has a very large size for its small luminosity. This provides a strong test of MOND, as Crater II should be in the deep MOND regime 2 −2 −1 2 −2 −1 (gin ≈ 34 km s kpc ≪ a0 = 3700 km s kpc ). Despite its great distance (≈ 120 kpc) from the Milky Way, the external eld of the host 2 −2 −1 (gex ≈ 282 km s kpc ) comfortably exceeds the internal eld. Consequently, Crater II should be subject to the external eld eect, a feature unique to MOND. This leads to the prediction of a very low velocity dispersion: +0:9 −1. σefe = 2:1−0:6 km s 26 The velocity dispersion of Crater II: recent measurement Nordita workshop on Dark Matter Distribution in the Era of Gaia From Twitter: Walker: Very diuse MW satellite Crater 2 has very, very cold velocity dispersion of 2.5 km/s. Implies very low dynamical density Walker: Crater 2's low velocity dispersion is also right where MOND predicts it. Boylan-Kolchin: Crater 2's velocity dispersion is pretty much exactly what DudeDarkmatter (McGaugh) predicted recently using MOND McGaugh: The MOND prediction was 2 km/s. Low because of EFE. Very hard to understand why this would happen in LCDM. 27.