MOdified Newtonian Dynamics an introductory review. Riccardo Scarpa European Southern Observatory

Transcription

1 MOdified Newtonian Dynamics an introductory review By Riccardo Scarpa European Southern Observatory

2 Everything started in 1933 with the work by Zwicky on the Coma cluster of galaxies, but were galaxy rotation curves to convince everybody there was dark matter in the universe Rotational velocity sensibly constant at large radii Implies an halo of non-luminous matter surrounds galaxies NGC 3198 (Begeman( 1987) Halo density 1/r, mass diverges

3 Justification for Modifying Newtonian Dynamics It t is increasingly difficult to explain observations with non- baryonic dark matter. Effects of non-baryonic dark matter appears when and only when the acceleration of gravity (computed including only baryons) falls below a certain value, baptized a 0. a 0 is smaller than n the smallest acceleration probed in the solar system,, e.g., the acceleration of Mercury on Pluto is > a 0 Thus the idea is simple: Newtonian dynamics breaks down below a 0

4 Proposed by M. Milgrom in 1983, MOND introduces a new constant of physics: a 0

5 Distance doesn t t matter! What matters is the strength of the acceleration, not distance/size of objects (though for any given object low accelerations are reached at correspondingly large distances).

6 MOND basic definition # a >> a 0 " % $ % & a << a 0 " a N = GM r 2 a = GMa 0 r Functional form derived from rotation curves, where we know v = constant a 1/r at large radii. Square root of Newtonian acceleration 1/r. Multiplied by an acceleration we get right dimensions. An interpolation function derived empirically joins the two regimes " µ a % " $ ' = (a /a 0 ) $ 1+ a2 # a 0 & # a 0 2 % ' & (1/ 2 " a N = aµ $ a # a 0 % ' &

7 Comparing MOND to real data DARK MATTER MOND

8 Galaxies Rotation Curves with MOND Sanders & Verheijen Rotation curves derived from stellar light and 21cm hydrogen line a = GMa 0 r Velocity in km/s Distance in kpc

9 Fits to v(r) for LSB & HSB Galaxies Sanders & McGaugh 02 a 0 =1.2 x10-8 cm s -2

10 Does MOND fit any rotation curve? MOND fails to fit this one. MOND DARK MATTER This is a fake galaxy! Photometry from one object and velocity from another! In this case, a failure is a good thing!

11 Counterexamples?! Romanowsky et al 2003 Claimed the discovery of 3 elliptical galaxies without dark matter halo. Dashed line: isothermal dark-matter halo Dotted line: constant mass-to-light ratio and NO dark matter.

12 No! These galaxies are in Newtonian regime a>a 0 Milgrom & Sanders 03 Dotted line: Newtonian prediction for constant M/L. Solid line: MOND prediction for the same M/L.

13 The Tully-Fisher Relation v A relation between asymptotic velocity and luminosity of galaxies v 4 " L

14 Galaxies mean surface brightness Σ High surface Brightness Low surface brightness Galaxy luminosity L = πr 2 Σ

15 Newtonian dynamics and T-F v 2 { { r 2 = L r = GM r 2 L = "r 2 # v 4 = (GM) 2 r 2 " v 4 " M 2 # L = $ 2 #L L 2 "# T-F requires τ 2 Σ = const. But M/L=τ depends on stellar population, basically the same in all galaxies Surface brightness Σ varies significantly going from HSB to LSB galaxies and has nothing to do with M/L. Therefore Newton implies a link of two very unrelated quantities and predicts LSB and HSB galaxies to follow different T-F relations.

