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Modified Newtonian Dynamics an Introductory Review

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MMOOddiififieedd NNeewwtotonniiaann DDyynnaammiicscs aann iinntrotrodduuctoctoryry rerevviieeww By RRicicccaarrddoo SSccaarrppaa EEuurrooppeeaann SSoouutthheerrnn OObbsseerrvvaattoorryy 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 Halo density ∝ 1/r, mass diverges NGC 3198 (Begeman 1987) JuJussttifificicaattioionn ffoorr MMooddififyyiningg NNeewwttoonniaiann DDyynnaammicicss It 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 a0. a0 is smaller than the smallest acceleration probed in the solar system, e.g., the acceleration of Mercury on Pluto is > a0 Thus the idea is simple: Newtonian dynamics breaks down below a0 PPrrooppoosseedd bbyy MM.. MMiillggrroomm iinn 11998833,, MONDMOND introducesintroduces aa newnew constantconstant ofof physics:physics: aa0 DDiisstatanncece ddooeessnn’’tt mmaattetter!r! 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). MOND basic definition GM a Functional form derived from # a >> a0 " N = 2 rotation curves, where we know % r v = constant ⇒ a ∝1/r at large radii. $ Square root of Newtonian GMa acceleration ∝ 1/r. % 0 Multiplied by an acceleration we get & a << a0 " a = r right dimensions. ! An interpolation function derived empirically joins the two regimes ! ! (1/ 2 " a % " a2 % " a % µ$ ' = (a/a0)$1 + ' a = aµ a a 2 N $ ' # 0 & # 0 & ⇒ # a0 & ! ! Comparing MOND to real data DARK MATTER MOND GGaalalaxxieiess RRoottaattioionn CCuurrvveess wwitithh MMOONNDD Sanders & Verheijen 1998. Rotation curves derived from stellar light and 21cm hydrogen line GMa a = 0 r Velocity in km/s ! Distance in kpc FFitsits toto vv((rr)) ffoorr LLSSBB && HHSSBB GGaalalaxxieiess Sanders & McGaugh 02 -8 -2 a0=1.2 x10 cm s 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! CCoouunntteerreexxaammppleless?!?! 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. NNoo!! ThTheseese ggaallaaxxiieses aarere iinn NewNewtotonniiaann regregiimmee a>a0 Milgrom & Sanders 03 Dotted line: Newtonian prediction for constant M/L. Solid line: MOND prediction for the same M/L. TThhee TTuullylly--FFisishheerr v ⇐ RReelalatiotionn A relation between asymptotic velocity and luminosity of galaxies v 4 " L ! GGaallaaxxiieess’’ mmeeaann ssuurrfafaccee bbrriigghhtntneessss Σ High surface Brightness Low surface brightness Galaxy luminosity L = πr2Σ NNeewwtotonniiaann ddyynnaammiiccss aanndd TT--FF 2 2 (GM) v GM 4 v = 2 2 = 2 r M # r r 4 2 " v " 2 L = $ #L 2 L L {L = "r2# { r = "# T-F requires τ2Σ = const. ! ! But M/L= depends on stellar population, basically the same τ ! 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. TTuullllyy--FFiisshheerr rreellaatitioonn aanndd MMOONNDD 2 v GMa 4 L # M & = 0 ⇒ v " M = % ( L r r L $ L ' MOND requires M/L= constant ! ! AND The T-F is universal TThhee TTuullllyy--FFiisshheerr iiss uunniivveerrssaall aass MMOONNDD pprreeddiicctetedd Sanders & Verheijen Note that data for low surface brightness galaxies became available some 10 years later LSB Milgrom made its prediction. HSB McGaugh et al. 2000 Baryonic Tully-Fisher 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 FFuunnddaammeennttaall pplalannee ooff eelliplliptticicaalsls 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 MMOONNDD eexxpplalannaattioionn ooff tthhee ttiltilt 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 MMOONNDD ddeeffinineess ssppeeccifificic ttrreennddss Log L/Lsun AccelerationAcceleration fromfrom velocityvelocity andand luminosityluminosity MOND agrees with real data over 7 orders of magnitudes UUltltrraa CCoommppaacctt DDwwaarrff GGaalalaxxieiess Drinkwater et al. 2003 DARK MATTER vs. MOND Dwarf galaxies are usually FULL UCD luminosity and size imply of dark matter with M/L~100, thus internal acceleration > a0 plenty of dark matter expected. everywhere, hence no dark matter should be found. NNoo DDaarrkk MMaatttteerr FFoouunndd inin UUCCDDss 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! CClulusstteerrss ooff GGaalalaxxieiess (Sanders 1998) This may be the only place where MOND fails (by a factor 2. MOND predicts some baryonic matter still to be discovered GGrraavvititaattioionnaall lleennssiningg 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. SSttrroonngg LLeennssiningg The critical surface density required for strong lensing is 1 cH " = 0 F c 4# G [35] where F~10 is a dimensionless function of the lens and source redshifts , MOND applies at surface densities below ~ a /G ~ /5 ! Σ 0 Σc Strong lensing NEVER occurs in MOND regime WWee aarree lelefftt wwitithh wweeaakk lleennssiningg For a point source Mortlock & Turner 2001 we get an asymptotic deviation: 2" A = GMa M c 2 0 12 AM= 2” for M=10 Msun ! The deflection is independent from the impact parameter as much as rotation velocity is independent from r. RReeaall ddaattaa aaggrreeee wwitithh MMOONNDD BBuulglgee vvss BBlalacckk HHoolele mmaasssseess 4 MBH∝σ In presence of dark matter these two AND relations are difficult to M ∝L explain because from BH the tilt of the fundamental plane we get M/L∝L0.25. Piece of cake for MOND Ferrarese & Merritt because Astro-ph 0206222 M∝L∝σ4 MMOONNDD aanndd WWMMAAPP 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 BBaarryyoonn ddeennssitityy ffrroomm PPrrimimoorrddiaiall NNuuccleleoossyynntthheessisis McGaugh 2004 ApJ 611, 26 ΛCDM fit to WMAP data (Spergel et al. 2003) implies ωb=0.024 ± 0.001 MMooddeerrnn CCoossmmoolologgyy isis bbaasseedd oonn:: 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. PPrroobbiningg GGrraavvityity inin ththee LLooww AAcccceelelerraatiotionn RReeggimimee wwithith GGlolobbuulalarr CClulussteterrss By Riccardo Scarpa, Gianni Marconi & Roberto Gilmozzi European Southern Observatory MMeemmbbeerrsshhipip ddeeteterrmmininaatiotionn ddififfificcuultlt Target selection based on: HR diagram Proper motion (when possible) Radial velocity 35'x35' ωω CCeenntatauurri:i: vveeloloccityity ddisisppeerrssioionn ccoonnsstatanntt aatt lalarrggee rraaddii.ii. 2.1×10-8 cm s-2 MM 1155 ccoonnffirirmmss wwhhaatt ffoouunndd ffoorr ωω CCeenn 1.7×10-8 cm s-2 AlsoAlso inin NGCNGC 61716171 thethe velocityvelocity dispersiondispersion profileprofile flattensflattens outout atat largelarge radiiradii All data together 206 stars 1.4×10-8 cm s-2 CCoonncclulussioionnss ffoorr MMOONNDD 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..
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