16 Tully-Fisher relation and MOND v 2 r = GMa 0 r v 4 " M L L = # % M $ L & ( L ' MOND requires M/L= constant AND The T-F is universal

17 The Tully-Fisher is universal as MOND predicted Note that data for low surface brightness galaxies became available some 10 years later Milgrom made its prediction. Sanders & Verheijen LSB HSB

18 Baryonic Tully-Fisher McGaugh et al ApJL, 533, 99 Left: Luminous mass vs. rotational Velocity. Galaxies with v<90 km/s fall below the relation. Right: Including gas the relation is restored. The solid line has slope 4 The T-F is a relation between MASS and Velocity, as indeed predicted by MOND

19 Fundamental plane of ellipticals LSB HSB Edge on view of the fundamental plane HSB define a a relation M/L L 0.25 LSB define an opposite trend M/L L -0.40

20 MOND explanation of the tilt Tilt due to the different trend in gravitational filed strength In HSB the acceleration decreases with size In LSB the acceleration increases with size This is demonstrated by their average surface brightness

21 MOND defines specific trends Log L/L sun

22 Acceleration from velocity and luminosity MOND agrees with real data over 7 orders of magnitudes

23 Ultra Compact Dwarf Galaxies Drinkwater et al DARK MATTER vs. MOND Dwarf galaxies are usually FULL of dark matter with M/L~100, thus plenty of dark matter expected. UCD luminosity and size imply internal acceleration > a 0 everywhere, hence no dark matter should be found.

24 No Dark Matter Found in UCDs Accepted explanation: The dark matter was there but was lost together with the halo. Possible but NOT predicted and ad hoc MOND explanation: simple, elegant, fully logic and exactly as predicted!

25 Clusters of Galaxies (Sanders 1998) This may be the only place where MOND fails (by a factor 2. MOND predicts some baryonic matter still to be discovered

26 Gravitational lensing Difficult to address because MOND lack a relativistic Extension The Usual assumption is that light is bent twice has much as predicted by Newton s law. That is: Compute field with MOND Double the effect Warning: Gravitational lensing NEVER occur in MOND regime.

27 Strong Lensing The critical surface density required for strong lensing is " c = 1 ch 0 4# G F where F~10 is a dimensionless function of the lens and source redshifts [35], MOND applies at surface densities below Σ ~ a 0 /G ~ Σ c /5 Strong lensing NEVER occurs in MOND regime

28 We are left with weak lensing Mortlock & Turner 2001 For a point source we get an asymptotic deviation: A M = 2" c 2 GMa 0 A M = 2 for M=10 12 M sun The deflection is independent from the impact parameter as much as rotation velocity is independent from r.

29 Real data agree with MOND

30 Bulge vs Black Hole masses M BH σ 4 AND M BH L In presence of dark matter these two relations are difficult to explain because from the tilt of the fundamental plane we get M/L L Ferrarese & Merritt Astro-ph Piece of cake for MOND because M L σ 4

31 MOND and WMAP Power spectrum of temperature fluctuations in CMB McGaugh 2004 ApJ 611, 26 The ratio of the second to first peak depends on the baryon density

32 Baryon density from Primordial Nucleosynthesis McGaugh 2004 ApJ 611, 26 ΛCDM fit to WMAP data (Spergel et al. 2003) implies ω b =0.024 ± 0.001

33 Modern Cosmology is based on: Cosmological principle FRW equations based on extrapolating General relativity to low accelerations (Newtonian limit). Thus: If any of these two hypothesis is wrong - MOND suggests the second - FRW equations are inappropriate to describe the universe. Progress in cosmology seems not to depend on one s ability to describe observations within one particular FRW based model, rather on re-writing these equations within the contest of a new theory of gravity.

34 Probing Gravity in the Low Acceleration Regime with Globular Clusters By Riccardo Scarpa, Gianni Marconi & Roberto Gilmozzi European Southern Observatory

35 Membership determination difficult Target selection based on: HR diagram Proper motion (when possible) Radial velocity 35'x35'

36 ω Centauri: velocity dispersion constant at large radii cm s -2

37 M 15 confirms what found for ω Cen cm s -2

38 Also in NGC 6171 the velocity dispersion profile flattens out at large radii All data together 206 stars cm s -2

39 Conclusions for MOND Amazing ability to describe many properties of astronomical objects. Explains many data taken after it was proposed. Keep focus on demonstrating whether Newtonian dynamics fails at low accelerations. At present, I would compare MOND to Borh s atom, which was based on un-justified assumptions and worked only for Hydrogen. This model eventually became the basis for quantum mechanics. Similarly, MOND might be the way to the next great step in physics.